Revealing Thermodynamics and Kinetics of Lipid Self-Assembly by Markov State Model Analysis

Self-assembly is ubiquitous in the realm of biology and has become an elegant bottom-up approach to fabricate new materials. Although molecular dynamics (MD) simulations can complement experiments by providing the missing atomic details, it still remains a grand challenge to reveal the thermodynamic and kinetic information on a self-assembly system. In this work, we demonstrate for the first time that the Markov state model analysis can be used to delineate the variation of free energy during the self-assembly process of a typical amphiphilic lipid dipalmitoyl-phosphatidylcholine (DPPC). Free energy profiles against the solvent-accessible surface area and the root-mean-square deviation have been derived from extensive MD results of more than five hundred trajectories, which identified a metastable crossing-cylinder (CC) state and a transition state of the distorted bilayer with a free energy barrier of ∼0.02 kJ mol^-1 per DPPC lipid, clarifying a long-standing speculation for 20 years that there exists a free energy barrier during lipid self-assembly. Our simulations also unearth two mesophase structures at the early stage of self-assembly, discovering two assembling pathways to the CC state that have never been reported before. Further thermodynamic analysis derives the contributions from the enthalpy and the entropy terms to the free energy, demonstrating the critical role played by the enthalpy-entropy compensation. Our strategy opens the door to quantitatively understand the self-assembly processes in general and provides new opportunities for identifying common thermodynamic and kinetic patterns in different self-assembly systems and inspiring new ideas for experiments. It may also contribute to the refinement of force field parameters of various self-assembly systems.