GPU-specific algorithms for improved solute sampling in grand canonical Monte Carlo simulations

The Grand Canonical Monte Carlo (GCMC) ensemble defined by the excess chemical potential, μ_ex , volume, and temperature, in the context of molecular simulations allows for variations in the number of particles in the system. In practice, GCMC simulations have been widely applied for the sampling of rare gasses and water, but limited in the context of larger molecules. To overcome this limitation, the oscillating μ_ex GCMC method was introduced and shown to be of utility for sampling small solutes, such as formamide, propane, and benzene, as well as for ionic species such as monocations, acetate, and methylammonium. However, the acceptance of GCMC insertions is low, and the method is computationally demanding. In the present study, we improved the sampling efficiency of the GCMC method using known cavity-bias and configurational-bias algorithms in the context of GPU architecture. Specifically, for GCMC simulations of aqueous solution systems, the configurational-bias algorithm was extended by applying system partitioning in conjunction with a random interval extraction algorithm, thereby improving the efficiency in a highly parallel computing environment. The method is parallelized on the GPU using CUDA and OpenCL, allowing for the code to run on both Nvidia and AMD GPUs, respectively. Notably, the method is particularly well suited for GPU computing as the large number of threads allows for simultaneous sampling of a large number of configurations during insertion attempts without additional computational overhead. In addition, the partitioning scheme allows for simultaneous insertion attempts for large systems, offering considerable efficiency. Calculations on the BK Channel, a transporter, including a lipid bilayer with over 760,000 atoms, show a speed up of ~53-fold through the use of system partitioning. The improved algorithm is then combined with an enhanced μ_ex oscillation protocol and shown to be of utility in the context of the site-identification by ligand competitive saturation (SILCS) co-solvent sampling approach as illustrated through application to the protein CDK2.