Kirill Zinovjev

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

We present a combination of the string method and a path collective variable for the exploration of the free energy surface associated to a chemical reaction in condensed environments. The on-the-fly string method is employed to find the minimum free energy paths on a multidimensional free energy surface defined in terms of interatomic distances, which is a convenient selection to study bond forming/breaking processes. Once the paths have been determined, a reaction coordinate is defined as a measure of the advance of the system along these paths. This reaction coordinate can be then used to trace the reaction Potential of Mean Force from which the activation free energy can be obtained. This combination of methodologies has been here applied to the study, by means of Quantum Mechanics/Molecular Mechanics simulations, of the reaction catalyzed by guanidinoacetate methyltransferase. This enzyme catalyzes the methylation of guanidinoacetate by S-adenosyl-l-methionine, a reaction that involves a methyl transfer and a proton transfer and for which different reaction mechanisms have been proposed.

A Collective Coordinate to Obtain Free Energy Profiles for Complex Reactions in Condensed Phases.

Exploration of chemical reactions in complex explicit environments has become an affordable task with the use of hybrid quantum mechanics/molecular mechanics potentials which allow calculating free energy profiles of chemical reactions under the influence of the surroundings. Tracing these free energy profiles requires the selection of a reaction coordinate, which can be cumbersome for those processes involving more than a single chemical event in a concerted step. We here propose a collective coordinate to be used in the calculation of free energy profiles for complex reactions in condensed phases. This coordinate is based in the definition of the advance along a path introduced by Branduardi et al. (J. Chem. Phys.2007, 126, 054103) but modified to use internal coordinates which are more adequate for the description of chemical reactions. The coordinate is tested with the analysis of the isochorismate transformation to pyruvate and salycilate in aqueous solution and in the active site of PchB, a reaction that involves a CO bond breaking simultaneously with a proton transfer between two carbon atoms. The coordinate introduced here allows obtaining smooth and meaningful free energy profiles of the reaction.

Dynamics and Reactivity in Thermus aquaticus N6-Adenine Methyltransferase

M.TaqI is a DNA methyltransferase from Thermus aquaticus that catalyzes the transfer of a methyl group from S-adenosyl-L-methionine to the N6 position of an adenine, a process described only in prokaryotes. We have used full atomistic classical molecular dynamics simulations to explore the protein-SAM-DNA ternary complex where the target adenine is flipped out into the active site. Key protein-DNA interactions established by the target adenine in the active site are described in detail. The relaxed structure was used for a combined quantum mechanics/molecular mechanics exploration of the reaction mechanism using the string method. According to our free energy calculations the reaction takes place through a stepwise mechanism where the methyl transfer precedes the abstraction of the proton from the exocyclic amino group. The methyl transfer is the rate-determining step, and the obtained free energy barrier is in good agreement with the value derived from the experimental rate constant. Two possible candidates to extract the leftover proton have been explored: a water molecule found in the active site and Asn105, a residue activated by the hydrogen bonds formed through the amide hydrogens. The barrier for the proton abstraction is smaller when Asn105 acts as a base. The reaction mechanisms can be different in other N6-DNA-methyltransferases, as determined from the exploration of the reaction mechanism in the Asn105Asp M.TaqI mutant.

Linking Electrostatic Effects and Protein Motions in Enzymatic Catalysis. A Theoretical Analysis of Catechol O-Methyltransferase

The role of protein motions in enzymatic catalysis is the subject of a hot scientific debate. We here propose the use of an explicit solvent coordinate to analyze the impact of environmental motions during the reaction process. The example analyzed here is the reaction catalyzed by catechol O-methyltransferase, a methyl transfer reaction from S-adenosylmethionine (SAM) to the nucleophilic oxygen atom of catecholate. This reaction proceeds from a charged reactant to a neutral product, and then a large electrostatic coupling with the environment could be expected. By means of a two-dimensional free energy surface, we show that a large fraction of the environmental motions needed to attain the transition state happens during the first stages of the reaction because most of the environmental motions are slower than changes in the substrate. The incorporation of the solvent coordinate in the definition of the transition state improves the transmission coefficient and the committor histogram in solution, while the changes are much less significant in the enzyme. The equilibrium solvation approach seems then to work better in the enzyme than in aqueous solution because the enzyme provides a preorganized environment where the reaction takes place.

Dehydrochlorination of Hexachlorocyclohexanes Catalyzed by the LinA Dehydrohalogenase. A QM/MM Study.

