An Isometry-Invariant Spectral Approach for Macro-Molecular Docking

Abstract

Proteins and the formation of large protein complexes are essential parts of living organisms. Proteins are present in all aspects of life processes, performing a multitude of various functions ranging from being structural components of cells, to facilitating the passage of certain molecules between various regions of cells. The 'protein docking problem' refers to the computational method of predicting the appropriate matching pair of a protein (receptor) with respect to another protein (ligand), when attempting to bind to one another to form a stable complex.

Research shows that matching the three-dimensional (3D) geometric structures of candidate proteins plays a key role in determining a so-called docking pair, which is one of the key aspects of the Computer Aided Drug Design process. However, the active sites which are responsible for binding do not always present a rigid-body shape matching problem. Rather, they may undergo sufficient deformation when docking occurs, which complicates the problem of finding a match.

To address this issue, we present an isometry-invariant and topologically robust partial shape matching method for finding complementary protein binding sites, which we call the ProtoDock algorithm. The ProtoDock algorithm comes in two variations. The first version performs a partial shape complementarity matching by initially segmenting the underlying protein object mesh into smaller portions using a spectral mesh segmentation approach. The Heat Kernel Signature (HKS), the underlying basis of our shape descriptor, is subsequently computed for the obtained segments. A final descriptor vector is constructed from the Heat Kernel Signatures and used as the basis for the segment matching. The three different descriptor methods employed are, the accepted Bag of Features (BoF) technique, and our two novel approaches, Closest Medoid Set (CMS) and Medoid Set Average (MSA).

The second variation of our ProtoDock algorithm aims to perform the partial matching by utilizing the pointwise HKS descriptors. The use of the pointwise HKS is mainly motivated by the suggestion that, at adequate times, the Heat Kernel Signature of a point on a surface sufficiently describes its neighbourhood. Hence, the HKS of a point may serve as the representative descriptor of its given region of which it forms a part. We propose three (3) sampling methods---Uniform, Random, and Segment-based Random sampling---for selecting these points for the partial matching. Random and Segment-based Random sampling both prove superior to the Uniform sampling method.

Our experimental results, run against the Protein-Protein Benchmark 4.0, demonstrate the viability of our approach, in that, it successfully returns known binding segments for known pairing proteins. Furthermore, our ProtoDock-1 algorithm still still yields good results for low resolution protein meshes. This results in even faster processing and matching times with sufficiently reduced computational requirements when obtaining the HKS.