Abstract
Molecular machines carry out their function by equilibrium mechanical motions in environments that are far from thermodynamic equilibrium. The mechanically equilibrated character of the trajectories of the macromolecule has allowed development of a powerful theoretical description, reminiscent of Onsager’s trajectory thermodynamics, that is based on the principle of microscopic reversibility. Unlike the situation at thermodynamic equilibrium, kinetic parameters play a dominant role in determining steady-state concentrations away from thermodynamic equilibrium, and kinetic asymmetry provides a mechanism by which chemical free-energy released by catalysis can drive directed motion, molecular adaptation, and self-assembly. Several examples drawn from the recent literature, including a catenane-based chemically driven molecular rotor and a synthetic molecular assembler or pump, are discussed.
Highlights
Molecular machines carry out their function by equilibrium mechanical motions in environments that are far from thermodynamic equilibrium
A major point of the present perspective article can be summarized succinctly: at thermodynamic equilibrium the distribution among states of a system is determined solely by the free energies of the states and there are no net fluxes between the states; away from thermodynamic equilibrium the deviation of the distribution from the values that would pertain at equilibrium, as well as the fluxes between the states, is determined by the kinetic asymmetry of the system, i.e., by the relative heights of energy barriers between the states, as well as by the strength of the non-equilibrium driving[15,16]
Kd;P > Kp;P, in such a way that Eq (6) is obeyed. We recognize that another very commonly asserted model known as “local detailed balance”[31] is wrong as discussed below. These seeming minutiae regarding quantitative analysis of models for molecular machines, or at least the conclusions arising from them, are very important for synthetic chemists because they reveal that the essential design feature for catalytically driven molecular motors is kinetic asymmetry owing to allosteric interaction, and not the incorporation of a power stroke[30,32], an insight that was key to the design of the rotor of Wilson et al.[29]
Summary
C, d The concentrations of substrate (S) and product (P) are taken as constant (i.e., chemo-stated) in all calculations, and can be written in terms of the chemical potential using activity coefficients 1⁄2S 1⁄4 aSeμþΔμ and 1⁄2P 1⁄4 aPeμÀΔμ. In ideal solutions both activity coefficients are ~ 1 in the units of concentration in which [S] and [P] are specified. Trajectories starting and ending at the same state and involving all four states—S binds, P is released; P binds, S is released; S binds, S is released; and P binds, and P is released Each of these has a microscopic reverse counter-clockwise cycle. In order to see how this plays out quantitatively let us first focus on kinetic asymmetry of a single Michaelis–Menten (MM) enzyme
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