Non-equilibrium Markov state modeling of periodically driven biomolecules

Knoch, Fabian; Speck, Thomas

doi:10.1063/1.5055818

Cited by 15 publications

(9 citation statements)

References 49 publications

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“…An interesting special case of non-equilibrium Markov State Modelling considers systems under periodic external driving [234,235,236,237]. As such systems eventually enter a non-equilibrium steady state (NESS), the interpretation and analysis of the coarse-grained dynamics is less involved than in the general case.…”

Section: Markov State Modelsmentioning

confidence: 99%

“…As such systems eventually enter a non-equilibrium steady state (NESS), the interpretation and analysis of the coarse-grained dynamics is less involved than in the general case. We briefly review a method to tackle this problem, which Knoch and Speck introduced in a series of articles [235,236,237]. Instead of the continuous state space X we consider a discrete and finite space (note that this is the space of the "microscopic" degrees of freedom which we intend to coarse-grain, not the state space of the coarse-grained model).…”

Section: Markov State Modelsmentioning

confidence: 99%

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Coarse-Grained Modelling Out of Equilibrium

Schilling

2021

Preprint

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Active matter, responsive ("smart") materials and materials under time-dependent load are systems out of thermal equilibrium. To construct coarse-grained models for such systems, one needs to integrate out a distribution of microstates that evolves in time. This is a challenging task. As a preparation to the topic, we recall equilibrium coarse-graining methods, both theoretical and numerical, such as projection operator formalisms, united atom simulations, numerical reconstruction of memory and Markov State Modelling. Then we review recent developments in theoretical approaches to the non-equilibrium coarse-graining problem, in particular, time-dependent projection operator formalisms, dynamic density functional theory and power functional theory, as well as numerical schemes to contruct explicitly time-dependent memory kernels.

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Section: Markov State Modelsmentioning

confidence: 99%

Section: Markov State Modelsmentioning

confidence: 99%

Coarse-Grained Modelling Out of Equilibrium

Schilling

2021

Preprint

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“…[111]). Periodically driven molecules (e.g., due to the coupling of a residual dipole moment with an external electric field) have also been addressed [112,113].…”

Section: B Coarse-graining and Metastable Basinsmentioning

confidence: 99%

Modeling of biomolecular machines in non-equilibrium steady states

Speck

2021

Preprint

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Numerical computations have become a pillar of all modern quantitative sciences. Any computation involves modeling-even if often this step is not made explicit-and any model has to neglect details while still being physically accurate. Equilibrium statistical mechanics guides both the development of models and numerical methods for dynamics obeying detailed balance. For systems driven away from thermal equilibrium such a universal theoretical framework is missing. For a restricted class of driven systems governed by Markov dynamics and local detailed balance, stochastic thermodynamics has evolved to fill this gap and to provide fundamental constraints and guiding principles. The next step is to advance stochastic thermodynamics from simple model systems to complex systems with ten thousands or even millions degrees of freedom. Biomolecules operating in the presence of chemical gradients and mechanical forces are a prime example for this challenge. In this Perspective, we give an introduction to isothermal stochastic thermodynamics geared towards the systematic multiscale modeling of the conformational dynamics of biomolecular and synthetic machines, and we outline some of the open challenges.

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“…Therefore, evaluating the consequences of the coarse graining on the physical properties of the system is a general issue of indisputable importance. For this reason, their effects on the thermodynamic properties, such as entropy production of the system, have been the focus of intense research [8][9][10][11][12] performing both spatial and time discretizations of continuous dynamics and constructing the transition rates of suitable Markov chains [13][14][15]. For instance, Busiello et al evaluate the difference between the entropy production of a discrete multibody process and an approximate description based on a continuous dynamics [16,17], while the authors of Ref.…”

Section: Introductionmentioning

confidence: 99%

Excess and loss of entropy production for different levels of coarse graining

2021

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We investigate the effect of coarse graining on the thermodynamic properties of a system, focusing on entropy production. As a case of study, we consider a one-dimensional colloidal particle in contact with a thermal bath, moving in a sinusoidal potential and driven out of equilibrium by a small constant force. Different levels of coarse graining are evaluated: At first, we compare the results in the underdamped dynamics with those in the overdamped one (first coarse graining). For large values of the friction coefficient, the two dynamics have the same thermodynamics properties, while, for smaller friction values, the overdamped approximation produces an excess of entropy production with respect to that of the underdamped dynamics. Moreover, for further smaller values of the drag coefficient, the excess of entropy production turns into a loss. These regimes are explained by evaluating the jump statistics, observing that the inertia is able to induce multiple jumps and affect the average jump rate. The periodic shape of the potential allows us to approximate the continuous dynamics via a Markov chain after the introduction of a suitable time and space discretization (second level of coarse graining). This discretization procedure is implemented starting both from the underdamped and the overdamped evolution and is analyzed for different values of the friction coefficient.

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Non-equilibrium Markov state modeling of periodically driven biomolecules

Cited by 15 publications

References 49 publications

Coarse-Grained Modelling Out of Equilibrium

Coarse-Grained Modelling Out of Equilibrium

Modeling of biomolecular machines in non-equilibrium steady states

Excess and loss of entropy production for different levels of coarse graining

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