Stabilization of Charges and Protonation States in the Active Site of

J. Phys. Chem. B 2000, 104, 11321-11333

11321

Stabilization of Charges and Protonation States in the Active Site of the Protein Tyrosine Phosphatases: A Computational Study† Vale´ rie Dillet,†,‡ Robert L. Van Etten,§ and Donald Bashford*,† Department of Molecular Biology, The Scripps Research Institute, 10550 North Torrey Pines Road, La Jolla, California 92037, and Department of Chemistry, Purdue UniVersity, West Lafayette, Indiana 47907 ReceiVed: April 25, 2000; In Final Form: August 29, 2000

The initial step of the dephosphorylation of phosphotyrosine by the protein tyrosine phosphatases (PTPases) requires an active-site cysteine residue to be in its deprotonated (thiolate) form so as to make a nucleophilic attack on the phosphate to form a phosphoenzyme intermediate. At the same time, an active-site aspartic acid residue must be in its protonated form to serve as a general acid donating a proton to the leaving tyrosyl moiety. The protein must therefore provide an unusual electrostatic environment in the active site to maintain these protonation states in the free enzyme and in the Michaelis complex with the substrate, whose phosphate group is in the -2 charged form. We present electrostatic calculations for the pKa of the ionizable side chains of four different PTPases. The study includes Michaelis complexes with the substrate, as well as free enzymes. The calculations consistently predict that in the neutral to mildly acidic pH range, the active-site cysteine residue is deprotonated and the aspartic acid residue is protonated, as required for optimal catalysis. This prediction is made even for the Michaelis complexes. Good quantitative agreement with measured pKa values of the aspartic acid residues are obtained, while the calculated pKa values of the cysteine residue are generally much lower than experimental estimates, suggesting that the protonation of the (normally unprotonated) cysteine residue may induce a conformational change in the active site. An analysis is made of the electrostatic factors responsible for maintaining the functionally essential protonation states. The phosphate-binding loop, whose backbone dipolar groups and conserved arginine side chain are oriented so as to stabilize negative charge in the active site, is found to be particularly important. However, structural features that are not conserved across the PTPase family make significant contributions in particular cases. The PTPases use dipoles more than positive charges to stabilize negative charge in the active site, and this helps to prevent the destabilization of the general acid by the longer range interactions with positive charges. The use of a low protein dielectric constant in the calculations is essential to obtaining calculated protonation states that are consistent with the catalytic mechanism. Models using a higher dielectric constant bring the calculated cysteine pKa values closer to some reported experimental values for the free enzyme, but fail to predict the protonation of the general acid, or the maintenance of the thiolate form of the cysteine residue in the Michaelis complex.

Protein phosphorylation is a common mechanism through which cellular processes are regulated, especially in response to extracellular signals.1 In particular, phosphorylation of tyrosine residues is implicated in the control of cell growth, proliferation, and death.2,3 As with serine or threonine phosphorylation, the level of tyrosine phosphorylation is the result of the balance between the action of protein kinases and protein phosphatases. Although lagging behind studies of protein tyrosine kinases, studies of protein tyrosine phosphatases (PTPases) have now emerged as an important topic in the regulation of intracellular processes.1,4 Recently, the PTPases have been the topic of several theoretical studies concerning reaction pathways, ionization states and molecular dynamics.5-10 The present study focuses on the ionization states of groups involved in catalysis in the free enzyme and in the Michaelis complex for several diverse members of the PTPase family. Approximately 100 PTPases are known, and they can be classified into three subfamilies.4,11,12 (i) High-molecular-weight †

The Scripps Research Institute. Permanent address: LEDSS, 301, rue de la Chimie, D. U. Saint Martin d’He`res - BP 53, 38000 Grenoble Cedex 9 - France § Purdue University. ‡

