Stochastic Dynamics of Proteins and the Action of Biological Molecular Machines
Biological molecular machines are proteins that operate under isothermal conditions 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. 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
... omposing their native state. A hypothesis is stated that, like higher level biological networks: the protein interaction network and the metabolic network, the protein conformational transition networks have evolved in a process of self-organized criticality. All three classes of networks are scale-free and, probably, display a transition from the fractal organization in a small length scale to the small-world organization in the large length scale. Good mathematical models of such networks are stochastic critical branching trees extended by long-range shortcuts. The 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 values cannot exceed unity. Study simulations of random walks on several model networks involving more extended gates indicate that the case of the degree of coupling with the value higher than one is realized on the mentioned above critical branching trees extended by long-range shortcuts.