Implementation of contact joint to resolve excluded volume constraints

Dr. Pascal Carrivain

I did a Ph.D with Jean-Marc Victor (Theoretical physics of condensed matter UMR CNRS 7600)

I did a post-doc with Cédric Vaillant and Ralf Everaers (Laboratoire de Physique, ENS de Lyon)

I am currently an E-CAM post-doc with Ralf Everaers (Centre Blaise Pascal, ENS de Lyon)

Host beneficiary: ENS Lyon, France

 

Description

To study the long term memory of the initial conformation of a highly entangle polymer we need to preserve the topology.
It means that two bonds of the polymer cannot cross. It is of great importance for the study of post-mitotic chromosome unfolding.
To resolve the excluded volume constraints you could use a soft or hard potential between the two points associated to the
minimal distance. Here, we propose to change the relative velocity between overlaped bonds to resolve the excluded volume
constraint in one time-step of molecular dynamics.
In a second time, we would like to create a python bindings for Open-Dynamics-Engine www.ode.org that is a open source physics engine.
All the actual physics engines can resolve excluded volume constraints for arbitrary complex shapes.
We can imagine to replace the protein by its surface, to simulate granular media ...
The python bindings for Open-Dynamics-Engine would be a new engine that can be interfaced with Open-Path-Sampling openpathsampling.org.

Development Plan

List of Tasks

  • Module 1 : minimal distance between two segments using the Karush-Kuhn-Tucker conditions
  • Module 2 : resolve the excluded volume constraints for a gas of capped-cylinders
  • Module 3 : Python bindings for "Open-Dynamics-Engine"
  • Module 4 : openmm_plectoneme
  • Module 5 : openmm_copolymer

List of Modules

Module 1:  minDist2segments_KKT

Status: Done

Description: The minDist2segments_KKT module returns the minimal distance between two line segments. It uses the Karush-Kuhn-Tucker conditions (KKT) for the minimization under constraints. To study the long term memory of the initial conformation of a highly entangled polymer we need to preserve the topology. It means that two polymer bonds cannot cross. This is of great importance for the study of post-mitotic chromosome unfolding. To resolve the excluded volume constraints one could use a soft or hard potential between the two points associated to the minimal distance.

Module 2: velocities_resolve_EVC module

Status: Done

Description: Polymer physics uses bead-spring model to ensure connectivity between consecutive monomers and Weeks-Chandler-Andersen (WCA) repulsive potential to avoid bond crossing. The present module proposes to implement a method that comes from physics engine. It uses velocity-based method to resolve the excluded volume constraints in one time-step of molecular dynamics. We can see it as a hard-potential that pushes away two bonds in one time-step while WCA can be seen as a soft potential that needs more time-step to remove/prevent bond overlapping. We adapt the method from 3D rigid body (position and orientation are given) to the bead-spring model where only the position of the beads are known.

Module 3

Status: Work in Progress

Expected delivery date: end of november

Description:

Module 4: openmm_plectoneme

Status: Work in Progress

Expected delivery date: end of october

Description: The openmm_plectoneme is a module that introduce twist to a ring plectoneme and sample the accessible conformations under
torsionnal constraints. This module takes advantage of the OpenMM software and GPU acceleration. It builds a Kremer-Grest polymer model with virtual sites to attach a frame to each of the bead.

Module 5: openmm_copolymer

Status: Work in Progress

Expected delivery date: end of october

Description: The OpenMM_Copolymer is a module that sample conformation of a block-copolymer given a epigenome.
This module takes advantage of the OpenMM software and GPU acceleration.
It builds a Kremer-Grest polymer model with uni-dimensionnal epigenetic informations and construct the epigenetic interactions based on the model you design.

Published Results

Outreach Material