Optimization problem and efficient partitioning algorithm for transitions to finer-scale models in adaptive resolution simulation of articulated biopolymers

Mohammad Poursina, Kurt S. Anderson

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Adaptive coarse graining of highly complex biomolecular systems is conducted by either imposing constraints on the system model to generate a coarser model, or releasing certain constraints from it to create a higher fidelity one. This paper addresses some of the challenges of transitions to finer-scale models. It is shown that the kinetic energy associated with ignored modes of motion during the coarse graining process must be estimated and put back into the simulation. As such, unlike real mechanical systems, transitioning back to a finer biomolecular model may result in an infinite number of solutions. Herein, an optimization-based approach subject to the satisfaction of impulse–momentum balance and desired kinetic energy is presented to arrive at a physically meaningful state of the system immediately after the transition. In order to reduce the cost of formulating and solving this optimization problem, generalized velocities of the system are partitioned into two categories: independent joint velocities associated with the released joints, and dependent joint velocities associated with the rest of the joints. This paper further develops a divide-and-conquer algorithm to efficiently perform this partitioning process and express dependent velocities in terms of independent ones. The presented method is highly parallelizable and avoids the construction of the mass and Jacobian matrices of the entire system, resulting in a significant improvement in computational efficiency.

Original languageEnglish (US)
Pages (from-to)97-117
Number of pages21
JournalMultibody System Dynamics
Volume42
Issue number1
DOIs
StatePublished - Jan 1 2018

Fingerprint

Biopolymers
Partitioning
Optimization Problem
Coarse-graining
Kinetic energy
Simulation
Divide-and-conquer Algorithm
Jacobian matrices
Dependent
Jacobian matrix
Number of Solutions
Computational efficiency
Model
Mechanical Systems
Computational Efficiency
Fidelity
Immediately
Large scale systems
Complex Systems
Express

Keywords

  • Adaptive coarse graining
  • Divide-and-conquer algorithm
  • Model transition
  • Molecular dynamics
  • Optimization

ASJC Scopus subject areas

  • Modeling and Simulation
  • Aerospace Engineering
  • Mechanical Engineering
  • Computer Science Applications
  • Control and Optimization

Cite this

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AB - Adaptive coarse graining of highly complex biomolecular systems is conducted by either imposing constraints on the system model to generate a coarser model, or releasing certain constraints from it to create a higher fidelity one. This paper addresses some of the challenges of transitions to finer-scale models. It is shown that the kinetic energy associated with ignored modes of motion during the coarse graining process must be estimated and put back into the simulation. As such, unlike real mechanical systems, transitioning back to a finer biomolecular model may result in an infinite number of solutions. Herein, an optimization-based approach subject to the satisfaction of impulse–momentum balance and desired kinetic energy is presented to arrive at a physically meaningful state of the system immediately after the transition. In order to reduce the cost of formulating and solving this optimization problem, generalized velocities of the system are partitioned into two categories: independent joint velocities associated with the released joints, and dependent joint velocities associated with the rest of the joints. This paper further develops a divide-and-conquer algorithm to efficiently perform this partitioning process and express dependent velocities in terms of independent ones. The presented method is highly parallelizable and avoids the construction of the mass and Jacobian matrices of the entire system, resulting in a significant improvement in computational efficiency.

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