title: Constrained Maximum Likelihood Estimation of Relative Abundances of Protein Conformation in a Heterogeneous Mixture from Small Angle X-Ray Scattering Intensity Measurements.
abstract: In this paper, we describe a model for maximum likelihood estimation (MLE) of the relative abundances of different conformations of a protein in a heterogeneous mixture from small angle X-ray scattering (SAXS) intensities. To consider cases where the solution includes intermediate or unknown conformations, we develop a subset selection method based on k-means clustering and the Cramér-Rao bound on the mixture coefficient estimation error to find a sparse basis set that represents the space spanned by the measured SAXS intensities of the known conformations of a protein. Then, using the selected basis set and the assumptions on the model for the intensity measurements, we show that the MLE model can be expressed as a constrained convex optimization problem. Employing the adenylate kinase (ADK) protein and its known conformations as an example, and using Monte Carlo simulations, we demonstrate the performance of the proposed estimation scheme. Here, although we use 45 crystallographically determined experimental structures and we could generate many more using, for instance, molecular dynamics calculations, the clustering technique indicates that the data cannot support the determination of relative abundances for more than 5 conformations. The estimation of this maximum number of conformations is intrinsic to the methodology we have used here.
authors.affiliation: Electrical and Computer Engineering Department, Northeastern University, Boston, MA.
authors.forename: A Emre
authors.initials: AE
authors.lastname: Onuk
authors.affiliation: Electrical and Computer Engineering Department, University of Pittsburgh, Pittsburgh, PA.
authors.forename: Murat
authors.initials: M
authors.lastname: Akcakaya
authors.affiliation: Department of Mechanical and Industrial Engineering, Northeastern University, Boston, MA.
authors.forename: Jaydeep P
authors.initials: JP
authors.lastname: Bardhan
authors.affiliation: Electrical and Computer Engineering Department, Northeastern University, Boston, MA.
authors.forename: Deniz
authors.initials: D
authors.lastname: Erdogmus
authors.affiliation: Electrical and Computer Engineering Department, Northeastern University, Boston, MA.
authors.forename: Dana H
authors.initials: DH
authors.lastname: Brooks
authors.affiliation: Bioengineering Department, Northeastern University, Boston, MA; Department of Chemistry and Chemical Biology, Northeastern University, Boston, MA.
authors.forename: Lee
authors.initials: L
authors.lastname: Makowski