JP5745263B2 - Chromatogram simulation method, system and program, and simulation result evaluation method - Google Patents

Description

  TECHNICAL FIELD The present invention relates to frontal gel filtration chromatography, and more specifically, a chromatogram simulation method and system capable of obtaining design parameters and analysis conditions of a microgel filtration column necessary for performing frontal gel filtration with a small amount of sample. And a program, a method for designing a gel filtration column, and a method for evaluating a column produced based on the design parameters.

  Of the methods for measuring the molecular interaction between a protein and a low molecular weight compound (hereinafter also referred to as a ligand) without performing labeling or immobilization on the sensor surface for either the protein or the ligand, the protein binds to the protein. The methods that can be used to measure the number of ligand molecules and the concentration of ligands that are not bound to proteins (hereinafter also referred to as free ligands) in a single measurement are the dialysis equilibrium method, ultrafiltration method, and frontal gel filtration. Is the law. Of these three methods, only the frontal gel filtration method can perform measurement without changing the concentration of the protein and ligand specified in advance. The dialysis equilibrium method and the ultrafiltration method use a membrane that allows only the ligand to pass through. Therefore, the volume of the membrane is relatively large for a small amount of sample, and accurate measurement is possible for adsorption and distribution of the ligand to the membrane. It is difficult in principle. On the other hand, the frontal gel filtration method requires a sample that is necessary for measurement compared to various methods that indirectly measure the interaction by immobilizing the protein on the sensor chip and measuring the physical property change of the sensor chip accompanying the binding of the ligand. The large amount of sewage has become a drawback, and its spread has been hindered.

Gel filtration chromatography In gel filtration chromatography, molecules that are hydrodynamically larger move faster. Then, using a column in which the porous filler is uniformly packed, how much can enter the pore region of the porous filler is determined by the size of the polymer (Stokes radius). The portion outside the packing material inside the column is called the mobile phase, and the inside of the packing hole is called the stationary phase without a net flow from the inlet to the outlet of the column. The column movement speed of the polymer is determined by how much the polymer enters the pore region (stationary phase region), and the smaller the Stokes radius, the closer to the stationary phase, the slower the column movement phase.

  Gel filtration chromatography is usually used for the purpose of purifying only a specific polymer from a polymer mixture. Each polymer in the sample elutes from the column, necessarily being wider than the width of the sample at the time of injection into the gel filtration column. Therefore, the sample is concentrated as much as possible to a small volume (less than 1/50 of the column volume) and injected into the column. For purification purposes, it is better that components of different sizes elute as far apart as possible and that the spread of each peak is smaller. In order to improve separation between polymer components as much as possible, micro columns are not suitable, and even small columns with an inner diameter of 4.6 mm or more and a length of about 30 cm (column capacity is at least several milliliters) are used.

Frontal analysis (frontal analysis, frontal chromatography) It is assumed that there are a large amount of a mixed solution composed of only two or three kinds of components, and there are columns in which the moving speed of each component is different. When this mixed liquid is continuously supplied to the above-mentioned column, the component that moves the fastest elutes alone with the concentration of the original mixed liquid. Until the second fastest moving component begins to elute, only the fastest moving component continues to elute. A method of taking out only a specific component from a large amount of a sample in its original concentration by the above method is called frontal analysis.

Example of frontal analysis: Desalination of protein solution For the purpose of removing salts such as sodium chloride from protein samples of about 1 mL, gel filtration columns for desalting are commercially available (for example, GE Healthcare HiTrap Desalting). The column is packed with approximately 5 mL of a porous packing with small pores that cannot contain any macromolecules such as proteins. Small ions such as sodium ions and low-molecular-weight organic compounds can enter every corner of this small hole. When a protein sample of about 1 mL flows through the column, the protein elutes without being diluted much, and the salts elute sufficiently late.

Practical example of frontal analysis: In order to directly examine the binding reaction between a frontal gel filtration chromatography (FGC) protein and a small molecule ligand, it is necessary to measure the equilibrium concentration of the free ligand. In the FGC method, frontal analysis of a reaction solution is performed using a gel filtration column. At that time, instead of continuing the flow of the reaction solution to the column, after a certain amount is flowed to the column, switching to the elution with the buffer solution is performed. As a result, the free ligand with the original concentration can be purely extracted at the rear end of the chromatogram. Of course, the protein at the original concentration is taken out at the front end of the chromatogram. Between them, the original reaction liquid is taken out as a trapezoidal part. The free ligand concentration in the reaction solution can be determined simply by measuring the ligand concentration in the trapezoidal portion at the rear end obtained by FGC.

  The following conditions are necessary to perform frontal analysis of a sample that undergoes a binding reaction and to extract only the free ligand with the equilibrium concentration of the original reaction solution at the rear end of the chromatogram. (1) The protein moves through the column faster than the small molecule ligand. (2) The protein migration rate does not change even when the ligand is bound. (3) The binding reaction rate is fast with respect to the time scale necessary for the separation mechanism of the column to function, and the binding reaction is in an equilibrium state locally in the column. The frontal gel filtration chromatography (FGC) that uses a gel filtration column for analysis only satisfies the above conditions for most samples. (There are some examples of frontal analysis by capillary electrophoresis, but there are only a limited number of ligands. Only applicable).

  In the frontal analysis, the sample is continuously passed through the column until the original sample elutes as it is. Therefore, a sample several times the volume of the column used for analysis is required. If frontal analysis is not possible with a small amount of sample, it will not be practical even if it has excellent characteristics. The present inventors have previously reported that a frontal chromatogram was obtained with a conventional sufficient sample amount (1-2.5 ml) (Non-patent Documents 1 and 2).

  Non-Patent Document 3 reports that the theoretical chromatogram of FGC was calculated for a system with an A + B = C type interaction.

M. Honjo, T. Ishida, and K. Horiike, J. Biochem., 122, 258-263 (1997) O. Sawada, T. Ishida, and K. Horiike, J. Biochem., 129, 899-907 (2001) JR. Cann, and DJ. Winzor, Arch. Biochem. Biophys., 256, 78-89 (1987)

  In order to perform FGC with a very small amount of sample, a micro-size gel filtration column is required. In order to perform frontal analysis with a trace amount sample of 100 microliters or less, it is necessary to make the analytical column small, that is, to use a microcolumn having a column capacity of less than 100 microliters.

In the microfrontal gel filtration method (mFGC method), a microgel filtration column having an inner diameter of 1 mm or less is used, and a micro sample of 100 microliters or less is separated into three parts as shown in FIG.
-In the trapezoidal portion indicated by 2 in the center, the original sample is eluted as it is (not diluted or concentrated).
In the part indicated by 1 in the front end part, the protein is eluted with the original concentration.
-In the trapezoidal part indicated by 3 at the rear end, only free low molecules are eluted, and the concentration is equal to the equilibrium concentration of free low molecules in the original sample.

The mFGC method can easily perform such pretreatment of a small amount of sample, and has the following advantages.
-The free ligand concentration in the sample can be determined directly.
-When a sample contains a plurality of ligands, a ligand that strongly binds to a protein appears in 1 more than 3, so that a strong binding ligand can be easily screened.
・ Since no protein is included in 3, ligand analysis by mass spectrometry can be easily performed.

  Because of these features, the mFGC method is a sample pretreatment method that is extremely effective not only for direct measurement of intermolecular interactions, but also for pharmacokinetic analysis, drug discovery, and search for new biomarkers.

  However, there is currently no objective method for evaluating column design guidelines, experimental apparatus construction methods, and experimental methods for use in FGC (mFGC) in microgel filtration columns. Conventional gel filtration chromatography is intended for protein purification, protein sample desalting, and buffer exchange, so conventional column evaluation methods and experimental guidelines are not useful for mFGC. Furthermore, the method described in Non-Patent Document 3 is not a method capable of performing a simulation useful for conducting an mFGC experiment.

  Therefore, the present invention provides a chromatogram simulation method, system, and program capable of obtaining a predicted chromatogram based on a simulation model and determining a minimum column size, a sample amount, and a flow rate necessary for mFGC. An object of the present invention is to provide a method for designing a gel filtration column.

