An Information-Theory-Based Approach for Optimal Model Reduction of Biomolecules

Abstract

In theoretical modeling of a physical system, a crucial step consists of the identification of those degrees of freedom that enable a synthetic yet informative representation of it. While in some cases this selection can be carried out on the basis of intuition and experience, straightforward discrimination of the important features from the negligible ones is difficult for many complex systems, most notably heteropolymers and large biomolecules. We here present a thermodynamics-based theoretical framework to gauge the effectiveness of a given simplified representation by measuring its information content. We employ this method to identify those reduced descriptions of proteins, in terms of a subset of their atoms, that retain the largest amount of information from the original model; we show that these highly informative representations share common features that are intrinsically related to the biological properties of the proteins under examination, thereby establishing a bridge between protein structure, energetics, and function.

A Deep Graph Network–Enhanced Sampling Approach to Efficiently Explore the Space of Reduced Representations of Proteins

“…In this section, we outline the technical ingredients that lie at the basis of the results obtained in this study. Specifically, in Mapping entropy we summarize the mapping entropy protocol for optimizing CG representations presented in Giulini et al (2020) ; in Protein structures and data sets we briefly describe the two proteins analyzed in this work as well as the data sets fed to the machine learning architecture; in Data Representation and Machine Learning model we illustrate our choice for the representation of the input data, together with theoretical and computational details about DGNs; finally, in Wang–Landau Sampling we describe our implementation of the Wang–Landau sampling algorithm as applied to the reconstruction of the mapping entropy landscape of a system.…”

“…A recently developed statistical mechanics-based strategy that aims at overcoming such limitations is the one relying on the minimization of the mapping entropy ( Giulini et al, 2020 ), which performs, in an unsupervised manner, the identification of the subset of a molecule’s atoms that retains the largest possible amount of information about its behavior. This scheme relies on the calculation of the mapping entropy S map ( Shell, 2008 ; Rudzinski and Noid, 2011 ; Shell, 2012 ; Foley et al, 2015 ), a quantity that provides a measure of the dissimilarity between the probability density of the system configurations in the original, high-resolution description and the one marginalized over the discarded atoms.…”

“…To this end, we rely on Deep Graph Networks (DGNs) ( Bacciu et al, 2020 ), a family of machine learning models that learn from graph-structured data, where the graph has a variable size and topology; by training the model on a set of tuples (protein, CG mapping, and S map ), we can infer the S map values of unseen mappings associated with the same protein making use of a tiny fraction of the extensive amount of information employed in the original method, i.e., the molecular structure viewed as a graph. Compared to the algorithmic workflow presented in Giulini et al (2020) , the trained DGN proves capable of accurately calculating the mapping entropy arising from a particular selection of retained atoms throughout the molecule in a negligible time.…”

“…This computational speedup can be leveraged to perform a thorough, quasi-exhaustive characterization of the mapping entropy landscape in the space of possible CG representations of a system, a notable advancement with respect to the relatively limited exploration performed in Giulini et al (2020) . Specifically, by combining inference of the DGNs with the Wang–Landau sampling technique, we here provide an estimate of the density of states associated with the S map , that is, the number of CG representations in the biomolecule mapping space that generate a specific amount of information loss with respect to the all-atom reference.…”

Bottom-Up Coarse-Grained Modeling of DNA

“…Typically one chooses CG sites according to the center-of-masses (COM) of the atom groups forming the CG units, while other choices (such as taking coordinates of specific atoms) are also possible. For instance, one can aim to minimize the information loss due to the mapping operation (Giulini et al, 2020 ), or choose beads representing collective motions (Zhang et al, 2008 ). The Hamiltonian H ( q 1 , ⋯ , q n ) defines all properties of the high-resolution system and, through the mapping functions (Equation 1), all properties of the CG system.…”