Toward an Automatic Determination of Enzymatic Reaction Mechanisms and Their Activation Free Energies

Computational Investigation of the Covalent Inhibition Mechanism of Bruton's Tyrosine Kinase by Ibrutinib

Covalent inhibitors represent a promising class of therapeutic compounds. Nonetheless, rationally designing covalent inhibitors to achieve a right balance between selectivity and reactivity remains extremely challenging. To better understand the covalent binding mechanism, a computational study is carried out using the irreversible covalent inhibitor of Bruton tyrosine kinase (BTK) ibrutinib as an example. A multi-μs classical molecular dynamics trajectory of the unlinked inhibitor is generated to explore the fluctuations of the compound associated with the kinase binding pocket. Then, the reaction pathway leading to the formation of the covalent bond with the cysteine residue at position 481 via a Michael addition is determined using the string method in collective variables on the basis of hybrid quantum mechanical-molecular mechanical (QM/MM) simulations. The reaction pathway shows a strong correlation between the covalent bond formation and the protonation/deprotonation events taking place sequentially in the covalent inhibition reaction, consistent with a 3-step reaction with transient thiolate and enolates intermediate states. Two possible atomistic mechanisms affecting deprotonation/protonation events from the thiolate to the enolate intermediate were observed: a highly correlated direct pathway involving proton transfer to the Cα of the acrylamide warhead from the cysteine involving one or a few water molecules and a more indirect pathway involving a long-lived enolate intermediate state following the escape of the proton to the bulk solution. The results are compared with experiments by simulating the long-time kinetics of the reaction using kinetic modeling.

Molecular Mechanism of Labelling Functional Cysteines by Heterocyclic Thiones

Heterocyclic thiones have recently been identified as reversible covalent warheads, consistent with their mild electrophilic nature. Little is known so far about their mechanism of action in labelling nucleophilic sidechains, especially cysteines. The vast number of tractable cysteines promotes a wide range of target proteins to examine; however, our focus was put on functional cysteines. We chose the main protease of SARS-CoV-2 harboring Cys145 at the active site that is a structurally characterized and clinically validated target of covalent inhibitors. We screened an in-house, cysteine-targeting covalent inhibitor library which resulted in several covalent fragment hits with benzoxazole, benzothiazole and benzimidazole cores. Thione derivatives and Michael acceptors were selected for further investigations with the objective of exploring the mechanism of inhibition of the thiones and using the thoroughly characterized Michael acceptors for benchmarking our studies. Classical and hybrid quantum mechanical/molecular mechanical (QM/MM) molecular dynamics simulations were carried out that revealed a new mechanism of covalent cysteine labelling by thione derivatives, which was supported by QM and free energy calculations and by a wide range of experimental results. Our study shows that the molecular recognition step plays a crucial role in the overall binding of both sets of molecules.

Minimum Free Energy Pathways of Reactive Processes with Nudged Elastic Bands

The determination of minimum free energy pathways (MFEP) is one of the most widely used strategies to study reactive processes. For chemical reactions in complex environments, the combination of quantum mechanics (QM) with a molecular mechanics (MM) representation is usually necessary in a hybrid QM/MM framework. However, even within the QM/MM approximation, the affordable sampling of the phase space is, in general, quite restricted. To reduce drastically the computational cost of the simulations, several methods such as umbrella sampling require performing a priori a selection of a reaction coordinate. The quality of the computed results, in an affordable computational time, is intimately related to the reaction coordinate election which is, in general, a nontrivial task. In this work, we provide an approach to model reactive processes in complex environments that does not require the a priori selection of a reaction coordinate. The proposed methodology combines QM/MM simulations with an extrapolation of the nudged elastic bands (NEB) method to the free energy surface (FENEB). We present and apply our own FENEB scheme to optimize MFEP in different reactive processes, using QM/MM frameworks at semiempirical and density functional theory levels. Our implementation is based on performing the FENEB optimization by uncoupling the optimization of the band in a perpendicular and tangential direction. In each step, a full optimization with the spring force is performed, which guarantees that the images remain evenly distributed. The robustness of the method and the influence of sampling on the quality of the optimized MFEP and its associated free energy barrier are studied. We show that the FENEB method provides a good estimation of the reaction barrier even with relatively short simulation times, supporting that its combination with QM/MM frameworks provides an adequate tool to study chemical processes in complex environments.

