Evaluating transition state structures of vanadium–phosphatase protein complexes using shape analysis

JIB-09705; No of Pages 12 Journal of Inorganic Biochemistry xxx (2015) xxx–xxx

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Evaluating transition state structures of vanadium–phosphatase protein complexes using shape analysis Irma Sánchez-Lombardo a, Santiago Alvarez b,⁎, Craig C. McLauchlan c, Debbie C. Crans a,⁎ a b c

Department of Chemistry, Colorado State University, Fort Collins, CO 80523, USA Departament de Química Inorganica, Institut de Química Teorica i Computacional (IQTCUB), Universitat de Barcelona, Martí i Franques, 1-11, 08028 Barcelona, Spain Department of Chemistry, Illinois State University, Campus Box 4160, Normal, IL 61790, USA

a r t i c l e

i n f o

Article history: Received 8 February 2015 Received in revised form 8 April 2015 Accepted 8 April 2015 Available online xxxx Keywords: Vanadium phosphatase complexes Transition state analog Phosphoryl group transfer Continuous shape measures Trigonal bipyramid

a b s t r a c t Shape analysis of coordination complexes is well-suited to evaluate the subtle distortions in the trigonal bipyramidal (TBPY-5) geometry of vanadium coordinated in the active site of phosphatases and characterized by X-ray crystallography. Recent studies using the tau (τ) analysis support the assertion that vanadium is best described as a trigonal bipyramid, because this geometry is the ideal transition state geometry of the phosphate ester substrate hydrolysis (C.C. McLauchlan, B.J. Peters, G.R. Willsky, D.C. Crans, Coord. Chem. Rev. http://dx.doi.org/ 10.1016/j.ccr.2014.12.012 ; D.C. Crans, M.L. Tarlton, C.C. McLauchlan, Eur. J. Inorg. Chem. 2014, 4450–4468). Here we use continuous shape measures (CShM) analysis to investigate the structural space of the fivecoordinate vanadium–phosphatase complexes associated with mechanistic transformations between the tetrahedral geometry and the five-coordinate high energy TBPY-5 geometry was discussed focusing on the protein tyrosine phosphatase 1B (PTP1B) enzyme. No evidence for square pyramidal geometries was observed in any vanadium– protein complexes. The shape analysis positioned the metal ion and the ligands in the active site reflecting the mechanism of the cleavage of the organic phosphate in a phosphatase. We identified the umbrella distortions to be directly on the reaction path between tetrahedral phosphate and the TBPY-5-types of high-energy species. The umbrella distortions of the trigonal bipyramid are therefore identified as being the most relevant types of transition state structures for the phosphoryl group transfer reactions for phosphatases and this may be related to the possibility that vanadium is an inhibitor for enzymes that support both exploded and five-coordinate transition states. © 2015 Elsevier Inc. All rights reserved.

1. Introduction The hydrolysis of phosphate esters is established to go through fivecoordinate phosphorus species and is recognized and referred to as the transition state geometry [1–5]. Because phosphorylation [6] is one of the key signal transduction messages [7], this reaction has an essential place in life-processes [8–11] on top of being an interesting reaction interconverting fundamentally different geometries. Although the ideal geometry of such transition states has the phosphorus or the metal replacement in a perfect trigonal bipyramidal (abbreviation recommended by IUPAC as TBPY-5) geometry, studies more often demonstrate that the TBPY-5 structures are distorted from the ideal geometry [12,13]. Many experimental [14–22] and theoretical experiments [3, 23–29] have been conducted to understand the reaction mechanism for phosphate ester hydrolysis [30–33], with some divergent conclusions, due to the multiple plausible mechanisms and subtle differences in experimental systems as protonation state and leaving group for phosphate ester hydrolysis varies [3]. Recent studies have used data ⁎ Corresponding authors. E-mail addresses: [email protected] (S. Alvarez), [email protected] (D.C. Crans).

