Moisture loss due to silicone tubing and its impact on protein concentration during pharmaceutical manufacturing.

Abstract

The present invention relates, in general, to a method for predicting water loss from a sample. In particular, the present invention relates to modeling water loss from a drug substance in a silicone tube based on the properties of the tube and the drug substance.

Description

[Technical Field]

[0001] (Cross-reference of related applications) This application claims the interests of U.S. Provisional Patent Application No. 63 / 421,103, filed on 31 October 2022, which is incorporated herein by reference in its entirety.

[0002] This application relates to a method for predicting moisture loss from a sample in a silicone tube. [Background technology]

[0003] The active pharmaceutical ingredient (DS) encounters various materials during the manufacturing or filling / finishing of the drug product (DP), making it crucial to evaluate the physicochemical compatibility between the DS and these contact components. Silicone tubing is one such elastomer component used during DP manufacturing to facilitate fluid transfer and filling operations. Silicone tubing is known to be permeable to a variety of low molecular weight species and gases, and it has been qualitatively demonstrated that moisture loss occurs due to silicone tubing. However, the potential impact of moisture loss by silicone tubing and other polymer tubing on the concentration of the drug and / or excipients in the context of DP manufacturing has not been quantified or thoroughly investigated to date. Since controlling the concentration of the drug and excipients is critical in the manufacturing process, understanding how the interaction between tubing properties and DP parameters affects moisture loss and concentration changes is important for designing more representative process characterization and development tests for DP technology transfer.

[0004] Therefore, there is a need for methods to predict and prevent moisture loss and concentration changes in active pharmaceutical ingredients stored in tubes. [Overview of the project]

[0005] Methods have been developed to predict water loss from a sample in a tube, for example, from a drug substance in a silicone tube. This disclosure explains that a linear relationship exists between water loss and concentration changes of proteins in the drug substance, and therefore, methods have been further developed to predict concentration changes of proteins in the drug substance in a tube. Considering the range of acceptable concentration changes of proteins, additional methods have been developed to select an acceptable range of retention times for a sample in a tube. Since the water loss rate depends on the characteristics of the tube, e.g., inner diameter (ID), tube wall thickness, and / or surface area to volume ratio, methods have also been developed to select a tube using a model of the predicted water loss of the sample.

[0006] This disclosure provides a method for predicting water loss from a protein-containing sample at a given point in time. In some exemplary embodiments, the method includes (a) obtaining a protein-containing sample stored in a tube; (b) using the sample and the tube to generate a model of water loss over time from the sample in the tube; and (c) using the model to predict the amount of water loss from the sample at a given point in time.

[0007] In one embodiment, the model is generated using equations 17, 18, and 20.

[0008] In one embodiment, the sample is a cell culture medium (CCF), a harvested cell culture medium (HCCF), any step in the downstream processing of the active pharmaceutical ingredient (DS), the active pharmaceutical ingredient, or a drug product (DP).

[0009] In one aspect, the inner diameter of the tube is known. In certain aspects, the inner diameter (ID) of the tube is from about 0.1 mm to about 32 mm, from about 0.2 mm to about 26 mm, from about 0.5 mm to about 16 mm, from about 0.8 mm to about 13 mm, from about 0.8 mm to about 10 mm, about 0.1 mm, about 0.2 mm, about 0.3 mm, about 0.5 mm, about 0.6 mm, about 0.8 mm, about 1 mm, about 1.2 mm, about 1.3 mm, about 1.6 mm, about 2.4 mm, about 3.2 mm, about 4.8 mm, about 6.4 mm, about 8 mm, about 9.6 mm, about 12.7 mm, about 15.9 mm, about 19 mm, about 25.4 mm, or about 31.8 mm.

[0010] In one aspect, the thickness of the tube is known. In certain aspects, the thickness of the tube is from about 0.1 mm to about 10 mm, from about 0.2 mm to about 8 mm, from about 0.5 mm to about 7 mm, about 0.25 mm, about 0.4 mm, about 0.5 mm, about 0.7 mm, about 0.8 mm, about 1.6 mm, about 1.8 mm, about 2.1 mm, about 2.4 mm, about 3.2 mm, about 4 mm, about 4.8 mm, about 6.4 mm, about 7 mm, about 8 mm, about 9 mm, or about 10 mm. The size of the tube can have any combination of the above ID and thickness, as well as the corresponding surface area to volume ratio.

[0011] In one aspect, the surface area to volume ratio of the tube is known. In certain aspects, the surface area to volume ratio of the tube is from about 0.5 mm -1 to about 5 mm -1 , about 0.5 mm -1 , about 0.83 mm -1 , about 1 mm -1 , about 1.25 mm -1 , about 1.26 mm -1 , about 1.5 mm -1 , about 1.54 mm -1 , about 1.57 mm -1 , about 1.67 mm -1 , about 2 mm -1 , about 2.11 mm -1 , about 2.5 mm -1 , about 2.52 mm -1 , about 3 mm -1 , about 3.1 mm -1 , about 3.15 mm -1 , about 3.33 mm-1 , about 3.5mm -1 , about 4mm -1 Approximately 4.12 mm -1 , about 4.5mm -1 , about 5mm -1 , about 6.25mm -1 , about 6.67mm -1 Approximately 8.0 mm -1 , about 13.33mm -1 Approximately 20.0 mm -1 , or approximately 40.0 mm -1 That is the case.

[0012] In one embodiment, at least one of the following characteristics is known: sample volume, excipient concentration, or density. In another embodiment, protein concentration is known. In yet another embodiment, the water activity of the sample is known. In a particular embodiment, the water activity is calculated using equations 12-15.

[0013] In one embodiment, the method further includes measuring relative humidity. In a particular embodiment, the method further includes calculating mean relative humidity using Equation 16.

[0014] In one embodiment, the time points are 10 seconds to 168 hours, 5 minutes to 168 hours, 3 hours to 168 hours, 6 hours to 240 hours, approximately 10 seconds, approximately 1 hour, approximately 6 hours, approximately 12 hours, approximately 24 hours, approximately 36 hours, approximately 48 hours, approximately 72 hours, approximately 96 hours, approximately 120 hours, approximately 144 hours, or approximately 168 hours, or approximately 240 hours. In one embodiment, manual measurements may be performed at the same frequency every 5 minutes to provide additional data points, and the process may be automated to perform measurements continuously and calculations in real time.

[0015] In one embodiment, the tube is a vinyl tube, a platinum-cured silicone tube, a peroxide-cured silicone tube, a high-density polyethylene (HDPE) tube, a fluoropolymer tube, a thermoplastic elastomer tube (TPE), or a similar thermoplastic elastomer tube material.

[0016] In one embodiment, the method further includes iteratively calculating the moisture loss at a subsequent time point at least once using the moisture loss calculated at a first time point. In a particular embodiment, the iterative calculation is performed using equations 4 and 6.

[0017] In one embodiment, the temperature of the tube is approximately 5°C to 30°C, approximately 15°C to 30°C, approximately 15°C to 25°C, approximately 15°C to 21°C, approximately 16°C to 24°C, approximately 17°C to 23°C, approximately 18°C ​​to 21°C, approximately 5°C, approximately 6°C, approximately 7°C, approximately 8°C, approximately 9°C, approximately 10°C, approximately 11°C, approximately 12°C, approximately 13°C, approximately 14°C, approximately 15°C, approximately 16°C, approximately 17°C, approximately 18°C, approximately 19°C, approximately 20°C, approximately 21°C, approximately 22°C, approximately 23°C, approximately 24°C, approximately 25°C, approximately 26°C, approximately 27°C, approximately 28°C, approximately 29°C, or approximately 30°C.

[0018] In one embodiment, water loss is due to diffusive mass transfer.

[0019] The disclosure also provides a method for predicting a change in the concentration of a protein at a given point in time. In some exemplary embodiments, the method includes (a) obtaining a sample containing a protein stored in a tube; (b) using the sample and the tube to generate a model of the change in the concentration of the protein in the tube over time; and (c) using the model to predict the change in the concentration of the protein at a given point in time.

[0020] In one embodiment, the model is generated using equations 17, 18, 20, and 21.

[0021] In one embodiment, the sample is a cell culture medium (CCF), a harvested cell culture medium (HCCF), any step in the downstream processing of the active pharmaceutical ingredient (DS), the active pharmaceutical ingredient, or a drug product (DP).

[0022] In one embodiment, the inner diameter of the tube is known. In a particular embodiment, the inner diameter (ID) of the tube is approximately 0.1 mm to 32 mm, approximately 0.2 mm to 26 mm, approximately 0.5 mm to 16 mm, approximately 0.8 mm to 13 mm, approximately 0.8 mm to 10 mm, approximately 0.1 mm, approximately 0.2 mm, approximately 0.3 mm, approximately 0.5 mm, approximately 0.6 mm, approximately 0.8 mm, approximately 1 mm, approximately 1.2 mm, approximately 1.3 mm, approximately 1.6 mm, approximately 2.4 mm, approximately 3.2 mm, approximately 4.8 mm, approximately 6.4 mm, approximately 8 mm, approximately 9.6 mm, approximately 12.7 mm, approximately 15.9 mm, approximately 19 mm, approximately 25.4 mm, or approximately 31.8 mm.

[0023] In one embodiment, the thickness of the tube is known. In a particular embodiment, the thickness of the tube is approximately 0.1 mm to approximately 10 mm, approximately 0.2 mm to approximately 8 mm, approximately 0.5 mm to approximately 7 mm, approximately 0.25 mm, approximately 0.4 mm, approximately 0.5 mm, approximately 0.7 mm, approximately 0.8 mm, approximately 1.6 mm, approximately 1.8 mm, approximately 2.1 mm, approximately 2.4 mm, approximately 3.2 mm, approximately 4 mm, approximately 4.8 mm, approximately 6.4 mm, approximately 7 mm, approximately 8 mm, approximately 9 mm, or approximately 10 mm. The size of the tube can have any combination of the above ID and thickness, as well as the corresponding surface area to volume ratio of the tube.

[0024] In one embodiment, the surface area-to-volume ratio of the tube is known. In a particular embodiment, the surface area-to-volume ratio of the tube is approximately 0.5 mm -1 ~about 5mm -1 , about 0.5mm -1 , about 0.83mm -1 , about 1mm -1 , about 1.25mm -1 , about 1.26mm -1 , about 1.5mm -1 , about 1.54mm -1 , about 1.57mm -1 , about 1.67mm -1 Approximately 2mm -1 , about 2.11mm -1 , about 2.5mm -1 , about 2.52mm -1 , about 3mm -1 , about 3.1mm -1 , about 3.15mm -1, about 3.33mm -1 , about 3.5mm -1 , about 4mm -1 Approximately 4.12 mm -1 , about 4.5mm -1 , about 5mm -1 , about 6.25mm -1 , about 6.67mm -1 Approximately 8.0 mm -1 , about 13.33mm -1 Approximately 20.0 mm -1 , or approximately 40.0 mm -1 That is the case.

[0025] In one embodiment, the sample volume is known. In another embodiment, the density is known. In another embodiment, the concentration of the excipient is known. In another embodiment, the water activity of the sample is known. In a particular embodiment, the water activity is calculated using equations 12-15.

[0026] In one embodiment, the method further includes measuring relative humidity. In a particular embodiment, the method further includes calculating mean relative humidity using Equation 16.

[0027] In one embodiment, the time points are 10 seconds to 168 hours, 5 minutes to 168 hours, 3 hours to 168 hours, 6 hours to 240 hours, approximately 10 seconds, approximately 1 hour, approximately 6 hours, approximately 12 hours, approximately 24 hours, approximately 36 hours, approximately 48 hours, approximately 72 hours, approximately 96 hours, approximately 120 hours, approximately 144 hours, or approximately 168 hours, or approximately 240 hours. In one embodiment, manual measurements may be performed at the same frequency every 5 minutes to provide additional data points, and the process may be automated to perform measurements continuously and calculations in real time.

[0028] In one embodiment, the tube is a vinyl tube, a platinum-cured silicone tube, a peroxide-cured silicone tube, a high-density polyethylene (HDPE) tube, a fluoropolymer tube, a thermoplastic elastomer tube (TPE), or a similar thermoplastic elastomer tube material.

[0029] In one embodiment, the method further includes iteratively calculating at least once the change in concentration at a subsequent time point using the calculated change in concentration at a first time point. In a particular embodiment, the iterative calculation is performed using equations 4 and 6.

[0030] In one embodiment, the temperature of the tube is approximately 5°C to 30°C, approximately 15°C to 30°C, approximately 15°C to 25°C, approximately 15°C to 21°C, approximately 16°C to 24°C, approximately 17°C to 23°C, approximately 18°C ​​to 21°C, approximately 5°C, approximately 6°C, approximately 7°C, approximately 8°C, approximately 9°C, approximately 10°C, approximately 11°C, approximately 12°C, approximately 13°C, approximately 14°C, approximately 15°C, approximately 16°C, approximately 17°C, approximately 18°C, approximately 19°C, approximately 20°C, approximately 21°C, approximately 22°C, approximately 23°C, approximately 24°C, approximately 25°C, approximately 26°C, approximately 27°C, approximately 28°C, approximately 29°C, or approximately 30°C.

[0031] In one embodiment, the change in concentration is due to water loss due to diffusive mass transfer.

[0032] The Disclosure further provides a method for selecting tubes for a protein-containing sample. In some exemplary embodiments, the method includes (a) obtaining a protein-containing sample stored in at least two tubes; (b) using the sample and each of the tubes to generate a model of water lost from the sample over time in each of the tubes; and (c) selecting the tubes in step (b) based on the less predicted water loss.

[0033] In one embodiment, the model is generated using equations 17, 18, and 20.

[0034] In one embodiment, the sample is a cell culture medium (CCF), a harvested cell culture medium (HCCF), any step in the downstream processing of the active pharmaceutical ingredient (DS), the active pharmaceutical ingredient, or a drug product (DP).

