Method of purification of biological molecules

Abstract

The present invention relates to a method for purification of a biomolecule from an impure sample comprising at least one contaminant; the method involves conducting a series of reverse-phase high performance liquid chromatography (HPLC) analyses of the impure sample using a mobile phase comprising water and an organic solvent with linear gradient elution at a range of gradients to obtain values for the median retention factor k* and solvent composition at peak elution (I) for said biomolecule and said at least one contaminant.

Description

[0001] Method of Purification of Biological Molecules Acknowledgement of Support

[0002] This work was supported by the Prosperity Partnerships and the Engineering and Physical Sciences Research Council (EPSRC) under grant reference EP / T005556 / 1.

[0003] Introduction

[0004] Emerging in the mid-20th century with the invention of liquid chromatography (LC), the development of gradient elution methods was a response to the advances in analytical chemistry that required more refined and efficient methods for chemical component separation. Early gradient elution methods were characterised by manual control and reliance on simple binary solvent systems. However, with the progression of technology, automated systems capable of handling complex, multisolvent gradients became the standard1. Today, linear gradient elution methods are the technique of first choice in various LC modes, including reversed-phase (RPLC), ion-exchange chromatography (IEC)2-4, hydrophilic interaction liquid chromatography (HILIC)5’6, and supercritical fluid chromatography (SFC)7’9. This utilisation includes use at both analytical and process scales of operation. It has also found utility in less common techniques where isocratic is the standard elution profile, such as size exclusion chromatography (SEC)10.

[0005] As chemical sample complexity increases and the demand for shorter separation times grows and improved separation performance, researchers have explored alternative elution profiles beyond the traditional linear binary solvent gradients.

[0006] These alternatives encompass adaptive gradients, such as nonlinear gradients (concave, convex, logarithmic, and power function-based), ternary gradients, one-segment-per-component gradients, and step gradients. Among these, step gradients are most frequently employed at both laboratory and manufacturing scales. This preference is attributed to their ability to decrease separation time without demanding extensive optimisation. This efficiency makes step gradient methods a practical choice in settings where time and resource management are crucial.

[0007] Isocratic-based elution profiles, such as multi-isocratic gradients, have also been proposed. However, a comprehensive understanding of these more complex elution profiles for bio-molecules remains an area of ongoing research. Exploring thesealternative elution profiles could advance the field, offering promising avenues for future research and application.

[0008] Fekete et al. introduced a novel method for separating large biomolecules using reversed-phase liquid chromatography (RPLC)11-13. This method employs a tailored multi-isocratic elution profile to separate subunits of IgG monoclonal antibodies and antibody-drug conjugates (ADCs). The technique is based on the on / off adsorption mechanism, in which large molecules / solutes strongly bind onto the column and elute with minimal resistance when subjected to slight variations in the organic content of the mobile phase. The combination of isocratic binding steps and steep gradient eluting segments allows for arbitrary selectivity, with the length of the isocratic steps enabling manipulation of selectivity and peak spacing.

[0009] Since antibodies and ADCs undergo an extensive series of purification steps during manufacturing14, RPLC methods are only used to differentiate positional isomers. These isomers typically exhibit peak resolution challenges during a standard linear gradient method. However, the use of a multi-isocratic method enhanced selectivity between closely related isomers. This type of elution profile could potentially be applied to more complex and intricate samples containing closely related chemical impurities from product synthesis. Synthetic peptides, for instance, exhibit similar on-and-off adsorption behaviour, suggesting that this technique could be applied to peptide separations.

[0010] While peptide adsorption onto liquid chromatographic resin is less sensitive to mobile phase composition than proteins due to their smaller size and simpler structures, the complexity of samples obtained from solid-phase peptide synthesis (SPPS) is closely tied to the sequence of the peptide, which is the main active pharmaceutical ingredient (API) and its closely-related impurities within the reaction mixture.

[0011] Impurities in SPPS-synthesized peptides arise from amino acid deletions, inefficient Fmoc-deprotection, racemization, incomplete removal of protecting groups, side chain reactions, oxidation, dimeric / oligomeric impurities, and unwanted peptide counter ions. Contamination with unrelated peptides can also occur due to inadequate GMP practices. Peptides also degrade via mechanisms like (3-elimination, diketopiperazine, pyroglutamate, and succinimide formation. Rigorous attention should be paid to the purification method in order to separate such complex samples.When transitioning chromatographic methods from one system to another (scale-up or scale-down), several factors are crucial to ensuring a successful transition and efficient separation of target compounds at the new scale. It is essential to understand the fundamentals of the separation mechanism employed in a robust chromatographic method at a determined scale and assess its applicability at a different scale. This implies the correct determination of scalable and non-scalable parameters in the process, the former being those that can be multiplied by an appropriate linear scale factor and optimised to reach a similar separation efficiency as the original method. Scalable parameters include column dimensions, flow rate, and column loading (injection mass). Column loading is normally used to choose appropriate column dimensions. Optimising the mobile phase flow rate ensures the LC system can handle the increased flow, pressure, and dead volumes. Non-scalable factors are intricate elements that determine the separation mechanism, including the choice of mobile phase components (solvents and additives) and the column resin. Particle size and pore size of the chromatographic media significantly impact the separation efficiency and resolution; therefore, they must be carefully selected to match the separation requirements. Additionally, system volumes, gradient profiles, and temperature control are critical aspects that can influence the reproducibility and performance of the scaled method. Understanding the interaction between these scalable and non-scalable parameters is essential to achieving consistent and high-quality separations during LC method transfer.

[0012] Summary of the Invention

[0013] According to a first embodiment, the invention provides a method for purification of a biomolecule from an impure sample, said impure sample comprising said biomolecule and at least one contaminant, said method includes the steps of:

[0014] i. conducting a series of reversed-phase high performance liquid chromatography (RPLC) analyses of the impure sample using a mobile phase comprising water and an organic solvent with linear gradient elution at a range of gradients to obtain values for the median retention factor k* and solvent composition at peak elution 4> B f°rsaid biomolecule and said at least one contaminant;ii. based on the values of median retention factor k* and solvent composition at peak elution obtained in step i, conducting a series of reversed-phase high performance liquid chromatography analyses of the impure sample using a mobile phase comprising water and an organic solvent with isocratic elution at a series of solvent compositions encompassing the 4> B values observed in step i, and measuring the retention factor kfor said biomolecule and said at least one contaminant;

[0015] iii. determining the solvent strength (S-value) for each of said biomolecule and said at least one contaminant;

[0016] iv. determining the optimal isocratic solvent composition (c|)B op) for said biomolecule and said at least one contaminant; and using the optimal isocratic solvent composition (4>B,op) determined in step iv to calculate a multi-isocratic elution profile that maximises separation of said biomolecule and said at least one contaminant.

