Determination of Active Concentrations and Association and Dissociation Rate Constants of Interacting Biomolecules:  An Analytical Solution to the Theory for Kinetic and Mass Transport Limitations in Biosensor Technology and Its Experimental Verification

Accurate determination of kinetic rate constants for interacting biomolecules requires knowledge of the active concentrations of the participating molecules. Also, in other biomedical and clinical applications, sensitive, precise and accurate methods are needed to determine the concentration of biologically active molecules, which frequently constitute only a fraction of the total molecular pool. Here we report a novel development of the approach to determining active concentrations based on surface plasmon resonance (SPR) technology. The method relies on changes in binding rates with varying flow rates under conditions of partial mass transport, and does not require standards of known concentrations, given that the molecular mass of the molecule of interest is known. We introduce an analytical solution to the differential equations describing the formation of a 1:1 bimolecular complex, taking into account both the association and dissociation reactions, under partial mass transport limitations. This solution can be used in global fitting to binding curves obtained at different flow rates. The accuracy, precision, and sensitivity of this approach were determined in experiments involving binding of tyrosine-phosphorylated recombinant proteins to anti-phosphotyrosine antibodies, where the active concentration could be determined independently by in vitro phosphorylation with (33)P. There was an excellent agreement between the active concentrations determined by the analytical SPR-based method and by determination of the level of radioactivity of the phosphorylated protein. The SPR-based method allows determination of protein concentrations at picomolar levels. A procedure for accurate determinations of association and dissociation rate constants, based on the analytical solution of the mass transport and binding theory, is outlined.