[0035] In one embodiment, the inner diameter of the tube is known. In a particular embodiment, the inner diameter (ID) of the tube is approximately 0.1 mm to 32 mm, approximately 0.2 mm to 26 mm, approximately 0.5 mm to 16 mm, approximately 0.8 mm to 13 mm, approximately 0.8 mm to 10 mm, approximately 0.1 mm, approximately 0.2 mm, approximately 0.3 mm, approximately 0.5 mm, approximately 0.6 mm, approximately 0.8 mm, approximately 1 mm, approximately 1.2 mm, approximately 1.3 mm, approximately 1.6 mm, approximately 2.4 mm, approximately 3.2 mm, approximately 4.8 mm, approximately 6.4 mm, approximately 8 mm, approximately 9.6 mm, approximately 12.7 mm, approximately 15.9 mm, approximately 19 mm, approximately 25.4 mm, or approximately 31.8 mm.

[0036] In one embodiment, the thickness of the tube is known. In a particular embodiment, the thickness of the tube is approximately 0.1 mm to approximately 10 mm, approximately 0.2 mm to approximately 8 mm, approximately 0.5 mm to approximately 7 mm, approximately 0.25 mm, approximately 0.4 mm, approximately 0.5 mm, approximately 0.7 mm, approximately 0.8 mm, approximately 1.6 mm, approximately 1.8 mm, approximately 2.1 mm, approximately 2.4 mm, approximately 3.2 mm, approximately 4 mm, approximately 4.8 mm, approximately 6.4 mm, approximately 7 mm, approximately 8 mm, approximately 9 mm, or approximately 10 mm. The size of the tube can have any combination of the above ID and thickness, as well as the corresponding surface area to volume ratio of the tube.

[0037] In one embodiment, the surface area-to-volume ratio of the tube is known. In a particular embodiment, the surface area-to-volume ratio of the tube is approximately 0.5 mm -1 ~about 5mm -1 , about 0.5mm -1 , about 0.83mm -1 , about 1mm -1 , about 1.25mm -1 , about 1.26mm -1 , about 1.5mm -1 , about 1.54mm -1 , about 1.57mm -1 , about 1.67mm -1 Approximately 2mm -1 , about 2.11mm -1 , about 2.5mm -1 , about 2.52mm -1 , about 3mm -1 , about 3.1mm -1 , about 3.15mm -1, approximately 3.33 mm -1 , approximately 3.5 mm -1 , approximately 4 mm -1 , approximately 4.12 mm -1 , approximately 4.5 mm -1 , approximately 5 mm -1 , approximately 6.25 mm -1 , approximately 6.67 mm -1 , approximately 8.0 mm -1 , approximately 13.33 mm -1 , approximately 20.0 mm -1 , or approximately 40. mm -1 is.

[0038] In one aspect, the sample volume is known. In another aspect, the density is known. In another aspect, the concentration of the excipient is known. In another aspect, the concentration of the protein is known. In a further aspect, the water activity of the sample is known. In a particular aspect, the water activity is calculated using equations 12 - 15.

[0039] In one aspect, the method further includes measuring the relative humidity. In a particular aspect, the method further includes calculating the average relative humidity using equation 16.

[0040] In one aspect, the time point is 10 seconds to 168 hours, 5 minutes to 168 hours, 3 hours to 168 hours, 6 hours to 240 hours, about 10 seconds, about 1 hour, about 6 hours, about 12 hours, about 24 hours, about 36 hours, about 48 hours, about 72 hours, about 96 hours, about 120 hours, about 144 hours, or about 168 hours, or about 240 hours. In one aspect, the manual measurements may be made at the same frequency every 5 minutes to provide additional data points, and the process may be automated to make measurements continuously and perform calculations in real time.

[0041] In one aspect, it is at least one of a tube, vinyl tube, platinum cured silicone tube, peroxide cured silicone tube, high density polyethylene (HDPE) tube, fluoropolymer tube, thermoplastic elastomer tube (TPE), or a similar thermoplastic elastomer tube material.

[0042] In one embodiment, the method further includes iteratively calculating the moisture loss at a later time point at least once using the moisture loss calculated at a first time point. In a particular embodiment, the iterative calculation is performed using equations 4 and 6.

[0043] In one embodiment, the temperature of each tube is approximately 5°C to 30°C, approximately 15°C to 30°C, approximately 15°C to 25°C, approximately 15°C to 21°C, approximately 16°C to 24°C, approximately 17°C to 23°C, approximately 18°C ​​to 21°C, approximately 5°C, approximately 6°C, approximately 7°C, approximately 8°C, approximately 9°C, approximately 10°C, approximately 11°C, approximately 12°C, approximately 13°C, approximately 14°C, approximately 15°C, approximately 16°C, approximately 17°C, approximately 18°C, approximately 19°C, approximately 20°C, approximately 21°C, approximately 22°C, approximately 23°C, approximately 24°C, approximately 25°C, approximately 26°C, approximately 27°C, approximately 28°C, approximately 29°C, or approximately 30°C.

[0044] In one embodiment, water loss is due to diffusive mass transfer.

[0045] The Disclosure further provides a method for selecting a range of retention times for a sample in a tube. In some exemplary embodiments, the method includes (a) obtaining a sample containing a protein stored in a tube, (b) using the sample and the tube to generate a model of the change in the concentration of the protein in the tube over time, and (c) selecting a range of retention times based on the predicted change in the concentration of the protein in step (b).

[0046] In one embodiment, the retention time range is selected to prevent changes in the protein concentration from exceeding a determined threshold for the rate of change of concentration. In a particular embodiment, the determined threshold for the rate of change of concentration is about 15%, about 10%, about 8%, about 5%, about 2%, or about 1%. In another particular embodiment, the determined threshold for the rate of change of concentration is about 10%.

[0047] In one embodiment, the model is generated using equations 17, 18, 20, and 21.

[0048] In one aspect, the sample is a cell culture fluid (CCF), harvested cell culture fluid (HCCF), any step in the downstream processing of a drug substance (DS), a drug substance, or a drug product (DP).

[0049] In one aspect, the inner diameter of the tube is known. In certain aspects, the inner diameter (ID) of the tube is from about 0.1 mm to about 32 mm, from about 0.2 mm to about 26 mm, from about 0.5 mm to about 16 mm, from about 0.8 mm to about 13 mm, from about 0.8 mm to about 10 mm, about 0.1 mm, about 0.2 mm, about 0.3 mm, about 0.5 mm, about 0.6 mm, about 0.8 mm, about 1 mm, about 1.2 mm, about 1.3 mm, about 1.6 mm, about 2.4 mm, about 3.2 mm, about 4.8 mm, about 6.4 mm, about 8 mm, about 9.6 mm, about 12.7 mm, about 15.9 mm, about 19 mm, about 25.4 mm, or about 31.8 mm.

[0050] In one aspect, the thickness of the tube is known. In certain aspects, the thickness of the tube is from about 0.1 mm to about 10 mm, from about 0.2 mm to about 8 mm, from about 0.5 mm to about 7 mm, about 0.25 mm, about 0.4 mm, about 0.5 mm, about 0.7 mm, about 0.8 mm, about 1.6 mm, about 1.8 mm, about 2.1 mm, about 2.4 mm, about 3.2 mm, about 4 mm, about 4.8 mm, about 6.4 mm, about 7 mm, about 8 mm, about 9 mm, or about 10 mm. The size of the tube can have any combination of the above-mentioned ID and thickness, as well as the corresponding surface area to volume ratio of the tube.

[0051] In one aspect, the surface area to volume ratio of the tube is known. In certain aspects, the surface area to volume ratio of the tube is from about 0.5 mm -1 to about 5 mm -1 , about 0.5 mm -1 , about 0.83 mm -1 , about 1 mm -1 , about 1.25 mm -1 , about 1.26 mm -1 , about 1.5 mm -1 , about 1.54 mm -1 , about 1.57 mm -1 , about 1.67 mm -1 , about 2 mm -1 , about 2.11 mm-1 , about 2.5mm -1 , about 2.52mm -1 , about 3mm -1 , about 3.1mm -1 , about 3.15mm -1 , about 3.33mm -1 , about 3.5mm -1 , about 4mm -1 Approximately 4.12 mm -1 , about 4.5mm -1 , about 5mm -1 , about 6.25mm -1 , about 6.67mm -1 Approximately 8.0 mm -1 , about 13.33mm -1 Approximately 20.0 mm -1 , or approximately 40.0 mm -1 That is the case.

[0052] In one embodiment, the sample volume, the concentration of the excipient, or the density is known.

[0053] In one embodiment, the water activity of the sample is known. In a specific embodiment, the water activity is calculated using equations 12-15.

[0054] In one embodiment, the method further includes measuring relative humidity. In a particular embodiment, the method further includes calculating mean relative humidity using Equation 16.

[0055] In one embodiment, the time points are 10 seconds to 168 hours, 5 minutes to 168 hours, 3 hours to 168 hours, 6 hours to 240 hours, approximately 10 seconds, approximately 1 hour, approximately 6 hours, approximately 12 hours, approximately 24 hours, approximately 36 hours, approximately 48 hours, approximately 72 hours, approximately 96 hours, approximately 120 hours, approximately 144 hours, or approximately 168 hours, or approximately 240 hours. In one embodiment, manual measurements may be performed at the same frequency every 5 minutes to provide additional data points, and the process may be automated to perform measurements continuously and calculations in real time.

[0056] In one embodiment, the tube is a vinyl tube, a platinum-cured silicone tube, a peroxide-cured silicone tube, a high-density polyethylene (HDPE) tube, a fluoropolymer tube, a thermoplastic elastomer tube (TPE), or a similar thermoplastic elastomer tube material.

[0057] In one embodiment, the method further includes iteratively calculating at least once the change in concentration at a later time point using the calculated change in concentration at a first time point. In a particular embodiment, the iterative calculation is performed using equations 4 and 6.

[0058] The change in concentration is calculated from the change in tube weight using Equation 21.

[0059] In one embodiment, the temperature of the tube is approximately 5°C to 30°C, approximately 15°C to 30°C, approximately 15°C to 25°C, approximately 15°C to 21°C, approximately 16°C to 24°C, approximately 17°C to 23°C, approximately 18°C ​​to 21°C, approximately 5°C, approximately 6°C, approximately 7°C, approximately 8°C, approximately 9°C, approximately 10°C, approximately 11°C, approximately 12°C, approximately 13°C, approximately 14°C, approximately 15°C, approximately 16°C, approximately 17°C, approximately 18°C, approximately 19°C, approximately 20°C, approximately 21°C, approximately 22°C, approximately 23°C, approximately 24°C, approximately 25°C, approximately 26°C, approximately 27°C, approximately 28°C, approximately 29°C, or approximately 30°C.

[0060] In one embodiment, the change in concentration is due to water loss due to diffusive mass transfer.

[0061] These and other aspects of the present invention will be better recognized and understood when considered in conjunction with the following description and accompanying drawings. The following description illustrates various embodiments and numerous specific details thereof, but these are given as examples only and are not limiting. Many substitutions, modifications, additions, or reconfigurations may be made within the scope of the present invention. [Brief explanation of the drawing]

[0062] [Figure 1]Figure 1 shows the arrangement of tubing inside a biosafety cabinet under ambient conditions according to an exemplary embodiment. [Figure 2A] Figure 2A shows the change in tube weight of tube A over time according to an exemplary embodiment. [Figure 2B] Figure 2B shows the change in tube weight of tube B over time according to an exemplary embodiment. [Figure 2C] Figure 2C shows the change in tube weight C over time according to an exemplary embodiment. [Figure 3A] Figure 3A shows the change in the concentration of mAb A over time at an initial concentration of 50 mg / mL in tubes A, B, and C, as measured by reversed-phase ultrahigh performance liquid chromatography (RP-UPLC), according to an exemplary embodiment. [Figure 3B] Figure 3B shows the change in the concentration of mAb A over time at an initial concentration of 150 mg / mL in tubes A, B, and C, as measured by reversed-phase ultrahigh performance liquid chromatography (RP-UPLC) according to an exemplary embodiment. [Figure 4] Figure 4 shows the change in tube weight (%) plotted against the change in protein concentration (%) for mAb A formulations filled in tubes A, B, and C at starting concentrations of 50 mg / mL and 150 mg / mL, according to an exemplary embodiment. [Figure 5] Figure 5 shows the change in tube weight over time based on the active pharmaceutical ingredient in tube A, according to an exemplary embodiment. [Figure 6] Figure 6 shows the change in tube weight over time based on the water activity of tube A using NaCl solution, according to an exemplary embodiment. [Figure 7] Figure 7 shows the change in tube weight over time based on the water activity of tube A using a CaCl2 solution, according to an exemplary embodiment. [Figure 8] Figure 8 shows the correlation between the rate of change in tube weight and water activity for various protein and salt solutions, water, and buffer solutions in tube A, according to an exemplary embodiment. [Figure 9] Figure 9 shows the correlation between the effective diffusion coefficient and water activity for various formulation-tube combinations according to exemplary embodiments. [Figure 10A] Figure 10A shows the predicted and experimentally obtained change in tube weight as a function of time for 0.5 mL of 50 mg / mL mAb ADS in a 0.8 mm ID tube according to an exemplary embodiment. [Figure 10B] Figure 10B shows the predicted and experimentally obtained changes in tube weight as a function of time for 3 mL of 50 mg / mL mAb ADS in a 1.2 mm ID tube according to an exemplary embodiment. [Figure 10C] Figure 10C shows the predicted and experimentally obtained changes in tube weight as a function of time for 3 mL of 50 mg / mL mAb ADS in a 3.2 mm ID tube, according to an exemplary embodiment. [Figure 10D] Figure 10D shows the predicted and experimentally obtained changes in tube weight as a function of time for 0.5 mL of 150 mg / mL mAb ADS in a 0.8 mm ID tube according to an exemplary embodiment. [Figure 10E] Figure 10E shows the predicted and experimentally obtained changes in tube weight as a function of time for 3 mL of 150 mg / mL mAb ADS in a 1.2 mm ID tube according to an exemplary embodiment. [Figure 10F] Figure 10F shows the predicted and experimentally obtained changes in tube weight as a function of time for 3 mL of 150 mg / mL mAb ADS in a 3.2 mm ID tube according to an exemplary embodiment. [Figure 10G] Figure 10G shows the predicted and experimentally obtained change in tube weight as a function of time for 0.5 mL of 175 mg / mL mAb ADS in a 0.8 mm ID tube according to an exemplary embodiment. [Figure 10H]Figure 10H shows the predicted and experimentally obtained changes in tube weight as a function of time for 3 mL of 175 mg / mL mAb ADS in a 1.2 mm ID tube according to an exemplary embodiment. [Figure 10I] Figure 10I shows the predicted and experimentally obtained changes in tube weight as a function of time for 3 mL of 175 mg / mL mAb ADS in a 3.2 mm ID tube according to an exemplary embodiment. [Figure 11] Figure 11 compares the average change in tube weight as a function of time for a C-flex tube (3.2 mm ID, 1.6 mm thickness) containing 150 mg / mL of mAb A DS, according to an exemplary embodiment, with the model-predicted change in weight for a platinum-cured silicone tube (3.2 mm ID, 1.6 mm thickness) containing 150 mg / mL of mAb A DS. [Modes for carrying out the invention]

[0063] Active pharmaceutical ingredients (DS) encounter various materials (metals, elastomers, disposable systems, etc.) during the manufacturing or filling / finishing of pharmaceutical products (DP), making it crucial to evaluate the physicochemical compatibility of the DS with these contact components. Silicone tubing is one such elastomer component used during DP manufacturing to facilitate fluid transfer and filling operations (Colas et al., “Silicone tubing for pharmaceutical processing,” DuPont, accessed February 2022).