[0017] According to a second embodiment, there is provided a computer system comprising a processor specifically programmed to calculate a multi-isocratic elution profile methods described herein.

[0018] According to a third embodiment, there is provided an apparatus comprising a reversed-phase HPLC column, a detector, and computer system comprising a processor specifically programmed to calculate a multi-isocratic elution profile.

[0019] According to a fourth embodiment, there is provided a computer readable media encoding a computer program for calculating a multi-isocratic elution profile according to the methods described herein.

[0020] Brief Description of the Figures

[0021] Figure 1 is a flowchart of the SMART algorithm.

[0022] Figures 2a and 2b are chromatograms illustrating gradient elution of model peptides P2, P3 and P4; Figure 2c illustrates the structure of model peptides P2, P3 and P4 Figure 3 | Multi-isocratic run for P2, P3, and P4. (A) Isocratic elution in terms of retention volume (VR) and UV absorbance (in mV) fitted to the LSS model. (B) Finalmulti-isocratic design to increase the chromatographic separation between peptides while keeping rapid elution (close to k = -0.2 where Vo is determined by an injection of uracil). Mobile phase: A: water B: acetonitrile (ACN). Elution profile: 0-11.5 mL at 5%ACN; 11.5-20 at 10%ACN; 20-26mL at 18%; 26-40 m at 28%ACN (upper). A hold at 5% for 30 mL was added to the lower profile.

[0023] Figure 4 | Gradient elution of crude glucagon mixture. Minj = 0.1 mg. Flow-rate: 1 mL / min. A: Water + 0.1%TFA. B: Acetonitrile+ 0.1%TFA

[0024] Figure 5 | Isocratic experiments for glucagon. Isocratic elution in terms of retention volume (VR) and (log k) fitted to the LSS model.

[0025] Figure 6 | LSS model applied to main peak and critical peaks.

[0026] Figure 7 | Final method design for glucagon in three analytical columns. 0-5mL at 25%B, 5-20mL at 30.5%B, 12-13 mL at 25%B, 13-40 mL at 29.6%B, 40-45 mL at 50% B, and 45-55 mL at 25% B.

[0027] Figure 8 | Comparative chromatograms of crude glucagon purification. The black chromatogram in both graphs represents an injection of crude glucagon sample. The pink chromatograms are the concentrated purified samples from a standard linear gradient method (upper graph) and the SMART method (lower graph).

[0028] Figure 9 | Analytical versus semi-prep columns in analytical LC system. The analytical and semi-prep C18 columns were connected to the analytical LC (Shimadzu Nexera). The same experiments were conducted, adjusting methods to the relevant scale-up factor.

[0029] Figure 10 | Semi-preparative and analytical LCs comparison. The C18 semipreparative column was connected to the analytical (Shimadzu Nexera) and preparative (Cytiva AKTA) systems. Same isocratic experiments were conducted in both systems.

[0030] Figure 11 | Purification elution profile derived using the SMART algorithm for glucagon and a C18 column.

[0031] Figure 12 | Purification elution profile derived using the SMART algorithm for glucagon and a C8 column.Figure 13 | Purification elution profile derived using the SMART algorithm for glucagon and a Phenyl-Hexyl column. Optimisation goal was to reduce purification time.

[0032] Detailed Description of the Preferred Embodiments

[0033] As used herein, the term “chromatography” refers to a separation technique wherein a mixture comprising an analyte is passed through a stationary phase and separates the analyte from other molecules in the mixture based on differential partitioning between the mobile and stationary phases.

[0034] As used herein, the term “reversed-phase chromatography” refers to a chromatographic separation technique wherein the stationary phase is non-polar. As used herein, the term “isocratic elution” means that the composition of the mobile phase remains constant throughout the chromatographic run.

[0035] As used herein, the term “gradient elution” means that the composition of the mobile phase changes during a chromatographic run.

[0036] The term “mobile phase” refers to a solution that is run through a chromatography column. A “mobile phase” can include one or more organic solvents, water and / or ion-pairing agents. The term “mobile phase” also includes one or more analytes, such as peptides, which are being separated in a column containing the stationary phase. Preferably, the mobile phase comprises an aqueous component and an organic solvent.

[0037] As used herein, the term “eluent” refers to a mobile phase as it is delivered through a chromatography column.

[0038] As used herein, the term “solvent gradient” refers to a rate of change in the concentration of a solvent in a mobile phase, as commonly understood in the art of reversed-phase chromatography. For example, the solvent gradient can be expressed as a percentage of organic solvent per unit time, i.e. 0.75% per minute. As used herein, the term “biomolecule” refers to any organic molecule present in or related to those present in living systems, including synthetic molecules, and includes peptides, polypeptides, proteins, oligosaccharides, lipids, steroids,prostaglandins, prostacyclins, and nucleic acids (including DNA, RNA and oligonucleotides). Peptides are a preferred class of biomolecule.

[0039] The term “impure sample” as used herein refers to a sample of material comprising the biomolecule of interest, together with one or more further substances. Although the further substances are referred to as “contaminants”, it may be that the impure sample comprises a mixture of more than one substance of interest, for example a mixture of two peptides both having commercial value.

[0040] As used herein the term "organic solvent" refers to an organic molecule capable of at least partially dissolving another substance (i.e., the solute). The skilled person will be aware of organic solvents typically used in the mobile phase in reversed-phase liquid chromatography. Preferred organic solvents include methanol and acetonitrile, with acetonitrile being particularly preferred.

[0041] As used herein, the "retention factor k" refers to a measure of how long a molecule spends interacting with the stationary phase of a chromatographic column compared to the time it spends in the mobile phase measured during isocratic elution, essentially indicating how strongly a compound is retained on the column; it is calculated as the ratio of the time a molecule spends in the stationary phase to the time it spends in the mobile phase.

[0042] As used herein, the "gradient or median retention factor k*" refers to a measure of how long a molecule spends interacting with the stationary phase of a chromatographic column compared to the time it spends in the mobile phase measured during gradient elution, essentially indicating how strongly a compound is retained on the column; it is calculated as the ratio of the time a molecule spends in the stationary phase to the time it spends in the mobile phase.

