Tyk2 inhibitors and uses thereof

Abstract

This invention provides compounds that can be used as inhibitors of tyrosine kinase 2 (Tyk2), their solid forms and compositions, methods for producing such compounds, and methods for using such compounds to treat Tyk2-mediated diseases.

Description

Technical Field

[0001] The present invention relates to compounds and methods useful for inhibiting non-receptor tyrosine-protein kinase 2 ("TYK2") (also known as tyrosine kinase 2). The present invention also provides solid forms of such compounds, pharmaceutically acceptable compositions containing such compounds, methods for producing such compounds, and methods for treating various disorders using such compounds and compositions. Background Art

[0002] In recent years, research on new therapeutic agents has been greatly assisted by a better understanding of the structures of enzymes and other biomolecules related to diseases. One important class of enzymes that has been the subject of extensive research is the protein kinase family. Protein kinases constitute a large family of structurally related enzymes responsible for controlling various signal transduction processes within cells. Protein kinases can be considered to have evolved from a common ancestral gene (due to the conservation of their structure and catalytic function). Almost all kinases contain a similar catalytic domain of 250-300 amino acids. Kinases can be divided into many families based on the substrates they phosphorylate (such as protein-tyrosine, protein-serine / threonine, lipids, etc.). Generally, protein kinases mediate intracellular signal transduction by effecting phosphoryl transfer from a nucleoside triphosphate to a protein receptor involved in a signal transduction pathway. These phosphorylation events serve as molecular on / off switches that can regulate or control the biological functions of target proteins. These phosphorylation events are ultimately triggered in response to various extracellular stimuli and other stimuli. Examples of such stimuli include environmental and chemical stress signals (such as osmotic shock, heat shock, ultraviolet radiation, bacterial endotoxin, and H2O2), cytokines (such as interleukin-1 (IL-1), interleukin-8 (IL-8), and tumor necrosis factor α (TNF-α)), and growth factors (such as granulocyte macrophage colony-stimulating factor (GM-CSF) and fibroblast growth factor (FGF)). Extracellular stimuli can affect one or more cell responses related to cell growth, migration, differentiation, hormone secretion, transcription factor activation, muscle contraction, glucose metabolism, control of protein synthesis, and regulation of the cell cycle. Many diseases are associated with abnormal cell responses triggered by kinase-mediated events. Such diseases include, but are not limited to, autoimmune diseases, inflammatory diseases, bone diseases, metabolic diseases, neurological and neurodegenerative diseases, cancer, cardiovascular diseases, allergies and asthma, Alzheimer's disease, and hormone-related diseases. Therefore, there is still a need to search for protein kinase inhibitors that can be used as therapeutic agents. Summary of the Invention

[0003] The present invention provides compounds, their solid forms and compositions that can be used as tyrosine kinase 2 (Tyk2) inhibitors, methods for producing the same, and methods for treating Tyk2-mediated diseases using the same. Brief Description of the Drawings

[0004] Figure 1 shows the X-ray powder diffraction (XRPD) pattern of Form I' of the free base of Compound 1. Figure 2 shows the X-ray powder diffraction pattern of Form I of the mesylate salt of Compound 1. Figure 3 shows the X-ray powder diffraction pattern of Form II of the mesylate salt of Compound 1. Figure 4 shows the X-ray powder diffraction pattern of Form III of the mesylate salt of Compound 1. Figure 5 shows the X-ray powder diffraction pattern of Form IV of the mesylate salt of Compound 1. Figure 6 shows the X-ray powder diffraction pattern of Form V of the mesylate salt of Compound 1. Figure 7 shows the results of the pharmacokinetic study of Compound 1 and Compound 9 in dogs. Embodiments