mining procedures to describe the vanadium–phosphatase complexes [12,34,35]. Because five-coordinate geometries are either TBPY-5 or square pyramidal (abbreviated by IUPAC as SPY-5), both geometries should be possible for vanadium to adopt in the protein active sites [12], although distortions in-between are also possible and, in fact, most frequently observed [34]. In small molecule (model) systems, geometric restrictions are generally attributed to coordinating ligands that distort the metal ion coordination environment, however, in a protein-complex such coordinating ligands are typically the protein. In the case of the phosphatases, the protein is generally coordinated in a monodentate manner, and such distortion would be expected to be minimal. However, as recently reported, the vanadium bound to phosphatases so far have been found to be in a TBPY-5 or distorted TBPY-5 geometry [12], even though the corresponding small molecules are overwhelmingly observed to have the square pyramidal geometry (SPY-5) [34]. In the present manuscript we examine the distortions observed in the vanadium bound in phosphatase complexes using the continuous shape measures (CShM) approach and examine how these distortions fall along the reaction pathway from a tetrahedral (unbound) to trigonal bipyramidal geometry (bound). Describing the geometry of five-coordinate complexes can be nontrivial because the geometries are often distorted from the ideal TBPY-5 and

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Please cite this article as: I. Sánchez-Lombardo, et al., Evaluating transition state structures of vanadium–phosphatase protein complexes using shape analysis, J. Inorg. Biochem. (2015), http://dx.doi.org/10.1016/j.jinorgbio.2015.04.005

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SPY-5 geometries. A well-known class of distortions includes those along the Berry interconversion path between TBPY-5 and SPY-5 geometries (Scheme 1a) [36,37]. The simple index angular parameter, tau (τ), was introduced by Addison et al. to calculate any potential distortion, where τ = (β − α) / 60 [38], although there are some limitations to τ. At one extreme as shown in Fig. 1a, τ = 0 for a simple ideal SPY-5 geometry: where B, C, D, E, and M are co-planar, and the two basal angles α and β (Fig. 1a) are each 180° [38]. For the ideal TBPY-5 geometry, τ = 1 because the α and β angles (as shown in Fig. 1c) lead to τ = (180 − 120) / 60 = 60 / 60. The more common distorted structures which fall “in between” these extremes, then, will have a τ value between 0 and 1. The choice of co-planar B, C, D, E, and M is one area of contention of the definition of this structure for the SPY geometry (Fig. 1b) and can perhaps be argued to be less defined, so other methods such as the CShM method can be used to better describe these systems (Scheme 1b, c and d) [39,40]. However, because of the simplicity of the τ analysis, distortions other than those on the Berry pathway are not properly identified in the simple τ analysis. The CShM is a quantitative measure that investigates distortions in a material and provides an output deviation value, S [41–44]. The material can be composed of simple or more complex molecules. A molecule can be subjected to a range of distortions including those found on the Berry pathway between the TBPY-5 and SPY-5 of a vanadium compound [41–44]. Depending on the molecule the distortion can be minor or more extensive and the S value small or large. Specifically, this analysis is based on the application of shape measures to determine how far or how close the geometries are from an ideal polyhedral shape, e.g. the D3h TBPY-5 for a compound with five identical ligands. This analysis therefore calculates the distance to this ideal reference shape, independent of size and orientation [45]. That is, the analysis simply calculates the distances between observed positions such as M–X and M–Y and compares them to the ideal location of a particular shape M–X0 and M–Y0. The CShM analysis allows us to compare (on the same scale) the distortion of different molecules from the same ideal shape, or of the same molecule to different shapes [43]. The calculation, then, provides a deviation to the particular shape investigated as output, S. For example, if the geometry is at the ideal 5-coordinate TBPY-5 geometry then the shape measure relative to the trigonal bipyramid is S(TBPY-