  Furthermore, an object of the present invention is to provide a method for evaluating a column produced based on a column design parameter obtained by the chromatogram simulation method using an actual sample.

In order to achieve the above object, a frontal gel filtration chromatogram simulation method according to the present invention is a chromatogram simulation method in a frontal method using a microgel filtration column in a computer including an arithmetic unit and a recording unit, The computing device sets the size rg of the packing material of the gel filtration column having a mobile phase and a stationary phase, and sets the volume vu of the minimum functional unit of the gel filtration column to the size rg of the packing material. A second step to set based on the separation characteristics of the gel filtration column, the mobile phase volume v0u, the stationary phase volume viu, and the volume vip in the stationary phase into which protein can enter, the volume of the minimum functional unit reversible binding of the ligand to the filler. A third step of setting a coefficient ng and Kg or k meaning, a fourth step of setting the number m of layers of the minimum functional unit in the gel filtration column, and the gel filtration column in one calculation step The fifth step of setting the liquid amount dV to flow to the value less than the mobile phase volume v0u based on the mobile phase volume v0u, and the liquid amount Vs of the sample applied to the gel filtration column, m and the sixth step that is set based on the mobile phase volume v0u, and the total liquid volume Vmax applied to the gel filtration column is the number m of the stack, the mobile phase volume v0u, and the stationary phase into which the protein can enter And an eighth step for setting a total protein concentration P0 of the sample and a total ligand concentration C0 of the sample. A ninth step of setting a dissociation constant Kd for the binding reaction of the protein and the ligand, a total protein concentration Pt of the mobile phase, a total protein amount QP, a total ligand concentration Lt of the mobile phase, and a total The initial value of the ligand amount QL is set, and the first minimum functional unit is sequentially ordered from the first minimum functional unit while the sample continues to flow into the gel filtration column. ,
Total protein amount QP = QP (1) + P0 × dV−Pt (1) × dV
Total ligand amount QL = QL (1) + C0 × dV−Lt (1) × dV
Based on the relationship, the total protein amount QP and the total ligand amount QL of a new mobile phase are calculated, and after the flow of the sample into the gel filtration column is completed,
Total protein amount QP = QP (1) −Pt (1) × dV
Total ligand amount QL = QL (1) −Lt (1) × dV
Based on the relationship, the total protein amount QP and the total ligand amount QL of a new mobile phase are calculated, and the i-th (i is a natural number of 2 or more) th smallest functional unit is
Total protein amount QP = QP (i) + Pt (i−1) × dV−Pt (i) × dV
Total ligand amount QL = QL (i) + Lt (i−1) × dV−Lt (i) × dV
Based on the relationship, the total protein amount QP and the total ligand amount QL of the new mobile phase are calculated, and the total protein concentration of the new mobile phase is calculated for the first minimum functional unit and the i th minimum functional unit. Pt and the total ligand concentration Lt,

and

And an eleventh step of obtaining a predicted chromatogram based on the elution volume, the total protein concentration of the eluate, and the total ligand concentration of the eluate.

A chromatogram simulation system according to the present invention includes a calculation device and a recording unit, and is a system for simulating a chromatogram in a frontal gel filtration method, wherein the calculation device has a mobile phase and a stationary phase. A first step of setting a column packing size rg; a second step of setting a minimum functional unit volume vu of the gel filtration column based on the size rg of the packing; and the gel filtration. The mobile phase volume v0u, the stationary phase volume viu, and the volume vip in the stationary phase into which the protein can enter are set based on the volume vu of the minimum functional unit, and the packing of the ligand. A third step of setting coefficients ng and Kg or k which mean reversible binding to the agent; A fourth step of setting the number m of layers of the minimum functional unit in the excess column, and a liquid volume dV to be passed through the gel filtration column in one calculation step based on the mobile phase volume v0u. a fifth step of setting the value to less than v0u, a sixth step of setting the liquid volume Vs of the sample applied to the gel filtration column based on the number of layers m and the mobile phase volume v0u, and the gel A seventh step of setting a total liquid volume Vmax to be applied to the filtration column based on the number of layers m, the mobile phase volume v0u, and the volume vip in the stationary phase into which the protein can enter; An eighth step of setting the protein concentration P0 and the total ligand concentration C0 of the sample; and a dissociation constant for the binding reaction of the protein and the ligand A ninth step of setting Kd, and setting initial values of total protein concentration Pt, total protein amount QP, total ligand concentration Lt, and total ligand amount QL of the mobile phase, and the first In order from the smallest functional unit, the first smallest functional unit, while the flow of the sample into the gel filtration column continues,
Total protein amount QP = QP (1) + P0 × dV−Pt (1) × dV
Total ligand amount QL = QL (1) + C0 × dV−Lt (1) × dV
Based on the relationship, the total protein amount QP and the total ligand amount QL of a new mobile phase are calculated, and after the flow of the sample into the gel filtration column is completed,
Total protein amount QP = QP (1) −Pt (1) × dV
Total ligand amount QL = QL (1) −Lt (1) × dV
Based on the relationship, the total protein amount QP and the total ligand amount QL of a new mobile phase are calculated, and the i-th (i is a natural number of 2 or more) th smallest functional unit is
Total protein amount QP = QP (i) + Pt (i−1) × dV−Pt (i) × dV
Total ligand amount QL = QL (i) + Lt (i−1) × dV−Lt (i) × dV
Based on the relationship, the total protein amount QP and the total ligand amount QL of the new mobile phase are calculated, and the total protein concentration of the new mobile phase is calculated for the first minimum functional unit and the i th minimum functional unit. Pt and the total ligand concentration Lt,

and

And an eleventh step of obtaining a predicted chromatogram based on the elution volume, the total protein concentration of the eluate, and the total ligand concentration of the eluate. .

Further, a chromatogram simulation program according to the present invention is a program for simulating a chromatogram in a frontal gel filtration method in a computer including an arithmetic device and a recording unit, and the computer has a mobile phase and a stationary phase. A first function for setting the size rg of the filler of the filtration column, a second function for setting the volume vu of the minimum functional unit of the gel filtration column based on the size rg of the filler, and the gel The mobile column volume v0u, the stationary phase volume viu, and the volume vip in the stationary phase into which the protein can enter, which are separation characteristics of the filtration column, are set based on the volume vu of the smallest functional unit, and the ligand A third that sets the coefficients ng and Kg or k, which means reversible binding to the filler A function, a fourth function for setting the number m of the minimum functional units in the gel filtration column, and a liquid amount dV to be passed through the gel filtration column in one calculation step based on the mobile phase volume v0u. , A fifth function for setting a value less than the mobile phase volume v0u, and a sixth function for setting the liquid volume Vs of the sample applied to the gel filtration column based on the number m of layers and the mobile phase volume v0u. And a seventh function for setting the total liquid volume Vmax applied to the gel filtration column based on the number m of the layers, the mobile phase volume v0u, and the volume vip in the stationary phase into which the protein can enter. An eighth function for setting the total protein concentration P0 of the sample and the total ligand concentration C0 of the sample, and a dissociation constant for the binding reaction of the protein and the ligand a ninth function for setting d, and initial values of the total protein concentration Pt, total protein amount QP, total ligand concentration Lt, and total ligand amount QL of the mobile phase, and the first In order from the smallest functional unit, the first smallest functional unit, while the flow of the sample into the gel filtration column continues,
Total protein amount QP = QP (1) + P0 × dV−Pt (1) × dV
Total ligand amount QL = QL (1) + C0 × dV−Lt (1) × dV
Based on the relationship, the total protein amount QP and the total ligand amount QL of a new mobile phase are calculated, and after the flow of the sample into the gel filtration column is completed,
Total protein amount QP = QP (1) −Pt (1) × dV
Total ligand amount QL = QL (1) −Lt (1) × dV
Based on the relationship, the total protein amount QP and the total ligand amount QL of a new mobile phase are calculated, and the i-th (i is a natural number of 2 or more) th smallest functional unit is
Total protein amount QP = QP (i) + Pt (i−1) × dV−Pt (i) × dV
Total ligand amount QL = QL (i) + Lt (i−1) × dV−Lt (i) × dV
Based on the relationship, the total protein amount QP and the total ligand amount QL of the new mobile phase are calculated, and the total protein concentration of the new mobile phase is calculated for the first minimum functional unit and the i th minimum functional unit. Pt and the total ligand concentration Lt,

and

And an eleventh function for obtaining a predicted chromatogram based on the elution volume, the total protein concentration of the eluate, and the total ligand concentration of the eluate. .

