Analytical Measuring and Evaluation Method for Molecular Interactions

Abstract

The invention relates to an analytical measuring and evaluation method for determining the interaction parameters between an analyte and a ligand, preferably in a biosensor. According to the inventive method, the concentration of the analyte is gradually changed at defined intervals ti and the initial association or dissociation rates or association and dissociation rate constants are determined. The invention further relates to a device for carrying out the inventive method.

We claim: 
     
         1 . An analytical measurement and evaluation method for determining kinetic constants for molecular interactions between a first binding partner L (ligand) and a second binding partner A (analyte) forming a complex LA, wherein the first binding partner L is immobilized on a sensor of a biosensor, the sensor surface is contacted with a solution containing the second binding partner A, and binding of the second binding partner A to the immobilized binding partner L on the sensor surface is detected over time providing measurement values, the method comprising the following steps:
 raising or lowering several times an analyte concentration c ii (A) of the second binding partner A in a stepwise fashion and before an equilibrium interaction state for the respective analyte concentration c ii (A) has been reached, and without any regeneration of the sensor surface between each raising or lowering of the analyte concentration;   and   determining one or more kinetic constants of the interaction from the measurement values;   
       wherein a dissociation equilibrium constant K D  is determined by determining an analyte concentration c 0 (A) at which R ass (t) and R diss It) intersect at about 0.618 of an equilibrium rate of R ass (t) and wherein the analyte concentration of a solution in the measurement chamber is kept constant. 
     
     
         2 . The method as defined in  claim 1 , wherein the initial association rate or the initial dissociation rate is ascertained using actual measured values of the rate of complexation between the ligand and the analyte, the actual measured values being acquired prior to the rate of complexation reaching equilibrium. 
     
     
         3 . The method of  claim 2 , wherein all initial rates are ascertained under an assumption of ideal conditions that no analyte depletion occurs upon association and that no analyte enrichment upon dissociation. 
     
     
         4 . The method of  claim 1 , wherein an analyte concentration c 0 (A) is ascertained at the beginning of the analytical measurement. 
     
     
         5 . The method of  claim 1 , wherein an analytical measurement and evaluation method is practiced in a cuvette system with a measurement chamber, and wherein the analyte concentration of a solution in the measurement chamber is kept constant during each stepwise raising or lowering of the analyte concentration by continuously removing a portion of the solution from the measurement chamber through a first hollow needle and adding a solution having the analyte concentration through a second hollow needle. 
     
     
         6 . The method of  claim 5 , wherein the analyte concentration in the measurement chamber is raised or lowered between the steps i-1 and I, and wherein the respective concentrations c 0 (A) of the analyte are determined for each i-th step. 
     
     
         7 . The method of  claim 1 , wherein determination of kinetic constants comprises determining an association constant k ass  and a dissociation constant k diss  by:
 determining an initial net association rate (dR ass,i,net /dt) t,0  as a different between an initial association rate (dR ass,i /dt) t,0  at a starting association value R′ st,ass,i  of i-th step and a final association rate of i-1 step, and determining a net starting analyte concentration c 0,I,net (A) as a difference between the analyte concentration of i-th step and the final association or dissociation rate of the i-1 step are derived from R ass (t), R diss (t) by non-linear approximation or from their time derivatives by non-linear or linear regression;   determining an initial net association rate dR/dt 0,dis-i  at a starting dissociation value R′ st,ass,i  by non-linear approximation R diss (t) or by regression of a time derivative of R diss (t);   determining a difference (R′ eq,diss,i −R ′   st,diss,i ) between an equilibrium dissociation value of i-th step R′ eq,diss,i  and the starting dissociation value at the i-th step R′ st,diss,i ; and   determining a dissociation rate constant k diss  from a relationship between dR/dt 0,diss-i  and (R′ eq,diss,i −R′ st,diss,i ), or determining an association rate constant k ass  from a relationship between a quotient (dR ass,i /dt) t=0 /c 0,i,net (A) and R′ st,ass,i .   
     
     
         8 . The method of  claim 1  wherein the dissociation rate constant k ass  is obtained from the initial dissociation rates and the respective equilibrium association values of the function R(t), and wherein the association rate constant k ass  is obtained from the initial dissociation rates and the respective equilibrium dissociation values of the function R(t). 
     
     
         9 . The method of  claim 1 , wherein said analyte concentration c ti (A) of the second binding partner A is the same during more than one of said stepwise raising or lowering of the analyte concentration by successive impingements of solutions or sample loops that contain the same analyte concentration. 
     
     
         10 . The method of  claim 1 , wherein said analyte concentration c ti (A) of the second binding partner A is varying over time within one or more of said individual steps by controlled activation of sample loops that contain different analyte concentrations or by mixing of solutions via frequent switching of specific valves that are connected to different solutions. 
     
     
         11 . The method of  claim 1 , wherein the kinetic constants are the association rate constant k ass  and the dissociation rate constant k diss . 
     
     
         12 . The method of  claim 1 , wherein the kinetic constants are a dissociation equilibrium constant K D =k diss /k ass  and an association equilibrium constant K A =/K D . 
     
     
         13 . The method of  claim 1 , wherein a dissociation equilibrium constant K D  and an association constant K A =1/K D  are ascertained from a relationship between an analyte concentration c ii (A) and an equilibrium value R eq,i  of said steps. 
     
     
         14 . The method of  claim 1 , wherein a maximum possible reaction R max  is ascertained from a relationship between the analyte concentration c ii (A) and an equilibrium value R eq,i  of said steps or from a relationship between the analyte concentration c ii (A) and an initial rate of said steps. 
     
     
         15 . The method of  claim 1 , wherein said raising or lowering of the analyte concentration of the second binding partner A is started at any point. 
     
     
         16 . The method of  claim 1 , wherein raising or lowering the concentration of c ii (A) is accomplished at a half-life point of the response data R(t). 
     
     
         17 . The method of  claim 1 , wherein multiple sample loops are present, and their contents can be introduced into the measurement chamber independently and opposite to their filling direction; in particular, the sample loops are each filled with different solutions. 
     
     
         18 . The method of  claim 1 , wherein the solution in the measurement chamber is mixed via multiple hollow needles by at least partial withdrawal and re-addition into the measurement chamber, in particular at least 1 Φl/min is circulated. 
     
     
         19 . The method of  claim 18 , wherein one or more pumps, in particular tubing pumps, injection pumps, or piezoelectric pumps, are provided on the hollow needles for metering the quantity of solutions to be exchanged. 
     
     
         20 . The method of  claim 19 , wherein the hollow needles are arranged on the measurement chamber separately or one coaxially inside the other.