Method in a surface plasmon resonance biosensor system

Abstract

A method for determining instrument-dependent parameters of a surface plasmon resonance, SPR, biosensor system, and using those instrument-dependent parameters to measure the concentration of an analyte is provided herein. Also disclosed are methods of monitoring surface binding interactions of the analyte using the instrument-dependent parameters.

Claims

1. A method for measuring the active concentration of an analyte having an unknown concentration using a surface plasmon resonance, SPR, biosensor system, the method comprising the steps of: a) measuring an active concentration of a known analyte using the SPR biosensor system according to a first method, the SPR biosensor including a chip to which the known analyte can bind, wherein said measuring an active concentration of the known analyte comprises determining the active concentration of the known analyte using an instrument-dependent constant of the SPR biosensor system, wherein the instrument dependent constant includes the width, the height and the length of a flow cell of the SPR biosensor and the known analyte has a known molecular weight, known diffusion constant, known refractive index increment and a known concentration at the time of measuring; b) comparing the known concentration of the known analyte with the active concentration measured in step a) to determine an instrument error c) adjusting the instrument-dependent constant of the SPR biosensor system used in the first method by the instrument error obtained in step b) to obtain an adjusted instrument-dependent constant of the SPR biosensor system; and d) measuring an active concentration of an analyte having an unknown concentration using the SPR biosensor with the adjusted instrument-dependent constant of the SPR biosensor system from step c).

2. The method according to claim 1, further comprising a step of calculating parameters used to convert SPR biosensor response into mass units from the adjusted instrument-dependent constant of the SPR biosensor system retrieved in step c).

3. The method according to claim 1, further comprising a step of calculating parameters of the flow cell, and/or parameters of a chip using the adjusted instrument-dependent constant of the SPR biosensor system retrieved in step c).

4. The method according to claim 1, wherein the first analyte has a known affinity parameter and a known kinetic parameter for a first binding partner.

5. The method according to claim 2, wherein a mass transport constant is used in the step of calculating said parameters.

6. The method according to claim 1, wherein step b) comprises measuring active concentration using a calibration-free concentration analysis.

7. The method of claim 1, wherein the method further comprises monitoring surface binding interactions of the second analyte in the SPR biosensor.

8. The method according to claim 1, wherein the first analyte is the same as the second analyte.

9. The method according to claim 1, wherein the measurement is conducted under mass transport limiting conditions.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is a flow chart showing the method steps of one embodiment of the invention.

DETAILED DESCRIPTION

(2) Calibration free concentration analysis, CFCA, can be described as the method that measures an active concentration, i.e. the concentration of molecules capable of binding to the target attached to sensor surface, by use of SPR-based biosensor systems.

(3) The active concentration of a protein is defined through the interaction of the protein with its binding partner and can differ from the total protein concentration if some of the molecules are incapable of binding. If a protein has several different binding sites, active concentration can be established for each binding site. In the current Biacore™ evaluation software, active concentration is called calibration free concentration analysis (CFCA).

(4) In a typical experiment, the interaction partner (ligand) is attached to the sensor surface and a molecule of interest (analyte), for which the concentration is measured, is delivered in a constant laminar flow in a well-defined flow cell. In this approach, only the concentration of analyte fraction that is capable of binding to the immobilized ligand is measured. The binding between the ligand and the analyte is a two-step process consisting of (i) the diffusion of analyte from bulk to the surface and (ii) the analyte-to-ligand binding. If the rate of diffusion is much slower than the rate of binding between the molecules, then the rate of complex formation is limited by the transport rate, and for the reversed case, the observed initial rate of complex formation corresponds to intrinsic reaction rate.

(5) A mass transport coefficient, k.sub.m, describes the flux of molecules with diffusion coefficient D, in the flow cell of height h, to the sensor surface as described by equation 1:

(6) $\begin{array}{cc}{k}_m=0.98.Math.\sqrt[3]{\frac{D^2.Math.f}{{1.5}^{-3}.Math.h^2.Math.w.Math.l}}& \left(1\right)\end{array}$

(7) In practical SPR detection systems, the effective length differs from the flow cell length and k.sub.m is defined as:

(8) $\begin{array}{cc}{k}_m=0.98.Math.\sqrt[3]{\frac{D^2.Math.f}{h^2.Math.w.Math.\left(\alpha -\beta /2+{1.5}^{-3}\beta \right)}}& \left(2\right)\end{array}$

(9) Where α is the distance from the flow cell inlet to the center of the detection area and β is the detection area length.

