Catalysis and Linear Free Energy Relationships in Aspartic Proteases

Calculation of Heat Capacity Changes in Enzyme Catalysis and Ligand Binding

It has been suggested that heat capacity changes in enzyme catalysis may be the underlying reason for temperature optima that are not related to unfolding of the enzyme. If this were to be a common phenomenon, it would have major implications for our interpretation of enzyme kinetics. In most cases, the support for the possible existence of a nonzero (negative) activation heat capacity, however, only relies on fitting such a kinetic model to experimental data. It is therefore of fundamental interest to try to use computer simulations to address this issue. One way is simply to calculate the temperature dependence of the activation free energy and determine whether the relationship is linear or not. An alternative approach is to calculate the absolute heat capacities of the reactant and transition states from plain molecular dynamics simulations using either the temperature derivative or fluctuation formula for the enthalpy. Here, we examine these different approaches for a designer enzyme with a temperature optimum that is not caused by unfolding. Benchmark calculations for the heat capacity of liquid water are first carried out using different thermostats. It is shown that the derivative formula for the heat capacity is generally the most robust and insensitive to the thermostat used and its parameters. The enzyme calculations using this method give results in agreement with direct calculations of activation free energies and show no sign of a negative activation heat capacity. We also provide a simple scheme for the calculation of binding heat capacity changes, which is of clear interest in ligand design, and demonstrate it for substrate binding to the designer enzyme. Neither in that case do the simulations predict any negative heat capacity change.

Correlating Thermodynamic and Kinetic Hydricities of Rhenium Hydrides

The kinetics of hydride transfer from Re(^Rbpy)(CO)₃H (bpy = 4,4'-R-2,2'-bipyridine; R = OMe, ^tBu, Me, H, Br, COOMe, CF₃) to CO₂ and seven different cationic N-heterocycles were determined. Additionally, the thermodynamic hydricities of complexes of the type Re(^Rbpy)(CO)₃H were established primarily using computational methods. Linear free-energy relationships (LFERs) derived by correlating thermodynamic and kinetic hydricities indicate that, in general, the rate of hydride transfer increases as the thermodynamic driving force for the reaction increases. Kinetic isotope effects range from inverse for hydride transfer reactions with a small driving force to normal for reactions with a large driving force. Hammett analysis indicates that hydride transfer reactions with greater thermodynamic driving force are less sensitive to changes in the electronic properties of the metal hydride, presumably because there is less buildup of charge in the increasingly early transition state. Bronsted α values were obtained for a range of hydride transfer reactions and along with DFT calculations suggest the reactions are concerted, which enables the use of Marcus theory to analyze hydride transfer reactions involving transition metal hydrides. It is notable, however, that even slight perturbations in the steric properties of the Re hydride or the hydride acceptor result in large deviations in the predicted rate of hydride transfer based on thermodynamic driving forces. This indicates that thermodynamic considerations alone cannot be used to predict the rate of hydride transfer, which has implications for catalyst design.

Exploring the concerted mechanistic pathway for HIV-1 PR-substrate revealed by umbrella sampling simulation

HIV-1 protease (HIV-1 PR) is an essential enzyme for the replication process of its virus, and therefore considered an important target for the development of drugs against the acquired immunodeficiency syndrome (AIDS). Our previous study shows that the catalytic mechanism of subtype B/C-SA HIV-1 PR follows a one-step concerted acyclic hydrolysis reaction process using a two-layered ONIOM B3LYP/6-31++G(d,p) method. This present work is aimed at exploring the proposed mechanism of the proteolysis catalyzed by HIV-1 PR and to ensure our proposed mechanism is not an artefact of a single theoretical technique. Hence, we present umbrella sampling method that is suitable for calculating potential mean force (PMF) for non-covalent ligand/substrate-enzyme association/dissociation interactions which provide thermodynamic details for molecular recognition. The free activation energy results were computed in terms of PMF analysis within the hybrid QM(DFTB)/MM approach. The theoretical findings suggest that the proposed mechanism corresponds in principle with experimental data. Given our observations, we suggest that the QM/MM MD method can be used as a reliable computational technique to rationalize lead compounds against specific targets such as the HIV-1 protease.