[0064] Silicone tubing exhibits known permeability to various low molecular weight species and gases (Colas et al., Saller et al., 2017, Eur J Pharm Biopharm, 112:109-118, Eisner et al., 2019, PDA Journal of Pharmaceutical Science and Technology, 73(5):443-458). The permeability of silicone tubing to gases and organic compounds has been quantified in the literature (Zhang et al., 2006, SAMPE Fall Technical Conference, proceedings, Coatings and Sealants Section, November 6-9 2006, Dallas, TX, “Permeability of Catheter and Tubing Materials,” Instech Blog, accessed January 2022). The permeability of tubing materials used in catheters for animal research to solutions of dyes in water has also been qualitatively studied, concluding that water loss is caused by the silicone tubing (Instech Blog). However, the potential impact of water loss by silicone tubing on drug and / or excipient concentrations in the context of DP manufacturing has not been quantified or widely discussed in the literature.

[0065] During process characterization and development testing to support the technology transfer of monoclonal antibody (mAb) DP, an increase in protein concentration over time was observed while the material remained in contact with the silicone tube. Therefore, the test was designed to develop a further understanding of this phenomenon and related factors. Silicone tubes with different inner diameters and wall thicknesses were evaluated for various mAb formulations and protein concentrations. Assuming that the increase in protein concentration occurs due to water permeability through the silicone tube, the water loss rate during static retention of DS inside the tube is a function of tube parameters, particularly the inner diameter and wall thickness of the tube.

[0066] First, tube weight loss was monitored for water and DS dilution buffer (also referred to as "buffer" in subsequent texts) as controls, and for one type of mAb formulation as a test. In addition to weight loss, the protein concentration in the tubes over time was also monitored. Both changes in tube weight and protein concentration were monitored as functions of tube parameters across three different tube types. A relationship was found between changes in protein concentration and changes in tube weight. Subsequently, the weight loss of additional mAb formulations held in silicone tube types was monitored to determine the effects on the weight loss rate of (1) mAb candidates, (2) initial protein concentration, and (3) formulation composition. Next, the effect of formulation water activity on water loss rate was investigated using NaCl and CaCl2 salt solutions of various concentrations. Finally, the mechanism of weight loss in silicone tubes was investigated through diffusion-based modeling. The effective diffusion coefficient based on Fick's first law of diffusion was calculated for the tube set. A diffusion-based water loss mechanism model incorporating tube dimensions and formulation characteristics was constructed based on collected data to predict the amount of weight loss over long retention times for a given tube-formulation combination. The model was validated by monitoring water loss with mAb-filled tubes of different dimensions than those used in model construction. This effort helped facilitate robust process characterization for DP technology transfer, with the aim of designing more representative process development studies.

[0067] Unless otherwise stated, all technical and scientific terms used herein have the same meaning as those generally understood by those skilled in the art to which this invention pertains. Any methods and materials similar to or equivalent to those described herein may be used for testing, but specific methods and materials are described herein.

[0068] The term "a" should be understood to mean "at least one." Where used herein, the terms "include," "includes," and "including" are intended to be non-restrictive and should be understood to mean "comprise," "comprises," and "comprising," respectively. The terms "about" and "approximately" should be understood to allow for a standard variation of ±5%, and, where a range is provided, the endpoints should be included.

[0069] As used herein, the terms “protein” or “protein of interest” may include any amino acid polymer having covalently linked amide bonds. A protein comprises one or more amino acid polymer chains commonly known in the art as a “polypeptide.” A “polypeptide” refers to a polymer composed of amino acid residues, associated naturally occurring structural variants, and their synthetic non-natural analogs, linked via peptide bonds. “Synthetic peptide or polypeptide” refers to a non-natural peptide or polypeptide. Synthetic peptides or polypeptides can be synthesized, for example, using automated polypeptide synthesizers. Various solid-phase peptide synthesis methods are known to those skilled in the art. A protein may comprise one or more polypeptides to form a single functional biomolecule. In another exemplary embodiment, a protein may include antibody fragments, nanobodies, recombinant antibody chimeras, cytokines, chemokines, peptide hormones, and the like. A protein of interest may include any of the following: a biological therapeutic protein, a recombinant protein used in research or therapy, a trap protein and other chimeric receptor Fc fusion proteins, a chimeric protein, an antibody, a monoclonal antibody, a polyclonal antibody, a human antibody, and a bispecific antibody. The proteins may be produced using recombinant cell lineage production systems, such as insect baculovirus lines, yeast lines (e.g., Pichia genus), and mammalian lines (e.g., CHO cells and CHO derivatives such as CHO-K1 cells).For a recent review discussing biotherapeutic proteins and their production, see Ghaderi et al., “Production platforms for biotherapeutic glycoproteins. Occurrence, impact, and challenges of non-human sialylation” (Darius Ghaderi et al., Production platforms for biotherapeutic glycoproteins. Occurrence, impact, and challenges of non-human sialylation, 28 BIOTECHNOLOGY AND GENETIC ENGINEERING REVIEWS 147-176 (2012), the entirety of which is incorporated herein by reference). In some exemplary embodiments, the protein includes modifications, adducts, and other covalent moieties. Examples of these modifications, adducts, and parts include avidin, streptavidin, biotin, glycans (e.g., N-acetylgalactosamine, galactose, neuraminic acid, N-acetylglucosamine, fucose, mannose, and other monosaccharides), PEG, polyhistidine, FLAG tags, maltose-binding proteins (MBPs), chitin-binding proteins (CBPs), glutathione-S-transferase (GST) myc-epitopes, fluorescent labels, and other dyes. Proteins can be classified based on their composition and solubility, and thus may include simple proteins such as globular and fibrous proteins, complex proteins such as nucleoproteins, glycoproteins, mucoproteins, chromoproteins, phosphoproteins, metalloproteins, and lipoproteins, as well as inducible proteins such as primary and secondary inducible proteins.

[0070] As used herein, the term “recombinant protein” refers to a protein produced as a result of the transcription and translation of a gene supported on a recombinant expression vector introduced into a suitable host cell. In certain exemplary embodiments, the recombinant protein may be an antibody, e.g., a chimeric antibody, a humanized antibody, or a fully human antibody. In certain exemplary embodiments, the recombinant protein may be an antibody of an isotype selected from the group consisting of: IgG, IgM, IgA1, IgA2, IgD, or IgE. In certain exemplary embodiments, the antibody molecule may be a full-length antibody (e.g., IgG1), or the antibody may be a fragment (e.g., an Fc fragment or a Fab fragment).

[0071] The term “antibody” as used herein includes immunoglobulin molecules comprising four polypeptide chains, two heavy (H) chains and two light (L) chains interconnected by disulfide bonds, and their polymers (e.g., IgM). Each heavy chain comprises a heavy chain variable region (abbreviated herein as HCVR or VH) and a heavy chain constant region. The heavy chain constant region comprises three domains, CH1, CH2, and CH3. Each light chain comprises a light chain variable region (abbreviated herein as LCVR or VL) and a light chain constant region. The light chain constant region comprises one domain (CL1). The VH and VL regions can be further subdivided into hypervariable regions called complementarity-determining regions (CDRs), which are interspersed with more conserved regions called framework regions (FRs). Each VH and VL consists of three CDRs and four FRs arranged from the amino terminus to the carboxyl terminus in the following order: FR1, CDR1, FR2, CDR2, FR3, CDR3, and FR4. In different embodiments of the present invention, the FRs of the anti-big ET-1 antibody (or its antigen-binding moiety) may be identical to the human germline sequence or may be naturally or artificially modified. The amino acid consensus sequence may be defined based on a parallel analysis of two or more CDRs. The term “antibody” as used herein also includes the antigen-binding fragment of a complete antibody molecule. The terms “antigen-binding moiety” of an antibody, “antigen-binding fragment” of an antibody, and similar terms, as used herein, include any naturally occurring, enzymatically available, synthetic, or genetically engineered polypeptide or glycoprotein that specifically binds to an antigen to form a complex. The antigen-binding fragment of an antibody may be derived from a complete antibody molecule using any suitable standard method, such as protein digestion or recombinant genetic engineering techniques, which include the manipulation and expression of DNA encoding the antibody variable domain and optionally the constant domain. Such DNA is publicly known and / or readily available, for example, from commercial sources, DNA libraries (e.g., including phage antibody libraries), or can be synthesized.DNA can be sequenced and manipulated chemically or by using molecular biological techniques, for example, by placing one or more variable domains and / or constant domains into a suitable configuration, introducing codons, creating cysteine ​​residues, modifying, adding, or deleting amino acids.

[0072] As used herein, “antibody fragment” includes, for example, a portion of an intact antibody, such as the antigen-binding region or variable region of an antibody. Examples of antibody fragments include, but are not limited to, Fab fragments, Fab' fragments, F(ab')2 fragments, scFv fragments, Fv fragments, dsFv diabodies, dAb fragments, Fd' fragments, Fd fragments, and isolation complementarity-determining region (CDR) regions, as well as triabodies, tetrabodies, linear antibodies, single-chain antibody molecules, and multispecific antibodies formed from antibody fragments. An Fv fragment is a combination of the variable regions of the immunoglobulin heavy and light chains, and an ScFv protein is a recombinant single-chain polypeptide molecule in which the immunoglobulin light and heavy chain variable regions are linked by a peptide linker. In some exemplary embodiments, an antibody fragment comprises a sufficient amino acid sequence of the parent antibody of the fragment, which is a fragment that binds to the same antigen as the parent antibody; in some exemplary embodiments, the fragment binds to the antigen with an affinity equivalent to that of the parent antibody and / or competes with the parent antibody for binding to the antigen. Antibody fragments may be generated by any means. For example, antibody fragments may be produced enzymatically or chemically by fragmentation of an intact antibody, and / or recombinantly from a gene encoding a partial antibody sequence. Alternatively, antibody fragments may be produced entirely or partially synthetically. Antibody fragments may optionally include single-chain antibody fragments. Alternatively, antibody fragments may include multiple chains linked together, for example, by disulfide bonds. Antibody fragments may optionally include multimolecular complexes. Functional antibody fragments typically contain at least about 50 amino acids, and more typically, at least about 200 amino acids.

[0073] The term "bispecific antibody" refers to an antibody that can selectively bind to two or more epitopes. A bispecific antibody typically contains two different heavy chains, each specifically binding to a different epitope—either on two different molecules (e.g., an antigen) or on the same molecule (e.g., the same antigen). When a bispecific antibody can selectively bind to two different epitopes (a first epitope and a second epitope), the affinity of the first heavy chain to the first epitope is generally at least one to two orders of magnitude, or even three or four orders of magnitude, lower than the affinity of the first heavy chain to the second epitope, and vice versa. The epitopes recognized by a bispecific antibody can be on the same target or on different targets (e.g., on the same protein or on different proteins). A bispecific antibody can be created, for example, by combining heavy chains that recognize different epitopes of the same antigen. For example, nucleic acid sequences encoding heavy chain variable regions that recognize different epitopes of the same antigen can be fused to nucleic acid sequences encoding different heavy chain constant regions, and such sequences can be expressed in cells that express immunoglobulin light chains.

[0074] A typical bispecific antibody comprises two heavy chains, each having three heavy chain CDRs followed by a CH1 domain, a hinge, a CH2 domain, and a CH3 domain; and an immunoglobulin light chain that does not confer antigen-binding specificity but is either associable with each heavy chain, or associable with each heavy chain and capable of binding to one or more epitopes that bind to the heavy chain antigen-binding region, or associable with each heavy chain and capable of binding one or both of the heavy chains to one or both epitopes. BsAbs can be divided into two main classes: those with an Fc region (IgG-like) and those without an Fc region, the latter of which are usually smaller than IgG and IgG-like bispecific molecules that contain Fc. IgG-like bsAbs may have different forms, but are not limited to, triomab, knob-in-hole IgG (kih IgG), crossMab, orth-Fab IgG, dual-variable domain Ig (DVD-Ig), two-in-one or dual-acting Fab (DAF), IgG single-chain Fv (IgG-scFv), or κλ body. Various non-IgG-like formats include tandem scFv, diabody formats, single-stranded diabodies, tandem diabodies (TandAb), dual-affinity retargeting molecules (DART), DART-Fc, nanobodies, or antibodies generated by the Dock-and-Lock (DNL) method (Gaowei Fan, Zujian Wang & Mingju Hao, Bispecific antibodies and their applications, 8 JOURNAL OF HEMATOLOGY & ONCOLOGY 130; Dafne Muller & Roland E. Kontermann, Bispecific Antibodies, HANDBOOK OF THERAPEUTIC ANTIBODIES 265-310 (2014), the entire teachings of which are incorporated herein).Methods for generating bsAb are not limited to quadroma technology based on somatic cell fusion of two different hybridoma cell lines, chemical conjugation including chemical crosslinking agents, and genetic approaches utilizing recombinant DNA technology.