Tautomer-Specific Deacylation and Ω-Loop Flexibility Explain the Carbapenem-Hydrolyzing Broad-Spectrum Activity of the KPC-2 β-Lactamase

KPC-2 (Klebsiella pneumoniae carbapenemase-2) is a globally disseminated serine-β-lactamase (SBL) responsible for extensive β-lactam antibiotic resistance in Gram-negative pathogens. SBLs inactivate β-lactams via a mechanism involving a hydrolytically labile covalent acyl-enzyme intermediate. Carbapenems, the most potent β-lactams, evade the activity of many SBLs by forming long-lived inhibitory acyl-enzymes; however, carbapenemases such as KPC-2 efficiently deacylate carbapenem acyl-enzymes. We present high-resolution (1.25-1.4 Å) crystal structures of KPC-2 acyl-enzymes with representative penicillins (ampicillin), cephalosporins (cefalothin), and carbapenems (imipenem, meropenem, and ertapenem) obtained utilizing an isosteric deacylation-deficient mutant (E166Q). The mobility of the Ω-loop (residues 165-170) negatively correlates with antibiotic turnover rates (kcat), highlighting the role of this region in positioning catalytic residues for efficient hydrolysis of different β-lactams. Carbapenem-derived acyl-enzyme structures reveal the predominance of the Δ1-(2R) imine rather than the Δ2 enamine tautomer. Quantum mechanics/molecular mechanics molecular dynamics simulations of KPC-2:meropenem acyl-enzyme deacylation used an adaptive string method to differentiate the reactivity of the two isomers. These identify the Δ1-(2R) isomer as having a significantly (7 kcal/mol) higher barrier than the Δ2 tautomer for the (rate-determining) formation of the tetrahedral deacylation intermediate. Deacylation is therefore likely to proceed predominantly from the Δ2, rather than the Δ1-(2R) acyl-enzyme, facilitated by tautomer-specific differences in hydrogen-bonding networks involving the carbapenem C-3 carboxylate and the deacylating water and stabilization by protonated N-4, accumulating a negative charge on the Δ2 enamine-derived oxyanion. Taken together, our data show how the flexible Ω-loop helps confer broad-spectrum activity upon KPC-2, while carbapenemase activity stems from efficient deacylation of the Δ2-enamine acyl-enzyme tautomer.

Finite temperature string method with umbrella sampling using path collective variables: application to secondary structure change in a protein

The transition of an α-helix to a β-sheet in proteins is among the most complex conformational changes seen in biomolecular systems. Due to long time scales involved in the transition, it is challenging to study such protein conformational changes using direct molecular dynamics simulations. This limitation is typically overcome using an indirect approach wherein one computes the free energy landscape associated with the transition. Computation of free energy landscapes, however, requires a suitable set of collective variables that describe the transition. In this work, we demonstrate the use of path collective variables [D. Branduardi, F. L. Gervasio and M. Parrinello, J. Chem. Phys., 2007, 126, 054103] and combine it with the finite temperature string (FTS) method [E. Weinan, W. Ren and E. Vanden-Eijnden, J. Phys. Chem. B, 2005, 109, 6688-6693] to determine the molecular mechanisms involved during the structural transition of the mini G-protein from an α-helix to a β-hairpin. The transition from the α-helix proceeds via unfolding of the terminal residues, giving rise to a β-turn unfolded intermediate to eventually form the β-hairpin. Our proposed algorithm uses umbrella sampling simulations to simulate images along the string and the weighted histogram analysis to compute the free energy along the computed transition path. This work demonstrates that the string method in combination with path collective variables can be exploited to study complex protein conformational changes such as a complete change in the secondary structure.

Reaction Path-Force Matching in Collective Variables: Determining Ab Initio QM/MM Free Energy Profiles by Fitting Mean Force