The elucidation of the catalytic role of LinA dehydrohalogenase in the degradation processes of hexachlorocyclohexane (HCH) isomers is extremely important to further studies on the bioremediation of HCH polluted areas. Herein, QM/MM free energy simulations are employed to provide the details of the dehydrochlorination reaction of two HCH isomers (γ and β). In particular, the role of the protonation state of one of the catalytic residues-His73-is explored. Based on our calculations, two distinct minimum free energy pathways (concerted and stepwise) were found for γ-HCH and β-HCH. The choice of the reaction channel for the dehydrochlorination reactions of γ- and β-HCH was shown to depend on the initial mutual orientations of the reacting species in the active site and the protonation form of His73. The sequential pathway comprises the transfer of the proton (Hδ1) between His73 and Asp25 and subsequently the H1/Cl2 pair elimination from the substrate molecule. Within a concerted mechanism, the dehydrochlorination reaction of γ-/β-HCH is initiated with neutral His73 and the Hδ1 proton is transferred upon final product formation. We found that the concerted pathway for β-HCH results in significantly higher free energy of activation than the stepwise route and therefore can be disregarded as not a feasible mechanism. On the other hand, the reaction that occurs with much lower energetic barrier requires a stronger base (i.e., anionic His73) to abstract the proton (H1) from the substrate molecule. The presence of such transient form of His results in higher energy than the respective Michaelis complex and was observed only in the stepwise pathway for both isomers. Furthermore, we have concluded that both pathways (concerted and stepwise) are feasible for the dehydrochlorination reaction of γ-HCH. The activation free energies obtained from the M05-2X/6-31+G(d,p) corrected path coordinate PMF profiles for the dehydrochlorination reactions of the γ-/β-HCH are in good agreement with the experimental values.

Exploring chemical reactivity of complex systems with path‐based coordinates: Role of the distance metric

Path‐based reaction coordinates constitute a valuable tool for free‐energy calculations in complex processes. When a reference path is defined by means of collective variables, a nonconstant distance metric that incorporates the nonorthonormality of these variables should be taken into account. In this work, we show that, accounting for the correct metric tensor, these kind of variables can provide iso‐hypersurfaces that coincide with the iso‐committor surfaces and that activation free energies equal the value that would be obtained if the committor function itself were used as reaction coordinate. The advantages of the incorporation of the variable metric tensor are illustrated with the analysis of the enzymatic reaction catalyzed by isochorismate‐pyruvate lyase. Hybrid QM/MM techniques are used to obtain the free energy profile and to analyze reactive trajectories initiated at the transition state. For this example, the committor histogram is peaked at 0.5 only when a variable metric tensor is incorporated in the definition of the path‐based coordinate.

Transition state ensemble optimization for reactions of arbitrary complexity

In the present work, we use Variational Transition State Theory (VTST) to develop a practical method for transition state ensemble optimization by looking for an optimal hyperplanar dividing surface in a space of meaningful trial collective variables. These might be interatomic distances, angles, electrostatic potentials, etc. Restrained molecular dynamics simulations are used to obtain on-the-fly estimates of ensemble averages that guide the variations of the hyperplane maximizing the transmission coefficient. A central result of our work is an expression that quantitatively estimates the importance of the coordinates used for the localization of the transition state ensemble. Starting from an arbitrarily large set of trial coordinates, one can distinguish those that are indeed essential for the advance of the reaction. This facilitates the use of VTST as a practical theory to study reaction mechanisms of complex processes. The technique was applied to the reaction catalyzed by an isochorismate pyruvate lyase. This reaction involves two simultaneous chemical steps and has a shallow transition state region, making it challenging to define a good reaction coordinate. Nevertheless, the hyperplanar transition state optimized in the space of 18 geometrical coordinates provides a transmission coefficient of 0.8 and a committor histogram well-peaked about 0.5, proving the strength of the method. We have also tested the approach with the study of the NaCl dissociation in aqueous solution, a stringest test for a method based on transition state theory. We were able to find essential degrees of freedom consistent with the previous studies and to improve the transmission coefficient with respect to the value obtained using solely the NaCl distance as the reaction coordinate.

Reaction coordinates and transition states in enzymatic catalysis

Enzymatic reactions are complex chemical processes taking place in complex dynamic environments. Theoretical characterization of these reactions requires the determination of the reaction coordinate and the transition state ensemble. This is not an easy task because many degrees of freedom may be involved in principle. We present recent efforts to find good enzymatic reaction coordinates and the implications of these findings in the interpretation of enzymatic efficiency. In particular, we analyze different strategies based on the use of minimum free energy paths and direct localization of the dividing surface on multidimensional free energy surfaces. Another strategy is based on the generation of reactive trajectories, using the transition path sampling method, from which transition state configurations can be harvested. Most of the applications carried out until now coincide to stress the change in the nature of the reaction coordinate, in terms of the participation of the chemical and environmental degrees of freedom, as the reaction advances. The degrees of freedom of the chemical system are dominant at the transition state while environmental participation can be more important at early or late stages of the process. WIREs Comput Mol Sci 2018, 8:e1329. doi: 10.1002/wcms.1329

Adaptive Finite Temperature String Method in Collective Variables

Here we present a modified version of the on-the-fly string method for the localization of the minimum free energy path in a space of arbitrary collective variables. In the proposed approach the shape of the biasing potential is controlled by only two force constants, defining the width of the potential along the string and orthogonal to it. The force constants and the distribution of the string nodes are optimized during the simulation, improving the convergence. The optimized parameters can be used for umbrella sampling with a path CV along the converged string as the reaction coordinate. We test the new method with three fundamentally different processes: chloride attack to chloromethane in bulk water, alanine dipeptide isomerization, and the enzymatic conversion of isochorismate to piruvate. In each case the same set of parameters resulted in a rapidly converging simulation and a precise estimation of the potential of mean force. Therefore, the default settings can be used for a wide range of processes, making the method essentially parameter free and more user-friendly.

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.