PTPases: these include both cytosolic and membrane-bound receptor enzymes and are perhaps the best understood in terms of biological function. They all share a conserved catalytic domain of approximately 250 residues, but are otherwise quite diverse. X-ray crystallographic structures have been obtained for two of them, PTP1B13,14 and Yersinia PTPase,15-18 both of which are nonreceptor enzymes containing a single catalytic domain. Despite having less than 15% sequence identity, both of these proteins have a similar R/β folding architecture. (ii) Low-molecular-weight (Mr =18 000) PTPases: the biological function of these enzymes is not as well understood as that of the high-Mr PTPases, but they are ubiquitous in mammalian tissues and are thought to be involved in cell-cycle regulation4 or cell-cell communication processes.19,20 Recently, a bacterial PTPase belonging to this family has been characterized, and an endogenous protein kinase has been identified as a substrate.21 Members of this subfamily are homologous, and exhibit substantial sequence similarity, but apart from a conserved active-site motif, they have very limited sequence similarity to the other PTPase subfamilies. High-resolution X-ray structures are available for bovine (BPTP),22,23 human24 and yeast25 lowMr PTPases, and the solution structure of the bovine enzyme

10.1021/jp001575l CCC: $19.00 © 2000 American Chemical Society Published on Web 11/04/2000

11322 J. Phys. Chem. B, Vol. 104, No. 47, 2000 has been studied by NMR.26 The structures of these enzymes have the classic βRβ motifs of the Rossmann dinucleotidebinding fold. (iii) Dual-specificity PTPases: although these enzymes are active against phosphoserine and phosphothreonine as well as phosphotyrosine, they are structurally and mechanistically related to the PTPases rather than the Ser/Thr phosphatases. They are ubiquitously expressed, and the regulatory function of several of them has been demonstrated.4 Apart from the active-site motif, they have little sequence similarity to the other PTPase subfamilies. An X-ray structure of one of them, VHR, has been determined, and aspects of structural similarity between VHR, PTP1B and Yersinia PTPase have been discussed.27 Although quite diverse in sequence and structure, all PTPases apparently share a common mechanism and a few common structural features.4,12 Hydrolysis of the phosphotyrosyl residue occurs in two steps. In the first step (enzyme phosphorylation) a covalent phosphoenzyme intermediate is formed by the nucleophilic attack on the substrate phosphorus atom of a strictly conserved cysteine, while an acidic group donates a proton to the oxygen atom of the leaving tyrosyl group. The second step (dephosphorylation) is the hydrolysis of the phosphoenzyme intermediate, releasing an inorganic phosphate anion and restoring the enzyme to its starting state. All of the PTPases share a common active-site sequence motif: (H/V)CX5R(S/T), where C indicates the strictly conserved nucleophilic cysteine residue, and R is a strictly conserved arginine residue. In the known three-dimensional structures, the residues of this motif form a loop, known as the phosphate binding loop or P-loop, that surrounds the phosphate binding site and is highly superimposable12 from one PTPase to another (Figure 1). The C-terminus of the P-loop coincides with the N-terminus of an R-helix, which is another structural feature conserved among all PTPases. Crystallographic and NMR solution structure data for the low Mr PTPases indicate that the P-loop is very rigid, while kinetic and site-directed mutagenesis results show that mutations that alter the structure of the P-loop lead to reductions in the catalytic activities of the

Dillet et al. mutant enzymes.23,25,26,28,29 The positively charged arginine side chain is absolutely essential for activity.30 These observations may be understood upon examination of structures such as one of the HEPES substrate analogue complexes (Figure 2). Such structures consistently show that six of the backbone NH groups of the P-loop, and two of the NH groups of the side chain of the conserved arginine are all positioned so as to form strong hydrogen bonds with a phosphate in the active site. Several hydrophobic residues near the entrance of the active site cavity help to bind the substrate and to position it12,22 with an axial symmetry similar to that which is observed in the trigonal bipyramidal, vanadate ion transition state analogue complex of BPTP.22,23 Moreover, the oriented hydrogen bonds contributed by the rigid P-loop are positioned such that they are even shorter in the trigonal bipyramidal transition state complex than they are in the reactant complex.23 The Ser/Thr at the end of the P-loop is close enough to form a hydrogen bond to the cysteine sulfur atom, and its mutation in BPTP (S19A) or VHR (S131A) has been shown to retard the enzymic phosphorylation step.29,31 This conserved Ser/Thr reduces the pKa of the conserved, active-site cysteine residue.29,31-33 It is known that the mutation of Ser-19 to Ala in BPTP causes only small changes in the positions of the P-loop atoms.25 Despite this, the kinetic behavior of this mutant is dramatically altered.29 Values of kcat/Km are reduced by several orders of magnitude, the rate determining step is changed from dephosphorylation to phosphorylation, and the pH dependence of kcat/Km clearly shows an ascending limb in the low pH region that cannot be seen with the wild-type enzyme.29 (In the case of wild-type BPTP, attempts to extend the pH dependence measurements below approximately pH 3.8 result in protein denaturation.) Thus, although the pKa of the active site cysteine of low Mr PTPases cannot be determined from measurements of kcat/Km, it is clearly less than 4. In contrast to the conserved P-loop motif, there is comparatively little sequence similarity across the PTPase family in the region of the general acid. For representative enzymes of each