First-principles determination of free energy profiles for condensed-phase chemical reactions is hampered by the daunting costs associated with configurational sampling on ab initio quantum mechanical/molecular mechanical (AI/MM) potential energy surfaces. Here, we report a new method that enables efficient AI/MM free energy simulations through mean force fitting. In this method, a free energy path in collective variables (CVs) is first determined on an efficient reactive aiding potential. Based on the configurations sampled along the free energy path, correcting forces to reproduce the AI/MM forces on the CVs are determined through force matching. The AI/MM free energy profile is then predicted from simulations on the aiding potential in conjunction with the correcting forces. Such cycles of correction-prediction are repeated until convergence is established. As the instantaneous forces on the CVs sampled in equilibrium ensembles along the free energy path are fitted, this procedure faithfully restores the target free energy profile by reproducing the free energy mean forces. Due to its close connection with the reaction path-force matching (RP-FM) framework recently introduced by us, we designate the new method as RP-FM in collective variables (RP-FM-CV). We demonstrate the effectiveness of this method on a type-II solution-phase SN2 reaction, NH3 + CH3Cl (the Menshutkin reaction), simulated with an explicit water solvent. To obtain the AI/MM free energy profiles, we employed the semiempirical AM1/MM Hamiltonian as the base level for determining the string minimum free energy pathway, along which the free energy mean forces are fitted to various target AI/MM levels using the Hartree-Fock (HF) theory, density functional theory (DFT), and the second-order Møller-Plesset perturbation (MP2) theory as the AI method. The forces on the bond-breaking and bond-forming CVs at both the base and target levels are obtained by force transformation from Cartesian to redundant internal coordinates under the Wilson B-matrix formalism, where the linearized FM is facilitated by the use of spline functions. For the Menshutkin reaction tested, our FM treatment greatly reduces the deviations on the CV forces, originally in the range of 12-33 to ∼2 kcal/mol/Å. Comparisons with the experimental and benchmark AI/MM results, tests of the new method under a variety of simulation protocols, and analyses of the solute-solvent radial distribution functions suggest that RP-FM-CV can be used as an efficient, accurate, and robust method for simulating solution-phase chemical reactions.

Studying the phosphoryl transfer mechanism of the E. coli phosphofructokinase-2: from X-ray structure to quantum mechanics/molecular mechanics simulations

Phosphofructokinases catalyze the ATP-dependent phosphorylation of fructose-6-phosphate and they are highly regulated.

Phosphofructokinases (Pfks) catalyze the ATP-dependent phosphorylation of fructose-6-phosphate (F6P) and they are regulated in a wide variety of organisms. Although numerous aspects of the kinetics and regulation have been characterized for Pfks, the knowledge about the mechanism of the phosphoryl transfer reaction and the transition state lags behind. In this work, we describe the X-ray crystal structure of the homodimeric Pfk-2 from E. coli, which contains products in one site and reactants in the other, as well as an additional ATP molecule in the inhibitory allosteric site adjacent to the reactants. This complex was previously predicted when studying the kinetic mechanism of ATP inhibition. After removing the allosteric ATP, molecular dynamic (MD) simulations revealed conformational changes related to domain packing, as well as stable interactions of Lys27 and Asp256 with donor (ATP) and acceptor (fructose-6-) groups, and of Asp166 with Mg²⁺. The phosphoryl transfer reaction mechanism catalyzed by Pfk-2 was investigated through Quantum Mechanics/Molecular Mechanics (QM/MM) simulations using a combination of the string method and a path-collective variable for the exploration of its free energy surface. The calculated activation free energies showed that a dissociative mechanism, occurring with a metaphosphate intermediate formation followed by a proton transfer to Asp256, is more favorable than an associative one. The structural analysis reveals the role of Asp256 acting as a catalytic base and Lys27 stabilizing the transition state of the dissociative mechanism.

Mapping Free Energy Pathways for ATP Hydrolysis in the E. coli ABC Transporter HlyB by the String Method

HlyB functions as an adenosine triphosphate (ATP)-binding cassette (ABC) transporter that enables bacteria to secrete toxins at the expense of ATP hydrolysis. Our previous work, based on potential energy profiles from combined quantum mechanical and molecular mechanical (QM/MM) calculations, has suggested that the highly conserved H-loop His residue H662 in the nucleotide binding domain (NBD) of E. coli HlyB may catalyze the hydrolysis of ATP through proton relay. To further test this hypothesis when entropic contributions are taken into account, we obtained QM/MM minimum free energy paths (MFEPs) for the HlyB reaction, making use of the string method in collective variables. The free energy profiles along the MFEPs confirm the direct participation of H662 in catalysis. The MFEP simulations of HlyB also reveal an intimate coupling between the chemical steps and a local protein conformational change involving the signature-loop residue S607, which may serve a catalytic role similar to an Arg-finger motif in many ATPases and GTPases in stabilizing the phosphoryl-transfer transition state.