[0005] [, General description of certain aspects of the present invention , ] [, : , ] [, , ] It has now been surprisingly found that the compounds of formula [I] and their pharmaceutically acceptable salts are potent selective Tyk2 inhibitors with favorable drug-likeness: [] wherein each of X, Y, and Z is independently hydrogen or deuterium. The compounds of formula [I] are active in various assay and therapeutic models, including those that exhibit inhibition of Tyk2, treatment of proliferative disorders, and treatment of inflammatory diseases. In addition, the present invention provides solid forms of the compounds of formula [I] and their pharmaceutically acceptable salts, which impart desirable characteristics such as improved aqueous solubility, stability, and ease of formulation. Also disclosed are methods for producing compounds of formula [I] Novel synthetic methods of compounds, and novel intermediates in the synthesis of such compounds. These methods and intermediates are suitable for large-scale production due to high yields, favorable physicochemical properties, and reduced use of toxic reagents or solvents compared to the state of the art. [Compound] [] As outlined above, the present invention provides compounds of formula I: [] wherein each of X, Y, and Z is independently hydrogen or deuterium. In some embodiments, X is hydrogen. In some embodiments, X is deuterium. In some embodiments, Y is hydrogen. In some embodiments, Y is deuterium. In some embodiments, Z is hydrogen. In some embodiments, Z is deuterium. In some embodiments, each of X, Y, and Z is hydrogen, thereby providing Compound 1: , Shown herein as its free base. However, for the avoidance of doubt, unless otherwise stated, the term "Compound 1" is intended to encompass the compound shown above as its free base or its pharmaceutically acceptable salts. In some embodiments, the present invention provides the mesylate salt of Compound 1, also designated herein as Compound 1M: 。 [Compound] [1M] In some embodiments, the present invention provides compounds of formula I bearing one or more deuterium atoms in place of hydrogen (i.e., wherein one or more of X, Y, or Z is deuterium) or their pharmaceutically acceptable salts. In some embodiments, such compounds include the following compounds or their pharmaceutically acceptable salts: 。 In some embodiments, the present invention provides the mesylate salts of compounds of formula I. In some embodiments, the present invention provides the mesylate salts of the compounds in the table above [2], [3], [4], [5] or [6]. [Compound] [1] [Solid form thereof] [] In some embodiments, the present invention provides a solid form of Compound 1. In some embodiments, the present invention provides a solid form of Compound 1 that is substantially free of impurities. As used herein, the term "substantially free of impurities" means that the compound does not contain a large amount of foreign substances. The foreign substances may include residual solvents or any other impurities that may be generated from the preparation and / or separation of Compound 1. In certain embodiments, there is at least about 95% by weight of Compound 1. In still other embodiments of the present invention, there is at least about 99% by weight of Compound 1. According to one embodiment, Compound 1 is present in an amount of at least about 97.0%, 97.5%, 98.0%, 98.5%, 99.0%, 99.5% or 99.8% by weight, wherein the weight ratio is based on the total weight of the composition. According to another embodiment, relative to the total area of the HPLC chromatogram, Compound 1 contains no more than about 3.0 area % of the total organic impurities of HPLC, and in certain embodiments no more than about 1.5 area % of the total organic impurities of HPLC. In other embodiments, relative to the total area of the HPLC chromatogram, Compound 1 contains no more than about 1.0 area % of any single impurity of HPLC, and in certain embodiments no more than about 0.5 area % of any single impurity of HPLC. In some embodiments, Compound 1 is present in the free base form. In some embodiments, Compound 1 is present in a pharmaceutically acceptable salt form. In some embodiments, the present invention provides a solid form of the free base of Compound 1. In some embodiments, the present invention provides a solid form of Compound 1 in a pharmaceutically acceptable salt form. In some embodiments, the present invention provides a solid form of Compound 1M. The results shown for Compound 1 also mean to include all tautomeric forms of Compound 1. Additionally, the structures shown herein also mean to include compounds that differ only in the presence of one or more isotopically enriched atoms other than any specifically defined isotopically enriched atoms. For example, compounds having the structure of the present invention (except those in which hydrogen is replaced by deuterium or tritium, or carbon is replaced by 13C- or 14C-enriched carbon) are within the scope of the present invention. It has been found that Compound 1 can exist in various solid forms. These forms include polymorphs, solvates, hydrates and amorphous forms. The present invention encompasses all such forms. In certain embodiments, the present invention provides Compound 1 in the form of a mixture of one or more solid forms of Compound 1 selected from polymorphs, solvates, hydrates and amorphous forms. In some embodiments, the solid form of Compound 1 is an amorphous solid. In certain embodiments, the present invention provides Compound 1 in an amorphous solid form that is substantially free of crystalline Compound 1. As used herein, the term "substantially free of crystalline Compound 1" means that the compound does not contain a substantial amount of crystalline Compound 1. In certain embodiments, there is at least about 95% by weight of amorphous Compound 1. In other embodiments of the present invention, there is at least about 99% by weight of amorphous Compound 1. In some embodiments, the present invention provides the amorphous Compound 1 free base. In some embodiments, the present invention provides the amorphous Compound 1 in its pharmaceutically acceptable salt form. In some embodiments, the present invention provides amorphous Compound 1M. As used herein, the term "polymorph" refers to any of the different crystal structures in which a compound can crystallize. As used herein, the term "solvate" refers to a crystalline form having a stoichiometric or non-stoichiometric amount of a solvent incorporated into the crystal structure. Similarly, the term "hydrate" particularly refers to a crystalline form having a stoichiometric or non-stoichiometric amount of water incorporated into the crystal structure. In certain embodiments, the solid form of Compound 1 is a crystalline solid. In some embodiments, Compound 1 is a crystalline solid that is substantially free of amorphous Compound 1. As used herein, the term "substantially free of amorphous Compound 1" means that the compound does not contain a substantial amount of amorphous Compound 1. In certain embodiments, there is at least about 95% by weight of crystalline Compound 1. In other embodiments of the present invention, there is at least about 99% by weight of crystalline Compound 1. In some embodiments, the solid form of Compound 1 is a neat crystal form and thus no water or other solvent is incorporated into its crystal structure. It has now been found that Compound 1 can exist in at least one different neat (i.e., anhydrous, non-solvate) crystal form. Such neat crystal forms of Compound 1 include Form I of Compound 1 methanesulfonate, which is elaborated herein. In some embodiments, the present invention provides a solvated crystalline form of Compound 1. Such solvated crystalline forms of Compound 1 include Form II, Form III, Form IV, and Form V of Compound 1 methanesulfonate and Form I' of Compound 1 free base. In some embodiments, the present invention provides a crystalline form of Compound 1 selected from any of those designated as Form I, Form II, Form III, Form IV, or Form V. Methods for preparing each of Forms I-V and I' of Compound 1 are described herein. In some embodiments, the present invention provides a polymorph of Compound 1 free base designated as Form I'. In some embodiments, the present invention provides Form I' of Compound 1, which has a substantially similar [Figure] The powder X-ray diffraction pattern shown in [1]. As used herein, the term "about" when referring to a 2θ value means the value ± 0.1 2θ obtained under the sample preparation and data collection conditions set forth in the examples. Those skilled in the art will appreciate that variations in specific XRPD acquisition parameters will affect the XRPD pattern and the specific 2θ values obtained. In some embodiments, Form I' of Compound 1 free base is characterized by having one or more of its peaks selected from those in Table 1 below. [Table] [1] [: Compound] [1] [Form] [I'] [of] [XRPD] [Peak] [] Position (2θ) Height (cts) Relative Intensity (%) 6.0700 3707.10 100.00 7.3496 836.02 22.55 7.8002 407.26 10.99 8.2782 265.83 7.17 10.6599 1241.31 33.48 11.3113 599.19 16.16 11.9037 2584.87 69.73 12.0950 1324.71 35.73 13.6129 990.01 26.71 13.9542 1758.35 47.43 14.2840 291.51 7.86 14.7169 877.59 23.67 15.2495 1647.47 44.44 16.1252 243.38 6.57 16.6247 2437.44 65.75 17.2152 1134.51 30.60 18.5017 1226.40 33.08 19.5802 480.66 12.97 20.3658 686.09 18.51 20.8783 910.68 24.57 21.0155 789.21 21.29 23.0207 1113.59 30.04 23.2783 802.57 21.65 24.0781 874.50 23.59 25.4085 960.57 25.91 25.7185 1165.97 31.45 27.7872 434.24 11.71 28.4799 712.66 19.22 29.6081 290.82 7.85 30.4683 272.67 7.36 In some embodiments, Form I' of Compound 1 free base is characterized by having two or more of those peaks selected from Table 1 in its powder X-ray diffraction pattern. In some embodiments, Form I' of Compound 1 is characterized by having three or more of those peaks selected from Table 1 in its powder X-ray diffraction pattern. In some embodiments, Form I' of Compound 1 is characterized by having four or more of those peaks selected from Table 1 in its powder X-ray diffraction pattern. In some embodiments, Form I' of Compound 1 is characterized by having five or more of those peaks selected from Table 1 in its powder X-ray diffraction pattern. In some embodiments, Form I' of Compound 1 is characterized by having 10 peaks from Table 1 in its X-ray diffraction pattern. In some embodiments, Form I' of Compound 1 is characterized by having 15 peaks from Table 1 in its X-ray diffraction pattern. In some embodiments, Form I' of Compound 1 is characterized by having 20 peaks from Table 1 in its X-ray diffraction pattern. In some embodiments, Form I' of Compound 1 is characterized by having all of the peaks from Table 1 in its X-ray diffraction pattern. In some embodiments, Form I of Compound 1 is characterized by having one or more peaks in its powder X-ray diffraction pattern at 2θ angles selected from: about 6.07, about 11.90, about 16.62, and about 13.95°. In some embodiments, Form I of Compound 1 is characterized by having two or more peaks in its powder X-ray diffraction pattern at 2θ angles selected from: about 6.07, about 11.90, about 16.62, and about 13.95°. In some embodiments, Form I of Compound 1 is characterized by having three or more peaks in its powder X-ray diffraction pattern at 2θ angles selected from: about 6.07, about 11.90, about 16.62, and about 13.95°. In some embodiments, Form I of Compound 1 is characterized by having four or more peaks in its powder X-ray diffraction pattern at 2θ angles selected from: about 6.07, about 11.90, about 16.62, and about 13.95°. In some embodiments, the present invention provides a neat crystalline form of Compound 1 mesylate designated Form I. In some embodiments, the present invention provides Form I of Compound 1, which has a powder X-ray diffraction pattern substantially similar to [Figure] [2] as depicted. In some embodiments, Form I of Compound 1 is characterized by having one or more of its peaks selected from those in Table 2 below. [Table] [2.] [Compound] [1] [Form] [I] [of] [XRPD] [Peak] [] Position (°2θ) Height (cts) Relative Intensity (%) 6.4222 1147.42 21.11 9.1780 3154.55 58.05 11.1364 942.06 17.34 12.8488 509.43 9.37 13.2993 550.44 10.13 13.7913 645.33 11.87 14.3702 2858.25 52.60 14.9145 974.99 17.94 15.9065 1315.52 24.21 16.8833 2940.50 54.11 17.4864 359.10 6.61 18.3945 689.97 12.70 19.4147 926.98 17.06 19.8920 5434.42 100.00 20.2035 2099.61 38.64 21.5878 728.59 13.41 22.0900 2636.56 48.52 22.3198 1378.87 25.37 22.9101 1703.48 31.35 24.1420 1656.01 30.47 24.3748 1723.15 31.71 24.8519 626.03 11.52 25.5296 695.16 12.79 25.8669 426.82 7.85 26.4749 531.54 9.78 28.4433 624.17 11.49 28.9463 417.47 7.68 33.4565 287.82 5.30 In some embodiments, Form I of Compound 1 is characterized in that its powder X-ray diffraction pattern has two or more of those peaks selected from Table 2. In some embodiments, Form I of Compound 1 is characterized in that its powder X-ray diffraction pattern has three or more of those peaks selected from Table 2. In some embodiments, Form I of Compound 1 is characterized in that its powder X-ray diffraction pattern has four or more of those peaks selected from Table 2. In some embodiments, Form I of Compound 1 is characterized in that its powder X-ray diffraction pattern has five or more of those peaks selected from Table 2. In some embodiments, Form I of Compound 1 is characterized in that its X-ray diffraction pattern has all of the peaks in Table 2. In some embodiments, Form I of Compound 1 is characterized by having one or more peaks in its powder X-ray diffraction pattern at 2θ angles selected from: about 19.89, about 9.17, about 16.88, about 14.37, and about 22.09 °. In some embodiments, Form I of Compound 1 is characterized by having two or more peaks in its powder X-ray diffraction pattern at 2θ angles selected from: about 19.89, about 9.17, about 16.88, about 14.37, and about 22.09 °. In some embodiments, Form I of Compound 1 is characterized by having three or more peaks in its powder X-ray diffraction pattern at 2θ angles selected from: about 19.89, about 9.17, about 16.88, about 14.37, and about 22.09 °. In some embodiments, Form I of Compound 1 is characterized by having four or more peaks in its powder X-ray diffraction pattern at 2θ angles selected from: about 19.89, about 9.17, about 16.88, about 14.37, and about 22.09 °. In some embodiments, Form I of Compound 1 is characterized by having all five peaks in its powder X-ray diffraction pattern at 2θ angles selected from: about 19.89, about 9.17, about 16.88, about 14.37, and about 22.09 °. In some embodiments, the present invention provides a solvated crystalline form of Compound 1 methanesulfonate, designated Form II. In some embodiments, the present invention provides Form II of Compound 1, which has a powder X-ray diffraction pattern substantially similar to [Figure] that shown in [3]. In some embodiments, Form II of Compound 1 is characterized by having one or more of its peaks selected from those in Table 3 below. [Table] [3.] [Compound] [1] [Form] [II] [of] [XRPD] [peaks] [] Position (°2θ) Height (cts) Relative intensity (%) 7.9701 468.93 9.76 8.5228 1009.03 21.00 8.8961 2628.33 54.70 11.1290 1097.72 22.84 12.8376 1017.53 21.18 13.5921 493.97 10.28 13.9687 389.59 8.11 14.3776 432.91 9.01 14.5002 381.24 7.93 15.5065 239.88 4.99 15.9553 884.48 18.41 16.3484 2878.72 59.91 16.8545 489.38 10.18 17.0635 2694.94 56.08 17.5257 2143.00 44.60 17.8231 481.65 10.02 18.2699 1426.17 29.68 18.6763 2651.44 55.18 20.0515 696.36 14.49 20.2098 2505.87 52.15 20.6367 1224.33 25.48 21.0566 403.56 8.40 21.2443 1588.61 33.06 21.6209 482.85 10.05 21.9825 357.82 7.45 22.2727 4805.20 100.00 23.4728 1259.25 26.21 23.8021 595.12 12.38 24.0065 446.43 9.29 25.1612 429.55 8.94 25.3060 372.12 7.74 25.8238 1488.96 30.99 26.0253 3229.27 67.20 26.4504 3972.97 82.68 26.7143 1826.14 38.00 27.3448 392.77 8.17 27.5209 998.53 20.78 27.8190 357.86 7.45 28.1462 1975.32 41.11 28.5573 694.14 14.45 29.1064 441.49 9.19 29.4033 598.69 12.46 29.5376 653.19 13.59 30.1886 278.35 5.79 31.8732 848.14 17.65 32.5997 670.08 13.94 33.0026 338.47 7.04 33.6470 268.16 5.58 In some embodiments, Form II of Compound 1 is characterized by having two or more of its peaks selected from those in Table 3 in its powder X-ray diffraction pattern. In some embodiments, Form II of Compound 1 is characterized by having three or more of its peaks selected from those in Table 3 in its powder X-ray diffraction pattern. In some embodiments, Form II of Compound 1 is characterized by having four or more of its peaks selected from those in Table 3 in its powder X-ray diffraction pattern. In some embodiments, Form II of Compound 1 is characterized by having five or more of its peaks selected from those in Table 3 in its powder X-ray diffraction pattern. In some embodiments, Form II of Compound 1 is characterized by having all of the peaks in Table 3 in its X-ray diffraction pattern. In some embodiments, Form II of Compound 1 is characterized by having one or more peaks with 2θ angles selected from the following: about 22.27, about 26.45, about 26.02, about 16.34, and about 17.06 °. In some embodiments, Form II of Compound 1 is characterized by having two or more peaks with 2θ angles selected from the following: about 22.27, about 26.45, about 26.02, about 16.34, and about 17.06 °. In some embodiments, Form II of Compound 1 is characterized by having three or more peaks with 2θ angles selected from the following: about 22.27, about 26.45, about 26.02, about 16.34, and about 17.06 °. In some embodiments, Form II of Compound 1 is characterized by having four or more peaks with 2θ angles selected from the following: about 22.27, about 26.45, about 26.02, about 16.34, and about 17.06 °. In some embodiments, Form II of Compound 1 is characterized by having all five peaks with 2θ angles selected from the following: about 22.27, about 26.45, about 26.02, about 16.34, and about 17.06 °. In some embodiments, the present invention provides a solvated crystalline form of Compound 1 mesylate designated Form III. In some embodiments, the present invention provides Form III of Compound 1, which has a powder X-ray diffraction pattern substantially similar to [Figure] [4] as depicted. In some embodiments, Form III of Compound 1 is characterized by having one or more of its peaks selected from those listed in Table 4 below. [Table] [4.] [Compound] [1] [Form] [III] [Of] [XRPD] [Peak] [] Position (°2θ) Height (cts) Relative Intensity (%) 7.6100 318.58 34.04 9.0773 96.96 10.36 9.8524 353.97 37.82 11.1997 78.66 8.41 11.8535 255.91 27.35 13.1453 165.85 17.72 14.2078 273.03 29.18 15.6943 148.26 15.84 16.9586 550.52 58.83 17.2500 324.76 34.70 18.1827 935.85 100.00 18.5648 603.68 64.51 19.7502 116.00 12.40 20.1432 91.76 9.81 21.9569 470.43 50.27 24.3804 135.50 14.48 25.4532 333.87 35.68 26.4804 285.80 30.54 In some embodiments, Form III of Compound 1 is characterized by having two or more of those peaks selected from Table 4 in its powder X-ray diffraction pattern. In some embodiments, Form IV of Compound 1 is characterized by having three or more of those peaks selected from Table 4 in its powder X-ray diffraction pattern. In some embodiments, Form IV of Compound 1 is characterized by having four or more of those peaks selected from Table 4 in its powder X-ray diffraction pattern. In some embodiments, Form IV of Compound 1 is characterized by having five or more of those peaks selected from Table 4 in its powder X-ray diffraction pattern. In some embodiments, Form IV of Compound 1 is characterized by having all of the peaks from Table 4 in its X-ray diffraction pattern. In some embodiments, Form IV of Compound 1 is characterized by having one or more peaks with 2θ angles selected from the following: about 18.18, about 18.56, about 16.95, about 21.95, and about 9.85 °. In some embodiments, Form IV of Compound 1 is characterized by having two or more peaks with 2θ angles selected from the following: about 18.18, about 18.56, about 16.95, about 21.95, and about 9.85 °. In some embodiments, Form IV of Compound 1 is characterized by having three or more peaks with 2θ angles selected from the following: about 18.18, about 18.56, about 16.95, about 21.95, and about 9.85 °. In some embodiments, Form IV of Compound 1 is characterized by having four or more peaks with 2θ angles selected from the following: about 18.18, about 18.56, about 16.95, about 21.95, and about 9.85 °. In some embodiments, Form IV of Compound 1 is characterized by having all five peaks with 2θ angles selected from the following: about 18.18, about 18.56, about 16.95, about 21.95, and about 9.85 °. In some embodiments, the present invention provides a solvated crystalline form of Compound 1 mesylate, referred to as Form IV. In some embodiments, the present invention provides Form IV of Compound 1, which has a powder X-ray diffraction pattern substantially similar to [Figure] [5] as depicted. In some embodiments, Form IV of Compound 1 is characterized by having one or more of its peaks selected from those in Table 5 below. [Table] [5.] [Compound] [1] [Form] [IV] [of] [XRPD] [Peak] [] Position (°2θ) Height (cts) Relative Intensity (%) 9.0868 217.58 16.34 9.9380 112.78 8.47 11.2015 139.55 10.48 11.6693 532.94 40.03 12.4562 1116.21 83.84 13.5565 475.43 35.71 14.3279 297.10 22.32 16.2841 734.91 55.20 17.5789 573.88 43.11 17.7956 1331.34 100.00 18.2686 633.58 47.59 20.8156 206.11 15.48 21.2458 669.21 50.27 22.7697 444.50 33.39 22.8359 453.11 34.03 24.3821 1035.69 77.79 24.4269 991.19 74.45 25.0192 343.23 25.78 26.0048 819.45 61.55 26.3650 561.69 42.19 26.6839 561.23 42.16 28.2069 458.32 34.43 29.0196 498.54 37.45 29.4230 75.94 5.70 In some embodiments, Form IV of Compound 1 is characterized by having two or more of those peaks selected from Table 5 in its powder X-ray diffraction pattern. In some embodiments, Form IV of Compound 1 is characterized by having three or more of those peaks selected from Table 5 in its powder X-ray diffraction pattern. In some embodiments, Form IV of Compound 1 is characterized by having four or more of those peaks selected from Table 5 in its powder X-ray diffraction pattern. In some embodiments, Form IV of Compound 1 is characterized by having five or more of those peaks selected from Table 5 in its powder X-ray diffraction pattern. In some embodiments, Form IV of Compound 1 is characterized by having all of the peaks in Table 5 in its X-ray diffraction pattern. In some embodiments, Form IV of Compound 1 is characterized by having one or more of those peaks at about 17.79, about 12.45, about 24.38, about 26.00, and about 16.28 ° 2θ in its powder X-ray diffraction pattern. In some embodiments, Form IV of Compound 1 is characterized by having two or more peaks with 2θ angles selected from the following: about 17.79, about 12.45, about 24.38, about 26.00, and about 16.28 ° in its powder X-ray diffraction pattern. In some embodiments, Form IV of Compound 1 is characterized by having three or more peaks with 2θ angles selected from the following: about 17.79, about 12.45, about 24.38, about 26.00, and about 16.28 ° in its powder X-ray diffraction pattern. In some embodiments, Form IV of Compound 1 is characterized by having four or more peaks with 2θ angles selected from the following: about 17.79, about 12.45, about 24.38, about 26.00, and about 16.28 ° in its powder X-ray diffraction pattern. In some embodiments, Form IV of Compound 1 is characterized by having all five of the peaks with 2θ angles selected from the following: about 17.79, about 12.45, about 24.38, about 26.00, and about 16.28 ° in its powder X-ray diffraction pattern. In some embodiments, the present invention provides a solvated crystalline form of Compound 1 mesylate, designated Form V. In some embodiments, the present invention provides Form V of Compound 1, which has a powder X-ray diffraction pattern substantially similar to [Figure] that shown in [6]. In some embodiments, Form V of Compound 1 is characterized by having those peaks selected from Table 6 below in its powder X-ray diffraction pattern. [Table] [6.] [Compound] [1] [Form] [V] [Of] [XRPD] [Peak] [] Position (°2θ) Height (cts) Relative Intensity (%) 8.8015 11290.03 90.50 9.1530 1790.47 14.35 11.0991 11252.14 90.19 13.3400 12475.81 100.00 13.8062 953.33 7.64 14.3632 1444.62 11.58 15.9141 1800.60 14.43 16.8514 6543.25 52.45 18.1930 941.79 7.55 18.2976 1975.37 15.83 19.4061 686.44 5.50 19.9458 2405.91 19.28 22.1386 654.92 5.25 22.2572 2187.88 17.54 23.9392 1769.38 14.18 25.4909 5485.33 43.97 25.5616 2667.47 21.38 26.8123 4452.31 35.69 26.8876 2092.66 16.77 28.4313 785.08 6.29 33.5285 664.61 5.33 In some embodiments, Form V of Compound 1 is characterized in that its powder X-ray diffraction pattern has two or more of those peaks selected from Table 5. In some embodiments, Form V of Compound 1 is characterized in that its powder X-ray diffraction pattern has three or more of those peaks selected from Table 5. In some embodiments, Form V of Compound 1 is characterized in that its powder X-ray diffraction pattern has four or more of those peaks selected from Table 5. In some embodiments, Form V of Compound 1 is characterized in that its powder X-ray diffraction pattern has five or more of those peaks selected from Table 5. In some embodiments, Form V of Compound 1 is characterized in that its X-ray diffraction pattern has all of the peaks in Table 5. In some embodiments, Form V of Compound 1 is characterized by having one or more peaks in its powder X-ray diffraction pattern at 2θ angles selected from: about 13.34, about 8.80, about 11.10, about 16.85, and about 25.49 °. In some embodiments, Form V of Compound 1 is characterized by having two or more peaks in its powder X-ray diffraction pattern at 2θ angles selected from: about 13.34, about 8.80, about 11.10, about 16.85, and about 25.49 °. In some embodiments, Form V of Compound 1 is characterized by having three or more peaks in its powder X-ray diffraction pattern at 2θ angles selected from: about 13.34, about 8.80, about 11.10, about 16.85, and about 25.49 °. In some embodiments, Form V of Compound 1 is characterized by having four or more peaks in its powder X-ray diffraction pattern at 2θ angles selected from: about 13.34, about 8.80, about 11.10, about 16.85, and about 25.49 °. In some embodiments, Form V of Compound 1 is characterized by having all five peaks in its powder X-ray diffraction pattern at 2θ angles selected from: about 13.34, about 8.80, about 11.10, about 16.85, and about 25.49 °. [ , Compounds and definitions , ] [ , : , ] [ , , ] The compounds of the present invention include those outlined above and are further illustrated by the classes, subclasses, and species disclosed herein. Unless otherwise stated, the following definitions shall apply as used herein. For the purposes of the present invention, chemical elements are identified according to the Periodic Table of the Elements (CAS version, Handbook of Chemistry and Physics, 75th Edition). Additionally, general principles of organic chemistry are set forth in “Organic Chemistry”, Thomas Sorrell, University Science Books, Sausalito: 1999 and “March’s Advanced Organic Chemistry”, 5th Edition, Editors: Smith, M.B. and March, J., John Wiley & Sons, New York: 2001, the entire contents of which are incorporated herein by reference. As used herein, the term "pharmaceutically acceptable salt" refers to salts that are suitable for contact with human and lower animal tissues within the scope of sound medical judgment, without undue toxicity, irritation, allergic response, and the like, and having a reasonable benefit / risk ratio. Pharmaceutically acceptable salts are well known in the art. For example, S. M. Berge et al. elaborated on pharmaceutically acceptable salts in J. Pharmaceutical Sciences, 1977, 66, 1-19, and also in Handbook of Pharmaceutical Salts: Properties, Selection, and Use, 2nd Revised Edition, edited by P. Heinrich Stahl and Camille G. Wermuth, Wiley, April 2011, each of which is incorporated herein by reference. Pharmaceutically acceptable salts of the compounds of the present invention include those derived from suitable inorganic and organic acids and bases. Examples of pharmaceutically acceptable non-toxic acid addition salts are salts formed by reacting an amino group with an inorganic acid such as hydrochloric acid, hydrobromic acid, phosphoric acid, sulfuric acid, and perchloric acid, or with an organic acid such as acetic acid, oxalic acid, maleic acid, tartaric acid, citric acid, succinic acid, or malonic acid, or by using other methods known in the art such as ion exchange. Other pharmaceutically acceptable salts include adipates, alginates, ascorbates, aspartates, benzenesulfonates, benzoates, bisulfates, borates, butyrates, camphorates, camphorsulfonates, citrates, cyclopentanepropionates, digluconates, dodecyl sulfates, ethanesulfonates, formates, fumarates, glucoheptanoates, glycerophosphates, gluconates, hemisulfates, heptanoates, hexanoates, hydroiodides, 2-hydroxyethanesulfonates, lactates, lactobionates, laurates, lauryl sulfates, malates, maleates, malonates, mesylates, 2-naphthalenesulfonates, nicotinates, nitrates, oleates, oxalates, palmitates, pamoates, pectates, persulfates, 3-phenylpropionates, phosphates, pivalates, propionates, stearates, succinates, sulfates, tartrates, thiocyanates, p-toluenesulfonates, undecanoates, valerates, and the like. Salts derived from suitable bases include metal ions (including aluminum, zinc, alkali metals, alkaline earth metals), ammonium, and N+(C1-4alkyl)4 salts. Representative alkali metal or alkaline earth metal salts include sodium salts, lithium salts, potassium salts, calcium salts, magnesium salts, and the like. Other pharmaceutically acceptable salts include (where appropriate) those derived from non-toxic ammonium, quaternary ammonium, and primary, secondary, or tertiary amine cations, including (but not limited to) those derived from natural or unnatural amino acids. Representative amine- or ammonium-based salts include but are not limited to those derived from: arginine, betaine, choline, choline, diethylamine, lysine, benzathine penicillin, 2-(diethylamino)-ethanol, ethanolamine, 1-(2-hydroxyethyl)-pyrrolidine, diethanolamine, ammonia, deanol, N-methyl-glucosamine, tromethamine, triethanolamine, 4-(2-hydroxyethyl)-morpholine, 1H-imidazole, ethylenediamine, hexahydropyrazine, procaine, and phenylethylbenzylamine. [, 3. , ] [, General methods for providing the compounds of the present invention , ] [, , ] In some embodiments, the present invention provides a synthetic method and synthetic intermediates for producing a compound of formula [I]. In some embodiments, the compound of formula [I] (including but not limited to Compound 1) can generally be prepared according to the method illustrated in Scheme 1 below, wherein each of X, Y, Z, RE, and RPG is defined as in the species and subclasses herein, both individually and in combination. [Synthesis] [1.] [Formula] [I] [Compound synthesis] [.] As used herein, RE is a C1-6 aliphatic group. In some embodiments, RE is a C1-6 alkyl group. In some embodiments, RE is methyl or ethyl. In some embodiments, RE is ethyl. As used herein, RPG is an amine protecting group. In some embodiments, RPG is optionally substituted benzyl or diphenylmethyl. In some embodiments, RPG is optionally substituted benzyl. In some embodiments, RPG is benzyl substituted with one or more methoxy groups. In some embodiments, RPG is 2,4-dimethoxybenzyl. In some embodiments, step [S-1] comprises oxidation of intermediate [A-1], thereby forming intermediate [A-2]. In some embodiments, the oxidation is mediated by periodate and ruthenium. In some embodiments, the periodate is sodium periodate. In some embodiments, the ruthenium is RuCl3 hydrate. In some embodiments, step [S-2] comprises esterification of diacid intermediate [A-2], thereby forming diester intermediate [A-3]. In some embodiments, the esterification is base-catalyzed. In some embodiments, the esterification reagent is dialkyl sulfate. In some embodiments, the esterification reagent is diethyl sulfate. In some embodiments, the base