Figure 1. (A) Superposition of the phosphate binding loop (from the nucleophilic cysteine to the invariant arginine) from PTP1B (1ptv.pdb),14 Yersinia PTPase (1ytw.pdb),17 BPTP (2pnt.pdb),23 and VHR (1vhr.pdb/A).27 The serine (mutated from the nucleophilic cysteine) and the arginine of 1ptv are displayed with heavier sticks, whereas the substrate of this same structure (a phosphotyrosine residue) is displayed with balls and sticks. (B) Side view showing position of the general acid, Asp, (upper right) relative to the phenyl phosphate (upper left) from the 1ptv structure. The superposition and graphics were done using the InsightII program from MSI of San Diego (Version 97.0).

pKa of Ionizable Side Chains of PTPases

J. Phys. Chem. B, Vol. 104, No. 47, 2000 11323 TABLE 1: Structural Models model

enzyme

PDB code of original structure

ligand in original structurea

2hnp 1ypt/A 1ypt/B

Unliganded (open) enzymes PTP1B 2hnp Yersinia PTPase 1ypt Yersinia PTPase 1ypt

1ptv 1ptt 1ptu 1pty 1yts 1ytw 1ytn 2pnt 1vhr/A 1vhr/B

Enzyme/phenyl phosphate complexes PTP1B 1ptv pTyr PTP1B 1ptt pTyr tetrapep.b PTP1B 1ptu pTyr hexapep.c PTP1B 1pty pTyr Yersinia PTPase 1yts sulfate Yersinia PTPase 1ytw tungstate Yersinia PTPase 1ytn nitrate BPTP 2pnt HEPES VHR 1vhr HEPES VHR 1vhr HEPES

a Only the ligands lying in the active-site binding pockets are given. In structural models of the complexes, these original ligands are replaced by phenyl phosphate (see text). b Phosphotyrosine-containing tetrapeptide (Ac-DEpYL-NH2). c Phosphotyrosine-containing hexa-peptide (DADEpYL-NH2).

TABLE 2: Numbering of Selected Key Residuesa

Figure 2. Hydrogen bonding pattern observed for the complex of HEPES buffer with the P-loop residues of the low Mr PTPase from Saccharomyces cereVisiae. (A) Hydrogen bond distances and residue identification. Shown are the multiple hydrogen bonds and distances from main-chain backbone NH’s and conserved Arg side chain to sulfonate oxygen atoms. Also indicated is the hydrogen bond between the active site nucleophile (Cys-13 in the yeast enzyme) and the hydroxyl group of the conserved Ser residue in the P-loop. (B) A stereoview illustrating the relative orientation of the substrate analogue with respect to the P-loop and the active site nucleophile. Residue numbering is omitted for the sake of clarity. Coordinates are from PDB file 1D1P.25

family, the general acid has been identified, and it is always an aspartic acid residue (ref 11 and references therein), but there is no consensus as to its position in the sequencesin the lowMr PTPases it lies approximately 110 residues to the C-terminal side of the P-loop, whereas in the high-Mr and dual-specificity subfamilies it lies 30 to 50 residues to the N-terminal side of the P-loop. In the high-Mr PTPases, the conserved aspartic acid is part of a flexible loop, termed the WpD loop,16 which apparently changes from an “open” to a “closed” conformation upon ligand binding.16,34 For PTP1B and Yersinia PTPase, X-ray crystallographic structures are available for both forms.13-18 On the other hand, there does not appear to be so much flexibility in the Asp-bearing loop of the low-Mr PTPases, which has no sequence similarity, apart from the Asp, to the corresponding loop of the other PTPases. The only common 3D-structural feature of the conserved Asp across all subfamilies is that it is positioned with its carboxylic acid group within hydrogenbonding distance from the apical oxygen of the substrate (Figure 1b), and is thus well-placed to protonate the leaving tyrosinate group during the initial step of catalysis.14,16,17,23,27 Measurements of kcat/Km as a function of pH show that for the first step of catalysis to proceed, the phosphate group of the substrate must be deprotonated to the dianionic form, the