Visualizing Tetrahedral Oxyanion Bound in HIV-1 Protease Using Neutrons: Implications for the Catalytic Mechanism and Drug Design

HIV-1 protease is indispensable for virus propagation and an important therapeutic target for antiviral inhibitors to treat AIDS. As such inhibitors are transition-state mimics, a detailed understanding of the enzyme mechanism is crucial for the development of better anti-HIV drugs. Here, we used room-temperature joint X-ray/neutron crystallography to directly visualize hydrogen atoms and map hydrogen bonding interactions in a protease complex with peptidomimetic inhibitor KVS-1 containing a reactive nonhydrolyzable ketomethylene isostere, which, upon reacting with the catalytic water molecule, is converted into a tetrahedral intermediate state, KVS-1_TI. We unambiguously determined that the resulting tetrahedral intermediate is an oxyanion, rather than the gem-diol, and both catalytic aspartic acid residues are protonated. The oxyanion tetrahedral intermediate appears to be unstable, even though the negative charge on the oxyanion is delocalized through a strong n → π* hyperconjugative interaction into the nearby peptidic carbonyl group of the inhibitor. To better understand the influence of the ketomethylene isostere as a protease inhibitor, we have also examined the protease structure and binding affinity with keto-darunavir (keto-DRV), which similar to KVS-1 includes the ketomethylene isostere. We show that keto-DRV is a significantly less potent protease inhibitor than DRV. These findings shed light on the reaction mechanism of peptide hydrolysis catalyzed by HIV-1 protease and provide valuable insights into further improvements in the design of protease inhibitors.

Coordination among Bond Formation/Cleavage in a Bifunctional-Catalyzed Fast Amide Hydrolysis: Evidence for an Optimized Intramolecular N-Protonation Event

A density functional theory (DFT) computational analysis, using the ωB97X-D functional, of a rapid amide cleavage in 2-carboxyphthalanilic acid (2CPA), where the amide group is flanked by two catalytic carboxyls, reveals key mechanistic information: (a) General base catalysis by a carboxylate coupled to general acid catalysis by a carboxyl is not operative. (b) Nucleophilic attack by a carboxylate on the amide carbonyl coupled to general acid catalysis at the amide oxygen can also be ruled out. (c) A mechanistic pathway that remains viable involves general acid proton delivery to the amide nitrogen by a carboxyl, while the other carboxylate engages in nucleophilic attack upon the amide carbonyl; a substantially unchanged amide carbonyl in the transition state; two concurrent bond-forming events; and a spatiotemporal-base rate acceleration. This mechanism is supported by molecular dynamic simulations which confirm a persistent key intramolecular hydrogen bonding. These theoretical conclusions, although not easily verified by experiment, are consistent with a bell-shaped pH/rate profile but are at odds with hydrolysis mechanisms in the classic literature.

Inhibitory and Cooperative Effects Regulated by pH in Host-Guest Complexation between Cationic Pillar[5]arene and Reactive 2-Carboxyphthalanilic Acid

The study of host-guest complexation between reactive 2-carboxyphthalanilic acid (CPA) and two cationic pillararenes has been carried out. Host-guest complexation with significant kinetic effects was observed only with the smaller cavity size pillararene (P5A). Kinetics in the pH range 1.50-6.40, ESI-MS, ¹H NMR titration, and ROESY experiments were performed to characterize the complexes. High binding stoichiometry (H:G₂) was observed for all CPA protonation states. The system is pH-dependent, and inversion of cooperativity (negative to positive) occurs by increasing the dianionic CPA^2- concentration (allosteric behavior). Toward physiological pH, association constant K_1:1 does not change (10⁴ M^-1), and K_1:2 increased from 10² to 10⁴ M^-1, as well as the inhibitory effect increased up to 222-fold. NMR results elucidated the structure of the complex and allowed us to create a map of H-H interactions that describes well the diversity and number of interactions in the complex.

Catalytic Adaptation of Psychrophilic Elastase

The class I pancreatic elastase from Atlantic salmon is considered to be a cold-adapted enzyme in view of the cold habitat, the reduced thermostability of the enzyme, and the fact that it is faster than its mesophilic porcine counterpart at room temperature. However, no experimental characterization of its catalytic properties at lower temperatures has actually been reported. Here we use extensive computer simulations of its catalytic reaction, at different temperatures and with different peptide substrates, to compare its characteristics with those of porcine pancreatic elastase, with which it shares 67% sequence identity. We find that both enzymes have a preference for smaller aliphatic residues at the P1 position, while the reaction rate with phenylalanine at P1 is predicted to be substantially lower. With the former class of substrates, the calculated reaction rates for salmon enzyme are consistently higher than those of the porcine ortholog at all temperatures examined, and the difference is most pronounced at the lowest temperature. As observed for other cold-adapted enzymes, this is caused by redistribution of the activation free energy in terms of enthalpy and entropy and can be linked to differences in the mobility of surface-exposed loops in the two enzymes. Such mobility changes are found to be reflected by characteristic sequence conservation patterns in psychrophilic and mesophilic species. Hence, calculations of mutations in a single surface loop show that the temperature dependence of the catalytic reaction is altered in a predictable way.

