Coarse graining molecular dynamics with graph neural networks

Abstract

Coarse graining enables the investigation of molecular dynamics for larger systems and at longer timescales than is possible at an atomic resolution. However, a coarse graining model must be formulated such that the conclusions we draw from it are consistent with the conclusions we would draw from a model at a finer level of detail. It has been proved that a force matching scheme defines a thermodynamically consistent coarse-grained model for an atomistic system in the variational limit. Wang et al. [ACS Cent. Sci. 5, 755 (2019)] demonstrated that the existence of such a variational limit enables the use of a supervised machine learning framework to generate a coarse-grained force field, which can then be used for simulation in the coarse-grained space. Their framework, however, requires the manual input of molecular features to machine learn the force field. In the present contribution, we build upon the advance of Wang et al. and introduce a hybrid architecture for the machine learning of coarse-grained force fields that learn their own features via a subnetwork that leverages continuous filter convolutions on a graph neural network architecture. We demonstrate that this framework succeeds at reproducing the thermodynamics for small biomolecular systems. Since the learned molecular representations are inherently transferable, the architecture presented here sets the stage for the development of machine-learned, coarse-grained force fields that are transferable across molecular systems.

Multi-body effects in a coarse-grained protein force field

“…In recent work, by our group 61,62 and others, 26,63,64 a different philosophy has been employed to take into account multibody effects in CG modeling: namely, taking advantage of the ability of modern machine learning techniques to approximate arbitrary complex multi-body functions. Given the recent success in the use of these techniques for the definition of the classical energy function from quantum mechanical calculations, [65][66][67][68][69][70][71][72][73][74][75][76][77][78][79][80][81][82][83][84] a similar idea has been applied for coarse-graining.…”

“…Given the recent success in the use of these techniques for the definition of the classical energy function from quantum mechanical calculations, [65][66][67][68][69][70][71][72][73][74][75][76][77][78][79][80][81][82][83][84] a similar idea has been applied for coarse-graining. To this end, we have used both neural networks (CGnets) 61,62 and kernel methods 85 as universal function approximators that can represent complex many-body terms on top of lower order terms. We have demonstrated on several simple systems and a mini-protein that, thanks to the general modeling of the full n-body interaction potential allowed by these techniques, it is possible to design CG models that accurately reproduce the free energy landscape of atomistic models.…”

“…We have demonstrated on several simple systems and a mini-protein that, thanks to the general modeling of the full n-body interaction potential allowed by these techniques, it is possible to design CG models that accurately reproduce the free energy landscape of atomistic models. 61,62,85 In the present work, we employ general CGnets and a multibody CGnet architecture in order to analyze to which degree multibody interactions are required to represent accurate coarse-grained force fields. We find that, on a test miniprotein, correction terms limited to three-body interactions are not sufficient for a CG model to reproduce the free energy of an atomistic model.…”

Differentiable molecular simulation can learn all the parameters in a coarse-grained force field for proteins

“…Meanwhile, deep learning has had a major impact on many areas of biology, achieving state of the art performance in fields such as protein structure prediction [10]. A number of groups have applied these advances to molecular simulations [11, 12, 13] including learning coarsegrained potentials [14, 15, 16, 17, 18], learning quantum mechanical potentials [19, 20, 21, 22], improving sampling [23], and improving atom typing [24]. Whilst promising, many of these approaches show limited success when used on systems they were not trained on.…”

Construction of a neural network energy function for protein physics

“…More recent works have developed neural network energy functions for multi-scale modeling of molecules following a bottom-up approach, e.g. fitting potentials at atomic resolution to QM calculations (17), or fit coarse grained potentials to atomic molecular dynamics simulations (18). These energy functions are still not transferable to general proteins but could lead to a paradigm shift in the field of force fields in the future.…”