  The gel filtration column design method according to the present invention is a method for obtaining the design parameters and analysis conditions of the gel filtration column, and using the design parameters and analysis conditions of the gel filtration column as input values, the model of the binding reaction system The chromatogram simulation is performed based on the analysis conditions, and the analysis parameters or the model is changed, and the chromatogram simulation is repeatedly performed to obtain the optimum value of the design parameter of the gel filtration column. The parameters include the size of the packing material of the gel filtration column, the volume of the minimum functional unit of the gel filtration column, the separation characteristics of the minimum functional unit, and the number of layers of the minimum functional unit, and the analysis parameter The amount of liquid to be passed through the gel filtration column in one calculation step and suitable for the gel filtration column And a total liquid amount to be applied to the gel filtration column, wherein the model includes a total protein concentration of the sample and a total ligand concentration of the sample, and a dissociation constant for a protein-ligand binding reaction. , Based on the interaction of the ligand and the filler.

  The gel filtration column evaluation method according to the present invention is a method for evaluating a gel filtration column produced based on the design parameter obtained by any one of the chromatogram simulation method, system and program according to the present invention. A first step of measuring a first chromatogram of a first sample containing only the ligand, a second step of measuring a second chromatogram of a second sample containing only the protein, and the gel A third step of calculating a mobile phase ratio and a stationary phase ratio occupying the volume of the filtration column; a fourth step of measuring a third chromatogram of a mixture of the protein and the ligand; The elution pattern of the protein between the second chromatogram and the third chromatogram, and the third chromatogram Based on the difference chromatogram obtained by subtracting the first chromatogram, characterized in that it comprises a and a fifth step of determining the validity of the design parameters.

  According to the chromatogram simulation method, system, or program of the present invention, a chromatogram predicted based on a simulation model can be obtained. In addition, the column size, flow rate, and minimum required sample amount can be obtained, and analysis column design of the microfrontal gel filtration method, analysis device design, and experimental conditions can be optimized.

  That is, it is possible to show that FGC in a trace amount sample can be realized even by using a commercially available filler, and the application target of FGC including protein-protein interaction can be shown. The development goals of the filler needed to expand can be indicated quantitatively.

  Moreover, according to the gel filtration column evaluation method of the present invention, it is possible to evaluate the gel filtration column produced based on the design parameters obtained by the chromatogram simulation method, system or program of the present invention.

FIG. 2 shows a typical mFGC chromatogram. It is a figure for demonstrating the minimum functional unit of the column used in the chromatogram simulation method which concerns on embodiment of this invention. It is a figure which shows the movement model of the protein and ligand between the minimum functional units of a column. It is a figure which shows the movement model of the protein and ligand between the minimum functional units of a column. It is a figure which shows the movement model of the protein and ligand between the minimum functional units of a column. It is a block diagram which shows schematic structure of the computer system which performs the chromatogram simulation method which concerns on embodiment of this invention. It is a figure for demonstrating the method of calculating | requiring a column design parameter and analysis information using the chromatogram simulation method which concerns on embodiment of this invention. It is a flowchart which shows the processing order of the chromatogram simulation method which concerns on embodiment of this invention. It is the schematic which shows an example of the apparatus structure which performs a microfrontal gel filtration method. It is an example of the chromatogram estimated by the chromatogram simulation which concerns on embodiment of this invention. It is an example of the chromatogram estimated by the chromatogram simulation which concerns on embodiment of this invention.

  Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings. Regarding the chromatogram simulation method according to the embodiment of the present invention, first, in (I), a mathematical relationship in the simulation will be described. Next, in (II), the processing content of the simulation method will be described with reference to a flowchart. Then, in (III), a method for evaluating a column produced based on the column design parameters obtained by the chromatogram simulation method using an actual sample will be described.

(I) Mathematical Relationship in Simulation FIGS. 2 to 5 are used to explain the concept of the minimum functional unit (MFU) of a column used in the chromatogram simulation method according to the embodiment of the present invention. FIG.

  FIG. 2 shows the contents of the minimum functional unit of the column. In FIG. 2, when the total volume is vu, the mobile phase volume is v0u, the stationary phase volume is viu, and the volume in which the protein in the stationary phase can enter is vip, the regions indicated by 1 are free protein, free ligand, protein -The volume v00 (= v0u + vip) in which all of the ligand complex (bound ligand) is present, and the region indicated by 2 is the volume in which only the free ligand is present.

  The transfer of proteins and ligands from MFU to MFU occurs only with the movement of the mobile phase. Next, the basic variable for describing this movement and the relationship between the variables will be described.

(1) Protein and ligand movement model between MFUs
In the chromatogram simulation method according to the embodiment of the present invention, a migration model of proteins and ligands between MFUs when elution proceeds by a volume dV is introduced.

(1.1) i-th (i ≧ 2) For i-th MFU, the relationship shown in FIG. 3 is established. In FIG. 3, QP (i) is the amount (pmol) of total protein present in the i-th MFU, QL (i) is the amount (pmol) of total ligand present in the i-th MFU, Pt (i) is the total protein concentration (μmol / L) in the mobile phase of the i-th MFU, and Lt (i) is the total ligand concentration (μmol / L) in the mobile phase of the i-th MFU. is there.

  When elution progresses by the volume dV, the i-th MFU has a protein of Pt (i-1) × dV pmol and a ligand of Lt (i-1) × dv pmol from the (i-1) -th MFU. Inflow. On the other hand, from the i-th MFU, a protein of Pt (i) × dV pmol and a ligand of Lt (i) × dV pmol flow out. As a result, the amount of total protein and total ligand present in the i-th MFU is as follows.

Total protein amount = QP (i) + Pt (i−1) × dV−Pt (i) × dV
Total ligand amount = QL (i) + Lt (i−1) × dV−Lt (i) × dV

(1.2) While the sample flows into the column for the first MFU (first MFU) at the column entrance, the relationship shown in FIG. 4 is established. After the injection of the sample into the column is completed and the solution is changed to liquid delivery using a buffer solution, the relationship shown in FIG.

  4 and 5, QP (1) is the amount of total protein (pmol) present in the first MFU, and QL (1) is the amount of total ligand (pmol) present in the first MFU. Pt (2) is the total protein concentration (μmol / L) in the mobile phase of the second MFU, and Lt (2) is the total ligand concentration (μmol / L) in the mobile phase of the second MFU. L). Here, P0 is the total protein concentration (μmol / L) of the sample, and C0 is the total ligand concentration (μmol / L) of the sample.

  Referring to FIG. 4, when elution progresses by dV, P0 × dV pmol protein and L0 × dv pmol ligand flow into the first MFU from the sample solution. On the other hand, Pt (1) × dV pmol protein and Lt (1) × dV pmol ligand flow out from the first MFU. As a result, the amount of total protein and total ligand present in the first MFU is as follows.

Total protein amount = QP (1) + P0 × dV−Pt (1) × dV
Total ligand amount = QL (1) + C0 × dV−Lt (1) × dV
Referring to FIG. 5, as dV elution progresses, the protein and ligand no longer flow into the first MFU. On the other hand, Pt (1) × dV pmol protein and Lt (1) × dV pmol ligand flow out from the first MFU. As a result, the amount of total protein and total ligand present in the first MFU is as follows.

Total protein amount = QP (1) −Pt (1) × dV
Total ligand amount = QL (1) −Lt (1) × dV
As described above with reference to FIGS. 2 to 5, to calculate the total amount of protein and the total amount of ligand present in each MFU after elution further proceeds by the volume dV,
-Total amount of protein QP (i) present in each MFU
-Total amount of ligands QL (i) present in each MFU
-Total protein concentration of mobile phase of each MFU Pt (i)
-Total ligand concentration Lt (i) of mobile phase of each MFU
It is understood that it is sufficient to know in advance.

