Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
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We present an efficient and numerically robust algorithm for solving the Smoluchowski equation (SE) to follow diffusive processes on smooth and rough potential energy surfaces. The hierarchical nature of the algorithm (hierarchical discrete approximation or HDA) allows to fully explore the fine- and coarse-grained structure of the free energy surface and can be extended to multidimensional problems. It is shown that for free energy surfaces where the minima are separated by considerable barriers the reaction kinetics can be captured using only a small number of eigenvalues of the corresponding rate matrix which leads to a considerable speedup of the computation. This technique, in combination with HDA, is applied to study the rebinding of carbon monoxide (CO) to native myoglobin (Mb) and a mutated protein (L29F), a process of fundamental importance in biophysics.