Learning transition path and membrane topological signatures in the folding pathway of bacteriorhodopsin (BR)...

Membrane protein folding in the viscous microenvironment of a lipid bilayer is an inherently slow process that challenges experiments and computational efforts alike. The folding kinetics is moreover associated with topological modulations of the biological milieu. Studying such structural changes in membrane-embedded proteins and understanding the associated topological signatures in membrane leaflets, therefore, remain relatively unexplored. Herein, we first aim to estimate the free energy barrier and the minimum free energy path (MFEP) connecting the membrane-embedded fully and partially inserted states of the bacteriorhodopsin fragment. To achieve this, we have considered independent sets of simulations from membrane-mimicking and membrane-embedded environments, respectively. An autoencoder model is used to elicit state-distinguishable collective variables for the system utilizing membrane-mimicking simulations. Our in-house Expectation Maximized Molecular Dynamics algorithm is initially used to deduce the barrier height between the two membrane-embedded states. Next, we develop the Geometry Optimized Local Direction search as a post-processing algorithm to identify the MFEP and the corresponding peptide conformations from the autoencoder-projected trajectories. Finally, we apply a graph attention neural network (GAT) model to learn the membrane surface topology as a function of the associated peptide structure, supervised by the membrane-embedded simulations. The resultant GAT model is then utilized to predict the membrane leaflet topology for the peptide structures along MFEP, obtained from membrane-mimicking simulations. The combined framework is expected to be useful in capturing key phenomena accompanying folding transitions in membranes. We discuss opportunities and avenues for further development.