5) = 0. Because the shape analysis is based on the use of atom positioning, when examining the positioning such as that in the bond lengths involved in bond breaking and bond forming processes (e.g. those in phosphate ester hydrolysis) the analysis is now directly examining the reaction coordinate of a reaction. The reaction progress can therefore easily be addressed by a shape analysis. In this work we obtain numerical values using CShM analysis [42] for the pentacoordinate vanadium molecules that are phosphate ester hydrolysis transition state analogs. The CShM approach provides a means for handling the cases where, for example, a metal ion is placed in an environment that is ill-defined with regard to the coordination geometry. Such cases often contain several secondary interactions to Lewis bases at distances significantly longer than those expected for a chemical bond, i.e. larger than the sum of the atomic covalent radii by 0.2 Å or more [43]. Within such a framework, CShM allows one to compare in a quantitative way the distance between a set of atoms from that given in an ideal shape (i.e., a polyhedron). One of the advantages of such an approach is that one can in many instances accurately describe structures that are along the path of interconverting two polyhedra with the same number of vertices (e.g., trigonal bipyramidal, TBPY-5, to square pyramidal, SPY-5) [43]. Although this method is generally used for the evaluation of inorganic materials, this approach could be used to examine the metal ion geometry in the active sites of proteins. The comprehensive exploration of the different distortions of the trigonal bipyramid of vanadium placed in the active sites of the vanadate– phosphatase complexes was exemplified by the reaction pathway of the protein tyrosine phosphatase 1B abbreviated PTP1B [46–49]. The PTP1B is the key protein tyrosine phosphatase that is implicated in the insulin enhancing properties of vanadate and vanadium complexes [50–55]. We therefore propose to use shape measures analysis S(TBPY-5) to provide insights on the distortion of the systems along the reaction pathway, which unlike the τ analysis will also involve distortions other than those defined by the Berry pathway. That is, whereas τ analysis could not differentiate between the two SPY-5 forms shown in Fig. 1a and b, CShM would conclude that only Fig. 1b is SPY-5 (S(SPY-5) = 1.74 vs. S(SPY-5) = 0). Furthermore, the CShM analysis defines an alternative ideal square pyramid to that of Fig. 1a, referred to as a vacant octahedron (vOC-5), and also to explore all intermediate square pyramids

Scheme 1. Distortions to the TBPY-5 geometry are illustrated. (a) the Berry distortion; (b) the anti-Berry distortion; (c) the umbrella distortion and (d) the conversion pathway describing the tetrahedron to TBPY-5.

Please cite this article as: I. Sánchez-Lombardo, et al., Evaluating transition state structures of vanadium–phosphatase protein complexes using shape analysis, J. Inorg. Biochem. (2015), http://dx.doi.org/10.1016/j.jinorgbio.2015.04.005

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Fig. 1. Three schematic drawings of five-coordinate covalent protein–vanadate complexes with vanadium in the (a) “square pyramidal” (SPY-5) geometry with M co-planar to the ligands, (b) square pyramidal geometry (SPY-5) with the M as commonly found above the plane of the ligands (typically 0.3–0.6 Å), and (c) trigonal bipyramidal geometry (TBPY-5).

along the path from SPY-5 to vOC-5 (Fig. S1). It must be noted, though, that of all the structures with pentacoordinated V in the Cambridge Structural Database (CSD) [56] none have a vOC-5 coordination sphere. The hydrolysis of an organic phosphate when initiated by a nucleophilic attack on the phosphate group will depend on the phosphate, its leaving group, spectator groups and nucleophiles convert the tetrahedral phosphorus to a five-coordinate transition state geometry or an exploded transition state [3,47,57–62]. The exact nature of the transition states are complex, with phosphate triesters or diesters with a poor leaving group the five-coordinate transition states are believed to form, whereas with the more reactive monoesters a more exploded transition state is to be expected [3]. In the case of PTP1B the reaction has been studied in detail and if the reaction is monoanionic– rather than dianionic– the transition state is less exploded [57,58]. Vanadium is larger than the phosphorus, as evidenced by the V\\O and P\\O bond lengths of 1.9 Å and 1.6 Å, respectively. As a result, vanadium will take up more space than the phosphorus-centered transition state, and in this case it may be that the vanadium inhibitors will capture both enzyme catalyzing reactions through the five-coordinate transition state as well as an exploded transition state. The shape analysis carried along the reaction pathway of the phosphate hydrolysis reaction will vary from the tetrahedral structure to the TBPY-5 (Scheme 1d) [34]. However, alternative distortions are possible (Fig. S1). The Berry pseudorotation pathway exchanges equatorial and axial ligands in a TBPY-5 structure through a square pyramidal intermediate in a concerted way (Scheme 1a, Fig. S1) [42]. The ecT-5 anti-Berry pathway can be thought of as being along the pathway for the dissociation of an equatorial X ligand in a TBPY-5 to render a tetrahedral complex, which could be alternatively described as an edge-capped tetrahedron (ecT-4, Scheme 1b) [43]. A third type of distortion is referred to as an umbrella distortion (Scheme 1c). This displacement involves moving three equatorial ligands from the basal plane of the TBPY-5 and is a non-Berry angular distortion [42]. The umbrella distortion of a TBPY-5 can be extrapolated to a tetrahedral coordination sphere in which an axial ligand capping a tetrahedral face is at infinite distance (fcT-5, Scheme 1c). Finally, we have chosen to apply the labels semi-Berry or semi-anti-Berry for those distortions in which only one of the two axial ligands is displaced from the trigonal symmetry axis, either toward an equatorial edge (semi-Berry) or vertex (semi-anti-Berry) (Fig. S1) [40,42]. Mechanistic studies are generally indirect because the intermediates and transition states per definition need to be high energy and generally very short-lived [16,17,63,64]. Such conundrum is coupled to the fact that mechanisms cannot be proven, but only disproven [23,29]. However, computational approaches allow for the visualization and optimization of lowest energy pathways. It is therefore not surprising that the current literature includes several computational studies which have explored the reaction mechanisms of the phosphoryl group transfer and hydrolysis of phosphate esters [3,23–29]. In a complementary approach,

