Restraint potential and free energy decomposition formalism for helical tilting

A restraint potential for the helical tilt angle has been developed and its efficacy is illustrated by calculating the potentials of mean force (PMFs) as a function of WALP19’s tilt angle in vacuum. Based on our formalism to calculate the projection forces acting along the tilt, the thermodynamic integration yields a free energy profile that is in good agreement with the PMF obtained by the weighted-histogram analysis method. The present work provides a rigorous framework to decompose the total PMF into any microscopic contributions, which will be useful to explore the helix tilting in membranes due to a hydrophobic mismatch.