is a carbonate base. In some embodiments, the base is potassium carbonate. In some embodiments, the esterification is carried out in a polar aprotic solvent. In some embodiments, the polar aprotic solvent is a cyclic urea. In some embodiments, the polar aprotic solvent is DMPU. In some embodiments, step [S-3] comprises selective monoreduction of diester intermediate [A-3] to provide intermediate of formula [A-4]. In some embodiments, the selective monoreduction is accomplished using a hydride reducing agent. In some embodiments, the hydride reducing agent is aluminum hydride. In some embodiments, the hydride reducing agent is DIBAL-H. In some embodiments, the selective monoreduction is carried out in an organic solvent. In some embodiments, the organic solvent is toluene. In some embodiments, the reaction is carried out at a temperature between -70 °C and -80 °C. In some embodiments, the reaction is maintained at a temperature between -70 °C and -80 °C until it is determined that [A-3] is completely consumed, and then quenched at a temperature between -70 °C and -80 °C. In some embodiments, the reagent used to quench the reaction comprises methanol. In some embodiments, the reagent used to quench the reaction comprises methanol and hydrochloric acid. In some embodiments, step [S-4] comprises reductive cyclization of intermediate of formula [A-4] using a protected ammonia synthon to provide intermediate of formula Intermediate of [A-5]. In some embodiments, the protected ammonia synthon has the formula R PG-NH 2. In some embodiments, the reduction is accomplished using a hydride reagent. In some embodiments, the hydride reagent is borohydride. In some embodiments, the hydride reagent is triacetoxyborohydride. In some embodiments, the hydride reagent is sodium triacetoxyborohydride. In some embodiments, the reaction is carried out in an organic solvent. In some embodiments, the organic solvent is toluene. In some embodiments, step [S-5] comprises aryl coupling of the intermediate of formula [A-5] with a difluorophenyl synthon to provide an intermediate of formula [A-6]. In some embodiments, the difluorophenyl synthon is an organometallic reagent. In some embodiments, the difluorophenyl synthon is an arylzinc reagent. In some embodiments, the aryl coupling is a palladium-catalyzed coupling. In some embodiments, the aryl coupling is a Negishi coupling. In some embodiments, the arylzinc reagent is prepared from the corresponding 2-bromo-1,3-difluorobenzene. In some embodiments, 2-bromo-1,3-difluorobenzene is treated with an organometallic precursor. In some embodiments, 2-bromo-1,3-difluorobenzene is treated with an isopropylmagnesium chloride – lithium chloride complex to form an arylmagnesium lithium chloride intermediate. In some embodiments, the arylmagnesium lithium chloride intermediate is contacted with a zinc salt to form an arylzinc reagent. In some embodiments, the zinc salt is ZnCl 2. In some embodiments, the aryl coupling with the intermediate of formula [A-5] is catalyzed by a palladium catalyst. In some embodiments, the palladium catalyst is Pd(PPh 3) 4. In some embodiments, the aryl coupling is carried out in an ether solvent. In some embodiments, the ether solvent is THF. In some embodiments, step [S-6] comprises arylamination of the intermediate of formula [A-6] with an aniline of formula [A-6a]: wherein Y and Z are independently hydrogen or deuterium, thereby forming an intermediate of formula [A-7]. In some embodiments, the aniline of formula [A-6a] is formed by aminating p-aminobenzoyl chloride with the corresponding pyrrolidine of formula [A6-b]: [] Wherein Y and Z are independently hydrogen or deuterium. In some embodiments, the arylamination is catalyzed by a palladium catalyst system. In some embodiments, the palladium catalyst system comprises Pd2(dba)3 and Xantphos. In some embodiments, the arylamination is carried out in an organic solvent. In some embodiments, the organic solvent is dioxane. In some embodiments, step [S-7] comprises removing RPG from the intermediate of formula [A-7], thereby forming a compound of formula [I], wherein X is hydrogen. In some embodiments, the removal of RPG comprises contacting the intermediate of formula A-7 with an acid. In some embodiments, the acid comprises albuminic acid. In some embodiments, the acid comprises hydrobromic acid. In some embodiments, the acid comprises hydrobromic acid in acetic acid. In some embodiments, the reaction is carried out in an additional solvent. In some embodiments, the additional solvent is dichloromethane. In some embodiments, step [S-8] comprises hydrogen / deuterium exchange of a compound of formula [I] (wherein X is hydrogen), thereby forming a compound of formula [I] (wherein X is deuterium). In some embodiments, the hydrogen / deuterium exchange occurs in a deuterated solvent. In some embodiments, the deuterated solvent comprises D2O. In some embodiments, the deuterated solvent comprises deuterated methanol. In some embodiments, the deuterated solvent comprises CH3OD. In some embodiments, the deuterated solvent comprises CD3OD. In some embodiments, the deuterated solvent comprises CDCl3. In some embodiments, the deuterated solvent comprises a mixture of two or more of D2O, CH3OD, CD3OD, or CDCl3. In some embodiments, the hydrogen / deuterium exchange is promoted by a base. In some embodiments, the base is derived from sodium metal in the deuterated solvent. [, Use, formulation and administration and pharmaceutically acceptable compositions , ] [, , ] According to another embodiment, the present invention provides a composition comprising a compound of the present invention or a pharmaceutically acceptable salt, ester, or salt of an ester thereof, and a pharmaceutically acceptable carrier, adjuvant, or vehicle. The amount of the compound in the composition of the present invention is such that it can effectively and measurably inhibit Tyk2 in a biological sample or a patient. In certain embodiments, the amount of the compound in the composition of the present invention is such that it can effectively and measurably inhibit Tyk2 in a biological sample or a patient. In certain embodiments, the composition of the present invention is formulated for administration to a patient in need thereof. In some embodiments, the composition of the present invention is formulated for oral administration to a patient. As used herein, the term "compound" means a Tyk2 inhibitor of formula I (including, but not limited to, Compound 1) or a solid form thereof. In some embodiments, the compound is Compound 1 or a pharmaceutically acceptable salt thereof. In some embodiments, the compound is the free base of Compound 1. In some embodiments, the compound is a solid form of Compound 1. In some embodiments, the compound is a crystalline form of Compound 1. In some embodiments, the compound is Form I', Form I, Form II, Form III, Form IV, or Form V of Compound 1. In some embodiments, the compound is a polymorph of the free base of Compound 1. In some embodiments, the compound is Form I' of Compound 1. In some embodiments, the compound is the mesylate salt of Compound 1. In some embodiments, the compound is Form I of Compound 1. In some embodiments, the compound is a solvate of Compound 1. In some embodiments, the compound is amorphous Compound 1. As used herein, the term "patient" means an animal, preferably a mammal, and most preferably a human. The term "pharmaceutically acceptable carrier, adjuvant or diluent" refers to a non-toxic carrier, adjuvant or vehicle that does not destroy the pharmacological activity of the compound formulated therewith. Pharmaceutically acceptable carriers, adjuvants or diluents that can be used in the compositions of the present invention include, but are not limited to, anti-adhesives, binders, coatings, colorants, disintegrants, flavoring agents, glidants, lubricants, preservatives, absorbents and vehicles. Examples of carriers, adjuvants and diluents include, but are not limited to, ion exchangers, alumina, aluminum stearate, lecithin, serum proteins (such as human serum albumin), buffers (such as phosphates), glycine, sorbic acid, potassium sorbate, partial glyceride mixtures of saturated vegetable fatty acids, water, salts or electrolytes (such as protamine sulfate, disodium hydrogen phosphate, potassium hydrogen phosphate, sodium chloride, zinc salts, colloidal silicon dioxide, magnesium trisilicate, polyvinylpyrrolidone, cellulose-based substances, polyethylene glycol, sodium carboxymethyl cellulose, polyacrylates, waxes, polyethylene-polypropylene block polymers, polyethylene glycol and lanolin. "Pharmaceutically acceptable derivative" means any non-toxic salt, ester, salt of an ester or other derivative of a compound of the present invention that, when administered to a recipient, is capable of directly or indirectly providing the compound of the present invention or its inhibitory active metabolite or residue. As used herein, the term "its inhibitory active metabolite or residue" means a metabolite or residue that is also an inhibitor of Tyk2. The compositions of the present invention can be administered orally, parenterally, by inhalation spray, topically, rectally, nasally, buccally, vaginally or via an implantable reservoir. As used herein, the term "parenteral" includes subcutaneous, intravenous, intramuscular, intra-articular, intrasynovial, intrasternal, intrathecal, intrahepatic, intralesional and intracranial injection or infusion techniques. Preferably, the compositions are administered orally, intraperitoneally or intravenously. The sterile injectable form of the compositions of the present invention can be an aqueous or oily suspension. These suspensions can be formulated according to techniques known in the art using suitable dispersing or wetting agents and suspending agents. The sterile injectable preparation can also be a sterile injectable solution or suspension in a non-toxic parenterally acceptable diluent or solvent, such as a solution in 1,3-butanediol. Acceptable media and solvents that can be employed are, in particular, water, Ringer's solution and isotonic sodium chloride solution. In addition, a sterile non-volatile oil is conventionally employed as a solvent or suspending medium. For this purpose, any mild non-volatile oil can be employed, including synthetic mono- or di-glycerides. Fatty acids (such as oleic acid and its glyceride derivatives) can be used in the preparation of injectables, such as natural pharmaceutically acceptable oils, such as olive oil or castor oil, especially in their polyoxylated form. These oil solutions or suspensions can also contain long-chain alcohol diluents or dispersing agents, such as carboxymethyl cellulose or similar dispersing agents, which are commonly used in formulating pharmaceutically acceptable dosage forms, including emulsions and suspensions. Other commonly used surfactants (such as Tween, Span and other emulsifiers or bioavailability enhancers commonly used in the manufacture of pharmaceutically acceptable solid, liquid or other dosage forms) can also be used for formulation purposes. The pharmaceutically acceptable compositions of the present invention can be administered orally in any orally acceptable dosage form, including but not limited to capsules, tablets, aqueous suspensions or solutions. In the case of tablets for oral use, commonly used carriers include lactose and corn starch. A lubricant, such as magnesium stearate, is usually also added. For oral administration in capsule form, useful diluents include lactose and dried corn starch. When an aqueous suspension is required for oral use, the active ingredient can be combined with emulsifying and suspending agents. If desired, certain sweetening, flavoring or coloring agents can also be added. Alternatively, the pharmaceutically acceptable compositions of the present invention can be administered in the form of suppositories for rectal administration. These compositions can be prepared by mixing the agent with a suitable non-irritating excipient that is solid at ambient temperature but liquid at rectal temperature and thus melts in the rectum to release the drug. Such materials include cocoa butter, beeswax and polyethylene glycol. The pharmaceutically acceptable compositions of the present invention may also be administered locally, particularly when the treatment targets include regions or organs that are readily accessible by local application, including diseases of the eye, skin, or lower intestine. Suitable topical formulations for each of these regions or organs can be readily prepared. Local application to the lower intestine can be achieved with a rectal suppository formulation (see above) or a suitable enema formulation. Topical transdermal patches can also be used. For local application, the provided pharmaceutically acceptable compositions can be formulated in suitable ointments containing the active ingredient suspended or dissolved in one or more carriers. Carriers for local administration of the compounds of the present invention include, but are not limited to, mineral oil, liquid petrolatum, white petrolatum, propylene glycol, polyoxyethylene, polyoxypropylene compounds, emulsifying wax, and water. Alternatively, the provided pharmaceutically acceptable compositions can be formulated in suitable lotions or creams containing the active ingredient suspended or dissolved in one or more pharmaceutically acceptable carriers. Suitable carriers include, but are not limited to, mineral oil, sorbitan monostearate, polysorbate 60, cetyl ester wax, cetyl alcohol, 2-octyldodecanol, benzyl alcohol, and water. For ocular applications, the provided pharmaceutically acceptable compositions can be formulated as a micronized suspension in isotonic, pH-adjusted sterile saline, or preferably as a solution in isotonic, pH-adjusted sterile saline, with or without a preservative such as benzalkonium chloride. Alternatively, for ocular applications, the pharmaceutically acceptable compositions can be formulated in an ointment (such as petrolatum). The pharmaceutically acceptable compositions of the present invention can also be administered by nasal aerosol or inhalation. These compositions are prepared according to techniques well known in the pharmaceutical formulation art and can be prepared as an aqueous salt solution using benzyl alcohol or other suitable preservatives, absorption promoters for enhancing bioavailability, fluorocarbons, and / or other conventional solubilizing or dispersing agents. Preferably, the pharmaceutically acceptable compositions of the present invention are formulated for oral administration. These formulations can be administered with or without food. In some embodiments, the pharmaceutically acceptable compositions of the present invention are not administered with food. In other embodiments, the pharmaceutically acceptable compositions of the present invention are administered with food. The amount of the compounds of the present invention that can be combined with a carrier material to produce a composition in a single dosage form will vary depending on the subject being treated and the particular mode of administration. Preferably, the provided compositions should be formulated such that a dosage between 0.01 mg / kg body weight / day and 100 mg / kg body weight / day of the inhibitor can be administered to a patient receiving the compositions. It should also be understood that the specific dosage and treatment regimen for any particular patient may depend on a variety of factors, including the activity of the specific compound employed, age, weight, general health, sex, diet, time of administration, rate of excretion, drug combination, and the judgment of the treating physician and the severity of the particular disease being treated. The amount of the compound of the invention in the composition will also depend on the particular compound in the composition. [ , Uses of the compounds and their compositions , ] [ , , ] [ , Medical uses , ] [ , , ] The compounds and compositions described herein are generally useful for inhibiting the kinase activity of one or more enzymes. In some embodiments, the kinase inhibited by the compounds and methods of the invention is TYK2. TYK2 is a non-receptor tyrosine kinase member of the Janus kinase (JAK) family of protein kinases. The mammalian JAK family consists of four members: TYK2, JAK1, JAK2, and JAK3. JAK proteins (including TYK2) are essential for cytokine signal transduction. TYK2 is associated with the cytoplasmic domains of type I and type II cytokine receptors and interferon type I and type III receptors, and is activated by these receptors upon cytokine binding. Cytokines involved in TYK2 activation include interferons (such as IFN-α, IFN-β, IFN-κ, IFN-δ, IFN-ε, IFN-τ, IFN-ω, and IFN-ζ (also known as limitin)) and interleukins (such as IL-4, IL-6, IL-10, IL-11, IL-12, IL-13, IL-22, IL-23, IL-27, IL-31, oncostatin M, ciliary neurotrophic factor, cardiotrophin 1, cardiotrophin-like cytokine, and LIF).Velasquez et al., "A protein kinase in the interferon α / β signaling pathway," Cell (1992) 70:313; Stahl et al., "Association and activation of Jak-Tyk kinases by CNTF-LIF-OSM-IL-6β receptor components," Science (1994) 263:92; Finbloom et al., "IL-10 induces the tyrosine phosphorylation of Tyk2 and Jak1 and the differential assembly of Stat1 and Stat3 complexes in human T cells and monocytes," J. Immunol. (1995) 155:1079; Bacon et al., "Interleukin 12 (IL-12) induces tyrosine phosphorylation of Jak2 and Tyk2: differential use of Janus family kinases by IL-2 and IL-12," J. Exp. Med. (1995) 181:399; Welham et al., "Interleukin-13 signal transduction in lymphohemopoietic cells: similarities and differences in signal transduction with interleukin-4 and insulin," J. Biol. Chem. (1995) 270:12286; Parham et al., "A receptor for the heterodimeric cytokine IL-23 is composed of IL-12Rβ1 and a novel cytokine receptor subunit, IL-23R," J. Immunol. (2002) 168:5699. The activated TYK2 then proceeds to further phosphorylate signaling proteins such as members of the STAT family, including STAT1, STAT2, STAT4, and STAT6. Activation of TYK2 by IL-23 is associated with inflammatory bowel disease (IBD), Crohn's disease, and ulcerative colitis. Duerr et al., "A Genome-Wide Association Study Identifies IL23R as an Inflammatory Bowel Disease Gene," Science (2006) 314:1461-1463. TYK2, as a downstream effector of IL-23, also plays a role in psoriasis, ankylosing spondylitis, and Behçet's disease. Cho et al., "Genomics and the multifactorial nature of human auto-immune disease," N. Engl. J. Med (2011) 365:1612-1623; Cortes et al., "Identification of multiple risk variants for ankylosing spondylitis through high-density genotyping of immune-related loci," Nat. Genet. (2013) 45(7):730-738; Remmers et al., "Genome-wide association study identifies variants in the MHC class I, IL10, and IL23R-IL12RB2 regions associated with Behçet's disease," Nat. Genet. (2010) 42:698-702. A genome-wide association study of 2,622 individuals with psoriasis identified an association between disease susceptibility and TYK2. Strange et al., "A genome-wide association study identifies new psoriasis susceptibility loci and an interaction between HLA-C and ERAP1," Nat. Genet. (2010) 42:985-992. Ablation of TYK2 or inhibition of tyrosine phosphorylation significantly alleviates dermatitis induced by both IL-23 and IL-22.Ishizaki et al., "Tyk2 is a therapeutic target for psoriasis-like skin inflammation," Intl. Immunol. (2013), doi: 10.1093 / intimm / dxt062... TYK2 also plays a role in respiratory diseases such as asthma, chronic obstructive pulmonary disease (COPD), lung cancer, and cystic fibrosis. Goblet cell hyperplasia (GCH) and mucus hypersecretion are mediated by TYK2 activation induced by IL-13, which in turn activates STAT6. Zhang et al., "Docking protein Gab2 regulates mucin expression and goblet cell hyperplasia through TYK2 / STAT6 pathway," FASEB J. (2012) 26:1-11. Reduced TYK2 activity protects joints from collagen antibody-induced arthritis, a model of human rheumatoid arthritis. Mechanistically, reduced Tyk2 activity decreases the production of Th1 / Th17-related cytokines and matrix metalloproteinases and major markers of inflammation. Ishizaki et al., "Tyk2 deficiency protects joints against destruction in anti-type II collagen antibody-induced arthritis in mice," Intl. Immunol. (2011) 23(9):575-582. Compared with controls, TYK2 knockout mice showed complete resistance in experimental autoimmune encephalomyelitis (EAE, an animal model of multiple sclerosis (MS)), with no infiltration of CD4 T cells in the spinal cord, indicating that in MS, TYK2 is crucial for the development of pathogenic CD4-mediated disease. Oyamada et al., "Tyrosine Kinase 2 Plays Critical Roles in the Pathogenic CD4 T Cell Responses for the Development of Experimental Autoimmune Encephalomyelitis," J. Immunol. (2009) 183:7539-7546. This confirms previous studies linking increased TYK2 expression to MS susceptibility. Ban et al., "Replication analysis identifies TYK2 as a multiple sclerosis susceptibility factor," Eur J. Hum. Genet. (2009) 17:1309-1313. Loss of function mutations in TYK2 result in reduced demyelination of neurons and increased myelin regeneration, further indicating the role of TYK2 inhibitors in the treatment of MS and other CNS demyelinating disorders. TYK2 is the only common signaling messenger for both IL-12 and IL-23. TYK2 knockout reduced the footpad thickness induced by methylated BSA injection, imiquimod-induced psoriasiform skin inflammation, and dextran sulfate sodium or 2,4,6-trinitrobenzenesulfonic acid-induced colitis in mice. Studies of the association and correlation of various type I IFN signaling genes with systemic lupus erythematosus (SLE), an autoimmune disorder, have shown a strong significant correlation between loss-of-function mutations and TYK2 and a reduced prevalence of SLE in families with affected members. Sigurdsson et al., "Polymorphisms in the Tyrosine Kinase 2 and Interferon Regulatory Factor 5 Genes Are Associated with Systemic Lupus Erythematosus," Am. J. Hum. Genet. (2005) 76:528-537. Genome-wide association studies of individuals with SLE relative to unaffected cohorts have shown a high correlation between the TYK2 locus and SLE. Graham et al., "Association of NCF2, IKZF1, IRF8, IFIH1, and TYK2 with Systemic Lupus Erythematosus," PLoS Genetics (2011) 7(10):e1002341. TYK2 has been shown to play an important role in maintaining tumor surveillance, and TYK2 knockout mice show impaired cytotoxic T cell responses and accelerated tumor development. However, this effect is associated with the effective inhibition of natural killer (NK) and cytotoxic T lymphocytes, suggesting that TYK2 inhibitors would be highly suitable for the treatment of autoimmune disorders or transplant rejection. Although other JAK family members, such as JAK3, have similar roles in the immune system, TYK2 is considered an excellent target because it is involved in fewer and more closely related signaling pathways, resulting in fewer off-target effects. Simma et al., "Identification of an Indispensable Role for Tyrosine Kinase 2 in CTL-Mediated Tumor Surveillance," Cancer Res. (2009) 69:203-211. However, paradoxically to the reduced tumor surveillance observed by Simma et al. in T-cell acute lymphoblastic leukemia (T-ALL), T-ALL highly depends on IL-10 via TYK2-mediated STAT1 signaling to maintain cancer cell survival by upregulating the anti-apoptotic protein BCL2. Attenuation of TYK2, but not other JAK family members, reduces cell growth. Specific activating mutations of TYK2 that promote cancer cell survival include those in the FERM domain (G36D, S47N, and R425H), JH2 domain (V731I), and kinase domain (E957D and R1027H). However, it has also been identified that the kinase function of TYK2 is essential for increasing cancer cell survival, as the TYK2 enzyme characterized by kinase-inactivating mutations (M978Y or M978F) in addition to the activating mutation (E957D) results in transformation failure. Sanda et al., 「TYK2-STAT1-BCL2 Pathway Dependence in T-Cell Acute Lymphoblastic Leukemia,」 Cancer Disc. (2013) 3(5):564-577. Therefore, the selective inhibition of TYK2 has been considered an appropriate target for patients with IL-10- and / or BCL2-addicted tumors, such as 70% of adult T-cell leukemia cases. Fontan et al., 「Discovering What Makes STAT Signaling TYK in T-ALL,」 Cancer Disc. (2013) 3:494-496. TYK2-mediated STAT3 signaling has also been shown to mediate neuronal cell death induced by amyloid-β (Aβ) peptide. Reduced TYK2 phosphorylation of STAT3 after Aβ administration results in decreased neuronal cell death, and increased phosphorylation of STAT3 was observed in the postmortem brains of Alzheimer's disease patients. Wan et al., 「Tyk / STAT3 Signaling Mediates β-Amyloid-Induced Neuronal Cell Death: Implications in Alzheimer’s Disease,」 J. Neurosci. (2010) 30(20):6873-6881. Inhibition of the JAK-STAT signaling pathway is also involved in hair growth and reversal of alopecia associated with alopecia areata. Xing et al., "Alopecia areata is driven by cytotoxic T lymphocytes and is reversed by JAK inhibition," Nat. Med. (2014) 20: 1043-1049; Harel et al., "Pharmacologic inhibition of JAK-STAT signaling promotes hair growth," Sci. Adv. (2015) 1(9):e1500973. Accordingly, compounds that inhibit TYK2 activity are beneficial, particularly those compounds that are selective for JAK2. Such compounds should deliver a pharmacological response that advantageously treats one or more of the conditions described herein without the side effects associated with JAK2 inhibition. Even though TYK2 inhibitors are known in the art, there continues to be a need to provide novel inhibitors having more effective or favorable pharmaceutical-related properties. For example, compounds having increased activity, selectivity for other JAK kinases, particularly JAK2, and ADMET (absorption, distribution, metabolism, excretion, and / or toxicity) properties. Accordingly, in some embodiments, the present invention provides TYK2 inhibitors that are selective for JAK2. The activity of the compounds used in the present invention as inhibitors of TYK2 or its mutants can be analyzed in vitro, in vivo, or in cell lines. In vitro analysis includes assays that measure the phosphorylation activity of activated TYK2 or its mutants and / or subsequent functional consequences or inhibition of ATPase activity. Alternatively, in vitro analysis quantifies the ability of the inhibitor to bind to TYK2. The inhibitor binding can be measured by radiolabeling the inhibitor prior to binding, separating the inhibitor / TYK2 complex, and measuring the amount of bound radiolabel. Alternatively, inhibitor binding can be determined by running a competition experiment in which the new inhibitor is incubated with TYK2 that is bound to a known radioligand. Representative in vitro and in vivo assays that can be used to analyze TYK2 inhibitors include, for example, those assays described and disclosed in each of the references incorporated herein by reference in their entirety. The detailed conditions for analyzing the compounds used in the present invention as inhibitors of TYK2 or its mutants are set forth in the examples below. As used herein, the terms "treatment", "treat", and "treating" refer to reversing, alleviating a disease or disorder or one or more symptoms thereof as set forth herein, delaying its onset, or inhibiting its progression. In some embodiments, treatment can be administered after one or more symptoms have occurred. In other embodiments, treatment can be administered in the absence of symptoms. For example, treatment can be administered to a susceptible individual prior to the onset of symptoms (e.g., in view of a history of symptoms and / or in view of genetic or other susceptibility factors). Treatment can also be continued after symptoms have subsided to, for example, prevent or delay their recurrence. The provided compounds are TYK2 inhibitors and can thus be used to treat one or more conditions associated with the activity of TYK2 or its mutants. Accordingly, in some embodiments, the present invention provides a method of treating a TYK2-mediated condition, comprising the step of administering to a patient in need thereof a compound of the present invention or a pharmaceutically acceptable composition thereof. As used herein, the terms "TYK2-mediated" conditions, diseases, and / or disorders mean any disease or other adverse condition in which TYK2 or its mutants are known to play a role. Accordingly, another embodiment of the present invention relates to treating or attenuating the severity of one or more diseases in which TYK2 or its mutants are known to play a role. Such TYK2-mediated conditions include, but are not limited to, autoimmune disorders, inflammatory disorders, proliferative disorders, endocrine disorders, neurological disorders, and transplantation-related disorders. In some embodiments, the present invention provides a method of treating one or more conditions selected from the group consisting of autoimmune disorders, inflammatory disorders, proliferative disorders, endocrine disorders, neurological disorders, and transplantation-related disorders, the method comprising administering to a patient in need thereof a pharmaceutical composition comprising an effective amount of a compound of the present invention or a pharmaceutically acceptable salt thereof. In some embodiments, the condition is an autoimmune disorder. In some embodiments, the condition is selected from the group consisting of type 1 diabetes, systemic lupus erythematosus, multiple sclerosis, psoriasis, Behçet's disease, POEMS syndrome, Crohn's disease, ulcerative colitis, and inflammatory bowel disease. In some embodiments, the condition is an inflammatory disorder. In some embodiments, the inflammatory disorder is rheumatoid arthritis, asthma, chronic obstructive pulmonary disease, psoriasis, hepatomegaly, Crohn's disease, ulcerative colitis, inflammatory bowel disease. In some embodiments, the condition is a proliferative disorder. In some embodiments, the proliferative disorder is a blood cancer. In some embodiments, the proliferative disorder is leukemia. In some embodiments, the leukemia is T cell leukemia. In some embodiments, the T cell leukemia is T cell acute lymphoblastic leukemia (T-ALL). In some embodiments, the proliferative disorder is polycythemia vera, myelofibrosis, essential thrombocythemia. In some embodiments, the disorder is an endocrine disorder. In some embodiments, the endocrine disorder is polycystic ovary syndrome, Crouzon’s syndrome, or type 1 diabetes. In some embodiments, the disorder is a neurological disorder. In some embodiments, the neurological disorder is Alzheimer's disease. In some embodiments, the proliferative disorder is associated with one or more activating mutations of TYK2. In some embodiments, the activating mutation of TYK2 is a mutation in the FERM domain, JH2 domain, or kinase domain. In some embodiments, the activating mutation of TYK2 is selected from G36D, S47N, R425H, V731I, E957D, and R1027H. In some embodiments, the disorder is related to transplantation. In some embodiments, the disorder related to transplantation is transplant rejection or graft-versus-host disease. In some embodiments, the disorder is related to type I interferon, IL-10, IL-12, or IL-23 signaling. In some embodiments, the disorder is related to type I interferon signaling. In some embodiments, the disorder is related to IL-10 signaling. In some embodiments, the disorder is related to IL-12 signaling. In some embodiments, the disorder is related to IL-23 signaling. The compounds of the present invention can also be used to treat inflammatory or allergic conditions of the skin, such as psoriasis, contact dermatitis, atopic dermatitis, alopecia areata, erythema multiforme, dermatitis herpetiformis, scleroderma, vitiligo, allergic vasculitis, urticaria, bullous pemphigoid, lupus erythematosus, systemic lupus erythematosus, pemphigus vulgaris, pemphigus foliaceus, paraneoplastic pemphigus, acquired epidermolysis bullosa, acne vulgaris, and other