(10) The diffusion coefficient of the analyte that is required for calculation of the concentration, can be obtained experimentally or from the three dimensional structure, if available, using Hydropro program. An empirical formula (equation 3) based on Stoke's law and the Einstein-Sutherland equation can also be used to assess D, although relative frictional ratio, f/f.sub.0 of the analyte, and viscosity of the solvent, .eta., must be known. For typical water-based buffers, the viscosity of water can be assumed.

(11) $\begin{array}{cc}D=\frac{324.3\times {10}^{-11}}{f/f_0\times \eta /{\eta }_0\times \sqrt[3]{\mathrm{MW}}}{m}^2\text{/}s& \left(3\right)\end{array}$

(12) η.sub.0 is the viscosity of the solvent at 20° C.

(13) To relate the transport coefficient to the SPR biosensor system (in this example the Biacore™) response and to allow specific input of the actual flow rate, t.sub.c is introduced as a transport coefficient.
t.sub.c=Form Factor×f.sup.(1/3)×G×MW×k.sub.m  (4)

(14) By expressing G, the surface concentration with unit g/m.sup.2, in RU, with 1 RU equal to 10.sup.−6 g/m.sup.2, and by setting the Form Factor to 0.81, the relation to k.sub.m is established and
t.sub.c=0.81×10.sup.9×f.sup.(1/3)>MW×k.sub.m  (5)

(15) G was initially calculated assuming a 100 nm dextran layer. However, the extension of the dextran layer may vary with immobilization level and varies between chip types. Therefore, some uncertainty in the calculation of G-factor exists and a user may need some flexibility to change it. The Form Factor allows this flexibility and the current value of 0.81 used in Biacore™ evaluation software has been determined empirically.

(16) The degree of mass transport limitation, MTL, depends on the combination of several parameters including flow cell dimensions, flow rate, density of the free binding sites on the surface, kinetic constant of the interaction, and the diffusion coefficient. For a given analyte-ligand pair and flow cell, MTL is promoted by a high concentration of free, unoccupied ligand, which is expected to happen at high immobilization and low response levels. Moreover, under these conditions, the effect of complex, deviating from 1:1 interaction scheme, binding, can be neglected.

(17) The degree of MTL can be estimated from initial binding rates observed under transport limited (eq. 6) and kinetic (eq. 7) conditions:
dR/dt=t.sub.c×C and  (6)
dR/dt=k.sub.a×C×R.sub.max  (7)
The degree of transport limitation can be estimated from:

(18) $\begin{array}{cc}\mathrm{MTL}=\frac{1}{1+\frac{t_c}{k_a\times R_{\max }}}& \left(8\right)\end{array}$

(19) For the transport limited case k.sub.a×R.sub.max>>t.sub.c and MTL approaches

(20) For the kinetic case k.sub.a×R.sub.max<<k.sub.t and MTL approaches 0

(21) These relationships can be used to estimate the possibility of CFCA for a specific interaction but is also impractical as the association rate constant for the interaction has to be known and this is not always the case.

(22) According to the invention a method for determining instrument-dependent parameters of a surface plasmon resonance, SPR, biosensor system is provided. FIG. 1 is a flow chart showing the method steps of one embodiment of the invention. The method comprises the steps:

(23) S1: Identifying an appropriate analyte for use in a calibration step. Said analyte needs to have a known molecular weight, a known diffusion constant, a known refractive index increment and a known concentration. Said analyte also needs to bind to a chip used in the biosensor system. Either the analyte can bind to the chip itself or to a binding partner, a ligand, that is attached to the chip.

(24) S3: Measuring active concentration by use of the SPR biosensor system according to a known method using the identified analyte and the chip. Said known method includes the use of an instrument-dependent constant that is not adapted for each specific instrument, chip and flow cell combination.

(25) S5: Comparing the known concentration of the analyte with the active concentration measured in step S3.

(26) S7: Adjusting the instrument-dependent constant used in the known method for measuring active concentration according to the difference retrieved in step S5.

(27) In one embodiment of the invention the method further comprises a step of calculating constants that convert responses into mass units from the adjusted instrument-dependent constant retrieved in step S7.

(28) In one embodiment of the invention the method further comprises a step of calculating other constants connected to flow cells, chips, and other instrument connected quantities from the adjusted instrument-dependent constant retrieved in step S7.

