Fast tensor-based electrostatic energy calculations in the perspective of protein-ligand docking problem

TL;DR

This paper introduces a fast tensor-based method for calculating electrostatic energies in protein-ligand docking, enabling efficient modeling of large biomolecular complexes with high accuracy and reduced computational cost.

Contribution

The authors develop a low-rank tensor representation approach that significantly accelerates electrostatic energy calculations in protein-ligand docking, allowing large grid modeling and complex system analysis.

Findings

Tensor techniques achieve $O(n)$ complexity in energy calculations.

Large 3D grids enable modeling of complexes with multiple large proteins.

Numerical tests demonstrate the method's effectiveness on synthetic and real data.

Abstract

We propose and justify a new approach for fast calculation of the electrostatic interaction energy of clusters of charged particles in constrained energy minimization in the framework of rigid protein-ligand docking. Our ``blind search'' docking technique is based on the low-rank range-separated (RS) tensor-based representation of the free-space electrostatic potential of the biomolecule represented on large $n\times n\times n$ 3D grid. We show that both the collective electrostatic potential of a complex protein-ligand system and the respective electrostatic interaction energy can be calculated by tensor techniques in $O(n)$-complexity, such that the numerical cost for energy calculation only mildly (logarithmically) depends on the number of particles in the system. Moreover, tensor representation of the electrostatic potential enables usage of large 3D Cartesian grids (of the order of $n^3 \sim 10^{12}$), which could allow the accurate modeling of complexes with several large proteins. In our approach selection of the correct geometric pose predictions in the localized posing process is based on the control of van der Waals distance between the target molecular clusters. Here, we confine ourselves by constrained minimization of the energy functional by using only fast tensor-based free-space electrostatic energy recalculation for various rotations and translations of both clusters. Numerical tests of the electrostatic energy-based ``protein-ligand docking'' algorithm applied to synthetic and realistic input data present a proof of concept for rather complex particle configurations. The method may be used in the framework of the traditional stochastic or deterministic posing/docking techniques.