[0043] The stationary phase on which the chromatographic methods of the invention may be conducted utilising a reversed-phase stationary phase. The stationary phase preferably consists of hydrophobic substrates, bonded to the surface of silica-gel particles in various geometries (spheric, irregular), at different diameters (sub-2, 3, 5, 7, 10 pm). The particles may preferably be porous, although non-porous media are contemplated. When porous particles are used, these may have varying pore diameters (60, 100, 150, 300 A). The particle's surface is suitably covered by chemically bonded hydrocarbons, such as C3, C4, C8, C18 and more. Preferredmethods of separation described herein use C-18 columns, sometimes called by trade names, such as ODS (octadecylsilane) or RP-18.

[0044] The stationary phase maybe a conventional particle / bead type stationary phase, or it maybe a core / shell or monolithic stationary phase.

[0045] In certain aspects, the methods of the invention allow optimisation of chromatographic methods of separation of a biomolecule from contaminants. In this regard, the methods of the invention may be conceptually separated into “scouting” or “exploratory” methods in which the experimental conditions are optimised, and preparative methods, in which the optimised conditions are utilized to prepare meaningful quantities of the biomaterial of interest.

[0046] The exploratory methods of the invention separate into three phases: i) the conduct of a series of gradient elution observational experiments which generate data to plan the second phase; ii) the conduct of a series of isocratic elution experimental observations which generate data from which can be calculated the optimal isocratic solvent composition (c|)B op) for each analyte where separation is maximised; and iii) the generation of a multi-isocratic elution profile that maximizes separation of the biomolecule and contaminants. The three phases will be explained in greater detail hereinafter.

[0047] Phase 1: Gradient elution evaluation

[0048] An appropriate reversed-phase column is selected, based on the properties of the biomolecule of interest. In the case of peptides, a C18 column is suitable. The components of the mobile phase are selected, typically water (optionally with 0.1 % trifluoroacetic acid) and acetonitrile (optionally with 0.1 % trifluoroacetic acid). The chromatography system is preferably equipped with a detector, suitably a UV, visible or diode array detector (DAD) system or mass spectrometer detector.

[0049] A number of chromatographic analyses of the crude biomaterial are conducted using the apparatus described above. In this initial experimental phase, gradient elution conditions are used employing gradients of different steepness. For example, utilizing water and acetonitrile (ACN or MeCN) as solvents, gradients of 5% ACN per column volume, and 10% ACN per column volume may be utilized. During each run, data on retention time (tp) of each peak together with the peak area and shape foreach analyte are collected and analysed. As will be apparent, each peak will correspond to either the biomolecule of interest or a contaminant.

[0050] For each peak observed in the chromatogram, the gradient or median retention factor (k*) is calculate using the formula:

[0051] vg

[0052] k

[0053]

[0054] " 1.15V0Ac|)B,gS

[0055] whereVgis the gradient volume, Vois the column dead volume,

[0056]

[0057] ;gis the change of 4>Bduring the gradient, and S is the S-value from the Linear-Solvent-Strength (LSS) model (High-Performance Gradient Elution: The Practical Application of the Linear-Solvent-Strength Mode\, L. R. Snyder and J. W. Dolan, 2007, John Wiley & Sons, Inc., incorporated by reference). Preferably, an initial value of S= 15 is used for peptides.

[0058] From the gradient elution runs, the organic solvent composition at peak elution based on the gradient slope (

[0059]

[0060] c|)B;e) and the corresponding theoretical isocratic organic composition (4>iso) for is calculated for each biomolecule or contaminant in the mixture. The following equations are employed:

[0061] A(|)B g

[0062] *B,e = -VM -VD -VEC)

[0063] Vg

[0064] = *B,0 + --p VR- VM- VD- 0.3

[0065] Vg \ D /

[0066]

[0067] Vgtg

[0068] logfe)

[0069] ^iso - ^B.e 1 - g -

[0070] The value of c|)isois used as the initial estimate for isocratic elution conditions.Phase 2: Isocratic Optimisation

[0071] Based on the c|)isovalues obtained in the scouting experiments, a series of isocratic elution runs is performed with varying solvent compositions. As initial conditions, a narrow range around the estimated c|)B(e.g., ±1-2%) is selected.

[0072] For each isocratic run, the analyte retention times (tp) and the corresponding peak areas for all analytes are recorded. The log(k) values from the isocratic runs are calculated for all analytes. Log(k) values are calculated using the equation:

[0073] log(fc) = log (tR to

[0074] 'co '

[0075] wherein to represents the column dead time.

[0076] The values of log(k) thus obtained are plotted against the organic solvent composition (c|)B) to visualise the retention behaviour. If necessary, the solvent composition range may be adjusted, expanding or narrowing it based on how well the peaks separate. The S-value (solvent strength) for each analyte is calculated using the LSS model:

[0077] logk = logkw- Sc|)B

[0078] If the S-value is too low (indicating poor separation), the isocratic range may be extended, and the tests repeated. Based on the isocratic runs and log(k) plots, the optimal isocratic solvent composition (

[0079]

[0080] 4>B,op) for each analyte is determined, where separation is maximised.

[0081] Phase 3 - Final Multi-lsocratic Method Design

[0082] The data from the isocratic optimisation in phase 2 is utilised to calculate a final, multi-isocratic profile that maximises peak separation. In a preferred embodiment, the profile includes the following three steps:

[0083] 1. Pre-elution step: Elution with a low solvent composition (e.g., 5-10% ACN) to remove early-eluting species (e.g. contaminants) with low retention;2. Focussed elution: the optimised isocratic solvent composition (c|)B op) for the main analytes of interest is applied, using multiple isocratic steps if necessary to optimise separation;

[0084] 3. Flushing step: elution is conducted with a strong organic solvent (e.g., 90- 100% ACN) to remove any remaining strongly retained species from the column.

[0085] Using a solvent elution profile calculated according to the foregoing methodology, a far higher degree of purity of biomolecule is obtained than using conventional gradient elution methodology. For example, when the purification of crude glucagon having a purity of 27% is undertaken, the purity using the methods according to the invention is in excess of 90%; conventional gradient elution achieved only 83.5% purity. Furthermore, the load capacity of the column using a solvent elution profile is doubled.

