Dynamics of the Davydov-Scott monomer in a thermal bath: comparison of the full quantum and semiclassical approaches.

The quantum state diffusion equation is applied to the problem of energy transfer in proteins. Lindblad operators, capable of coupling the full quantum Davydov-Scott monomer to a thermal bath, are derived. Numerical simulations with the QSD equation show that the Lindblad operators derived do recreate the exact equilibrium ensemble for the Davydov-Scott monomer. Comparison of the results obtained with the full quantum and with the semiclassical systems shows that, at biological temperatures, the latter provides a good approximation of the former.

Dynamics of a nonconserving Davydov monomer.

The Davydov-Scott model describes the transfer of energy along hydrogen-bonded chains, like those that stabilize the structure of alpha helices. It is based on the hypothesis that amide I excitations are created (by the hydrolysis of ATP, for instance) and kept in the system. Recent experimental results confirm that the energy associated with amide I excitations does indeed last for tens of picoseconds in proteins and model systems. However, the Davydov-Scott model cannot describe the conversion of that energy into work, because it conserves the number of excitations. With the aim of describing conformational changes, we consider, in this paper, a nonconserving generalization of the model, which is found to describe essentially a contraction of the hydrogen bond adjacent to the site where an excitation is present. Unlike the one-site Davydov-Scott model, that contraction is time dependent because the number of excitations is not conserved. However, considering the time average of the dynamical variables, the results reported here tend to the known results of the Davydov-Scott model.

What is the shape of the distribution of protein conformations at equilibrium?

According to the thermodynamic hypothesis, the native state of proteins is that in which the free energy of the system is at its lowest, so that at normal temperature and pressure, proteins evolve to that state. We selected four proteins representative of each of the four classes, and for each protein make four simulations, one starting from the native structure and the other three starting from the structure obtained by threading the sequence of one protein onto the native backbone fold of the other three proteins. Because of their large conformational distances with respect to the native structure, the three alternative initial structures cannot be considered as local minima within the native ensemble of the corresponding protein. As expected, the initial native states are preserved in the .5 µs simulations performed here and validate the simulations. On the other hand, when the initial state is not native, an analysis of the trajectories does not reveal any evolution towards the native state, during that time. These results indicate that the distribution of protein conformations is multipeak shaped, so that apart from the peak corresponding to the native state, there are other peaks associated with average structures that are very different from the native and that can last as long as the native state.