Coarse-grained Monte Carlo simulations of non-equilibrium systems

Liu, Xiao; Crocker, John C.; Sinno, Talid

doi:10.1063/1.4811656

Cited by 7 publications

(9 citation statements)

References 32 publications

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“…To study the assembly of virus capsids as a paradigm of a biological self-assembly process for which these elements are essential, coarse-grained MD simulations [56][57][58][59] and Monte Carlo (MC) techniques [60][61][62][63] have been used. Similarly the interaction of colloidal particles has been investigated on various scales with different simulation techniques [21], including MD simulations [64], MC simulations [65,66] and BD studies [67,68].…”

Section: Introductionmentioning

confidence: 99%

Studying protein assembly with reversible Brownian dynamics of patchy particles

Klein¹,

Schwarz²

2014

The Journal of Chemical Physics

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Assembly of protein complexes like virus shells, the centriole, the nuclear pore complex, or the actin cytoskeleton is strongly determined by their spatial structure. Moreover, it is becoming increasingly clear that the reversible nature of protein assembly is also an essential element for their biological function. Here we introduce a computational approach for the Brownian dynamics of patchy particles with anisotropic assemblies and fully reversible reactions. Different particles stochastically associate and dissociate with microscopic reaction rates depending on their relative spatial positions. The translational and rotational diffusive properties of all protein complexes are evaluated on-the-fly. Because we focus on reversible assembly, we introduce a scheme which ensures detailed balance for patchy particles. We then show how the macroscopic rates follow from the microscopic ones. As an instructive example, we study the assembly of a pentameric ring structure, for which we find excellent agreement between simulation results and a macroscopic kinetic description without any adjustable parameters. This demonstrates that our approach correctly accounts for both the diffusive and reactive processes involved in protein assembly.

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Section: Introductionmentioning

confidence: 99%

Studying protein assembly with reversible Brownian dynamics of patchy particles

Klein¹,

Schwarz²

2014

The Journal of Chemical Physics

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“…The result is a rewriting of the correspondence between Langevin dynamics and Monte Carlo dynamics as a correspondence between the simplest forms of gradient descent and neuroevolution. Just as the Langevin-Monte Carlo correspondence provides a basis for understanding why Monte Carlo simulations of particles can approximate real dynamics 31,[36][37][38][39][40][41] , so the neuroevolutiongradient descent correspondence shows how we can effectively perform gradient descent on the loss function without explicit calculation of gradients. The correspondence holds exactly only in the limit of vanishing mutation scale, but we use numerics to show in section "Numerical illustration of the neuroevolutiongradient descent correspondence" that it can be observed for neuroevolution done with finite mutations and gradient descent enacted with a finite timestep.…”

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confidence: 99%

Correspondence between neuroevolution and gradient descent

et al. 2021

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We show analytically that training a neural network by conditioned stochastic mutation or neuroevolution of its weights is equivalent, in the limit of small mutations, to gradient descent on the loss function in the presence of Gaussian white noise. Averaged over independent realizations of the learning process, neuroevolution is equivalent to gradient descent on the loss function. We use numerical simulation to show that this correspondence can be observed for finite mutations, for shallow and deep neural networks. Our results provide a connection between two families of neural-network training methods that are usually considered to be fundamentally different.

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“…In particular, the method may find use in the characterization of two-dimensional free energetic landscapes that serve as a starting point for recent spatial coarse-graining schemes. 91 Supporting …”

Section: Discussionmentioning

confidence: 99%

Sparse Sampling of Water Density Fluctuations in Interfacial Environments

Remsing

Patel

2016

J. Chem. Theory Comput.

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The free energetics of water density fluctuations near a surface, and the rare low-density fluctuations in particular, serve as reliable indicators of surface hydrophobicity; the easier it is to displace the interfacial waters, the more hydrophobic the underlying surface. However, characterizing the free energetics of such rare fluctuations requires computationally expensive, non-Boltzmann sampling methods like umbrella sampling. This inherent computational expense associated with umbrella sampling makes it challenging to investigate the role of polarizability or electronic structure effects in influencing interfacial fluctuations. Importantly, it also limits the size of the volume, which can be used to probe interfacial fluctuations. The latter can be particularly important in characterizing the hydrophobicity of large surfaces with molecular-level heterogeneities, such as those presented by proteins. To overcome these challenges, here we present a method for the sparse sampling of water density fluctuations, which is roughly two orders of magnitude more efficient than umbrella sampling. We employ thermodynamic integration to estimate the free energy differences between biased ensembles, thereby circumventing the umbrella sampling requirement of overlap between adjacent biased distributions. Further, a judicious choice of the biasing potential allows such free energy differences * To whom correspondence should be addressed 1 arXiv:1511.01518v1 [cond-mat.stat-mech] 4 Nov 2015 to be estimated using short simulations, so that the free energetics of water density fluctuations are obtained using only a few, short simulations. Leveraging the efficiency of the method, we characterize water density fluctuations in the entire hydration shell of the protein, ubiquitin; a large volume containing an average of more than six hundred waters.

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Coarse-grained Monte Carlo simulations of non-equilibrium systems

Cited by 7 publications

References 32 publications

Studying protein assembly with reversible Brownian dynamics of patchy particles

Studying protein assembly with reversible Brownian dynamics of patchy particles

Correspondence between neuroevolution and gradient descent

Sparse Sampling of Water Density Fluctuations in Interfacial Environments

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