[0086] In chromatography, the retention of an analyte is represented by a band migrating through the column; therefore, retention volume VR can be expressed simply as:

[0087] VR=VM(1+k) (1)

[0088] where VM is the column mobile-phase volume and k is the peak (band) retention factor. The fractional migration of the peak travels through at a speed determined in units per column-volume VM of the mobile phase and not per simply column volume (CV). The latter CV is the volume of an empty column (no resin). It is important to note that VM is marginally different to void volume (Vo) as it considers both interstitial and pore volumes. In some cases, depending on the estimation method, Vo and VM are the same.

[0089] The movement of the peak through the column and the factors that affect it are different for each system, as multiple physicochemical interactions coexist in the adsorption-partition phenomena of liquid chromatography. ‘System’ refers to the microenvironment constituted by the analytes, mobile phase, and stationary phase at the moving infinitesimal space within the column length. This infinitesimal space can be measured by volume (dV) or distance (dx=dV / (VR-VM)=dV / VMk). The sum of all these fractional migrations with dx=1 when dV=VR-VM=V’R can be expressed with the following equations:rv« 1 dV > f 1 dt >

[0090] kj Ju tMkj

[0091]

[0092] (2)

[0093] Isocratic elution

[0094] In absolute RPLC, the retention of an analyte is a strong function of the mobile phase composition or solvent strength. The linear solvent strength (LSS) model conveys that ideality in the form:

[0095] log k=log kw— SC|> B (3)

[0096] where k is a function of the volume-fraction of organic solvent (|)B (expressed in decimal form or 0.01 percent B in aqueous solvent A). Parameter S is a constant for a single analyte and fixed experimental conditions, it is also often referred as solvent strength value, and kw is the extrapolated theoretical value of k at 100% aqueous conditions (C|)B=O).

[0097] Despite the wide use of the empirical LSS model, it is important to note that it ignores other effects, such as dynamics of the band profile and physicochemical interactions other than hydrophobic.

[0098] Gradient elution

[0099] When a linear gradient is applied to RPLC, the composition of the mobile phase in terms of solvent B leaving the column (<|> B) changes over time after the initiation of the gradient (t) and, assuming ideal mixing at the pump outlet, can be described by:

[0100] (4)

[0101] >

[0102] <t»B ~ 4^B,0 + I. I t ~ ^B, D + IvW

[0103]

[0104] \ \ *K /

[0105] where <|)B, O is the value of (|)B at the start of the gradient, A<|> B,g is the change of (|)B during the gradient and tgis the gradient time. The equivalent expression in terms of volume (V) is only valid when the volumetric flowrate is kept constant.

[0106] Because the values of k vary as the band migrates through the column during gradient system, a median or equivalent value of k is used in gradient elution (k*). This median value is defined as the value of k when then analyte is at half the length of the column. Similarly, ‘B is the corresponding value of (|)B at that position. TheLSS model can be applied to these values (Equations 5-7) using different gradient slopes to estimate values of S and log kw:

[0107] l-15VniA(f»B-gS

[0108]

[0109] However, elution occurs once the peak completely exits from the column, the equations above, and in particular Eq. 6, can be transformed into the following:

[0110]

[0111] where the elution is obtained from the retention volume measured at the apex of the peak. This formula can also be inferred logically as it is a simple translation of retention volume into mobile phase composition by considering the slope of the gradient and adjustments to additional volumes in the system other than the column volume.

[0112] As the values of mobile phase composition would vary depending on the efficiency of the solvent mobile phase mixing in the LC system. An equivalent isocratic composition (c iso) can be estimated from <|)B,e values using the following formula:

[0113]

[0114] In one embodiment, the methods described herein may be implemented in hardware or software, or a combination of both. However, these embodiments may be implemented in computer programs executing on programmable computers, each computer including at least one processor, a data storage system (including volatile and non-volatile memory and / or storage elements), and at least one communicationinterface. For example, the programmable computers may be a server, network appliance, set-top box, embedded device, computer expansion module, personal computer, laptop, personal data assistant, or mobile device. Program code is applied to input data to perform the functions described herein and to generate output information. The output information is applied to one or more output devices, in known fashion. For example, in one embodiment, the output information is the multi-isocratic elution profile for a particular impure sample.

[0115] Each program may be implemented in a high-level procedural or object-oriented programming or scripting language, or both, to communicate with a computer system. However, alternatively the programs may be implemented in assembly or machine language, if desired. In any case, the language may be a compiled or interpreted language. Each such computer program may be stored on a storage media or a device (e.g. ROM or magnetic diskette), readable by a general or special purpose programmable computer, for configuring and operating the computer when the storage media or device is read by the computer to perform the procedures described herein. Embodiments of the system may also be considered to be implemented as a non-transitory computer-readable storage medium, configured with a computer program, where the storage medium so configured causes a computer to operate in a specific and predefined manner to perform the functions described herein.

[0116] Furthermore, the system, processes and methods of the described embodiments are capable of being distributed in a computer program product including a physical non-transitory computer-readable medium that bears computer-usable instructions for one or more processors. The medium may be provided in various forms, including one or more diskettes, compact disks, tapes, chips, magnetic and electronic storage media, and the like. The computer-useable instructions may also be in various forms, including compiled and non-compiled code.

[0117] All publications, patents and patent applications referenced herein are incorporated by reference in their entirety to the same extent as if each individual publication, patent or patent application was specifically and individually indicated to be incorporated by reference in its entirety.Examples

[0118] Materials and Methods

[0119] Crude human glucagon (1-29) was purchased from GenScript (USA) with no termini modification (27.0 ± 0.73% purity based on HPLC area). HPLC-grade acetonitrile (ACN, >99.8% purity) was purchased from Fisher Scientific (USA). Type I water with a resistivity of 18 MQ.cm was obtained from a Purelab Chorus 1 system (Elga LabWater, USA). Trifluoroacetic Acid (TFA, >99.0%) was purchased from Sigma-Aldrich (USA).

[0120] Instrumentation

[0121] All analytical experiments were conducted using a modular analytical HPLC Nexera LC-40 (Shimadzu, Japan). Mobile phase solutions were continuously filtered with a 10 pm in-line filter and degassed using a DGU-405 degassing unit and an LC-40D pump. Mobile phases comprised in Type I water (A) and acetonitrile (B) for peptide standards. A 0.1 % TFA (v / v) was added to both A and B for glucagon. These mobile phases were delivered in separate lines, denoted as Line A and Line B, at the inlet of the quaternary pump. The temperature was controlled using a CTO-40C column oven fitted with a column selection valve. The extra columns and the dwell volumes were estimated for each valve position as independent systems. The chromatographic data were recorded during injection and elution by positioning a dual channel SPD-40 UVA / is detector and two SPD-M40 photo-diode array (PDA) detectors, one before and one after the column, respectively. All samples were injected using a SIL-40C autosampler.