Misunderstanding the preorganization concept can lead to confusions about the origin of enzyme catalysis

Understanding the origin of the catalytic power of enzymes has both conceptual and practical importance. One of the most important finding from computational studies of enzyme catalysis is that a major part of the catalytic power is due to the preorganization of the enzyme active site. Unfortunately, misunderstanding of the nontrivial preorganization idea lead some to assume that it does not consider the effect of the protein residues. This major confusion reflects a misunderstanding of the statement that the interaction energy of the enzyme group and the transition state (TS) is similar to the corresponding interaction between the water molecules (in the reference system) and the TS, and that the catalysis is due to the reorganization free energy of the water molecules. Obviously, this finding does not mean that we do not consider the enzyme groups. Another problem is the idea that catalysis is due to substrate preorganization. This more traditional idea is based in some cases on inconsistent interpretation of the action of model compounds, which unfortunately, do not reflect the actual situation in the enzyme active site. The present article addresses the above problems, clarifying first the enzyme polar preorganization idea and the current misunderstandings. Next we take a specific model compound that was used to promote the substrate preorganization proposal and establish its irrelevance to enzyme catalysis. Overall, we show that the origin of the catalytic power of enzymes cannot be assessed uniquely without computer simulations, since at present this is the only way of relating structure and energetics.

Cold Adaptation of Triosephosphate Isomerase

The main problem for enzymes from psychrophilic species, which need to work near the freezing point of liquid water, is the exponential decay of reaction rates as the temperature is decreased. Cold-adapted enzymes have solved this problem by shifting the activation enthalpy-entropy balance for the catalyzed reaction compared to those of their mesophilic orthologs. To understand the structural basis of this universal feature, it is necessary to examine pairs of such orthologous enzymes, with known three-dimensional structures, at the microscopic level. Here, we use molecular dynamics free energy calculations in combination with the empirical valence bond method to evaluate the temperature dependence of the activation free energy for differently adapted triosephosphate isomerases. The results show that the enzyme from the psychrophilic bacterium Vibrio marinus indeed displays the characteristic shift in enthalpy-entropy balance, compared to that of the yeast ortholog. The origin of this effect is found to be located in a few surface-exposed protein loops that show differential mobilities in the two enzymes. Key mutations render these loops more mobile in the cold-adapted triosephosphate isomerase, which explains both the reduced activation enthalpy contribution from the protein surface and the lower thermostability.

Transforming a Stable Amide into a Highly Reactive One: Capturing the Essence of Enzymatic Catalysis

Aspartic proteinases, which include HIV-1 proteinase, function with two aspartate carboxy groups at the active site. This relationship has been modeled in a system possessing an otherwise unactivated amide positioned between two carboxy groups. The model amide is cleaved at an enzyme-like rate that renders the amide nonisolable at 35 °C and pH 4 owing to the joint presence of carboxy and carboxylate groups. A currently advanced theory attributing almost the entire catalytic power of enzymes to electrostatic reorganization is shown to be superfluous when suitable interatomic interactions are present. Our kinetic results are consistent with spatiotemporal concepts where embedding the amide group between two carboxylic moieties in proper geometries, at distances less than the diameter of water, leads to enzyme-like rate enhancements. Space and time are the essence of enzyme catalysis.

Probing the Time Dependency of Cyclooxygenase-1 Inhibitors by Computer Simulations

Time-dependent inhibition of the cyclooxygenases (COX) by a range of nonsteroidal anti-inflammatory drugs has been described since the first experimental assays of COX were performed. Slow tight-binding inhibitors of COX-1 bind in a two-step mechanism in which the EI → EI* transition is slow and practically irreversible. Since then, various properties of the inhibitors have been proposed to cause or affect the time dependency. Conformational changes in the enzyme have also been proposed to cause the time dependency, but no particular structural feature has been identified. Here, we investigated a series of inhibitors of COX-1 that are either time-independent or time-dependent using a combination of molecular dynamics simulations, binding free energy calculations, and potential of mean force calculations. We find that the time-dependent inhibitors stabilize a conformational change in the enzyme mainly identified by the rotation of a leucine side chain adjacent to the binding pocket. The induced conformation has been previously shown to be essential for the high binding affinities of tight-binding inhibitors in COX-1. The results of this work show that the structural features of the enzyme involved in both time-dependent and tight-binding inhibition are identical and further identify a structural mechanism responsible for the transition between the two enzyme-inhibitor complexes characteristic of slow tight-binding COX-1 inhibitors.