[0075] As used herein, “multispecific antibody” refers to an antibody that has binding specificity to at least two different antigens. While such molecules typically bind to only two antigens (i.e., bispecific antibodies, bsAb), antibodies with further specificity, such as triplicate antibodies and KIH triplicate antibodies, can also be addressed by the systems and methods disclosed herein.

[0076] As used herein, the term “monoclonal antibody” is not limited to antibodies produced via hybridoma technology. Monoclonal antibodies may be derived from any single clone, including any eukaryotic cell, prokaryotic cell, or phage clone, by any means available or known in the art. Monoclonal antibodies useful in this disclosure can be prepared using a wide variety of techniques known in the art, including the use of hybridoma, recombination, and phage display technologies, or combinations thereof.

[0077] As used herein, “protein drug,” “biopharmaceutical,” or “biopharmaceutical” comprises an active ingredient that may be entirely or partially biological in nature. In one embodiment, a protein drug may include peptides, proteins, fusion proteins, antibodies, antigens, vaccines, peptide-drug conjugates, antibody-drug conjugates, protein-drug conjugates, cells, tissues, or combinations thereof. In another embodiment, a protein drug may include recombinant, manipulated, modified, mutant, or cleaved forms of peptides, proteins, fusion proteins, antibodies, antigens, vaccines, peptide-drug conjugates, antibody-drug conjugates, protein-drug conjugates, cells, tissues, or combinations thereof.

[0078] As used herein, “sample” can be obtained from any step in a bioprocess, such as a cell culture medium (CCF), a harvested cell culture medium (HCCF), any step in downstream processing, a drug substance (DS), or a pharmaceutical product (DP) including the final formulation product. In some other specific exemplary embodiments, the sample may be selected from any step in downstream processing such as clarification, chromatographic generation, or filtration.

[0079] As used herein, the term “liquid chromatography” refers to a process in which a biological / chemical mixture carried by a liquid can be separated into its components as a result of the differential distribution of those components as they flow through (or flow into) a fixed liquid or solid phase. Non-limiting examples of liquid chromatography include reversed-phase liquid chromatography, ion exchange chromatography, size exclusion chromatography, affinity chromatography, hydrophobic interaction chromatography, hydrophilic interaction chromatography, or mixed-mode chromatography. In some embodiments, a sample containing at least one target protein or peptide digestion can be subjected to any one or a combination thereof of the aforementioned chromatographic methods. Analytes separated using chromatography are characterized by specific retention times that reflect the rate at which the analytes move through the chromatography column. Analytes may be compared using a chromatogram plotting retention time on one axis and a measured signal on another axis, the measured signal may be generated, for example, from UV detection or fluorescence detection.

[0080] This disclosure provides, for example, methods for predicting water loss from a sample, methods for predicting changes in protein concentration, methods for selecting a range of retention times for a protein-containing sample in a tube, and methods for selecting a tube based on the predicted water loss, using formulas 1 to 21 described herein. Naturally, embodiments and aspects described herein may relate to any of these described methods.

[0081] In some exemplary embodiments, the sample is water, buffer, cell culture medium (CCF), collected cell culture medium (HCCF), any step in the downstream processing of the active pharmaceutical ingredient (DS), the active pharmaceutical ingredient, or the drug (DP). In some specific embodiments, the drug includes a therapeutic protein. In further specific embodiments, the therapeutic protein is an antibody, monoclonal antibody, bispecific antibody, fusion protein, receptor, antibody-drug conjugate, or antibody fragment.

[0082] In some exemplary embodiments, the inner diameter of the tube is known. In some exemplary embodiments, the inner diameter of the tube is approximately 0.1 mm to approximately 32 mm, approximately 0.2 mm to approximately 26 mm, approximately 0.5 mm to approximately 16 mm, approximately 0.8 mm to approximately 13 mm, approximately 0.8 mm to approximately 10 mm, approximately 0.1 mm, approximately 0.2 mm, approximately 0.3 mm, approximately 0.5 mm, approximately 0.6 mm, approximately 0.8 mm, approximately 1 mm, approximately 1.2 mm, approximately 1.3 mm, approximately 1.6 mm, approximately 2.4 mm, approximately 3.2 mm, approximately 4.8 mm, approximately 6.4 mm, approximately 8 mm, approximately 9.6 mm, approximately 12.7 mm, approximately 15.9 mm, approximately 19 mm, approximately 25.4 mm, or approximately 31.8 mm.

[0083] In some exemplary embodiments, the tube thickness is known. In some exemplary embodiments, the tube thickness is about 0.1 mm to about 10 mm, about 0.2 mm to about 8 mm, about 0.5 mm to about 7 mm, about 0.25 mm, about 0.4 mm, about 0.5 mm, about 0.7 mm, about 0.8 mm, about 1.6 mm, about 1.6 mm, about 2.1 mm, about 2.4 mm, about 3.2 mm, about 4 mm, about 4.8 mm, about 6.4 mm, about 7 mm, about 8 mm, about 9 mm, or about 10 mm. The tube size can have any combination of the above ID and thickness, as well as the corresponding surface area to volume ratio of the tube.

[0084] In one embodiment, the surface area-to-volume ratio of the tube is known. In a particular embodiment, the surface area-to-volume ratio of the tube is approximately 0.5 mm -1 ~about 5mm -1 , about 0.5mm -1 , about 0.83mm -1 , about 1mm -1 , about 1.25mm-1 , about 1.26mm -1 , about 1.5mm -1 , about 1.54mm -1 , about 1.57mm -1 , about 1.67mm -1 Approximately 2mm -1 , about 2.11mm -1 , about 2.5mm -1 , about 2.52mm -1 , about 3mm -1 , about 3.1mm -1 , about 3.15mm -1 , about 3.33mm -1 , about 3.5mm -1 , about 4mm -1 Approximately 4.12 mm -1 , about 4.5mm -1 , about 5mm -1 , about 6.25mm -1 , about 6.67mm -1 Approximately 8.0 mm -1 , about 13.33mm -1 Approximately 20.0 mm -1 , or approximately 40.0 mm -1 That is the case.

[0085] In some exemplary embodiments, the water activity of the sample is known. In some exemplary embodiments, the water activity of the sample is approximately 0.7 to 1, approximately 0.8 to 1, approximately 0.85 to 1, approximately 0.9 to 1, approximately 0.95 to 1, approximately 0.95 to 0.99, approximately 0.7, approximately 0.71, approximately 0.72, approximately 0.73, approximately 0.74, approximately 0.75, approximately 0.76, approximately 0.77, approximately 0.78, approximately 0.79, and approximately 0. 80, approximately 0.81, approximately 0.82, approximately 0.83, approximately 0.84, approximately 0.85, approximately 0.86, approximately 0.87, approximately 0.88, approximately 0.89, approximately 0.90, approximately 0.91, approximately 0.92, approximately 0.93, approximately 0.94, approximately 0.95, approximately 0.96, approximately 0.97, approximately 0.98, approximately 0.985, approximately 0.99, approximately 0.995, or approximately 1.

[0086] In some exemplary embodiments, the method further includes measuring relative humidity. In some exemplary embodiments, the relative humidity is about 35% to about 65%, about 40% to about 50%, about 35%, about 36%, about 37%, about 38%, about 39%, about 40%, about 41%, about 42%, about 43%, about 44%, about 45%, about 46%, about 47%, about 48%, about 49%, about 50%, about 51%, about 52%, about 53%, about 54%, about 55%, about 56%, about 57%, about 58%, about 59%, about 60%, about 61%, about 62%, about 63%, about 64%, or about 65%.

[0087] In some exemplary embodiments, the time points are 10 seconds to 168 hours, 5 minutes to 168 hours, 3 hours to 168 hours, 6 hours to 240 hours, about 10 seconds, about 1 hour, about 6 hours, about 12 hours, about 24 hours, about 36 hours, about 48 hours, about 72 hours, about 96 hours, about 120 hours, about 144 hours, or about 168 hours, or about 240 hours. In one embodiment, manual measurements may be performed at the same frequency every 5 minutes to provide additional data points, and the process may be automated to perform measurements continuously and calculations in real time.

[0088] In some exemplary embodiments, the tubing is platinum-cured silicone tubing. Examples of exemplary tubing include, for example, Masterflex tubing with the following catalog numbers: 96410-14, 96410-15, 96410-25, C-flex® tubing from Saint-Gobain (374-125-2), Watson Accusil® silicone tubing from Watson-Marlow Limited, and any other tubing that may be used for the storage, transport, or processing of samples. It should be understood that the present invention is not limited to the aforementioned tubing. The principle of the present invention, namely water loss by diffusive mass transfer through polymer tubing, may be applied to any potentially porous tubing material, and therefore the method of the present invention is not limited to tubing made of silicone. Similarly, the same principle of water loss by diffusive mass transfer through polymer surfaces is applicable to any aqueous sample, and is not limited to samples containing proteins or pharmaceuticals.

[0089] The acceptable range of retention time for a sample in a tube may be determined by using predictions of changes in protein concentration at some point in time or several points in time. The threshold may be determined as the maximum acceptable rate of change in protein concentration for a given process or a particular step in the process, and the range of retention time for which the predicted change in protein concentration falls below the threshold may be determined. In some exemplary embodiments, the threshold for the maximum acceptable rate of change in protein concentration during retention time is about 15%, about 14%, about 13%, about 12%, about 11%, about 10%, about 9%, about 8%, about 7%, about 6%, about 5%, about 4%, about 3%, about 2%, about 1%, or about 0.1%. In certain embodiments, the threshold for the maximum acceptable rate of change in protein concentration during retention time is about ±10%.

[0090] It is understood that the present invention can be selected by any appropriate means, without being limited to any of the aforementioned proteins, target proteins, antibodies, samples, sample volumes, tubes, chromatographic methods, databases, bioinformatics tools, pH, temperature, or concentration.

[0091] The present invention will be better understood by referring to the following embodiments. However, they should not be construed as limiting the scope of the invention. [Examples]

[0092] Materials. The materials used include: Water for Injection (WFI) (USP sterile grade, Intermountain Life Sciences), L-histidine (USP grade, Ph. Eur. grade, Ajinomoto USA Inc.), L-histidine monohydrochloride monohydrate (Ph. Eur. grade, Ajinomoto USA Inc.), L-proline (USP grade, Ph. Eur. grade, Ajinomoto USA Inc.), L-arginine hydrochloride (USP grade, Ph. Eur. grade, Avantor Performance Chemicals), ultra-purified polysorbate 80 (10% w / w, sourced in-house), mAb A DS (150 mg / mL, Regeneron Pharmaceuticals), mAb B DS (120 mg / mL, Regeneron Pharmaceuticals), mAb C DS (100 mg / mL, Regeneron Pharmaceuticals), mAb D DS (175 mg / mL, Regeneron Pharmaceuticals) The formulations include (Pharmaceuticals), trifluoroacetic acid (TFA, Honeywell, biosynthesis, HPLC grade), acetonitrile (UV grade, Honeywell), monobasic sodium phosphate (ACS grade, JTBaker), dibasic sodium phosphate, heptahydrate, crystals (ACS grade, JTBaker), sodium chloride (ACS grade, JTBaker), calcium chloride (ACS grade, Spectrum Chemical), and ethanol (200 proof, Koptec). Note that the formulation composition varied between mAb A and D. The compositions used in the tests are shown in Table 1.

[0093] [Table 1]

[0094] The following platinum-cured silicone peristaltic pump tubing (Masterflex) with catalog numbers were used: 96410-14 (tube A), 96410-15 (tube B), 96410-25 (tube C), and C-flex® tubing, manufactured by Saint-Gobain (374-125-2). Flexicon Accusil® silicone tubing (part numbers: 84-103-012, 84-103-008, 84-103-032) from Watson-Marlow Limited was also used. The tubing was cut into pieces long enough to hold 3 mL of liquid, autoclaved at 250°F for 20 minutes, and then dried for 30 minutes before use. Flexicon 0.8 mm ID tubing (part number: 84-103-008) was cut into pieces long enough to hold 0.5 mL to facilitate handling of the tubing length. All prepared solutions were filtered through a sterile Stericup® Quick Release Durapore® 0.22 μm polyvinylidene fluoride (PVDF) filter unit (Millipore) before use.

[0095] Instrument: A Mettler Toledo XSE205 DualRange balance was used to weigh the tubes and measure potential water loss. Three weights were recorded for each tube at each collection point, and the average value was used for further analysis.

[0096] Reverse-phase ultrahigh performance liquid chromatography (RP-UPLC) analysis was performed using a Waters Acquity UPLC system with an Agilent Technologies Zorbax 300 SB-CN column and an adjustable UV detector to measure protein concentrations. Two mobile phases were prepared for RP-UPLC: 0.1% TFA in water (solvent A) and 0.1% TFA in acetonitrile (solvent B). A gradient method was used, with 90% solvent A and 10% solvent B for 1 minute, followed by 10% solvent A and 90% solvent B for 5.4 minutes, and then 90% solvent A and 10% solvent B for 9 minutes. The total flow rate was maintained at 1 mL / min, and the run time was 5 minutes. The column temperature was maintained at 60°C, and the detection wavelength was maintained at 280 nm. Three injections were performed for each sample for accuracy.

[0097] The osmolar concentrations of the mAb A formulation and buffer were recorded using a Vapro® 5600 vapor pressure osmometer. Measurements were performed three times for accuracy. Air ratio data was recorded using a TES 1340 hot-wire anemometer. Relative humidity data was obtained by Regeneron's facility management department using a VWR Traceable® hygrometer (catalog no. 35519-050) hygrometer.

