Bayesian Analysis of Heterogeneity in the Distribution of Binding Properties of Immobilized Surface Sites

Once a homogeneous ensemble of a protein ligand is taken from solution and immobilized to a surface, for many reasons the resulting ensemble of surface binding sites to soluble analytes may be heterogeneous. For example, this can be due to the intrinsic surface roughness causing variations in the local microenvironment, nonuniform density distribution of polymeric linkers, or nonuniform chemical attachment producing different protein orientations and conformations. We previously described a computational method for determining the distribution of affinity and rate constants of surface sites from analysis of experimental surface binding data. It fully exploits the high signal/noise ratio and reproducibility provided by optical biosensor technology, such as surface plasmon resonance. Since the computational analysis is ill conditioned, the previous approach used a regularization strategy assuming a priori all binding parameters to be equally likely, resulting in the broadest possible parameter distribution consistent with the experimental data. We now extended this method in a Bayesian approach to incorporate the opposite assumption, i.e., that the surface sites a priori are expected to be uniform (as one would expect in free solution). This results in a distribution of binding parameters as close to monodispersity as possible given the experimental data. Using several model protein systems immobilized on a carboxymethyl dextran surface and probed with surface plasmon resonance, we show microheterogeneity of the surface sites in addition to broad populations of significantly altered affinity. The distributions obtained are highly reproducible. Immobilization conditions and the total surface density of immobilized sites can have a substantial impact on the functional distribution of the binding sites.