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A New, Fundamental Multiscale Modeling Framework Based on the Relative Entropy
Abstract   Open access   Peer reviewed

A New, Fundamental Multiscale Modeling Framework Based on the Relative Entropy

M. Scott Shell and Aviel Chaimovich
Biophysical journal, v 98(3), pp 388a-388a
Jan 2010
DOI: https://doi.org/10.1016/j.bpj.2009.12.2090
url
https://doi.org/10.1016/j.bpj.2009.12.2090View
Published, Version of Record (VoR)Open Access (License Unspecified),  Open

Abstract

Our understanding of biology stems from models at many resolutions, as we seek from detailed atomic-scale interactions simpler emergent physical principles to support our understanding and to produce useful theoretical reductions and tractable simulations. In particular, multiscale methods coupling coarse-grained and atomic models are essential to modeling, predicting, and understanding the basic driving forces that operate across many biomolecular length and time scales. Yet, though coarse-graining strategies exist, it has been challenging to identify universal approaches to the multiscale problem that build systematic, quantitative connections between atomic interactions and reduced models. We have created a powerful, rigorous theoretical framework that addresses this problem. Its focus is the relative entropy, an information-theoretic and statistical-thermodynamic quantity that measures the information lost when moving from a detailed to coarse-grained description of a system. We postulate that the most descriptive physical principles and simple models are those that minimize this quantity, hence minimizing the physical information lost when atomic detail is removed. Importantly, we show that this concept unifies and broadens a number of established statistical-mechanical principles. For the first time, the relative entropy provides a general, systematic framework for multiscale modeling. A practical benefit is that the relative entropy suggests how to transform atomistic models into reduced ones that capture the same physics, enabling seamless integration of models spanning scales. We describe a family of algorithms that optimize coarse-grained molecular models by minimizing the relative entropy numerically. These coarse-graining algorithms are general to arbitrary models and the first to offer a universal metric for model quality. We describe the application of these algorithms to the development of simple models of water for modeling large-scale association processes driven by hydrophobic interactions, and to models of peptides for interrogating early steps in aggregation.

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