D Kinetic Isotope Effect in

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Path Integral Simulation of the H/D Kinetic Isotope Effect in Monoamine Oxidase B Catalyzed Decomposition of Dopamine Janez Mavri, Ricardo A. Matute, Zhen T. Chu, and Robert Vianello J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.6b00894 • Publication Date (Web): 24 Mar 2016 Downloaded from http://pubs.acs.org on March 26, 2016

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The Journal of Physical Chemistry

Path Integral Simulation of the H/D Kinetic Isotope Effect in Monoamine Oxidase B Catalyzed Decomposition of Dopamine Janez Mavri,1* Ricardo A. Matute,2 Zhen T. Chu2 and Robert Vianello3 1

Laboratory for Biocomputing and Bioinformatics, National Institute of Chemistry, Hajdrihova

19, SI–1000 Ljubljana, Slovenia. 2

University of Southern California, Department of Chemistry SGM 418, 3620 McClintock

Avenue Los Angeles, CA 90089-1062, U.S.A. 3

Computational Organic Chemistry and Biochemistry Group, Ruđer Bošković Institute,

Bijenička 54, HR–10000 Zagreb, Croatia

Corresponding Author * [email protected]

ACS Paragon Plus Environment

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ABSTRACT

Brain monoamines regulate many centrally mediated body functions, and can cause adverse symptoms when they are out of balance. A starting point to address challenges raised by the increasing burden of brain diseases is to understand, at atomistic level, the catalytic mechanism of an essential amine metabolic enzyme - monoamine oxidase B (MAO B). Recently we demonstrated that the rate-limiting step of MAO B catalyzed conversion of amines into imines represents the hydride anion transfer from the substrate α–CH2 group to the N5 atom of the flavin co-factor moiety. In this article we simulated for MAO B catalyzed dopamine decomposition the effects of nuclear tunneling by the calculation of the H/D kinetic isotope effect. We applied path integral quantization of the nuclear motion for the methylene group and the N5 atom of the flavin moiety in conjunction with the QM/MM treatment on the Empirical Valence Bond (EVB) level for the rest of the enzyme. The calculated H/D kinetic isotope effect of 12.8 ± 0.3 is in a reasonable agreement with the available experimental data for closely related biogenic amines, which gives strong support for the proposed hydride mechanism. The results are discussed in the context of tunneling in enzyme centers and advent of deuterated drugs into clinical practice.


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INTRODUCTION Biogenic amines are an important group of naturally occurring biologically active compounds, most of which act as neurotransmitters – endogenous chemicals that allow the transmission of signals from a neuron to target cells across synapses. There are five established amine neurotransmitters: the three catecholamines (dopamine, noradrenaline and adrenaline), and histamine and serotonin. These substances are active in regulating many centrally mediated body functions, including behavioral, cognitive, motor and endocrine processes, and can cause adverse symptoms when they are out of balance.1 Dopamine represents one of the most physiologically important biogenic amines and regulation of its level in the central nervous system is prerequisite for homeostasis. An essential enzyme for the maintenance of dopamine level is monoamine oxidase B (MAO B), which is a mitochondrial outer membrane-bound flavoenzyme that catalyzes the oxidative deamination of a broad range of biogenic and dietary amines into their corresponding imines, thus playing a critical role in the degradation of monoamine neurotransmitters in the central and peripheral nervous systems.2 The chemical mechanism of the reductive half-reaction of flavoprotein amine oxidases has been the source of controversy and debate.3–6 Several different mechanisms have been proposed that differ in the nature of the hydrogen atom that is transferred in the rate limiting step from the substrate α–CH2 group to the N5 atom of the flavin co-factor moiety. Radical mechanism7 involving the transfer of the hydrogen atom seems to be less probable because of the lack of both the paramagnetic resonance signal and the influence of the magnetic field on the reaction rate constant.8,9 In the polar nucleophilic mechanism the substrate amino group nitrogen atom forms a covalent adduct with the C4a atom of the flavin moiety, substantial electron transfer from the substrate to the flavin moiety takes place, and proton transfer follows.3,8,10 Kästner and coworkers have shown by


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QM/MM calculations on the DFT level that the electron transfer event critically depends on the the amino group nitrogen atom–C4a distance, associated susbtrate-flavin orientation and polarization effects of the enzyme environment;11,12 however these authors failed to provide firm evidence for the substrate-flavin adduct formation, which was proposes to facilitate the proton transfer. Moreover, in agreement with our previous results,13 Kästner and coworkers have clearly demonstrated that the barrier for protonated substrate is too high to contribute to kinetics, and they proposed that the reaction mechanism is not a textbook polar nucleophilic mechanism since it involves substantial hydride transfer character. Hydride transfer seems to be the most plausible choice for MAO mechanism.14–16 Please note that formally hydride transfer mechanism means concerted transfer of electron lone pair and proton transfer.

