Spherical Crowders Research Articles

An Fft-Based Method for Modeling Crowding Effects when Both Test Proteins and Crowders are Represented at the Atomic Level

Macromolecular crowding affects protein folding, binding, and aggregation, and such effects have been studied by computer simulations. In direct simulations of test proteins mixed with crowders, the proteins have been represented at a coarse-grained level and the crowders modeled as spheres; protein-crowder interactions are assumed to be repulsive. Our recently developed postprocessing approach has allowed test proteins to be represented at the atomic level [1]. In this approach, the motions of a test protein and those of the crowders are followed in two separate simulations. The effects of crowding are then modeled by calculating Δμ, the crowding-induced change in the chemical potential of the test protein. For a repulsive type of protein-crowder interactions, Δμ is related to the fraction, f, of allowed placements of the test protein into a box of crowders. An algorithm has been developed to calculate f for spherical crowders. Here we present a new algorithm that enables the calculation of f for atomistic crowders. We express f as the correlation function of two spatial functions, one defined for the crowders and one for the test protein. The correlation function was calculated by fast Fourier transform. As the first application, we studied the effects of ellipsoidal crowders on the folding and binding free energies of atomistic proteins, and found that the nonspherical shapes of the crowders lead to greater stabilization effects than spherical crowders of the same volume. This finding has significant physiological implications since the macromolecules inside cells have many different shapes. Additional applications to proteins as crowders and other in vitro crowding agents are underway, marking a major step toward realistic modeling of intracellular environments.[1] S. Qin, and H.-X. Zhou, Biophys J 97, 12 (2009).

Atomistic Simulations of Macromolecular Crowding

Protein folding, binding, and aggregation are known to be affected by macromolecular crowding [1], which is an integral part of intracellular environments. Realistic modeling of intracellular crowding requires computer simulations. In direct simulations of test proteins mixed with crowders, it has only been practical to represent the proteins at a coarse-grained level. Our recently developed “postprocessing” approach has made it possible to represent test proteins at the atomic level [2, 3]. In this approach, the motions of a test protein and those of the crowders are followed in two separate simulations. The effects of crowding are then modeled by calculating Δμ, the crowding-induced change in the chemical potential of the test protein. For a repulsive type of protein-crowder interactions, Δμ is related to the fraction, f, of allowed placements of the test protein into a box of crowders. For spherical crowders, two methods have been devised to calculate f. The first is an efficient implementation of Widom's insertion method. The second is a theoretical prediction, which uses the volume, surface area, and linear size defined on a “crowder-exclusion” surface. These methods have been applied to study crowding effects on protein folding, binding, and internal dynamics. We have also tested the postprocessing approach against direct simulations of folding-unfolding and open-to-closed transitions in the presence of crowders. To calculate f for atomistic crowders, we have just devised an algorithm based on fast Fourier transform. These computational tools establish a solid foundation for realistic modeling of intracellular environments.[1] H.-X. Zhou, G. Rivas, and A. P. Minton, Annu Rev Biophys 37, 375 (2008).[2] S. Qin and H.-X. Zhou, Biophys J 97, 12 (2009).[3] J. Batra, K. Xu, S. Qin, and H.-X. Zhou, Biophys J 97, 906 (2009).