A combination of classical and quantum mechanical approaches are described in Chapter 1 and utilized in this dissertation to study catalysis and allostery in the metalloprotein IspH, as well as to probe protonation equilibria in a variety of macromolecules. Chapters 2 and 3 are dedicated to characterizing the oxidized [4Fe-4S] IspH protein, which is biologically important as an antimicrobial drug target. In Chapter 2, the protonation states of active site residues in substrate-bound IspH are characterized using broken-symmetry density functional theory to provide a foundation for exploring IspH catalysis. Subsequently, a more coarse-grained approach is used in Chapter 3 to assess the internal motions of IspH, both with and without its substrate bound, using classical molecular dynamics. Both these studies reveal rational approaches for the design of novel IspH inhibitors. Chapters 4 and 5 deviate from the metalloprotein theme established in Chapters 2 and 3 to consider classical approaches for treating proton binding and unbinding in the context of molecular dynamics simulations. The ability of the constant pH molecular dynamics method to predict protein pKa values is assessed in Chapter 4 using an experimental test set comprising Staphylococcal nuclease variants. Building on this work, Chapter 5 provides proof of concept for the constant pH molecular dynamics method to obtain pH-dependent binding free energies in conjunction with Wyman's binding polynomial formalism

The binding of a series of metal-binding pharmacophores (MBPs) related to the ligand 1-hydroxypyridine-2-(1H)-thione (1,2-HOPTO) in the active site of human carbonic anhydrase II (hCAII) has been investigated. The presence and/or position of a single methyl substituent drastically alters inhibitor potency and can result in coordination modes not observed in small-molecule model complexes. It is shown that this unexpected binding mode is the result of a steric clash between the methyl group and a highly ordered water network in the active site that is further stabilized by the formation of a hydrogen bond and favorable hydrophobic contacts. The affinity of MBPs is dependent on a large number of factors including donor atom identity, orientation, electrostatics, and van der Waals interactions. These results suggest that metal coordination by metalloenzyme inhibitors is a malleable interaction and that it is thus more appropriate to consider the metal-binding motif of these inhibitors as a pharmacophore rather than a "chelator". The rational design of inhibitors targeting metalloenzymes will benefit greatly from a deeper understanding of the interplay between the variety of forces governing the binding of MBPs to active site metal ions.

In protein-ligand binding, the electrostatic environments of the two binding partners may vary significantly in bound and unbound states, which may lead to protonation changes upon binding. In cases where ligand binding results in a net uptake or release of protons, the free energy of binding is pH-dependent. Nevertheless, conventional free energy calculations and molecular docking protocols typically do not rigorously account for changes in protonation that may occur upon ligand binding. To address these shortcomings, we present a simple methodology based on Wyman's binding polynomial formalism to account for the pH dependence of binding free energies and demonstrate its use on cucurbit[7]uril (CB[7]) host-guest systems. Using constant pH molecular dynamics and a reference binding free energy that is taken either from experiment or from thermodynamic integration computations, the pH-dependent binding free energy is determined. This computational protocol accurately captures the large pKa shifts observed experimentally upon CB[7]:guest association and reproduces experimental binding free energies at different levels of pH. We show that incorrect assignment of fixed protonation states in free energy computations can give errors of >2 kcal/mol in these host-guest systems. Use of the methods presented here avoids such errors, thus suggesting their utility in computing proton-linked binding free energies for protein-ligand complexes.

BACE-1 is the β-secretase responsible for the initial amyloidogenesis in Alzheimer's disease, catalyzing hydrolytic cleavage of substrate in a pH-sensitive manner. The catalytic mechanism of BACE-1 requires water-mediated proton transfer from aspartyl dyad to the substrate, as well as structural flexibility in the flap region. Thus, the coupling of protonation and conformational equilibria is essential to a full in silico characterization of BACE-1. In this work, we perform constant pH replica exchange molecular dynamics simulations on both apo BACE-1 and five BACE-1-inhibitor complexes to examine the effect of pH on dynamics and inhibitor binding properties of BACE-1. In our simulations, we find that solution pH controls the conformational flexibility of apo BACE-1, whereas bound inhibitors largely limit the motions of the holo enzyme at all levels of pH. The microscopic pKa values of titratable residues in BACE-1 including its aspartyl dyad are computed and compared between apo and inhibitor-bound states. Changes in protonation between the apo and holo forms suggest a thermodynamic linkage between binding of inhibitors and protons localized at the dyad. Utilizing our recently developed computational protocol applying the binding polynomial formalism to the constant pH molecular dynamics (CpHMD) framework, we are able to obtain the pH-dependent binding free energy profiles for various BACE-1-inhibitor complexes. Our results highlight the importance of correctly addressing the binding-induced protonation changes in protein-ligand systems where binding accompanies a net proton transfer. This work comprises the first application of our CpHMD-based free energy computational method to protein-ligand complexes and illustrates the value of CpHMD as an all-purpose tool for obtaining pH-dependent dynamics and binding free energies of biological systems.