Measurement and Prediction of Chlorine Kinetic Isotope Effects in Enzymatic Systems

Approaches to determine chlorine kinetic isotope effects (Cl-KIEs) on enzymatic dehalogenations are discussed and illustrated by representative examples. Three aspects are considered. First methodology for experimental measurement of Cl-KIEs, with stress being on FAB-IRMS technique developed in our laboratory, is described. Subsequently, we concentrate our discussion on the consequences of reaction complexity in the interpretation of experimental values, a problem especially important in cases of polychlorinated reactants. The most fruitful studies of enzymatic dehalogenations by Cl-KIEs require their theoretical evaluation, hence the computational focus of the second part of this chapter.

Thermal Isomerization Mechanism in Dronpa and Its Mutants

The photoswitching speed of the reversibly switchable fluorescent proteins (RSFPs) from the family of green fluorescent proteins (GFPs) changes upon mutation which is of direct importance for various high-resolution techniques. Dronpa is one of the most used RSFPs. Its point mutants rsFastLime (Dronpa V157G) and rsKame (Dronpa V157L) exhibit a striking difference in their photoswitching speed. Here the QM/MM on-the-fly string method is used in order to explore the details of the thermal isomerization mechanism. The four principal ways in which isomerization may occur have been scrutinized for each of the three proteins. It has been shown that thermal isomerization occurs via a one-bond-flip mechanism in all three proteins, although, in rsKame, where the chromophore is constrained more, the activation free energy difference between hula-twist and one-bond-flip is significantly smaller. Functional mode analysis has been applied to examine the motions of the amino acids during the isomerization. It clearly identifies the importance of Val/Leu 157 as well as the amino acids in the α-helix during the isomerization.

Generalized Ensemble Sampling of Enzyme Reaction Free Energy Pathways

Free energy path sampling plays an essential role in computational understanding of chemical reactions, particularly those occurring in enzymatic environments. Among a variety of molecular dynamics simulation approaches, the generalized ensemble sampling strategy is uniquely attractive for the fact that it not only can enhance the sampling of rare chemical events but also can naturally ensure consistent exploration of environmental degrees of freedom. In this review, we plan to provide a tutorial-like tour on an emerging topic: generalized ensemble sampling of enzyme reaction free energy path. The discussion is largely focused on our own studies, particularly ones based on the metadynamics free energy sampling method and the on-the-path random walk path sampling method. We hope that this minipresentation will provide interested practitioners some meaningful guidance for future algorithm formulation and application study.

Molecular simulation of homogeneous nucleation of crystals of an ionic liquid from the melt

The homogeneous nucleation of crystals of the ionic liquid [dmim(+)][Cl(-)] from its supercooled liquid phase in the bulk (P = 1 bar, T = 340 K, representing a supercooling of 58 K) was studied using molecular simulations. The string method in collective variables [Maragliano et al., J. Chem. Phys. 125, 024106 (2006)] was used in combination with Markovian milestoning with Voronoi tessellations [Maragliano et al., J. Chem. Theory Comput. 5, 2589-2594 (2009)] and order parameters for molecular crystals [E. E. Santiso and B. L. Trout, J. Chem. Phys. 134, 064109 (2011)] to sketch a minimum free energy path connecting the supercooled liquid and the monoclinic crystal phases, and to determine the free energy and the rates involved in the homogeneous nucleation process. The physical significance of the configurations found along this minimum free energy path is discussed with the help of calculations based on classical nucleation theory and with additional simulation results obtained for a larger system. Our results indicate that, at a supercooling of 58 K, the liquid has to overcome a free energy barrier of the order of 60 kcal/mol and to form a critical nucleus with an average size of about 3.6 nm, before it reaches the thermodynamically stable crystal phase. A simulated homogeneous nucleation rate of 5.0 × 10(10) cm(-3) s(-1) was obtained for our system, which is in reasonable agreement with experimental and simulation rates for homogeneous nucleation of ice at similar degrees of supercooling. This study represents our first step in a series of studies aimed at understanding the nucleation and growth of crystals of organic salts near surfaces and inside nanopores.