Scheme 1. Complete two-step mechanism for MAO catalyzed amine degradation. The first step involves H– abstraction from the substrate to form the flavin(N5)–substrate(α–C) adduct, which then decomposes to the final products, namely neutral imine and fully reduced flavin, FADH2, a reaction promoted by amine deprotonation facilitated by two water molecules.


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Recently we have shown by quantum chemical calculations17 and multiscale simulations18 that the rate-limiting step in MAO catalysis involves a hydride ion transfer from the substrate α– methylene group to the flavin N5 atom (Scheme 1). The latter scheme within the Empirical Valence Bond QM/MM methodology gave the calculated activation free energy for the MAO B catalyzed degradation of dopamine of ∆G‡ = 16.1 kcal/mol,18 being in excellent agreement with the available experimental value of 16.5 kcal/mol,5 thus providing a strong support for our mechanistic picture. The present article focuses on the utilization of the path integration quantized motion of the nuclear motion in order to elucidate the H/D isotope effect on the MAO B catalytic mechanism, thus providing further arguments in favor of the hydride transfer. The quantum-mechanical nature of nuclei motion in chemical reactions is experimentally evident in kinetic isotope effect (KIE) that is, by definition, the ratio of the rate constants for the species involving various isotopomers. The most pronounced are always the KIE values involving H/D isotopes, because of the relative differences in masses among the corresponding isotopes. The rate limiting step of MAO catalyzed reaction involves a hydride transfer and, as a light particle, its motion obeys the laws of quantum rather than classical mechanics. Tunneling in MAO-catalyzed reactions was addressed by several experimental studies. Husain and coworkers19 studied bovine liver MAO B with benzylamine and deduced kinetic parameters spectrophotometrically from UV/VIS detection of an aldehyde signal as a function of time at 25oC. The H/D KIE turned out to be dependent on the oxygen level, and, under the oxygen and benzylamine saturation, the observed H/D KIE was 6.4–6.7, while at low oxygen levels the value increased to 8.7. Following from this, Walker and Edmondson5 applied advanced data processing techniques to study a series of para and meta substituted benzylamines with bovine MAO B at 25°C. The H/D KIE value for unsubstituted benzylamine was between 8.2–10.1, depending on


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the level of oxygen, while for substituted derivatives, the H/D KIE values ranged between 6.5 for p-Br substitution and 14.1 for m-Cl derivative. For the recombinant human liver MAO A with para-substituted benzylamines, Miller and Edmondson8 reported H/D KIE values in the range of 6–13. Scrutton and co-workers studied pH dependence of KIE in recombinant human liver MAO A with benzylamine and the value decreases from approximately 13 to 8 with increasing pH value.20 Such significant pH dependence of H/D KIE values strongly supports the idea that only the neutral substrate will enter the reaction. Wang and Edmondson addressed tunneling in a rat MAO A for a series of para-substituted benzylamines,6 and concluded that the H/D KIE values are pH–independent and range from 7 to 14, demonstrating a rate-limiting α–CH bond cleavage step in catalysis. Unfortunately, no experimental data are available for dopamine in any of the mentioned studies. Since for MAO B the rate constant depends on the oxygen level this gives strong evidence that at low oxygen levels the rate constant is controlled or is at least comparable with flavin regeneration rather than by C–H bond cleavage. Therefore at low oxygen levels the observed H/D kinetic isotope effect is masked by flavin regeneration. The pH dependence adds additional complexity. Please note that for MAO A, the flavin regeneration if never the ratelimiting step. The above survey of H/D KIE in MAO at high oxygen levels gives some evidence that the value for the MAO B catalyzed dopamine decomposition should be around 10. In this article we report the results of the path integration calculated H/D kinetic isotope effect of the rate-limiting step of dopamine decomposition catalyzed by MAO B. We used multiscale approach in the framework of Empirical Valence Bond, while quantization of nuclear motion was performed by quantum classical path method. We decided to proceed with dopamine, because of its immense importance in neuroscience and because we have developed simulation protocol for this reaction for classical treatment of nuclear motion.


