Calculation of conformational transitions and barriers in solvated systems: Application to the alanine dipeptide in water

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Abstract
Optimal free energy paths (OFEPs) for conformational transitions are parallel to the mean force at every nonstationary point of the free energy landscape. In contrast to adiabatic paths, which are parallel to the force, OFEPs include the effect of entropy and are relevant even for systems with diffusive degrees of freedom. In this study the OFEPs are computed for the alanine dipeptide in solution. The potential of mean force is calculated and an effective potential is derived that is used to obtain the paths with a minimization based algorithm. The comparison of the calculated paths with the adiabatic paths in vacuo shows the influence of the environment on conformational transitions. The dynamics of the alanine dipeptide in water are more complex, since there are more minima and the barriers are lower. Two simpler methods for the calculation of reaction pathways in solution are evaluated by comparing their results with the OFEPs. In the first method the mean electrostatic field of the water is approximated by an analytical continuum model. The obtained paths show qualitative agreement with the OFEPs and the height of the barriers are similar. Targeted molecular dynamics (TMD), the second approach, constrains the distance to a target conformation to accelerate the transition. In the general case, however, it is difficult to assess the physical significance of the obtained paths. Changing the initial conditions by assigning different velocities leads to different solutions for the conformational transition. Furthermore, it is shown that by performing the simulations with different reaction coordinates or in opposite directions different pathways are preferred. This result can be explained by the structure of the free energy landscape around the initial conformations. In a first approximation the physical significance of different pathways is assumed to depend mainly on the free energy at the highest saddle point. In the literature the total energy of the system has often been used to estimate the position and the height of the energy barriers in the path. By comparing the total energy with the calculated free energy it is shown that the former largely overestimates the height of the barriers. Furthermore, the positions of the maxima of the total energy do not coincide with the free energy barriers. Simple approximations to the free energy lead to good quantitative agreement.

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