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Recently, we (Qin, S.; Zhou, H. X. J. Chem. Theory Comput.  2013 , 9 , 4633-4643) developed the FFT-based method for Modeling Atomistic Proteins-crowder interactions, henceforth FMAP. Given its potential wide use for calculating effects of crowding on protein folding and binding free energies, here we aimed to optimize the accuracy and speed of FMAP. FMAP is based on expressing protein-crowder interactions as correlation functions and evaluating the latter via fast Fourier transform (FFT). The numerical accuracy of FFT improves as the grid spacing for discretizing space is reduced, but at increasing computational cost. We sought to speed up FMAP calculations by using a relatively coarse grid spacing of 0.6 Å and then correcting for discretization errors. This strategy was tested for different types of interactions (hard-core repulsion, nonpolar attraction, and electrostatic interaction) and over a wide range of protein-crowder systems. We were able to correct for the numerical errors on hard-core repulsion and nonpolar attraction by an 8% inflation of atomic hard-core radii and on electrostatic interaction by a 5% inflation of the magnitudes of protein atomic charges. The corrected results have higher accuracy and enjoy a speedup of more than 100-fold over those obtained using a fine grid spacing of 0.15 Å. With this optimization of accuracy and speed, FMAP may become a practical tool for realistic modeling of protein folding and binding in cell-like environments.

Further Development of the FFT-based Method for Atomistic Modeling of Protein Folding and Binding under Crowding: Optimization of Accuracy and Speed