Entropy and Enzyme Catalysis

The role played by entropy for the enormous rate enhancement achieved by enzymes has been debated for many decades. There are, for example, several confirmed cases where the activation free energy is reduced by around 10 kcal/mol due to entropic effects, corresponding to a rate enhancement of ∼10⁷ compared to the uncatalyzed reaction. However, despite substantial efforts from both the experimental and theoretical side, no real consensus has been reached regarding the origin of such large entropic contributions to enzyme catalysis. Another remarkable instance of entropic effects is found in enzymes that are adapted by evolution to work at low temperatures, near the freezing point of water. These cold-adapted enzymes invariably show a more negative entropy and a lower enthalpy of activation than their mesophilic orthologs, which counteracts the exponential damping of reaction rates at lower temperature. The structural origin of this universal phenomenon has, however, remained elusive. The basic problem with connecting macroscopic thermodynamic quantities, such as activation entropy and enthalpy derived from Arrhenius plots, to the 3D protein structure is that the underlying detailed (microscopic) energetics is essentially inaccessible to experiment. Moreover, attempts to calculate entropy contributions by computer simulations have mostly focused only on substrate entropies, which do not provide the full picture. We have recently devised a new approach for accessing thermodynamic activation parameters of both enzyme and solution reactions from computer simulations, which turns out to be very successful. This method is analogous to the experimental Arrhenius plots and directly evaluates the temperature dependence of calculated reaction free energy profiles. Hence, by extensive molecular dynamics simulations and calculations of up to thousands of independent free energy profiles, we are able to extract activation parameters with sufficient precision for making direct comparisons to experiment. We show here that the agreement with the measured quantities, for both enzyme catalyzed and spontaneous solution reactions, is quite remarkable. Importantly, we can now address some of the most spectacular entropy effects in enzymes and clarify their detailed microscopic origin. Herein, we discuss as examples the conversion of cytidine to uridine catalyzed by cytidine deaminase and reactions taking place on the ribosome, namely, peptide bond formation and GTP hydrolysis by elongation factor Tu. It turns out that the large entropy contributions to catalysis in these cases can now be rationalized by our computational approach. Finally, we address the problem of cold adaptation of enzyme reaction rates and prove by computational experiments that the universal activation enthalpy-entropy phenomenon originates from mechanical properties of the outer protein surface.

Dynamic and Electrostatic Effects on the Reaction Catalyzed by HIV-1 Protease

HIV-1 Protease (HIV-1 PR) is one of the three enzymes essential for the replication process of HIV-1 virus, which explains why it has been the main target for design of drugs against acquired immunodeficiency syndrome (AIDS). This work is focused on exploring the proteolysis reaction catalyzed by HIV-1 PR, with special attention to the dynamic and electrostatic effects governing its catalytic power. Free energy surfaces for all possible mechanisms have been computed in terms of potentials of mean force (PMFs) within hybrid QM/MM potentials, with the QM subset of atoms described at semiempirical (AM1) and DFT (M06-2X) level. The results suggest that the most favorable reaction mechanism involves formation of a gem-diol intermediate, whose decomposition into the product complex would correspond to the rate-limiting step. The agreement between the activation free energy of this step with experimental data, as well as kinetic isotope effects (KIEs), supports this prediction. The role of the protein dynamic was studied by protein isotope labeling in the framework of the Variational Transition State Theory. The predicted enzyme KIEs, also very close to the values measured experimentally, reveal a measurable but small dynamic effect. Our calculations show how the contribution of dynamic effects to the effective activation free energy appears to be below 1 kcal·mol^-1. On the contrary, the electric field created by the protein in the active site of the enzyme emerges as being critical for the electronic reorganization required during the reaction. These electrostatic properties of the active site could be used as a mold for future drug design.

Long-Range Electrostatics-Induced Two-Proton Transfer Captured by Neutron Crystallography in an Enzyme Catalytic Site

Neutron crystallography was used to directly locate two protons before and after a pH-induced two-proton transfer between catalytic aspartic acid residues and the hydroxy group of the bound clinical drug darunavir, located in the catalytic site of enzyme HIV-1 protease. The two-proton transfer is triggered by electrostatic effects arising from protonation state changes of surface residues far from the active site. The mechanism and pH effect are supported by quantum mechanics/molecular mechanics (QM/MM) calculations. The low-pH proton configuration in the catalytic site is deemed critical for the catalytic action of this enzyme and may apply more generally to other aspartic proteases. Neutrons therefore represent a superb probe to obtain structural details for proton transfer reactions in biological systems at a truly atomic level.

Enzyme catalysis by entropy without Circe effect

Entropic effects have often been invoked to explain the extraordinary catalytic power of enzymes. In particular, the hypothesis that enzymes can use part of the substrate-binding free energy to reduce the entropic penalty associated with the subsequent chemical transformation has been very influential. The enzymatic reaction of cytidine deaminase appears to be a distinct example. Here, substrate binding is associated with a significant entropy loss that closely matches the activation entropy penalty for the uncatalyzed reaction in water, whereas the activation entropy for the rate-limiting catalytic step in the enzyme is close to zero. Herein, we report extensive computer simulations of the cytidine deaminase reaction and its temperature dependence. The energetics of the catalytic reaction is first evaluated by density functional theory calculations. These results are then used to parametrize an empirical valence bond description of the reaction, which allows efficient sampling by molecular dynamics simulations and computation of Arrhenius plots. The thermodynamic activation parameters calculated by this approach are in excellent agreement with experimental data and indeed show an activation entropy close to zero for the rate-limiting transition state. However, the origin of this effect is a change of reaction mechanism compared the uncatalyzed reaction. The enzyme operates by hydroxide ion attack, which is intrinsically associated with a favorable activation entropy. Hence, this has little to do with utilization of binding free energy to pay the entropic penalty but rather reflects how a preorganized active site can stabilize a reaction path that is not operational in solution.