(2) Calculation of Total Protein Concentration Pt and Total Ligand Concentration Lt of MFU Mobile Phase Once the total amount of protein QP and total amount QL of ligand present in MFU are known, the total protein concentration Pt and total ligand of the MFU mobile phase The concentration Lt can be calculated. In the following, the binding reaction between a protein and a ligand will be considered with the most general reaction equation so that all types of binding reaction systems can be handled.

  • The protein has n binding sites for the ligand. That is, it is assumed that up to n ligand molecules can bind to one molecule of protein. This multiple bond system is expressed by the following format 0a, which includes the case where there is cooperativity between the binding sites.

In the above equation, K _i is the equilibrium constant of the i-th binding reaction, and the letters written in italics represent the molar concentration of the corresponding component (unit is μmol / L).

  In this binding equilibrium system, the following relational expression holds between the total protein concentration Pt and the free protein concentration P and free ligand concentration L.

Further, the following relational expression holds between the total ligand concentrations Lt, Pt, and L.

  -In MFU, protein is considered to be freely distributed in the mobile phase (volume v0u) and the region (volume vip) that can enter the stationary phase regardless of the binding state of the ligand. In the region of v0u + vip), the total protein concentration Pt is constant. Therefore, the following relationship is established between the total amount QP of the MFU protein and Pt.

From this equation, Pt can be easily obtained from QP.

In the simulation according to the present embodiment, reversible adsorption between the ligand and the filler itself is considered as follows. That is, the MFU filler has a total of _ng picomoles (pmo) l of ligand binding sites, which are considered to be independent and equivalent to each other. At this time, the following relational expression holds between the free ligand concentration L and the amount of ligand L _bg (unit: pmol) bound to the filler.

Here, K _g is a dissociation constant (unit: μmol / L) for the binding reaction of the filler to each binding site.

  In MFU, the ligand can exist in any binding state in the mobile phase (volume v0u) and the region in the stationary phase where the protein can enter (volume vip), and the region in which the protein in the stationary phase cannot enter (volume is viu) -Vip) exists only in the free form. Thus, the total ligand amount of MFU is given by the following equation by adding what is bound to the filler.

Substituting the previously derived equation 3a into this equation yields the following equation:

Equation 7a is a multidimensional equation for L.

  By using Equation 4a and Equation 7a, the total protein concentration Pt and the total ligand concentration Lt of the mobile phase of MFU can be calculated from the total protein amount QP of MFU and the total number of ligands QL. Equation 7a can be solved using a normal multidimensional equation solving method (such as Newton's method).

-In the simplest binding reaction, 1: 1 binding reaction, and when the interaction between the ligand and the filler is relatively weak and it can be considered that K _g >> L in Formula 5a, Formula 7a is very It becomes the following simple formula.

Here, k = n _g / K _g . Since equation 9a is a quadratic equation of L, it can be easily solved. The simplest system is used in the processing contents of (II) simulation method described later and an example of a program attached to the embodiment.

  Based on the movement model of (1) and the calculation of (2) described above, in the chromatogram simulation method according to the embodiment of the present invention, the following items 1) to 5) are introduced into the simulation. ing.

Feature 1) Introduction of the concept of minimum functional unit (MFU) of a column.
• Based on the actual packing diameter, assume 50 times the diameter of the packing particles as the minimum thickness that can be packed uniformly into the column (actually this thickness is determined by the packing technique of the column) ).
-At least tens of thousands of gel particles are accommodated in the minimum functional unit, and considering the flow path volume of a normal capillary HPLC device, the MFU mobile phase volume is several tens of nanoliters or more. Set the diameter (= inner diameter of the column).

Feature 2) The column is composed of the smallest functional units in series, and the transfer of substances from one MFU to the next MFU occurs only by the transfer of the mobile phase solution of MFU.
・ Assuming that the column has at least 200 MFUs in series.
・ In FGC, the rise and fall of the chromatogram itself is not a problem, and a trapezoidal part is used. In this region, since the concentration of each substance is constant, the diffusion of the substance due to the concentration gradient in the axial direction can be ignored.

Characteristic 3) The amount of eluate for 1 unit time (2 seconds by default) is calculated based on the mobile phase volume of the minimum functional unit.
・ It may be less than the volume of the mobile phase of the minimum functional unit, and the default is set to 80%

  Characteristic 4) It is set so that it can handle the case where reversible adsorption exists between the filler and the low molecular ligand.

Characteristic 5) It is set so that it can be handled even when the protein can penetrate a part of the stationary phase.
For example, serum albumin is localized only in the mobile phase in Superdex Peptide, but can penetrate about 30% of the stationary phase in TSKgel SuperSW2000.

(II) Processing Contents of Simulation Method FIG. 6 is a block diagram showing a schematic configuration of a computer system that performs the chromatogram simulation method according to the embodiment of the present invention. A computer system 1 (hereinafter also simply referred to as a computer 1) that performs a chromatogram simulation method according to the embodiment includes a CPU 10 that performs calculation of data to be described later, a memory 11 that is used in a calculation work area, and calculation data. A recording unit 12 for recording, a bus 13 for transmitting data between the units, and an interface unit 14 (hereinafter referred to as an I / F unit) for inputting / outputting data to / from an external device are provided. Although omitted from FIG. 6, the computer is also provided with operation means (keyboard or the like) or display means (display or the like) normally provided in the computer.

  In the following description, it will be described as a chromatogram simulation method performed by the computer 1 unless otherwise specified. Further, the processing performed by the computer 1 actually means processing performed by the CPU 10 of the computer 1. The CPU 10 temporarily stores necessary data (intermediate data during processing, etc.) using the memory 11 as a work area, and appropriately records data to be stored for a long time such as calculation results in the recording unit 12. In addition, the computer 1 records a program used for performing the processes of steps S1 to S11 described below in an execution format (for example, generated by being converted from a programming language such as C language by a compiler). 12 is recorded in advance, and the computer 1 performs processing using the program recorded in the recording unit 12.

  The input parameters used in the chromatogram simulation method according to the embodiment of the present invention are as follows.

-Diameter rg of filler particles used
The ratio rout of the mobile phase volume (volume outside the packing material) to the total column volume
The ratio rin of the volume of the stationary phase (volume of pores of the filler) in the total column volume
The ratio of the area where the protein to be analyzed can penetrate to the total stationary phase volume rip
These four parameters are the basic parameters of the gel filtration column itself. Other than that, it is determined by the size of the protein to be analyzed and the degree of adsorption interaction between the ligand to be analyzed and the packing material. Therefore, in the simulation described below, these parameters are changed variously as shown in FIG. Investigate. In addition, the chromatographic pattern is examined by changing the sample addition amount and the total elution amount freely from the default values. It is important to be able to simulate interactively.

  Of the four input parameters described above, for the diameter rg of the filler particles, the values in the attached data sheet can be used for the commercially available filler for gel filtration. The mobile phase volume ratio rout, the stationary phase volume ratio rin, and the ratio rip of the region into which the protein to be analyzed can permeate are read from the standard protein analysis data attached to a commercially available column and used. be able to.

  The output parameters obtained by the chromatogram simulation method according to the embodiment of the present invention are as follows.

Column size Flow rate Minimum required sample amount Predicted chromatogram FIG. 8 is a flowchart showing processing of a chromatogram simulation method according to an embodiment of the present invention. Hereinafter, the processing configuration of the chromatogram simulation method according to the embodiment of the present invention will be described in detail based on the flowchart shown in FIG.

  In step S1, the diameter of the filler is set. As the diameter rg [unit: mm] of the filler, the value written in the data sheet attached to the commercially available filler for gel filtration is used. The computer 1 records the input filler diameter rg. For example, an operator inputs values using the operation means. Alternatively, as an example in which no operation means is used, for example, the computer 1 records a data file in which input values are recorded in the recording unit 12 in advance, and the computer 1 records the data file in the data file in the processing of each step. The input value may be appropriately read from the recording unit 12 and used.