inflammatory or allergic conditions of the skin. The compounds of the present invention can also be used for treating other diseases or conditions (such as diseases or conditions having inflammatory components), for example, treating eye diseases and conditions (such as eye allergies, conjunctivitis, keratoconjunctivitis sicca, and vernal conjunctivitis), diseases affecting the nose (including allergic rhinitis), and inflammatory diseases involving or having an autoimmune component or etiology, including autoimmune hematological disorders (such as hemolytic anemia, aplastic anemia, pure red cell anemia, and idiopathic thrombocytopenia), systemic lupus erythematosus, rheumatoid arthritis, polychondritis, scleroderma, Wegener granulamatosis, dermatomyositis, chronic active hepatitis, myasthenia gravis, Stevens-Johnson syndrome, idiopathic sprue, autoimmune inflammatory bowel diseases (such as ulcerative colitis and Crohn's disease), irritable bowel syndrome, celiac disease, periapical osteitis, hyaline membrane disease, kidney diseases, glomerular diseases, alcoholic liver disease, multiple sclerosis, endocrine ophthalmopathy, Grave's disease, sarcoidosis, alveolitis, chronic allergic pneumonia, multiple sclerosis, primary biliary sclerosis, uveitis (anterior uveitis and posterior uveitis), Sjogren’s syndrome, keratoconjunctivitis sicca and vernal keratoconjunctivitis, interstitial lung fibrosis, psoriatic arthritis, systemic juvenile idiopathic arthritis, cryopyrin-associated periodic syndromes, nephritis, vasculitis, diverticulitis, interstitial cystitis, glomerulonephritis (with and without nephrotic syndrome,Such as including idiopathic nephrotic syndrome or minimal change nephropathy), chronic granulomatous disease, endometriosis, leptospirosis nephropathy, glaucoma, retinal diseases, aging, headache, pain, complex regional pain syndrome, cardiac hypertrophy, muscular atrophy, catabolic disorders, obesity, fetal growth retardation, hypercholesterolemia, heart disease, chronic heart failure, mesothelioma, anhidrotic ectodermal dysplasia, Behcet's disease, dyschromatosis, Paget's disease, pancreatitis, hereditary periodic fever syndrome, asthma (allergic and non-allergic, mild, moderate, severe, bronchitic and exercise-induced asthma), acute lung injury, acute respiratory distress syndrome, eosinophilia, allergy, hypersensitivity reaction, sinusitis, ocular allergy, silica-induced diseases, COPD (damage, airway inflammation, bronchial hyperreactivity, remodeling or reduced disease progression), lung diseases, cystic fibrosis, acid-induced lung injury, pulmonary hypertension, polyneuropathy, cataract, muscle inflammation combined with systemic sclerosis, inclusion body myositis, myasthenia gravis, thyroiditis, Addison's disease, lichen planus, type 1 diabetes or type 2 diabetes, appendicitis, atopic dermatitis, asthma, allergy, blepharitis, bronchiolitis, bronchitis, bursitis, cervicitis, cholangitis, cholecystitis, chronic graft rejection, colitis, conjunctivitis, Crohn's disease, cystitis, dacryoadenitis, dermatitis, dermatomyositis, encephalitis, endocarditis, endometritis, enteritis, enterocolitis, epicondylitis, epididymitis, fasciitis, fibrositis, gastritis, gastroenteritis, Henoch-Schonlein purpura, hepatitis, hidradenitis suppurativa, immunoglobulin A nephropathy, interstitial lung disease, laryngitis, mastitis, meningitis, myelitis myocarditis, myositis, nephritis, oophoritis, orchitis, osteitis, otitis, pancreatitis, parotitis, pericarditis, peritonitis, pharyngitis, pleuritis, phlebitis, pneumonitis, pneumonia, polymyositis, proctitis, prostatitis, pyelonephritis, rhinitis, salpingitis, sinusitis, stomatitis, synovitis, tendinitis, tonsillitis, ulcerative colitis, uveitis, vaginitis, vasculitis or vulvitis., In some embodiments, the inflammatory diseases treatable according to the methods of the present invention are selected from acute and chronic gout, chronic gouty arthritis, psoriasis, psoriatic arthritis, rheumatoid arthritis, juvenile rheumatoid arthritis, systemic juvenile idiopathic arthritis (SJIA), cryopyrin-associated periodic syndrome (CAPS) and osteoarthritis. In some embodiments, the inflammatory diseases treatable by the methods of the invention are Th1 or Th17-mediated diseases. In some embodiments, the Th17-mediated diseases are selected from systemic lupus erythematosus, multiple sclerosis, and inflammatory bowel disease (including Crohn's disease or ulcerative colitis). In some embodiments, the inflammatory diseases treatable by the methods of the invention are selected from Sjogren's syndrome, allergic conditions, osteoarthritis, eye conditions (such as eye allergy, conjunctivitis, keratoconjunctivitis sicca, and vernal conjunctivitis), and diseases affecting the nose (such as allergic rhinitis). Furthermore, the present invention provides the use of a compound or a pharmaceutically acceptable salt or hydrate or solvate thereof as defined herein for the preparation of an agent for treating an autoimmune disorder, an inflammatory disorder, or a proliferative disorder or a condition commonly occurring in connection with transplantation. [, Combination therapies , ] [, , ] Depending on the particular condition or disease to be treated, additional therapeutic agents may be administered in combination with the compounds and compositions of the invention, which are typically administered to treat the condition. As used herein, additional therapeutic agents that are typically administered to treat a particular disease or condition are referred to as "suitable for the disease or condition being treated". In certain embodiments, the provided combination or its composition is administered in combination with another therapeutic agent. Examples of agents that can also be combined with the combinations of the present invention include, but are not limited to: therapeutic agents for Alzheimer's disease, such as Aricept® and Excelon®; therapeutic agents for HIV, such as ritonavir; therapeutic agents for Parkinson's disease, such as L-DOPA / carbidopa, entacapone, ropinirole, pramipexole, bromocriptine, pergolide, trihexephendyl, and amantadine; agents for the treatment of multiple sclerosis (MS), such as beta interferon (e.g., Avonex® and Rebif®), Copaxone®, and mitoxantrone; therapeutic agents for asthma, such as albuterol and Singulair®; therapeutic agents for the treatment of schizophrenia, such as zyprexa, risperdal, seroquel, and haloperidol; anti-inflammatory agents, such as corticosteroids, TNF blockers, IL-1 RA, azathioprine, cyclophosphamide, and sulfasalazine; immunomodulatory and immunosuppressive agents, such as cyclosporine, tacrolimus, rapamycin, mycophenolate mofetil, interferon, corticosteroids, cyclophosphamide, azathioprine, and sulfasalazine; neurotrophic factors, such as acetylcholinesterase inhibitors, MAO inhibitors, interferon, anticonvulsants, ion channel blockers, riluzole, and anti-Parkinson's drugs; agents for the treatment of cardiovascular diseases, such as beta-blockers, ACE inhibitors, diuretics, nitrates, calcium channel blockers, and statins; agents for the treatment of liver diseases, such as corticosteroids, cholestyramine, interferon, and antiviral drugs; agents for the treatment of blood disorders, such as corticosteroids, anti-leukemia drugs, and growth factors; agents for prolonging or modifying pharmacokinetics, such as cytochrome P450 inhibitors (i.e., metabolic disruption inhibitors) and CYP3A4 inhibitors (e.g., ketoconazole and ritonavir), and agents for the treatment of immunodeficiency disorders, such as gamma-globulin. In certain embodiments, the combination therapies of the present invention or pharmaceutically acceptable compositions thereof are administered in combination with monoclonal antibody or siRNA therapeutic agents. These additional agents can be administered separately from the provided combination therapy as part of a multiple-dose regimen. Alternatively, these agents can be part of a single dosage form, which is mixed with the compound of the present invention into a single composition. If administered as part of a multiple-dose regimen, the two active agents can be presented to each other simultaneously, sequentially, or over a period of time, usually within 5 hours of each other. As used herein, the terms "combination", "combined" and related terms refer to the administration of the therapeutic agent of the present invention simultaneously or sequentially. For example, the combination of the present invention can be administered simultaneously or sequentially with another therapeutic agent in separate unit dosage forms or in a single unit dosage form together. The amount of the additional therapeutic agent present in the composition of the present invention will not exceed the amount usually administered in a composition containing the therapeutic agent as the sole active drug. Preferably, the amount of the additional therapeutic agent in the composition disclosed herein will be in the range of about 50% to 100% of the amount usually present in a composition containing the agent as the sole therapeutically active agent. In one embodiment, the present invention provides a composition comprising a compound of formula [I] and one or more additional therapeutic agents. The therapeutic agent can be administered together with the compound of formula [I], or can be administered before or after the administration of the compound of formula [I]. Suitable therapeutic agents are further elaborated in detail below. In certain embodiments, the compound of formula [I] can be administered up to 5 minutes, 10 minutes, 15 minutes, 30 minutes, 1 hour, 2 hours, 3 hours, 4 hours, 5 hours, 6 hours, 7 hours, 8 hours, 9 hours, 10 hours, 11 hours, 12 hours, 13 hours, 14 hours, 15 hours, 16 hours, 17 hours or 18 hours before the therapeutic agent. In other embodiments, the compound of formula [I] can be administered up to 5 minutes, 10 minutes, 15 minutes, 30 minutes, 1 hour, 2 hours, 3 hours, 4 hours, 5 hours, 6 hours, 7 hours, 8 hours, 9 hours, 10 hours, 11 hours, 12 hours, 13 hours, 14 hours, 15 hours, 16 hours, 17 hours or 18 hours after the therapeutic agent. In another embodiment, the present invention provides a method of treating a patient in need by administering a compound of formula [I] Methods of treating inflammatory diseases, disorders or conditions with a compound and one or more additional therapeutic agents. The additional therapeutic agents can be small molecules or recombinant biological agents and include, for example, acetaminophen, non-steroidal anti-inflammatory drugs (NSAIDs) (such as aspirin, ibuprofen, naproxen, etodolac (Lodine®), and celecoxib), colchicine (Colcrys®), corticosteroids (such as prednisone, prednisolone, methylprednisolone, hydrocortisone, and the like), probenecid, allopurinol, febuxostat (Uloric®), sulfasalazine (Azulfidine®), anti-malarial drugs (such as hydroxychloroquine (Plaquenil®) and chloroquine (Aralen®)), methotrexate (Rheumatrex®), gold salts (such as aurothioglucose (Solganal®), aurothiomalate (Myochrysine®), and auranofin (Ridaura®)), D-penicillamine (Depen® or Cuprimine®), azathioprine (Imuran®), cyclophosphamide (Cytoxan®), chlorambucil (Leukeran®), cyclosporine (Sandimmune®), leflunomide (Arava®), and "anti-TNF" agents (such as etanercept (Enbrel®), infliximab (Remicade®), golimumab (Simponi®), certolizumab pegol (Cimzia®), and adalimumab (Humira®)), "anti-IL-1" agents (such as anakinra (Kineret®) and rilonacept (Arcalyst®)), canakinumab(Ilaris®), anti-Jak inhibitors (such as tofacitinib), antibodies (such as rituximab (Rituxan®)), "anti-T cell" agents (such as abatacept (Orencia®)), "anti-IL-6" agents (such as tocilizumab (Actemra®)), diclofenac, cortisone, hyaluronic acid (Synvisc® or Hyalgan®), monoclonal antibodies (such as tanezumab), anticoagulants (such as heparin (Calcinparine® or Liquaemin®) and warfarin (Coumadin®)), antidiarrheal drugs (such as diphenoxylate (Lomotil®) and loperamide (Imodium®)), bile acid binders (such as cholestyramine), alosetron (Lotronex®), lubiprostone (Amitiza®), laxatives (such as Milk of Magnesia, polyethylene glycol (MiraLax®), Dulcolax®), Correctol® and Senokot®), anticholinergic or antispasmodic drugs (such as dicyclomine (Bentyl®), Singulair®), β-2 agonists (such as albuterol (Ventolin® HFA, Proventil® HFA), levalbuterol (Xopenex®), metaproterenol (Alupent®), pirbuterol acetate (Maxair®), terbutaline sulfate (Brethaire®), salmeterol xinafoate (Serevent®) and formoterol (Foradil®)), anticholinergic agents (such as ipratropium bromide (Atrovent®) and tiotropium (Spiriva®)), inhaled corticosteroids (such as beclomethasone dipropionate (Beclovent®), Qvar® and Vanceril®), triamcinolone acetonide(Azmacort®), mometasone (Asthmanex®), budesonide (Pulmocort®), and flunisolide (Aerobid®)), Afviar®, Symbicort®, Dulera®, cromolyn sodium (Intal®), methylxanthines (such as theophylline (Theo-Dur®, Theolair®, Slo-bid®, Uniphyl®, Theo-24®) and aminophylline), IgE antibodies (such as omalizumab (Xolair®)), nucleoside reverse transcriptase inhibitors (such as zidovudine (Retrovir®), abacavir (Ziagen®), abacavir / lamivudine (Epzicom®), abacavir / lamivudine / zidovudine (Trizivir®), didanosine (Videx®), emtricitabine (Emtriva®), lamivudine (Epivir®), lamivudine / zidovudine (Combivir®), stavudine (Zerit®), and zalcitabine (Hivid®)), non-nucleoside reverse transcriptase inhibitors (such as delavirdine (Rescriptor®), efavirenz (Sustiva®), nevirapine (Viramune®), and etravirine (Intelence®)), nucleotide reverse transcriptase inhibitors (such as tenofovir (Viread®)), protease inhibitors (such as amprenavir (Agenerase®), atazanavir (Reyataz®), darunavir (Prezista®), fosamprenavir (Lexiva®), indinavir (Crixivan®), lopinavir and ritonavir (Kaletra®), nelfinavir (Viracept®), ritonavir (Norvir®), saquinavir (Fortovase® or Invirase®), and tipranavir(Aptivus®), entry inhibitors (such as enfuvirtide (Fuzeon®) and maraviroc (Selzentry®)), integrase inhibitors (such as raltegravir (Isentress®), doxorubicin (Hydrodaunorubicin®), vincristine (Oncovin®), bortezomib (Velcade®), and the combination of dexamethasone (Decadron®) and lenalidomide (Revlimid®)), or any combination thereof. In another embodiment, the present invention provides a method for treating rheumatoid arthritis, which comprises administering to a patient in need thereof a [I] compound and one or more additional therapeutic agents selected from the following: non-steroidal anti-inflammatory drugs (NSAIDs) (such as aspirin, ibuprofen, naproxen, etodolac (Lodine®), and celecoxib), corticosteroids (such as prednisone, prednisolone, methylprednisolone, hydrocortisone, and the like), sulfasalazine (Azulfidine®), antimalarial drugs (such as hydroxychloroquine (Plaquenil®) and chloroquine (Aralen®)), methotrexate (Rheumatrex®), gold salts (such as aurothioglucose (Solganal®), aurothiomalate (Myochrysine®), and auranofin (Ridaura®)), D-penicillamine (Depen® or Cuprimine®), azathioprine (Imuran®), cyclophosphamide (Cytoxan®), chlorambucil (Leukeran®), cyclosporine (Sandimmune®), leflunomide (Arava®), and "anti-TNF" agents (such as etanercept (Enbrel®), infliximab (Remicade®), golimumab (Simponi®), pegylated certolizumab (Cimzia®), and adalimumab (Humira®)), "anti-IL-1" agents (such as anakinra (Kineret®) and rilonacept (Arcalyst®)), antibodies (such as rituximab (Rituxan®)), "anti-T cell" agents (such as abatacept (Orencia®)), and "anti-IL-6" agents (such as tocilizumab (Actemra®)). In some embodiments, the present invention provides a method for treating osteoarthritis, which comprises administering to a patient in need thereof a [I] a compound and one or more additional therapeutic agents selected from the following: acetaminophen, non-steroidal anti-inflammatory drugs (NSAIDs) (such as aspirin, ibuprofen, naproxen, etodolac (Lodine®), and celecoxib), diclofenac, cortisone, hyaluronic acid (Synvisc® or Hyalgan®), and monoclonal antibodies (such as tanizumab). In some embodiments, the present invention provides a method for treating systemic lupus erythematosus, which comprises administering to a patient in need thereof a [I] a compound and one or more additional therapeutic agents selected from the following: acetaminophen, non-steroidal anti-inflammatory drugs (NSAIDs) (such as aspirin, ibuprofen, naproxen, etodolac (Lodine®), and celecoxib), corticosteroids (such as prednisone, prednisolone, methylprednisolone, hydrocortisone, and the like), antimalarial drugs (such as hydroxychloroquine (Plaquenil®) and chloroquine (Aralen®)), cyclophosphamide (Cytoxan®), methotrexate (Rheumatrex®), azathioprine (Imuran®), and anticoagulants (such as heparin (Calcinparine® or Liquaemin®) and warfarin (Coumadin®)). In some embodiments, the present invention provides a method for treating Crohn's disease, ulcerative colitis, or inflammatory bowel disease, which comprises administering to a patient in need thereof a [I] a compound and one or more additional therapeutic agents selected from the following: mesalamine (Asacol®), sulfasalazine (Azulfidine®), antidiarrheal drugs (such as diphenoxylate (Lomotil®) and loperamide (Imodium®)), bile acid binders (such as cholestyramine), alosetron (Lotronex®), lubiprostone (Amitiza®), laxatives (such as milk of magnesia, polyethylene glycol (MiraLax®), Dulcolax®, Correctol®, and Senokot®), and anticholinergic or antispasmodic drugs (such as dicyclomine (Bentyl®)), anti-TNF therapy, corticosteroids, and antibiotics (such as metronidazole (Flagyl) or ciprofloxacin). In some embodiments, the present invention provides a method for treating asthma, which comprises administering to a patient in need thereof a [I] A compound and one or more additional therapeutic agents selected from the following: Singulair®, β-2 agonists (such as albuterol (Ventolin® HFA, Proventil® HFA), levalbuterol (Xopenex®), metaproterenol (Alupent®), pirbuterol acetate (Maxair®), terbutaline sulfate (Brethaire®), salmeterol xinafoate (Serevent®), and formoterol (Foradil®)), anticholinergics (such as ipratropium bromide (Atrovent®) and tiotropium (Spiriva®)), inhaled corticosteroids (such as prednisone, prednisolone, beclomethasone dipropionate (Beclovent®, Qvar®, and Vanceril®), triamcinolone acetonide (Azmacort®), mometasone (Asthmanex®), budesonide (Pulmocort®), flunisolide (Aerobid®), Afviar®, Symbicort®, and Dulera®), cromolyn sodium (Intal®), methylxanthines (such as theophylline (Theo-Dur®, Theolair®, Slo-bid®, Uniphyl®, Theo-24®) and aminophylline), and IgE antibodies (such as omalizumab (Xolair®)). In some embodiments, the present invention provides a method for treating COPD, which comprises administering to a patient in need thereof a [I] A compound and one or more additional therapeutic agents selected from the following: β-2 agonists (such as albuterol (Ventolin® HFA, Proventil® HFA), levalbuterol (Xopenex®), metaproterenol (Alupent®), pirbuterol acetate (Maxair®), terbutaline sulfate (Brethaire®), salmeterol xinafoate (Serevent®), and formoterol (Foradil®)), anticholinergics (such as ipratropium bromide (Atrovent®) and tiotropium (Spiriva®)), methylxanthines (such as theophylline (Theo-Dur®, Theolair®, Slo-bid®, Uniphyl®, Theo-24®) and aminophylline), inhaled corticosteroids (such as prednisone, prednisolone, beclomethasone dipropionate (Beclovent®, Qvar®, and Vanceril®), triamcinolone acetonide (Azmacort®), mometasone (Asthmanex®), budesonide (Pulmocort®), flunisolide (Aerobid®)). In another embodiment, the present invention provides a method for treating hematological malignancies, which comprises administering to a patient in need thereof a [I] a compound and one or more additional therapeutic agents selected from the following: Rituxan®, Cyclophosphamide (Cytoxan®), Doxorubicin (Hydrodaunorubicin®), Vincristine (Oncovin®), Prednisone, hedgehog signaling inhibitors, BTK inhibitors, JAK / pan-JAK inhibitors, PI3K inhibitors, SYK inhibitors, and combinations thereof. In another embodiment, the present invention provides a method for treating solid tumors, which comprises administering to a patient in need thereof a [I] a compound and one or more additional therapeutic agents selected from the following: Rituxan®, Cyclophosphamide (Cytoxan®), Doxorubicin (Hydrodaunorubicin®), Vincristine (Oncovin®), Prednisone, hedgehog signaling inhibitors, BTK inhibitors, JAK / pan-JAK inhibitors, PI3K inhibitors, SYK inhibitors, and combinations thereof. In another embodiment, the present invention provides a method for treating hematological malignancies, which comprises administering to a patient in need thereof a [I] a compound and a Hedgehog (Hh) signaling pathway inhibitor. In some embodiments, the hematological malignancy is DLBCL (Ramirez et al., "Defining causative factors contributing in the activation of hedgehog signaling in diffuse large B-cell lymphoma" Leuk. Res. (2012), published online on July 17, and the entire content of which is incorporated herein by reference). In another embodiment, the present invention provides a method for treating diffuse large B-cell lymphoma (DLBCL), which comprises administering to a patient in need thereof a [I] a compound and one or more additional therapeutic agents selected from the following: Rituxan®, Cyclophosphamide (Cytoxan®), Doxorubicin (Hydrodaunorubicin®), Vincristine (Oncovin®), Prednisone, hedgehog signaling inhibitors, and combinations thereof. In another embodiment, the present invention provides a method for treating multiple myeloma, which comprises administering to a patient in need thereof a [I]A compound and one or more additional therapeutic agents selected from the following: the combination of bortezomib (Velcade®) and dexamethasone (Decadron®), hedgehog signaling inhibitors, BTK inhibitors, JAK / pan-JAK inhibitors, TYK2 inhibitors, PI3K inhibitors, SYK inhibitors, and lenalidomide (Revlimid®). In another embodiment, the present invention provides a method of treating a disease or reducing the severity of a disease, which comprises administering to a patient in need thereof a formula [I] Compounds and BTK inhibitors, wherein the disease is selected from inflammatory bowel disease, arthritis, systemic lupus erythematosus (SLE), vasculitis, idiopathic thrombocytopenic purpura (ITP), rheumatoid arthritis, psoriatic arthritis, osteoarthritis, Still’s disease, juvenile arthritis, diabetes, myasthenia gravis, Hashimoto’s thyroiditis, Ord’s thyroiditis, Graves’ disease, autoimmune thyroiditis, Sjogren’s syndrome, multiple sclerosis, systemic sclerosis, Lyme neuroborreliosis, Guillain-Barre syndrome, acute disseminated encephalomyelitis, Addison’s disease, opsoclonus-myoclonus syndrome, ankylosing spondylitis, antiphospholipid antibody syndrome, aplastic anemia, autoimmune hepatitis, autoimmune gastritis, pernicious anemia, celiac disease, Goodpasture’s syndrome, idiopathic thrombocytopenic purpura, optic neuritis, scleroderma, primary biliary sclerosis, Reiter’s syndrome, Takayasu’s arteritis, temporal arteritis, warm autoimmune hemolytic anemia, Wegener’s granulomatosis, psoriasis, alopecia universalis, Behcet’s disease, chronic fatigue, autonomic neuropathy, membranous glomerulonephropathy, endometriosis, interstitial cystitis, pemphigus vulgaris, bullous pemphigoid, neuromyotonia, scleroderma, vulvodynia, hyperproliferative diseases, transplant organ or tissue rejection, acquired immunodeficiency syndrome (AIDS, also known as HIV), type 1 diabetes, graft-versus-host disease, transplantation, transfusion, allergic reactions, hypersensitivity (e.g.,Allergic to plant pollen, latex, drugs, foods, insect toxins, animal hair, animal dander, dust mites or cockroach exuviae), type I hypersensitivity, allergic conjunctivitis, allergic rhinitis and atopic dermatitis, asthma, appendicitis, atopic dermatitis, asthma, allergies, blepharitis, bronchiolitis, bronchitis, bursitis, cervicitis, cholangitis, cholecystitis, chronic graft rejection, colitis, conjunctivitis, Crohn's disease, cystitis, dacryoadenitis, dermatitis, dermatomyositis, encephalitis, endocarditis, endometritis, enteritis, enterocolitis, epicondylitis, epididymitis, fasciitis, fibrositis, gastritis, gastroenteritis, Henoch-Schönlein purpura, hepatitis, hidradenitis suppurativa, immunoglobulin A nephropathy, interstitial lung disease, laryngitis, mastitis, meningitis, myelitis, myocarditis, myositis, nephritis, oophoritis, orchitis, osteitis, otitis, pancreatitis, parotitis, pericarditis, peritonitis, pharyngitis, pleuritis, phlebitis, pneumonitis, pneumonia, polymyositis, proctitis, prostatitis, pyelonephritis, rhinitis, salpingitis, sinusitis, stomatitis, synovitis, tendinitis, tonsillitis, ulcerative colitis, uveitis, vaginitis, vasculitis, or vulvitis, B cell proliferative disorders (such as diffuse large B cell lymphoma, follicular lymphoma, chronic lymphocytic lymphoma, chronic lymphocytic leukemia, acute lymphocytic leukemia, B cell prolymphocytic leukemia, lymphoplasmacytic lymphoma / Waldenstrom macroglobulinemia, splenic marginal zone lymphoma, multiple myeloma (also known as plasma cell myeloma), non-Hodgkin's lymphoma, Hodgkin's lymphoma, plasmacytoma, extranodal marginal zone B cell lymphoma, nodal marginal zone B cell lymphoma, mantle cell lymphoma, mediastinal (thymic) large B cell lymphoma, intravascular large B cell lymphoma, primary effusion lymphoma, Burkitt lymphoma / leukemia or lymphomatoid granulomatosis), breast cancer, prostate cancer or mast cell cancer (e.g., mastocytoma, mast cell leukemia, mast cell sarcoma, systemic mastocytosis), bone cancer, colorectal cancer, pancreatic cancer, bone and joint diseases (including but not limited to rheumatoid arthritis, seronegative spondyloarthropathies (including ankylosing spondylitis, psoriatic arthritis and Reiter's disease), Behçet's disease, Sjögren's syndrome, systemic sclerosis, osteoporosis, bone cancer, bone metastases), thromboembolic disorders (e.g.,Myocardial infarction, angina pectoris, restenosis after angioplasty, re-stenosis after angioplasty, restenosis after aortic coronary artery bypass grafting, restenosis after aortic coronary artery bypass grafting, stroke, transient ischemia, peripheral arterial obstructive disease, pulmonary embolism, deep vein thrombosis), inflammatory pelvic disease, urethritis, skin sunburn, sinusitis, pneumonia, encephalitis, meningitis, myocarditis, nephritis, osteomyelitis, myositis, hepatitis, gastritis, enteritis, dermatitis, gingivitis, appendicitis, pancreatitis, cholecystitis, agammaglobulinemia, psoriasis, allergy, Crohn's disease, irritable bowel syndrome, ulcerative colitis, Sjogren's disease, tissue graft rejection, hyperacute rejection of transplanted organs, asthma, allergic rhinitis, chronic obstructive pulmonary disease (COPD), autoimmune polyendocrine disease (also known as autoimmune polyendocrine syndrome), alopecia areata, pernicious anemia, glomerulonephritis, dermatomyositis, multiple sclerosis, scleroderma, vasculitis, autoimmune hemolytic and thrombocytopenic states, Goodpasture's syndrome, atherosclerosis, Addison's disease, Parkinson's disease, Alzheimer's disease, diabetes, septic shock, systemic lupus erythematosus (SLE), rheumatoid arthritis, psoriatic arthritis, juvenile arthritis, osteoarthritis, chronic idiopathic thrombocytopenic purpura, Waldenstrom's macroglobulinemia, myasthenia gravis, Hashimoto's thyroiditis, atopic dermatitis, degenerative joint disease, vitiligo, autoimmune hypopituitarism, Guillain-Barre syndrome, Behcet's disease, scleroderma, mycosis fungoides, acute inflammatory responses (such as acute respiratory distress syndrome and ischemia / reperfusion injury) and Graves' disease., In another embodiment, the present invention provides a method for treating a disease or reducing the severity of a disease, which comprises administering to a patient in need a [I] compound and a PI3K inhibitor, wherein the disease is selected from cancer, neurodegenerative disorders, angiogenesis disorders, viral diseases, autoimmune diseases, inflammatory disorders, hormone-related diseases, conditions related to organ transplantation, immunodeficiency disorders, destructive bone disorders, proliferative disorders, infectious diseases, conditions related to cell death, thrombin-induced platelet aggregation, chronic myelogenous leukemia (CML), chronic lymphocytic leukemia (CLL), liver diseases, pathological immune conditions involving T cell activation, cardiovascular disorders and CNS disorders. In another embodiment, the present invention provides a method for treating a disease or reducing the severity of a disease, which comprises administering to a patient in need a [I] Compounds and PI3K inhibitors, wherein the disease is selected from benign or malignant tumors, brain, kidney (e.g., renal cell carcinoma (RCC)), liver, adrenal gland, bladder, breast, stomach, gastric tumor, ovary, colon, rectum, prostate, pancreas, lung, vagina, endometrium, cervix, testis, genitourinary tract, esophagus, larynx, skin, bone or thyroid carcinoma or solid tumor, sarcoma, glioblastoma, neuroblastoma, multiple myeloma or gastrointestinal cancer (especially colon cancer or colorectal adenoma) or head and neck tumors, epidermal hyperplasia, psoriasis, prostatic hyperplasia, neoplasia, epithelial dysplasia, adenoma, adenocarcinoma, keratoacanthoma, epidermoid carcinoma, large cell carcinoma, non-small cell lung cancer, lymphoma (including (e.g.) non-Hodgkin's lymphoma (NHL) and Hodgkin's lymphoma (also known as Hodgkin's or Hodgkin's disease)), breast cancer, follicular carcinoma, undifferentiated carcinoma, papillary carcinoma, seminoma, melanoma or leukemia, diseases including Cowden syndrome, Lhermitte-Dudos disease and Bannayan-Zonana syndrome or diseases with abnormal activation of the PI3K / PKB pathway, asthma of any type or cause (including intrinsic (non-allergic) asthma and non-intrinsic (allergic) asthma, mild asthma, moderate asthma, severe asthma, bronchitic asthma, exercise-induced asthma, occupational asthma and post-bacterial infection-induced asthma), acute lung injury (ALI), adult / acute respiratory distress syndrome (ARDS), chronic obstructive pulmonary, airway or lung disease (COPD, COAD or COLD) (including chronic bronchitis or associated dyspnea, emphysema) and exacerbation of airway hypersensitivity occurring with other drug therapies (specifically, other inhaled drug therapies), bronchitis of any type or cause (including but not limited to acute, peanut aspiration, catarrhal, croupous, chronic or tuberculous bronchitis), pneumoconiosis of any type or cause (an inflammatory, usually occupational lung disease,Both chronic and acute cases are often accompanied by airway obstruction and are caused by repeated inhalation of dust (including, for example, aluminosis, anthracosis, asbestosis, silicosis, siderosis, byssinosis, hair dust pneumoconiosis, iron dust pneumoconiosis, silicosis, tobacco dust pneumoconiosis, and cotton dust pneumoconiosis), Löffler's syndrome, eosinophilic pneumonia, parasitic (specifically metazoan) infections (including tropical eosinophilia), allergic bronchopulmonary aspergillosis, polyarteritis nodosa (including Churg-Strauss syndrome), eosinophilic granuloma, and eosinophil-related disorders of the airway caused by drug reactions, psoriasis, contact dermatitis, atopic dermatitis, alopecia areata, erythema multiforme, dermatitis herpetiformis, scleroderma, vitiligo, allergic vasculitis, urticaria, bullous pemphigoid, lupus erythematosus, pemphigus, acquired epidermolysis bullosa, conjunctivitis, keratoconjunctivitis sicca, and vernal conjunctivitis, diseases that invade the nose (including allergic rhinitis), and inflammatory diseases involving or having an autoimmune component or etiology, including autoimmune hematological disorders (such as hemolytic anemia, aplastic anemia, pure red cell anemia, and idiopathic thrombocytopenia), systemic lupus erythematosus, rheumatoid arthritis, polychondritis, scleroderma, Wegener's granulomatosis, dermatomyositis, chronic active hepatitis, myasthenia gravis, Stevens-Johnson syndrome, idiopathic sprue, autoimmune inflammatory bowel disease (such as ulcerative colitis and Crohn's disease), endocrine ophthalmopathy, Graves' disease, sarcoidosis, alveolitis, chronic allergic pneumonia, multiple