[0122] Analytical RPLC columns Luna C18(2), Luna C8 and Luna phenyl-hexyl (PH) with dimensions of 150 x 4.6 mm (L x ID) were purchased from Phenomenex (USA). All columns had an average particle size (dp) of 5 pm, average pore size (np) of 100 A, specific surface area (SA) of 400 m2 / g, and incorporated TMS end-capping according to the manufacturing information. Columns were connected to valve positions 1, 2, and 3 of the Shimadzu system, respectively. Extra pre-column and post-column volumes were estimated to be the same for all ports, around 87 and 172 pL, respectively. Dwell volumes varied between ports, resulting in 1.27 (port 1), 1.49 (port 2), and 1.38 mL (port 3).Scale-up experiments were conducted in the system described above and in an AKTA Pure 25 system (Cytiva, USA). Solvents were filtered and sonicated to reduce the amount of dissolved gas. An RPLC column Luna C18(2) with dimensions of 150 x 10 mm (L x ID). This column will be referred to hereinafter as the ‘semi-prep column’.

[0123] Algorithm

[0124] In the present study, the inventors have devised a new SMART (Systematic, Multi-parametric, Adaptive, Responsive, Tailored) algorithm for RPLC method development and optimisation. A flowchart of the algorithm can be found in Figure 1. The algorithm initiates with a scouting method encompassing 2-3 linear gradient elution method based experiments. The average values of k* and 0B* for each peak of interest are computed based on these linear gradients. To provide a more realistic understanding of the mobile phase mixing capacity of the LC unit, the steepness of the linear gradients are varied significantly different between these scouting experiments.

[0125] The mean value of 0B* serves as an initial estimate for the elution range during isocratic runs. The isocratic ranging test is chosen in accordance with the predicted behaviour of the analyte. From these runs, a plot of log k vs 0B is generated. If the S-value is significantly low, the range is extended. These experiments are iteratively performed until sufficient information is gathered for all species (peaks) of interest. Upon the collection of these data, a final design is formulated based on the objectives of the separation. Typically, final designs comprise three steps: (1) preelution or flushing of early species that exhibit less affinity to the resin, (2) focalised elution region, which can be a combination of multi-isocratic runs ensuring optimised separation between the primary species of interest, and (3) flushing of the column, which involves an organic-rich mobile phase that elutes all species exhibiting higher adsorption to the resin. This comprehensive approach ensures a robust and efficient separation process.

[0126] Purity check runs

[0127] To compare the performance of the purification process, crude and fraction-collected samples were run through a C18 analytical column. Mobile phases were the sameas described in ‘instrumentation’ above. Gradient steepness was maintained at 2.5 %B for every geometrical column volume.

[0128] RESULTS AND DISCUSSION

[0129] Despite the clear benefit of using multi-isocratic runs for biomolecules, it is important to recognise that the higher the compositional complexity of a sample, the more challenging the separation optimisation will be. Optimising the chromatographic separation of a specific column for complex solutions requires detailed analysis chromatographically of the close-eluting impurities in the vicinity of the main peak of interest.

[0130] Standard peptides - proof of concept

[0131] This disclosure explores the efficiency of the SMART algorithm, tested using Krokhin peptide standards P2, P3, and P4. The selection of these peptides was based on their subtle sequence differences, which produced measurable differential hydrophobic separation. This separation can be observed during the gradient scouting step, which also facilitates the understanding of the separation capabilities and constraints of the tested column.

[0132] The elution order of the peptides, as anticipated, aligns with the computational log P values, a hydrophobicity metric, as depicted in Figure 2. An additional 5-minute delay at 0B— 0.05 was incorporated to ensure complete adsorption at the column’s head. Using equations 5 and 6, the values of 0B* and k* were calculated, which allowed for the estimation of log kwand S for each peptide across the four scouting gradient runs. This led to the determination of 0iso for each peptide, with results presented in Table 1 (Left). The gradient data indicates isocratic elution at 7.24 ± 0.06%B for P2, 13.19 ± 0.02%B for P3, and 19.71 ± 0.17%B for P4.

[0133]

[0134] Table 1 | Gradient analysis for P1, P2, and P3. (Left) Calculations of initial parameter for isocratic elution using gradient results from Figure 2 and equations 3, 5-9. (Right) Calculations of the Linear Strength Model (equations 3) based on isocratic elution.

[0135] Given the distinctive hydrophobic differences among these standard peptides, isocratic runs were performed using a range of (|)B values for each peptide: 0.1 -0.175 for P2, 0.175 - 0.275 for P3, and 0.275 - 0.375 for P4. The results, reported in Figure 3A, were used to calculate new values for S and log kw

[0136] (Table 1, Right). The percent errors between the isocratic and gradient methods were found to be 28.7 ± 11.2% for S and 82 ± 47% for log kw.

[0137] Interestingly, S-values for biomolecules are typically higher than those for small molecules15. While this may not surprise separation scientists specialising in biomolecules, it contradicts much of the existing literature, where recommended S-values usually range around 4-516. This discrepancy arises from the limited data sets collected from biomolecule separations compared to small molecules data sets. A large S-value might be viewed as a disadvantage as the analyte is significantly affected by the solvent composition. However, this also implies that under more aqueous conditions, the analyte will be robustly adsorbed onto the stationary phase (higher log kw). This strong adsorption of biomolecules, coupled with a low longitudinal axial dispersion17, creates an environment where the analyte can be robustly adsorbed and desorbed with a degree of control, referred to as the on-and-off effect. A multi-isocratic method was developed based on the obtained LSS parameters. The aim of this separation was to elute the peptides from the head of the column with minimal separation (close to VM values) to reduce both separation time and solvent consumption. The method was thus developed based on the values where two peptides are eluted together, as shown in Figure 3A. An initial delay at a lower concentration of B was incorporated to drive adsorption at the column inlet. If the on-and-off effect holds true, then the elution volume of each peptide remains the same as in the isocratic runs after changing the concentration. In essence, provided the adsorption is sufficiently robust such that the retention factor (k) is virtually zero, the peptide will remain stationary / immobile on the chromatographic media until the mobile phase conditions are changed to allow migration. If this change in conditions is sudden, the peptide will migrate at a rate equivalent to that as if injected at the exact moment of change. This nuanced understanding of peptide behaviour under varying conditions provides valuable insights for developing efficient separation methods.