[0098] Data analysis. Necessary statistical analyses were performed using JMP® statistical software. The weight change data obtained from the experiment were fitted to Fick's first law of diffusion (Bird et al., 1960, “Transport Phenomena,” John Wiley and Sons, Inc.) to obtain the effective diffusion coefficient at each time point, as shown in Equation 2. The following calculations were involved in the diffusion-based modeling. Fick's first law, shown in Equation 1, was used as the basis.

[0099]

number

[0100] By rearranging Equation 1, we can obtain Equation 2.

[0101]

number

[0102] Equation 2

number

[0103]

number

[0104]

number

[0105]

number

[0106]

number

[0107] Water concentration gradient (Equation 2)

number

[0108]

number

[0109]

number

[0110]

number

[0111]

number

[0112] Here,

number

number

[0113] Substituting equations 8a and 8b into equation 7 yields equations 9a and 9b.

[0114]

number

[0115]

number

[0116]

number

[0117] Overall, substituting equations 7-10 into equation 2 yields equation 11.

[0118]

number

[0119] Equations 12-15 are,

number

number

number

number

number

[0120]

number

[0121] [Number]

[0122] [Number]

[0123] [Number]

[0124] Equation 16 is for the ambient water activity [Number] uses the relative humidity in the atmosphere that describes the calculation of. The relative humidity is averaged over a time interval [Number] and is averaged over.

[0125] [Number]

[0126] t = time point during the test, 0 < t ≤ 96 hours (hours), [Number]

[0127] In these calculations, the following assumptions were made: (1) The weight of water lost is equal to the volume of the solution lost in the tube because the density of water is 1 g / mL.

[0128] (2) For protein / buffer solutions, the concentrations of the protein and excipient are calculated using the dilution method, assuming that the total weight of the protein and excipient is constant, since water is the only diffusive component (for salt solutions, the dilution method is used, assuming that salt is the only excipient and its weight is constant over time). (3) For protein / buffer solutions, the initial osmolality is experimentally known, and the osmolality of the solution at subsequent times is directly proportional to the concentrations of the protein and excipient present in the solution at that time. (4) The ambient water activity can be estimated using the mean relative humidity of a given time interval instead of the instantaneous relative humidity at each time point, and the mean relative humidity is calculated as the average of the relative humidity reported at the two ends of the time interval.

[0129] The effective diffusion coefficients obtained at each time point for each combination of tube formulations were used for further mechanism modeling. The effective diffusion coefficient values ​​obtained using Equation 11 at each test time point were averaged over all time points from 0 to 96 hours to obtain the overall effective diffusion coefficient for each formulation and tube type.

[0130] mAb A buffer preparation. A buffer was prepared as a control and for subsequent dilution of mAb A DS. The buffer consisted of 10 mM histidine, 70 mM arginine-HCl, 3% w / w proline, and 0.1% w / w polysorbate 80 added to WFI, with a pH of 6.0 ± 0.2. This was filtered through a 0.22 μm PVDF filter after preparation.

[0131] Preparation of mAb A formulation. A diluted formulation of mAb A at the desired concentration (50 mg / mL) was prepared from the mAb A DS (150 mg / mL) obtained at that time. The required amount of DS was mixed with the required amount of buffer using a sterile pipette. The formulation was filtered through a 0.22 μm PVDF filter before use.

[0132] Preparation of salt solutions. NaCl and CaCl2 solutions of various concentrations were prepared in Milli-Q water by weight. The salts were completely dissolved to ensure complete dissolution. The concentrated CaCl2 solution generated heat after preparation and was cooled completely before use. Table 7 lists the concentrations of the prepared NaCl and CaCl2 solutions.

[0133] Study setup. First, five tube sets were prepared: a water-filled, buffer-filled, and empty tube set as a control; a mAb A 50 mg / mL filled set; and a mAb A 150 mg / mL filled set. Each tube set consisted of three tube types: A, B, and C. One tube of each type (A, B, and C), along with an empty tube, was prepared for water and buffer. Four tubes of each type (A, B, and C), corresponding to four collection time points, were prepared for each of the two formulations. Each tube piece, excluding the tube in the empty set, was filled with 3 mL of solution using a syringe, and the ends of the tubes were sealed with cable ties. The tubes were placed in a biosafety cabinet at ambient temperature (approximately 22°C) throughout the study. Air circulation in the biosafety cabinet was stopped during the study. First, the weight of all tubes was recorded at 0 hours. Subsequently, the weights of the mAb A 50 mg / mL and mAb A 150 mg / mL filled tubes were recorded at four predetermined time intervals: 24, 48, 72, and 96 hours. The solutions were collected from the tubes and stored in frozen tubes at 5°C until further analysis of protein concentration by RP-UPLC. The weights of the water, buffer, and empty tubes were recorded at each point in time when the tubes were returned to the biosafety cabinet. The test setup for the formulations of water, buffer, mAb A 150 mg / mL, and mAb A 50 mg / mL in the tubes is shown in Figure 1. One tube piece of each type was used for the water and buffer control set, while four tube pieces of each type corresponding to the four time points were used for the formulation set. Three weights per tube were recorded.

[0134] For all formulation tube combinations used in subsequent experiments (0.8mm ID, 1.2mm ID, 3.2mm ID, or mAb B-D in tubes filled with tube A), one tube piece was filled with either 3 mL of formulation (1.2mm ID, 3.2mm ID, or tube A) or 0.5 mL of formulation (0.8mm ID). The weight of this tube was triplicately monitored at four time points over 96 hours for mAb A, water, and buffer formulation, without collecting any samples from the tube for further analysis. The tube was returned to the biosafety cabinet after each weighing. Air circulation in the biosafety cabinet was turned off for all tests. Manual weighing may have been performed at the same frequency every 5 minutes to provide additional data points, and the process may be automated to perform measurements continuously and calculate in real time.

[0135] Throughout the entire test, the temperature inside the biosafety cabinet was approximately 22°C, and the air velocity was measured to be approximately 0.000–0.002 m / s near the tube with the airflow turned off.

[0136] Example 1. Change in tube weight over time First, water loss through silicone tubing filled with controls (water, buffer) and mAb A DS (50 mg / mL and 150 mg / mL) was investigated. Previous literature predicted that water loss through silicone tubing could occur over time due to the permeable nature of the tubing (Instech Blog). Mass transfer of water from the inside to the outside of the tubing was expected to depend on the difference in water activity, the surface area-to-volume ratio (SA / V) of the tubing, and the resistance to molecular diffusion. The mass transfer rate within the tubing was expected to increase with increasing SA / V and decreasing resistance to diffusion provided by the tubing wall thickness. Table 2 lists the physical parameters relevant to each type of tubing used in the tests. Table 2 describes the physical parameters of the tubing used in tests involving water, buffer, and mAb A formulations, including tubing inner diameter (ID), wall thickness, and surface area-to-volume ratio (SA / V), which can be calculated based on the tubing ID. All tubing was platinum-cured silicone peristaltic pump tubing purchased from MasterFlex. A constant fill volume of 3 mL was used for all tubing. Tubes A and C have the same wall thickness, and tubes B and C have the same SA / V. It was assumed that the mass transfer velocity was highest for tube A, which has the largest SA / V, followed by tube C, which has the smaller thickness, and slowest for tube B.

[0137] [Table 2]

[0138] Mass transfer rate or water loss rate can be estimated by the change in tube weight over time. Therefore, the weight of each tube set was analyzed as a function of time. The recorded weights as a function of time for water, buffer, mAb A 150 mg / mL DS, and mAb A 50 mg / mL DS filled tube sets are listed in Tables 3 and 4. The weight of empty tubes was also monitored over time as a negative control. The difference between the initial weight and the current weight at various time points for empty tubes (types A, B, and C) was found to be less than 0.1%. For other tube sets and types, a decrease in weight over time was observed.

[0139] For Table 3, the weights of the tubing sets containing water, buffer, and empty tubing were recorded from 0 to 96 hours after setup. Three tubing types (A, B, and C) were used in the test. One tubing of each type was used per set. Weights were recorded at 24, 48, 72, and 96 hours after test setup. Three weights were recorded for each tubing, and the mean and standard deviation are reported. The tubing was kept in a biosafety cabinet at ambient temperature (approximately 22°C) throughout the test. Relative humidity data was recorded internally by Regeneron's facility management department.

[0140] For Table 4, the weights of the tube sets for formulations mAb A 50 mg / mL DS and mAb A 150 mg / mL DS were recorded from 0 to 96 hours after setup. Three tube types (A, B, and C) were used in the study. One tube of each type was dedicated to each time point, resulting in four tubes of each type for 24, 48, 72, and 96 hours. At the start of the study, the initial weight of each tube was recorded. Weights were also recorded at the specified time points for each tube after the study setup; for example, the weight of the tube dedicated to 72 hours was recorded only at the study setup and at 72 hours. Three weights were recorded for each tube, and the mean and standard deviation were reported. The tubes were placed in a biosafety cabinet at ambient temperature (approximately 22°C) throughout the study. Relative humidity data was recorded internally by Regeneron's facility management department.

[0141] [Table 3]

[0142] [Table 4]

[0143] For four tube sets containing water, buffer, mAb A 50 mg / mL DS, and mAb A 150 mg / mL DS, the difference between the initial weight and the weight over a maximum of 96 hours was plotted against time for each tube type A, B, and C, as shown in Figures 2A, 2B, and 2C, respectively. Weights were recorded at 24, 48, 72, and 96 hours after the test setup. Each tube set consisted of three tube types. One tube piece of each type was used for the water and buffer control sets, while four tube pieces of each type corresponding to the four time points were used for the formulation sets. Three weights were recorded for each tube, the average weight was plotted, and error bars were plotted using the standard deviation. The tubes were maintained at ambient temperature (approximately 22°C) throughout the test. Relative humidity data was recorded internally by Regeneron's facility management department. Air circulation in the biosafety cabinet was turned off.

[0144] The points representing the change in tube weight for all four plotted sets were observed to overlap with each other for tubes A, B, and C, suggesting that the rate of weight change is equivalent for the four types of solutions for a given tube type. To estimate the rate of change in tube weight, linear regression was performed on the data plotted in Figures 2A, 2B, and 2C, obtained from all four sets for each tube type. The slope, intercept, and coefficient of determination (R) obtained for three tube types were calculated. 2 The results are reported in Table 5. All four solution sets were considered in the regression for each tube type. A high R > 0.9 for each fit. 2As evidenced by the values, linear fit was observed to be acceptable for all tube types. Overall, it was concluded that the rate of change in tube weight depended only on the tube type and was independent of the initial mAb concentration. Furthermore, the rate of change in weight obtained for water and buffer controls was comparable to that obtained for the mAb formulation. This observation confirms that the loss of tube weight over time is due to water loss by the tubes, and that water is the only common component in the contents of all four tube sets.

[0145] [Table 5]

[0146] Furthermore, for the four tube sets, the average rate of weight change for tubes of types A, B, and C was observed to be 0.0075 g / hour, 0.0019 g / hour, and 0.0026 g / hour, respectively. This observation suggests that the water loss rate was highest in tube A, which has a higher SA / V compared to tubes B and C, and higher in tube C, which has a similar SA / V but a smaller wall thickness compared to tube B. Overall, these results are consistent with the hypothesis that the water loss rate depends on the SA / V and wall thickness of the tubes.

[0147] Example 2. Changes in protein concentration of mAb A DS over time. The water loss rate through the silicone tubing was directly estimated from the percentage change in tubing weight, as discussed in previous examples. The water loss rate could also be indirectly estimated by analyzing the mAb A protein concentration as a function of time for mAb A DS-filled tubing sets. The change in protein concentration (%) obtained via RP-UPLC as a function of time for tubing A, B, and C containing mAb A 50 mg / mL DS and mAb A 150 mg / mL DS-filled tubing sets was plotted in Figure 3. Each tubing set consisted of three tubing types: A, B, and C. RP-UPLC analysis was performed at 0, 24, 48, 72, and 96 hours after the test setup. Three injections were performed per tubing. The mean and standard deviation of each reading were plotted. The tubing was maintained at ambient temperature (approximately 22°C) throughout the test. Air circulation in the biosafety cabinet was turned off.

[0148] Protein concentration was observed to increase over time for all tubes. The rate of increase in protein concentration, given by the slope of the plot in Figure 3, was highest for tube A, followed by tube C, and lowest for tube B, for both mAb A formulations. This trend supports the hypothesis that tube A, having the highest SA / V, would experience a higher water loss rate compared to tubes B and C, which would further correspond to a higher rate of increase in protein concentration. Interestingly, the rate of increase in protein concentration was equivalent for both mAb A formulations for a given tube type, as seen by the equivalent slopes, suggesting that changes in both tube weight and protein concentration (%) are independent of the formulation composition.

[0149] The percentage change in tube weight was plotted against the percentage change in protein concentration for all tube types and for both mAb A formulation sets with starting concentrations of 50 mg / mL and 150 mg / mL, as shown in Figure 4. The percentage change in protein concentration was calculated by dividing the difference between the initial protein concentration and the percentage of concentration at a given time by the initial concentration of the given formulation. The percentage change in weight corresponds to the initial solution volume of 3 mL filled in each tube. Protein concentration was analyzed using RP-UPLC. Three injections were given per tube piece, and the average was plotted. Three weight measurements were also performed per tube piece at a given time.

[0150] The rate of change in tube weight appeared to change linearly with the rate of change in protein concentration. Linear regression was applied to the combined data using JMP®, and the significance of the slope was analyzed. The results are shown in Table 6.

[0151] [Table 6]

[0152] The p-value obtained from the analysis of variance was observed to be smaller than the significance level (0.05), suggesting that the linear model is significant. Furthermore, the slope obtained from the fitting also has a p-value lower than the significance level, suggesting that the slope is significant.

[0153] These results suggest that the relative change in protein concentration per unit mass of lost water is comparable for both mAb formulations and all tube types. From the linear fit obtained for all data, it was concluded that the same mechanism in all tubes leads to water loss over time, confirming that water loss is the primary driving factor for changes in protein concentration. Furthermore, these results suggest that changes in tube weight may indicate changes in protein concentration and can be used as a tracker. Therefore, a subsequent analysis of changes in tube weight was performed.

