Two Dimensional Window Exchange Umbrella Sampling for Transmembrane Helix Assembly

The method of window exchange umbrella sampling molecular dynamics (WEUSMD) with a preoptimized parameter set was recently used to obtain the most probable conformations and the energetics of transmembrane (TM) helix assembly of a generic TM sequence. When applied to glycophorin A TM domain (GpA-TM) using the restraint potentials along the helix?helix distance, however, tight interfacial packing of GpA-TM resulted in insufficient conformational sampling at short helix?helix separation. This sampling issue is addressed by extending the WEUSMD into two dimensions with the restraint potentials along the helix?helix distance and crossing angle. The two-dimensional WEUSMD results demonstrate that the incomplete sampling in the one-dimensional WEUSMD arises from high barriers along the crossing angle between the GpA-TM helices. Together with the faster convergence in both the assembled conformations and the potential of mean force, the 2D-WEUSMD can be a general and efficient approach in computational studies of TM helix assembly.