  In step S2, the minimum functional unit (MFU) volume is set. Assuming that the diameter is ru [unit: mm] and the length is lu [unit: mm] as the size of the MFU, the computer 1 records, for example, a diameter ru = 50 rg and a length lu = 50 rg as default values. This default value is based on the above feature 1). If the inner diameter and length of the column to be used are predetermined, enter those values. Then, the computer 1 calculates and records the volume vu [unit: μL] of the MFU. The volume vu is obtained from, for example, vu = π · ru · ru · lu / 4.

  In step S3, MFU separation characteristics are set. When the mobile phase volume is v0u [unit: μL], the stationary phase volume is viu [unit: μL], and the volume in which the protein in the stationary phase can enter is vip [unit: μL], the computer 1 uses, for example, v0u as a default value. = 0.4 vu, vin = 0.4 vu, and vip = 0 are recorded. These default values are based on manufacturer evaluation data attached to the packed column. For example, the above-described values of rout = v0u / vu, rin = viu / vu, rip = vip / vin are calculated from the manufacturer evaluation data and used. If there is analysis data for the protein or ligand to be actually analyzed, enter these values. Further, the computer 1 records, for example, k = 0 as a default value of the value k. The value k [unit: μL] indicates reversible weak binding of the ligand to the filler. The introduction of the value k is based on the above feature 4).

  In step S4, the number of MFU stacks in the analysis column is set. If the number of stacks is m, the computer 1 records m = 200 as a default value, for example. This default value is based on the above feature 2). If the column size is determined in advance, the integer part of the value obtained by dividing the column length by the MFU length is input as the number of layers.

  In step S5, the amount of liquid to be flowed is set by calculation in one step. Assuming that the amount of liquid flowing in one step of calculation is dV [unit: μL], the computer 1 records, for example, dV = 0.8 · v0u as a default value. This default value is based on the above feature 3). Note that dV is less than v0u (dV <v0u).

  In step S6, the liquid amount of the sample to be applied is set. Assuming that the liquid volume of the sample to be applied is Vs [unit: μL], the computer 1 records, for example, Vs = 2 · m · v0u as a default value.

  In step S7, the total amount of liquid to be applied is set. Assuming that the total liquid volume to be applied is Vmax [unit: μL], the computer 1 records, for example, Vmax = 2.5 · m · (v0u + vip) as a default value.

  In step S8, the total protein concentration and total ligand concentration of the sample are set. When the total protein concentration of the sample is P0 [unit: μM] and the total ligand concentration is C0 [unit: μM], the computer 1 records the input values of P0 and C0.

  In step S9, a dissociation constant is set. Assuming that the dissociation constant is Kd [unit: μM], the computer 1 records Kd = 20 as a default value, for example.

  In step S10, calculation based on the movement model is performed. The migration model is the migration model described in “(1) Migration model of protein and ligand between MFUs”. That is, the computer 1 calculates the new total protein amount QP and the total number of ligands QL for each MFU in order from the first MFU, and then formulas 4a and 9a (formula 7a in the general case) To calculate the total protein concentration Pt and total ligand concentration Lt of the new mobile phase. The computer 1 repeats this calculation by moving the mobile phase by dV to the last MFU, and records the calculation result. At this time, the predicted chromatogram is recorded in the computer 1 as the elution volume, the total protein concentration of the eluate, and the total ligand concentration of the eluate.

  In step S11, the calculation result of step S10 is output. The items of the calculation result output from the computer 1 are as follows.

-Column size-Flow rate (local equilibrium arrival time inside the column)
・ Minimum required sample amount ・ Predicted chromatogram (Note that, as shown in the example of the program attached to the example, parameters such as column size, flow rate, minimum required sample amount, and free ligand concentration are output in the 17th column of the cell. (The predicted chromatograms are output in columns 10, 11, and 12 of the cell.)
The computer 1 displays the predicted chromatogram pattern as a graph on the display means, for example. Then, based on the predicted chromatogram pattern displayed graphically on the display means, the operator can obtain a typical FGC chromatogram having a portion where the original sample is eluted as it is. Determine whether the ligand concentration in the second trapezoidal portion of the pattern (portion 3 in FIG. 1) is equal to the equilibrium concentration of free ligand in the original sample. When the total protein concentration, the total ligand concentration, and the dissociation constant of the hypothetical sample to be analyzed are input, the computer 1 calculates the equilibrium concentration of the free ligand in the binding reaction system. This calculated value should match the ligand concentration in the second trapezoidal part of the elution pattern of the ligand in the predicted chromatogram.

  If the operator determines that a typical FGC chromatogram has not been obtained, it can also change the chromatogram pattern by changing various conditions such as the concentration of protein and ligand in the virtual sample and the strength of interaction. When it is desired to investigate in detail, the operator changes the default value of each set value using the operation means and inputs it again to the computer 1, and the computer 1 executes the simulation shown in steps S1 to S11 again.

  In the actual experiment, the purpose is to determine the free ligand concentration of the sample, but since the virtual sample concentration and dissociation constant are input in advance in the simulation, the free ligand concentration is also automatically determined. If this value does not match the ligand concentration of the second trapezoidal part, the simulation is not correct. The mFGC method is primarily a unique sample division (pretreatment method) shown in FIG. 1, and the measurement of the free ligand concentration of the sample is one of the important results obtained by this division. Only.

(III) Evaluation of Column Design Parameters Using Actual Samples FIG. 9 is a schematic diagram showing an example of the configuration of an apparatus for performing the microfrontal gel filtration method. The apparatus includes a gel filtration column 20, a sample injection port 21, a sample loop 22, a first pump 23, a second pump 24, and a detector 25. As shown in FIG. 9, the sample injection port 21, the sample loop 22, and the first pump 23 are connected to the upstream side of the gel filtration column 21, and the second pump 24 and the detector 25 are connected to the gel filtration column 20. Connected to the downstream side. The sample / buffer solution is injected into the gel filtration column 20 by the first pump 23, and the first pump 23 accurately controls the flow rate. The second pump 24 is used when it is necessary to dilute the eluate at the outlet of the gel filtration column 20.

  The gel filtration column 20 only needs to have a micro size with a column volume of less than 1000 μl that enables frontal analysis of a small amount of sample, and a packing material for gel filtration that is usually used for gel filtration chromatography is used. Examples of such fillers include TSKgel Super SW2000, Superdex Peptide, Superdex 75, and the like. The sample injection port 21 is for injecting a sample or a buffer solution to be analyzed by a syringe or the like into the sample loop 22, and the sample loop 22 temporarily holds the sample and the buffer solution before being injected into the gel filtration column. It is for keeping. The first pump 23 is suitable to have a low flow rate and high flow accuracy, and the second pump 24 can be a pump generally used in HPLC or the like. The detector 25 detects proteins and / or ligands coming out of the column, and examples thereof include a photodiode array, an ultraviolet-visible monitor, and a fluorescence monitor.

Next, a method for analyzing and evaluating an actual sample using the microcolumn prepared based on the result of the model calculation described in “ (II) Processing contents of simulation method ” will be described.

  Prepare an empty column of appropriate size based on the simulation results and fill with packing material. In the actual analysis, the interface of the sample component due to various factors occurs, so the length of the sample can be simulated by using a column larger than the simulation result, specifically, for example, an available empty column with an inner diameter of 1 mm that can be easily packed. Prepare one larger than the column volume, and select the optimal one from among the commercially available packing materials and pack them in-house. Analytical flow rate and sample volume are first calculated by correcting the values obtained by simulation by multiplying the ratio between the actual column size and the virtual column size in the simulation, and then optimized based on the actual chromatogram. .

(1) Measure the chromatogram of a sample of a low-molecular-weight ligand alone. The measurement is performed by changing the volume (volume) of the sample to be injected into the column. Determine the volume. Check that the total amount of ligand injected into the column is eluted from the column (check for irreversible adsorption of the ligand to the packing material). The elution volume of the ligand is determined from the rising pattern of the chromatogram.

(2) Measurement of chromatogram of sample of protein alone The sample amount obtained in (1) is injected into the column. The protein elution volume is determined from the rising pattern of the chromatogram.

(3) Calculate the effective value of the ratio of the mobile phase to the column volume and the ratio of the stationary phase Calculate the ratio of the mobile phase to the column volume from the data in (2) assuming that the protein is localized only in the mobile phase (Rout = protein elution volume / column volume). The effective value of the ratio of the stationary phase to the column volume is calculated from the data of (1) and the data of (2) (rin = (elution volume of ligand−elution volume of protein) / column volume). In addition, if there is reversible adsorption between the ligand and the filler, the stationary phase appears to be large.

