Activator, Substrate, and Inhibitor of Human Aspartoacylase

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Three Faces of N-Acetylaspartate: Activator, Substrate and Inhibitor of Human Aspartoacylase Maria G. Khrenova, Ekaterina D Kots, Sergey D. Varfolomeev, Sofya V. Lushchekina, and Alexander V. Nemukhin J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b08759 • Publication Date (Web): 13 Sep 2017 Downloaded from http://pubs.acs.org on September 24, 2017

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The Journal of Physical Chemistry

Three Faces of N-Acetylaspartate: Activator, Substrate and Inhibitor of Human Aspartoacylase

Maria G. Khrenova, † Ekaterina D. Kots, †,‡ Sergey D. Varfolomeev, †,‡ Sofya V. Lushchekina, ‡ Alexander V. Nemukhin*,†,‡

†

‡

Department of Chemistry, Lomonosov Moscow State University, Moscow, 119991, Russia Emanuel Institute of Biochemical Physics, Russian Academy of Sciences, Moscow, 119991,

Russia

* Corresponding author: Prof. Alexander V. Nemukhin, Chemistry Department, M.V. Lomonosov Moscow State University, Leninskie Gory 1/3, Moscow, 119991, Russian Federation Phone: +7-495-939-10-96 E-mail: [email protected]; [email protected]

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Abstract Hydrolysis of N-acetylaspartate (NAA), one of the most concentrated metabolites in brain, catalyzed by human aspartoacylase (hAsp) shows a remarkable dependence of the reaction rate on substrate concentration. At low NAA concentrations, sigmoidal shape of kinetic curve is observed, followed by typical rate growth of the enzyme-catalyzed reaction, whereas at high NAA concentrations selfinhibition takes place. We show that this rate dependence is consistent with a molecular model, in which N-acetylaspartate appears to have three faces in the enzyme reaction, acting as activator at low concentrations, substrate at moderate concentrations, and inhibitor at high concentrations. To support this conclusion we identify binding sites of NAA at the hAsp dimer including those on the protein surface (activating sites) and at the dimer interface (inhibiting site). Using the Markov state model approach we demonstrate that population of either activating or inhibiting site shifts the equilibrium between the hAsp dimer conformations with the open and closed gates leading to the enzyme active site buried inside the protein. These conclusions are in accord with the calculated values of binding constants of NAA at the hAsp dimer, indicating that the activating site with a higher affinity to NAA should be occupied first, whereas the inhibiting site with a lower affinity to NAA should be occupied later. Application of the dynamical network analysis shows that communication pathways between the regulatory sites (activating or inhibiting) and the gates to the active site do not interfere. These considerations allow us to develop a kinetic mechanism and to derive the equation for the reaction rate covering the entire NAA concentration range. Perfect agreement between theoretical and experimental kinetic data provides strong support to the proposed catalytic model.


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Introduction N-acetylaspartate (NAA) is an abundant amino acid derivative in human brain.1 The NAA degrading enzyme human aspartoacylase (hAsp) performs the hydrolysis reaction producing aspartate and acetate (Scheme 1).

-

O O

Ñs

+ H2O

Ns H O

-

-

O

O

hAsp O

Ñs

-

O

O

O

+ H N+ 3 s O

N-acetylaspartate

acetate

-

O

aspartate

Scheme 1. Chemical reaction of NAA hydrolysis catalyzed by hAsp.

Recent enhanced interest in this reaction has resulted from a request to treat severe health threats associated with an unbalanced regulation of NAA concentration in the central nervous system. Development of schizophrenia, multiple sclerosis and Alzheimer’s disease is associated with abnormally low values of NAA concentration, whereas hAsp deficiency causes Canavan disease, in which NAA accumulates to high concentrations.2 Given the significance of this catalytic process related to development of severe human diseases, it is important to gain a full understanding of molecular mechanisms behind the catalytic cycle of hAsp. Experimental studies of kinetics of NAA hydrolysis catalyzed by hAsp reveal a remarkable reaction rate dependency on the substrate concentration, which the authors of the work 3 classify as “unusual” one. At low NAA concentrations (1.0 mM) substrate inhibition takes place. According to these results,3 hAsp efficiently operates within a rather narrow concentration window with the optimal NAA concentration around 1 mM. It should be emphasized that the whole-brain NAA concentration may amount up to 15 mM,