PTP1B

Yersinia PTPase

Arg45 Glu115 Lys120 His175 Asp181 His214 Cys215 Ser216 Arg221 Ser222 Arg257

Arg228 Glu290 Gly297 His350 Asp356 His402 Cys403 Arg404 Arg409 Thr410 Arg440

BPTP

Asp129 Cys12 Arg18 Ser19

VHR Met69 Asn74 Gly87 Asp92 His123 Cys124 Arg125 Arg130 Ser131 Arg158

a Based on the sequence alignment of ref 27 for PTP1B, Yersinia PTPase and VHR. Bold: important catalytic residues conserved in the PTPase family (numbering of these residues for BPTP is also included).

active-site cysteine residue must be deprotonated, and the activesite aspartic acid residue must be protonated.29,31,32,35-37 These studies and others38 establish that the active-site cysteine pKa is shifted downward into the acidic range, whereas the aspartic acid pKa is shifted upward into the neutral to mildly acidic range. Kinetic isotope effect experiments indicate that the tyrosine leaving group departs in its neutral, protonated, form.39-41 These observations, together with structural studies, lead to the following picture of the initial step of catalysis:29 In the free enzyme, the cysteine is initially unprotonated and the aspartic acid is protonated. The free phosphotyrosyl substrate moiety is initially unprotonated. These protonation states are maintained as the Michaelis complex is formed. Then, as the aspartic acid donates a proton to the leaving tyrosyl group, the thiolate of the active-site cysteine residue makes a nucleophilic attack on the substrate phosphorus atom. This results in the transfer of the phosphate group from the substrate to the enzyme, to form a covalent phosphocysteinyl enzyme intermediate.30 (The subsequent dephosphorylation step is outside the scope of the present study.) The aim of the present study is to give a quantitative account of the means by which the PTPases stabilize the unusual charge states in the free enzyme and in the Michaelis complex that are required for the initial step of protonation. In particular, the requirement that the cysteine thiol group and the substrate phosphate group both be unprotonated means that the enzyme must stabilize a charge of -1 in the free enzyme and -3 in the

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TABLE 3: Charges and Radii atom chargea radiusb radiusc

P 0.90 2.15 1.8

O1 -0.85 1.77 1.4

O2 -0.85 1.70 1.4

Phenyl Phosphate O3 -0.85 1.70 1.4

O4 -0.38 1.70 1.4

C1 0.03 1.992 1.7

C(ar) -0.10 1.992 1.7

H(ar) 0.10 1.358 1.0

Cysteined atom charge protonated form deprotonated form radius atom charge protonated form deprotonated form radius

CG

CB

SG

HG1

0.00 -0.08 2.00

-0.29 -0.92 1.85

0.29 0.00 1.00

Aspartic Acidd OD1

0.55 0.1 1.70

-0.495 -0.55 1.40

OD2

HD2

-0.49 -0.55 1.40

0.435 0.00 1.00

a Charges for the deprotonated form (adapted from the CVFF parameters of the protonated form). b Radii (in Å) used for the energy minimizations, taken from the CHARMM22 parameters for tyrosine and methyl phosphate. c Radii (in Å) used for the electrostatic calculations, taken from the PARSE parameter set53 for oxygen, carbon and hydrogen atoms and equal to the mean van der Waals radius defined by Bondi72 for the phosphorus atom. d Charges and radii for the MEAD calculations only. These parameters are from the PARSE set, as are parameters for all other atoms not shown.