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CALCULATION DETAILS In order to calculate the H/D kinetic isotope effect it is necessary to quantize nuclear motion for few relevant atoms, while keeping for the rest of the systems classical description of nuclear motion. Path integration was employed on the full enzyme dimensionality in the form of quantum classical path (QCP) method with an EVB potential energy surface.21 The QCP approach is based on the isomorphism between the nuclear wave-function and the ring of quasiparticles that are propagated on the "quantum mechanical" potential Uqm. The quantum mechanical free-energy barrier is calculated using the following potential:

=

1 1 + 2

Here ∆xk = xk+1 – xk, where xp+1 = x1. The last equality ensures that the necklace is closed. Moreover, Ω = p / ħ·β, while M is the mass of the quantum atom, where U is the actual potential used in the simulation. The total quantum mechanical partition function can then be obtained by running classical trajectories of the quasiparticles with the potential Uqm and β = 1 / kB·T. The probability of being at the transition state is approximated by a probability distribution of the center of mass of the quasiparticles (the centroid) rather than the classical single point. At the temperature values approaching zero, the quantum correction to free energy reduces to the contribution of the zeroth vibrational level and matches the zero point energy. At the finite temperature values contributions from all the excited states are included. Traditional "on-the-fly" path integral simulations are demanding because of the poor equilibration between quantum and classical particles. The QCP approach offers an effective and rather simple way to overcome this problem by propagating classical trajectories on the classical potential energy surface of the reacting system and using the atom positions to generate the centroid position for the quantum


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mechanical partition function. This treatment is based on the finding that the quantum mechanical partition function can be expressed as: ̅ = ̅ 〈〈 − − ̅ 〉" 〉#

〈L〉 fp where x is the centroid position, designates an average over the free particle quantum

mechanical distribution obtained with the implicit constraint that x coincides with the current position of the corresponding classical particle, and 〈L〉 U designates an average over the classical potential U. The quantum mechanical free energy correction calculated from the partition function reads AQM = –1 / βln(Z). We applied the same simulation parameters as in previous EVB calculations of the reaction profile for dopamine decomposition catalyzed by MAO B.18 The EVB region is electronically polarizable since the atomic charges of polar enzyme environment are included into the Hamiltonian and the atomic charges of the EVB region change. In this respect, the full dimensionality of the enzyme was included. The EVB region consisted of lumiflavin moiety and dopamine (FAD and dopamine in the enzyme), see Figure 1. The system was solvated in a spherical water droplet with a radius of 20 Å (centered in the reactive region) subject to surfaceconstrained all-atom solvent (SCAAS) boundary conditions.22 The spherical droplet was embedded in a 3 Å cubic grid of Langevin dipoles with a radius of 22 Å, which was in turn placed in a continuum with the dielectric constant of water. A cut-off of 10 Å was used for protein-protein interactions and the local reaction field was applied for the long range interactions beyond the 10 Å. A cut-off of 22 Å was used for EVB region-protein and EVB region-water interactions. The system was subsequently relaxed with a time step size of 1 fs and


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gradually heated for 50 ps at 30 K, 100 ps at 100 K and 500 ps at 300 K. The system obtained in that way was relaxed, what we have seen from system potential energy that was fluctuating around a stable low level, not getting lower any more. The system was mutated from a reactant to product diabatic states in 51 mapping frames, each consisting of a molecular dynamics simulation of 30 ps, using a 1 fs time step, for a total simulation time of 1.53 ns. The EVB simulation of the reactive trajectory was performed 10 times starting from different initial configurations, giving rise to eight independent free energy profiles. All EVB calculations were performed using the standard EVB free energy perturbation/umbrella sampling (EVB– FEP/US) procedure23 and the MOLARIS simulation package in combination with the ENZYMIX force field. The reactant and the transition state structures were generated by performing simulation with fixed value of EVB coupling parameter λ of 0.0 and 0.48. respectively. In order to calculate the H/D kinetic isotope effect it is enough to evaluate the nuclear quantum mechanical correction to the activation free energy for the ensemble of structures corresponding to the transition state and the reactant minimum. Simulations are performed for H and D, respectively. Since the deuterium wave function is more delocalized for hydrogen than for deuterium, the corresponding AQM values are different. The procedure was as follows: Initially, we used exactly the same protocol as for calculation of the reaction profile with the classical treatment, followed by running additional 600 ps of MD simulation at the reactant and transition states. We quantized nuclear motion for the dopamine methylene group next to the amino group and the N5 atom of the flavin moiety using 18 beads (see Figure 1). In this way, the motion of four atoms was quantized corresponding to 12 degrees of freedom. 100 ps of QCP simulation were performed both for H and D derivatives. When performing calculations for the D isotopomer, both hydrogen atoms of the methylene group were replaced by D in order to facilitate comparison


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with the experiment. The error was estimated as standard deviation by using 8 different starting points that were 1 ps apart.

