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Symmetry-Driven Discovery of Dynamical Variables in Molecular Simulations

ICML 2025 · Probabilistic and scientific modeling › Molecules and proteins · approach: Diffusion for molecular conformations

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Discovers effective degrees of freedom in molecular dynamics by finding approximate symmetries of the force-field energy (symmetry loss and Hessian-based methods), without trajectory data, and uses them to sample alanine dipeptide and chignolin conformers.

Problem

Identifying low-energy effective degrees of freedom (collective variables) for efficient conformational sampling in molecular dynamics, which normally requires trajectory data or prior knowledge.

Approach

Map low-energy DOF to approximate symmetries of the energy function: minimize a symmetry loss (grad E · L x)^2 over Lie algebra generators, with Hessian-based analytic solutions (slow eigenspaces and degenerate eigenspaces of H^2), then navigate the landscape along the discovered DOF and relax with short OpenMM simulations.

Key results

• Hessian and direct-optimization DOF recover all major alanine dipeptide conformers (C5, C7eq, C7ax) within about 2 ps of simulation, whereas a 500 ns baseline MD misses rarer states (C7ax at 0 fraction until 25 ns in vacuum).
• Chignolin folded and misfolded conformers are found with the discovered DOF, including with implicit solvent force field.
• Reported Hessian computation cost is 2 s for alanine dipeptide and 200 s for chignolin; direct optimization takes 15 s and 450 s.

Measured effects reported in the paper

Surprising findings

• DOF discovered in vacuum transfer well to the solvent setting, finding conformers even though the Hessian methods cannot use stochastic solvent forces.
• Long 500 ns simulations sample the conformational landscape poorly, with some conformers absent until late in the run.

Limitations

• Hessian-based methods do not apply to stochastic (explicit or solvent) force fields, so solvent cases rely on vacuum-derived DOF or direct optimization.
• Hessian computation scales quadratically with system size and is a bottleneck for large systems.
• Evaluated only on two small peptide systems (alanine dipeptide and chignolin).

Experimental setup

Benchmarks: alanine dipeptide conformers (Ramachandran plot) chignolin folded/misfolded conformers

Metrics: fractional distribution of conformers vs simulation time conformer discovery in ps vs ns

Baselines: long OpenMM MD simulation (500 ns) replica exchange molecular dynamics (8 replicas)

Builds on: LieGG metadynamics replica exchange molecular dynamics

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