Cycle representatives for the coarse-graining of systems driven into a non-equilibrium steady state

Knoch, Fabian; Speck, Thomas

doi:10.1088/1367-2630/17/11/115004

Cited by 30 publications

(37 citation statements)

References 41 publications

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“…With stochastic processes it is possible to investigate energy-conversion in molecular motors [10][11][12][13], error correction via kinetic proofreading [14][15][16], as well as information processing in small sensing networks [17][18][19]. In this field, different suggestions arose for coarse grainings motivated by thermodynamic consistency [20][21][22]. In these cases, the dissipation in a nonequililibrium process is typically underestimated-although also overestimations may occur [23].…”

Section: Introductionmentioning

confidence: 99%

Thermodynamically consistent coarse graining of biocatalysts beyond Michaelis–Menten

2018

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Starting from the detailed catalytic mechanism of a biocatalyst we provide a coarse-graining procedure which, by construction, is thermodynamically consistent. This procedure provides stoichiometries, reaction fluxes (rate laws), and reaction forces (Gibbs energies of reaction) for the coarse-grained level. It can treat active transporters and molecular machines, and thus extends the applicability of ideas that originated in enzyme kinetics. Our results lay the foundations for systematic studies of the thermodynamics of large-scale biochemical reaction networks. Moreover, we identify the conditions under which a relation between one-way fluxes and forces holds at the coarse-grained level as it holds at the detailed level. In doing so, we clarify the speculations and broad claims made in the literature about such a general flux-force relation. As a further consequence we show that, in contrast to common belief, the second law of thermodynamics does not require the currents and the forces of biochemical reaction networks to be always aligned.

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Section: Introductionmentioning

confidence: 99%

Thermodynamically consistent coarse graining of biocatalysts beyond Michaelis–Menten

2018

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“…For systems showing dynamical reversibility the algorithm leads to a Schnakenberg decomposition with a clever choice of the fundamental set of cycles, such that all the terms in the sum are positive. Therefore a positive entropy production can be assigned to each cycle, which is required in many applications [50,51]. The algorithm is based on choosing an orientation for the graph such that all the fluxes (C.2) for the directed edges are positive.…”

Section: Appendix E Other Decompositions Of the Entropy Productionmentioning

confidence: 99%

Relation between topology and heat currents in multilevel absorption machines

2017

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The steady state heat currents of continuous absorption machines can be decomposed into thermodynamically consistent contributions, each of them associated with a circuit in the graph representing the master equation of the thermal device. We employ this tool to study the functioning of absorption refrigerators and heat transformers with an increasing number of active levels. Interestingly, such an analysis is independent of the particular physical implementation (classical or quantum) of the device. We provide new insights into the understanding of scaling up thermal devices concerning both the performance and the magnitude of the heat currents. Indeed, it is shown that the performance of a multilevel machine is smaller or equal than the corresponding to the largest circuit contribution. Besides, the magnitude of the heat currents is well-described by a purely topological parameter which in general increases with the connectivity of the graph. Therefore, we conclude that for a fixed number of levels, the best of all different constructions of absorption machines is the one whose associated graph is as connected as possible, with the condition that the performance of all the contributing circuits is equal.The analysis of the thermodynamic quantities can be realized at different levels of description [24]. From a macroscopic point of view, where the relevant quantities are the bath temperatures and the physical (total) heat currents, to a microscopic description that considers in addition the device structure. This latter perspective is more and more relevant as the advance of the experimental techniques allows for the design and the manipulation of the device. A prominent tool for this microscopic analysis is graph theory, where the stochastic master equation for the populations is represented by a graph. Schnakenberg theory [25] is a popular approach that gives a decomposition of the total entropy production based on a set of fundamental circuits in the graph. Basically, Schnakenberg applies Kirchhoff's current laws to reduce the number of terms appearing in the entropy production, which may be highly beneficial for optimization procedures. It has been used for example in linear irreversible thermodynamics [26] and in the study of steady-state fluctuation theorems [27,28]. This method does not intend to associate an entropy production with each circuit. In particular, the attempt to interpret individually each term in the decomposition may lead to apparent negative entropy productions, although this problem can be avoided by a convenient choice of the fundamental circuits [29][30][31]. However, it has been shown that the diagnosis of the machine performance greatly benefits from considering the thermodynamic analysis of not only the fundamental but all the possible circuits in the graph [32][33][34]. A convenient approach is then Hill theory [35]. Schnakenberg and Hill theory assign the same affinity to each circuit, but the latter considers all the possible circuits and leads to thermodynamically consistent ent...

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“…While VAC only describes the scenario of equilibrium dynamics, i.e. where our dynamics have a unique equilibrium distribution and obey detailed balance, much recent research has focused on non-equilibrium Markov models [47][48][49][50][51][52] . While nonequilibrium MSM studies are still in their infancy, several theoretical principles are known in oder to make progress here.…”

Section: Coarse-grainingmentioning

confidence: 99%

Markov Models of Molecular Kinetics

Noé

2013

Encyclopedia of Biophysics

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a. Introduction The Journal of Chemical Physics article collection on Markov Models of Molecular Kinetics (MMMK)features recent advances developing and using Markov State Models (MSMs) 1-6 in atomistic molecular simulations and related applications -see 7-10 for recent MSM reviews. MSMs have been an important driving force in molecular dynamics (MD), as they facilitate divide-and-conquer integration of short, distributed MD simulations into long-timescale predictions, they are conceptually simple and provide readily-interpretable models of kinetics and thermodynamics.Most MSM estimation approaches proceed by a sequence, or pipeline, of data processing steps that is also represented by MSM software packages [11][12][13] , and typically includes:1. Featurization: The MD coordinates are transformed into features, such as residue distances, contact maps or torsion angles 11,12,14,15 , that form the input of the MSM analysis. Dimension reduction:The dimension is reduced to much fewer (typically 2-100) slow collective variables (CVs), [16][17][18][19][20][21][22][23][24][25][26] . The resulting coordinates may be scaled, in order to embed them in a metric space whose distances correspond to some form of dynamical distance 27,28 . Discretization:The space may be discretized by clustering the projected data 4,7,11,[29][30][31][32][33] , typically resulting in 100-1000 discrete "microstates". MSM estimation:A transition matrix or rate matrix describing the transition probabilities or rate between the discrete states at some lag time τ is estimated 5,6,34,35 .5. Coarse-graining: In order to get an easier interpretable kinetic model, the MSM from step 5 is often coarse-grained to a few states [36][37][38][39][40][41][42][43][44] .Some method skip or combine some of these steps, novel machine learning methods attempt to integrate most or all of them in an end-to-end learning framework.

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Cycle representatives for the coarse-graining of systems driven into a non-equilibrium steady state

Cited by 30 publications

References 41 publications

Thermodynamically consistent coarse graining of biocatalysts beyond Michaelis–Menten

Thermodynamically consistent coarse graining of biocatalysts beyond Michaelis–Menten

Relation between topology and heat currents in multilevel absorption machines

Markov Models of Molecular Kinetics

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