[0154] Example 3. Effect of protein type on water loss by tubes As described in the previously mentioned examples, the weight loss rate in the tube was found to be independent of the mAb A concentration and to be due to water loss by the tube. To support this conclusion, it was further hypothesized that the water loss rate is also independent of the type of mAb filled in the tube. The following formulations, having various protein concentrations and formulation compositions, were separately filled into tube A pieces: mAb B DS, 120 mg / mL; mAb C DS, 100 mg / mL; mAb D DS, 175 mg / mL. The change in tube weight over time was measured for mAb B DS, mAb C DS, and mAb D DS, and the tube weight was monitored for up to 96 hours after setup. The change in tube weight as a function of time for the various formulations is plotted in Figure 5 along with the previously obtained change in weight for mAb A formulations at concentrations of 50 mg / mL and 150 mg / mL in tube A. Weights were recorded at 24, 48, 72, and 96 hours after the test setup. All data are shown for the formulations filled in tube A. Three weights were recorded for each tube, the average weight was plotted, and error bars were plotted using the standard deviation. The tubes were maintained at ambient temperature (approximately 22°C) throughout the experiment. Relative humidity data was recorded internally by Regeneron's facility management department. Air circulation in the biosafety cabinet was turned off. Note that the mean relative humidity over 96 hours was comparable between the run duration of previously conducted experiments using water, buffer, and mAb A DS (48%) and experiments including other mAbs (52%), allowing for comparisons between datasets.

[0155] The weight changes observed for all formulations overlap, suggesting that the weight change of the tube is independent of protein type and concentration. Furthermore, it should be noted that the same weight changes obtained for low to moderate protein concentrations DS (mAb A-C) also occur for high concentration mAb D DS. Overall, it can be concluded that the water loss rate by the tube is independent of protein concentration, protein type, and formulation type. Therefore, the method of the present invention is not limited to a specific protein or protein concentration, but can be applied to samples containing any target protein at any concentration.

[0156] Example 4. Effect of water activity on water loss by tubes The water activity of a formulation determines the concentration of available "free" water in the tube and therefore can affect the water loss rate. The effect of formulation water activity on water loss rate was investigated for salt solutions of NaCl and CaCl2 prepared at specified concentrations. Solutions of NaCl and CaCl2 at various concentrations were prepared in Milli-Q water over various initial water activities, and 3 mL of each was packed into separate A-piece tubes. The initial water activity of all solutions was first calculated by calculating the freezing point depression of the solution from the theoretically calculated osmolal concentration of the solution and feeding the freezing point depression into the Hildebrand-Scott equation (Equation 15) (Muchiwaki et al.). Table 7 shows the concentrations (by weight) of the NaCl and CaCl2 solutions, the calculated initial osmolal concentrations, and the corresponding initial calculated water activities from the Hildebrand-Scott equation prepared to test the effect of water activity on water loss over time by tubes packed with these salt solutions. The tubes were placed in a biosafety cabinet at ambient temperature (approximately 22°C) throughout the test. Relative humidity data was recorded internally by Regeneron's facility management department. Airflow in the biosafety cabinet was turned off. The change in tube weight over 96 hours was measured at predetermined points in time. Three weights were recorded for each tube, and the average weight was plotted using the standard deviation, with error bars plotted. The change in tube weight as a function of time for solutions with varying water activity is shown for the NaCl solution in Figure 6 and the CaCl2 solution in Figure 7, and plotted together with the weight change data for pure water, buffer, and mAb A formulations (50 mg / mL and 150 mg / mL) held in tube A obtained from previous tests. Note that the average relative humidity over 96 hours was comparable between the run-through period of the test conducted in Example 1 (48%) and the salt solution test in Example 4 (44%), allowing for comparison between the datasets.

[0157] For all NaCl and CaCl2 solutions, collectively, aw チューブThe percentage change in tube weight accompanied by tube water activity at <0.988 was observed for mAb A formulations (for mAb A 150 mg / mL DS, aw チューブ =0.991, mAb A, 50 mg / mL DS (aw tube =0.992), water (aw チューブ =1), and buffer (aw チューブ It was found to be different from (=0.993). The water loss rate increased with increasing water activity in both NaCl and CaCl2 solutions.

[0158] Next, the weight change rates obtained from the slopes in Figures 6 and 7 for the NaCl and CaCl2 salt solutions, and from the slope in Figure 2 for the mAb A protein solution, buffer, and water held in tube A, were plotted as a function of the initial water activity calculated by the Hildebrand-Scott equation, as shown in Figure 8. For all solutions, R was approximately 0.96. 2 A linear relationship was found between the weight loss rate and the initial water activity. Therefore, it was concluded that the water loss rate is a linear function of the initial water activity, regardless of the properties of the solute.

[0159] Furthermore, Figure 6 shows that the weight change rate of the NaCl-filled tubes has a weak dependence on water activity exceeding the initial activity value of 0.988. From Table 7, the corresponding osmolality of a 1.91% (w / w) NaCl solution with a water activity of 0.988 is 667 mOsm / kg. This value is relatively high compared to the typical average osmolality of protein formulations used for parenteral administration to maintain isotonic conditions (Banks et al., 2018, ProteinScience, 27(12):2073-2083). Therefore, it can be concluded that the effect of water activity on the water loss rate in the highly active protein formulations used in this study is expected to be negligible. Nevertheless, water activity is considered an important parameter in determining the water loss rate in subsequent modeling calculations (Equations 1-16).

[0160] [Table 7]

[0161] Example 5. Mechanism modeling of moisture loss using tubes The mass transfer of water originating from a silicone tube is expected to occur primarily through diffusion in nature, given the absence of bulk fluid flow, pressure, or other convective sources. Fick's first law (Bird et al.) is assumed to explain this mass transfer phenomenon and is used to develop a mechanism model that can estimate the weight loss occurring in a formulation-filled tube. The development of this mechanism model is useful for explaining the data obtained from this experiment and will also be beneficial for future applications such as small-scale process development testing and large-scale filling operations.

[0162] The following steps were performed for the mechanism modeling of Fick's first law: (1) First, the effective diffusion coefficient (D) for the tube under test was generated using experimental data. Water activity using Fick's first law (Equation 11) and the Hildebrand-Scott equation (Equation 15) was calculated for each time interval and combination of formulation tubes investigated in the tests of Examples 1 and 4. The tests included combinations of tube formulations such as tubes A, B, and C containing water, buffer, and mAb A formulation, and tube A containing NaCl and CaCl2 solutions at various concentrations, respectively. (2) D and water activity (aw チューブ An empirical relationship (referred to as Equation 17) between ) was established from combination data from these formulation-tube combinations, and the variability of D was taken into account in Equation 17 by applying a 99% prediction interval, (3) then, using Equation 20, D and aw チューブ The moisture loss rate was predicted using the empirical relationship obtained for . Finally, the weight change Δt over a given period (Equations 18-21, Equations 1-16) was calculated using Equation 18, and (4) Model validation was performed with D and aw チューブPerformed using tubes with different IDs and wall thicknesses than those used to develop the relationship with. The tube weight was experimentally recorded over time and also calculated using the derived model. The upper and lower limits of the calculated moisture loss range obtained were compared with the moisture loss obtained experimentally for specific combinations of mAb tubes.

[0163] Report the effective diffusion constant (D) calculated from the experimental data at each time point described in Step 1, along with the corresponding moisture activity, for each of tubes A, B, C containing water, buffer, mAb A 50 mg / mL DS, and mAb A 150 mg / mL DS, and (2) for each tube A containing NaCl and CaCl2 solutions, in Table 8.

[0164] Report the average D of the mAb A, buffer, and water sets for each tube type in Table 9, along with the standard deviation. Also report the overall average D across all four formulations and three tube types in Table 9. The average effective diffusion coefficient was calculated from the effective diffusion coefficients obtained for the four formulation types of water, buffer, mAb A 50 mg / mL DS, and mAb A 150 mg / mL DS.

[0165]

Table 8-1

Table 8-2

Table 8-3

[0166]

Table 9

[0167] The average effective diffusion coefficient of all tubes is 9.5*10 -13 m 2 / s, and 10-11- 10- 1 3 m2 The diffusivity of water through porous membranes or materials of approximately 1 / s was observed to be comparable to literature values ​​(Fasano et al., 2016, Nat Commun, 7:12762, Hoch et al., 2003, Journal of Membrane Science, 214(2):199-209).

[0168] Next, the effective diffusion coefficient values ​​obtained for the protein and salt solutions were plotted against the water activity at all time points for each combination of tube formulations. As shown in Figure 9, D and aw チューブ Linear regression was performed between [the specified values]. Furthermore, the 99% prediction intervals for individual predicted values ​​D are also shown by shaded areas and plotted in Figure 9 using JMP®. チューブ Table 10 shows the fitting parameters related to linear regression between D and aw. The formulation tube combinations include mAb A (50 mg / mL and 15 mg / mL) DS, water, and buffer held in tubes A, B, and C, as well as salt solutions of various concentrations (NaCl and CaCl2) held in tube A. The effective diffusion coefficient and water activity values ​​were calculated for each formulation tube combination at various time points. Linear regression was performed using JMP®. The p-values ​​related to ANOVA were found to be <0.0001 compared to the significance level of 0.05, suggesting that the linear fit was significant. This was supported by the p-values ​​of <0.0001 related to the slope of the fit. チューブ The following relationship was established between them:

[0169]

number

[0170] Upper and lower 99% prediction limits were also established, coupled to the shaded region shown in Figure 9. The resulting linear relationships are shown in Table 11. The equations are D and aw in Figure 9. チューブIt is derived from the linear regression performed among. In the generation of the plots, data points such as mAb A (50 mg / mL and 15 mg / mL) DS, water, and buffer solution held in tubes A, B, and C; and various concentrations of salt solutions (NaCl and CaCl2) held in tube A were used.

[0171]

Table 10

[0172]

Table 11

[0173] Next, between D and aw チューブ Using these relationships between and, the upper and lower limits of the expected weight loss by the tube were calculated as a function of time for the dimensions and formulation characteristics of a given tube. An iterative process was used to calculate the weight loss after a specified time interval. The assumptions described in the data analysis section were used. Equation 18 shows the model used.

[0174]

Equation

[0175] Here,

Equation

[0176] Substitute Equations 3 and 5 for Δweight(t) in Equation 18,

[0177]

Equation

[0178] Where,

Equation

[0179]

number

[0180] Here, D(t) was established using experimental data in Equation 17.

number

[0181] The approach used in the mechanism modeling of the expected weight loss over interval Δt is to calculate B' at time t using equation 20 and apply it in equation 18. In the test setup (time = t0), using known solution osmolality, equations 14 and 15 are used to calculate aw チューブ Calculate the relative humidity of the ambient air over a time interval Δt, and calculate aw according to Equation 16. 周囲雰囲気 Provides the following: Using known filling solution volume and tube ID, calculate the surface area exposed to tube 4V / ID using Equation 5. D and aw are listed in Table S6. チューブ Using the relationship between the upper and lower bounds, aw チューブ The upper and lower limits of D were calculated as a function of . Setting Δt = t1 to t0, these parameters are supplied to equations 18 and 20, yielding the upper and lower limits of weight loss from the test setup t0 to time t1.

[0182] Next, using the upper and lower weight losses over (t1 to t0) time, the updated solution volume at time t1 is calculated using equations 4 and 6. Using the updated solution volume, the updated surface area of ​​the solution in contact with the tube is calculated using equation 5. Incorporating equations 12-15, the aw of the solution at time t1 is calculated. チューブ This is calculated. Using the relationship in Table S6, a new aw is created to calculate D at time t1. チューブ Use aw. 周囲雰囲気 The calculations are performed during the period from t1 to t2 hours according to the method used in the previous paragraph. Thus, the upper and lower limits of the expected weight loss from t1 to t2 hours can be calculated. These calculations may be repeated iteratively until the end of the test to construct the upper and lower limits of the weight loss profile over time for a given formulation-tube combination. Manual measurements may be performed at the same frequency every 5 minutes to provide additional data points, or the process may be automated to perform measurements continuously and calculations in real time. The additional data points may be used to verify and construct a detailed weight loss profile.

[0183] The change in tube weight can be converted into a change in protein concentration using the following relationship.

[0184]

number

[0185] Example 6. Model Verification The mechanism model constructed in Example 5 was tested by comparing the calculations with experimentally measured weight losses using platinum-cured silicone tubing. The following tubing was used for verification: 0.8 mm ID tubing with a wall thickness of 1.6 mm ID; 1.2 mm ID tubing with a wall thickness of 1.6 mm ID; and 3.2 mm ID tubing with a wall thickness of 1.8 mm ID. Three formulations, each containing two types of mAbs and ranging from various protein concentrations (mAb A DS (50 mg / mL), mAb A DS (150 mg / mL), and mAb D DS (175 mg / mL)), were filled into each type of tubing. Overall, the following nine combinations of formulation tubes were analyzed: (a) 0.5 mL of mAb A (50 mg / mL) DS in a 0.8 mm ID tube, (b) 3 mL of mAb A (50 mg / mL) DS in a 1.2 mm ID tube, (c) 3 mL of mAb A (50 mg / mL) DS in a 3.2 mm ID tube, (d) 0.5 mL of mAb A (150 mg / mL) DS in a 0.8 mm ID tube, (e) 3 mL of mAb A (150 mg / mL) DS in a 1.2 mm ID tube, (f) 3 mL of mAb A (150 mg / mL) DS in a 3.2 mm ID tube, (g) 0.5 mL of mAb D (175 mg / mL) DS in a 0.8 mm ID tube, (h) 3 mL of mAb D (175 mg / mL) DS in a 1.2 mm ID tube, and (i) 3 mL of mAb in a 3.2 mm ID tube. The study included D(175 mg / mL)DS. Each formulation was filled into a tube, sealed, and placed in a biosafety cabinet with air circulation and light turned off. The weight of each tube was measured at the time of the test setup and then every 24 hours thereafter. Tubes a-c and g-i were monitored for a maximum of 168 hours, and tubes d-f were monitored for a maximum of 96 hours. Three weight measurements were performed. In parallel, the theoretically expected upper and lower weight loss limits as a function of time based on initial mAb characteristics and filling volume were calculated for each formulation tube combination using a mechanism model. Relative humidity measured during the test period was averaged every 24 hours as shown in Equation 16 and used to estimate theoretical weight loss.