4

which is far away from the optimum of hAsp activity towards NAA

hydrolysis. Therefore, we believe that kinetics of NAA hydrolysis by hAsp presents an important case of enzyme catalysis not only due to its complexity. 3 ACS Paragon Plus Environment


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Basing on experimental results only it is difficult to disclose molecular level understanding of the catalytic process, since the same kinetic data, in particular, dependences of the reaction rate on substrate concentration, can be described with quite different mechanisms. In this respect, computational simulations contribute considerably to studies of elementary steps of the catalytic reaction. The aim of the present work is to develop a model, which explains the observed kinetic features of the NAA hydrolysis by hAsp at the atomic level by using modern methods of molecular modeling. Results of few experimental studies of hAsp,3,5–8 as well as results of previous computational simulations 9–13 form a basis of our consideration. Two papers

3,7

reported the estimated parameters

of the Michaelis-Menten kinetics. As noted above, Le Coq et al.3 measured dependence of hydrolysis rate on NAA concentration. The X-ray data on the crystal structures of hAsp in the apoand holo-forms provide an important contribution to understanding catalytic properties of this enzyme.6,14,15 According to these data the protein appears as a dimer composed of two chemically identical monomers A and B, which are designated here as ASPA and ASPB, respectively. In both monomers, the enzyme active site responsible for the chemical reaction shown in Scheme 1 is located deeply inside the protein at the bottom of a transport channel. The following molecular groups form the active site: the Zn2+ ion coordinated by the side chains of His21, Glu24, His116 and the side chain of Glu178 serving as a general base that activates the nucleophilic water molecule. Here the residue numbering is given according to the entry PDB ID: 2O53.6 Fig. 1 illustrates the structure of the hAsp dimer. One of the insets in Fig. 1 shows composition of the active site, another inset shows entrance to the active site, which is controlled by the so-called gate residues. The salt bridge Arg71-Glu293 and the hydrogen-bonded pair Tyr64-Lys291 are the key participants of the gates. Both monomers, ASPA and ASPB, contain the active site and the gates. Fig. 1 was drawn by motifs of the crystal structure PDB ID: 2O53

6

and the results of the

quantum mechanics/molecular mechanics (QM/MM) modeling11 consistent with the experimental findings. It is important to note that the gates to the active sites are closed in the crystal structure of the apo-protein in the sense that short hydrogen-bond distances between the pairs Arg71-Glu293 and Tyr64-Lys291 are observed.


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Figure 1. The hAsp dimer composed of two monomers, ASPA and ASPB, drawn by motifs of the crystal structure PDB ID: 2O53 6 and results of computer modeling. Insets show composition of the active sites and of the gates leading to the active sites. Previous theoretical study devoted to modeling the complete catalytic cycle of hAsp 11 described a chain of elementary reactions upon NAA hydrolysis. According to these simulations, initial chemical steps of hydrolysis include nucleophilic attack of a zinc-bound nucleophilic water molecule at the carbonyl carbon (Cs) of the substrate, proton transfer from Glu178 to the amide nitrogen atom (Ns) of the substrate, and the Cs-Ns bond cleavage (see Scheme 1). The constructed free energy diagram, including steps of formation of the enzyme-substrate complex, chemical transformations at the active site, formation of products and regeneration of the enzyme suggests that the enzyme regeneration corresponds to the rate-determining stage of the full catalytic cycle of hAsp.11 Computer simulations described in ref

12

reveal that consideration of the hAsp dimer is an

essential issue in explaining the observed 3 self-inhibition of NAA hydrolysis. In the apo-form, the gates which control substrate deposition to the active site of one monomer (here, ASPB) are predominantly closed along MD trajectories, whereas two types of protein conformations with either open or closed gates in another monomer (here, ASPA) are observed. Substrate deposition through the open gates to the active site finally results in the chemical reaction (Scheme 1). Binding of NAA 5 ACS Paragon Plus Environment


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at the specific site at the dimer interface causes transitions between protein conformations favoring the structure with the closed gates in ASPA, which qualitatively explains kinetic data at high substrate concentrations. In this study, we follow an ambitious task to develop a catalytic model capable to provide a full quantitative description of the ‘unusual’ experimental kinetic data.