(29) In one embodiment of the invention the step of identifying an appropriate analyte also includes that the analyte needs to have a known affinity and known kinetic constants to the binding partner. Furthermore, in one embodiment of the invention a mass transport constant is used in calculation algorithms used for the calculations described above.

(30) In one embodiment of the invention step S3 comprises measuring active concentration by a method called calibration free concentration analysis, CFCA. Furthermore, in one embodiment of the invention the constants calculated that convert responses into mass units are a constant called G and a constant called Form Factor which both are used in calculating a transport coefficient needed for the calibration free concentration analysis.

(31) Furthermore according to the invention a method for monitoring surface binding interactions in an SPR biosensor is provided. Said method comprises the steps of:

(32) determining instrument-dependent parameters for the currently used specific instrument, chip and flow cell combination according to the steps S1-S7 described above;

(33) using this new instrument-dependent constant retrieved in step S7 for determining SPR-related responses.

(34) In one embodiment of the invention the new instrument-dependent constant retrieved in step S7 is used for determining concentration of the analyte.

(35) A new, instrument/system/chip/-depending constant, retrieved in step S7, can also be used for other purposes, like to uniform signals retrieved from different systems.

(36) Calibration free concentration analysis is used to determine concentration without standards. The method works in conditions of mass transport limitation existing in the flow cell and on the sensor surface.

(37) The events in the flow cell and on the sensor surface can be described as follows:

(38) The binding of a macromolecular particle, e.g., a protein in the bulk (A.sub.bulk) to the molecule on the chip surface (B) is a two-step process. In the first step protein from the bulk is transported to the surface (A.sub.surf) with mass transport coefficient k.sub.m, and in the second step, the binding between k.sub.surf and B occurs with association constant k.sub.a and dissociation constant k.sub.d and complex AB is formed.

(39) If the transport of A.sub.bulk to sensor surface is slower than binding of A.sub.surf to B, then the mass transport limitation occurs and active concentration can be measured.

(40) $A_{\mathrm{bulk}}\underset{k_m}{\stackrel{k_m}{\rightleftarrows }}{A}_{\mathrm{surf}}+B$$A_{\mathrm{bulk}}\underset{k_m}{\stackrel{k_m}{\rightleftarrows }}{A}_{\mathrm{surf}}+B\underset{k_d}{\stackrel{k_a}{\rightleftarrows }}\mathrm{AB}$

(41) The experimental procedure includes monitoring of responses on at least two widely separated flow rates and evaluation with appropriate model.

(42) The binding phases of the curves (i.e., sensorgrams) obtained from such an experiment are fitted to a bi-molecular interaction model with mass transfer term (k.sub.t), in which active concentration (Conc) is a fitted parameter:
A(solution)=Conc
A[0]=0
dA/dt=kt*(Conc-A)−(ka*A*B−kd*AB)
B[0]=RMax
dB/dt=−(ka*A*B−kd*AB)
AB[0]=0
dAB/dt=(ka*A*B−kd*AB)

(43) Total response:
AB+RI

(44) In this model, the value of the mass transport constant, k.sub.t, is introduced as a constant, which is calculated according to a formula:

(45) ##STR00001##

(46) If we group the parameters in this formula into protein-dependent and instrument-dependent, we obtain:

(47) ##STR00002##

(48) Or:
k.sub.t=G×Const.sub.analyte×Const.sub.instr×∛f

(49) For a proposed calibration of an SPR biosensor system, we would need:

(50) A model system, fulfilling mass transport limited conditions, in which an analyte has well defined concentration and Const.sub.analyte, i. e., molecular weight and diffusion coefficient.

(51) In a calibration procedure, the experiment will be performed in the same manner as in CFCA, but the experimental data would be fitted to a bi-molecular interaction model with mass transfer term (k.sub.t), in which Concentration (Conc) is a constant and k.sub.t is fitted. Const.sub.instr is then calculated from

(52) ${\mathrm{Const}}_{\mathrm{instr}}=\frac{k_1}{{\mathrm{Const}}_{\mathrm{analyte}}}\times \frac{1}{\sqrt[3]{f}}$

(53) Alternatively, the concentration is fitted in same way as in CFCA and the calculated concentration is then compared with true, well-defined concentration of analyte. The difference is an “instrument error” and Const.sub.instr can be adjusted.

(54) Candidates to model system that fulfills the requirements for a calibrant (i.e., mass transport limited conditions and well-defined concentration and Const.sub.analyte) are, for example, certified vitamin standards (analytes with well-defined concentrations) with their interaction partners.