Figure 1. Structure of MAO B active site with neutral dopamine. The active site aromatic tyrosine residues are shown in brown gray, while for FAD prosthetic group and dopamine atom specific coloring is applied. Atom motion for the flavin N5 atom and the dopamine α–methylene group was quantized by QCP approach and those atoms are labeled light green.

RESULTS AND DISCUSSION The values along with the formula for the calculation of the KIE are collected in Table 1. Our computational strategy evaluates the relevant nuclear quantum corrections and gives the average H/D kinetic isotope effect of 12.8 ± 0.3, being in reasonable agreement with the experimental values in the range of 6.4–14.1 for MAO B with structurally related benzylamines.5 The calculated H/D KIE gives additional very strong evidence that MAO enzymes operate through


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our hydride transfer mechanism (Scheme 1).17,18 The H/D KIE values for the enzymes where the contribution to the rate constant comes only from the zero point energy of the reactant well are between 3–8. The elevated value for MAO B indicates that non-negligible contribution comes from the tunneling effects. Our calculations showed once more that the QCP approach is a reliable computational tool for determining the quantum mechanical contributions to the activation free energies even in the case when significant tunneling contributions to the rate constant are present. The value of H/D kinetic isotope effect of 12.8 ± 0.3 indicates that, in addition to zero point correction, some contribution from tunneling through the barrier is present. Kästner and coworkers calculated H/D KIE for benzylamine decomposition catalyzed by MAO B.11,12 H/D KIE was calculated by diagonalizing mass weighted Hessian for reactant well and transition state, respectively by considering DFT described reactive QM part of the system. Zero point energy corrections were calculated for both isotopomers. The “through the barriers” contribution to tunneling was calculated by one-dimensional Eckart model allowing for the analytical solution. The authors obtained for the lowest barrier conformation H/D KIE value of 3.5, while for three others conformations the values 2.4, 2.7 and 3.7 were reported. We feel that the H/D KIE value reported by Kästner and coworkers represents the lower limit, since it did not include anharmonicities of the vibrational modes associated with the reaction.


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Table 1. Calculation of H/D kinetic isotope effect for MAO B catalyzed decomposition of dopamine. Please note that we quantized motion of the dopamine methylene group vicinal to the amino group and N5 atom of lumiflavin. Given are nuclear quantum corrections to free energy for reactants (RS) for species with hydrogen (H) and deuterium (D) and the corresponding values for the transition state (TS). All free energy corrections are given in kcal/mol. The kinetic isotope effect is calculated via the difference in free energy of activation for species involving D and H and by assumption of the transition state theory validity. H/DKIE= e [TS(D)-R(D) - (TS(H)R(H)]/k T B .

The value of kBT at room temperature is 0.59kcal/mol. Reactants H

D

Transition state

H/D KIE

H

D

11.89 8.36

3.94

1.90

12.50

11.89 8.35

3.94

1.90

12.71

11.90 8.35

3.93

1.90

13.15

11.89 8.35

3.94

1.89

12.50

11.88 8.33

3.97

1.93

12.93

11.87 8.33

3.99

1.95

12.71

11.88 8.34

4.05

2.01

12.71

11.88 8.34

4.03

2.02

13.37 a

a

Mean value of

H/D

12.8 ± 0.3

KIE was calculated as an average over eight starting points with the value of 12.8 with

standard deviation of 0.3 that is a measure of uncertainty.