sclerosis, primary biliary sclerosis, uveitis (anterior uveitis and posterior uveitis), keratoconjunctivitis sicca, and vernal keratoconjunctivitis, interstitial lung fibrosis, psoriatic arthritis, and glomerulonephritis (with and without nephrotic syndrome, such as including idiopathic nephrotic syndrome or minimal change nephropathy, restenosis, cardiac enlargement, atherosclerosis, myocardial infarction, ischemic stroke, and congestive heart failure, Alzheimer's disease, Parkinson's disease, amyotrophic lateral sclerosis, Huntington's disease, and neurodegenerative diseases caused by traumatic injury, glutamate neurotoxicity, and hypoxia., In some embodiments, the present invention provides a method for treating a disease or reducing the severity of a disease, which comprises administering to a patient in need a [I] compound and a Bcl-2 inhibitor, wherein the disease is an inflammatory disorder, an autoimmune disorder, a proliferative disorder, an endocrine disorder, a neurological disorder, or a transplantation-related disorder. In some embodiments, the disorder is a proliferative disorder, lupus, or lupus nephritis. In some embodiments, the proliferative disorder is chronic lymphocytic leukemia, diffuse large B-cell lymphoma, Hodgkin's disease, small cell lung cancer, non-small cell lung cancer, myelodysplastic syndrome, lymphoma, hematological tumor, or solid tumor. In some embodiments, the present invention provides methods for treating a disease or reducing the severity of a disease, which comprise administering to a patient in need thereof a TYK2 pseudokinase (JH2) domain-binding compound and a TYK2 kinase (JH1) domain-binding compound. In some embodiments, the disease is an autoimmune disorder, an inflammatory disorder, a proliferative disorder, an endocrine disorder, a neurological disorder, or a transplantation-related disorder. In some embodiments, the JH2-binding compound is of formula [I] compound. Other suitable JH2 domain-binding compounds include those described in the following: WO2014074660A1, WO2014074661A1, WO2015089143A1, the content of each of which is incorporated herein by reference. Suitable JH1 domain-binding compounds include those described in WO2015131080A1, the content of which is incorporated herein by reference. The compounds and compositions according to the methods of the present invention can be administered in any amount and by any route of administration that can effectively treat or reduce the severity of an autoimmune disorder, an inflammatory disorder, a proliferative disorder, an endocrine disorder, a neurological disorder, or a transplantation-related disorder. Depending on the individual species, age and general condition, severity of the infection, the particular agent, its mode of administration and the like, the exact amount required can vary from individual to individual. The compounds of the present invention are preferably formulated in unit dosage form for ease of administration and uniform dosage. As used herein, the expression "unit dosage form" refers to physically discrete units suitable for the medicaments to be administered to the patient to be treated. However, it should be understood that the total daily dosage of the compounds and compositions of the present invention will be determined by the attending physician within the scope of reasonable medical judgment. The specific effective dosage value for any particular patient or organism depends on a variety of factors, including the disease being treated and the severity of the disease; the activity of the specific compound used; the specific composition used; the age, weight, general health, sex and diet of the patient; the time of administration, route of administration and excretion rate of the specific compound used; the duration of treatment; the drugs used in combination with or concurrently with the specific compound used; and similar factors well known in the medical art. As used herein, the term "patient" means an animal, preferably a mammal, and most preferably a human. Depending on the severity of the infection being treated, the pharmaceutically acceptable compositions of the present invention can be administered to humans and other animals in the following ways: orally, rectally, parenterally, intracisternally, vaginally, intraperitoneally, topically (in the form of powder, ointment or drops), buccally (in the form of oral or nasal spray) or the like. In certain embodiments, the compounds of the present invention can be administered orally or parenterally once or more times a day at a dosage value of about 0.01 mg / kg to about 50 mg / kg and preferably about 1 mg / kg to about 25 mg / kg of the individual body weight / day to obtain the desired therapeutic effect. Liquid dosage forms for oral administration include, but are not limited to, pharmaceutically acceptable emulsions, microemulsions, solutions, suspensions, syrups, and elixirs. In addition to the active compound, the liquid dosage forms may contain inert diluents commonly used in the art (such as water or other solvents), solubilizing agents, and emulsifying agents, such as ethanol, isopropyl alcohol, ethyl carbonate, ethyl acetate, benzyl alcohol, benzyl benzoate, propylene glycol, 1,3 - butanediol, dimethylformamide, oils (specifically cottonseed oil, peanut oil, corn oil, germ oil, olive oil, castor oil, and sesame oil), glycerin, tetrahydrofurfuryl alcohol, polyethylene glycol, and fatty acid esters of sorbitan and mixtures thereof. In addition to the inert diluent, the oral compositions may also include adjuvants such as wetting agents, emulsifying and suspending agents, sweetening agents, flavoring agents, and perfuming agents. Injectable formulations can be prepared using suitable dispersing or wetting agents and suspending agents in accordance with known techniques, such as sterile injectable aqueous or oily suspensions. Sterile injectable formulations can also be sterile injectable solutions, suspensions, or emulsions in a non - toxic parenterally acceptable diluent or solvent, such as a solution in 1,3 - butanediol. Acceptable vehicles and solvents that can be employed are, in particular, water, Ringer's solution, U.S.P., and isotonic sodium chloride solution. Additionally, sterile, fixed oils are conventionally employed as a solvent or suspending medium. For this purpose, any bland fixed oil can be used, including synthetic mono - or di - glycerides of fatty acids. In addition, fatty acids such as oleic acid are used in injectable formulations. Injectable preparations can be sterilized, for example, by filtration through a bacteria - retaining filter or by incorporating a sterilizing agent in the form of a sterile solid composition that can be dissolved or dispersed in sterile water or other sterile injectable medium before use. To prolong the effect of the compounds of the present invention, it is generally desirable to slow the absorption of the compounds from subcutaneous or intramuscular injection. This can be accomplished by using a liquid suspension of a crystalline or amorphous material with poor water solubility. The rate of absorption of the compound depends on its rate of dissolution, which in turn can depend on crystal size and crystal form. Alternatively, delayed absorption of the parenterally administered compound is accomplished by dissolving or suspending the compound in an oily vehicle. Injectable depot forms are prepared by forming a microencapsulation matrix of the compound in a biodegradable polymer, such as polylactic - polyglycolic acid. The release rate of the compound can be controlled according to the ratio of the compound to the polymer and the nature of the specific polymer employed. Examples of other biodegradable polymers include poly(orthoesters) and poly(anhydrides). Depot injectable formulations are also prepared by entrapping the compound in liposomes or microemulsions compatible with body tissues. Compositions for rectal or vaginal administration are preferably suppositories, which can be prepared by mixing the compounds of the present invention with suitable non-irritating excipients or carriers (such as cocoa butter, polyethylene glycol or suppository wax), which are solid at ambient temperature but liquid at body temperature, and can thus melt and release the active compound in the rectal or vaginal cavity. Solid dosage forms for oral administration include capsules, tablets, pills, powders and granules. In these solid dosage forms, the active compound is mixed with at least one inert, pharmaceutically acceptable excipient or carrier (such as sodium citrate or dibasic calcium phosphate) and / or the following: a) fillers or extenders, such as starch, lactose, sucrose, glucose, mannitol and silicic acid; b) binders, such as carboxymethyl cellulose, alginate, gelatin, polyvinylpyrrolidone, sucrose and acacia; c) humectants, such as glycerol; d) disintegrants, such as agar, calcium carbonate, potato or tapioca starch, alginic acid, certain silicates and sodium carbonate; e) dissolution retardants, such as paraffin wax; f) absorption promoters, such as quaternary ammonium compounds; g) wetting agents, such as cetyl alcohol and glycerol monostearate; h) absorbents, such as kaolin and bentonite; and i) lubricants, such as talc, calcium stearate, magnesium stearate, solid polyethylene glycol, sodium lauryl sulfate; and mixtures thereof. In the case of capsules, tablets and pills, the dosage form may also contain buffering agents. In soft and hard gelatin capsules using excipients such as lactose (lactose or milk sugar) and high molecular weight polyethylene glycol, similar types of solid compositions can also be used as fillers. Solid dosage forms of tablets, dragees, capsules, pills and granules can be prepared with coatings and shells, such as enteric coatings and other coatings well known in the pharmaceutical formulation art. They may optionally contain opacifying agents and may also be compositions that release the active ingredient only or preferentially in a delayed manner in a certain part of the intestine, as the case may be. Examples of embedding compositions that can be used include polymeric materials and waxes. In soft and hard gelatin capsules using excipients such as lactose (lactose or milk sugar) and high molecular weight polyethylene glycol, similar types of solid compositions can also be used as fillers. The active compound may also be in the form of microcapsules with one or more of the above excipients. Tablets, dragees, capsules, pills and granules can be prepared as solid dosage forms using coatings and shells such as enteric coatings, release control coatings and other coatings well known in pharmaceutical formulation techniques. In such solid dosage forms, the active compound can be mixed with at least one inert diluent (such as sucrose, lactose or starch). These dosage forms may also include additional substances as is common practice, such as tableting lubricants and other tableting aids (such as magnesium stearate and microcrystalline cellulose). In the case of capsules, tablets and pills, the dosage forms may also contain buffering agents. Optionally, it may contain opacifying agents and may also be a composition that releases the active ingredient only or preferentially in a delayed manner in a certain part of the intestine. Examples of embedding compositions that can be used include polymeric substances and waxes. Dosage forms for topical or transdermal administration of the compounds of the present invention include ointments, pastes, creams, lotions, gels, powders, solutions, sprays, inhalants or patches. The active ingredient is mixed with a pharmaceutically acceptable carrier and any desired preservatives or buffering agents as may be required under aseptic conditions. Ophthalmic formulations, ear drops and eye drops are also within the scope of the present invention. Additionally, the present invention encompasses the use of transdermal patches, which have the additional advantage of providing controlled delivery of the compound to the body. These dosage forms can be prepared by dissolving or dispersing the compound in a suitable medium. Penetration enhancers can also be used to increase the flux of the compound across the skin. The rate can be controlled by providing a rate controlling membrane or by dispersing the compound in a polymeric matrix or gel. According to one embodiment, the present invention relates to a method for inhibiting protein kinase activity in a biological sample, which comprises the step of contacting the biological sample with a compound of the present invention or a composition comprising the compound. According to another embodiment, the present invention relates to a method for inhibiting TYK2 or a mutant thereof in a biological sample, which comprises the step of contacting the biological sample with a compound of the present invention or a composition comprising the compound. In certain embodiments, the present invention relates to a method for irreversibly inhibiting TYK2 or a mutant thereof in a biological sample, which comprises the step of contacting the biological sample with a compound of the present invention or a composition comprising the compound. In another embodiment, the present invention provides a method for selectively inhibiting TYK2 relative to one or more of JAK1, JAK2 and JAK3. In some embodiments, the compounds of the present invention are more than 2-fold selective relative to JAK1 / 2 / 3. In some embodiments, the compounds of the present invention are more than 5-fold selective relative to JAK1 / 2 / 3. In some embodiments, the compounds of the present invention are more than 10-fold selective relative to JAK1 / 2 / 3. In some embodiments, the compounds of the present invention are more than 50-fold selective relative to JAK1 / 2 / 3. In some embodiments, the compounds of the present invention are more than 100-fold selective relative to JAK1 / 2 / 3. As used herein, the term "biological sample" includes, but is not limited to, cell cultures or extracts thereof; biopsy materials obtained from mammals or extracts thereof; and blood, saliva, urine, feces, semen, tears or other body fluids or extracts thereof. Inhibition of the activity of TYK2 (or mutants thereof) in biological samples can be used for a variety of purposes known to those skilled in the art. Examples of such purposes include, but are not limited to, blood transfusion, organ transplantation, biological sample storage and bioanalysis. Another embodiment of the present invention relates to a method of inhibiting the protein kinase activity of a patient, which comprises the step of administering to the patient a compound of the present invention or a composition comprising the compound. According to another embodiment, the present invention relates to a method of inhibiting the activity of TYK2 or a mutant thereof in a patient, which comprises the step of administering to the patient a compound of the present invention or a composition comprising the compound. According to certain embodiments, the present invention relates to a method of irreversibly inhibiting the activity of one or more of TYK2 or mutants thereof in a patient, which comprises the step of administering to the patient a compound of the present invention or a composition comprising the compound. In other embodiments, the present invention provides a method of treating a disorder mediated by TYK2 or a mutant thereof in a patient in need thereof, which comprises the step of administering to the patient a compound of the present invention or a pharmaceutically acceptable composition thereof. Such disorders are described in detail herein. Depending on the particular condition or disease to be treated, additional therapeutic agents that are commonly administered to treat the condition may also be present in the compositions of the present invention. As used herein, an additional therapeutic agent that is commonly administered to treat a particular disease or condition is referred to as "suitable for the disease or condition being treated". The compounds of the present invention can also be advantageously used in combination with other therapeutic compounds. In some embodiments, the other therapeutic compounds are anti-proliferative compounds. Such anti-proliferative compounds include, but are not limited to, aromatase inhibitors; anti-estrogens; topoisomerase I inhibitors; topoisomerase II inhibitors; microtubule-active compounds; alkylating compounds; histone deacetylase inhibitors; compounds that induce the process of cell differentiation; cyclooxygenase inhibitors; MMP inhibitors; mTOR inhibitors; antitumor antimetabolites; platinum compounds; compounds that target / reduce protein or lipid kinase activity and other anti-angiogenic compounds; compounds that target / reduce or inhibit protein or lipid phosphatase activity; gonadorelin agonists; anti-androgens; methionine aminopeptidase inhibitors; matrix metalloproteinase inhibitors; bisphosphonate compounds; biological response modifiers; anti-proliferative antibodies; heparanase inhibitors; inhibitors of Ras oncogenic isoforms; telomerase inhibitors; proteasome inhibitors; compounds for treating blood malignancies; compounds that target / reduce or inhibit Flt-3 activity; Hsp90 inhibitors such as 17-AAG (17-allylaminogeldanamycin, NSC330507), 17-DMAG (17-dimethylaminoethylamino-17-demethoxygeldanamycin, NSC707545), IPI-504, CNF1010, CNF2024, CNF1010 available from Conforma Therapeutics; temozolomide (Temodal®); kinesin spindle protein inhibitors such as SB715992 or SB743921 available from GlaxoSmithKline, or pentamidine / chlorpromazine available from CombinatoRx; MEK inhibitors such as ARRY142886 available from Array BioPharma, AZD6244 available from AstraZeneca, PD181461 available from Pfizer, and leucovorin. As used herein, the term "aromatase inhibitor" refers to a compound that inhibits estrogen production (e.g., the conversion of the substrates androstenedione and testosterone into estrone and estradiol, respectively).The term includes (but is not limited to) steroids, in particular atamestane, exemestane and formestane, and specifically non-steroids, in particular aminoglutethimide, rogletimide, pyridoglutethimide, trilostane, testolactone, ketoconazole, vorozole, fadrozole, anastrozole and letrozole. Exemestane is sold under the trade name Aromasin™. Formestane is sold under the trade name Lentaron™. Fadrozole is sold under the trade name Afema™. Anastrozole is sold under the trade name Arimidex™. Letrozole is sold under the trade name Femara™ or Femar™. Aminoglutethimide is sold under the trade name Orimeten™. The combination of chemotherapeutic agents of the present invention comprising an aromatase inhibitor is particularly useful for treating hormone receptor positive tumors (such as breast tumors). The term "antiestrogen" as used herein refers to a compound that antagonizes the action of estrogen at the estrogen receptor level. The term includes (but is not limited to) tamoxifen, fulvestrant, raloxifene and raloxifene hydrochloride. Tamoxifen is sold under the trade name Nolvadex™. Raloxifene hydrochloride is sold under the trade name Evista™. Fulvestrant can be administered under the trade name Faslodex™. The combination of chemotherapeutic agents of the present invention comprising an antiestrogen is particularly useful for treating estrogen receptor positive tumors (such as, breast tumors). The term "antiandrogen" as used herein refers to any substance capable of inhibiting the effects of androgens and includes (but is not limited to) bicalutamide (Casodex™). The term "gonadorelin agonist" as used herein includes (but is not limited to) abarelix, goserelin and goserelin acetate. Goserelin can be administered under the trade name Zoladex™. As used herein, the term "topoisomerase I inhibitor" includes (but is not limited to) topotecan, gimatecan, irinotecan, camptothecian and its analogues (9-nitro-camptothecian) and the macromolecular camptothecian conjugate PNU-166148. Irinotecan can be administered, for example, in its commercially available form (e.g., under the trademark Camptosar™). Topotecan is sold under the trade name Hycamptin™. As used herein, the term "topoisomerase II inhibitor" includes (but is not limited to) anthracyclines (anthracyclines), such as doxorubicin (including liposomal formulations, such as Caelyx™), daunorubicin, epirubicin, idarubicin and nemorubicin, the anthraquinone mitoxantrone and losoxantrone, and the podophyllotoxin derivatives etoposide and teniposide. Etoposide is sold under the trade name Etopophos™. Teniposide is sold under the trade name VM 26-Bristol. Doxorubicin is sold under the trade name Acriblastin™ or Adriamycin™. Epirubicin is sold under the trade name Farmorubicin™. Idarubicin is sold under the trade name Zavedos™. Mitoxantrone is sold under the trade name Novantron. The term "microtubule active agent" refers to microtubule stabilizing, microtubule destabilizing compounds and microtubulin polymerization inhibitors, including but not limited to taxanes, such as paclitaxel and docetaxel; vinca alkaloids, such as vinblastine or vinblastine sulfate, vincristine or vincristine sulfate and vinorelbine; discodermolide; colchicine and epothilone and its derivatives. Paclitaxel is sold under the trade name Taxol™. Docetaxel is sold under the trade name Taxotere™. Vinblastine sulfate is sold under the trade name Vinblastin R.P™. Vincristine sulfate is sold under the trade name Farmistin™. As used herein, the term "alkylating compound" includes, but is not limited to, cyclophosphamide, ifosfamide, melphalan, or nitrosoureas (BCNU or Gliadel). Cyclophosphamide is sold under the trade name Cyclostin™. Ifosfamide is sold under the trade name Holoxan™. The term "histone deacetylase inhibitor" or "HDAC inhibitor" refers to a compound that inhibits histone deacetylase and has antiproliferative activity. This includes, but is not limited to, suberoylanilide hydroxamic acid (SAHA). The term "antineoplastic antimetabolite" includes, but is not limited to, 5-fluorouracil or 5-FU, capecitabine, gemcitabine, DNA demethylating compounds (such as 5-azacytidine and decitabine), methotrexate, and edatrexate, and folic acid antagonists (such as pemetrexed). Capecitabine is sold under the trade name Xeloda™. Gemcitabine is sold under the trade name Gemzar™. As used herein, the term "platinum compound" includes, but is not limited to, carboplatin, cis-platin (cisplatinum), and oxaliplatin. Carboplatin can be administered, for example, in its commercially available form (such as under the trademark Carboplat™). Oxaliplatin can be administered, for example, in its commercially available form (such as under the trademark Eloxatin™). As used herein, the term "compound that targets / reduces protein or lipid kinase activity, or protein or lipid phosphatase activity; or other anti-angiogenic compound" includes (but is not limited to) protein tyrosine kinases and / or serine and / or threonine kinase inhibitors or lipid kinase inhibitors, such as a) compounds that target, reduce or inhibit the activity of platelet-derived growth factor-receptor (PDGFR), such as compounds that target, reduce or inhibit the activity of PDGFR, especially compounds that inhibit the PDGF receptor, such as N-phenyl-2-pyrimidinamine derivatives, such as imatinib, SU101, SU6668 and GFB111; b) compounds that target, reduce or inhibit the activity of fibroblast growth factor-receptor (FGFR); c) compounds that target, reduce or inhibit the activity of insulin-like growth factor receptor I (IGF-IR), such as compounds that target, reduce or inhibit the activity of IGF-IR, especially compounds that inhibit the IGF-I receptor or the kinase activity of an antibody that targets the extracellular domain of the IGF-I receptor or its growth factor; d) compounds that target, reduce or inhibit the activity of the Trk receptor tyrosine kinase family or ephrin B4 inhibitors; e) compounds that target, reduce or inhibit the activity of the Axl receptor tyrosine kinase family; f) compounds that target, reduce or inhibit the activity of the Ret receptor tyrosine kinase; g) compounds that target, reduce or inhibit the activity of the Kit / SCFR receptor tyrosine kinase, such as imatinib; h) compounds that target, reduce or inhibit the activity of the c-Kit receptor tyrosine kinase, which is part of the PDGFR family, such as compounds that target, reduce or inhibit the activity of the c-Kit receptor tyrosine kinase family, especially compounds that inhibit the c-Kit receptor, such as imatinib; i) compounds that target, reduce or inhibit the activity of members of the c-Abl family, their gene fusion products (such as the BCR-Abl kinase) and mutants, such as compounds that target, reduce or inhibit the activity of members of the c-Abl family and their gene fusion products, such as N-phenyl-2-pyrimidinamine derivatives, such as imatinib or nilotinib (AMN107); PD180970; AG957; NSC 680410; PD173955 from Parke Davis; or dasatinib (BMS-354825);j) Compounds that target, reduce or inhibit the activity of protein kinase C (PKC) and members of the Raf family of serine / threonine kinases, MEK, SRC, JAK / pan-JAK, FAK, PDK1, PKB / Akt, Ras / MAPK, PI3K, SYK, BTK and members of the TEC family and / or members of the cyclin-dependent kinase family (CDK), including staurosporine derivatives such as midostaurin; examples of other compounds include UCN-01, safingol, BAY 43-9006, Bryostatin 1, Perifosine; ilmofosine; RO 318220 and RO 320432; GO 6976; Isis 3521; LY333531 / LY379196; isoquinoline compounds; FTI; PD184352 or QAN697 (PI3K inhibitor) or AT7519 (CDK inhibitor); k) Compounds that target, reduce or inhibit the activity of protein tyrosine kinase inhibitors, such as compounds that target, reduce or inhibit the activity of protein tyrosine kinase inhibitors include imatinib mesylate (Gleevec™) or tyrosine phosphorylation inhibitors such as tyrosine phosphorylation inhibitor A23 / RG-50810; AG 99; tyrosine phosphorylation inhibitor AG 213; tyrosine phosphorylation inhibitor AG 1748; tyrosine phosphorylation inhibitor AG 490; tyrosine phosphorylation inhibitor B44; tyrosine phosphorylation inhibitor B44 (+) enantiomer; tyrosine phosphorylation inhibitor AG 555; AG 494; tyrosine phosphorylation inhibitors AG 556, AG957 and adaphostin (4-{[(2,5-dihydroxyphenyl)methyl]amino}-benzoic acid adamantyl ester; NSC 680410, adaphostin); l) Compounds that target, reduce or inhibit the activity of the epidermal growth factor family of receptor tyrosine kinases (EGFR 1ErbB2, ErbB3, ErbB4 in homo- or heterodimeric form) and their mutants, such as compounds that target, reduce or inhibit the activity of the epidermal growth factor receptor family are particularly those that inhibit members of the EGF receptor tyrosine kinase family (such as the EGF receptor, ErbB2, ErbB3 and ErbB4) or compounds, proteins or antibodies that bind to EGF or EGF-related ligands, CP 358774, ZD 1839, ZM 105180;Trastuzumab (Herceptin™), cetuximab (Erbitux™), Iressa, Tarceva, OSI-774, Cl-1033, EKB-569, GW-2016, E1.1, E2.4, E2.5, E6.2, E6.4, E2.11, E6.3 or E7.6.3 and 7H-pyrrolo-[2,3-d]pyrimidine derivatives; m) Compounds that target, reduce or inhibit the activity of the c-Met receptor, such as compounds that target, reduce or inhibit the activity of c-Met, especially compounds that inhibit the kinase activity of the c-Met receptor or target the extracellular domain of c-Met or antibodies that bind to HGF, n) Compounds that target, reduce or inhibit the kinase activity of one or more members of the JAK family (JAK1 / JAK2 / JAK3 / TYK2 and / or pan-JAK), including (but not limited to) PRT-062070, SB-1578, baricitinib, pacritinib, momelotinib, VX-509, AZD-1480, TG-101348, tofacitinib and ruxolitinib; o) Compounds that target, reduce or inhibit the kinase activity of PI3 kinase (PI3K), including (but not limited to) ATU-027, SF-1126, DS-7423, PBI-05204, GSK-2126458, ZSTK-474, buparlisib, pictrelisib, PF-4691502, BYL-719, dactolisib, XL-147, XL-765 and idelalisib; and q) Compounds that target, reduce or inhibit the signal transduction effect of the hedgehog protein (Hh) or smoothened receptor (SMO) pathway, including (but not limited to) cyclopamine, vismodegib, itraconazole, erismodegib and IPI-926 (saridegib). ; As used herein, the term "PI3K inhibitor" includes (but is not limited to) compounds having inhibitory activity against one or more enzymes of the phosphatidylinositol-3-kinase family (including but not limited to PI3Kα, PI3Kγ, PI3Kδ, PI3Kβ, PI3K-C2α, PI3K-C2β, PI3K-C2γ, Vps34, p110-α, p110-β, p110-γ, p110-δ, p85-α, p85-β, p55-γ, p150, p101, and p87). Examples of PI3K inhibitors useful in the present invention include (but are not limited to) ATU-027, SF-1126, DS-7423, PBI-05204, GSK-2126458, ZSTK-474, buparlisib, pictilisib, PF-4691502, BYL-719, duvelisib, XL-147, XL-765, and idelalisib. As used herein, the term "BTK inhibitor" includes (but is not limited to) compounds having inhibitory activity against Bruton's Tyrosine Kinase (BTK), including but not limited to AVL-292 and ibrutinib. As used herein, the term "SYK inhibitor" includes (but is not limited to) compounds having inhibitory activity against spleen tyrosine kinase (SYK), including (but not limited to) PRT-062070, R-343, R-333, Excellair, PRT-062607, and fostamatinib. As used herein, the term "Bcl-2 inhibitor" includes, but is not limited to, compounds having inhibitory activity against B-cell lymphoma 2 protein (Bcl-2), including, but not limited to, ABT-199, ABT-731, ABT-737, apogossypol, Ascenta's pan-Bcl-2 inhibitor, curcumin (and its analogs), dual Bcl-2 / Bcl-xL inhibitors (Infinity Pharmaceuticals / Novartis Pharmaceuticals), Genasense (G3139), HA14-1 (and its analogs; see WO2008118802), navitoclax (and its analogs, see US7390799), NH-1 (Shenayng Pharmaceutical University), obatoclax (and its analogs, see WO2004106328), S-001 (Gloria Pharmaceuticals), TW series compounds (Univ. of Michigan), and venetoclax. In some embodiments, the Bcl-2 inhibitor is a small molecule therapeutic agent. In some embodiments, the Bcl-2 inhibitor is a peptidomimetic. Other examples of BTK inhibitory compounds and conditions treatable by combinations of such compounds with the compounds of the present invention can be found in WO2008039218 and WO2011090760, the contents of which are incorporated herein by reference. Other examples of SYK inhibitory compounds and conditions treatable by combinations of such compounds with the compounds of the present invention can be found in WO2003063794, WO2005007623, and WO2006078846, the contents of which are incorporated herein by reference. Other examples of PI3K inhibitory compounds and conditions treatable by combinations of such compounds with the compounds of the present invention can be found in WO2004019973, WO2004089925, WO2007016176, US8138347, WO2002088112, WO2007084786, WO2007129161, WO2006122806, WO2005113554, and WO2007044729, the contents of which are incorporated herein by reference. Other examples of JAK inhibitory compounds and conditions treatable by combinations of such compounds with the compounds of the present invention can be found in WO2009114512, WO2008109943, WO2007053452, WO2000142246, and WO2007070514, the contents of which are incorporated herein by reference. Other anti-angiogenic compounds include compounds that have another mechanism of action with respect to their activity (e.g., unrelated to protein or lipid kinase inhibition), such as thalidomide (Thalomid™) and TNP-470. Examples of proteasome inhibitors useful for combination with the compounds of the present invention include, but are not limited to, bortezomib, disulfiram, epigallocatechin-3-gallate (EGCG), salinosporamide A, carfilzomib, ONX-0912, CEP-18770, and MLN9708. Compounds that target, reduce, or inhibit the activity of a protein or lipid phosphatase are, for example, inhibitors of phosphatase 1, phosphatase 2A, or CDC25, such as okadaic acid or its derivatives. Compounds that induce the process of cell differentiation include, but are not limited to, retinoic acid, α-, γ-, or δ-tocopherol, or α-, γ-, or δ-tocotrienol. The term cyclooxygenase inhibitor as used herein includes, but is