Membrane protein diffusion without more molecular dynamics: a neural stochastic model stretches trajectories to 40,000 frames while holding near-Brownian motion
Synopsis
Coarse-grained molecular dynamics gives short membrane-protein trajectories, but long-time diffusion statistics are costly to obtain. A neural stochastic model combines a transformer encoding of protein configurations, recurrent memory at multiple time scales and a stochastic latent process with learned memory to generate correlated displacements autoregressively. In the seven-PIEZO system it yields a mean anomalous diffusion exponent of 1.048±0.012 against 1.049±0.022 for MD, where the earlier VAR-SDE model gives 1.563±0.016, and its trajectories extend to 40,000 frames.
Interpretation
Collective membrane-protein diffusion can be extrapolated forward without running further molecular dynamics, producing trajectories longer than the reference simulation itself. An earlier variational autoregressive model captured short-time multi-protein membrane diffusion but could not reproduce long-time dynamics, showing superdiffusion in the seven-PIEZO system. In the seven-PIEZO system the mean anomalous diffusion exponent is 1.049±0.022 for MD, 1.048±0.012 for the neural stochastic model and 1.563±0.016 for VAR-SDE; the neural stochastic trajectories extend to 40,000 frames, about four times the reference.
Each step advances from the previous frame's displacement and the current protein separations, and positions are updated by sampled displacements. Configurations are first encoded into a geometry vector by attention, then summarized over history by LSTM cells with strides from 1 to 300 frames, while the latent state evolves as a discrete Ornstein-Uhlenbeck process with a memory coefficient and a noise amplitude. A cross-attention decoder outputs a mean and a 3×3 covariance for each protein's three-dimensional displacement, which is sampled and wrapped into the periodic box; training covers two coarse-grained systems, seven PIEZO and seven PIEZO plus ten TREK, with five training seeds each.
The differing diffusion of the two channel species in the mixed system is also retained. PIEZO and TREK channels diffuse together in one bilayer, and MD shows shorter displacements for PIEZO and longer ones for TREK. In the seven-PIEZO plus ten-TREK system, MD gives mean anomalous exponents of 0.943±0.016 for PIEZO and 0.995±0.019 for TREK, while the model predicts 1.015±0.013 and 1.011±0.011, differences within the standard errors.
Perspective
The demonstrated scope is two coarse-grained membrane systems, seven PIEZO channels and seven PIEZO plus ten TREK channels; evaluation compares mean squared displacement, non-Gaussian parameter, van Hove distributions and velocity autocorrelation at lags up to 5,000 frames, with generated trajectories of 40,000 frames. The authors state that generated trajectories should be regarded as statistical surrogates of the simulated dynamics rather than exact reconstructions of individual molecular trajectories or replacements for molecular dynamics.
The model does not explicitly enforce the underlying molecular force field or membrane energetics, so predictions depend on statistical information captured during training; generalization to different protein compositions, membrane properties and simulation conditions remains to be established. The authors propose future work adding physical constraints and evaluating across a broader range of membrane systems.