The nonmevalonate pathway is responsible for isoprenoid production in microbes, including H. pylori, M. tuberculosis and P. falciparum, but is nonexistent in humans, thus providing a desirable route for antibacterial and antimalarial drug discovery. We coordinate a structural study of IspH, a [4Fe-4S] protein responsible for converting HMBPP to IPP and DMAPP in the ultimate step in the nonmevalonate pathway. By performing accelerated molecular dynamics simulations on both substrate-free and HMBPP-bound [Fe4S4](2+) IspH, we elucidate how substrate binding alters the dynamics of the protein. Using principal component analysis, we note that while substrate-free IspH samples various open and closed conformations, the closed conformation observed experimentally for HMBPP-bound IspH is inaccessible in the absence of HMBPP. In contrast, simulations with HMBPP bound are restricted from accessing the open states sampled by the substrate-free simulations. Further investigation of the substrate-free simulations reveals large fluctuations in the HMBPP binding pocket, as well as allosteric pocket openings - both of which are achieved through the hinge motions of the individual domains in IspH. Coupling these findings with solvent mapping and various structural analyses reveals alternative druggable sites that may be exploited in future drug design efforts.

The recently discovered methylerythritol phosphate (MEP) pathway provides new targets for the development of antibacterial and antimalarial drugs. In the final step of the MEP pathway, the [4Fe-4S] IspH protein catalyzes the 2e(-)/2H(+) reductive dehydroxylation of (E)-4-hydroxy-3-methyl-but-2-enyl diphosphate (HMBPP) to afford the isoprenoid precursors isopentenyl pyrophosphate (IPP) and dimethylallyl pyrophosphate (DMAPP). Recent experiments have attempted to elucidate the IspH catalytic mechanism to drive inhibitor development. Two competing mechanisms have recently emerged, differentiated by their proposed HMBPP binding modes upon 1e(-) reduction of the [4Fe-4S] cluster: (1) a Birch reduction mechanism, in which HMBPP remains bound to the [4Fe-4S] cluster through its terminal C4-OH group (ROH-bound) until the -OH is cleaved as water; and (2) an organometallic mechanism, in which the C4-OH group rotates away from the [4Fe-4S] cluster, allowing the HMBPP olefin group to form a metallacycle complex with the apical iron (η(2)-bound). We perform broken-symmetry density functional theory computations to assess the energies and reduction potentials associated with the ROH- and η(2)-bound states implicated by these competing mechanisms. Reduction potentials obtained for ROH-bound states are more negative (-1.4 to -1.0 V) than what is typically expected of [4Fe-4S] ferredoxin proteins. Instead, we find that η(2)-bound states are lower in energy than ROH-bound states when the [4Fe-4S] cluster is 1e(-) reduced. Furthermore, η(2)-bound states can already be generated in the oxidized state, yielding reduction potentials of ca. -700 mV when electron addition occurs after rotation of the HMBPP C4-OH group. We demonstrate that such η(2)-bound states are kinetically accessible both when the IspH [4Fe-4S] cluster is oxidized and 1e(-) reduced. The energetically preferred pathway gives 1e(-) reduction of the cluster after substrate conformational change, generating the 1e(-) reduced intermediate proposed in the organometallic mechanism.

With current therapies becoming less efficacious due to increased drug resistance, new inhibitors of both bacterial and malarial targets are desperately needed. The recently discovered methylerythritol phosphate (MEP) pathway for isoprenoid synthesis provides novel targets for the development of such drugs. Particular attention has focused on the IspH protein, the final enzyme in the MEP pathway, which uses its [4Fe-4S] cluster to catalyze the formation of the isoprenoid precursors IPP and DMAPP from HMBPP. IspH catalysis is achieved via a 2e^-/2H⁺ reductive dehydroxylation of HMBPP; the mechanism by which catalysis is achieved, however, is highly controversial. The work presented herein provides the first step in assessing different routes to catalysis by using computational methods. By performing broken-symmetry density functional theory (BS-DFT) calculations that employ both the conductor-like screening solvation model (DFT/COSMO) and a finite-difference Poisson-Boltzmann self-consistent reaction field methodology (DFT/SCRF), we evaluate geometries, energies, and Mössbauer signatures of the different protonation states that may exist in the oxidized state of the IspH catalytic cycle. From DFT/SCRF computations performed on the oxidized state, we find a state where the substrate, HMBPP, coordinates the apical iron in the [4Fe-4S] cluster as an alcohol group (ROH) to be one of two, isoenergetic, lowest-energy states. In this state, the HMBPP pyrophosphate moiety and an adjacent glutamate residue (E126) are both fully deprotonated, making the active site highly anionic. Our findings that this low-energy state also matches the experimental geometry of the active site and that its computed isomer shifts agree with experiment validate the use of the DFT/SCRF method to assess relative energies along the IspH reaction pathway. Additional studies of IspH catalytic intermediates are currently being pursued.

The binding of three closely related chelators: 5-hydroxy-2-methyl-4H-pyran-4-thione (allothiomaltol, ATM), 3-hydroxy-2-methyl-4H-pyran-4-thione (thiomaltol, TM), and 3-hydroxy-4H-pyran-4-thione (thiopyromeconic acid, TPMA) to the active site of human carbonic anhydrase II (hCAII) has been investigated. Two of these ligands display a monodentate mode of coordination to the active site Zn(2+) ion in hCAII that is not recapitulated in model complexes of the enzyme active site. This unprecedented binding mode in the hCAII-thiomaltol complex has been characterized by both X-ray crystallography and X-ray spectroscopy. In addition, the steric restrictions of the active site force the ligands into a 'flattened' mode of coordination compared with inorganic model complexes. This change in geometry has been shown by density functional computations to significantly decrease the strength of the metal-ligand binding. Collectively, these data demonstrate that the mode of binding by small metal-binding groups can be significantly influenced by the protein active site. Diminishing the strength of the metal-ligand bond results in unconventional modes of metal coordination not found in typical coordination compounds or even carefully engineered active site models, and understanding these effects is critical to the rational design of inhibitors that target clinically relevant metalloproteins.