Helix propensities calcualtions for amino acids in alanine based peptides using Jarzynski's equality

Jarzynski's equality (Jarzynski, Phys Rev E 1997; 56:5018 and Jarzynski, Phys Rev Lett 1997; 78:2690) relates equilibrium free energy differences between two states A and B to the work done when the system is driven repeatedly and irreversibly from an equilibrium state A to equilibrium state B. We present calculations of helix propensities using a novel procedure based on this equality. In particular, a work probability distribution is built based on combinations of multi-step trajectories that give representative work distributions without requiring computing an unreasonable large number of trajectories between states. A small number of trajectories (15) are used to construct a distribution that contains millions of work values. This distribution is used to calculate ΔG_AB using Jarsynski's equation. To apply and test this method, we used as a model system a dodeca-alanine helix, analyzing its extension using mechanical force. This helix was used as the basis of a host guest system in which two of the 12 residues are substituted by some other amino acid (as the guests). The differences between the unfolding free energies of the substituted peptides and the all-alanine peptide provided values for ΔΔG that can be interpreted as the helix propensities of each amino acid. Results show good correlation with the experimental measurements of Baldwin and coworkers (Chakrabartty et al., Protein Sci 1994; 3:843-852).