[0186] The predicted and experimental weight loss ranges were plotted for each time point in the test for nine formulation tube combinations, as shown in Figure 10. All weight losses were normalized to a starting volume of 3 mL, regardless of the actual volume filled at the start. Each plot shows a shaded area correlated with the expected range of tube weight loss, and the theoretical weight loss limit is calculated using the 99% predicted level of the effective water diffusion coefficient. Corresponding experimental data are plotted as black scattering crossovers. Calculated and experimental weights are also listed in Tables 11A-C. Weights were recorded at 24, 48, 72, and 96 hours after the test setup for Figures 10A-10C and 10G-10I, and further every 24 hours for Figures 10D-10F, up to a maximum of 168 hours. The average of the three recorded weights is plotted for each tube, and the standard deviation is plotted as error bars. The tubes were placed in a biosafety cabinet at ambient temperature (approximately 22°C) throughout the test. Relative humidity data was recorded internally and used for data processing. The relative humidity measured during the test was averaged every 24 hours to calculate the theoretical weight change. Air circulation inside the biosafety cabinet was turned off.

[0187] [Table 12]

[0188] [Table 13]

[0189] [Table 14]

[0190] The experimental weight loss was found to fall within the range of model-derived weight loss for all formulation tube combinations at each time point, as shown in Figure 10. This suggests that the experimental and calculated weight losses align across a range of protein concentrations, and that experimental water loss occurring over long-term retention periods from formulation-filled platinum-cured silicone tubes can be successfully predicted using the derived mechanism model based on Fick's first law. Furthermore, it should be noted that the model derivation and validation were performed using platinum-cured silicone tubes from different manufacturers. The alignment between experimental and predicted weight changes suggests that the tube bender does not affect the water loss rate when the same material is used. It should be noted that additional factors, including temperature and airflow that were not precisely controlled, may also affect the water loss rate.

[0191] Example 8. Influence on the moisture loss rate of the tube structure material. Changing the tubing material can affect the water diffusion rate depending on the permeability of the material. Previous studies testing the water evaporation rate from catheters made of various materials have found that silicone is highly permeable compared to materials including polyurethane and polyethylene (Instech Blog). Therefore, it was hypothesized that platinum-cured silicone tubing would be more permeable to water than, for example, C-Flex tubing (polymer thermoplastic elastomer). This hypothesis was tested by studying the weight loss in C-Flex tubing (3.2 mm ID, 1.6 mm thickness) filled with mAb A DS at a protein concentration of 150 mg / mL. The tubing was filled in two ways. Three weights per tubing were recorded. The average observed change in weight of the C-Flex tubing was compared to the range of weight change predicted through a diffusion-based model for platinum-cured silicone tubing filled with mAb A 150 mg / mL DS of comparable dimensions (3.2 mm ID, 1.6 mm thickness). Using a 99% prediction interval, the comparison is shown in Figure 11. Error bars for the C-flex tube were plotted using the standard deviation of the weights of the two tubes. The tubes were placed in a biosafety cabinet at ambient temperature (approximately 22°C) with airflow turned off throughout the test. Relative humidity data was recorded internally by Regeneron's facility management department.

[0192] The weight change of the C-Flex tube was found to be considerably lower than the predicted weight change range for Pt-cured silicone tubes of similar dimensions. Overall, this result suggests that the permeability of Pt-cured silicone to water is higher than that of C-Flex tubes. Therefore, compared to Pt-cured silicone, the use of C-Flex material during filling may reduce moisture loss by the tubes during the retention period. This result demonstrates that the present invention can be used to select containers based on reducing the predicted moisture loss of the sample. This result further demonstrates that the method of the present invention can be applied to any permeable material used for tubes or containers.

[0193] Silicone tubing is primarily used in the pharmaceutical industry for several unit operations, and therefore, determining its effect on protein formulations is beneficial for pharmaceutical process development. Silicone tubing is known to be semipermeable, and moisture diffusion can occur through it. We hypothesized that the moisture loss rate through platinum-cured silicone tubing is a function of tubing parameters. We monitored the weight of platinum-cured silicone tubing filled with several mAb formulations. Changes in protein concentration as a function of time were also analyzed for some tubing. The above examples confirm that moisture loss occurs from the protein formulation over the retention time through the silicone tubing, as evidenced by weight loss and increased protein concentration. Furthermore, the moisture loss rate is independent of protein type, concentration, and other typical solutes dissolved in the formulation. It was also observed that the moisture loss rate increased with decreasing tubing ID and wall thickness. A relationship linking changes in protein concentration to changes in tubing weight was also derived from the data and found to be independent of protein concentration.

[0194] Next, the effect of formulation water activity on water loss rates was tested using NaCl and CaCl2 salt solutions of various weight concentrations. It was found that high water activity (>0.988), which is typically associated with protein formulations, had only a slight effect on water loss rates. However, for low water activity formulations, water loss rates decreased with decreasing water activity.

[0195] The mechanism of water loss was assumed to be via the diffusion of water through the tube wall, according to Fick's first law of diffusion. Using Fick's first law, the average effective diffusion coefficient of water through tubes containing protein formulations and salt solutions was calculated. The relationship between the effective diffusion coefficient and water activity of these solutions was derived. This relationship, along with known formulation properties and tube parameters, was used to develop a diffusion-based mechanism model to capture experimental water loss data. The applicability of the constructed model was tested by studying experimentally obtained water loss in additional platinum-cured silicone tubes with dimensions not used to derive the model for several tube formulation combinations spanning a wide range of protein concentrations. The experimental water loss was compared to the theoretical upper and lower limits of water loss derived using the model. It was observed that the experimental water loss for all tubes fell within the boundaries calculated using the model, suggesting that the model can successfully explain the water loss arising from formulation-filled platinum-cured silicone tubes for a given formulation and tube combination.

[0196] This study highlights some of the factors influencing the water loss rate in protein formulation-filled platinum-cured silicone tubing subjected to long-term retention and attempts to explain the amount of water lost based on diffusive mass transfer. It should be noted that further investigation is needed into environmental factors, including ambient temperature and airflow around the tubing, that may affect the water loss rate. Overall, these findings suggest that water loss by silicone tubing and its impact on protein concentration should be considered during filling and retention, small-scale material compatibility testing, and related biopharmaceutical process development and characterization work.

Claims

1. A method for predicting water loss from a protein-containing sample at a given point in time, (a) Obtain a sample containing protein stored in a tube, (b) Using the sample and the tube, generate a model of the water lost from the sample in the tube over time, (c) A method comprising using the model to predict the amount of water lost from the sample at a given time.

2. The method according to claim 1, wherein the model is generated using formulas 17, 18, and 20.

3. The method according to claim 1, wherein the sample is a cell culture medium (CCF), a harvested cell culture medium (HCCF), any step in the downstream processing of a drug substance (DS), a drug substance, or a pharmaceutical product (DP).

4. The method according to claim 1, wherein the inner diameter of the tube is known.

5. The method according to claim 4, wherein the inner diameter of the tube is approximately 0.1 mm to approximately 32 mm, approximately 0.2 mm to approximately 26 mm, approximately 0.5 mm to approximately 16 mm, approximately 0.8 mm to approximately 13 mm, approximately 0.8 mm to approximately 10 mm, approximately 0.1 mm, approximately 0.2 mm, approximately 0.3 mm, approximately 0.5 mm, approximately 0.6 mm, approximately 0.8 mm, approximately 1 mm, approximately 1.2 mm, approximately 1.3 mm, approximately 1.6 mm, approximately 2.4 mm, approximately 3.2 mm, approximately 4.8 mm, approximately 6.4 mm, approximately 8 mm, approximately 9.6 mm, approximately 12.7 mm, approximately 15.9 mm, approximately 19 mm, approximately 25.4 mm, or approximately 31.8 mm.

6. The method according to claim 1, wherein the thickness of the tube is known.

7. The method according to claim 6, wherein the thickness of the tube is approximately 0.1 mm to approximately 10 mm, approximately 0.2 mm to approximately 8 mm, approximately 0.5 mm to approximately 7 mm, approximately 0.25 mm, approximately 0.4 mm, approximately 0.5 mm, approximately 0.7 mm, approximately 0.8 mm, approximately 1.6 mm, approximately 1.8 mm, approximately 2.1 mm, approximately 2.4 mm, approximately 3.2 mm, approximately 4 mm, approximately 4.8 mm, approximately 6.4 mm, approximately 7 mm, approximately 8 mm, approximately 9 mm, or approximately 10 mm.

8. The method according to claim 1, wherein the surface area to volume ratio of the tube is known.

9. The surface area to volume ratio of the tube is about 0.5 mm －１ to about 5 mm －１ about 0.5 mm －１ about 0.83 mm －１ about 1 mm －１ about 1.25 mm －１ about 1.26 mm －１ about 1.5 mm －１ about 1.54 mm －１ about 1.57 mm －１ about 1.67 mm －１ about 2 mm －１ about 2.11 mm －１ about 2.5 mm －１ about 2.52 mm －１ about 3 mm －１ about 3.1 mm －１ about 3.15 mm －１ about 3.33 mm －１ about 3.5 mm －１ about 4 mm －１ about 4.12 mm －１ about 4.5 mm －１ about 5 mm －１ about 6.25 mm －１ about 6.67 mm －１ about 8.0 mm －１ about 13.33 mm －１ about 20.0 mm －１ or about 40.0 mm －１ The method according to claim 8, wherein it is so.

10. The method according to claim 1, wherein at least one of the following properties is known: sample volume, excipient concentration, or density.

11. The method according to claim 1, wherein the concentration of the protein is known.

12. The method according to claim 1, wherein the water activity of the sample is known.

13. The method according to claim 12, wherein the water activity is calculated using formulas 12 to 15.

14. The method according to claim 1, further comprising measuring the relative humidity.

15. The method according to claim 14, further comprising calculating the mean relative humidity using formula 16.

16. The method according to claim 1, wherein the aforementioned time is between 10 seconds and 168 hours.

17. The method according to claim 1, wherein the tube is a vinyl tube, a platinum-cured silicone tube, a peroxide-cured silicone tube, a high-density polyethylene (HDPE) tube, a fluoropolymer tube, or a thermoplastic elastomer tube (TPE).

18. The method according to claim 1, further comprising iteratively calculating the moisture loss at a later time point at least once using the moisture loss calculated at a first time point.

19. The method according to claim 18, wherein the iterative calculation is performed using equations 4 and 6.

20. The method according to claim 1, wherein the temperature of the tube is approximately 5°C to approximately 30°C, approximately 15°C to approximately 30°C, approximately 15°C to approximately 25°C, approximately 15°C to approximately 21°C, approximately 16°C to approximately 24°C, approximately 17°C to approximately 23°C, approximately 18°C ​​to approximately 21°C, approximately 5°C, approximately 6°C, approximately 7°C, approximately 8°C, approximately 9°C, approximately 10°C, approximately 11°C, approximately 12°C, approximately 13°C, approximately 14°C, approximately 15°C, approximately 16°C, approximately 17°C, approximately 18°C, approximately 19°C, approximately 20°C, approximately 21°C, approximately 22°C, approximately 23°C, approximately 24°C, approximately 25°C, approximately 26°C, approximately 27°C, approximately 28°C, approximately 29°C, or approximately 30°C.

21. The method according to claim 1, wherein the moisture loss is due to diffusible mass transfer.

22. A method for predicting changes in protein concentration at a given point in time, (a) Obtain a sample containing protein stored in a tube, (b) Using the sample and the tube, generate a model of the change in the concentration of the protein in the tube over time, (c) A method comprising using the model to predict a change in the concentration of the protein at a given time.

23. The method according to claim 22, wherein the model is generated using formulas 17, 18, 20, and 21.

24. The method according to claim 22, wherein the sample is a cell culture medium (CCF), a harvested cell culture medium (HCCF), any step in the downstream processing of a drug substance (DS), a drug substance, or a pharmaceutical product (DP).

25. The method according to claim 22, wherein the inner diameter of the tube is known.

26. The method according to claim 25, wherein the inner diameter of the tube is approximately 0.1 mm to approximately 32 mm, approximately 0.2 mm to approximately 26 mm, approximately 0.5 mm to approximately 16 mm, approximately 0.8 mm to approximately 13 mm, approximately 0.1 mm, approximately 0.2 mm, approximately 0.3 mm, approximately 0.5 mm, approximately 0.6 mm, approximately 0.8 mm, approximately 1 mm, approximately 1.2 mm, approximately 1.3 mm, approximately 1.6 mm, approximately 2.4 mm, approximately 3.2 mm, approximately 4.8 mm, approximately 6.4 mm, approximately 8 mm, approximately 9.6 mm, approximately 12.7 mm, approximately 15.9 mm, approximately 19 mm, approximately 25.4 mm, or approximately 31.8 mm.

27. The method according to claim 22, wherein the thickness of the tube is known.

28. The method according to claim 27, wherein the thickness of the tube is approximately 0.1 mm to approximately 10 mm, approximately 0.2 mm to approximately 8 mm, approximately 0.5 mm to approximately 7 mm, approximately 0.25 mm, approximately 0.4 mm, approximately 0.5 mm, approximately 0.7 mm, approximately 0.8 mm, approximately 1.6 mm, approximately 2.1 mm, approximately 2.4 mm, approximately 3.2 mm, approximately 4 mm, approximately 4.8 mm, approximately 6.4 mm, approximately 7 mm, approximately 8 mm, approximately 9 mm, or approximately 10 mm.

