Molecular free energy optimization on a computational graph

Factorization in molecular modeling and belief propagation algorithms

Factorization reduces computational complexity, and is therefore an important tool in statistical machine learning of high dimensional systems. Conventional molecular modeling, including molecular dynamics and Monte Carlo simulations of molecular systems, is a large research field based on approximate factorization of molecular interactions. Recently, the local distribution theory was proposed to factorize joint distribution of a given molecular system into trainable local distributions. Belief propagation algorithms are a family of exact factorization algorithms for (junction) trees, and are extended to approximate loopy belief propagation algorithms for graphs with loops. Despite the fact that factorization of probability distribution is the common foundation, computational research in molecular systems and machine learning studies utilizing belief propagation algorithms have been carried out independently with respective track of algorithm development. The connection and differences among these factorization algorithms are briefly presented in this perspective, with the hope to intrigue further development of factorization algorithms for physical modeling of complex molecular systems.

DeepRefiner: high-accuracy protein structure refinement by deep network calibration

The DeepRefiner webserver, freely available at http://watson.cse.eng.auburn.edu/DeepRefiner/, is an interactive and fully configurable online system for high-accuracy protein structure refinement. Fuelled by deep learning, DeepRefiner offers the ability to leverage cutting-edge deep neural network architectures which can be calibrated for on-demand selection of adventurous or conservative refinement modes targeted at degree or consistency of refinement. The method has been extensively tested in the Critical Assessment of Techniques for Protein Structure Prediction (CASP) experiments under the group name 'Bhattacharya-Server' and was officially ranked as the No. 2 refinement server in CASP13 (second only to 'Seok-server' and outperforming all other refinement servers) and No. 2 refinement server in CASP14 (second only to 'FEIG-S' and outperforming all other refinement servers including 'Seok-server'). The DeepRefiner web interface offers a number of convenient features, including (i) fully customizable refinement job submission and validation; (ii) automated job status update, tracking, and notifications; (ii) interactive and interpretable web-based results retrieval with quantitative and visual analysis and (iv) extensive help information on job submission and results interpretation via web-based tutorial and help tooltips.

"Dividing and Conquering" and "Caching" in Molecular Modeling

Molecular modeling is widely utilized in subjects including but not limited to physics, chemistry, biology, materials science and engineering. Impressive progress has been made in development of theories, algorithms and software packages. To divide and conquer, and to cache intermediate results have been long standing principles in development of algorithms. Not surprisingly, most important methodological advancements in more than half century of molecular modeling are various implementations of these two fundamental principles. In the mainstream classical computational molecular science, tremendous efforts have been invested on two lines of algorithm development. The first is coarse graining, which is to represent multiple basic particles in higher resolution modeling as a single larger and softer particle in lower resolution counterpart, with resulting force fields of partial transferability at the expense of some information loss. The second is enhanced sampling, which realizes "dividing and conquering" and/or "caching" in configurational space with focus either on reaction coordinates and collective variables as in metadynamics and related algorithms, or on the transition matrix and state discretization as in Markov state models. For this line of algorithms, spatial resolution is maintained but results are not transferable. Deep learning has been utilized to realize more efficient and accurate ways of "dividing and conquering" and "caching" along these two lines of algorithmic research. We proposed and demonstrated the local free energy landscape approach, a new framework for classical computational molecular science. This framework is based on a third class of algorithm that facilitates molecular modeling through partially transferable in resolution "caching" of distributions for local clusters of molecular degrees of freedom. Differences, connections and potential interactions among these three algorithmic directions are discussed, with the hope to stimulate development of more elegant, efficient and reliable formulations and algorithms for "dividing and conquering" and "caching" in complex molecular systems.