Mechanisms of peptide hydrolysis by aspartyl and metalloproteases

Peptide hydrolysis has been involved in a wide range of biological, biotechnological, and industrial applications.

Chemical reaction mechanisms in solution from brute force computational Arrhenius plots

Decomposition of activation free energies of chemical reactions, into enthalpic and entropic components, can provide invaluable signatures of mechanistic pathways both in solution and in enzymes. Owing to the large number of degrees of freedom involved in such condensed-phase reactions, the extensive configurational sampling needed for reliable entropy estimates is still beyond the scope of quantum chemical calculations. Here we show, for the hydrolytic deamination of cytidine and dihydrocytidine in water, how direct computer simulations of the temperature dependence of free energy profiles can be used to extract very accurate thermodynamic activation parameters. The simulations are based on empirical valence bond models, and we demonstrate that the energetics obtained is insensitive to whether these are calibrated by quantum mechanical calculations or experimental data. The thermodynamic activation parameters are in remarkable agreement with experiment results and allow discrimination among alternative mechanisms, as well as rationalization of their different activation enthalpies and entropies.

Obtaining activation entropies and enthalpies of a reaction is important for distinguishing between alternative reaction mechanisms. Here the authors use computational methods to accurately obtain the enthalpic/entropic components of the activation free energy for hydrolytic deamination reactions.

Understanding intramembrane proteolysis: from protein dynamics to reaction kinetics

Intramembrane proteolysis - cleavage of proteins within the plane of a membrane - is a widespread phenomenon that can contribute to the functional activation of substrates and is involved in several diseases. Although different families of intramembrane proteases have been discovered and characterized, we currently do not know how these enzymes discriminate between substrates and non-substrates, how site-specific cleavage is achieved, or which factors determine the rate of proteolysis. Focusing on γ-secretase and rhomboid proteases, we argue that answers to these questions may emerge from connecting experimental readouts, such as reaction kinetics and the determination of cleavage sites, to the structures and the conformational dynamics of substrates and enzymes.

The conformation of a catalytic loop is central to GTPase activity on the ribosome

The translational GTPases hydrolyze GTP on the ribosome at several stages of the protein synthesis cycle. Because of the strong conservation of their catalytic center, these enzymes are expected to operate through a universal hydrolysis mechanism, in which a critical histidine residue together with the sarcin-ricin loop of the large ribosomal subunit is necessary for GTPase activation. Here we examine different possible pathways for GTP hydrolysis by EF-Tu through extensive computer simulations. We show that a conformational change of the peptide plane preceding this histidine has a decisive effect on the energetics of the reaction. This transition was predicted earlier by us and has recently been confirmed experimentally. It is found to promote early proton transfer from water to the γ-phosphate group of GTP, followed by nucleophilic attack by hydroxide ion. The calculated reaction energetics is in good agreement with available kinetic data, for both wild-type and mutant versions of EF-Tu, and indicates that the latter may enforce a change in mechanism toward more concerted pathways.

Mathematical and computational modeling in biology at multiple scales

A variety of topics are reviewed in the area of mathematical and computational modeling in biology, covering the range of scales from populations of organisms to electrons in atoms. The use of maximum entropy as an inference tool in the fields of biology and drug discovery is discussed. Mathematical and computational methods and models in the areas of epidemiology, cell physiology and cancer are surveyed. The technique of molecular dynamics is covered, with special attention to force fields for protein simulations and methods for the calculation of solvation free energies. The utility of quantum mechanical methods in biophysical and biochemical modeling is explored. The field of computational enzymology is examined.

Computational Insights into Substrate and Site Specificities, Catalytic Mechanism, and Protonation States of the Catalytic Asp Dyad of β -Secretase

In this review, information regarding substrate and site specificities, catalytic mechanism, and protonation states of the catalytic Asp dyad of β-secretase (BACE1) derived from computational studies has been discussed. BACE1 catalyzes the rate-limiting step in the generation of Alzheimer amyloid beta peptide through the proteolytic cleavage of the amyloid precursor protein. Due to its biological functioning, this enzyme has been considered as one of the most important targets for finding the cure for Alzheimer's disease. Molecular dynamics (MD) simulations suggested that structural differences in the key regions (inserts A, D, and F and the 10s loop) of the enzyme are responsible for the observed difference in its activities towards the WT- and SW-substrates. The modifications in the flap, third strand, and insert F regions were found to be involved in the alteration in the site specificity of the glycosylphosphatidylinositol bound form of BACE1. Our QM and QM/MM calculations suggested that BACE1 hydrolyzed the SW-substrate more efficiently than the WT-substrate and that cleavage of the peptide bond occurred in the rate-determining step. The results from molecular docking studies showed that the information concerning a single protonation state of the Asp dyad is not enough to run an in silico screening campaign.

