The Renormalization Group and Its Applications to Generating Coarse-Grained Models of Large Biological Molecular Systems

Koehl, Patrice; Poitevin, Frédéric; Navaza, Rafael; Delarue, Marc

doi:10.1021/acs.jctc.6b01136

Cited by 18 publications

(15 citation statements)

References 78 publications

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“…It is the local network, namely the list of edges in the EN that connect to an atom k that defines the local environment of an atom. To test if this is the case, we have assigned to each atom i a frequency Ω i 92 such that

Ω_{i}^{2} = \sum_{j = 1}^{N ((), i)} k_{ij} = \sum_{j = 1}^{N ((), i)} \sqrt{k_{j} k_{i}},

where the summation extends over all atoms j such that ij is an edge in the EN considered. We computed Ω i for all C α atoms of all proteins in our dataset, for the Delaunay based EN and the cutoff based EN, with constant, or optimized values for the force constants k ij .…”

Section: Resultsmentioning

confidence: 99%

Parameterizing elastic network models to capture the dynamics of proteins

2021

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Coarse-grained normal mode analyses of protein dynamics rely on the idea that the geometry of a protein structure contains enough information for computing its fluctuations around its equilibrium conformation. This geometry is captured in the form of an elastic network (EN), namely a network of edges between its residues. The normal modes of a protein are then identified with the normal modes of its EN. Different approaches have been proposed to construct ENs, focusing on the choice of the edges that they are comprised of, and on their parameterizations by the force constants associated with those edges. Here we propose new tools to guide choices on these two facets of EN. We study first different geometric models for ENs. We compare cutoff-based ENs, whose edges have lengths that are smaller than a cutoff distance, with Delaunay-based ENs and find that the latter provide better representations of the geometry of protein structures. We then derive an analytical method for the parameterization of the EN such that its dynamics leads to atomic fluctuations that agree with experimental B-factors. To limit overfitting, we attach a parameter referred to as flexibility constant to each atom instead of to each edge in the EN. The parameterization is expressed as a non-linear optimization problem whose parameters describe both rigid-body and internal motions. We show that this parameterization leads to improved ENs, whose dynamics mimic MD simulations better than ENs with uniform force constants, and reduces the number of normal modes needed to reproduce functional conformational changes.

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Ω_{i}^{2} = \sum_{j = 1}^{N ((), i)} k_{ij} = \sum_{j = 1}^{N ((), i)} \sqrt{k_{j} k_{i}},

Section: Resultsmentioning

confidence: 99%

Parameterizing elastic network models to capture the dynamics of proteins

2021

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“…These techniques rely on specific properties of the system under examination: examples include quasi-rigid domain decomposition 24−31 or graphtheory-based model construction methods that attempt to create CG representations of chemical compounds based only on their static graph structure; 32,33,85 other approaches aim at selecting those representations that closely match the highresolution model's energetics. 22,35 Finally, more recent strategies rooted in the field of machine learning generate discrete CG variables by means of variational autoencoders. 86 All of these methods take into account the system structure, or its conformational variability, or its energy, but none of them integrates these complementary properties in a consistent framework embracing topology, structure, dynamics, and thermodynamics.…”

Section: Discussionmentioning

confidence: 99%

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

Giulini

Menichetti

Shell

et al. 2020

J. Chem. Theory Comput.

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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.

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“…The impact of resolution distribution was later studied by Koehl and coworkers, also in this case making use of ENMs: the Decimate ( Koehl et al, 2017 ) algorithm progressively reduces the resolution of a biomolecule by creating a hierarchy of increasingly simplified models, in the spirit of the renormalization group theory. As expected, such CG mappings show an uneven distribution of detail: in the case of globular proteins, for example, optimal models tend to concentrate atoms on the surface of the molecule, thus heavily coarse-graining the inner region—whose mechanical properties require fewer degrees of freedom to be aptly reproduced.…”

Section: On Choosing the Optimal Resolution Level And Distribution And On Modeling As An Analysis Toolmentioning

confidence: 99%

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

Giulini

Rigoli

Mattiotti

et al. 2021

Front. Mol. Biosci.

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The ever increasing computer power, together with the improved accuracy of atomistic force fields, enables researchers to investigate biological systems at the molecular level with remarkable detail. However, the relevant length and time scales of many processes of interest are still hardly within reach even for state-of-the-art hardware, thus leaving important questions often unanswered. The computer-aided investigation of many biological physics problems thus largely benefits from the usage of coarse-grained models, that is, simplified representations of a molecule at a level of resolution that is lower than atomistic. A plethora of coarse-grained models have been developed, which differ most notably in their granularity; this latter aspect determines one of the crucial open issues in the field, i.e. the identification of an optimal degree of coarsening, which enables the greatest simplification at the expenses of the smallest information loss. In this review, we present the problem of coarse-grained modeling in biophysics from the viewpoint of system representation and information content. In particular, we discuss two distinct yet complementary aspects of protein modeling: on the one hand, the relationship between the resolution of a model and its capacity of accurately reproducing the properties of interest; on the other hand, the possibility of employing a lower resolution description of a detailed model to extract simple, useful, and intelligible information from the latter.

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The Renormalization Group and Its Applications to Generating Coarse-Grained Models of Large Biological Molecular Systems

Cited by 18 publications

References 78 publications

Parameterizing elastic network models to capture the dynamics of proteins

Parameterizing elastic network models to capture the dynamics of proteins

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

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

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