mechanistic scientists have also invoked structural information by characterization of X-ray crystal structures along the reaction pathway [27,47, 65–68]. These studies provide some experimental data that can support the efforts of the computational scientists [33,69], however, because these X-ray structures are mathematically solved [70,71], how close they are to actual structures on the reaction pathway and energy surface is rarely evaluated, because tools to prove these questions are not readily available. In the present manuscript we demonstrate that CShM analysis can be used to evaluate the known X-ray structures with regard to their role in the reaction pathway. Because the method is excellent at investigating bond-breaking and bond-forming processes, it could become an excellent tool for the mechanistic chemist. Here we have been able to identify structures that are likely to be on the reaction path of phosphate ester hydrolysis for the PTP1B phosphatase and provided additional insights into the use of the available X-ray structures in a mechanistic analysis. 2. Methods According to the proposal of Avnir and coworkers [39,72], in order to obtain a shape measure for a structure X relative to an ideal shape A, we need first to search for the ideal shape A that is closest to our problem structure. This search requires optimization with respect to size, orientation in space and pairing of vertices of the two structures. Once the reference shape is found, we calculate the distances between the equiv! ! alent atomic sites from their position vectors xk and ak , and the shape measure is calculated according to Eq. (1), in which the denominator is a normalization factor that makes the continuous shape measures (CShM) size independent. By definition, SX(A) must be minimized with respect to size, orientation and vertex pairing. 2 3 N  2 X ! 6 ! x k− a k 7 6 7 6 7 SX ðAÞ ¼ min6 k¼1 N 7100 6 7 X !2 5 4 ak

ð1Þ

k¼1

From the shape measures we can derive path deviation functions [45] and generalized polyhedral interconversion coordinates [73]. All shape parameters have been calculated with the SHAPE 2.1 program [74], which can be obtained from the authors upon request. To disregard the deviations from ideal geometries due to differences in bond distances, we have used throughout this paper normalized coordination polyhedra versions of the X-ray coordination polyhedra, that reveal therefore only the angular distortions, as discussed elsewhere [43]. The structural data analyzed was retrieved from the Protein Data Bank (PDB) [75] and from the Cambridge Structural Database (CSD), version 5.36 [56].