3

Namely, we aim to reproduce

the dependence of the rate of NAA hydrolysis by hAsp for the entire range of NAA concentrations dissecting the corresponding molecular mechanisms. To this goal, we apply modern molecular modeling methods including molecular dynamics, molecular docking, dynamical network analysis and Markov state model analysis. These approaches allowed us to identify possible binding sites of NAA at the hAsp dimer, to develop the kinetic scheme and to solve the corresponding set of equations of chemical kinetics, finally estimating the rate dependence on NAA concentration. Agreement of the computational and experimental kinetic data forms a solid basis for understanding molecular mechanisms of NAA hydrolysis by hAsp. According to our model, N-acetylaspartate plays different roles in the enzyme reaction, acting as activator at low concentrations, substrate at moderate concentrations, and inhibitor at high concentrations.

Models and Methods Model systems for the hAsp dimer were constructed by motifs of the crystal structure of the protein in the apo-form (PDB ID: 2O536). The corresponding all-atom structure illustrated in Fig. 1 was refined in our previous molecular dynamics (MD) and quantum mechanics/molecular mechanics (QM/MM) simulations.11 To locate and characterize binding sites of NAA at the surface of the hAsp dimer we applied MD calculations and molecular docking procedures. The model macromolecule system was solvated in a box of TIP3P water molecules with the minimal distance of 15 Å from the protein to the box walls. Sodium ions were added to neutralize the system. MD trajectories were executed using NAMD2.1016 with the CHARMM36 all atom force field17 following 5000 steps of steepest-decent minimization before MD runs. Each simulation was performed in NPT-ensemble at 300 K and 1 atm. The temperature control was implemented by means of Langevin dynamics and the pressure was maintained by using Nosé-Hoover Langevin Piston method. For electrostatic, Particle Mesh Ewald method was implied. The long-ranged van der Waals interactions were given a cutoff distance of 13.5 Å and a switching distance at 10 Å. The integration step was set to 1 fs.


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To examine possible binding sites of NAA on the surface of the hAsp dimer, the NAA molecules were allowed to migrate from the water bulk to the hAsp dimer. More specifically, 15 NAA molecules were distributed randomly in the water box around the protein at the distances exceeding 10 Å from the protein surface. The 250 ns MD trajectory showed migration of the negatively charged NAA molecule toward the areas at the hAsp surface with the positively charged molecular groups. Inspection of all NAA-hAsp contacts allowed us to distinguish the most possible spot composed of a cluster of the positively charged residues Arg56, Lys59, Lys60. To estimate the binding energy of this binding site we applied local search procedure using the Autodock4.2 18 and FlexX

19

programs. The binding site at the dimer interface found in our previous study by using

AlloSite, SiteMap and Autodock4.2 algorithms12 was re-examined with the FlexX program. Application of the Markov state model (MSM) approach

20,21

constitutes an important

contribution to this work, since transitions between hAsp conformations with the open and closed gates leading to the active sites (Fig. 1) should play a decisive role in our model. As explained in Results we employed the MSM analysis for the model systems composed of the hAsp dimer in solution with and without a NAA molecule attached at the protein at the binding sites. MD trajectories of the 0.5 µs length for each system were executed for the MSM analysis. Cartesian coordinates of C-alpha and C-beta atoms of all residues in hAsp dimer were chosen to construct a lower dimensional model. The Time-lagged Independent Component Analysis (TICA) was applied to reduce the dimensionality of the system. To define the microstates for MSM we applied the Voronoi method to create a set of k centers (k=100), and then assigned each data point to the closest center using the standard Euclidian distances. Accordingly, the high-dimensional trajectory was projected onto a discrete sequence of metastable states. We examined two-dimensional projections with the TICA components referred to the two slowest collective variables (the second TICA component helped us to check how well two slowest components were separated). Transition probability matrix in MSM was computed with the lag times τ chosen from the set of values [1, 2, 3, 4, 5, 10, 20] ns with the help of PyEMMA meta-estimator ImpliedTimescales.22 Choice of lag-time and discretization was validated with the Chapman-Kolmogorov test illustrating the consistency level of the Markov model with the MD data within statistical error bars. The model was split into 6 macrostates by using the Perron cluster analysis. For these macrostates the MSM-trajectoires were extracted and representative structures were recognized as those responsible for the transition between the hAsp dimer conformations (states) with the closed and open gates. Correspondingly, general flux, mean first passage time and rate constants were computed between these states for 7 ACS Paragon Plus Environment