not limited to, Cox-2 inhibitors, 5-alkyl-substituted 2-arylaminophenylacetic acids and derivatives (such as celecoxib (Celebrex™), rofecoxib (Vioxx™), etoricoxib, valdecoxib), or 5-alkyl-2-arylaminophenylacetic acids (such as 5-methyl-2-(2'-chloro-6'-fluoroanilino)phenylacetic acid, lumiracoxib). As used herein, the term "bisphosphonic acid compound" includes (but is not limited to) etridonic acid, clodronic acid, tiludronic acid, pamidronic acid, alendronic acid, ibandronic acid, risedronic acid, and zoledronic acid. Etridonic acid is sold under the trade name Didronel™. Clodronic acid is sold under the trade name Bonefos™. Tiludronic acid is sold under the trade name Skelid™. Pamidronic acid is sold under the trade name Aredia™. Alendronic acid is sold under the trade name Fosamax™. Ibandronic acid is sold under the trade name Bondranat™. Risedronic acid is sold under the trade name Actonel™. Zoledronic acid is sold under the trade name Zometa™. The term "mTOR inhibitor" refers to a compound that inhibits mammalian target of rapamycin (mTOR) and has antiproliferative activity, such as sirolimus (Rapamune®), everolimus (Certican™), CCI-779, and ABT578. As used herein, the term "heparanase inhibitor" refers to a compound that targets, reduces, or inhibits the degradation of heparan sulfate. The term includes (but is not limited to) PI-88. As used herein, the term "biological response modifier" refers to a lymphokine or interferon. As used herein, the term "Ras oncogenic isoform inhibitor" (such as H-Ras, K-Ras, or N-Ras) refers to a compound that targets, reduces, or inhibits the oncogenic activity of Ras, such as a "farnesyl transferase inhibitor", such as L-744832, DK8G557, or R115777 (Zarnestra™). As used herein, the term "telomerase inhibitor" refers to a compound that targets, reduces, or inhibits telomerase activity. A compound that targets, reduces, or inhibits telomerase activity is particularly a compound that inhibits the telomerase receptor, such as telomestatin. As used herein, the term "methionine aminopeptidase inhibitor" refers to a compound that targets, reduces, or inhibits methionine aminopeptidase activity. Compounds that target, reduce, or inhibit methionine aminopeptidase activity include (but are not limited to) bengamide or its derivatives. As used herein, the term "proteasome inhibitor" refers to a compound that targets, reduces, or inhibits proteasome activity. Compounds that target, reduce, or inhibit proteasome activity include, but are not limited to, bortezomib (Velcade™) and MLN 341. As used herein, the term "matrix metalloproteinase inhibitor" or "(MMP) inhibitor" includes, but is not limited to, peptidomimetic and non-peptidomimetic inhibitors of collagen, tetracycline derivatives, such as the hydroxamate peptidomimetic inhibitor batimastat and its orally bioavailable analogue marimastat (BB-2516), prinomastat (AG3340), metastat (NSC 683551), BMS-279251, BAY 12-9566, TAA211, MMI270B, or AAJ996. As used herein, the term "compound for treating hematological malignancies" includes, but is not limited to, FMS-like tyrosine kinase inhibitors, which are compounds that target, reduce, or inhibit the activity of the FMS-like tyrosine kinase receptor (Flt-3R); interferons, 1-β-D-arabinofuransylcytosine (ara-c), and busulfan; ALK inhibitors, which are compounds that target, reduce, or inhibit anaplastic lymphoma kinase; and Bcl-2 inhibitors. Compounds that target, reduce, or inhibit the activity of the FMS-like tyrosine kinase receptor (Flt-3R) are particularly compounds, proteins, or antibodies that inhibit members of the Flt-3R receptor kinase family, such as PKC412, midostaurin, staurosporine derivatives, SU11248, and MLN518. As used herein, the term "HSP90 inhibitor" includes, but is not limited to, compounds that target, reduce, or inhibit the intrinsic ATPase activity of HSP90; compounds that degrade, target, reduce, or inhibit HSP90 client proteins via the ubiquitin-proteasome pathway. Compounds that target, reduce, or inhibit the intrinsic ATPase activity of HSP90 are particularly compounds, proteins, or antibodies that inhibit the ATPase activity of HSP90, such as 17-allylamino, 17-demethoxygeldanamycin (17AAG, a geldanamycin derivative); other geldanamycin-related compounds; radicicol; and HDAC inhibitors. As used herein, the term "anti-proliferative antibody" includes, but is not limited to, trastuzumab (Herceptin™), trastuzumab-DM1, erbitux, bevacizumab (Avastin™), rituximab (Rituxan®), PRO64553 (anti-CD40), and 2C4 antibody. Antibody means a complete monoclonal antibody, polyclonal antibody, multispecific antibody formed by at least two complete antibodies, and antibody fragments, so long as they exhibit the desired biological activity. For the treatment of acute myeloid leukemia (AML), the compounds of the present invention can be used in combination with standard leukemia therapies, particularly in combination with therapies for the treatment of AML. Specifically, the compounds of the present invention can be administered in combination with, for example, farnesyl transferase inhibitors and / or other drugs for the treatment of AML, such as daunorubicin, Adriamycin, Ara-C, VP-16, teniposide, mitoxantrone, idarubicin, carboplatin, and PKC412. In some embodiments, the present invention provides a method for treating AML associated with ITD and / or D835Y mutations, which comprises co-administering a compound of the present invention with one or more FLT3 inhibitors. In some embodiments, the FLT3 inhibitor is selected from quizartinib (AC220), staurosporine derivatives (such as midostaurin or lestaurtinib), sorafenib, tandutinib, LY-2401401, LS-104, EB-10, famitinib, NOV-110302, NMS-P948, AST-487, G-749, SB-1317, S-209, SC-110219, AKN-028, fedratinib, tozasertib, and sunitinib. In some embodiments, the FLT3 inhibitor is selected from quizartinib, midostaurin, lestaurtinib, sorafenib, and sunitinib. Other anti-leukemia compounds include, for example, Ara-C (a pyrimidine analogue), which is a 2-α-hydroxyribose (arabinoside) derivative of deoxycytidine. Also included are purine analogues such as hypoxanthine, 6-mercaptopurine (6-MP), and fludarabine phosphate. Compounds that target, reduce, or inhibit the activity of histone deacetylase (HDAC) inhibitors (such as sodium butyrate and suberoylanilide hydroxamic acid (SAHA)) inhibit the activity of an enzyme called histone deacetylase. Specific HDAC inhibitors include MS275, SAHA, FK228 (previously called FR901228), Trichostatin A, and the compounds disclosed in US 6,552,065, including but not limited to N-hydroxy-3-[4-[[[2-(2-methyl-1H-indol-3-yl)-ethyl]-amino]methyl]phenyl]-2E-2-propenamide or a pharmaceutically acceptable salt thereof and N-hydroxy-3-[4-[(2-hydroxyethyl){2-(1H-indol-3-yl)ethyl]-amino]methyl]phenyl]-2E-2-propenamide or a pharmaceutically acceptable salt thereof, especially the lactate salt. The somatostatin receptor antagonists used herein refer to compounds that target, treat, or inhibit somatostatin receptors, such as octreotide and SOM230. Methods of tumor cell destruction refer to methods such as ionizing radiation. The term "ionizing radiation" as mentioned above and below means ionizing radiation in the form of electromagnetic rays (such as X-rays and γ-rays) or particles (such as α and β particles). Ionizing radiation is provided in (but not limited to) radiation therapy and is known in the art. See Principles of Radiation Therapy in Principles and Practice of Oncology by Hellman, Cancer, edited by Devita et al., 4th Edition, Volume 1, pages 248 to 275 (1993)). Also included are EDG adhesives and ribonucleotide reductase inhibitors. The term "EDG adhesive" as used herein refers to a class of immunosuppressants that regulate lymphocyte recirculation, such as FTY720. The term "ribonucleotide reductase inhibitor" refers to pyrimidine or purine nucleoside analogues, including but not limited to fludarabine and / or cytarabine (ara-C), 6-thioguanine, 5-fluorouracil, cladribine, 6-mercaptopurine (especially in combination with ALL-active ara-C), and / or pentostatin. Ribonucleotide reductase inhibitors are especially hydroxyurea or 2-hydroxy-1H-isoindole-1,3-dione derivatives. Specifically, also included are those compounds, proteins or monoclonal antibodies that also include VEGF, such as 1-(4-chloroanilino)-4-(4-pyridylmethyl)phthalazine or a pharmaceutically acceptable salt thereof, 1-(4-chloroanilino)-4-(4-pyridylmethyl)phthalazine succinate; Angiostatin™; Endostatin™; anthranilamide; ZD4190; ZD6474; SU5416; SU6668; bevacizumab; or an anti-VEGF antibody or an anti-VEGF receptor antibody, such as rhuMAb and RHUFab, a VEGF ligand, such as Macugon; an FLT-4 inhibitor, an FLT-3 inhibitor, a VEGFR-2 IgGI antibody, Angiozyme (RPI 4610) and bevacizumab (Avastin™). As used herein, "photodynamic therapy" refers to a therapy for treating or preventing cancer using certain chemical substances that are conventionally known as photosensitive compounds. Examples of photodynamic therapy include treatment using compounds such as Visudyne™ and porfimer sodium. As used herein, "angiostatic steroid" refers to a compound that blocks or inhibits angiogenesis, such as anecortave, triamcinolone, hydrocortisone, 11-α-epi-hydrocortisol, 11-dehydrocorticosterone, 17α-hydroxyprogesterone, corticosterone, desoxycorticosterone, testosterone, estrone and dexamethasone. Implants containing corticosteroids refer to compounds such as fluocinolone and dexamethasone. Other chemotherapeutic compounds include (but are not limited to) alkaloids, hormonal compounds and antagonists; biological response modifiers, preferably lymphokines or interferons; antisense oligonucleotides or oligonucleotide derivatives; shRNA or siRNA; or various compounds or compounds with other or unknown mechanisms of action. The compounds of the present invention can also be used in combination with other drugs as co-therapeutic compounds (e.g., anti-inflammatory, bronchodilator or antihistamine active ingredients), especially as (e.g.) a synergist of the therapeutic activity of such drugs or as a method of reducing the dosage or potential side effects required for such drugs in the treatment of obstructive or inflammatory airway diseases (e.g., those mentioned above). The compounds of the present invention can be mixed with other drugs in a fixed pharmaceutical composition or can be administered alone before, simultaneously or after other active ingredients. Accordingly, the present invention includes combinations of the compounds of the present invention as described above with anti-inflammatory, bronchodilator, antihistamine or antitussive active ingredients, the compound and the active ingredient of the present invention being in the same or different pharmaceutical compositions. Suitable anti-inflammatory drugs include steroids, specifically glucocorticoids such as budesonide, beclomethasone dipropionate, fluticasone propionate, ciclesonide or mometasone furoate; non-steroidal glucocorticoid receptor agonists; LTB4 antagonists such as LY293111, CGS025019C, CP-195543, SC-53228, BIIL 284, ONO 4057, SB 209247; LTD4 antagonists such as montelukast and zafirlukast; PDE4 inhibitors such as cilomilast (Ariflo® GlaxoSmithKline), roflumilast (Byk Gulden), V-11294A (Napp), BAY19-8004 (Bayer), SCH-351591 (Schering-Plough), arofylline (Almirall Prodesfarma), PD189659 / PD168787 (Parke-Davis), AWD-12-281 (Asta Medica), CDC-801 (Celgene), SeICID, apremilast (Celgene), VM554 / UM565 (Vernalis), T-440 (Tanabe), KW-4490 (Kyowa Hakko Kogyo); A2a agonists; A2b antagonists; and β-2 adrenergic receptor agonists such as albuterol (salbutamol), isoetharine, terbutaline, salmeterol, fenoterol, procaterol and especially formoterol and pharmaceutically acceptable salts thereof. Suitable bronchodilator drugs include anticholinergic or antimuscarinic compounds, specifically ipratropium bromide, oxitropium bromide, tiotropium salts and CHF 4226 (Chiesi) and glycopyrrolate. In some embodiments, the compounds or compositions according to the invention are administered together with apremilast in the same composition or in different pharmaceutical compositions. Suitable antihistamine raw materials include cetirizine hydrochloride, acetaminophen, clemastine fumarate, promethazine, loratidine, desloratidine, diphenhydramine, fexofenadine hydrochloride, activastine, astemizole, azelastine, ebastine, epinastine, mizolastine, and terfenadine. Other useful combinations of the compounds of the present invention with anti-inflammatory drugs include the following: chemokine receptor (such as CCR-1, CCR-2, CCR-3, CCR-4, CCR-5, CCR-6, CCR-7, CCR-8, CCR-9, and CCR10, CXCR1, CXCR2, CXCR3, CXCR4, CXCR5) antagonists, especially CCR-5 antagonists, such as Schering-Plough antagonists SC-351125, SCH-55700, and SCH-D, and Takeda antagonists, such as N-[[4-[[[6,7-dihydro-2-(4-methylphenyl)-5H-benzo-cyclohepten-8-yl]carbonyl]amino]phenyl]-methyl]tetrahydro-N,N-dimethyl-2H-pyran-4-ammonium chloride (TAK-770). The structures of the active compounds identified by code, generic name, or trade name can be obtained from the current version of the standard compendium "The Merck Index" or from databases such as (for example) international patents (such as IMS World Publications). The compounds of the present invention can also be used in combination with known treatment processes (such as administration of hormones or radiation). In certain embodiments, the provided compounds are used as radiation sensitizers, especially for treating tumors that exhibit poor sensitivity to radiotherapy. The compounds of the present invention can be administered alone or in combination with one or more other therapeutic compounds. The combination therapy may take the form of a fixed combination, or the administration of the compounds of the present invention and one or more other therapeutic compounds may be staggered or given independently of each other, or in the form of a combined administration of a fixed combination and one or more other therapeutic compounds. Additionally or alternatively, the compounds of the present invention can be administered in combination with chemotherapy, radiotherapy, immunotherapy, photoelectric therapy, surgical intervention, or a combination of these therapies for tumor therapy. Long-term therapy is also possible, just as in the case of adjuvant therapy in the context of other treatment strategies, as described above. Other possible treatments are therapies for maintaining the state of the patient after tumor regression or even chemoprevention therapy in patients at risk (for example). These additional agents can be administered separately from the composition containing the compound of the present invention as part of a multiple-dose regimen. Alternatively, these agents can be part of a single dosage form, which is mixed with the compound of the present invention into a single composition. If administered as part of a multiple-dose regimen, the two active agents can be presented to each other simultaneously, sequentially, or over a period of time, usually within 5 hours. As used herein, the terms "combination (combination, combined)" and related terms refer to the simultaneous or sequential administration of the therapeutic agents of the present invention. For example, the compound of the present invention can be administered with another therapeutic agent simultaneously or sequentially in separate unit dosage forms or in a single unit dosage form together. Therefore, the present invention provides a single unit dosage form comprising the compound of the present invention, an additional therapeutic agent, and a pharmaceutically acceptable carrier, adjuvant, or vehicle. The amounts of the compound of the present invention and the additional therapeutic agent (in their compositions containing the therapeutic agents as described above) that can be combined with the carrier material to produce a single dosage form can vary depending on the host being treated and the particular mode of administration. Preferably, the compositions of the present invention should be formulated such that a dose of 0.01 - 100 mg / kg body weight / day of the compound of the present invention can be administered. In their compositions containing an additional therapeutic agent, the additional therapeutic agent and the compound of the present invention can act synergistically. Therefore, the amount of the additional therapeutic agent in these compositions will be less than the amount required in a single therapy using only that therapeutic agent. In these compositions, a dose of 0.01 - 1,000 μg / kg body weight / day of the additional therapeutic agent can be administered. The amount of the additional therapeutic agent present in the compositions of the present invention will not exceed the amount usually administered in a composition containing that therapeutic agent as the sole active drug. Preferably, the amount of the additional therapeutic agent in the compositions disclosed herein will be in the range of about 50% to 100% of the amount usually present in a composition containing that agent as the sole therapeutically active agent. The compounds of the present invention or their pharmaceutical compositions can also be incorporated into compositions for coating implantable medical devices (such as prostheses, artificial valves, vascular grafts, stents, and catheters). For example, vascular stents have been used to overcome restenosis (re-narrowing of the blood vessel wall after injury). However, patients using stents or other implantable devices are at risk of blood clot formation or platelet activation. These unwanted effects can be prevented or alleviated by pre-coating the device with a pharmaceutically acceptable composition containing a kinase inhibitor. The implantable device coated with the compound of the present invention is another embodiment of the present invention. [Illustration] [] As illustrated in the examples below, in certain exemplary embodiments, the compounds and solid forms are prepared according to the foregoing general procedures. It should be understood that although the general methods illustrate the synthesis of certain compounds of the present invention, the following methods and other methods known to those skilled in the art are applicable to all compounds as described herein and to each subclass and species of such compounds. [] [Experimental procedures:] [] [Examples] [1.] [] Sodium periodate (10.4 kg, 12.0 eq.), acetonitrile (8 L, 10 V), carbon tetrachloride (8 L, 10 V), and water (12 L, 15 V) were charged into a 50 L reactor. Ruthenium(III) chloride trihydrate (4.9 g, 0.6 % eq.) was added and the mixture was stirred at 25 °C for 30 minutes. 2,4-Dichloroquinoline (800 g, 1.0 eq.) was added portionwise over 60 minutes at 25 °C, and then the mixture was stirred vigorously at that temperature for 24 hours. When the starting quinoline was completely consumed, the mixture was filtered and the filter cake was washed with 34 L of hot ethyl acetate. The aqueous layer was separated and extracted with 13 L of hot ethyl acetate. The organic layers were combined, dried over anhydrous sodium sulfate, filtered, and evaporated under vacuum at 50 °C. The residue was triturated with 4.8 L of dichloromethane, and the solid formed was filtered and dried under vacuum to give the product as an off-white solid [A-2] (1153 g, 97.2 % yield). [Examples] [2.] [] The diacid of the foregoing step [A-2] (1153 g, 1.0 eq.) and DMPU (8 L, 7 V) were charged into a 20 L reactor and the mixture was heated to 85 °C and maintained for 1 hour. Potassium carbonate (1553 g, 2.3 eq.) was added in two portions over 10 minutes and the mixture was stirred at 85 °C for 20 minutes. Diethyl sulfate (1.73 L, 4.3 eq.) was added over 90 minutes, the temperature was maintained between 80 °C and 90 °C, and the mixture was stirred at this temperature for an additional 10 hours. Once the starting diacid and monoester were determined by LC-MS to be present at less than 2%, the mixture was cooled to room temperature over 50 minutes and then further cooled to 0 °C. Water (17 L, 15 V) and heptane (11.5 L, 10 V) were added and the aqueous and organic layers were separated. The aqueous layer was extracted twice with heptane (11.5 L, then 6 L), and the combined organic layers were washed with brine (11.5 L) and then concentrated under vacuum at 50 °C to give an oily diester product (1112 g, 78% yield). [Example] [3.] [] The diester of Example 2 (500 g, 1.0 eq.) and toluene (10 L, 20 V) were charged into a 20 L reactor and cooled to -78 °C. DIBAL-H (1 M in toluene, 3 L, 1.75 eq.) was added dropwise to the reactor over 70 minutes, the temperature was maintained between -80 °C and -70 °C, and the mixture was stirred at this temperature for an additional 20 minutes. When TLC showed complete consumption of the starting material, methanol (1 L, 2 V) was added dropwise over 40 minutes, the temperature was maintained between -80 °C and -70 °C. 4 N HCl (400 mL, 8 V) was added dropwise to the above reaction mixture over 30 minutes, keeping the temperature below -50 °C. The reaction was warmed to room temperature and the aqueous layer was separated and extracted with toluene (2.5 L, 5 V). The combined organic layers were dried over anhydrous sodium sulfate and then concentrated under vacuum at 50 °C to give a 7.5 L solution which was used directly in the next step. [Example] [4.] [] A solution of the aldehyde from Example 3 in toluene (7.5 L, 1.0 eq.) was added to a 10 L reactor and cooled to 0 °C. 2,4-Dimethoxybenzylamine (286 g, 1.0 eq.) was added dropwise to the reactor over 20 minutes, maintaining the temperature between 0 °C and 10 °C. Sodium triacetoxyborohydride (544.5 g, 1.5 eq.) was added portionwise to the reactor over 50 minutes, and the mixture was stirred at room temperature for 3 hours. When TLC indicated complete consumption of the starting material, 1 N NaOH (aq.) was added until the pH was between 6 - 7, followed by saturated Na2CO3 (aq.) until the pH was between 9 - 10. The aqueous layer was separated and washed with ethyl acetate (2 x 5 L), and the combined organic layers were washed with brine (1.25 L) and dried over anhydrous sodium sulfate, then concentrated in vacuo at 50 °C to give the crude product. The crude product was dissolved in acetonitrile (6 L) at 80 °C to obtain a clear solution, which was cooled to 0 °C over 2 hours, then stirred for an additional 1 hour. The solid formed was collected by filtration and dried in vacuo at 50 °C to yield the desired product (1.57 kg, 65% yield over 2 steps, 98.9% purity). [Example] [5.] [] 2-Bromo-1,3-difluorobenzene (700 g, 1.6 eq.) and THF (8 L, 10 V) were charged into a 20 L reactor and cooled to -78 °C. Isopropylmagnesium chloride–lithium chloride complex in THF (4 L, 2.3 eq.) was added dropwise to the reactor over 2 hours, maintaining the temperature between -80 °C and -70 °C, and the mixture was stirred at this temperature until TLC analysis indicated complete consumption of the starting 2-bromo-1,3-difluorobenzene. Zinc chloride (1.5 kg, 4.8 eq.) was added to the reactor in a single batch and the mixture was stirred at a temperature between -80 °C and -70 °C for 30 minutes, then warmed to 0 °C. Pd(PPh3)4 (131 g, 0.05 eq.) was added to the reactor, followed by the product of Example 4 (800 g, 1.0 eq.), and the mixture was stirred at room temperature for 15 hours, whereupon complete consumption of the dichloropyridine starting material was determined by HPLC. The mixture was cooled to 0 °C, and saturated aqueous NH4Cl solution (8 L, 10 V) was added dropwise to the reactor over 1 hour, and the mixture was stirred for 30 minutes, then filtered. The aqueous solution was extracted twice with 8 L of ethyl acetate, and the combined organic layers were washed with brine (4 L), dried over anhydrous sodium sulfate, and then concentrated under vacuum at 50 °C to give the crude product. This crude product was combined with the crude product from a separate batch using 900 g of the product of Example 4, and triturated with MTBE (34 L) and filtered, then the solid was charged into a 20 L reactor with 3.8 L of acetonitrile and stirred at room temperature for 1 hour. MTBE (9.5 L) was added dropwise at room temperature and held for 1 hour and stirred for an additional 1 hour. The solid was collected by filtration and dried at room temperature to afford 1.1 kg of the desired product with 97% purity. The mother liquor from the purification was evaporated and purified by silica gel chromatography (33% to 55% gradient of ethyl acetate in petroleum ether), yielding an additional 550 g of crude product, which was dissolved in acetonitrile (500 mL) and precipitated by dropwise addition of MTBE (1500 mL). The solid formed was collected by filtration and dried to afford an additional 430 g of product with 100% purity. [Example] [6.] [] The product of Example 5 (500 g, 1.0 eq.), N-(p-aminobenzoyl)pyrrolidine (224 g, 1.0 eq.), potassium carbonate (400 g, 2.5 eq.), and 1,4-dioxane (12.5 L, 25 V) were added to a 20 L reactor and stirred for 30 minutes while degassing with a nitrogen stream. Pd2(dba)3 (72.2 g, 0.06 eq.) and Xantphos (80.6 g, 0.12 eq.) were added to the reactor and the mixture was stirred at room temperature for 10 minutes, then heated to 100 °C and stirred for 15 hours, whereupon complete consumption of the chloropyridine starting material was determined by HPLC. The mixture was filtered and water (12.5 L) was added to the filtrate, whereupon the mixture was extracted twice with 5 L of ethyl acetate. The combined organic layers were washed four times with 0.15 N aqueous citric acid solution (5 L each), once with saturated aqueous sodium bicarbonate solution (2.5 L), and once with brine (2.5 L), then dried over anhydrous sodium sulfate and concentrated in vacuo at 50 °C to afford the crude product as a solid. The crude solid was slurried with acetonitrile (2 V) and MTBE (10 V) at room temperature for 30 minutes, and the resulting solid was filtered and dried to afford the desired compound with 95% purity. The compound can be further purified to 98.6% purity by repeating the acetonitrile / MTBE slurrying process. [Example] [7.] [Compound] [1] [Free base] [] The product of Example 6 (1.2 kg, 1.0 eq.) and dichloromethane (12 L, 10 V) were charged into a 20 L reactor. Under a nitrogen atmosphere, hydrobromic acid (33%, in acetic acid, 7.2 L, 6 V) was added to the reactor at 20 °C to 30 °C, and the mixture was stirred at room temperature for 15 h. Thus, the complete consumption of the dimethoxybenzyl starting material was determined by HPLC. The solution was cooled to 0 °C to 10 °C and 2 N aqueous sodium hydroxide solution was added until the pH was greater than 2, followed by the addition of solid sodium bicarbonate powder until the pH was between 8 and 9. The mixture was filtered and the filtrate was extracted twice with dichloromethane (12 L). The combined organic layers were washed with brine (20 L), dried over anhydrous sodium sulfate, filtered, and concentrated under vacuum at 40 °C to obtain a crude product (1.5 kg, 95% purity). The crude solid was charged into a 20 L reactor with dichloromethane (3 L) and MTBE (7.5 L), and the mixture was stirred overnight at 20 °C to 30 °C. The resulting solid was collected by filtration and dried at 50 °C to a constant weight (800 g, 97% purity). This intermediate purity product was dissolved in 32 L of dichloromethane while warming to 30 °C, and the solution was filtered. The filtrate was concentrated under vacuum at 50 °C until 3 volumes remained, then cooled to room temperature. The solid formed was collected and dried at 50 °C to a constant weight (700 g, 98.7% purity). The product was dissolved in 32 L of dichloromethane at 30 °C, SiliaMetS (30% w / w) was added, and the mixture was heated to reflux overnight, then cooled to room temperature. The mixture was filtered and the filtrate was treated again with SiliaMetS (30% w / w) and heated to reflux overnight, then cooled to room temperature. The mixture was filtered and the filtrate was concentrated under vacuum at 30 °C to 40 °C. MTBE (5 V) was added to the residue and the mixture was stirred at room temperature for 1 h. The solid formed was collected by filtration and dried under vacuum at 70 °C to a constant weight to obtain 575 g of Compound 1 free base (99.5% purity). This material was determined to be Form I’ of Compound 1 free base, which has the XRPD pattern shown in Figure 1. The amorphous Compound 1 free base was prepared by dissolving Form I’ in dichloromethane and then rapidly evaporating. [Example] [8.] [] Charge 4-aminobenzoic acid (700 g, 1.0 eq.) and thionyl chloride (4 L, 13 eq.) into a 20 L reactor and stir overnight at 50 °C to 60 °C. Then concentrate under vacuum at 50 °C to provide the crude acyl chloride, which is used without further purification. Charge pyrrolidine (1300 g, 5 eq.) and dichloromethane (3.5 L, 5V) into a 20 L reactor and cool the mixture to 0 °C. Add the acyl chloride in dichloromethane (3.5 L, 5 V) dropwise to the reactor at 0 °C to 5 °C. Once the reaction is complete as determined by HPLC, add water (7 L) and filter the mixture. Wash the filter cake with dichloromethane (1.4 L) and water (2.8 L). Separate the aqueous phase and extract with dichloromethane (7 L). Combine the organic layers, then wash with brine (3.5 L) and dry over anhydrous sodium sulfate. Then concentrate under vacuum at 50 °C to obtain the crude product. Stir the crude product in n-heptane:dichloromethane (5:1, 3.5 L) overnight at room temperature, then collect the solid by filtration. Wash the filter cake with dichloromethane (1.4 L) and water (2.8 L) and combine the two filter cakes. Then stir with dichloromethane (2.8 L) overnight at 35 °C to 40 °C, then cool to 15 °C and stir for 4 hours. Collect the solid by filtration and dry under vacuum at 50 °C to a constant weight to provide the desired product (660 g, 99% purity). The deuterated analogues (i.e., those in which Y and / or Z are D) are prepared by the same procedure using the corresponding deuterated pyrrolidine. [Example] [9.] [Form] [I] [and amorphous compound] [1] [Methanesulfonate] [] Dissolve the free base of Compound 1 (418.5 mg, 0.963 mmol) in THF (15 mL) with stirring at 60 °C. Add neat methanesulfonic acid (62.6 μL, 0.963 mmol) dropwise to this mixture over 5 minutes, resulting in the precipitation of a cream-colored solid. Maintain heating for 30 minutes, then cool the mixture to room temperature and filter, wash with cold isopropanol and dry under vacuum. This material was determined to be Form I of Compound 1 methanesulfonate, which has the XRPD pattern shown in Figure 2. Redissolve the material in 1,4-dioxane in 50% water and lyophilize to provide amorphous Compound 1 methanesulfonate. [Example] [10.] [Compound] [1] [in the form of methanesulfonate] [II] [Production of] [] The amorphous compound 1 methanesulfonate (10 mg) was dissolved in 95% acetonitrile, 5% water (% v / v) and allowed to evaporate for one week. The crystalline material produced was found to be form II of compound 1 methanesulfonate, which has the XRPD pattern shown in Figure 3. [Examples] [11.] [Compound] [1] [in the form of methanesulfonate] [III] [and form] [IV] [Production of] [] The amorphous compound 1 methanesulfonate (10 mg) was dissolved in N,N’-dimethylformamide to form a saturated solution, which was subjected to rapid cooling at -20 °C, causing the formation of a crystalline solid. This material was found to be form III of compound 1 methanesulfonate, which has the XRPD pattern shown in Figure 4. When dried under ambient conditions, form III was found to transform into form IV of compound 1 methanesulfonate, which has the XRPD pattern shown in Figure 5. Form IV was found to be stable under ambient conditions. [Examples] [12.] [Compound] [1] [in the form of methanesulfonate] [V] [Production of] [] The amorphous compound 1 methanesulfonate (10 mg) was dissolved in dioxane in 50% water (% v / v) and allowed to evaporate for one week. The crystalline material formed was found to be form V of compound 1 methanesulfonate, which has the XRPD pattern shown in Figure 6. Upon grinding, form V was found to transform into form I. [] [Examples]