[0138] To further investigate the on-and-off effect in peptide adsorption / desorption phenomena, an extra hold step was added to the multi-isocratic profile between P3 and P4. The mobile phase was abruptly decreased to the initial delay composition. After a hold of 30 mL, P4 was eluted at 28% ACN. Interestingly, no differences in retention volume or peak width were found (Figure 3B, lower). The same results were found after a 24-hour hold-up time, reinforcing the on-and-off effect theory (data not shown).

[0139] Glucagon - analytical scale

[0140] Native glucagon plays an important physiological role in glucose-dependent insulin secretion when it binds to its receptor. Consequently, its sequence has been optimised for a class of synthetic peptides known as glucagon receptor agonists (GRAs), which are used in the treatment of type 2 diabetes18-20. Despite the current limited commercial advantage of native glucagon, it serves as a representative model peptide for GRAs when testing new purification strategies.

[0141] The gradient scouting experiments shown in Figure 4 reveal that the crude glucagon sample contains a middle peak corresponding to the primary compound of interest. The selectivity of this peak relative to the two adjacent peaks improves as thegradient slope decreases. Moreover, the resolution of the C8 column converges faster than the other two columns, indicating faster retention volumes. The combined effects of a reduced base shift caused by rapid solvent mixing and slower mass transfer during shallow gradients result in a reduction of peak height and an increase in peak width.

[0142] Following the same procedure as with the peptide standards, we estimated the values of <|)iso for the separation of the main peak in each column using equations 5-9. Isocratic runs in the range of 0.29 - 0.305 for (|)B were conducted to assess the effect of the solvent strength on the separation performance of glucagon. By plotting log k vs (|)B for the main peak of interest, we obtained a comparative graph for column selection (Figure 5). It is noteworthy that the S-values for glucagon are higher than 10, providing insight into the scale of the effect of the mobile phase composition on the RPLC separation despite being specific for the systems tested in this work.

[0143] Considering the known chemistry of glucagon, the surface properties of the resin, and the mobile phase contents, it is reasonable to assume that the adsorptionpartition phenomena are governed by more types of interactions other than hydrophobicity, such as electrostatic interactions and size exclusion effects, as well as dynamics. In fact, without the addition of the organic modifier TFA to the mobile phase, glucagon does not elute from the columns tested in this work.

[0144] Despite the multifaceted process, the isocratic chromatographic system for glucagon adheres to the LSS model (r2> 0.95). This is beneficial as it can assist with column selection, depending on the requirements. For instance, if a faster separation is required, PH would be preferred as its log kwis lower than other columns, and its importance over the control of solvent mixing is similar to C8 and less relevant than C18 (SPH=SC8< SCI8). From a method design perspective, S is a measure of how carefully solvent mixing must occur at the pump of the LC unit. Considering an S of 15, the retention factor k would be reduced by approximately 40% by increasing 1 %ACN of organic solvent. The parameter log kw is an indicator of the affinity of the analyte to the surface of the chromatographic resin. Smaller values indicate low affinity, thereby reducing the amount of solvent required to elute the analyte. Another useful application of the LSS model, briefly demonstrated in the previous case, is identifying if the peaks closer (critical peaks) to the main analyte of interest are ofrelated or unrelated structures. When the analytes are highly related, the plots of log k vs (|)B of the critical peaks vary parallel to the main analyte, meaning the order of elution remains the same during the entire (|)B range. Critical peaks in a crude peptide sample are expected to be highly related structurally (i.e., homologues), meaning they are most likely to follow LSS behaviour.

[0145] In accordance with Figure 6, the analyte of interest and the critical peaks follow the LSS model, and the elution order does not change within the (|)B range. Here, we can identify that the most challenging separation is with the critical peak before the main peak for all columns, as the log kwvalues for that peak and the main peak of interest are too close to each other. Additionally, even though PH reduces the amount of mobile phase required, separation at low (|)B can become difficult as the resolution between the critical peak after the main peak and the main peak worsens at lower solvent strength (SMAIN+I< SMAIN). This type of analysis can be executed towards all peaks in the chromatogram, however, application on critical peaks is more convenient.

[0146] Method design based on the LSS model is useful, but analysis beyond log k vs (|)B plots must be done. This model only considers the first moment of the chromatographic peak (i.e., retention volume at the apex), so it does not incorporate resolution or selectivity (risk of peak overlapping) data. Therefore, attention should be paid to these parameters along with the plots.

[0147] Based on the findings from the LSS model, a final multi-isocratic elution design was developed. In order to reduce the complexity of the separation, no specific goal was set. Instead, a single comparative method was developed in order to assess the difference between the three columns. Results can be observed in Figure 7. A clear distinction of the main peak can be observed, which confirms the efficacy of this type of rational method design.

[0148] The efficiency of purification comparing a standard gradient elution method and the new designed method in Figure 7 was assessed using the analytical C18 column. The maximum purity recovery observed was less than 85% when the crude sample was purified using the gradient elution method. This suboptimal purification is ascribed to the inadequate resolution of a co-eluted shoulder and other closely associated impurities, requiring the ‘shaving’ of the primary peak of interest.Additionally, as is commonly observed for this specific molecule, process aggregation and degradation products of glucagon were found as early peaks21 22. Conversely, the multi-isocratic method of purification yielded a purity approaching 94%. There was a substantial reduction in sample impurities as well as aggregation and degradation products. The chromatograms can be examined in the Figure 8. A summary of the purification analysis is presented in Table 2.

[0149] Mas Mahi peakporty Piirityfmprwe6iiieut Sample impwrilta Crude 03 mg 27.0 * 073% - -72.90% N / A Gradient 2.1 mg (7 batches wv ™ w 25%ACNCV mg) 833 * I A» Ms,.8,-. SMART algorithm 1 J batches of 93.6* 0.82% <0.1% -5%

[0150]

[0151] Table 2 | Purification analysis of crude glucagon reaction mixture in C18 analytical column.

[0152] It is important to mention that the multi-isocratic SMART method allows for a two-fold increase in the load capacity of the column compared to the gradient method. This is attributed to the method’s calibration, which is designed to elute the primary peak of interest as a singular peak, thereby eliminating the necessity for peak shaving. If the same loading conditions were applied to the gradient method, it would result in the merging of closely related peaks, leading to a substantial reduction in recovery. This highlights a significant advantage of the multi-isocratic SMART method, as it necessitates fewer batches to achieve a specified yield.