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every model system. Computed direct and reverse rate constants for open- and closed-gate states were then converted to equilibrium constants between two terminal states. It is important to emphasize that thus obtained equilibrium constants are estimated entirely from MD trajectories, i.e., independent on the values of binding energies computed in molecular docking. Dynamical network analysis

23

was also employed here to analyze coupled motions and possible

conformational transition shifts in hAsp dimer upon NAA attachment to binding sites. The method enables one to elaborate communication pathways between selected areas at the protein from timedependent variables defined as nodes of the network. In this work, an α-carbon nodal method was employed. Calculation of covariance and correlation values for all pre-defined nodes was performed with the Carma 0.8 program 23,24 for the last 20 ns of equilibrated MD trajectories of the hAsp dimer without and with NAA molecule attached either at the activating or at the inhibiting binding site. The resulting covariance matrices were then represented as a network where nodes stand for C-alpha atoms, and edges illustrates signaling paths between them. The interaction between nodes is characterized as a length in a network space evaluated with positions of C-alpha atoms. The network edges were defined as distances between pairs of nodes whose residues are within a cutoff (4.5 Å) for at least 75% of MD trajectory. The overall length of an optimal signaling path in a network space is defined as a sum of edges. Here suboptimal path search was performed by subopt script provided with Dynamical Network Analysis tutorial files.24 Analysis of topology was carried out using the NetworkAnalyzer software.

27,28

25,26

plugin of Cytoscape3

To mark out the main signaling pipes in model systems we applied the advanced

filtration. The most relevant nodes in both ASPA and ASPB monomers were defined as a set with the highest betweenness centrality value.29 Betweenness centrality (B(n)) refers to the impact of the node on the interactions of other nodes in the network. Specifically, B(n) for the nth node is calculated as follows: =

,

where s and t are the nodes in the network different from n, qst represents the number of shortest paths from s to t, and qst(n) is a number of the shortest paths from s to t that contain n. This information was used to analyze possible interference of the signaling pathways from different binding sites of NAA to the flexible loop with the residues 282-294 including the gate-forming Glu293 and Lys291.


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Results Activating binding sites As explained in Models and Methods, we applied molecular dynamics and molecular docking to locate and to characterize a binding site of NAA at the exterior surface of the hAsp dimer. During 250 ns MD simulations, the negatively charged NAA molecules distributed in the water box around the protein migrated toward its surface making multiple temporal contacts with the positively charged residues at the protein surface. The only permanent contacts were detected between the NAA molecule and the group of the positively charged residues Arg56, Lys59, Lys60. These sites were recognized in both monomers, ASPA and ASPB. We shall discuss below that this site on the surface of hAsp is responsible for self-activation of NAA hydrolysis; by this reasons it is called the activating site. Fig. 2 illustrates the location and composition of the activating sites at the hAsp dimer. For better visibility, the inset in Fig. 2 shows the key interacting molecular groups only for one monomer, here ASPB.

Figure 2. Activating sites at the surface of the hAsp dimer.

Application of molecular docking programs Autodock4.2 and FlexX allowed us to specify the corresponding pose (Scheme 2) and to estimate the binding energy. Remarkably, both docking ° programs predicted the same binding energy ∆ = -6.5 kcal/mol.