(4) Measurement of chromatogram of protein-ligand mixture liquid A mixture liquid containing protein and ligand at the same concentration as in (1) and (2) is injected into the column in the same amount as in (1) and (2). If the obtained chromatogram does not show a trapezoidal portion in which the original sample is eluted as it is, increase the amount of sample injected into the column until it appears. If the sample amount is increased, the measurements (1) and (2) are performed with the sample amount.

(5) Confirmation of FGC preconditions It is confirmed in the chromatograms of (2) and (4) that the protein elution patterns completely match. A difference chromatogram obtained by subtracting the chromatogram of (2) from the chromatogram of (4) is calculated, and it is confirmed that the absolute values of the areas of the positive peak before and the negative peak after that are equal.

  This is because the second trapezoidal portion showing the free ligand is scraped from the original height by the amount of the ligand that elutes quickly due to the interaction with the protein (see FIG. 1).

If (1) to (5) are completed successfully, it is guaranteed that FGC can be executed correctly.
・ Theoretical simulation is performed using the obtained effective parameters rout and rin, and the final column is designed.

(6) Measurement of binding curve Measurement is performed by changing the concentration of the protein-ligand mixture, and analysis of protein alone and ligand alone is also put in between. A binding curve (relationship between the concentration of free ligand and the average number of ligand molecules bound per protein molecule) is calculated from the measurement results. The average number (r) of ligand molecules bound per protein molecule can be determined from the free ligand concentration.

  The coupling curve is expressed by the following formula in the multiple coupling system of Formula 0a.

  Here, the function f is Equation 2a.

Fit the binding curve to the above equation (using the modified Markat method) and determine the binding parameters. For example, when there are n independent and equivalent binding sites, the above formula becomes the following simple formula.
r = n ・ L (K _d + L)
Kd: dissociation constant
L: Free ligand concentration
r: average number of ligand molecules bound per protein molecule
n: number of binding sites

  Examples of the present invention will be described below to clarify the features of the present invention. In the calculation method shown in Step 1) to Step 6) below, “MICROSOFT EXCEL” and “VISUAL BASIC” (both registered trademarks) of Microsoft Corporation of the United States were used for calculation simulation.

  Step 1) The total protein concentration Pt of the mobile phase of the i-th MFU in the previous calculation stage is set to the cell (cells (i, 5)) in the fifth row and the total protein amount QP is set to six columns. The total ligand concentration Lt of the mobile phase is set to the cell (cells (i, 7)) in the seventh column, the total ligand amount QL is set to 8 in the cell (cells (i, 6)) in the i-th row of the eye. It is stored in the cell (cells (i, 8)) in the i-th row of the column. In the first calculation, the values of these cells are naturally zero (i = 1 to m).

  Step 2) The mobile phase was moved by dV, and the value of Step 1) and “(1) Mathematical relationship in simulation” described in “(1) Model of protein and ligand transfer between MFUs” described above. According to the formula, in order from the first MFU, for each MFU, first, a new total protein amount QP and a total ligand amount QL are calculated, and then according to formula 4a and formula 9a (generally formula 7a), Calculate the total protein concentration Pt and total ligand concentration Lt of the new mobile phase.

  Step 3) The new Pt, QP, Lt, and QL values of the i-th MFU calculated in step 2) are stored in the i-th cells in the first, second, third, and fourth columns, respectively.

  Step 4) The Pt and Lt values of the mobile phase of the last MFU, that is, the MFU at the m-th column outlet, are stored in the j-th cell in the 11th and 12th columns, respectively (j is the number of calculations). The value of j × dV (the elution volume from the column at this time) is stored in the 10th cell in the 10th row.

  Step 5) The values stored in step 3) are moved to the corresponding cells in the fifth, sixth, seventh and eighth columns.

  Step 6) Repeat steps 1) to 5). Predicted chromatograms are stored in the 10th column (elution volume), 11th column (total protein concentration of eluate), and 12th column (total ligand concentration of eluate).

(Example 1) In the case of TSK-gel SuperSW2000 In this case, the filler particle diameter is 0.004 millimeters, and the ratio of the mobile phase and the stationary phase in the total column volume is 0.38 and 0.36, respectively. . The results obtained by inputting these values are as follows. The column size is 0.8 millimeters inside diameter, 40 millimeters long, the flow rate is 0.9 microliters / minute, and the sample volume is 7.6 microliters. A chromatogram predicted under these conditions is shown in FIG. Reference numeral 1 in the figure indicates protein elution, and reference numeral 2 indicates low molecule elution. The protein concentration was 30 micromol / liter, the low molecular concentration was 20 micromol / liter, and the dissociation constant was 20 micromol / liter.

(Example 2) Superdex Peptide In this case, the particle diameter of the filler is 0.013 millimeters, and the ratio of the mobile phase and the stationary phase in the total column volume is 0.32 and 0.49, respectively. The results obtained by inputting these values are as follows. The column size is 0.65 millimeters inside diameter, 130 millimeters long, the flow rate is 1.7 microliters / minute, and the sample volume is 19 microliters. A chromatogram expected under these conditions is shown in FIG. Reference numeral 1 in the figure indicates protein elution, and reference numeral 2 indicates low molecule elution. The protein concentration was 30 micromol / liter, the low molecular concentration was 20 micromol / liter, and the dissociation constant was 20 micromol / liter.

(Example of the program used for the calculation shown in the examples)
A description example of the program described in “VISUAL BASIC” is shown below. The description example of this program is an example, and the processing content of the program is not limited to the content shown in this description example.

Sub SimulationFGC1 ()

rg = 0.013 'mm gel particle diameter
lu = 50 * rg 'mm length of the functional unit
ru = 50 * rg 'mm diameter of the functinal unit
vu = 3.14 * ru * ru * lu / 4 'uL volume of the functinal unit
rout = 0.32
v0u = rout * vu 'uL void volume of the functinal unit
rin = 0.49
viu = rin * vu 'uL internal volume of the functinal unit
rip = 0
vip = rip * viu 'uL the volume of the internal space accesible for protein
rk = 0
k = rk * viu 'uL k = ng / Kg binding to the gel matrix Kg >> C0

m = 200 'total number of the functinal unit
B = m * lu 'the length of the column
V0 = m * v0u 'uL void volume of the column
Vi = m * viu 'uL internal volume of the column
Vp = m * vip
dV = 0.8 * v0u 'elution volume per unit calculation step

Vmax = (V0 + Vi) * 2.5 'total elution volume (including sample volume)
nv = Int (Vmax / dV) 'total number of calculation step

Vs = 2 * V0 'sample volume applied

ns = Int (Vs / dV)

C0 = 20 'uM the total concentration of ligand (L)
P0 = 30 'uM the total concentration of acceptor protein (P)
kd = 20 'uM dissociation constant (one to one stoichiometry)

d00 = kd + P0-C0
d01 = d00 ^ 2 + 4 * kd * C0
d02 = d01 ^ 0.5
lf = 2 * kd * C0 / (d00 + d02)

Cells (2, 15) = nv
Cells (1, 17) = B 'mm length of the column
Cells (2, 17) = ru 'mm internal diameter of the column
Cells (3, 17) = V0 'uL void volume of the column
Cells (4, 17) = Vi 'uL internal volume of the column
Cells (5, 17) = V0 + Vp 'uL elution volume of the protein
dt = 2 'sec
Cells (6, 17) = dV * 60 / dt 'uL / min flow rate
Cells (7, 17) = Vmax
Cells (8, 17) = Vs' uL sample volume applied
Cells (9, 17) = C0
Cells (10, 17) = P0
Cells (11, 17) = kd
Cells (12, 17) = lf 'free ligand concentration of the original sample
Cells (13, 17) = k
Cells (14, 17) = m * vu 'bed volume of the column

v00 = v0u + vip
v01 = v0u + viu + k


QP = P0 * dV
QL = C0 * dV

Pt = QP / v00
a00 = v01 * kd + Pt * v00-QL
b00 = 4 * v01 * QL * kd
a01 = a00 ^ 2 + b00
a02 = a01 ^ 0.5

