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Kurzynski, Michal; Chelminiak, Przemyslaw

doi:10.1023/a:1021018728312

Cited by 25 publications

(33 citation statements)

References 67 publications

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“…The transitions between them proceed at the rate constants k + and k − , depending on the molar concentrations of substrates taking part in this process. In a non-equilibrium steady state, the average reaction flux [2,3] …”

Section: Introductionmentioning

confidence: 99%

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Steady-state distributions of probability fluxes on complex networks

Chelminiak

Kurzynski

2017

Physica A: Statistical Mechanics and its Applications

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The methodology based on the random walk processes is adapted and applied to a comprehensive analysis of the statistical properties of the probability fluxes. To this aim we define a simple model of the Markovian stochastic dynamics on a complex network extended by the additional transition, called hereafter the gate. The random skips through the gate, driven by the external constant force, violate the detailed balance in the network. We argue, using a theoretical approach and numerical simulations, that the stationary distributions of the probability fluxes emergent under such conditions converge, regardless of the network topology, to the normal distribution. This result, combined with the stationary fluctuation theorem, permits to show that its standard deviation depends directly on the square root of the average flux. In turn, the central result of our paper relates this quantity to the external constant force and the two parameters that entirely characterize the normal distribution of the probability fluxes both close to as well as far from the equilibrium state. Also, the other effects that modify these parameters, such as the addition of shortcuts to the tree-like network, the extension and configuration of the gate and a change in the network size studied by means of the computer simulations are widely discussed in terms of the rigorous theoretical predictions.

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Section: Introductionmentioning

confidence: 99%

“…As we have mentioned in the introduction, Eq. 20 was at first derived in the context of chemical processes for which a total concentration of the reacting substrates is assumed to be conserved [2,3]. In the present model, the conserved quantity is the probability flux.…”

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confidence: 99%

Steady-state distributions of probability fluxes on complex networks

Chelminiak

Kurzynski

2017

Physica A: Statistical Mechanics and its Applications

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“…In the open reactor under stationary conditions (the concentrations of reactants and products of the reaction kept constant), the general situation is more complex but for reactions gated by single conformational transition substates ( Fig. 1(c)) a simple analytical theory was proposed [6,38]. A consequence of the slow conformational transition dynamics is that the steady-state kinetics, like the transient stage kinetics, cannot be described in terms of [38] where transitions between intermediates within E and M were expanded to quasi-continuous networks of conformational transitions described by parts of Eqs.…”

Section: Introductionmentioning

confidence: 99%

“…This possibility was suggested almost forty years ago by Blumenfeld [39]. Later on, we have shown that more adequate physical quantities that should be used are the mean first-passage times between distinguished transition substates [6,38]. An application of the formalism to two coupled enzymatic reactions was considered in the context of the free energy transduction in biological molecular machines [38].…”

Section: Introductionmentioning

confidence: 99%

“…Later on, we have shown that more adequate physical quantities that should be used are the mean first-passage times between distinguished transition substates [6,38]. An application of the formalism to two coupled enzymatic reactions was considered in the context of the free energy transduction in biological molecular machines [38]. We understand the word 'machine' quite generally as denoting any physical system that enables two other physical systems to perform work one on another.…”

Section: Introductionmentioning

confidence: 99%

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Output-input ratio in thermally fluctuating biomolecular machines

2014

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Biological molecular machines are proteins that operate under isothermal conditions and hence are referred to as free energy transducers. They can be formally considered as enzymes that simultaneously catalyze two chemical reactions: the free energy-donating (input) reaction and the free energy-accepting (output) one. Most if not all biologically active proteins display a slow stochastic dynamics of transitions between a variety of conformational substates composing their native state. This makes the description of the enzymatic reaction kinetics in terms of conventional rate constants insufficient. In the steady state, upon taking advantage of the assumption that each reaction proceeds through a single pair (the gate) of transition conformational substates of the enzyme-substrates complex, the degree of coupling between the output and the input reaction fluxes has been expressed in terms of the mean first-passage times on a conformational transition network between the distinguished substates. The theory is confronted with the results of random-walk simulations on the five-dimensional hypercube. The formal proof is given that, for single input and output gates, the output-input degree of coupling cannot exceed unity. As some experiments suggest such exceeding, looking for the conditions for increasing the degree of coupling value over unity challenges the theory. Performed simulations of random walks on several model networks involving more extended gates indicate that the case of the degree of coupling value higher than 1 is realized in a natural way on critical branching trees extended by long-range shortcuts. Such networks are scale-free and display the property of the small world. For short-range shortcuts, the networks are scale-free and fractal, representing a reasonable model for biomolecular machines displaying tight coupling, i.e., the degree of coupling equal exactly to unity. A hypothesis is stated that the protein conformational transition networks, as just as higher-level biological networks, the protein interaction network, and the metabolic network, have evolved in the process of self-organized criticality.

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Stochastic Reachability Concepts

Bujorianu

2012

Communications and Control Engineering

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Cited by 25 publications

References 67 publications

Steady-state distributions of probability fluxes on complex networks

Steady-state distributions of probability fluxes on complex networks

Output-input ratio in thermally fluctuating biomolecular machines

Stochastic Reachability Concepts

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