Michaelis complex. At the same time, a nearby aspartic acid residue must be kept protonated, so as to serve as a general acid. This paper reports the use of a semi-macroscopic electrostatic model to study this problem for set of enzymes representative of the PTPase family. Calculations of pKa values based on the model are presented, and an analysis of the contributions to the calculated pKa shifts from various parts of the protein, and across different members of the family is made. We also compare our results to previous theoretical studies of active-site ionization states.8,9 Because the large electrostatic effects in the PTPases present a greater challenge to electrostatic models than the more common application to the prediction of the pKa shifts of surface residues, this study also provides a test of the applicability and parametrization of the electrostatic model. In particular, we address the question of the appropriate value for the interior dielectric constant of the protein in such models. Structural Models The source and principal characteristics of the PTPase structural models used in the present study are summarized in Table 1. The numbering of homologous functionally important residues in PTP1B, Yersinia PTPase, BPTP, and VHR is listed in Table 2. Only PTP1B13 and Yersinia PTPase15 have been successfully crystallized in the absence of ligand. Therefore, structural models for the unliganded form of the enzyme were derived from these two structures, and no other PTPases were modeled in the unliganded form. Structural models of the Michaelis complex were derived from X-ray structures of PTPase/ligand complexes available for PTP1B,14,18 Yersinia PTPase,16,17 BPTP,23 and VHR.27 A common hydrogen building and energy-minimization scheme was used for all models: Crystallographic water molecules were removed from the original PDB files. Coordinates for the hydrogen atoms were generated using the HBUILD42 module of CHARMM43 and refined by steepestdescent energy minimization (200 steps) in the absence of electrostatic interactions, followed by conjugate-gradient minimization including electrostatic interactions (13.0 Å cutoff, dielectric constant 4.0). Unless stated otherwise for a particular model, only hydrogen atoms were allowed to move during these

minimizations. The CHARMM computer program43 and the CHARMM22 empirical potential energy function44 were used for these energy minimizations. During all minimizations, the nucleophilic cysteine was modeled in the deprotonated (thiolate) state, to preserve the hydrogen bond from the hydroxyl of the Ser/Thr conserved residue to the sulfur atom of the cysteine. Coordinates for the thiol hydrogen were subsequently generated using HBUILD. For all of the Michaelis complexes, the phenyl phosphate was modeled in its fully deprotonated state. The charges and radii used for this group during the minimizations are given in Table 3. These charges were adapted from those of the protonated form in the CVFF force field45 and compare well with the values derived by Hansson et al.6 for phosphate esters. The radii of the phenyl phosphate atoms were taken from the CHARMM parameters for tyrosine and methyl phosphate. Models for the Unliganded Enzyme: PTP1B and Yersinia PTPase. Models for the free enzyme were taken from the crystal structure of the unliganded form of PTP1B (2hnp.pdb)13 and Yersinia PTPase (1ypt.pdb).15 In the latter case, the two protein molecules present in the crystal unit were treated independently, and the two distinct structural models are referred to here as 1ypt/A and 1ypt/B. Models for the Michaelis Complex. A number of models for Michaelis complexes of a PTPase and a phenyl phosphate substrate were produced using available crystallographic structures of various PTPases complexed with various ligands as starting points. A first model of the Michaelis complex was derived from the X-ray crystallographic coordinates of the C251S mutant of PTP1B complexed with phosphotyrosine (1ptv.pdb).14 The mutation inactivates the enzyme by replacing the nucleophilic cysteine side chain with the sterically similar serine side chain, so the structure should closely resemble the Michaelis complex of the native enzyme. In the modeling procedure, Ser215 was changed back to a deprotonated cysteine residue by removing the Hγ atom and replacing the Oγ atom by a sulfur atom. The Cβ and backbone atoms of the phosphotyrosine ligand were removed, so that the ligand in the model structure was phenyl phosphate. The structure was further refined as described above, with the difference that (in addition to the hydrogen atoms) the substrate atoms and the sulfur atom of Cys215 were allowed to move during the minimization. This was intended to model an enzyme-substrate geometry more