[0153] Glucagon - scaling up

[0154] To evaluate the scalability of the method, a scale-up column was integrated into both the analytical and semi-preparative systems. These columns, while identical in length and resin, differ in their internal diameters, resulting in a scale-up ratios of 4.73 (Vc, Semi-prepA / c, analytical) and 4.32 (VM, Semi-prepA / M, analytical).

[0155] One of the primary objectives at the manufacturing scale is to reduce solvent consumption. To this end, isocratic runs for the semi-preparative column in the analytical system were conducted within the (|)B range of 30.0-35.0%. This range overlaps at the higher end with the experiments conducted using the analyticalcolumn. If the scale-up is direct, considering only the change of VM, this would ensure a log k value of less than or equal to 1.

[0156] The results, as depicted in Figure 9A, reveal significant disparities in retention values between the analytical and semi-preparative columns in relation to the required mobile phase volume. However, when distinct VM values are considered and the logarithm of the capacity factor (log k) is calculated, the results display a favourable overlap. This observation remains consistent even when the retention volume is converted to the number of column volumes.

[0157] While the use of CV (column volume) is a common practice, it assumes identical column packing. In contrast, employing VM provides a more informative indicator in such cases, as shown in Figure 9B. These types of graphs are invaluable for assessing solvent usage and the scalability of the process. Therefore, it is crucial to consider factors beyond log k vs (|)B plots in the analysis. Although the LSS model only considers the first moment of the chromatographic peak (i.e., retention volume at the apex), it does not express resolution or selectivity (extent of peak overlapping). Hence, these parameters should be given due consideration alongside the plots. When transferring methodology across systems, an additional disadvantage arises when using CV. This disadvantage is attributed to the variations in extra column volumes (ECV) within the system, which can be due to differences in tubing size, the mixing chamber, or the pump heads.

[0158] In an experiment depicted in Figure 10, the semi-prep column was installed in the Cytiva AKTA (semi-prep) LC, and an isocratic range identical to the one previously described was executed. Following the adjustment of VR values to align with the correct ECV of the semi-prep system and VM of the column, it was observed that the units yielded comparable results in terms of mobile phase consumption.

[0159] Solvent profiles generated using the SMART algorithm described herein are illustrated in Figures 11, 12 and 13.

[0160] It is hypothesised that minor variations at certain points are attributable to the inaccuracy of the mixing chamber in the semi-prep system. More significant variations, particularly at lower <|)B, are believed to be caused by the different pump types employed by the two units.The analytical LC utilises a parallel-type pump (quaternary and binary), whereas the semi-prep unit has dual pumps and a gradient mixer. These features in the semiprep system are ideally suited for gradient purification as they minimise pulsation; thereby, accuracy in blending solvents during isocratic runs would be expected. However, it is postulated that the higher ratio of tubing volume to mixing chamber volume in the semi-prep system, coupled with less precise flow rate control, could have significant implications if regular calibration is not performed. This highlights the importance of routine calibration in ensuring the accuracy and reliability of the system.

[0161] CONCLUSIONS

[0162] The inventors have introduced a comprehensive analysis and application of a new SMART (Systematic, Multi-parametric, Adaptive, Responsive, Tailored) algorithm for optimising multi-isocratic elution methods in reversed-phase liquid chromatography (RPLC).

[0163] This study focused on the separation and purification of complex biomolecular samples, specifically peptides, and demonstrated the efficacy and advantages of the SMART algorithm in enhancing chromatographic performance.

[0164] The SMART algorithm was found to be highly effective in optimising the separation of peptide standards and glucagon, resulting in significant improvements in the purity and resolution of the target compounds. For the peptide standards P2, P3, and P4, the algorithm facilitated better control over peak elution and spacing during multi-isocratic runs, leading to higher selectivity and reduced separation times compared to traditional gradient methods.

[0165] In the case of glucagon, the SMART algorithm enabled the development of a multi-isocratic method that achieved a purity of 93.6%, markedly higher than the 83.5% purity obtained using a gradient elution method. This method also allowed for a twofold increase in column load capacity, reducing the number of required purification batches and enhancing overall process efficiency. These results highlight the algorithm's ability to manage complex separations effectively, offering substantial advantages in terms of purity and throughput.

[0166] The potential scalability of the SMART algorithm was demonstrated by successfully transitioning from analytical to semi-preparative scales while maintaining consistentperformance and solvent usage. This robustness underscores the algorithm's suitability for various scales of operation, making it a valuable tool for both research and industrial applications where scalability is crucial.

[0167] The study also highlighted several advantages of the multi-isocratic approach over traditional gradient methods. The SMART algorithm provided better resolution of closely eluting impurities and significantly reduced the presence of aggregation and degradation products. Additionally, the efficiency in solvent usage and the ability to handle higher load capacities make this approach particularly advantageous for industrial applications where resource management is a critical factor.

[0168] In conclusion, the SMART algorithm represents a significant advance in chromatographic separation and purification processes for complex biomolecules. Its application can lead to enhanced efficiency, selectivity, and scalability, offering a promising alternative to traditional gradient methods.

[0169] REFERENCES

[0170] 1. Snyder, L. R.; Kirkland, J. J.; Dolan, J. W., Introduction to Modern Liquid Chromatography. 2009.

[0171] 2. Gallant, S. R.; Vunnum, S.; Cramer, S. M., Optimization of preparative ionexchange chromatography of proteins: linear gradient separations. Journal of Chromatography A 1996, 725(2), 295-314.

[0172] 3. Kim, B.; Velayudhan, A., Preparative gradient elution chromatography of chemotactic peptides. Journal of Chromatography A 1998, 796 (1), 195-209.

[0173] 4. Kristi, A.; Luksic, M.; Pompe, M.; Podgornik, A., Effect of Pressure Increase on Macromolecules’ Adsorption in Ion Exchange Chromatography. Analytical Chemistry 2020, 92 (6), 4527-4534.

[0174] 5. Chapel, S.; Rouviere, F.; Guillarme, D.; Heinisch, S. Reversed HILIC Gradient: A Powerful Strategy for On-Line Comprehensive 2D-LC Molecules [Online], 2023. 6. Mant, C. T.; Jiang, Z.; Boyes, B. E.; Hodges, R. S., An improved approach to hydrophilic interaction chromatography of peptides: Salt gradients in the presence of high isocratic acetonitrile concentrations. Journal of Chromatography A 2013, 1277,7. Wang, W.; Li, P.; Wu, F.; Wang, Z.; Zhang, T., Development and optimization of a supercritical fluid chromatography tandem mass spectrometry method for the high-throughput determination of nimodipine in beagle plasma. Journal of Separation Science 2019, 42 (12), 2179-2186.

