Determination of rate and equilibrium binding constants for macromolecular interactions using surface plasmon resonance: use of nonlinear least squares analysis methods

Abstract

Surface plasmon resonance (SPR) is a label-free, real time, optical detection method which has recently been commercialized as the BIAcore (Pharmacia). The technique relies on the immobilization of one of the interactants, the ligand, onto a dextran-coated gold surface. The second interactant, the ligate, is then injected across the surface and the interaction of the soluble ligate with the immobilized ligand is observed continuously and directly. The process of dissociation of bound ligate may also be observed directly after the sample plug has traversed the layer. Thus, the data generated contain information on the kinetic rate and equilibrium binding constants for the interaction under investigation. Historically, data from this instrument have been analyzed in terms of linear transformations of the primary data and requires that data from several ligate concentrations be analyzed to determine a single value for the association and dissociation rate constants. Here we discuss the analysis of untransformed BIAcore data by nonlinear least squares methods. The primary data are analyzed according to the integrated rate equations which describe the kinetics of the interaction of soluble ligate with immobilized ligand and the dissociation of the formed complex from the surface, respectively. Such analyses allow the direct determination of the association and dissociation rate constants for each binding experiment and, further, allow the analysis of data over a wider concentration range with lower associated errors compared to previously described methods. Through the use of modeling these interactions, we also demonstrate the limitations in determining the dissociation rate constant from the association phase of the interaction, thereby requiring that the dissociation process be analyzed. Indeed, the dissociation phase should be analyzed first to yield a relatively precise and unambiguous value of the dissociation rate constant, kd, which can then be used to constrain the analysis of the association phase to yield a better estimate of the association rate constant, k(a). We further demonstrate that, at least for the interaction investigated, the apparent rate and equilibrium binding constants determined using SPR are concentration independent and can be determined with good reproducibility.