Seminarium Fizyki Materii Skondensowanej

All biological molecular machines can be formally considered as enzymesthat simultaneously catalyze two chemical reactions: the freeenergy-donating (input) reaction and the free energy-accepting (output)one. A challenge to the theory is to determine the value of the degree ofcoupling between both reaction fluxes and answer a question if this valuecan exceed unity. Most if not all enzymatic proteins display a slowstochastic dynamics of transitions between a variety of conformationalsubstates composing their native state. The value of the degree ofcoupling is related to mean first-passage times between various substates.A hypothesis is presented that the protein conformational transitionnetworks have evolved in a process of self-organized criticality anddisplay both scale-free and small-world or fractal organization. Studysimulations of random walks on several model networks indicate that thecase of the degree of coupling higher than one is realized in a naturalway for the scale-free critical branching trees extended by long-rangeshortcuts and having the small-world topology. For short-range shortcuts,the networks are fractal, and represent a reasonable model for themolecular machines with the tight coupling, i.e., with the degree ofcoupling value equal exactly to unity.