[13] [:] [X] [X-ray powder diffraction] [(XRPD)] [Analytical Method] [] XRPD analysis of Forms I', I, II, III, IV, and V of Compound 1 was performed on a PANalytical X'pert Pro diffractometer. The substance was gently ground to release any aggregates and loaded onto a porous plate with a Kapton or Mylar polymer film to support the sample. The porous plate was then placed in the diffractometer and analyzed using Cu K radiation (α1 λ = 1.54060 Å; α2 1.54443 Å; β - 1.39225 Å; α1:α2 ratio = 0.5), operating in transmission mode with a 40 kV / 40 mA generator setting (step size 0.0130 °2θ), starting the scan at 3.0100 °2θ and ending at 35.0100 °2θ. [Example] [14. Tyk2] [Radioactive Kinase Assay] [] The peptide substrate [KKSRGDYMTMQIG] (20 µM) was prepared in reaction buffer (20 mM Hepes pH 7.5, 10 mM MgCl2, 1 mM EGTA, 0.02% Brij35, 0.02 mg / mL BSA, 0.1 mM Na3PO4, 2 mM DTT, 1% DMSO). TYK2 (Invitrogen) kinase was added, followed by the compound in DMSO. 33PATP was added to initiate the reaction at 10 µM ATP. The kinase reaction was incubated at room temperature for 120 min and spotted onto P81 ion exchange paper (Whatman No. 3698-915), and then washed thoroughly in 0.75% phosphoric acid before reading the radioactivity counts. For the Tyk2 radioactive kinase assay, Compound 1 and its isotopologs [2], [3], [4], and [5] each provided IC50 values of less than 1 nM. [Example] [15.] [Human] [PBMC] [in] [IL-12] [induced] [pSTAT4] Human PBMCs were isolated from the buffy coat and cryopreserved for analysis as needed. The cells for analysis were thawed and resuspended in complete medium containing serum, and then the cells were diluted to 1.67E6 cells / ml such that 120 μl per well was 200,000 cells. 15 μl of the compound or DMSO was added to the wells at the desired concentration and incubated at 37 °C for 1 hour. 15 μl of the stimulant (final concentration 1.7 ng / mL IL-12) was added for 30 minutes prior to the pSTAT4 and total STAT4 analysis of the cell lysates prepared and analyzed using MSD reagents according to the manufacturer's protocol. The final DMSO concentration of the compound in the assay was 0.1%. For the IL-12-induced pSTAT4 analysis in human PBMCs, compound 1 and its isotopologues [2], [3], [4] and [5] each provided IC50 values of less than 150 nM. [Example] [16. CACO-2] [Cell permeability analysis] [] Dilute Caco-2 cells to 6.86×10 5 cells / mL with the culture medium, and dispense 50 μL of the cell suspension into the pores of a 96-well HTS Transwell plate. Incubate the cells in a cell culture incubator at 37 °C, 5% CO2, and 95% relative humidity for 14 - 18 days. Replace the cell culture medium every 2 days, starting no later than 24 hours after the initial plate seeding. 3) After 14 - 18 days of incubation, remove the plate from the incubator. Wash the insert twice with pre-warmed HBSS (10 mM HEPES, pH 7.4) and place it in the receiver plate. Add 75 μL and 235 μL of buffer to each Transwell insert and receiver well, respectively. Then incubate the plate at 37 °C with shaking at 150 rpm for 30 min. Prepare the control compound stock solution at 10 mM in DMSO, and then dilute it with DMSO to 1 mM, and further dilute it with HBSS (10 mM HEPES, pH 7.4) to obtain the compound working solution. Prepare the test compound stock solution at 10 mM in DMSO, and then dilute it with DMSO to 1 mM, and further dilute it with HBSS (10 mM HEPES, pH 7.4, 4% BSA) to obtain the compound working solution. The final concentrations of the test compound and the control compound are 5 μM. To determine the drug transport rate in the apical-to-basolateral direction, add 75 μL of the compound working solution to the pore (apical compartment) and add 235 μL of HBSS (10 mM HEPES, pH 7.4, or 4% BSA) to the receiver plate (basolateral compartment). To determine the drug transport rate in the basolateral-to-apical direction, add 235 μL of the compound working solution to each well of the receiver plate (basolateral compartment), and add 75 μL of HBSS (10 mM HEPES, pH 7.4, or 4% BSA) to the pore (apical compartment). This analysis is performed in duplicate. 6) Incubate the plate at 37 °C for 2 hours. At the end of the transport period, directly remove 50 μL aliquots from the apical and basolateral wells and transfer them to the wells of a new plate. Add 4 volumes of cold methanol containing internal standards (IS, 100 nM Alprazolam, 200 nM Labetalol, and 200 nM Diclofenac) to each well. Centrifuge the samples at 3,220 g for 30 minutes. Perform LC-MS / MS analysis using an aliquot of 100 μL of the supernatant mixed with 100 μL of ultrapure water. 7) Discard the solution from the Transwell plate. Add 100 μL of lucifer yellow solution (100 μM, in HBSS) and 300 μL of HBSS to each well of the Transwell insert and receiver for leakage measurement.Incubate the plate at 37 °C for 30 minutes. Transfer 80 μL aliquots from the apical and basolateral outer wells to a solid black plate and read the plate using a Tecan Infinite M 200 (excitation / emission wavelengths 485 nm / 530 nm). Analyze the liquid portion, apical and basolateral outer layers by LC-MS to determine P app(A-B), P app(B-A) and recovery. [Example] [17. 1 mM ATP Tyk2] [Diameter analysis] [] Dilute the compound serially in DMSO and then further dilute in 1x kinase buffer: First add 5 uL of the buffer-diluted compound to the well, then add 10 uL of the Tyk2 enzyme mixture to the well, and then add 10 uL of the substrate mixture to start the reaction. Incubate the reaction at 28 °C for 25 minutes and then add 25 uL of the stop buffer. Read the reaction mixture using a diameter mass spectrometer. The final concentrations of the analysis conditions are: 25 mM HEPES pH 7.5, 0.01% Brij-35, 0.01% Triton, 0.5 mM EGTA, 2 mM DTT, 10 mM MgCl 2, TYK2 4 nM, ATP concentration 1000 uM and P30 3 uM. The results of the 1 mM ATP Tyk2 diameter analysis of various compounds are provided in [Table] [8]. [Example] [18.] [Analysis of metabolic clearance rate in microsomes] [] Prepare a master solution containing 0.5 mg / mL of rat or human liver microsomes, 5 mM MgCl2, 100 mM phosphate buffer, and 25 μg / mL alamethacin. Add 40 μL of 10 mM NADPH solution and 40 μL of 20 mM UDPGA solution to each well. The final concentrations of NADPH and UDPGA are 1 mM and 2 mM, respectively. Pre-warm the mixture at 37 °C for 5 minutes. Prepare a negative control sample by replacing the NADPH and UDPGA solutions with 80 μL of ultrapure H2O. The negative control is used to exclude misleading factors caused by the instability of the chemical itself. This study was conducted in duplicate. Initiate the reaction by adding 2 μL of 400 μM of the control compound or test compound solution. Diclofenac was used as a positive control in this study. The final concentration of the test compound or control compound is 2 μM. Take 50 μL aliquots from the reaction solution at 0, 15, 30, 45, and 60 minutes. Terminate the reaction by adding 4 volumes of cold acetonitrile (or methanol) with internal standards (IS) (100 nM alprazolam, 200 nM imipramine, 200 nM labetalol, and 2 μM ketoprofen) at the designated time points. Centrifuge the samples at 3,220 g for 40 minutes to precipitate the proteins. Perform LC-MS / MS analysis using an aliquot of 100 μL of the supernatant diluted with 100 μL of water. Calculate the in vitro half-life, scaled intrinsic clearance, and predicted hepatic clearance according to the standard calculations. The intrinsic clearance values (HLM Clint) in human liver microsomes for the selected compounds are provided in [Table] [8]. [Example] [19.] [Kinetic solubility determination analysis] [] A stock solution of the test compound was prepared at a concentration of 10 mM in DMSO. A stock solution of the positive control compound was prepared at a concentration of 30 mM in DMSO. Progesterone was used as the positive control in this assay. 30 μL of the stock solution of each compound was sequentially placed into its appropriate 96-well rack, and then 970 μL of PBS (pH 7.4) was added to each vial of the uncapped solubility sample plate. This study was conducted in duplicate. A stir bar was added to each vial, and the vials were then sealed using a molded PTDE / SIL 96-well plate lid. The solubility sample plate was transferred to a Thermomixer Comfort plate shaker and incubated at RT for 2 hours with shaking at 1100 rpm. After 2 hours of incubation, the stir bars were removed using a large magnet, and all the samples of the solubility sample plate were transferred to a filter plate. All the samples were filtered using a vacuum manifold. The filtered samples were diluted with methanol. Standards of each test compound at concentrations of 0.3 μM, 0.09 μM, and 0.15 μM were prepared, and the test samples and standards were analyzed by LC-MS, and the test samples were quantified against the standards of known concentrations in DMSO using mass spectral peak identification and quantification. The results of the kinetic solubility determination for the selected compounds are provided in [Table] [8]. [Example] [21.] [Dissolution analysis in simulated gastric and intestinal fluids for fed and fasted states] [] The dissolution bath was filled with 900 mL of the culture medium for testing, the bath temperature was maintained at 37 °C, the rotation rate of the device was 50 rpm, and the draw point of the sampling probe was set exactly midway between the culture medium surface and the disk surface. The test article (0.4 g) was compressed into the disk using a Woods device. The sampling time points were 10, 30, 60, 90, 120, 150, and 180, respectively. The concentration of the sample was analyzed by HPLC against a sample preparation of known concentration (about 0.5 mg / ml). The dissolution rate was obtained from the concentration-time curve. [] The dissolution rate of Compound 1 in fasted simulated gastric fluid (FaSSGF) was 57.5 μg / cm 2 / min, and the dissolution rate of Compound 9 in fasted simulated gastric fluid was 21.2 μg / cm 2 / min. [] [Example] [22.] [Pharmacokinetic study in dogs] [] Male Beagle dogs (9 - 14 kg; 2.5 to 5.5 years old) housed individually in cages under standard test conditions were fasted for approximately 16 to 17 hours, then fed, and returned approximately 2 hours after feeding. The test article was administered at 10 mg / kg by oral gavage through an orogastric tube. The test article was formulated at 1.0 mg / mL in 20% HPβCD aq. (pH = 5), and then flushed with 10 mL of tap water. Blood samples (approximately 1.5 mL) were collected from the jugular vein by venipuncture and stored in tubes treated with K2EDTA, followed by centrifugation (3000 g, 4 °C, 5 min). Plasma samples were transferred and stored at -70 °C until analysis. Bioanalysis: After extraction by precipitation of plasma with cold acetonitrile (4:1 ACN / plasma, v / v) containing verapamil as the internal standard, the concentrations of the experimental samples and plasma calibration standards were determined by LC / MS / MS (API - 5500, reversed - phase chromatography, APCI). PK analysis: Individual animal plasma concentration - time data were analyzed by non - compartmental analysis (linear trapezoidal fitting) using PK Solver software (v2.0). The results of the pharmacokinetic studies of compounds 1 and 9 in dogs are shown in [Figure] [7]. Compound 1 exhibited a Cmax of 2105 ng / mL, while compound 9 exhibited a Cmax of 1071 ng / mL. Compound 1 exhibited an AUC(0 - t) of 18747 ng*hr / mL and compound 9 exhibited an AUC(0 - t) of 10182 ng*hr / mL. [Example] [22.] [Calculation of topological polar surface area] [] Topological polar surface areas were calculated according to the method of Ertl et al., J. Med. Chem. (2000), 43, 3714 - 3717, and the values for the selected compounds are reported in [Table] [8]. [] [Example] [23.] [Calculation of atom - based partition coefficient] [] AlogP values were calculated using the AlogP function in Schrodinger LiveDesign 8.1, and the values for the selected compounds are provided in [Table] [8]. The structures of various additional compounds that can be used as compounds for Tyk2 inhibitors are shown in [Table] [7]. [, , ] [[] [Table] [7.] [Structure of the compound] [[] [[] [, , ] [[] [Table] [8.] [Physicochemical, pharmacodynamic and pharmacokinetic data] [[] [Compound] [1 mM ATP] [under] [Tyk2 IC, 50 , (nM), , ] [Kin. Sol.] [pH 7.4 (µM)] [Caco-2 A-B (x10e, -6 , cm / s)] [Ertl TPSA (Å, 2 , )] [AlogP] [HLM Clint (mL / min / kg)] [1] 56.9 274.31 5.77 74.3 4.1 0.62 [2] 85.3 74.3 4.1 [3] 74.3 4.1 [4] 78.5 74.3 4.1 [5] 72.6 74.3 4.1 [6] 93.2 74.3 4.1 [7] 390 <0.5 13.47 70.2 3.9 10.91 [8] 33 11.92 13.08 79.4 3.2 1.2 [9] 134 171.55 3.43 83.6 3.4 3