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H Arg56

O

Сs

N

H +

N H

N H

O

O

Ns H

H

-

Lys59 -

O

H H + N H

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O

H H

+

N

H

Lys60 Scheme 2. Illustration of the activating site of NAA by results of molecular docking with FlexX.

Inhibiting binding site As mentioned in Introduction, we previously investigated dynamical properties of the hAsp dimer in the apo-form as well as in another form (called holo-Asp in ref 12), in which the NAA molecule was attached to a binding site located at the dimer interface. The latter site, which is responsible for self-inhibition in NAA hydrolysis,

12

is called the inhibiting site in this work; its location and

composition is illustrated in Fig. 3 drawn in the same perspective view on the dimer as in Figs. 1 and 2.


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Figure 3. Inhibiting binding site for NAA located at the hAsp dimer interface. The role of NAA binding at the inhibiting site was partly disclosed in ref 12. An important feature of the apo-hAsp dimer dynamics is that the gates controlling substrate deposition to the active sites (Fig. 1) are closed for ASPB, whereas opening and closing the gates in ASPA takes place along MD trajectories. When NAA binds to the inhibiting site, equilibrium between the hAsp conformations shifts towards those with the closed gates leading to the active site, which is related to decrease of reaction rate of NAA hydrolysis. To extend previous analysis we applied here a more advanced molecular docking program, FlexX, as compared to the Autodock4.2 program which was used previously. The pose identified by FlexX is illustrated in Scheme 3. The binding energies estimated by Autodock4.2 and FlexX are ° ° = -4.7 kcal/mol and ∆ = -4.8 kcal/mol, respectively. fairly close, ∆



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H Arg233

N H N

+

N H

H H O O

O

H N Tyr289

Сs

O

Ns H

-

Lys292

O

-

O

H H

+

N

H

R

Scheme 3. Illustration of the inhibiting site of NAA by results of molecular docking with FlexX.

For the present work it is important that NAA has a higher affinity to hAsp at the activating site ° ° (∆ =-6.5 kcal/mol) and lower affinity at the inhibiting site (∆ =-4.7÷-4.8 kcal/mol).

Comparison of the dissociation constants derived from these binding energies (2.0·10-5 M for the activating site and 3.4·10-4 M or 4.1·10-4 M for the inhibiting site) shows that the dissociation constant for the surface binding is approximately 17-20 times lower than the dissociation constant for NAA binding at the dimer interface. Therefore, binding of NAA at the activating sites is preferable compared to NAA binding at the inhibiting site, and in experiments, the activating sites should be occupied at low NAA concentrations. The activating site is also preferred from kinetic point of view because it is positioned on the protein surface, whereas it would take longer for NAA to reach the inhibiting site located deeper inside the structure.

Markov state model for hAsp dimer conformations In the present work, we deepen a study of the relation between protein conformations with the closed or open gates to the active sites and NAA binding at the hAsp dimer. We apply the Markov state model (MSM) approach, which predicts kinetic quantities on long timescales using a set of atomistic MD simulations that are individually much shorter. Here, we computed the rates of interconversion between hAsp dimer conformations focusing on those with the closed and open 12 ACS Paragon Plus Environment

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gates to the active site. The corresponding information was extracted from the results of MD simulations performed for three model systems: (i) the hAsp dimer in the apo-form; (ii) the hAsp dimer with NAA molecule attached at the activating site of the ASPB monomer (see Fig. 2); (iii) the hAsp dimer with NAA molecule attached at the inhibiting site at the dimer interface (see Fig. 3). Fig. 4 shows simulated trajectories projected on the first two components of time-lagged independent component analysis (TICA) for these three model systems. The results demonstrate presence of two terminal conformations corresponding to the open gates (green dots in Fig. 4) and closed gates (magenta dots in Fig. 4) in ASPA and intermediate states involved in transitions between the terminal states.

Figure 4. Time-lagged independent component analysis (TICA) in ASPA performed for the three systems: dimeric protein in apo-form (upper left panel), dimeric protein with the NAA molecule bound at the activating site (upper right panel) or at the inhibiting site (bottom panel). Dots colored in magenta refer to the MSM metastates corresponding to the hAsp conformations with the closed gates, whereas dots colored in green refer to the MSM states corresponding to the hAsp conformations with the open gates.

