Maximum a posteriori estimation of relative abundances of protein conformations

Estimation of mixture coefficients of protein conformations find applications in understanding protein behavior. We describe a method for maximum a posteriori (MAP) estimation of the mixture coefficients of ensemble of conformations in a protein mixture solution using measured small angle X-ray scattering (SAXS) intensities. The proposed method builds upon a model for the measurements of crystallographically determined conformations. Assuming that a priori information on the protein mixture is available and this prior follows a Dirichlet distribution we develop a method to estimate the relative abundances with MAP estimator. Adenylate kinase (ADK) protein is selected as the test bed due to its known conformations. Known conformations are assumed to form the full vector bases that span the measurement space. A subset selection method that chooses an identifiable subset from these bases is developed. Using the selected subset, in Monte Carlo simulations, mixture coefficient estimation performances of MAP and maximum likelihood (which assumes uniform prior on mixture coefficients) estimators are compared. The results show that prior knowledge improves estimation accuracy, but performance is sensitive to perturbations in the prior distribution parameters.