pKa of Ionizable Side Chains of PTPases

J. Phys. Chem. B, Vol. 104, No. 47, 2000 11325

representative of the catalytically active Michaelis complex, in which the cysteine is deprotonated. Models for other complexes are based on the crystallographic coordinates of (i) PTP1B (C215S mutant) complexed with a phosphotyrosine tetrapeptide (1ptt.pdb),14 a phosphotyrosine hexapeptide (1ptu.pdb),14 or a phosphotyrosine (1pty.pdb);18 (ii) Yersinia PTPase complexed with a sulfate (1yts.pdb),17 a tungstate (1ytw.pdb),16 or a nitrate ligand (1ytn.pdb);17 (iii) BPTP with a HEPES ligand (2pnt.pdb)23 and (iV) VHR (1vhr.pdb)27 with a HEPES ligand (Table 1). The two protein molecules present in 1vhr.pdb were treated independently and will be referred to as model structures 1vhr/A and 1vhr/B. For these nine liganded structures, after deletion of the crystallographic water and substrate molecules, the P-loop backbone atoms were superimposed with those of the complex modeled using the 1ptv.pdb structure to obtain the initial phenyl phosphate coordinates. Further processing was as described previously for the 1ptv model, with the sulfur atom of the nucleophilic cysteine and the substrate atoms allowed to move during the minimizations. Theory and Computations The calculations are based on the assumptions that any difference between the pH-titration behavior of a group in a protein versus that in an analogous model compound is the result of differences in the electrostatic interactions of the group in the protein versus the model compound, and that these electrostatic interactions can be treated by the MEAD (macroscopic electrostatic with atomic detail) model, in which the protein interior is a medium of dielectric constant p, the exterior is a medium with the dielectric constant and ionic strength of the bulk solvent, the boundary between interior and exterior is the Connolly46 surface, as determined from the atomic coordinates and radii, and the electrostatic interactions within this system can be found by solving the corresponding linearized Poisson-Boltzmann equation. Methods for the pKa Calculations. Here we briefly summarize the procedure used to compute the pKa values of titratable residues from the protein structures. More details are given elsewhere.47,48 To compute the pKa of a given residue i we first evaluate its intrinsic pKa (pKintr), defined as the pKa of that residue when all the other ionizable groups are neutral.49 This quantity can be written as

pKintr ) pKmod + ∆pKBorn + ∆pKback

(1)

where pKmod is the pKa of the N-formyl-N-methylamide derivative of the residue (i.e., the model compound), and ∆pKBorn and ∆pKback are the pK shifts due to the desolvation of the residue and its interaction with the atomic partial charges of the protein (in its neutral form), respectively. To compute the pKa we also need the charge-charge interactions between residue i and the other ionizable groups j. In our model this quantity is expressed as a sum of pairwise terms (Wij). The ∆pKBorn, ∆pKback and Wij terms are evaluated using a continuum electrostatic model. In this model, the protein (or the model compound) is regarded as a low dielectric medium (with a dielectric constant of 4), in which the protein partial atomic charges are embedded, and the solvent is regarded as a high dielectric medium (with a dielectric constant of 80). The counterion atmosphere in the solvent is modeled using the Debye-Hu¨ckel approximation. The ∆pKBorn, ∆pKback, and the Wij terms of all the titrating groups can be evaluated by solving the linearized Poisson-Boltzmann equation for various subsets of partial charges (see refs 47, 50 for details).

Given these quantities, the fractional protonation of all residues at a given pH can, in principle, be evaluated using a Boltzmann distribution over the possible protonation microstates of the system (for a protein with N ionizable sites, there are 2N possible protonation microstates). After computing the fractional protonation for all of the ionizable residues over a sufficient range of pH, the ∆pKa of any titratable group is obtained as the pH value at which this group is half protonated. To permit more detailed analysis, it is useful to split ∆pKback into individual contributions (∆pKback,k) from all other residues k as Nres

∆pKback )

∑ ∆pKback,k

(2)

k)1

where Nres is the total number of residues in the protein. The ∆pKback term can also be subdivided into backbone and side chain contributions. Parameters and Programs for the Electrostatic Calculations. For the PTP1B and Yersinia PTPase Michaelis complexes, the electrostatic potential was evaluated using the finitedifference method with the grid-focusing technique51 over three successive grids with spacing of 2, 1.0, and 0.25 Å. In all other cases only two successive grids, with spacing of 1.0 and 0.25 Å, were used. Cubic lattices of 813 and 613 points were used for the calculations on the enzyme (or Michaelis complex) and the model compounds, respectively. The dielectric boundary between the interior (unliganded enzyme, Michaelis complex or model compound) and the exterior (solvent) media was defined by the contact and reentrant surfaces52 using a solvent probe radius of 1.4 Å. Dielectric constants of 80 and 4 were used for the exterior and the interior media, respectively. An ionic strength of 0.15 M was used together with an ion exclusion region extending 2.0 Å beyond the atomic radii. Atomic radii and charges were taken from the PARSE parameter set.53 The charges and radii used for the phenyl phosphate are those listed in Table 3. The N-formyl N-methylamide derivatives of the ionizable amino acids were chosen as model compounds. The pKmod values were taken from Nozaki and Tanford54 (Asp 4.0, Glu 4.4, His 7.0, Cys 9.5, Tyr 9.6, Lys 10.4, Arg 12.0, C-terminus 3.8, N-terminus 7.5). All protein groups of the above types were included as titrating sites in the calculations. The phenyl phosphate was assumed to be fully deprotonated. The ∆pKBorn, ∆pKback and the charge-charge pairwise terms (Wij) for all of the titrating sites were evaluated with the multiflex module of the MEAD program suite,47,55 which uses finitedifference methods56,57 to solve the linearized Poisson-Boltzmann equation. Protonation fractions were calculated for pH values ranging from -4 to 15, by increments of 0.1 pH unit, using the Monte Carlo method developed by Beroza et al.,58 because a direct summation over all 2N protonation states is not feasible. In cases where the protein’s electrostatic environment strongly stabilizes either the protonated or deprotonated form of a site, the program will predict the site to be mostly deprotonated even at pH -4 or mostly protonated at pH 15. In these cases the results are reported as “15,” respectively. The MEAD program suite and input data files needed to reproduce most of the results presented here are available from the web page, http://www.scripps.edu/bashford. The Beroza Monte Carlo program is available from ftp://ftp.scripps.edu/pub/ case/beroza.