Binding site preorganization and ligand discrimination in the purine riboswitch

The progress of RNA research has suggested a wide variety of RNA molecules as possible targets for pharmaceutical drug molecules. Structure-based computational methods for predicting binding modes and affinities are now important tools in drug discovery, but these methods have mainly been focused on protein targets. Here we employ molecular dynamics free-energy perturbation calculations and the linear interaction energy method to analyze the energetics of ligand binding to purine riboswitches. Calculations are carried out for 14 different purine complexes with the guanine and adenine riboswitches in order to examine their ligand recognition principles. The simulations yield binding affinities in good agreement with experimental data and rationalize the selectivity of the riboswitches for different ligands. In particular, it is found that these receptors have an unusually high degree of electrostatic preorganization for their cognate ligands, and this effect is further quantified by explicit free-energy calculations, which show that the standard electrostatic linear interaction energy parametrization is suboptimal in this case. The adenine riboswitch specifically uses the electrostatic preorganization to discriminate against guanine by preventing the formation of a G-U wobble base pair.

Modeling stopped-flow data for nucleic acid duplex formation reactions: the importance of off-path intermediates

Evidence for unexpected off-path intermediates to DNA duplex formation is presented. These off-path intermediates are shown to involve unimolecular and, in one case, bimolecular structure in one of the single strands of complementary DNA. Three models are developed to account for the observed single-stranded structures that are formed in parallel with duplex formation. These models are applied to the analysis of stopped-flow data for eight different nonself-complementary duplex formation reactions in order to extract the elementary rate constant for formation of the duplex from the complementary random coil single-stranded DNA. The free energy of activation (at 25 °C) for the denaturation of each duplex is calculated from these data and is shown to have a linear correlation to the overall standard free energy for duplex formation (also at 25 °C). Duplexes that contain mismatches obey a parallel linear free-energy (LFE) relationship with a y-intercept that is greater than that of duplexes without mismatches. Slopes near unity for the LFE relationships indicate that all duplexes go through an early, unstructured transition state.

Cathepsin D activity and selectivity in the acidic conditions of a tumor microenvironment: Utilization in the development of a novel Cathepsin D substrate for simultaneous cancer diagnosis and therapy

Pro-Cathepsin D (pCD) is an aspartyl endopeptidase which is over expressed in many cancers. This over expression generally led to its secretion into the extracellular culture medium of cancer cells. Moreover, pCD can auto activate and cleave its substrates at an acidic pH compatible with that found in tumor microenvironments (TME). Thus, exploiting these two pathological characteristics of TME offers the opportunity to develop new protease-activated vector on the basis of their specific substrate structures. The aim of this study was to validate new pCD substrates in the extracellular pH conditions of TME. As a first step, we investigated the effect of pH on the catalytic activity and selectivity of mature Cathepsin D (CD). It was found that the increase in the pH of the media led to a decrease in the reaction rate. However, the specificity of mature CD was not affected by a variation in pH. In the second step, the effect of the substrate structure was studied. We demonstrated that the substrate structure had a significant effect on the catalytic activity of CD. In fact, some modifications in peptide structure induced a change in the catalytic behavior that involved a substrate activation phenomenon. We suggest that this activation may be related to the amphiphilic nature of the modified peptide that may induce an interfacial activation mechanism. Finally, pCD, which is the major form found in the extracellular culture medium of cancer cells, was used. We demonstrated that the proform of CD cleave the modified peptide 5 at pH 6.5 with the same cleavage selectivity obtained with the mature form of the protease. These data provide a better understanding of CD behavior in tumor microenvironment conditions and this knowledge can be used to develop more specific tools for diagnosis and drug delivery.

New cathepsin D inhibitor library utilizing hydroxyethyl isosteres with cyclic tertiary amines

The design and synthesis of hydroxyethylamine isosteres as inhibitors of cathepsin D based on SAR data have been accomplished. A library of 96 of these hydroxyethylamine isosteres are described and many have proven to be very potent inhibitors of human cathepsin D activity as measured using a fluorometric assay technique, via peptide substrate Ac-Glu-Glu(Edans)-Lys-Pro-Ile-Cys-Phe-Phe-Arg-Leu-Gly-Lys(Methyl Red)-Glu-NH(2). Compounds showing strongest inhibition of cathepsin D activity were those that contain a hydroxyethyl-N'-2- or N'-(4-chlorophenyl)piperazine moiety (IC(50) values range from 0.55 to 8.5 nM), with N'-(2-pyrimidyl)piperizine (IC(50) values range from 0.5 to 21.6 nM), with N-N'- L-piperazinocolinamide (IC(50) values range from 0.001 - 0.25 nM), or N-N'-L-piperazinocolin-N-methylamide (IC(50) values range from 0.015 - 7.3 nM).