[10] 90 1.45 4.03 74.3 4.6 7.81

[11] 119 1.86 5.62 74.3 4.4

[12] 136 236.96 0.41 94.6 3.3

[13] 251.64 2.89 96.5 2.6 1.9

[14] 24.2 271.19 2.08 107.4 3.2 0

[15] 74.1 3.75 7.59 74.3 3.5 1.78

[16] 17.7 32.86 2.63 98.1 4.0 0

[17] 88.6 204.67 1.52 83.6 3.1 Although many embodiments of the present invention have been described, it will be apparent that basic examples can be changed to provide other embodiments that utilize the inventive compounds and methods. Accordingly, it is to be understood that the scope of the present invention will be defined by the appended claims rather than by the specific embodiments represented by way of example.

Claims

1. A pharmaceutical composition comprising a crystalline form of a compound of the formula in a therapeutically effective amount and a pharmaceutically acceptable carrier, adjuvant, or diluent, wherein the crystalline form has a powder X-ray diffraction (XRPD) pattern substantially similar to that shown in Figure 1.

2. The pharmaceutical composition of claim 1, wherein the crystal form has three or more 2θ angles selected from the following peaks in its XRPD plot: 6.07±0.1, 11.90±0.1, 16.62±0.1 and 13.95±0.1 °.

3. A pharmaceutical composition comprising a crystalline form of a methanesulfonate of a compound of the formula in a therapeutically effective amount and a pharmaceutically acceptable carrier, adjuvant, or diluent.

4. The pharmaceutical composition of claim 3, wherein the crystalline form has a powder X-ray diffraction (XRPD) pattern substantially similar to that shown in Figure 2.

5. The pharmaceutical composition of claim 3, wherein the crystal form has three or more 2θ angles selected from the following peaks in its XRPD plot: 19.89±0.1, 9.17±0.1, 16.88±0.1, 14.37±0.1 and 22.09±0.1 °.

6. The pharmaceutical composition of claim 3, wherein the crystal form has three or more 2θ angles selected from the following peaks in its XRPD plot: 22.27±0.1, 26.45±0.1, 26.02±0.1, 16.34±0.1 and 17.06±0.1 °.

7. The pharmaceutical composition of claim 3, wherein the crystalline form has a powder X-ray diffraction (XRPD) pattern substantially similar to that shown in Figure 3.

8. The pharmaceutical composition of claim 3, wherein the crystalline form has a powder X-ray diffraction (XRPD) pattern substantially similar to that shown in Figure 4.

9. The pharmaceutical composition of claim 3, wherein the crystal form has three or more 2θ angles selected from the following peaks in its XRPD plot: 18.18 ± 0.1, 18.56 ± 0.1, 16.95 ± 0.1, 21.95 ± 0.1 and 9.85 ± 0.1 °.

10. The pharmaceutical composition of claim 3, wherein the crystalline form has a powder X-ray diffraction (XRPD) pattern substantially similar to that shown in Figure 5.

11. The pharmaceutical composition of claim 3, wherein the crystal form has three or more 2θ angles selected from the following peaks in its XRPD plot: 17.79 ± 0.1, 12.45 ± 0.1, 24.38 ± 0.1, 26.00 ± 0.1 and 16.28 ± 0.1 °.

12. The pharmaceutical composition of claim 3, wherein the crystal form has three or more 2θ angles selected from the following peaks in its XRPD plot: 13.34 ± 0.1, 8.80 ± 0.1, 11.10 ± 0.1, 16.85 ± 0.1 and 25.49 ± 0.1 °.

13. The pharmaceutical composition of claim 3, wherein the crystalline form has a powder X-ray diffraction (XRPD) pattern substantially similar to that shown in Figure 6.

14. Use of a pharmaceutical composition as claimed in any one of claims 1 to 13, for manufacturing a medicament for treating Tyk2-mediated conditions.

15. As claimed in claim 14, wherein the Tyk2-mediated condition is selected from autoimmune diseases, inflammatory diseases, proliferative diseases, endocrine diseases, neurological diseases, or transplant-related diseases.

16. As claimed in claim 15, wherein the autoimmune disease is selected from adhesive spondylitis, systemic lupus erythematosus, psoriasis, Crohn's disease, and ulcerative colitis.

17. As claimed in claim 15, wherein the inflammatory condition is selected from psoriasis and inflammatory bowel disease.

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