Table 1 lists the computed rate constants for the direct (from ‘closed’ to ‘open’) and reverse (from ‘open’ to ‘closed’) reactions and the corresponding equilibrium constants for the process



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of transitions between hAsp conformations with the closed and open gates.

Table 1. Rate constants and equilibrium constants for transitions between conformations of the enzyme in the apo-form (E) and in the protein with a NAA molecule attached either at the activating site (ESact), or at the inhibiting site (ESinh). The corresponding trajectory projections are shown in Fig. 4. System

ko , s-1

kc , s-1

K

E

6.7·106

6.1·106

1.1

ESact

1.0·107

5.0·105

20

ESinh

6.3·107

1.1·109

0.06

According to these data, formation of the hAsp complex with NAA at the activating site results in increase of the ratio between the open and closed gates conformations as compared with the apoform. Contrary, binding to the inhibiting site considerably decreases this ratio. These results together with the dissociation constants estimated in docking studies allow us to conclude that the binding site with the higher NAA affinity to hAsp (activating site) is responsible for increasing rate of hydrolysis reaction at low NAA concentrations, whereas attachment of NAA to the binding site with the lower affinity (inhibiting site) is responsible for decreasing the rate.

Dynamic network analysis The activating site at the ASPB surface (Fig. 2) and the inhibiting site at the dimer interface (Fig. 3) are located spatially close to each other (approximately within 15 Å). Therefore, it should be verified that signal transmission over dynamical networks from these two types of sites to the gates controlling substrate deposition to the active site at ASPA proceeds without overlap of the regulation effects. Application of the dynamical network analysis enabled us to construct optimal and collateral paths that transfer perturbation signal from the activating and inhibiting sites to the loop 282-294 of monomer ASPA. This loop is flexible in dynamics and it contains critical residues 14 ACS Paragon Plus Environment

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Glu293 and Lys291, which couple with Arg71 and Tyr64, respectively, forming the gates to the active site (Fig. 1). We illustrate the procedure by showing the results for the case of hAsp dimer with the NAA molecule attached to the inhibiting site. The signaling pathways indicated by dark green arrows in Fig. 5 connect the node 289B, which corresponds to the residue Tyr289 in ASPB closest to NAA at the inhibiting site (see Scheme 3), and the nodes 290A, 291A and 293A, which correspond to the residues at the loop 282-294 in ASPA, including the gate-forming Glu290, Lys291 and Glu293. Fig. 6 shows this primary signaling pathway (dark green pipe) at the molecular model.

Figure 5. Dynamical network composed from the nodes with the highest betweenness centrality for the case of NAA bound to the inhibiting site. ASPA nodes are colored pink, ASPB nodes are colored lime. Dark green arrows indicate the signaling pathways.



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Figure 6. Highly populated principle optimal pathways (colored dark blue or dark green) from the activating site (dark blue) and from the inhibiting site (dark green) to the flexible loop 282-294 in ASPA responsible for closing/opening gates to the active site.

For the case of hAsp dimer with the NAA molecule attached to the activating site signaling pathways from the nodes corresponding to the residues Arg56, Lys59, Lys60 in ASPB (see Scheme 2) to the loop 282-294 in ASPA are considerably shorter. Fig. 6 illustrates the corresponding paths indicated by dark blue pipes. An important conclusion from the dynamical network analysis is that the main signaling paths from the regulatory sites toward the flexible loop (282-294) with the gate residues do not interfere.

Kinetic model Summarizing the data obtained here and in the previous studies of the hAsp,

3,11,12

we propose

the following scheme of NAA interactions with the hAsp dimer (Scheme 4).


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K1

K1

K2

K3

+S

+S

+S

+S

E ⇌ ES ⇌ ESS ⇌ SESS ⇌ SESSS kcat activating sites

active site

inhibiting site

P Scheme 4. Kinetic scheme of NAA hydrolysis by the hAsp enzyme (E). The letter S colored in blue, red and green refers to interactions of NAA with the activating binding sites, active site and inhibiting binding site, respectively.

