| Summary: | 博士 === 國立臺灣大學 === 生化科學研究所 === 106 === Computational characterization of molecular interaction energetics is central to molecular biophysics and is so far the only way to bridge the gap between free energies of interaction and underlying mechanistic details. The molecular simulations; such as molecular dynamic (MD) (or Monte-Carlo (MC)); are used to compute free energy difference between thermodynamically well-defined end-states. For example, a well-established potential of mean force (PMF) calculation gives free energy profile for physically achievable processes such as molecular association and/or dissociation, dihedral angle fluctuations, conformational flipping of domains/loops, etc. Usually, these molecular reactions involve crossing over several energy barriers and the unbiased MD simulations cannot sample wider configurational space in shorter time-scaled simulations. In such situations the umbrella sampling simulation, a widely-used sampling enhancement method, is an effective way to sample the desired configurational space.
Umbrella sampling was often implemented in such a way that the samplings were enhanced along a predefined vector as a reaction coordinate. However, any slight change in the predefined vector significantly varies the PMF, and therefore the energetics using any such random choice of vector may mislead. A non-predefined curvilinear path-based sampling enhancement approach is a natural alternative, but was relatively less explored for protein-protein systems. In this thesis, dissociation of the barnase-barstar protein complex is rigorously studied by implementing generalized curvilinear-path approach in umbrella sampling simulations.
There can be multiple reaction channels along the reaction coordinate. Therefore, umbrella sampling simulations are conducted with multiple-walkers to explore free energy difference along different channels. The sampling data is analyzed and PMFs are constructed for each walker. Since the starting conformation is the same crystal pose, all the PMFs are expected to converge to around same value. However, to our surprise, not all but a subset of PMFs converged. There were several such subsets observed that converged to different values. Since the reaction was simulated for dissociation, as per the principle of least action, i.e. variational principle, a PMF that constitute a lower bound is chosen. Interestingly, we found that not just PMF but one but there profiles constitute a robust lower-bound. The theoretical framework is optimized for correcting the PMF to the standard free energy of binding. Combining curvilinear-path approach with variational principle based optimized corrections to standard free energy of binding is a novel implementation. Further, the pathways are traced using clustering of the sampled data. The traced physical trajectories for the robust lower-bound are observed to be different.
The curvilinear-path umbrella sampling approach is highly generalized to simulate dissociation reaction in more natural manner. The estimated free energy of binding is in good agreement with the experimental values. Further, the traced physical trajectories are consistent with the two major dissociation pathways, which are reported recently from milliseconds-long unbiased adaptive MD simulations of barnase-barstar association. Several aspects of implementation of the approach are discussed in detail.
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