Stochastic Dynamics of Proteins and the Action of Biological Molecular Machines
It is now well established that most if not all enzymatic proteins display a slow stochastic dynamics of transitions between a variety of conformational substates composing their native state. A hypothesis is stated that the protein conformational transition networks, as just as higher-level biologi...
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MDPI AG
2014-04-01
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| Series: | Entropy |
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| Online Access: | http://www.mdpi.com/1099-4300/16/4/1969 |
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| author | Michal Kurzynski Przemyslaw Chelminiak |
| author_facet | Michal Kurzynski Przemyslaw Chelminiak |
| author_sort | Michal Kurzynski |
| collection | DOAJ |
| description | It is now well established that most if not all enzymatic proteins display a slow stochastic dynamics of transitions between a variety of conformational substates composing their native state. 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. Here, the criticality means that all the three classes of networks are scale-free and, moreover, display a transition from the fractal organization on a small length-scale to the small-world organization on the large length-scale. Good mathematical models of such networks are stochastic critical branching trees extended by long-range shortcuts. 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. The far-from-equilibrium degree of coupling between the output and the input reaction fluxes have been studied both theoretically and by means of the Monte Carlo simulations on model networks. For single input and output gates the degree of coupling cannot exceed unity. Study simulations of random walks on model networks involving more extended gates indicate that the case of the degree of coupling value higher than one is realized on the mentioned above critical branching trees extended by long-range shortcuts. |
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| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T22:36:49Z |
| publishDate | 2014-04-01 |
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| spelling | doaj.art-7f8113548dcf483abd05c60d6cc3c21f2022-12-22T03:59:12ZengMDPI AGEntropy1099-43002014-04-011641969198210.3390/e16041969e16041969Stochastic Dynamics of Proteins and the Action of Biological Molecular MachinesMichal Kurzynski0Przemyslaw Chelminiak1Faculty of Physics, Adam Mickiewicz University, Umultowska 85, Poznan 61-614, PolandFaculty of Physics, Adam Mickiewicz University, Umultowska 85, Poznan 61-614, PolandIt is now well established that most if not all enzymatic proteins display a slow stochastic dynamics of transitions between a variety of conformational substates composing their native state. 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. Here, the criticality means that all the three classes of networks are scale-free and, moreover, display a transition from the fractal organization on a small length-scale to the small-world organization on the large length-scale. Good mathematical models of such networks are stochastic critical branching trees extended by long-range shortcuts. 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. The far-from-equilibrium degree of coupling between the output and the input reaction fluxes have been studied both theoretically and by means of the Monte Carlo simulations on model networks. For single input and output gates the degree of coupling cannot exceed unity. Study simulations of random walks on model networks involving more extended gates indicate that the case of the degree of coupling value higher than one is realized on the mentioned above critical branching trees extended by long-range shortcuts.http://www.mdpi.com/1099-4300/16/4/1969protein dynamicsconformational transition networksfractal-small world transitionfluctuation theorembiological molecular machinesfree energy transduction |
| spellingShingle | Michal Kurzynski Przemyslaw Chelminiak Stochastic Dynamics of Proteins and the Action of Biological Molecular Machines Entropy protein dynamics conformational transition networks fractal-small world transition fluctuation theorem biological molecular machines free energy transduction |
| title | Stochastic Dynamics of Proteins and the Action of Biological Molecular Machines |
| title_full | Stochastic Dynamics of Proteins and the Action of Biological Molecular Machines |
| title_fullStr | Stochastic Dynamics of Proteins and the Action of Biological Molecular Machines |
| title_full_unstemmed | Stochastic Dynamics of Proteins and the Action of Biological Molecular Machines |
| title_short | Stochastic Dynamics of Proteins and the Action of Biological Molecular Machines |
| title_sort | stochastic dynamics of proteins and the action of biological molecular machines |
| topic | protein dynamics conformational transition networks fractal-small world transition fluctuation theorem biological molecular machines free energy transduction |
| url | http://www.mdpi.com/1099-4300/16/4/1969 |
| work_keys_str_mv | AT michalkurzynski stochasticdynamicsofproteinsandtheactionofbiologicalmolecularmachines AT przemyslawchelminiak stochasticdynamicsofproteinsandtheactionofbiologicalmolecularmachines |