We assume the equilibrium conditions at every step of binding NAA to the protein. The dissociation constant K1 corresponds to the NAA binding to one of two equivalent activating sites in the protein monomers. The dissociation constant K2 describes the interaction of NAA with the active site. The constant K3 corresponds to the NAA binding to the inhibiting site. The analytical expression (Eq. 4) for the rate of product formation V for the proposed kinetic mechanism is derived as follows:

=

= , = , =

= + + + +

=

= "#$ = ! =

"#$

% + + + &$'

% + + +

(1) (2) (3)

(4)

In Eq.(4), the third power of substrate concentration in the numerator corresponds to the observed sigmoidal behavior at low concentrations (self-activation), whereas the fourth power of the



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substrate concentration in the denominator is responsible for the reaction rate decrease, i.e. the substrate self-inhibition. To make a direct comparison of the experimental and theoretical results for the concentration dependence of the rate of NAA hydrolysis by hAsp (illustrated in Fig. 7), we digitized the graph with the experimental data published by Le Coq et al.3 and fitted the kinetic parameters according to the scheme proposed in the present study (Eqs. 1-4).

Figure 7. Dependence of the rate of NAA hydrolysis by hAsp. Black squares correspond to the experimental data from ref 3. Red curve corresponds to the results of our simulations (Eq. 4).

We should note that the proposed kinetic model describes the dominating pathway since other channels can also contribute to the reaction mechanism. For example, the system can go into inhibition directly from the states E, ES and EES. In addition, the transition to the active site can take place already from the ES state. Nevertheless, we emphasize an excellent agreement between the computed kinetic curve (red line) and the experimental data (black squares) shown in Fig. 7, which provides a strong support to the proposed molecular mechanism of NAA hydrolysis by hAsp. Table 2 compares the equilibrium constants and the corresponding binding energies for the proposed kinetic scheme (Eqs. 1-4) obtained computationally and derived from the experimental data (Fig. 2 in ref 3) assuming this kinetic mechanism. We intentionally did not estimate the binding 18 ACS Paragon Plus Environment

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energy at the active site of hAsp, because of the known difficulties to treat the sites containing the Zn2+ ions by docking programs. Therefore, only comparison of the K1 and K3 constants is of value. In particular, we note that the K3/K1 ratio obtained from molecular simulations equals 17÷20, which is in perfect agreement with the amount 23 obtained from the experimental data.

Table 2. Equilibrium constants for the kinetic equations (Eqs. 1-4) and the corresponding binding energies. The column entitled ‘Experiment’ corresponds to the values extracted from the experimental graph (Fig. 2 in ref 3) by fitting the constants K1, K2, K3 according to the proposed kinetics scheme (Eqs. 1-4). Theoretical values of the binding energies are estimated in molecular docking studies (both programs, Autodock4.2 and FlexX give the same value -6.5 kcal/mol for the activating site). Experiment

Theory

K1 = 6.4·10-5 ± 2.3·10-5 M

K1 = 2.0·10-5 M

° ∆ = -5.8 kcal/mol

° ∆ = -6.5 kcal/mol

K2 = 4.50·10-4 ± 0.2·10-5 M

n/a

° ∆ = -4.6 kcal/mol

K3 = 1.5·10-3± 0.1·10-4 M ° ∆ =

-3.9 kcal/mol

Autodock4.2

FlexX

K3 = 4.1·10-4 M

K3 = 3.4·10-4 M

° ∆ = -4.7 kcal/mol

° ∆ = -4.8 kcal/mol

Using the derived kinetic equations (Eq. 4) we can compute the value of NAA concentration corresponding to the velocity maximum, 0.88 mM. The reaction velocity at such concentration is 0.88Vmax, where Vmax=kcat[E]0. We can estimate efficiency of hAsp at the detected whole-brain NAA concentrations for the control group of patients (14 mM) and for the group with the mild cognitive impairment or Alzheimer’s disease (10 mM).30 In the first case the rate is 0.11Vmax, in the second case - 0.15Vmax; thus, hAsp works only on 12.5% of its power.