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TABLE 4: Experimental pKasa

Results and Discussion

free enzyme PTP1e Yersinia PTPase BPTPi VHR

complexes

Cysb

Cysc

Aspc

Aspd

5.57 4.67f

5.44

4.9 5.1g 5.3 5.7k

6.7 5.2, 5.8g,h

5.6j

6).29,31,32,36 This indicates that enzymatic activity requires two ionizable groups to be in their deprotonated form and one to be in its protonated form. The descending slopes in the basic domain can be unambiguously attributed to Asp181, Asp356, Asp129, and Asp92 in the unliganded forms of PTP1,32 Yersinia PTPase,36 BPTP,29 and VHR,31 respectively. The pKas are listed in Table 4. The substrate (generally pNPP) and the nucleophilic cysteine are responsible for the ascending slope in the acidic domain. The cysteine pKas obtained in this way are listed in Table 4. The cysteine pKas obtained from the pH dependence of iodoacetate inactivation of the enzymes PTP1 and VHR are also reported32,35 and are in reasonable agreement with the former estimates. In the Michaelis Complexes. Because the pH dependence of kcat may reflect the kinetic properties of several different states along the reaction path59 (in our case, the Michaelis complex or the phosphoenzyme intermediate), the pKas of the general acid obtained from these curves, and reported in the last column of Table 4, should be interpreted with caution. Burst kinetic experiments suggest that the rate-limiting step of the enzymatic reaction is the hydrolysis of the phosphoenzyme intermediate (i.e., the second step of the catalytic process) in the case of BPTP60 and Yersinia PTPase,33 and the formation of the phosphoenzyme (i.e., the first step of the catalytic process) for PTP132 and VHR.31 Consequently, in the case of Yersinia PTPase, the intermediate should accumulate and the pKa extracted from the pH dependence of kcat should reflect the pKa of the general acid in the phosphoenzyme intermediate rather than in the Michaelis complex. Conversely, in the cases of PTP1 and VHR, the concentration of the phosphoenzyme intermediate will be much smaller than the concentration of the Michaelis complex, and thus the experimental pKa values of 6.7 and 7.2 (see Table 4) should be more representative of the pKa of the general acid in the Michaelis complex. (The log kcat versus pH data61 do not appear to provide pKa values for the nucleophilic cysteine in the Michaelis complex.)

