Free Energy Profile and Mechanism of Self-Assembly of Peptide Amphiphiles Based on a Collective Assembly Coordinate

By combining targeted molecular dynamics (TMD) simulations, umbrella sampling, and the weighted histogram analysis method (WHAM), we have calculated the potential of mean force (PMF) for the transition between the bound and free states of 90 peptide amphiphiles (PM) in aqueous solution, with the bound state corresponding to a cylindrical micelle fiber. We specifically consider a collective reaction coordinate, the radius of gyration of the PAs, to describe assembly in this work. It is found that the free energy, enthalpy, and entropy differences between the free and bound states are -126 kcal/mol, -185 kcal/mol, and -190 cal/(mol K), respectively, for the self-assembly process. This indicates that the driving force to form the micelle structure is enthalpic. The enthalpic driving forces originate from several factors, including the conformational energy of PAs and the electrostatic and van der Waals interaction energy between solvent molecules and between solvent and PAs. Among these interactions, the solvent electrostatic interaction is the dominating one, contributing 54% of the total driving force. The PMF profile can be recognized as involving two stages of assembly: (1) PAs initially approach each other in mostly random configurations and loosely aggregate, resulting in significant desolvation and initiation of head-tail conformational reorganization; (2) PM undergo a conformational disorder-to-order transition, including forming secondary structures that include more beta-sheets and fewer random coils, along with tail-head core-shell alignment and condensation that leads to total exclusion of water from the core. The PMF decreases slowly in the first stage, but rapidly in the second. This study demonstrates a hierarchy of assembly steps in which PA structural changes, solvation, and redistribution of solvent molecules play significant roles in the PA self-assembly process.