Please cite this article as: I. Sánchez-Lombardo, et al., Evaluating transition state structures of vanadium–phosphatase protein complexes using shape analysis, J. Inorg. Biochem. (2015), http://dx.doi.org/10.1016/j.jinorgbio.2015.04.005

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of a wide sample of other vanadium–protein complexes in the PDB. The results are plotted in a Berry shape map in Fig. 2 with the x-axis being the deviation from the TBPY-5 geometry (abbreviated S(TBPY5)) and the y-axis being the deviation from the SPY-5 geometry (abbreviated S(SPY-5)). As shown in Fig. 2 the observed vanadium geometries associated with the proteins in the PDB are strikingly in favor of the TBPY-5 structures (or no well-described geometry) with no examples of SPY-5 geometries. This observation is in contrast to the small molecules found in the CSD, where the SPY-5 geometry was the major geometry found for 5-coordinate vanadium compounds [34]. The vanadium–phosphatase protein geometries are compared to the minimal distortion pathways from TBPY-5 (a) to SPY-5 (Berry pathway; Scheme 1a), to the edge-capped tetrahedron ecT-5 (anti-Berry

3. Results and discussion 3.1. CShM analysis of V-atoms in vanadate–phosphatase crystallographically characterized materials The structural data of a set of five-coordinate vanadium centers in metalloproteins in the PDB analyzed previously [12] using the τ parameter [38] was subjected to a shape analysis (Table 1). For all structures we have calculated the continuous shape measures (CShM) of the normalized coordination spheres relative to the trigonal bipyramid S(TBPY5) and relative to the square pyramid S(SPY-5). If one of the shape measures S is less than or equal to 0.4, the corresponding shape is assigned. Besides the vanadium–phosphatase complexes, we carried an analysis

Table 1 Selected shape measures S(TBPY-5), path deviation functions Δa, and tentative shape assignment for the coordination environment of the vanadium centers in vanadium phosphatase complexes with VO4X (where X is anything but an O or a N atom) coordination environments obtained from the PDB. See Fig. S1 for shape illustrations and abbreviations. Name

PDB IDb

X

S(TBPY-5)

Δ(Berry)

PTP1B PTP1B W179F Purple acid phosphatase PTP1B Acid phosphatase Glucosyl-3-phosphoglycerate phosphatase Purple acid phosphatase Purple acid phosphatase Purple acid phosphatase W354F PTPase Bact KDN-9P Bact KDN-9P HPTP-b-CD HPTP-b-CD Bact KDN-9P Bact KDN-9P Low Mr PTP Alkaline phosphatase SSu72 phosphatase Alkaline phosphatase Alkaline phosphatase Phox Alkaline phosphatase Phox SSu72 phosphatase SSu72 phosphatase Mannosyl-3-phosphoglycerate HPP wild type NPP Acid phosphatase A (AcpA) NPP Glucosyl-3-phosphoglycerate phosphatase SSu72 phosphatase RPTPγ Phosphoacetate hydrolase RPTPγ YopH protein tyrosine phosphatase N-acylneuraminate-9-phosphatase N-acylneuraminate-9-phosphatase RPTPγ N-acylneuraminate-9-phosphatase RPTPγ Mannosyl-3-phosphoglycerate Acid phosphatase A (AcpA) Survival protein E (SurE) Survival protein E (SurE) W354F PTPase Phosphatase PhoE (fka YhfR) Phosphatase PhoE (fka YhfR) PTP10D HPP D10A mutant VHZ — short PTP

3i80 3qkq 4kkz_a 3i7z 1rpt 4qih_a 4kkz_b 4kkz_c 4kkz_d 3f9b_c 3e81_d 3e81_c 2i4e_b 2i4e_a 3e81_a 3e81_b 1z12 1b8j_a 3omx_c 1b8j_b 3zwu_b 3zwu_a 3omx_a 3omx_b 3zx5_b 2rbk 2gso_b 2d1g_a 2gso_a 4qih_b 3omx_d 3qcd 3t00 3qcc 2i42 4knw_a 4knw_b 2hy3_a 4knw_c 2hy3_b 3zwk 2d1g_b 1j9L_a 1j9L_b 3f9b_b 1h2f_a 1h2f_b 3s3f 2rar 4erc

S S O S N N O O O S O O S S O O S O S O O O S S O O O O O N S S O S S O O S O S O N O O O N O S O S

0.08 0.1 0.12 0.13 0.17 0.18 0.19 0.19 0.2 0.22 0.23 0.25 0.26 0.27 0.31 0.32 0.48 0.63 0.71 0.82 0.85 0.89 0.91 0.94 0.97 1.29 1.33 1.43 1.56 1.67 2.08 2.09 2.42 2.64 3.34 3.43 3.88 4.66 4.75 5.66 5.74 5.92 8.28 10.55 8.6