We first examine the results of the calculations on the unliganded enzymes, PTP1B and Yersinia PTPase. These results are summarized in Table 5. The calculated pKas for the nucleophilic cysteine and the general acid are analyzed in terms of desolvation (∆pKBorn), dipoles (∆pKback) and charged side chain contributions. For the Michaelis complexes (PTP1B, Yersinia PTPase, BPTP, and VHR), the same kind of analysis is done and reported in Table 6, with an additional contribution due to the presence of the negatively charged phenyl phosphate. The ∆pKback terms are further broken down into contributions due to the P-loop and the nearby R-helix backbone dipoles, the conserved Ser/Thr side chain of the PTPase signature motif, and the remaining dipoles of the protein (see Table 7). The individual contributions to ∆pKback (based on eq 2) of the cysteine and the general acid in the Michaelis complex of BPTP are displayed in Figure 3. Finally, we compare the results obtained for the four PTPases in the Michaelis complex (PTP1B, Yersinia PTPase, BPTP, and VHR) to bring out the similarities and differences among them with respect to electrostatic interactions within the active site. Protonation state in the unliganded enzyme: PTP1B and Yersinia PTPase. pKa of the nucleophilic cysteine. The calculated pKas for the nucleophilic cysteine based on the structural models for the unliganded enzyme are shown in Table 5. These calculated values are substantially smaller (always < -4.0) than the experimental values of 5.6/5.4 and 4.7 for PTP1B and Yersinia PTPase, respectively. Although the calculations are qualitatively correct in predicting that the cysteine residue is deprotonated in the pH range of the enzyme activity, the magnitude of the downward pKa shift appears to be significantly overestimated. This is probably the result of using a single-conformational model, which does not allow for any acid-induced structural change in the active site coupled to the protonation of the cysteine residue. In general, extreme calculated pKa values such as these should not be interpreted as literal predictions of pKa measurements but as predictions that the protein cannot accommodate the change of protonation without undergoing some significant conformational rearrangement.47,62 In this context, our calculations are consistent with the experimental finding that the cysteine titration in BPTP is obscured by acid denaturation below pH 4.29 Both charge-dipole and charge-charge interactions stabilize the deprotonated (negatively charged) form of the reactive cysteine. These influences are more than enough to offset the Born desolvation term, which destabilizes the charged form. The backbone dipoles of the P-loop make the largest contribution to the stabilization of the thiolate form, decreasing the pKa of the cysteine by -8.3 to -10.1. The backbone dipoles of the first 14 residues of the conserved R-helix located at the C-terminus of the PTPase signature motif provide an additional contribution of about -2.5. Finally, the side-chain dipole of the conserved hydroxyl group (Ser222 in PTP1B and Thr410 in Yersinia PTPase) further stabilizes the thiolate form, lowering its pKa by -2.9 to -3.6. This last observation is opposite to the result of Peters et al.,8 namely that the Ser/Thr residue destabilizes the thiolate form. Kinetic studies on the Ser/Thr f Ala mutants, of PTP1B,32 Yersinia PTPase,33 BPTP,29 and VHR,31 all support the conclusion that the thiolate form is stabilized by the conserved hydroxyl group, in agreement with the present calculations. Calculations were also done using structural models prepared with an energy minimization protocol that did not constrain any heavy atoms, but was otherwise the same as that described in

pKa of Ionizable Side Chains of PTPases

J. Phys. Chem. B, Vol. 104, No. 47, 2000 11327

TABLE 5: Calculated ∆pKs and pKa for the General Acid and the Nucleophilic Cysteine in the Unliganded Enzymesa general acid PTP1B 2hnp ∆pKBorn ∆pKback pKintr charged side chains pKa

nucleophilic cysteine

Yersinia PTPase

2.0 -0.6 5.4 -0.8 4.6

PTP1B

1ypt/A

1ypt/B

3.0 -2.0 5.0 0.8 5.8

2.9 -2.3 4.6 0.6 5.2

Yersinia PTPase

2hnp

1ypt/A

1ypt/B

6.1 -15.6 0.0 < -4.0 < -4.0

5.7 -14.8 0.4 < -4.4 < -4.0

5.9 -15.0 0.4 < -4.4 < -4.0

a pK intr is obtained by adding the pKa of the model compound to ∆pKBorn and ∆pKback. pKa - pKintr gives the contribution of the charged side chains. Regarding calculated pKa values < -4.0, see the description of the methods of pKa calculation under Models and Theory.

TABLE 6: Calculated ∆pKs and pKa for the General Acid and the Nucleophilic Cysteine in the Michaelis Complexesa PTP1B 1ptv

1ptt

Yersinia PTPase

1ptu

∆pKBorn ∆pKbackb pKintrb phenyl phosphatec charged side chains pKa

4.8 -4.4 4.4 10.4 >0.2 >15.0

5.2 -2.8 6.4 8.9 -9.9 5.4

4.5 -2.9 5.6 7.9 -6.8 6.7

∆pKBorn ∆pKbackb pKintrb phenyl phosphatec charged side chains pKa

10.6 -31.3 -11.2 25.0