Discussion Several issues should be highlighted, when discussing molecular level of hydrolysis of NAA catalyzed by hAsp. The enzyme operates as a dimer composed of two dynamically distinct 19 ACS Paragon Plus Environment


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monomers. Equivalence of the protein monomers observed in the crystal structures is destroyed in dynamics of the water-solvated dimer.12 This observation should not be a cause of troubles; there is a large field of research devoted to the role of structural symmetry and asymmetry of oligomeric proteins, including appearance of asymmetry between chemically identical protein subunits, e.g., recent refs

31,32

. In the case of hAsp dimer, symmetry breaking has dramatic consequences with

respect to the way, how NAA (acting as a substrate) reaches the enzyme active sites buried inside the protein. For the apo-form of the enzyme, the gates to the active site, which are formed by salt bridges (Arg-Glu) and other strongly interacting pairs (e.g., Tyr-Lys), are predominantly closed in one monomer (called ASPB in this work), whereas transitions between hAsp dimer conformations with the closed and open gates in another monomer (ASPA) take place. This picture observed for the apo-enzyme is strongly affected by temporary binding of NAA at the hAsp dimer upon NAA migration in the solution. First, a NAA molecule can be attached to specific sites at the surface of both monomers formed by a cluster of positively charged residues (see Fig. 2 and Scheme 2). The corresponding binding energy estimated in molecular docking is ° ° = -6.5 kcal/mol. Second, another binding site with lower binding energy (∆ = -4.7÷-4.8 ∆

kcal/mol) located at the dimer interface from the side of ASPB can be also populated at higher concentrations. The Markov state model approach reveals that occupation of these binding sites shift equilibria between the terminal conformations corresponding to the open and closed gates in ASPA, acting in different directions. While population of the site with greater binding energy favor conformations with the open gates, population of the site with lower binding energy favor conformations with the closed gates. Apparently, at low NAA concentration the sites with greater binding energy are predominant; therefore, we deduce that acceleration of the reaction rate at very low amount of NAA in solution is connected with these activating sites (Fig. 2). At high NAA concentration, the site with lower binding energy (inhibiting site, Fig. 3) is occupied leading to decrease of the rate of hydrolysis due to favoring the hAsp dimer conformations with the closed gates to the active site. As a consequence, NAA appears to have three faces in the hAsp catalyzed hydrolysis reaction, acting as activator at low concentrations, substrate at moderate concentrations, and inhibitor at high concentrations. This very unusual model of an enzyme catalysis is justified by comparing the kinetic curves, showing dependence of the hydrolysis rate on NAA concentration, obtained experimentally 3 and constructed computationally on the base of the proposed molecular mechanism.


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Following the authors of the study, 3 we may assume that such complex kinetics presents a rare case for enzyme catalysis. Natural enzymes usually catalyze chemical transformations in natural substrates following simpler kinetics schemes describing the Michaelis-Menten type equation or its extensions, e.g., refs

33–35

; although, there are many enzyme systems, in which substrate activation

and/or inhibition is observed. 36–39

Conclusions Molecular mechanism of NAA hydrolysis by hAsp developed in this work ultimately explain the observed dependence of enzyme activity on substrate concentration. The remarkable kinetic features of this important reaction result from the interplay of several issues: operation of hAsp as a dimer, occurrence of specific binding sites for NAA at the dimer surface and at the dimer interface, control of the gates leading to the enzyme active site by the presence of NAA at these binding sites. Computational characterization of the critical sites of the hAsp dimer, including calculation of the binding energies and the rates of transitions between protein conformations with the closed and open gates, allow us to conclude that NAA acts as activator of hydrolysis at small concentrations, as substrate at moderate concentrations, and inhibitor at large concentrations. This model is supported by a perfect agreement between computed and experimental kinetic data.

Acknowledgements This study was supported by the Russian Science Foundation (project # 14-13-00124). We acknowledge the use of supercomputer resources of the Lomonosov Moscow State University40 and of the Joint Supercomputer Center of the Russian Academy of Sciences.



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TOC Graphic


Activator, Substrate, and Inhibitor of Human Aspartoacylase

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