2 11 8 12 13 4 3 4 2 12 16 21 3 6 22 21 29 26 29 30 37 39 30 13 37 40 24 48 28 52 50 62 67 76 81 101 102 93 101 104 126 127 154 166 116

a b c d e f g

Δ(Anti)

13 13 16 17 16 18

20 9 25 21 7 18 7 33 38 38 34 38 45 47 42 37 33 34 60 36 85 81 68

Δ(Umb5)

Δ(Umb4)

14

12

5 5 25

6 5

21 44

7

36

3

36 47 14 29 14 135 14 47 81 77 111 169 110 140 152 215

18 7 13 8 6 4 1 23 1 26 17

5 2 4 5 1

Shapec

Ref.

TBPY-5 TBPY-5 TBPY-5 TBPY-5 TBPY-5 TBPY-5 TPBY-5 TBPY-5 TBPY-5 TBPY-5 TBPY-5 TBPY-5 TBPY-5 TBPY-5 TBPY-5 TBPY-5 TBPY-5 TBPY-5 Umb TBPY-5 Umb Umb TBPY-5 TBPY-5 Umb SemiBerry + umbd Anti-Berryd Umb Anti-Berryd Umb SemiAnti + Umbd Tetrahedral Tetrahedral Tetrahedral 5 + 2e Tetrahedral Tetrahedral Tetrahedral Tetrahedral Tetrahedral TP-3f Tetrahedral Tetrahedral Tetrahedral vPPY(4.26)g Tetrahedral Tetrahedral Tetrahedral Umb Umb

[47] [48] [76] [47] [77] [78] [76] [76] [76] [79] [80] [80] [81] [81] [80] [80] [82] [83] [84] [83] [85] [85] [84] [84] [86] [87] [13] [88] [13] [78] [84] [89] [90] [89] [91] [92] [92] [93] [92] [93] [86] [88] [94] [94] [79] [95] [95] [96] [87] [97]

Relative to the Berry, anti-Berry and umbrella pathways, in the latter case considering (Umb5) or disregarding (Umb4) the ligand at a longer distance. When more than one crystallographically unique center is present, it is indicated by _a, _b, etc. Geometry intermediate along the umbrella pathway. Strong distortion of the TBP with the mode indicated. 5 + 2 indicates pentacoordination with two additional weakly coordinated ligands. TP-3 indicates a trigonal planar geometry. vPPY-4 indicates a pentagonal pyramid with a vacant basal position (the corresponding shape measure is given in parentheses).

Please cite this article as: I. Sánchez-Lombardo, et al., Evaluating transition state structures of vanadium–phosphatase protein complexes using shape analysis, J. Inorg. Biochem. (2015), http://dx.doi.org/10.1016/j.jinorgbio.2015.04.005

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Fig. 2. Structural deviation of the normalized coordination spheres of all vanadium– protein complexes reported in the PDB from the trigonal bipyramid and the square pyramid, represented by the corresponding shape measures S(TBPY-5) and S(SPY-5), respectively, showing the Berry interconversion pathway (continuous line). Phosphatases are shown as red squares and all other vanadium–protein complexes are displayed as blue crosses. The majority of red squares cluster near the y axis that indicates small deviations from the TBPY-5 geometry (S(TBPY-5) ≈ 0) and assignment as having trigonal bipyramidal geometry. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

