Neural Network Based Prediction of Conformational Free Energies - A New Route toward Coarse-Grained Simulation Models

Abstract

Coarse-grained (CG) simulation models have become very popular tools to study complex molecular systems with great computational efficiency on length and time scales that are inaccessible to simulations at atomistic resolution. In so-called bottom-up coarse-graining strategies, the interactions in the CG model are devised such that an accurate representation of an atomistic sampling of configurational phase space is achieved. This means the coarse-graining methods use the underlying multibody potential of mean force (i.e., free-energy surface) derived from the atomistic simulation as parametrization target. Here, we present a new method where a neural network (NN) is used to extract high-dimensional free energy surfaces (FES) from molecular dynamics (MD) simulation trajectories. These FES are used for simulations on a CG level of resolution. The method is applied to simulating homo-oligo-peptides (oligo-glutamic-acid (oligo-glu) and oligo-aspartic-acid (oligo-asp)) of different lengths. We show that the NN not only is able to correctly describe the free-energy surface for oligomer lengths that it was trained on but also is able to predict the conformational sampling of longer chains.

Adversarial-residual-coarse-graining: Applying machine learning theory to systematic molecular coarse-graining

“…Additionally, ARCG bears resemblance to a recent CG method based on distinguishability and classification. 28 In this section we make explicit connections between the f -divergence implementation presented in this article and such external methods. The applications of the f -divergence duality presented here are in the infinite sampling limit with a fully expressive variational search; in practice, significant differences in seemingly equivalent methods may arise.…”

“…Classification has been recently used to train a CG model by using the resulting decision functionη † to directly update the CG configurational free energy. 28 This is motivated by noticing that the η that satisfies the variational bound in Eq. (17) can be related to the pointwise free energy difference as…”

“…17 Previous CG parameterization methods have used similar, but not identical, motivations to produce parameterization strategies. 17,24,28 ARCG theory serves to connect, clarify, and reframe these methods where possible while extending beyond the classification metaphor.…”

Combining statistical and neural network approaches to derive energy functions for completely flexible protein backbone design

“…The method, named NC-NN, comprises using adaptive-cutoff neighborcounting (NC) to estimate properly gauged high-dimensional statistical energies, followed by representing the high-dimensional statistical energy surfaces as neural networks (NN). (Behler and Parrinello, 2007;Galvelis and Sugita, 2017;Lemke and Peter, 2017;Shen and Yang, 2018) The energy terms obtained by this NC-NN approach have analytical gradients, allowing them to be used directly to drive (stochastic) molecular dynamics simulations. The SCUBA model contains NC-NN-derived energy terms to describe the main chain local conformation, the main chain through-space packing, the backbone-dependent side chain conformation, and so on, the relative weights of different energy components calibrated on the basis of SCUBA-driven stochastic dynamics (SD) simulations of natural proteins.…”

“…we use NNs to represent the NC-derived statistical energies as analytical functions of multiplexes of geometrical variables (Galvelis and Sugita, 2017;Lemke and Peter, 2017). Here, the inputs of a NN are the geometric variables (i.e.…”