Exploring the landscape of model representations

Abstract

The success of any physical model critically depends upon adopting an appropriate representation for the phenomenon of interest. Unfortunately, it remains generally challenging to identify the essential degrees of freedom or, equivalently, the proper order parameters for describing complex phenomena. Here we develop a statistical physics framework for exploring and quantitatively characterizing the space of order parameters for representing physical systems. Specifically, we examine the space of low-resolution representations that correspond to particle-based coarse-grained (CG) models for a simple microscopic model of protein fluctuations. We employ Monte Carlo (MC) methods to sample this space and determine the density of states for CG representations as a function of their ability to preserve the configurational information, I, and large-scale fluctuations, Q, of the microscopic model. These two metrics are uncorrelated in high-resolution representations but become anticorrelated at lower resolutions. Moreover, our MC simulations suggest an emergent length scale for coarse-graining proteins, as well as a qualitative distinction between good and bad representations of proteins. Finally, we relate our work to recent approaches for clustering graphs and detecting communities in networks.

A journey through mapping space: characterising the statistical and metric properties of reduced representations of macromolecules

“…The observations reported in this section resonate with those made by Foley and collaborators in a recent work [15]: there, they observed a phase transition in a system whose degrees of freedom were the retained sites of a reduced model of proteins. In that case, the energy of a given mapping was obtained from the calculation of the spectral quality of the associated model, a quantity related to the sum of the eigenvalues of the covariance matrix obtained integrating exactly a Gaussian network model (GNM).…”

“…in the case of proteins, to extremely accurate and sophisticated CG potentials such as OPEP [9,10], AWSEM [11,12] and UNRES [13,14]. The former task a e-mail: raffaello.potestio@unitn.it (corresponding author) has been the object of a smaller number of works, however its centrality in and beyond the process of coarse graining has recently started to emerge [8,15]; indeed, a deep relationship exists between the degrees of freedom one selects to construct a CG model of the system, and those one employs to analyse the system's behaviour from a more detailed representation.…”

From System Modeling to System Analysis: The Impact of Resolution Level and Resolution Distribution in the Computer-Aided Investigation of Biomolecules

“…Foley and coworkers ( Foley et al, 2015 ; Foley et al, 2020 ) have pioneered the analysis of the CG model spectrum in a formal and systematic way. In Foley et al (2015) they considered a one-bead-per-residue Gaussian network model (GNM) of proteins as the reference, high-resolution representation; then, taking advantage of the exact integrability of GNMs, they performed a systematic decimation of the system’s beads to investigate how reduced models at varying degrees of resolution manage to reproduce fluctuations and correlations of the original model.…”

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

“…While acceptable in most practical applications, this approach entails substantial limitations: in fact, the CG process implies a loss of information and, through the application of universal mapping strategies, system-specific properties, albeit relevant, might be “lost in translation” from a higher to a lower resolution representation ( Foley et al, 2015 ; Jin et al, 2019 ; Foley et al, 2020 ). Hence, a method would be required that enables the automated identification of which subset of retained degrees of freedom of a given system preserves the majority of important detail from the reference, while at the same time reducing the complexity of the problem.…”