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Extending Non-Equilibrium Pulling Method in GROMACS with Arbitrary User-Defined Atom Weight Factor Expressions

Vedran Miletić, Matea Turalija

😎 Group for Applications and Services on Exascale Research Infrastructure, Faculty of Informatics and Digital Technologies, University of Rijeka

Third Infinity 2022, Max Planck Institute for Multidisciplinary Sciences, Göttingen, 23rd of September 2022

Outline

  • Molecular dynamics simulation
  • Non-equilibrium pulling
  • Uniform flow simulation
  • Atom weight factor expression
  • Applications

Molecular dynamics simulation

  • Simulation of physical movement of atoms and molecules
  • Trajectories of atoms and molecules are obtained by solving Newton's equations of motion many times
    • Typical time step: 1-2 femtoseconds
    • Typical simulated time: nanoseconds to microseconds (10^6 to 10^9 steps)

Non-equilibrium pulling

Schematic picture of pulling a lipid out of a lipid bilayer with umbrella pulling. bg 120% right:45%

Pull coordinate

  • Pull coordinate = distance, angle, or dihedral angle betwen centers of mass of two groups of atoms
    • Alternatively, one group can be replaced by a reference position in space
    • Combination of coordinates using (optionally time-dependent) expressions: transformation pull coordinate, e.g. 0.5*(x1 + x2)

Pull groups and force

  • Pull group = a group of atoms weighted by their mass
    • Aditional per-atom weighting factor can be used
      • Defined in the simulation parameters, remains the same during simulation
  • Constant force pulling applies constant force between the centers of mass of two groups

Processes activated by flow

  • Many biological processes occur under flow conditions, e.g.
    • Hemostasis to stop bleeding
    • Leukocyte adhesion at sites of inflammation
    • Spider silk spinning
  • The biomolecules involved in the flow-dependent processes undergo specific conformational changes triggered (or influenced) by the flow

Simulating uniform flow (1/3)

100 ps molecular dynamics simulation of water. width:700px

Simulating uniform flow (2/3)

  • Flow is a movement of solvent atoms
  • Pulling all solvent atoms works when no other molecules except water are present in the simulation
  • Just a slice of solvent molecules should be pulled to allow the solvent atoms to interact with the biomolecule(s) without being "dragged away"

Simulating uniform flow (3/3)

A rectangular water box with ~32,000 water molecules is shown. width:900px

The previous approach (1/4)

  • This approach is flow-specific
  • Uses atom weighting factors in GROMACS to non-uniformly distribute the pulling force
    • Atoms of the solvent inside the slice -> weighting factor is non-zero
    • Atoms of the solvent outside the slice -> weighting factor is zero

The previous approach (2/4)

  • GROMACS limitation: weighting factors are defined once at the begining of the simulation
    • Problem: solvent atoms move during flow simulation, weighting factors should be recomputed each step
    • Solution: hack GROMACS to introduce the concept of the slice and recompute atom weighting factors each step

The previous approach (3/4)

  • Each atom is weighted with the weight factor:

    \[w_{sp} = x_{unit}^4 - 2x_{unit}^2 + 1\]

  • Coordinate \(x\) of each atom in the arbitrary slice is normalized from the interval \([s_{min}, s_{max}]\) to the coordinate \(x_{unit}\) in the interval \([−1, 1]\):

    \[x_{unit} = \frac{x - \frac{s_{min} + s_{max}}{2}}{\frac{s_{min} - s_{max}}{2}}\]

The previous approach (4/4)

Water density varies along the flow direction. width:600px

The new, general approach (1/3)

The new, general approach (2/3)

  • Weight factor expression variables:
    • Atom position in 3D (x, y, z)
    • Atom velocity in 3D (vx, vy, vz)
  • Examples:
    • Atom weight factor is sum of squares of positions: x^2 + y^2 + z^2
    • Atom weight factor is a linear combination of velocities: 1.75 * vx + 1.5 * vy + 1.25 * vz

The new, general approach (3/3)

  • Covers the requirements of uniform flow simulation
  • Non-smooth slice: x >= 1 && x < 5 ? 1 : 0
  • Smooth slice: x >= 1 && x < 5 ? (x - 2)^4 - 2 * (x - 2)^2 + 1 : 0

Possible applications of atom weight factor expressions

  • Simulating uniform flow in arbitrary direction
  • Pulling a protein domain with a non-uniform force applied to different residues
  • Introducing external force in a subset of the periodic metal/material system
  • Your ideas?

Future plans

  • Providing the option to configure the number of steps when weight factors are recomputed
  • Adding heuristics that avoid recomputation of factors for atoms that did not move or accelerate very much
  • Adding time as a variable in the expression
  • More extensive testing and physical validation
  • Inclusion in a future version of GROMACS (2024?)

Acknowledgments

Matea Turalija bg 95% right:30%

How to play with the code

Questions?

GROMACS developer workshop

  • Planned ~= spring 2023 (time and location TBA)
  • Entry-level development workshop
    • Primarily targeted for new developers
    • Non-developers interested in exploring development are welcome
  • Follow GROMACS forums or @GMX_TWEET for announcements

Author: Vedran Miletić