[0175] 8. Neumann, J.; Schmidtsdorff, S.; Schmidt, A. H.; Parr, M. K., Application of sub- / supercritical fluid chromatography for the fingerprinting of a complex therapeutic peptide. Journal of Separation Science 2022, 45 (16), 3095-3104.

[0176] 9. Molineau, J.; Hideux, M.; West, C., Chromatographic analysis of biomolecules with pressurized carbon dioxide mobile phases - A review. Journal of Pharmaceutical and Biomedical Analysis 2021, 193, 113736.

[0177] 10. Wang, C.; Cheng, Y., Urea-gradient protein refolding in size exclusion chromatography. Current Pharmaceutical Biotechnology 2010, 11 (3), 289-92.

[0178] 11. Fekete, S.; Murisier, A.; Nguyen, J. M.; Lauber, M. A.; Guillarme, D., Negative gradient slope methods to improve the separation of closely eluting proteins. J ChromatogrA 2021, 1635, 461743.

[0179] 12. Fekete, S.; Ritchie, H.; Lawhorn, J.; Veuthey, J. L.; Guillarme, D., Improving selectivity and performing online on-column fractioning in liquid chromatography for the separation of therapeutic biopharmaceutical products. J Chromatogr A 2020, 1618, 460901.

[0180] 13. Fekete, S.; Beck, A.; Veuthey, J. L.; Guillarme, D., Proof of Concept To Achieve Infinite Selectivity for the Chromatographic Separation of Therapeutic Proteins. Anal Chem 2019, 91, 12954-61.

[0181] 14. Hui F. Liu, J. M. C. W.; Robert, B., Recovery and purification process development for monoclonal antibody production. mAbs 2010, 2 (5), 480--499.

[0182] 15. Tyteca, E.; De Vos, J.; Vankova, N.; Cesla, P.; Desmet, G.; Eeltink, S., Applicability of linear and nonlinear retention-time models for reversed-phase liquid chromatography separations of small molecules, peptides, and intact proteins.

[0183] Journal of Separation Science 2016, 39 (7), 1249-1257.

[0184] 16. Colin, F. P.; Sanka, N. A., Analysis of the solvent strength parameter (linear solvent strength model) for isocratic separations in reversed-phase liquid chromatography. Journal of Chromatography A 2022, 1675, 463153.17. Gonzalez-Lopez, N. M.; Insuasty-Cepeda, D. S.; Huertas-Ortiz, K. A.; Reyes-Calderon, J. E.; Martinez-Ramirez, J. A.; Fierro-Medina, R.; Jenny Rivera-Monroy, Z.; Garcia-Castaneda, J. E., Gradient Retention Factor Concept Applied to Method Development for Peptide Analysis by Means of RP-HPLC. ACS Omega 2022, 7 (49), 44817-44824.

[0185] 18. Hruby, V. J., Chapter 16 - Glucagon:: Molecular Biology and Structure-Activity. In Principles of Medical Biology, Bittar, E. E.; Bittar, N., Eds. Elsevier: 1997; Vol. 10, pp 387-401.

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Claims

CLAIMS1. A method for purification of a biomolecule from an impure sample, said impure sample comprising said biomolecule and at least one contaminant, said method including the steps of:i. conducting a series of reverse-phase high performance liquid chromatography (HPLC) analyses of the impure sample using a mobile phase comprising water and an organic solvent with linear gradient elution at a range of gradients to obtain values for the median retention factor k* and solvent composition at peak elution 4> B for said biomolecule and said at least one contaminant;ii. based on the values of median retention factor k* and solvent composition at peak elution 4> B obtained in step i, conducting a series of reverse-phase high performance liquid chromatography analyses of the impure sample using a mobile phase comprising water and an organic solvent with isocratic elution at a series of solvent compositions encompassing the 4> B values observed in step i, and measuring the retention factor k for said biomolecule and said at least one contaminant;iii. determining the solvent strength (S-value) for each of said biomolecule and said at least one contaminant;iv. determining the optimal isocratic solvent composition (c|)B op) for said biomolecule and said at least one contaminant;v. using the optimal isocratic solvent composition (4>B,op) determined in step iv to calculate a multi-isocratic elution profile that maximises separation of said biomolecule and said at least one contaminant.

2. The method according to claim 1 wherein the biomolecule is selected from the group consisting of peptides, polypeptides, proteins, oligosaccharides, lipids, steroids, prostaglandins, prostacyclins, and nucleic acids, including oligonucleotides.

3. The method according to claim 1 or 2 wherein the organic solvent is selected from methanol and acetonitrile.

4. The method according to any preceding claim wherein the mobile phase comprises a mobile phase modifier, preferably trifluoroacetic acid, in an amount of up to 0.5 % v / v.

5. The method according to any preceding claim wherein the method includes between 2 and 5 linear gradient elution analyses in step i.

6. The method according to any preceding claim wherein the gradient elutions are conducted at a gradient steepness of between 1 % organic solvent per column volume and 10% organic solvent per column volume / 7. The method according to any preceding claim wherein the method includes between 2 and 5 isocratic elution analyses in step ii.

8. A method according to any preceding claim wherein the multi-isocratic elution profile of step v. includes at leasti. a pre-elution step at an organic solvent concentration of between 5 and 10%;ii. at least one focussed elution step at optimal isocratic solvent composition (c|)B,op) f°rthe biomolecule;iii. optionally, one or more focussed elution steps at optimal isocratic solvent composition (c|)B op) for each contaminant;iv. a flushing step at an organic solvent concentration of between 90 and 100%.

9. A method according to any preceding claim comprising a further step of purifying a biomolecule using reversed-phase high performance liquid chromatography employing the multi-isocratic elution profile calculated in step v.

10. A computer system comprising a processor specifically programmed to calculate a multi-isocratic elution profile as defined in claim 1.

11. An apparatus comprising a reverse phase HPLC column, a detector, and a computer system comprising a processor specifically programmed to calculate a multi-isocratic elution profile as defined in claim 1.

12. A computer readable media encoding a computer program for calculating a multi-isocratic elution profile as defined in claim 1.

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