Development of Fast Biomolecular Simulation Algorithms with 

Applications to Heme Proteins

While much progress has been made in numerical algorithm and software development in the past 25 years, including several well developed program packages such as DelPhi, UHBD, and APBS, which have been successively applied to many applications, developing faster and more robust numerical algorithms for solving the Poisson-Boltzmann equation (PBE), especially for the challenging nonlinear PBE problem, is still an imperative research task. Minimization of the biomolecular potential energy function is also a fundamental task in biomolecular simulations. It can be used to predict the structure of biomolecules, and to optimize the fit of structures to the experimental data. However, solving such a minimization problem is particularly challenging due to the large dimensionality of the search space, the strong nonlinearity of the energy function, and the expensive costs of evaluating, the energy function E, the gradient vector g, and the Hessian matrix H. The computer time for evaluating E, g and H usually comprise more than 90 percent of the total CPU time in a local minimum searching. Thus, the efficiency of a local minimum algorithm is particularly important in minimizing the biomolecular potential energy function. In this proposal we seek to develop: 1) two fast nonlinear iterative algorithms for solving the nonlinear PBE problem based on the new minimization protocol we developed earlier and other advanced numerical techniques including mortar finite element, multigrid, parallel computing, and globalization techniques; 2) one fast minimization algorithm, called the adaptive truncated Newton method, for minimizing the biomolecular potential energy function; 3) a computer program package to turn the above three new numerical algorithms as a powerful tool for molecular mechanics and molecular dynamics simulations and 4) to simulate several mutants of cytochrome c to rigorously test the above three new algorithms and to understand and develop biophysical hypotheses regarding reduction potential control and modulation and other key properties (e.g., stability) including the prediction of midpoint reduction potentials (Em) of native and variant cytochromes to test and confirm the efficiency and robustness of the proposed new numerical algorithms. The cytochromes c are outstanding models for developing new protein simulation techniques since many of their properties have been experimentally established. The two problems to be initially investigated are predicting the Em values for the six site specific mutants of iso-1-cytochrome c at the Phe82 position. The native iso-1-cytochrome c serves as the ``references" protein Em. A ``collapsing protein" hypothesis is proposed and will be tested with these calculations. A second important problem to be investigated is the Tyr48Lys variant of iso-1-cytochrome c, which has the unusually high reduction potential of 420 mV vs. 290 mV for native protein. We seek to predict and understand this unusually high reduction potential. .