CL = 2 * QL * kd / (a00 + a02)
CP = Pt / (1 + CL / kd)
CPL = Pt * CL / (kd + CL)
Lt = CL + CPL


Cells (1, 1) = Pt
Cells (1, 2) = QP
Cells (1, 3) = Lt
Cells (1, 4) = QL


For j = 2 To m
Cells (j, 1) = 0
Cells (j, 2) = 0
Cells (j, 3) = 0
Cells (j, 4) = 0
Next j

Cells (1, 10) = dV
Cells (1, 11) = Cells (m, 1) 'Pt
Cells (1, 12) = Cells (m, 3) 'Lt

For j = 1 To m
Cells (j, 5) = Cells (j, 1)
Cells (j, 6) = Cells (j, 2)
Cells (j, 7) = Cells (j, 3)
Cells (j, 8) = Cells (j, 4)
Next j


For i = 2 To ns

QP = Cells (1, 6) + P0 * dV-Cells (1, 5) * dV
QL = Cells (1, 8) + C0 * dV-Cells (1, 7) * dV

Pt = QP / v00
a00 = v01 * kd + Pt * v00-QL
b00 = 4 * v01 * QL * kd
a01 = a00 ^ 2 + b00
a02 = a01 ^ 0.5

CL = 2 * QL * kd / (a00 + a02)
CP = Pt / (1 + CL / kd)
CPL = Pt * CL / (kd + CL)
Lt = CL + CPL


Cells (1, 1) = Pt
Cells (1, 2) = QP
Cells (1, 3) = Lt
Cells (1, 4) = QL

For j = 2 To m
QP = Cells (j, 6) + Cells (j-1, 5) * dV-Cells (j, 5) * dV
QL = Cells (j, 8) + Cells (j-1, 7) * dV-Cells (j, 7) * dV

Pt = QP / v00
a00 = v01 * kd + Pt * v00-QL
b00 = 4 * v01 * QL * kd
a01 = a00 ^ 2 + b00
a02 = a01 ^ 0.5

CL = 2 * QL * kd / (a00 + a02)
CP = Pt / (1 + CL / kd)
CPL = Pt * CL / (kd + CL)
Lt = CL + CPL


Cells (j, 1) = Pt
Cells (j, 2) = QP
Cells (j, 3) = Lt
Cells (j, 4) = QL

Next j

Cells (i, 10) = i * dV
Cells (i, 11) = Cells (m, 1) 'Pt
Cells (i, 12) = Cells (m, 3) 'Lt

For j = 1 To m
Cells (j, 5) = Cells (j, 1)
Cells (j, 6) = Cells (j, 2)
Cells (j, 7) = Cells (j, 3)
Cells (j, 8) = Cells (j, 4)
Next j

Cells (1, 15) = i

Next i

For i = ns + 1 To nv

QP = Cells (1, 6)-Cells (1, 5) * dV
QL = Cells (1, 8)-Cells (1, 7) * dV

Pt = QP / v00
a00 = v01 * kd + Pt * v00-QL
b00 = 4 * v01 * QL * kd
a01 = a00 ^ 2 + b00
a02 = a01 ^ 0.5

CL = 2 * QL * kd / (a00 + a02)
CP = Pt / (1 + CL / kd)
CPL = Pt * CL / (kd + CL)
Lt = CL + CPL


Cells (1, 1) = Pt
Cells (1, 2) = QP
Cells (1, 3) = Lt
Cells (1, 4) = QL



For j = 2 To m

QP = Cells (j, 6) + Cells (j-1, 5) * dV-Cells (j, 5) * dV
QL = Cells (j, 8) + Cells (j-1, 7) * dV-Cells (j, 7) * dV

Pt = QP / v00
a00 = v01 * kd + Pt * v00-QL
b00 = 4 * v01 * QL * kd
a01 = a00 ^ 2 + b00
a02 = a01 ^ 0.5

CL = 2 * QL * kd / (a00 + a02)
CP = Pt / (1 + CL / kd)
CPL = Pt * CL / (kd + CL)
Lt = CL + CPL


Cells (j, 1) = Pt
Cells (j, 2) = QP
Cells (j, 3) = Lt
Cells (j, 4) = QL

Next j

Cells (i, 10) = i * dV
Cells (i, 11) = Cells (m, 1) 'Pt
Cells (i, 12) = Cells (m, 3) 'Lt

For j = 1 To m
Cells (j, 5) = Cells (j, 1)
Cells (j, 6) = Cells (j, 2)
Cells (j, 7) = Cells (j, 3)
Cells (j, 8) = Cells (j, 4)
Next j

Cells (1, 15) = i


Next i




End Sub

1 computer 10 CPU
DESCRIPTION OF SYMBOLS 11 Memory 12 Recording part 13 Bus 14 Interface part 20 Gel filtration column 21 Sample injection port 22 Sample loop 23 1st non-pulsating flow pump 24 2nd non-pulsating flow pump 25 Detector

Claims (5)

