Calculation of Free-​Energy Differences by Confinement Simulations. Application to Peptide Conformers

Conformational free-​energy differences are key quantities for understanding important phenomena in mol. biol. that involve large structural changes of macromols. In this paper, an improved version of the confinement approach, which is based on earlier developments, is used to det. the free energy of individual mol. states by progressively restraining the corresponding mol. structures to pure harmonic basins, whose abs. free energy can be computed by normal-​mode anal. The method is used to calc. the free-​energy difference between two conformational states of the alanine dipeptide in vacuo, and of the β-​hairpin from protein G with an implicit solvation model. In all cases, the confinement results are in excellent agreement with the ones obtained from converged equil. mol. dynamics simulations, which have a much larger computational cost. The systematic and statistical errors of the results are evaluated and the origin of the errors is identified. The sensitivity of the calcd. free-​energy differences to structure-​based definitions of the mol. states is discussed. A variant of the method, which closes the thermodn. cycle by a quasi-​harmonic rather than harmonic anal., is introduced. The latter is proposed for possible use with explicit solvent simulations.