Kinetics and thermodynamics of DNA, RNA, and hybrid duplex formation

The rates of duplex formation for two octamers of DNA (5' d-CACGGCTC/5' d-GAGCCGTG and 5' d-CACAGCAC/5' d-GTGCTGTG), the homologous RNA, and both sets of hybrids in 1 M NaCl buffer have been measured using stopped-flow spectroscopy. In addition, the thermodynamic parameters, ΔH° and ΔS°, have been determined for the same sequences under the same buffer conditions using optical melting techniques. These data reveal a linear free energy relationship between the free energy of activation for denaturation and the change in free energy for formation of the duplexes. This relationship indicates that these duplex formation reactions occur through a common unstructured transition state that is more similar to the single strands in solution than to the ensuing duplex. In addition, these data confirm that the greater stability of RNA duplexes relative to that of homologous DNA and hybrid duplexes is controlled by the denaturation rate and not the duplex formation rate.

Elucidating the catalytic mechanism of β-secretase (BACE1): a quantum mechanics/molecular mechanics (QM/MM) approach

In this quantum mechanics/molecular mechanics (QM/MM) study, the mechanisms of the hydrolytic cleavage of the Met2-Asp3 and Leu2-Asp3 peptide bonds of the amyloid precursor protein (WT-substrate) and its Swedish mutant (SW) respectively catalyzed by β-secretase (BACE1) have been investigated by explicitly including the electrostatic and steric effects of the protein environment in the calculations. BACE1 catalyzes the rate-determining step in the generation of Alzheimer amyloid beta peptides and is widely acknowledged as a promising therapeutic target. The general acid-base mechanism followed by the enzyme proceeds through the following two steps: (1) formation of the gem-diol intermediate and (2) cleavage of the peptide bond. The formation of the gem-diol intermediate occurs with the barriers of 19.6 and 16.1 kcal/mol for the WT- and SW-substrate respectively. The QM/MM energetics predict that with the barriers of 21.9 and 17.2 kcal/mol for the WT- and SW-substrate respectively the cleavage of the peptide bond occurs in the rate-determining step. The computed barriers are in excellent agreement with the measured barrier of ∼18.0 kcal/mol for the SW-substrate and in line with the experimental observation that the cleavage of this substrate is sixty times more efficient than the WT-substrate.

Computational enzymology

Techniques for modelling enzyme-catalyzed reaction mechanisms are making increasingly important contributions to biochemistry. They can address fundamental questions in enzyme catalysis and have the potential to contribute to practical applications such as drug development.

Protonation states of the catalytic dyad of β-secretase (BACE1) in the presence of chemically diverse inhibitors: a molecular docking study

In this molecular docking study, the protonation states of the catalytic Asp dyad of the beta-secretase (BACE1) enzyme in the presence of eight chemically diverse inhibitors have been predicted. BACE1 catalyzes the rate-determining step in the generation of Alzheimer amyloid beta peptides and is widely considered as a promising therapeutic target. All the inhibitors were redocked into their corresponding X-ray structures using a combination of eight different protonation states of the Asp dyad for each inhibitor. Five inhibitors were primarily found to favor two different monoprotonated states, and the remaining three favor a dideprotonated state. In addition, five of them exhibited secondary preference for a diprotonated state. These results show that the knowledge of a single protonation state of the Asp dyad is not sufficient to search for the novel inhibitors of BACE1 and the most plausible state for each inhibitor must be determined prior to conducting in-silico screening.

Placevent: an algorithm for prediction of explicit solvent atom distribution-application to HIV-1 protease and F-ATP synthase

We have created a simple algorithm for automatically predicting the explicit solvent atom distribution of biomolecules. The explicit distribution is coerced from the three-dimensional (3D) continuous distribution resulting from a 3D reference interaction site model (3D-RISM) calculation. This procedure predicts optimal location of solvent molecules and ions given a rigid biomolecular structure and the solvent composition. We show examples of predicting water molecules near the KNI-272 bound form of HIV-1 protease and predicting both sodium ions and water molecules near the rotor ring of F-adenosine triphosphate (ATP) synthase. Our results give excellent agreement with experimental structure with an average prediction error of 0.39-0.65 Å. Further, unlike experimental methods, this method does not suffer from the partial occupancy limit. Our method can be performed directly on 3D-RISM output within minutes. It is extremely useful for examining multiple specific solvent-solute interactions, as a convenient method for generating initial solvent structures for molecular dynamics calculations, and may assist in refinement of experimental structures. © 2012 Wiley Periodicals, Inc.

