In 1894 Pierre Curie postulated that any system with broken symmetry is capable of directed motion from random thermal interactions. Smoluchowski and Feynman later showed that directional flux can only occur if the system is out of equilibrium, to preserve the second law of thermodynamics. The nineteen chiral amino acids that compose cellular enzymes can act as molecular motors when the proteins they belong to are held out of equilibrium with their substrates and products. In general, enzymes must cycle through at least two states during their catalytic cycle: bound to substrate and free in solution. In each protein state, every amino acid has a statistical distribution of dihedral angles and these distributions may not be the same when the protein is bound to substrate or free in solution. By being driven between those probability distributions, some dihedral angles generate directed motion along their angular degree of freedom and pass through 2π radians in one catalytic cycle. In the same way that a Brownian ratchet can use a temperature gradient to do mechanical work, these dihedral angles use a concentration gradient to do mechanical work.<br/>We performed molecular dynamics simulations of protein kinase A and adenylate kinase in both bound and unbound conformations. From these simulations, we determined the probability density for each torsion angle and used a nonequilibrium catalytic model to switch between the probability densities and calculate probability flux. At physiological levels of ATP and using experimental estimates for the catalytic rate and bimolecular rate constant, we show that individual amino acid torsions rotate across 2π up to tens of cycles per second. These rotations apply forces on the order 10<sup>-2</sup> pN, about two orders of magnitude lower than the force of the power stroke in skeletal muscle myosin.

Directional motion in chiral molecules out of equilibrium

253rd National Meeting (2017)

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