Using persistent homology and dynamical distances to analyze protein binding

Abstract

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.

Persistent homology detects curvature

“…Related work. Persistence landscapes have been used to study the geometry of microstructures [12]; protein conformations [24]; and financial times series [17]. Average persistence landscapes and average death vectors were used to detect differences in images of leaves in [29].…”

PHoS: Persistent Homology for Virtual Screening

“…Ours is not the first application of topology to medicinal chemistry: One of the early applications of persistent homology was to protein docking [3], which continues to be an area of active exploration [69,70,44], though the details of the approach taken in those work are rather different than ours. More recently, there have been results in structure-based screening using standard (single-parameter) persistent homology together with machine learning [14].…”

Topological Data Analysis

“…They achieved a classification accuracy of 69.86 percent. Kovacev-Nikolic et al (2016) used TDA to study the maltose binding protein which is a protein found in Escherichia coli. An example of such a protein is given in Figure 24; the figure is from http://lilith.nec.aps.anl.gov/ Structures/Publications.htm.…”