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Molecular unfolding formulation with enhanced quantum annealing approach

Arit Kumar Bishwas, Arish Pitchai, Anuraj Som

TL;DR

In this paper, quantum annealing based solution to solve Molecular unfolding (MU) problem, a specific phase within molecular docking, is explored and compared with a state-of-the-art classical algorithm named"GeoDock".

Abstract

Molecular docking is a crucial phase in drug discovery, involving the precise determination of the optimal spatial arrangement between two molecules when they bind. The such analysis, the 3D structure of molecules is a fundamental consideration, involving the manipulation of molecular representations based on their degrees of freedom, including rigid roto-translation and fragment rotations along rotatable bonds, to determine the preferred spatial arrangement when molecules bind to each other. In this paper, quantum annealing based solution to solve Molecular unfolding (MU) problem, a specific phase within molecular docking, is explored and compared with a state-of-the-art classical algorithm named "GeoDock". Molecular unfolding focuses on expanding a molecule to an unfolded state to simplify manipulation within the target cavity and optimize its configuration, typically by maximizing molecular area or internal atom distances. Molecular unfolding problem aims to find the torsional configuration that increases the inter-atomic distance within a molecule, which also increases the molecular area. Quantum annealing approach first encodes the problem into a Higher-order Unconstrained Binary Optimization (HUBO) equation which is pruned to an arbitrary percentage to improve the time efficiency and to be able to solve the equation using any quantum annealer. The resultant HUBO is then converted to a Quadratic Unconstrained Binary Optimization equation (QUBO), which is easily embedded on a D-wave annealing Quantum processor.

Molecular unfolding formulation with enhanced quantum annealing approach

TL;DR

In this paper, quantum annealing based solution to solve Molecular unfolding (MU) problem, a specific phase within molecular docking, is explored and compared with a state-of-the-art classical algorithm named"GeoDock".

Abstract

Molecular docking is a crucial phase in drug discovery, involving the precise determination of the optimal spatial arrangement between two molecules when they bind. The such analysis, the 3D structure of molecules is a fundamental consideration, involving the manipulation of molecular representations based on their degrees of freedom, including rigid roto-translation and fragment rotations along rotatable bonds, to determine the preferred spatial arrangement when molecules bind to each other. In this paper, quantum annealing based solution to solve Molecular unfolding (MU) problem, a specific phase within molecular docking, is explored and compared with a state-of-the-art classical algorithm named "GeoDock". Molecular unfolding focuses on expanding a molecule to an unfolded state to simplify manipulation within the target cavity and optimize its configuration, typically by maximizing molecular area or internal atom distances. Molecular unfolding problem aims to find the torsional configuration that increases the inter-atomic distance within a molecule, which also increases the molecular area. Quantum annealing approach first encodes the problem into a Higher-order Unconstrained Binary Optimization (HUBO) equation which is pruned to an arbitrary percentage to improve the time efficiency and to be able to solve the equation using any quantum annealer. The resultant HUBO is then converted to a Quadratic Unconstrained Binary Optimization equation (QUBO), which is easily embedded on a D-wave annealing Quantum processor.
Paper Structure (17 sections, 20 equations, 8 figures, 4 tables)

This paper contains 17 sections, 20 equations, 8 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Molecular Unfolding
  4. Problem Definition
  5. Quantum Annealing
  6. Higher order Unconstrained Binary Optimization (HUBO)
  7. Proposed Methodology
  8. Preprocessing phase
  9. Hard constraint preparation
  10. Symbolic transformation of coordinates
  11. Extracting solution from final HUBO
  12. Results and Discussion
  13. Volume gain in time with different torsionals
  14. Influence of threshold value in volume gain
  15. Time taken for same volume gain percentage
  16. ...and 2 more sections

Figures (8)

  • Figure 1: Representation of a ligand molecule.
  • Figure 2: Solving an optimization problem using a quantum annealer.
  • Figure 3: Framework of quantum molecular unfolding.
  • Figure 4: Variation in Volume Gain(VG%) with change in the Number of rotations.
  • Figure 5: Variation in Volume Gain(VG%) with change in the threshold value for Lumateperone.
  • ...and 3 more figures