Perspective: Maximum caliber is a general variational principle for dynamical systems

Dixit, Purushottam D.; Wagoner, Jason A.; Weistuch, Corey; Pressé, Steve; Ghosh, Kingshuk; Dill, Ken A.

doi:10.1063/1.5012990

Cited by 95 publications

(91 citation statements)

References 85 publications

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“…First of all, the constraints that can be imposed have to be static topological properties of the network. Only recently, cases of dynamical constraints have been considered using either the principle of Maximum Caliber-which is to dynamical pathways what the principle of maximum entropy is to equilibrium states [29,156], or definitions of the entropy functional alternative to Shannon's (see Box 3). Second, the possibility to consider in these models semi-local network properties heavily relies on numerical sampling, which becomes unfeasible or much biased for non-trivial patterns involving more than two or three nodes.…”

Section: Perspectives and Conclusionmentioning

confidence: 99%

The statistical physics of real-world networks

Cimini¹,

Squartini²,

Saracco³

et al. 2019

Nat Rev Phys

326

308

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In the last 15 years, statistical physics has been a very successful framework to model complex networks. On the theoretical side, this approach has brought novel insights into a variety of physical phenomena, such as self-organisation, scale invariance, emergence of mixed distributions and ensemble non-equivalence, that display unconventional features on heterogeneous networks. At the same time, thanks to their deep connection with information theory, statistical physics and the principle of maximum entropy have led to the definition of null models for networks reproducing some features of real-world systems, but otherwise as random as possible. We review here the statistical physics approach and the various null models for complex networks, focusing in particular on the analytic frameworks reproducing the local network features. We then show how these models have been used to detect statistically significant and predictive structural patterns in real-world networks, as well as to reconstruct the network structure in case of incomplete information. We further survey the statistical physics models that reproduce more complex, semi-local network features using Markov chain Monte Carlo sampling, as well as the models of generalised network structures such as multiplex networks, interacting networks and simplicial complexes. arXiv:1810.05095v2 [physics.soc-ph]

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Section: Perspectives and Conclusionmentioning

confidence: 99%

The statistical physics of real-world networks

Cimini¹,

Squartini²,

Saracco³

et al. 2019

Nat Rev Phys

326

308

View full text Add to dashboard Cite

show abstract

“…As an alternative to using Eq. (2) in the last stage of our approach, a method such as maximum caliber [74][75][76] , which does not take the derivatives of landscape topology into account, could be supplied with the sizes of the energy barriers and used to infer MFPTs. However, we found that owing to the dependence of the MFPTs on the prefactors in Eq.…”

Section: Preserving Landscape Topology Under Dimensionality Reductionmentioning

confidence: 99%

Learning dynamical information from static protein and sequencing data

Pearce

Woodhouse

Forrow

et al. 2018

Preprint

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Many complex processes, from protein folding and virus evolution to brain activity and neuronal network dynamics, can be described as stochastic exploration of a high-dimensional energy landscape. While efficient algorithms for cluster detection and data completion in high-dimensional spaces have been developed and applied over the last two decades, considerably less is known about the reliable inference of state transition dynamics in such settings. Here, we introduce a flexible and robust numerical framework to infer Markovian transition networks directly from time-independent data sampled from stationary equilibrium distributions. Our approach combines Gaussian mixture approximations and self-consistent dimensionality reduction with minimal-energy path estimation and multi-dimensional transition-state theory. We demonstrate the practical potential of the inference scheme by reconstructing the network dynamics for several protein folding transitions, gene regulatory network motifs and HIV evolution pathways. The predicted network topologies and relative transition time scales agree well with direct estimates from time-dependent molecular dynamics data, stochastic simulations and phylogenetic trees, respectively. The underlying numerical protocol thus allows the recovery of relevant dynamical information from instantaneous ensemble measurements, effectively alleviating the need for time-dependent data in many situations. Owing to its generic structure, the framework introduced here will be applicable to high-throughput RNA and protein sequencing datasets and future cryo-electron-microscopy data, and can guide the design of new experimental approaches towards studying complex multiphase phenomena.

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“…In fact, much of recent effort is devoted to develop methodologies to achieve this integration. [10][11][12][13][14][15][16][17][18][19][20] In this paper, we develop a particle filter method to integrate HS-AFM data with MD simulations.…”

Section: Introductionmentioning

confidence: 99%

The Particle Filter Method to Integrate High-Speed Atomic Force Microscopy Measurement with Biomolecular Simulations

Fuchigami

Niina

Takada

2020

Preprint

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The high-speed atomic force microscopy (HS-AFM) can observe structural dynamics of biomolecules at single-molecule level in real time near physiological condition, but its spatiotemporal resolution is limited. Complementarily, molecular dynamics (MD) simulations have higher spatiotemporal resolutions albeit with some artifact. Here, in order to integrate the HS-AFM data and coarse-grained (CG)-MD simulations, we develop a particle filter method, one of the sequential Bayesian data assimilation approaches. We tested the method in a twin experiment.We first made a reference HS-AFM movie from a CG-MD trajectory of a test molecule, a nucleosome, which serves as an "experimental measurement". Then, we performed the particle filter simulation with 512 particles that captured large-scale nucleosome structural dynamics compatible with the AFM movie. Comparing the particle filter simulations with 8 -8192 particles, we found that the use of more particles consistently results in larger likelihood for the whole AFM movie. By comparing the likelihoods from different ionic concentrations and from different timescales, we found that the "true" concentration and timescale can be inferred as the largest likelihood of the whole AFM movie, but not that of each AFM image. The particle filter method provides a general approach to integrate the HS-AFM data with MD simulations.

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Perspective: Maximum caliber is a general variational principle for dynamical systems

Cited by 95 publications

References 85 publications

The statistical physics of real-world networks

The statistical physics of real-world networks

Learning dynamical information from static protein and sequencing data

The Particle Filter Method to Integrate High-Speed Atomic Force Microscopy Measurement with Biomolecular Simulations

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