pathway, Scheme 1b) and to the face-capped tetrahedron fcT-5 (umbrella pathway, Scheme 1c). In addition, the geometries are also compared to the minimal distortion pathway between the square pyramid (SPY-5) and the vacant octahedron vOC-5 (pyramidalization pathway, Fig. S1d). Each structure is assigned to the structure on the pathway that gives the smallest value of the path deviation function (Δ(Berry), Δ(Anti) and Δ(Umb5) in Table 1), provided it does not exceed 20%. Within each pathway, they are assigned the alternative ideal shape if it is less than 40% distorted along the path to the TBPY-5. Structures that are in the central part of the chosen pathway (from 40 to 60% along the path from one polyhedron to another), have not been assigned a shape, but we specify in Table 1 the type of distortion from the TBPY-5 that best describes their stereochemistries. In some compounds the vanadium atom appears as four-coordinate, or with a fifth donor atom at a longer distance, i.e. larger than the sum of the atomic covalent radii by 0.2 Å or more, and away from the trigonal axis of the VO4 moiety such as to make it deviate from the distortion paths of the TBPY-5. The structures of these compounds were thus compared with structures on the pyramidalization pathway without one axial ligand, i.e., the path from the tetrahedron to the vacant trigonal bipyramid and structures that deviate little from that path (Δ(Umb4) in Table 1) but cannot be classified as TBPY-5 are described as umbrellas. Using this approach we can detect a weak coordination of an incoming ligand even without locating it, by just observing how the rest of the coordination sphere is affected by the increase in coordination number [43]. The most relevant numerical results and the resulting stereochemical assignments are given in Table 1. The values of path deviation functions that are not required are omitted for simplicity, and so are those that are too large to merit consideration, focusing on those that may be interesting for comparison. The general interpretation that can be deduced from the stereochemical assignments of V centers proposed in Table 1 is rather similar to that obtained by an earlier analysis using τ parameters [12]. Both analyses conclude that the most common coordination geometry is the TBPY-5, while practically no SPY-5 structures are found. Also, a number of tetrahedral vanadium centers barely affected in their geometries by a nearby donor atom from a protein were identified in both analyses.

5

Allowing for a more detailed stereochemical description of each particular compound, some relevant differences appear. The results are plotted in a Berry shape map in Fig. 3. Table 2 summarizes the original assignment reported by the authors, stereochemical assignments based on the Addison's parameter (τ) and the trigonal bipyramidal shape measure S(TBPY-5) for the CShM approach. Some key stereochemical characteristics were expanded on and listed in Table 1. In many cases, both approaches similarly describe the vanadium coordination spheres as TBPY-5 with some degree of distortion. The main difference is that the τ parameters assume that the distortions are of the Berry type, whereas our present CShM shape analysis measures three different types of distortions and provides a quantitative estimate of the degree of distortion of each type. Specifically, we compare in a quantitative manner how well is a compound described as Berry, anti-Berry or umbrella distorted. Therefore, when previously vanadium in the bacterial enzyme KDN-9P from Bacteroides thetaiotaomicron (3e81_c) [80] was described as an “almost ideal TBPY-5” [12] (τ = 0.95 presumably of the Berry type distortion) when using the CShM method we can be more explicit and correctly identify it as a TBPY-5 with a strong antiBerry distortion. Clarification on the distortions emerges in several cases using the CShM analysis, due to the ability of the CShM analysis to detect the non-Berry distortions, anti-Berry distortion, and umbrella distortion. One example is in the only small molecule example in the CSD with a VO4S coordination geometry (Refcode ebigif) [98], the vanadium center is classified as a square pyramid based on its τ parameter of 0.17 [34]. The CShM analysis, however, gives a large shape measure relative to the SPY-5 (1.84) showing that it cannot simply be assigned that stereochemistry but instead is a trigonal bipyramid with a strong (58%) antiBerry distortion. Also W354F PTPase (PDB ID 3f9b_b) [79], which is described with a τ = 0.07 has been classified as a square pyramid, whereas its square pyramidal shape measure of 4.26 indicates that such an assignment does not properly reflect the real geometry of this system. Visual inspection suggests that this structure is closer to a pentagonal pyramid with a missing vertex (Fig. S1e), a description that is supported by shape measures that place that structure approximately 83% along the pathway from the trigonal bipyramid to the pentagonal pyramid. Other examples such as phosphoacetate hydrolase (PDB ID 3t00) [90] and RPTPγ (PDB ID 3qcc) [89] have τ values of 0.83 and 0.98, respectively. Although their τ values indicate that these geometries are close to the TBPY-5, the CShM shape measures relative to that polyhedron (2.42 and 2.64, respectively) show that they are far from a trigonal bipyramidal geometry. Our shape analysis reveals that these structures are best described as VO4 tetrahedra with a weakly coordinated X atom, with 33 and 22% along the umbrella path to trigonal bipyramid (Scheme 1d). Another example is NPP (PDB ID 2gso_a) [13], which has a τ value of 0.55. This τ value places it roughly midway between the TBPY-5 and the SPY-5 geometries, i.e., along the Berry pathway. However, its deviation from the Berry pathway according to CShM analysis is rather large (28%), and comparison with other distortions of the TBPY-5 nicely identifies an anti-Berry distortion from TBPY-5. 3.2. Comparison with the V-sites in Cambridge Structural Database A search carried out in the CSD [56] for all V atoms with five bonds to elements of groups 14–17, excluding those with disorder, returns 2619 crystallographically independent structural data sets. The shape measures of the normalized coordination polyhedra relative to the TBPY-5 and the SPY-5 are presented in Fig. 3. Fig. 3a illustrates the conversion from SPY-5 through a Berry pathway to TBPY-5. On the other hand the histogram in Fig. 3b shows that there are a large number of structures that deviate significantly from the Berry pseudorotation pathway. For small molecules the large deviations from the Berry path may in part be attributed to bi- and multidentate ligands that introduce geometrical constraints to the vanadium coordination sphere, and in part depend on electronic and steric intramolecular preferences and other

