Mixture models for protein structure ensembles

Abstract

Protein structure ensembles provide important insight into the dynamics and function of a protein and contain information that is not captured with a single static structure. However, it is not clear a priori to what extent the variability within an ensemble is caused by internal structural changes. Additional variability results from overall translations and rotations of the molecule. And most experimental data do not provide information to relate the structures to a common reference frame. To report meaningful values of intrinsic dynamics, structural precision, conformational entropy, etc., it is therefore important to disentangle local from global conformational heterogeneity. We consider the task of disentangling local from global heterogeneity as an inference problem. We use probabilistic methods to infer from the protein ensemble missing information on reference frames and stable conformational sub-states. To this end, we model a protein ensemble as a mixture of Gaussian probability distributions of either entire conformations or structural segments. We learn these models from a protein ensemble using the expectation-maximization algorithm. Our first model can be used to find multiple conformers in a structure ensemble. The second model partitions the protein chain into locally stable structural segments or core elements and less structured regions typically found in loops. Both models are simple to implement and contain only a single free parameter: the number of conformers or structural segments. Our models can be used to analyse experimental ensembles, molecular dynamics trajectories and conformational change in proteins. The Python source code for protein ensemble analysis is available from the authors upon request.