Multiscale Simulations of Biomolecules in Condensed Phase: from Solutions to Proteins
The thesis contains two directions in the simulations of biomolecular systems. The first part (Chapter 2 - Chapter 4) mainly focuses on the simulations of electron transfer processes in condensed phase; the second part (Chapter 5 - Chapter 6) investigates the conformational sampling of polysaccharides and proteins. Electron transfer (ET) reaction is one of the most fundamental processes in chemistry and biology. Because of the quantum nature of the processes and the complicated roles of the solvent, calculating the accurate kinetic and dynamic properties of ET reactions is challenging but extremely useful. Based on the Marcus theory for thermal ET in weak coupling limit, we combined the rigorous ab initio quantum mechanical (QM) method and well-established molecular mechanical (MM) force field and developed an approach to directly calculate a key factor that affects the ET kinetics: the redox free energy. A novel reaction order parameter fractional number of electrons (FNE) was used to characterize the ET progress and to drive the QM/MMMD sampling of the nonadiabatic free energy surface. This method was used for two aqueous metal cations, iron and ruthenium in solution, and generated satisfactory results compared to experiments. In order to further reduce the computational cost, a QM/MM-minimum free energy path (MFEP) method is implemented and combined with the FNE in the calculation of redox free energies. The calculation results using QM/MM-MFEP+FNE generated identical results as the direct QM/MM-MD method for the two metal cations, demonstrating the consistency of the two different sampling strategy. Furthermore, this new method was applied to the calculation of organic molecules and enhanced the computational efficiency 15-30 times than the direct QM/MM-MD method, while maintaining high accuracy. Finally, I successfully extended the QM/MM-MFEP+FNE method to a series of redox proteins, azurin and its mutants, and obtained very accurate redox free energy differences with relative error less than 0.1 eV. The new method demonstrated its excellent transferability, reliability and accuracy among various conditions from aqueous solutions to complex protein systems. Therefore, it shows great promises for applications of the studies on redox reactions in biochemistry. In the studies of force-induced conformational transitions of biomolecules, the large time-scale difference from experiments presents the challenge of obtaining convergent sampling for molecular dynamics simulations. To circumvent this fundamental problem, an approach combining the replica-exchange method and umbrella sampling (REM-US) is developed to simulate mechanical stretching of biomolecules under equilibrium conditions. Equilibrium properties of conformational transitions can be obtained directly from simulations without further assumptions. To test the performance, we carried out REM-US simulations of atomic force microscope (AFM) stretching and relaxing measurements on the polysaccharide pustulan, a (1→6)-β-D-glucan, which undergoes well-characterized rotameric transitions in the backbone bonds. With significantly enhanced sampling convergence and efficiency, the REMUS approach closely reproduced the equilibrium force-extension curves measured in AFM experiments. Consistent with the reversibility in the AFM measurements, the new approach generated identical force-extension curves in both stretching and relaxing simulations, an outcome not reported in previous studies, proving that equilibrium conditions were achieved in the simulations. In addition, simulations of nine different polysaccharides were performed and the conformational transitions were reexamined using the REM-US approach. The new approach demonstrated consistent and reliable performance among various systems. With fully converged samplings and minimized statistical errors, both the agreement and the deviations between the simulation results and the AFM data were clearly presented. REM-US may provide a robust approach to modeling of mechanical stretching on polysaccharides and even nucleic acids. However, the performance of the REM-US in protein systems, especially with explicit solvent model, is limited by the large system size and the complex interactions. Therefore, a Go-like model is employed to simulate the protein folding/unfolding processes controlled by AFM. The simulations exquisitely reproduced the experimental unfolding and refolding force extension relationships and led to the full reconstruction of the vectorial folding pathway of a large polypeptide, the 253-residue consensus ankyrin repeat protein, NI6C. The trajectories obtained in the simulation captured the critical conformational transitions and the rate-limiting nucleation event. Together with the AFM experiments, the coarse-grained simulations revealed the protein folding and unfolding pathways under the mechanical tension.
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