Extended Phase-Space Methods for Enhanced Sampling in Molecular Simulations: A Review

Molecular Dynamics simulations are a powerful approach to study biomolecular conformational changes or protein-ligand, protein-protein, and protein-DNA/RNA interactions. Straightforward applications, however, are often hampered by incomplete sampling, since in a typical simulated trajectory the system will spend most of its time trapped by high energy barriers in restricted regions of the configuration space. Over the years, several techniques have been designed to overcome this problem and enhance space sampling. Here, we review a class of methods that rely on the idea of extending the set of dynamical variables of the system by adding extra ones associated to functions describing the process under study. In particular, we illustrate the Temperature Accelerated Molecular Dynamics (TAMD), Logarithmic Mean Force Dynamics (LogMFD), and Multiscale Enhanced Sampling (MSES) algorithms. We also discuss combinations with techniques for searching reaction paths. We show the advantages presented by this approach and how it allows to quickly sample important regions of the free-energy landscape via automatic exploration.

Understanding DNA under oxidative stress and sensitization: the role of molecular modeling

DNA is constantly exposed to damaging threats coming from oxidative stress, i.e., from the presence of free radicals and reactive oxygen species. Sensitization from exogenous and endogenous compounds that strongly enhance the frequency of light-induced lesions also plays an important role. The experimental determination of DNA lesions, though a difficult subject, is somehow well established and allows to elucidate even extremely rare DNA lesions. In parallel, molecular modeling has become fundamental to clearly understand the fine mechanisms related to DNA defects induction. Indeed, it offers an unprecedented possibility to get access to an atomistic or even electronic resolution. Ab initio molecular dynamics may also describe the time-evolution of the molecular system and its reactivity. Yet the modeling of DNA (photo-)reactions does necessitate elaborate multi-scale methodologies to tackle a damage induction reactivity that takes place in a complex environment. The double-stranded DNA environment is first characterized by a very high flexibility, but also a strongly inhomogeneous electrostatic embedding. Additionally, one aims at capturing more subtle effects, such as the sequence selectivity which is of critical important for DNA damage. The structure and dynamics of the DNA/sensitizers complexes, as well as the photo-induced electron- and energy-transfer phenomena taking place upon sensitization, should be carefully modeled. Finally the factors inducing different repair ratios for different lesions should also be rationalized. In this review we will critically analyze the different computational strategies used to model DNA lesions. A clear picture of the complex interplay between reactivity and structural factors will be sketched. The use of proper multi-scale modeling leads to the in-depth comprehension of DNA lesions mechanisms and also to the rational design of new chemo-therapeutic agents.

Atomic-resolution dissection of the energetics and mechanism of isomerization of hydrated ATP-Mg(2+) through the SOMA string method

The atomic mechanisms of isomerization of ATP-Mg(2+) in solution are characterized using the recently developed String Method with Optimal Molecular Alignment (SOMA) and molecular-dynamics simulations. Bias-Exchange Metadynamics simulations are first performed to identify the primary conformers of the ATP-Mg(2+) complex and their connectivity. SOMA is then used to elucidate the minimum free-energy path (MFEP) for each transition, in a 48-dimensional space. Analysis of the per-atom contributions to the global free-energy profiles reveals that the mechanism of these transitions is controlled by the Mg(2+) ion and its coordinating oxygen atoms in the triphosphate moiety, as well as by the ion-hydration shell. Metadynamics simulations in path collective variables based on the MFEP demonstrate these isomerizations proceed across a narrow channel of configurational space, thus validating the premise underlying SOMA. This study provides a roadmap for the examination of conformational changes in biomolecules, based on complementary enhanced-sampling techniques with different strengths. © 2015 Wiley Periodicals, Inc.

Challenges in computational studies of enzyme structure, function and dynamics

In this review we give an overview of the field of Computational enzymology. We start by describing the birth of the field, with emphasis on the work of the 2013 chemistry Nobel Laureates. We then present key features of the state-of-the-art in the field, showing what theory, accompanied by experiments, has taught us so far about enzymes. We also briefly describe computational methods, such as quantum mechanics-molecular mechanics approaches, reaction coordinate treatment, and free energy simulation approaches. We finalize by discussing open questions and challenges.

Heavy enzymes--experimental and computational insights in enzyme dynamics

The role of protein motions in the chemical step of enzyme-catalyzed reactions is the subject of an open debate in the scientific literature. The systematic use of isotopically substituted enzymes has been revealed as a useful tool to quantify the role of these motions. According to the Born-Oppenheimer approximation, changing the mass of the protein does not change the forces acting on the system but alters the frequencies of the protein motions, which in turn can affect the rate constant. Experimental and theoretical studies carried out in this field are presented in this article and discussed in the framework of Transition State Theory.