As shown by Warshel and co-workers the origin of enzyme catalysis dominantly emerges from preorganized electrostatics.24 It is worth to stress that nuclear tunneling in MAO B most probably does not contribute to catalysis since the same effects are present in the reference


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reaction in solution, as was shown in the case of lipoxygenase with the spectacular isotope effect of 81. It remains, however, a challenge to find an enzymatic reaction where tunneling contributes to catalysis. Decomposition of dopamine perdeuterated isotopomer is 12.8 times slower than of H isotopomer, giving rise to one order of magnitude slower metabolism and significantly elongated clearance time for D isotopomers. In the present case it would be worth to think about the treatment of Parkinson disease by the administration of the dopamine precursor (per)deuterated L-dopa25,26 that should give rise to significantly prolonged pharmacokinetics. With the advent of deuterated drug isotopomers27 the need for advanced methods for the quantization of nuclear motion in the context of computational support of pharmacokinetics and pharmacodynamics will emerge. In line with previous reports, this work demonstrates that QCP is a robust and practical method of choice for the simulation of H/D kinetic isotope effects,28–30 and provides convincing piece of evidence that MAO catalysis involves that abstraction of the hydride anion from the substrate in the rate limiting step. In long terms, this work will help in the design of novel and improved MAO B inhibitors2,31 as transition-state analogues for antiparkinsonian and neuroprotective use.32

AUTHOR INFORMATION Notes The authors declare no competing financial interests.


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ACKNOWLEDGMENT We would like to thank Prof. Arieh Warshel (University of Southern California, USA) and Prof. Lynn Kamerlin (University of Uppsala, Sweden) for many stimulating discussions concerning multiscale modeling of enzyme reactions. We would like to thank Dr. Matej Repič and Ms. Aleksandra Maršavelski for the design of graphical content. R. V. gratefully acknowledges the European Commission for an individual FP7 Marie Curie Career Integration Grant (contract number PCIG12–GA–2012–334493). J. M. would like to thank the Slovenian Research Agency for the financial support in the framework of the programme group P1–0012. Part of this work was supported by the COST Action CM1103.


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(22) Warshel, A.; King, G. Polarization Constraints in Molecular Dynamics Simulation of Aqueous Solutions: The Surface Constraint All Atom Solvent (SCAAS) Model. Chem. Phys. Lett. 1985, 121, 124–129. (23) Kamerlin, S. C. L.; Warshel, A. The Empirical Valence Bond Model: Theory and Applications. WIREs Comput. Mol. Sci. 2011, 1, 30–45. (24) Olsson, M. H. M.; Siegbahn, P. E. M.; Warshel, A. Simulations of the Large Kinetic Isotope Effect and the Temperature Dependence of the Hydrogen Atom Transfer in Lipoxygenase. J. Am. Chem. Soc. 2004, 126, 2820–2828 (25) Nagatsua, T.; Sawada, M. L-dopa therapy for Parkinson's disease: Past, present, and future. Parkinsonism Rel. Disord. 2009, 15, S3–S1. (26) Biagio Mercuri, N.; Bernardi, G. The "magic" of L-dopa: why is it the gold standard Parkinson's disease therapy? Trends Pharmacol. Sci. 2005, 26, 341–344. (27) Katsnelson, A. Heavy Drugs Draw Heavy Interest from Pharma Backers. Nat. Med. 2013, 19, 656. (28) Olsson, M. H. M.; Mavri, J.; Warshel, A. Transition State Theory Can Be Used in Studies of Enzyme Catalysis – Lessons From Simulation of Tunneling in Lipoxygenase and Other Systems. Phil. Trans. Roy. Soc. B 2006, 361, 1417–1432. (29) Braun-Sand, S.; Olsson, M. H. M.; Mavri, J.; Warshel, A. Computer Simulation of Proton Transfer in Proteins and Solutions, in Hynes, J. T.; Klinman, J. P.; Limbach, H.-H.; Schowen, R. L. (Eds.), Hydrogen Transfer Reactions, Wiley-VCH Verlag GmbH, Weinhein, 2007, pp. 1171–1205.


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(30) Mavri, J.; Liu, H.; Olsson, M. H. M.; Warshel, A. Simulation of Tunneling in Enzyme Catalysis by Combining a Biased Propagation Approach and the Quantum Classical Path Method: Application to Lipoxygenase. J. Phys. Chem. B 2008, 112, 5950–5954. (31) Borštnar, R.; Repič, M.; Kržan, M.; Mavri, J.; Vianello, R. Irreversible Inhibition of Monoamine Oxidase B by the Antiparkinsonian Medicines Rasagiline and Selegiline: a Computational Study. Eur. J. Org. Chem. 2011, 6419–6433. (32) Pavlin, M.; Repič, M.; Vianello, R.; Mavri, J. The Chemistry of Neurodegeneration: Kinetic Data and Their Implications. Mol. Neurobiol. 2016, DOI: 10.1007/s12035-0159284-1.


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TOC GRAPHIC


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D Kinetic Isotope Effect in

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