In a computer comprising an arithmetic unit and a recording unit, a chromatogram simulation method in a frontal gel filtration method,
The arithmetic unit is
And Luz step to set the size rg of filler gel filtration column with a mobile phase and a stationary phase,
The volume vu minimal functional unit of the gel filtration column, and answering step be set based on the size rg of the filler,
The mobile phase volume v0u, the stationary phase volume viu, and the volume vip in the stationary phase into which the protein can enter, which are separation characteristics of the gel filtration column, are set based on the volume vu of the minimum functional unit, and a ligand and Luz step to set the coefficient k to mean reversible binding of to the filler,
And Luz step to set the stacking number m of the minimal functional unit in the gel filtration column,
A liquid volume dV passing the gel filtration column in one calculation step, based on said mobile phase volume V0u, and answering step be set to a value less than said mobile phase volume V0u,
The liquid volume Vs of the sample to flow to the gel filtration column, and answering step be set based on the stack number m and the mobile phase volume V0u,
The total volume Vmax to be supplied to the gel filtration column, the number of stacked layers m, and answering step be set based on the volume vip of the mobile phase volume V0u, and the stationary phase in which the protein is Hairikomeru,
And Luz step to set the total ligand concentration C0 of the total protein concentration P0 and the sample of the sample,
And Luz step to set the dissociation constant Kd for the binding reaction of the protein and the ligand,
Set initial values of total protein concentration Pt, total protein amount QP, total ligand concentration Lt, and total ligand amount QL of the mobile phase, and in order from the first minimum functional unit,
For the first minimum functional unit,
While the sample continues to flow into the gel filtration column,
Total protein amount QP = QP (1) + P0 × dV−Pt (1) × dV
Total ligand amount QL = QL (1) + C0 × dV−Lt (1) × dV
And calculating the total protein amount QP and the total ligand amount QL of the new mobile phase,
After the flow of the sample into the gel filtration column is complete,
Total protein amount QP = QP (1) −Pt (1) × dV
Total ligand amount QL = QL (1) −Lt (1) × dV
And calculating the total protein amount QP and the total ligand amount QL of the new mobile phase,
With respect to the i-th (i is a natural number of 2 or more) th smallest functional unit,
Total protein amount QP = QP (i) + Pt (i−1) × dV−Pt (i) × dV
Total ligand amount QL = QL (i) + Lt (i−1) × dV−Lt (i) × dV
And calculating the total protein amount QP and the total ligand amount QL of the new mobile phase,
For the first minimal functional unit and the ith minimal functional unit, the total protein concentration Pt and the total ligand concentration Lt of the new mobile phase are:
and
And Luz steps be calculated on the basis of,
Elution volume, total protein concentration of the eluate, based on the total ligand concentration of the eluate, and away step to obtain a predicted chromatogram,
Method for simulating a chromatogram including A system that includes an arithmetic unit and a recording unit, and simulates a chromatogram in a frontal gel filtration method,
The arithmetic unit is
And Luz step to set the size rg of filler gel filtration column with a mobile phase and a stationary phase,
The volume vu minimal functional unit of the gel filtration column, and answering step be set based on the size rg of the filler,
The mobile phase volume v0u, the stationary phase volume viu, and the volume vip in the stationary phase into which the protein can enter, which are separation characteristics of the gel filtration column, are set based on the volume vu of the minimum functional unit, and a ligand and Luz step to set the ng and Kg or coefficients k, which means reversible binding of to the filler,
And Luz step to set the stacking number m of the minimal functional unit in the gel filtration column,
A liquid volume dV passing the gel filtration column in one calculation step, based on said mobile phase volume V0u, and answering step be set to a value less than said mobile phase volume V0u,
The liquid volume Vs of the sample to flow to the gel filtration column, and answering step be set based on the stack number m and the mobile phase volume V0u,
The total volume Vmax to be supplied to the gel filtration column, the number of stacked layers m, and answering step be set based on the volume vip of the mobile phase volume V0u, and the stationary phase in which the protein is Hairikomeru,
And Luz step to set the total ligand concentration C0 of the total protein concentration P0 and the sample of the sample,
And Luz step to set the dissociation constant Kd for the binding reaction of the protein and the ligand,
Set initial values of total protein concentration Pt, total protein amount QP, total ligand concentration Lt, and total ligand amount QL of the mobile phase, and in order from the first minimum functional unit,
For the first minimum functional unit,
While the sample continues to flow into the gel filtration column,
Total protein amount QP = QP (1) + P0 × dV−Pt (1) × dV
Total ligand amount QL = QL (1) + C0 × dV−Lt (1) × dV
And calculating the total protein amount QP and the total ligand amount QL of the new mobile phase,
After the flow of the sample into the gel filtration column is complete,
Total protein amount QP = QP (1) −Pt (1) × dV
Total ligand amount QL = QL (1) −Lt (1) × dV
And calculating the total protein amount QP and the total ligand amount QL of the new mobile phase,
With respect to the i-th (i is a natural number of 2 or more) th smallest functional unit,
Total protein amount QP = QP (i) + Pt (i−1) × dV−Pt (i) × dV
Total ligand amount QL = QL (i) + Lt (i−1) × dV−Lt (i) × dV
And calculating the total protein amount QP and the total ligand amount QL of the new mobile phase,
For the first minimal functional unit and the ith minimal functional unit, the total protein concentration Pt and the total ligand concentration Lt of the new mobile phase are:
and
And Luz steps be calculated on the basis of,
Elution volume, the total protein concentration of the eluate, based on the total ligand concentration of the eluate, and away step to obtain a predicted chromatogram,
Perform a chromatogram simulation system. In a computer comprising an arithmetic unit and a recording unit, a program for simulating a chromatogram in a frontal gel filtration method,
In the computer,
A mobile phase and to that function sets the size rg of filler gel filtration column with a stationary phase,
The volume vu minimal functional unit of the gel filtration column, and to that function set based on the size rg of the filler,
The mobile phase volume v0u, the stationary phase volume viu, and the volume vip in the stationary phase into which the protein can enter, which are separation characteristics of the gel filtration column, are set based on the volume vu of the minimum functional unit, and a ligand wherein the reversible ng and Kg or machine to set the coefficient k ability which means binding of filler,
Wherein the minimum feature to that function sets the stacking number m of units in the gel filtration column,
A liquid volume dV passing the gel filtration column in one calculation step, and on the basis of the mobile phase volume V0u, the mobile phase volume set to that feature to a value less than V0u,
The liquid volume Vs of the sample to flow to the gel filtration column, and to that function set based on the stack number m and the mobile phase volume V0u,
The total volume Vmax to be supplied to the gel filtration column, and the number of laminations m, the mobile phase volume V0u, and to that function set based on the volume vip of the stationary phase in which the protein is Hairikomeru,
And that functions to set the total ligand concentration C0 of the total protein concentration P0 and the sample of the sample,
Wherein the protein and to that function set to the dissociation constant Kd for the binding reaction of the ligand,
Set initial values of total protein concentration Pt, total protein amount QP, total ligand concentration Lt, and total ligand amount QL of the mobile phase, and in order from the first minimum functional unit,
For the first minimum functional unit,
While the sample continues to flow into the gel filtration column,
Total protein amount QP = QP (1) + P0 × dV−Pt (1) × dV
Total ligand amount QL = QL (1) + C0 × dV−Lt (1) × dV
And calculating the total protein amount QP and the total ligand amount QL of the new mobile phase,
After the flow of the sample into the gel filtration column is complete,
Total protein amount QP = QP (1) −Pt (1) × dV
Total ligand amount QL = QL (1) −Lt (1) × dV
And calculating the total protein amount QP and the total ligand amount QL of the new mobile phase,
With respect to the i-th (i is a natural number of 2 or more) th smallest functional unit,
Total protein amount QP = QP (i) + Pt (i−1) × dV−Pt (i) × dV
Total ligand amount QL = QL (i) + Lt (i−1) × dV−Lt (i) × dV
And calculating the total protein amount QP and the total ligand amount QL of the new mobile phase,
For the first minimal functional unit and the ith minimal functional unit, the total protein concentration Pt and the total ligand concentration Lt of the new mobile phase are:
and
And to that function calculated on the basis of,
Elution volume, the total protein concentration of the eluate, based on the total ligand concentration of the eluate, and the resulting Ru function prediction chromatogram,
Chromatogram simulation program that realizes A method of analyzing and evaluating the actual sample using gel filtration columns,
The method, system or program according to any one of claims 1 to 3, wherein the gel filtration column is prepared based on design parameters used for simulation input, and the design parameters are determined by the gel filtration column. The size rg of the packing material, the volume vu of the minimum functional unit of the gel filtration column, the separation characteristics of the minimum functional unit, the mobile phase volume v0u, the stationary phase volume viu, and the volume in the stationary phase into which the protein can enter vip and the number m of the minimum functional units stacked,
A first step of measuring a first chromatogram of a first sample containing only the ligand;
A second step of measuring a second chromatogram of a second sample containing only protein;
A third step of calculating a ratio of the mobile phase and a ratio of the stationary phase in the volume of the gel filtration column;
A fourth step of measuring a third chromatogram of a mixture of the protein and the ligand;
Based on the elution pattern of the protein between the second chromatogram and the third chromatogram and the difference chromatogram obtained by subtracting the first chromatogram from the third chromatogram, the design parameter And a fifth step of determining the validity of the gel filtration column evaluation method. The first step comprises:
The measurement of the first chromatogram is performed by changing the amount of the first sample injected into the gel filtration column, and the amount of sample required for the ligand to elute in a trapezoidal shape with the original concentration is obtained. Step 1A;
Step 1B for confirming that the total amount of the ligand injected into the gel filtration column is eluted from the gel filtration column;
1C of determining the elution volume of the ligand from the rising pattern of the first chromatogram,
The second step comprises:
Step 2A for injecting the same amount of protein as the amount of sample obtained in Step 1A into the gel filtration column;
2B of determining the elution volume of the protein from the rising pattern of the second chromatogram,
The third step is
Assuming that the protein is localized only in the stationary phase, from the elution volume of the protein determined in the step 2B, the ratio of the mobile phase to the volume of the gel filtration column and the stationary phase The step 3A of calculating the ratio;
Effective ratio of the stationary phase in the volume of the gel filtration column from the elution volume of the ligand determined in the step 1C and the elution volume of the protein determined in the step 2B. A 3B step of calculating a value,
The fourth step includes
Step 4A injecting a mixture containing the same concentration and amount of protein as in Step 1A and the same concentration and amount of ligand as in Step 2A into the gel filtration column;
Step 4B of increasing the amount of sample injected into the gel filtration column until the trapezoidal portion appears when the trapezoidal portion in which the original sample is eluted as it is is not recognized in the third chromatogram. ,
In the step 4B, when the amount of the sample to be injected is increased, the step 4C includes performing the first step and the second step again with the increased amount of the sample. ,
The fifth step comprises
Step 5A for confirming that the elution pattern of the protein matches between the second chromatogram and the third chromatogram;
The gel filtration column of claim 4, comprising the step of 5B confirming that the area of the positive peak before the difference chromatogram and the area of the negative peak after the difference chromatogram are equal. Evaluation method.