<p> Due to high sensitivity of biomolecular systems to the electrostatic environments, coupled treatment of conformational and protonation equilibria is required for an accurate characterization of true ensemble of a given system. The research presented in this dissertation examines the effects of conformational and protonation equilibria of varying extent on diverse aspects of computational biomolecular modeling, as introduced in Chapter 1. The effects of protonation and stereoisomerism of two histidines on virtual screening against the M. tuberculosis enzyme RmlC are presented in Chapter 2. In Chapter 3, conformational flexibility of three M. tuberculosis prenyl synthases is probed using molecular dynamics simulations, with implications for computer-aided drug discovery effort for the new generation antibacterial and antivirulence therapeutics. Chapters 4 and 5 consider the conformational and protonation equilibria simultaneously by utilizing constant pH molecular dynamics, in which fluctuations in both conformation and protonation state are possible. In Chapter 4, a computational protocol utilizing constant pH molecular dynamics to compute pH-dependent binding free energies is presented. The methodology is further applied to protein-ligand complexes in Chapter 5, where the thermodynamic linkage between protonation equilibria, conformational dynamics, and inhibitor binding is illustrated.</p>

<p> As human understandings of physics, chemistry and biology converge and the development of computers proceeds, computational chemistry or computational biophysics has become a substantial field of research. It serves to explore the fundamentals of life and also has extended applications in the field of medicine. Among the many aspects of computational chemistry, this Ph. D. work focuses on the numerical methods for studying diffusion and electrostatics of biomolecules at the nanoscale. Diffusion and electrostatics are two independent subjects in terms of their physics, but closely related in applications. In living cells, the mechanism of diffusion powers a ligand to move towards its binding target. And electrostatic forces between the ligand and the target or the ligand and the environment guide the direction of the diffusion, the correct binding orientation and, together with other molecular forces, ensure the stability of the bound complex. More abstractly, diffusion describes the stochastic manner biomolecules move on their energy landscape and electrostatic forces are a major contributor to the shape of the energy landscape. This Ph. D. work aims to acquire a good understanding of both biomolecular diffusion and electrostatics and how the two are used together in numerical calculations. Three projects are presented. The first project is a proof of concept of the bead-model approach to calculate the diffusion tensor. The second project is the benchmark for a new electrostatics method, the size-modified Poisson-Boltzmann equation. The third project is an application that combines diffusion and electrostatics to calculate the substrate channeling efficiency between the human thymidylate synthase and dihydrofolate reductase.</p>

<p> Improving our understanding of nonadiabatic processes is essential for informed development of photoelectric technologies. Nonadiabatic dynamics arise due to nuclear motion on coupled potential energy surfaces. These nonadiabatic couplings are high in the regions of avoided crossings, where potential energy surfaces approach each other, and near infinity at conical intersections, where two potential energy surfaces are degenerate. Regions of high nonadiabatic coupling play an important role in the electronic dynamics of a system because of their ability to create very rapid (on the order of tens of femtoseconds) radiationless transitions between potential energy surfaces. Recent computational work has shown conical intersections to be prevalent in photochemical reactions; however, there are very few experimental investigations of conical intersections in condensed phase reactions. This is due to the extreme difficulty of detecting their subtle signatures experimentally. In biophysical chemistry, the only system that has been investigated is rhodopsin. In this photoisomerization reaction, the conical intersection produces a very rapid photoproduct formation with a quantum yield of approximately 85%. This led to the idea that the mere presence of a conical intersection in a biophysical system results in photoproducts formed with high quantum yields. In contrast, computational work shows conical intersections to be ubiquitous in all types of photoisomerization reactions. In this thesis I provide experimental evidence of conical intersections in a system with a quantum yield of &lt;15%, thereby showing that the topography of the conical intersection has an effect on the quantum yield of the photoisomerization, and does not just by its mere presence result in a high quantum yield. </p><p> The system we investigate here is phytochrome Cph1&Delta;. It is an ideal model system because it is reversibly photoisomerizable and has known single--site mutations that result in altered potential energy surfaces. However, this system is experimentally very challenging to investigate. Conical intersections already have very subtle signatures, and low quantum yield, combined with the potential for overlapping signals due to the forward and reverse reactions, make detecting these signals even more difficult. In this thesis, I first describe our design and construction of a two--dimensional electronic spectroscopy (2D ES) and visible femtosecond transient transmittance spectrometer capable of performing these measurements. We perform a set of experiments on cresyl violet perchlorate, a laser dye, to show the importance of using our balanced detection methods and correct signal averaging schemes to maximize signal--to--noise and to ensure the signals converge to the correct value. We then use our spectrometer to probe for the presence of nonadiabatic dynamics in both the forward and reverse photoisomerization reactions of Cph1&Delta;. First, we use high sensitivity 2D ES and vibrational coherence spectroscopy to resolve a long--standing controversy about whether the forward reaction proceeds adiabatically. We find no evidence of nonadiabatic dynamics, and our results are consistent with a single ground state population undergoing a purely excited--state photoisomerizaion process. In the reverse reaction we identify and characterize a conical intersection using transient transmittance spectroscopy and 2D and 3D ES. This result expands on the notion that the presence of a conical intersection results in ultrafast dynamics and high photochemical quantum yield, showing that the topography of the conical intersection plays a role in determining the outcome of a photoexcitation. We also perform the same experiments on two single--site phytochrome mutants as control measurements. Finally, I present the theory of nonadiabatic coupling, and through simulations and experiments demonstrate the ability of our methods to identify signatures of non--Condon activity.</p><p>

<p> This dissertation will focus on my work in biophysics, and my work in mean field games and glucose predictive analysis will not be presented. Several problems relating to the effects of thermodynamic coupling and hydrodynamic coupling within the membrane stack system are discussed. Three theoretical approaches are employed and proposed to study the membrane stack system: a diffuse-interface approach is utilized for numerical simulations; a coarse-grained sharp-interface approach is utilized to provide physical understanding of various kinetics; a hybrid intermediate sharp-interface approach is adopted to study the domain coalescence in the absence of diffusion. </p><p> In the first part of the thesis, we discuss the thermodynamic coupling in membrane stack systems. Comprehensive analyses are presented to understand the accelerated coarsening kinetics with respect to single layer and long-range alignment. Numerical simulations are conducted for three systems, namely a diffusion dominated system, an advective interlayer friction dominated system, and an advective membrane viscosity dominated system. Experimental results regarding the advective interlayer friction dominated system are supported by simulations. We investigate the mechanism of the enhanced coarsening kinetics in membrane stack systems and the relationship between the coarsening process and vertical alignment. An intuitive understanding along with analytical explanations are further presented. Moreover, numerical results regarding the critical mixture are also discussed. </p><p> We then investigate the interfacial fluctuation behavior within membrane stack systems. The hydrodynamic coupling is found to play a significant role and several physical length scales are found to be crucial. Both a sharp-interface approach and a diffuse-interface approach are employed to numerically simulate decay of interface fluctuations in representative two-membrane systems. </p><p> To measure the thermodynamic coupling in experiments, the hydrodynamic force needs to be quantified, especially for the non-circular domains. In the last part of this thesis, the drag coefficient relating domain velocity and force acting on the domain is calculated using perturbation theory within two limits: the first limit refers to a domain much larger than the hydrodynamic screening length; the second limit refers to a domain that is much smaller than the hydrodynamic screening length.</p><p>