Persistent homology captures the evolution of topological features of a model as a parameter changes. The most commonly used summary statistics of persistent homology are the barcode and the persistence diagram. Another summary statistic, the persistence landscape, was recently introduced by Bubenik. It is a functional summary, so it is easy to calculate sample means and variances, and it is straightforward to construct various test statistics. Implementing a permutation test we detect conformational changes between closed and open forms of the maltose-binding protein, a large biomolecule consisting of 370 amino acid residues. Furthermore, persistence landscapes can be applied to machine learning methods. A hyperplane from a support vector machine shows the clear separation between the closed and open proteins conformations. Moreover, because our approach captures dynamical properties of the protein our results may help in identifying residues susceptible to ligand binding; we show that the majority of active site residues and allosteric pathway residues are located in the vicinity of the most persistent loop in the corresponding filtered Vietoris-Rips complex. This finding was not observed in the classical anisotropic network model.

This study identifies dynamical properties of maltose-binding protein (MBP) useful in unveiling active site residues susceptible to ligand binding. The described methodology has been previously used in support of novel topological techniques of persistent homology and statistical inference in complex, multi-scale, high-dimensional data often encountered in computational biophysics. Here we outline a computational protocol that is based on the anisotropic elastic network models of 14 all-atom three-dimensional protein structures. We introduce the notion of dynamical distance matrices as a measure of correlated interactions among 370 amino acid residues that constitute a single protein. The dynamical distance matrices serve as an input for a persistent homology suite of codes to further distinguish a small subset of residues with high affinity for ligand binding and allosteric activity. In addition, we show that ligand-free closed MBP structures require lower deformation energies than open MBP structures, which may be used in categorization of time-evolving molecular dynamics structures. Analysis of the most probable allosteric coupling pathways between active site residues and the protein exterior is also presented.

No abstract