Multiscale simulations of biochemically reacting systems

My work focuses on gaining a deeper understanding on the catalytic mechanism of enzymes and reaction-diffusion relations in various biological systems, using computational methods and theories. It is of profound interest and great practical value to explore the physical and biological chemistry of drug diffusion and binding at multiple time and size scales. For example, it helps us understand why a drug can or cannot bind with the mutation(s) of its target protein, how efficient the binding process is and how we can design synthetic receptors to serve as drug carriers or to separate chemical mixtures. A brief summary of this dissertation is as follows. Combined quantum mechanics and molecular mechanics (QM/MM) and molecular dynamics (MD) have enabled probing the potential surface accurately in various enzymatic reactions. For an unusual residue or drug molecule, the RESP charge parameters were first prepared with quantum mechanics calculations. Since the resolution of the X-ray crystal structures were not high enough to determine the protonated state of each residue, pKa calculations were carried out. Then molecular dynamics was used to study the conformational changes of the enzymes. Finally, QM/MM studies were conducted to calculate the reaction barrier and even the free energy path. When I was in the Laboratory of Biomass Clean Energy (BCEL) at University of Science and Technology of China, I focused on studying the stability of various radicals, pi-cation interactions and the reaction mechanisms in several organic reactions, using the quantum chemistry. This experience provided the fundamental base for my first PhD project, ab initio QM/MM studies on the catalytic subunit of cAMP-Dependent Protein Kinase (PKA) (Chapter I). The QM /MM calculations confirmed that the phosphorylation reaction catalyzed by PKA is mainly dissociative, and Asp166 serves as the catalytic base to accept the proton delivered by the substrate peptide. Furthermore, we have studied the effects of the residues on the reaction barrier using the QM/MM free energy perturbation theory, and analyzed the role of the phosphorylated Thr-197 in the activation segment. We have found that pThr-197 not only facilitates the phosphoryl transfer reaction by stabilizing the transition state through electrostatic interactions, but also strongly affects the functional protein dynamics as well as the active site conformation. Similarly, we have carried out QM/MM calculations to explore the reaction mechanism in both the wild-type and His447Ile mouse acetylcholinesterase (mAChE). Our studies indicated that the catalytic base His447 can be replaced with the catalytic water molecule in the binding of some inhibitors to the mAChE. Although the QM/MM and MD methods can play important roles in determining reaction mechanisms, as well as the motion and folding of the protein, these methods are still quite expensive to probe larger spatial and time scale problems, such as modeling the synaptic transmission and determining the ligand association rate constant kon, as shown in the first and second stages of my research (see Fig.0.1). To model these biological systems, we have developed the SMOL package (http://mccammon.ucsd.edu/smol). The SMOL package mainly aims to model the electrostatics and time-dependent diffusion in various biological systems using the finite element method. We have implemented it to solve the diffusion and reaction equations at the molecular level, as well as for the cholinergic synapse. Different from the QM/MM and classical MD simulations, the problem domain is discretized by Delaunay tessellation instead of atomic positions. The application of the adaptive finite element meshes can adjust the quality of the computation according the user's specific requirements. In summary, Chapter I of this dissertation addresses my QM/MM and MD work for probing the enzymatic reaction mechanism in the protein kinase A and acetylcholinesterase, Chapter II considers the time-dependent Smoluchowski diffusion equation in the acetylcholinesterase monomer and tetramers, and Chapter III considers the time-dependent diffusion equation with chemically reactive boundaries in the cholinergic synaps