Validating the vitality strategy for fighting drug resistance

The current challenge in designing effective drugs against HIV-1 is to find novel candidates with high potency, but with a lower susceptibility to mutations associated with drug resistance. Trying to address this challenge, we developed in our previous study (Ishikita and Warshel, Angew Chem Int Ed Engl 2008; 47:697-700) a novel computational strategy for fighting drug resistance by predicting the likely moves of the virus through constraints on binding and catalysis. This has been based on calculating the ratio between the vitality values ((K(i) k(cat)/K(M))(mutant)/(K(i) k(cat)/K(M))(wild-type)) and using it as a guide for predicting the moves of the virus. The corresponding calculations of the binding affinity, K(i), were carried out using the semi-macroscopic version of the protein dipole Langevin dipole (PDLD/S) in its linear response approximation (LRA) in its β version (PDLD/S-LRA/β). We also calculate the proteolytic efficiency, k(cat)/K(M), by evaluating the transition state (TS) binding free energies using the PDLD/S-LRA/β method. Here we provide an extensive validation of our strategy by calculating the vitality of six existing clinical and experimental drug candidates. It is found that the computationally determined vitalities correlate reasonably well with those derived from the corresponding experimental data. This indicates that the calculated vitality may be used to identify mutations that would be most effective for the survival of the virus. Thus, it should be possible to use our approach in screening for mutations that would provide the most effective resistance to any proposed antiviral drug. This ability should be very useful in guiding the design of drug molecules that will lead to the slowest resistance.

Computational insights into the development of novel therapeutic strategies for Alzheimer's disease

BACKGROUND

β-amyloidosis and oxidative stress have been implicated as root causes of Alzheimer's disease (AD). Current potential therapeutic strategies for the treatment of AD include inhibition of amyloid β (Aβ) production, stimulation of Aβ degradation and prevention of Aβ oligomerization. However, efforts in this direction are hindered by the lack of understanding of the biochemical processes occurring at the atomic level in AD.

DISCUSSION

A radically different approach to achieve this goal would be the application of comprehensive theoretical and computational techniques such as molecular dynamics, quantum mechanics, hybrid quantum mechanics/molecular mechanics, bioinformatics and rotational spectroscopy to investigate complex chemical and physical processes in β-amyloidosis and the oxidative stress mechanism.

CONCLUSION

Results obtained from these studies will provide an atomic level understanding of biochemical processes occurring in AD and advance efforts to develop effective therapeutic strategies for this disease.

Computational modeling of substrate specificity and catalysis of the β-secretase (BACE1) enzyme

In this combined MD simulation and DFT study, interactions of the wild-type (WT) amyloid precursor protein (APP) and its Swedish variant (SW), Lys670 → Asn and Met671 → Leu, with the beta-secretase (BACE1) enzyme and their cleavage mechanisms have been investigated. BACE1 catalyzes the rate-limiting step in the generation of 40-42 amino acid long Alzheimer amyloid beta (Aβ) peptides. All key structural parameters such as position of the flap, volume of the active site, electrostatic binding energy, structures, and positions of the inserts A, D, and F and 10s loop obtained from the MD simulations show that, in comparison to the WT-substrate, BACE1 exhibits greater affinity for the SW-substrate and orients it in a more reactive conformation. The enzyme-substrate models derived from the MD simulations were further utilized to investigate the general acid/base mechanism used by BACE1 to hydrolytically cleave these substrates. This mechanism proceeds through the following two steps: (1) formation of the gem-diol intermediate and (2) cleavage of the peptide bond. For the WT-substrate, the overall barrier of 22.4 kcal/mol for formation of the gem-diol intermediate is 3.3 kcal/mol higher than for the SW-substrate (19.1 kcal/mol). This process is found to be the rate-limiting in the entire mechanism. The computed barrier is in agreement with the measured barrier of ca. 18.00 kcal/mol for the WT-substrate and supports the experimental observation that the cleavage of the SW-substrate is 60 times more efficient than the WT-substrate.

Computational analysis of aspartic protease plasmepsin II complexed with EH58 inhibitor: a QM/MM MD study

Plasmepsin (PM) II is one of four enzymes in the food vacuole of Plasmodium falciparum. It has become an attractive target for combating malaria through research regarding its importance in the P. falciparum metabolism and life cycle, making it the target of choice for structure-based drug design. This paper reports the results of hybrid quantum mechanics / molecular mechanics (QM/MM) molecular dynamics (MD) simulations employed to study the details of the interactions established between PM II and N-(3-{(2-benzo[1, 3]dioxol-5-yl-ethyl)[3-(1-methyl-3-oxo-1,3-dihydro-isoindol-2-yl) propionyl]-amino}-1-benzyl-2-(hydroxyl-propyl)-4-benzyloxy-3,5dimethoxy-benzamide (EH58), a well-known potent inhibitor for this enzyme. Electrostatic binding free energy and energy terms decomposition have been computed for PM II complexed with the EH58 inhibitor. The results reveal that there is a strong interaction between Asp34, Val78, Ser79, Tyr192 and Asp214 residues and the EH58 inhibitor. In addition, we have computed the potential of the mean force (PMF) profile in order to assign the protonation state of the two catalytic aspartates in PM II-EH58 complex. The results indicate that the protonation of Asp214 favors a stable active site structure, which is consistent with our electrostatic binding free energy calculation and with previous published works.