Machine-guided path sampling to discover mechanisms of molecular self-organization

Abstract

Molecular self-organization driven by concerted many-body interactions produces the ordered structures that define both inanimate and living matter. Here we present an autonomous path sampling algorithm that integrates deep learning and transition path theory to discover the mechanism of molecular self-organization phenomena. The algorithm uses the outcome of newly initiated trajectories to construct, validate and—if needed—update quantitative mechanistic models. Closing the learning cycle, the models guide the sampling to enhance the sampling of rare assembly events. Symbolic regression condenses the learned mechanism into a human-interpretable form in terms of relevant physical observables. Applied to ion association in solution, gas-hydrate crystal formation, polymer folding and membrane-protein assembly, we capture the many-body solvent motions governing the assembly process, identify the variables of classical nucleation theory, uncover the folding mechanism at different levels of resolution and reveal competing assembly pathways. The mechanistic descriptions are transferable across thermodynamic states and chemical space.

Optimal Reaction Coordinates and Kinetic Rates from the Projected Dynamics of Transition Paths

“…We start by proposing a pool of eight basis CVs to be used as building blocks for RC optimization: the set ranges from geometry-inspired CVs like the distance d and the total number of carbon–carbon or carbon–water contacts ( cc , c 2 w , c 1 w ) to physics-inspired CVs like the approximate two-body carbon or water entropy ( sc , sw ) and the carbon–carbon or carbon–water interaction energy ( ucc , ucw ). We remark that it is customary, in published CV-optimization studies, to combine together like in our case CVs of different nature. ,,,, It is not obvious a priori which CVs or a combination thereof could be the best approximations of an optimal RC.…”

“…For each CV q under scrutiny, the 300 committor values p B ( q ( x )) are used to fit the parameters a , b of the following sigmoid function (see e.g. refs and ): P B fit ( q false( x false) ; a , b ) = 1 1 + e − ( q − a ) / b = 1 2 ( 1 + tanh ⁡ q − a 2 b ) The residual sum of squares (RSS) of the fit is used as a measure of the deviation from an ideal committor distribution.…”

“…Several methods based on different theoretical principles have been put forward to estimate optimal RCs from MD data. Given the customary identification of the optimal RC with the committor function, a possibility consists in optimizing a parametrization of the committor function based on p B ( x ) values estimated from transition path sampling (TPS), exploiting, e.g., the histogram test, maximum-likelihood approaches, , or artificial intelligence. , …”

Accurate and Efficient Multilevel Free Energy Simulations with Neural Network-Assisted Enhanced Sampling

“…The performance of our neural network-assisted approach, which first learns an optimal latent space and then constructs an intermediate distribution to facilitate the convergence of free energy correction, can be further enhanced with more sophisticated molecular features, such as those representing the nearby solvent distributions. ,, In fact, we note that the two levels of theory can differ significantly in not only structural distributions but also electronic properties, such as charge distributions, , which lead to different interactions with the environment. For such cases, including the environmental features in the training of the latent space is expected to be particularly important.…”

Spectral Map: Embedding Slow Kinetics in Collective Variables

“…Failure to encode this can hinder the description of the underlying physical mechanisms. To address this, several techniques for learning CVs directly from simulation data have been developed. − …”