Motion and conformation of side chains in peptides. A comparison of 2D umbrella-sampling molecular dynamics and NMR results

An extension of the technique of umbrella sampling to two dimensions is presented and applied to the study of the kinetic and thermodynamic properties of side chains in peptides. Four two-dimensional potential-of-mean-force surfaces for the two degrees of freedom (chi 1) and (chi 2) of the four phenylalanine residues in antamanide at 300 K are calculated using the stochastic dynamics simulation method with the molecular force field GROMOS. From these surfaces, time constants for the transitions between the favored conformations along (chi 1) and (chi 2) are calculated using transition state theory. The results are compared with experimental values determined by NMR. In addition, motionally averaged (3)J-coupling constants are calculated from the-rotamer probability distributions derived from the (chi 1), (chi 2) potential-of-mean-force surfaces using the generalized Karplus equations. The average values are compared to the experimental NMR results. It is shown that the two-dimensional umbrella-sampling approach is capable of providing detailed information on the motional behavior of side chains and can be used to interpret and complement the experimental findings. Furthermore, by comparing the simulation results to results obtained with energy minimization, the importance of sampling a representative set of conformations is demonstrated. Although the GROMOS force field and the stochastic treatment of solvent effects produce transition rates of the correct order of magnitude, the experimental differences between the rate constants of the four residues are not reproduced. The root-mean-square difference between simulated and experimental averaged (3)J-coupling constants ranges between 1.92 Hz (Phe(10)) and 3.22 Hz (Phe(5)).