29. The method according to claim 22, wherein the surface area to volume ratio of the tube is known.

30. The surface area-to-volume ratio of the tube is approximately 0.5 mm －１ ~about 5mm －１ , about 0.5mm －１ , about 0.83mm －１ , about 1mm －１ , about 1.25mm －１ , about 1.26mm －１ , about 1.5mm －１ , about 1.54mm －１ , about 1.57mm －１ , about 1.67mm －１ Approximately 2 mm －１ , about 2.11mm －１ , about 2.5mm －１ , about 2.52mm －１ , about 3mm －１ , about 3.1mm －１ , about 3.15mm －１ , about 3.33mm －１ , about 3.5mm －１ , about 4mm －１ Approximately 4.12 mm －１ , about 4.5mm －１ , about 5mm －１ , about 6.25mm －１ , about 6.67mm －１ Approximately 8.0 mm －１ , about 13.33mm －１ Approximately 20.0 mm －１ , or approximately 40.0 mm －１ The method according to claim 29.

31. The method according to claim 22, wherein at least one of the following properties is known: sample volume, excipient concentration, or density.

32. The method according to claim 22, wherein the water activity of the sample is known.

33. The method according to claim 32, wherein the water activity is calculated using formulas 12 to 15.

34. The method according to claim 22, further comprising measuring the relative humidity.

35. The method according to claim 34, further comprising calculating the mean relative humidity using formula 16.

36. The method according to claim 22, wherein the aforementioned time interval is 10 seconds to 168 hours, 5 minutes to 168 hours, 3 hours to 168 hours, 6 hours to 240 hours, approximately 10 seconds, approximately 1 hour, approximately 6 hours, approximately 12 hours, approximately 24 hours, approximately 36 hours, approximately 48 hours, approximately 72 hours, approximately 96 hours, approximately 120 hours, approximately 144 hours, or approximately 168 hours, or approximately 240 hours.

37. The method according to claim 22, wherein the tube is a vinyl tube, a platinum-cured silicone tube, a peroxide-cured silicone tube, a high-density polyethylene (HDPE) tube, a fluoropolymer tube, or a thermoplastic elastomer tube (TPE).

38. The method according to claim 22, further comprising iteratively calculating at least once a change in concentration at a later time point using the calculated change in concentration at a first time point.

39. The method according to claim 38, wherein the iterative calculation is performed using formulas 4 and 6.

40. The method according to claim 22, wherein the temperature of the tube is approximately 5°C to approximately 30°C, approximately 15°C to approximately 30°C, approximately 15°C to approximately 25°C, approximately 15°C to approximately 21°C, approximately 16°C to approximately 24°C, approximately 17°C to approximately 23°C, approximately 18°C ​​to approximately 21°C, approximately 5°C, approximately 6°C, approximately 7°C, approximately 8°C, approximately 9°C, approximately 10°C, approximately 11°C, approximately 12°C, approximately 13°C, approximately 14°C, approximately 15°C, approximately 16°C, approximately 17°C, approximately 18°C, approximately 19°C, approximately 20°C, approximately 21°C, approximately 22°C, approximately 23°C, approximately 24°C, approximately 25°C, approximately 26°C, approximately 27°C, approximately 28°C, approximately 29°C, or approximately 30°C.

41. The method according to claim 22, wherein the change in concentration is due to water loss due to diffusible mass transfer.

42. A method for selecting a tube for a sample containing protein, (a) Obtain a sample containing protein stored in at least two tubes, (b) Using the sample and the tubes, generate a model of the water lost from the sample over time in each of the tubes, (c) A method comprising selecting a tube based on less predicted moisture loss in step (b).

43. The method according to claim 42, wherein the model is generated using formulas 17, 18, and 20.

44. The method according to claim 42, wherein the sample is a cell culture medium (CCF), a harvested cell culture medium (HCCF), any step in the downstream processing of a drug substance (DS), a drug substance, or a pharmaceutical product (DP).

45. The method according to claim 42, wherein the inner diameter of each tube is known.

46. The method according to claim 45, wherein the inner diameter of each tube is approximately 0.1 mm to approximately 32 mm, approximately 0.2 mm to approximately 26 mm, approximately 0.5 mm to approximately 16 mm, approximately 0.8 mm to approximately 13 mm, approximately 0.1 mm, approximately 0.2 mm, approximately 0.3 mm, approximately 0.5 mm, approximately 0.6 mm, approximately 0.8 mm, approximately 1 mm, approximately 1.2 mm, approximately 1.3 mm, approximately 1.6 mm, approximately 2.4 mm, approximately 3.2 mm, approximately 4.8 mm, approximately 6.4 mm, approximately 8 mm, approximately 9.6 mm, approximately 12.7 mm, approximately 15.9 mm, approximately 19 mm, approximately 25.4 mm, or approximately 31.8 mm.

47. The method according to claim 42, wherein the thickness of each tube is known.

48. The method according to claim 47, wherein the thickness of each tube is approximately 0.1 mm to approximately 10 mm, approximately 0.2 mm to approximately 8 mm, approximately 0.5 mm to approximately 7 mm, approximately 0.25 mm, approximately 0.4 mm, approximately 0.5 mm, approximately 0.7 mm, approximately 0.8 mm, approximately 1.6 mm, approximately 2.1 mm, approximately 2.4 mm, approximately 3.2 mm, approximately 4 mm, approximately 4.8 mm, approximately 6.4 mm, approximately 7 mm, approximately 8 mm, approximately 9 mm, or approximately 10 mm.

49. The method according to claim 42, wherein the surface area to volume ratio of each tube is known.

50. The surface area to volume ratio of each tube is from about 0.5 mm －１ to about 5 mm －１ about 0.5 mm －１ about 0.83 mm －１ about 1 mm －１ about 1.25 mm －１ about 1.26 mm －１ about 1.5 mm －１ about 1.54 mm －１ about 1.57 mm －１ about 1.67 mm －１ about 2 mm －１ about 2.11 mm －１ about 2.5 mm －１ about 2.52 mm －１ about 3 mm －１ about 3.1 mm －１ about 3.15 mm －１ about 3.33 mm －１ about 3.5 mm －１ about 4 mm －１ about 4.12 mm －１ about 4.5 mm －１ about 5 mm －１ about 6.25 mm －１ about 6.67 mm －１ about 8.0 mm －１ about 13.33 mm －１ about 20.0 mm －１ or about 40.0 mm －１ The method according to claim 49.

51. The method according to claim 42, wherein at least one of the following properties is known: sample volume, excipient concentration, or density.

52. The method according to claim 42, wherein the concentration of the protein is known.

53. The method according to claim 42, wherein the water activity of the sample is known.

54. The method according to claim 53, wherein the water activity is calculated using formulas 12 to 15.

55. The method according to claim 42, further comprising measuring the relative humidity.

56. The method according to claim 55, further comprising calculating the mean relative humidity using formula 16.

57. The method according to claim 42, wherein the aforementioned time interval is 10 seconds to 168 hours, 5 minutes to 168 hours, 3 hours to 168 hours, 6 hours to 240 hours, approximately 10 seconds, approximately 1 hour, approximately 6 hours, approximately 12 hours, approximately 24 hours, approximately 36 hours, approximately 48 hours, approximately 72 hours, approximately 96 hours, approximately 120 hours, approximately 144 hours, or approximately 168 hours, or approximately 240 hours.

58. The method according to claim 42, wherein at least one of the tubes is a vinyl tube, a platinum-cured silicone tube, a peroxide-cured silicone tube, a high-density polyethylene (HDPE) tube, a fluoropolymer tube, or a thermoplastic elastomer tube (TPE).

59. The method according to claim 42, further comprising iteratively calculating the moisture loss at a later time point at least once using the moisture loss calculated at a first time point.

60. The method according to claim 59, wherein the iterative calculation is performed using equations 4 and 6.

61. The method according to claim 42, wherein the temperature of each of the tubes is approximately 5°C to approximately 30°C, approximately 15°C to approximately 30°C, approximately 15°C to approximately 25°C, approximately 15°C to approximately 21°C, approximately 16°C to approximately 24°C, approximately 17°C to approximately 23°C, approximately 18°C ​​to approximately 21°C, approximately 5°C, approximately 6°C, approximately 7°C, approximately 8°C, approximately 9°C, approximately 10°C, approximately 11°C, approximately 12°C, approximately 13°C, approximately 14°C, approximately 15°C, approximately 16°C, approximately 17°C, approximately 18°C, approximately 19°C, approximately 20°C, approximately 21°C, approximately 22°C, approximately 23°C, approximately 24°C, approximately 25°C, approximately 26°C, approximately 27°C, approximately 28°C, approximately 29°C, or approximately 30°C.

62. The method according to claim 42, wherein the moisture loss is due to diffusible mass transfer.

63. A method for selecting a range of retention times for a sample in a tube, (a) Obtain a sample containing protein stored in a tube, (b) Using the sample and the tube, generate a model of the change in the concentration of the protein in the tube over time, A method comprising (c) selecting a range of retention times based on the predicted change in the concentration of the protein in step (b).

64. The method according to claim 63, wherein the range of retention time is selected to prevent changes in the concentration of the protein from exceeding a determined threshold of the rate of change of concentration.

65. The method according to claim 64, wherein the threshold for the determined rate of change in concentration is about 15%, about 10%, about 8%, about 5%, about 2%, or about 1%.

66. The method according to claim 65, wherein the threshold for the determined rate of change in concentration is approximately 10%.

67. The method according to claim 63, wherein the model is generated using formulas 17, 18, 20, and 21.

68. The method according to claim 63, wherein the sample is a cell culture medium (CCF), a harvested cell culture medium (HCCF), any step in the downstream processing of a drug substance (DS), a drug substance, or a pharmaceutical product (DP).

69. The method according to claim 63, wherein the inner diameter of the tube is known.

70. The method according to claim 69, wherein the inner diameter of the tube is approximately 0.1 mm to approximately 32 mm, approximately 0.2 mm to approximately 26 mm, approximately 0.5 mm to approximately 16 mm, approximately 0.8 mm to approximately 13 mm, approximately 0.1 mm, approximately 0.2 mm, approximately 0.3 mm, approximately 0.5 mm, approximately 0.6 mm, approximately 0.8 mm, approximately 1 mm, approximately 1.2 mm, approximately 1.3 mm, approximately 1.6 mm, approximately 2.4 mm, approximately 3.2 mm, approximately 4.8 mm, approximately 6.4 mm, approximately 8 mm, approximately 9.6 mm, approximately 12.7 mm, approximately 15.9 mm, approximately 19 mm, approximately 25.4 mm, or approximately 31.8 mm.

71. The method according to claim 63, wherein the thickness of the tube is known.

72. The method according to claim 71, wherein the thickness of the tube is approximately 0.1 mm to approximately 10 mm, approximately 0.2 mm to approximately 8 mm, approximately 0.5 mm to approximately 7 mm, approximately 0.25 mm, approximately 0.4 mm, approximately 0.5 mm, approximately 0.7 mm, approximately 0.8 mm, approximately 1.6 mm, approximately 2.1 mm, approximately 2.4 mm, approximately 3.2 mm, approximately 4 mm, approximately 4.8 mm, approximately 6.4 mm, approximately 7 mm, approximately 8 mm, approximately 9 mm, or approximately 10 mm.

73. The method according to claim 63, wherein the surface area to volume ratio of the tube is known.

74. The surface area to volume ratio of the tube is about 0.5 mm －１ to about 5 mm －１ about 0.5 mm －１ about 0.83 mm －１ about 1 mm －１ about 1.25 mm －１ about 1.26 mm －１ about 1.5 mm －１ about 1.54 mm －１ about 1.57 mm －１ about 1.67 mm －１ about 2 mm －１ about 2.11 mm －１ about 2.5 mm －１ about 2.52 mm －１ about 3 mm －１ about 3.1 mm －１ about 3.15 mm －１ about 3.33 mm －１ about 3.5 mm －１ about 4 mm －１ about 4.12 mm －１ about 4.5 mm －１ about 5 mm －１ about 6.25 mm －１ about 6.67 mm －１ about 8.0 mm －１ about 13.33 mm －１ about 20.0 mm －１ or about 40.0 mm －１ The method according to claim 73, wherein it is so.

75. The method according to claim 63, wherein at least one of the following properties is known: sample volume, excipient concentration, or density.

76. The method according to claim 63, wherein the water activity of the sample is known.

77. The method according to claim 76, wherein the water activity is calculated using formulas 12 to 15.

78. The method according to claim 63, further comprising measuring the relative humidity.

79. The method according to claim 78, further comprising calculating the mean relative humidity using formula 16.

80. The method according to claim 63, wherein the aforementioned time interval is 10 seconds to 168 hours, 5 minutes to 168 hours, 3 hours to 168 hours, 6 hours to 240 hours, approximately 10 seconds, approximately 1 hour, approximately 6 hours, approximately 12 hours, approximately 24 hours, approximately 36 hours, approximately 48 hours, approximately 72 hours, approximately 96 hours, approximately 120 hours, approximately 144 hours, or approximately 168 hours, or approximately 240 hours.

81. The method according to claim 63, wherein the tube is a vinyl tube, a platinum-cured silicone tube, a peroxide-cured silicone tube, a high-density polyethylene (HDPE) tube, a fluoropolymer tube, or a thermoplastic elastomer tube (TPE).

82. The method according to claim 63, further comprising iteratively calculating at least once a change in concentration at a later time point using the calculated change in concentration at a first time point.

83. The method according to claim 82, wherein the iterative calculation is performed using equations 4 and 6.

84. The method according to claim 63, wherein the temperature of the tube is approximately 5°C to approximately 30°C, approximately 15°C to approximately 30°C, approximately 15°C to approximately 25°C, approximately 15°C to approximately 21°C, approximately 16°C to approximately 24°C, approximately 17°C to approximately 23°C, approximately 18°C ​​to approximately 21°C, approximately 5°C, approximately 6°C, approximately 7°C, approximately 8°C, approximately 9°C, approximately 10°C, approximately 11°C, approximately 12°C, approximately 13°C, approximately 14°C, approximately 15°C, approximately 16°C, approximately 17°C, approximately 18°C, approximately 19°C, approximately 20°C, approximately 21°C, approximately 22°C, approximately 23°C, approximately 24°C, approximately 25°C, approximately 26°C, approximately 27°C, approximately 28°C, approximately 29°C, or approximately 30°C.

85. The method according to claim 63, wherein the change in concentration is due to water loss due to diffusible mass transfer.

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