Please cite this article as: I. Sánchez-Lombardo, et al., Evaluating transition state structures of vanadium–phosphatase protein complexes using shape analysis, J. Inorg. Biochem. (2015), http://dx.doi.org/10.1016/j.jinorgbio.2015.04.005

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Fig. 3. (a) Shape map showing the structural data for all VL5 complexes (L = group 14–17) found in the CSD (triangles), compared to the Berry pathway (continuous line, n = 2619). The drawings indicate the position of the ideal TBPY-5, which appears at S(TBPY-5) = 0, and therefore on the S(SPY-5) axis, and conversely for the ideal SPY-5. (b) Probability density distribution of the deviation from the Berry pathway among the set of all non-disordered five-coordinate vanadium complexes found in the CSD (white bins) and for the subset of complexes with monodentate ligands (gray bins). (c) Shape map showing the structural data for all VO4X (where X is everything but an O or a N atom) complexes found in the CSD [34], compared to the Berry pathway (continuous line). The solid circles correspond to complexes with only monodentate ligands; empty squares to complexes forming chelate rings. (d) Probability density distribution of the deviation from the Berry pathway for the two sets of structures shown in the VO4X shape map in (c): white bins for the chelated and gray bins for the non-chelated complexes.

crystallographic effects such as intermolecular interactions. If we restrict our exploration to pentacoordinate vanadium complexes with monodentate ligands only, then most of the structures can be classified as SPY-5, TBPY-5 or intermediate geometries along the Berry pseudorotation pathway, according to their shape measures relative to the two ideal polyhedra and their path deviation function relative to the Berry pathway (Fig. 3b). Classifying the structures with monodentate ligands as being along the Berry pathway if they present path deviation functions of a 20% at most, 73% of those structures are found to be along the Berry path. These include 13% of TBPY-5s and a 38% of SPY-5s (using a cutoff for the corresponding polyhedral shape measures of 0.5), with the remaining 22% having intermediate Berry shapes. The preference for the SPY-5 compared to the TBPY-5 geometry is in qualitative agreement with our previous analysis based on the τ parameter [34]. Considering only the subset of VO 4X species analyzed that are relevant for the present study (Fig. 3c), we see the same trend: There are structures that present geometries along the Berry pathway, whereas other structures present significant non-Berry distortions. If we concentrate

on molecules with monodentate ligands, then the picture is simpler, since they are all aligned along the Berry pathway (Fig. 3d), pointing to the chelate rings as the major cause of the non-Berry distortions. 3.3. Distortion along the tetrahedral–TBPY-5 pathway for the phosphate ester hydrolysis The basic geometry for the V-atoms in crystallized vanadate–protein complexes is generally some type of distorted TBPY-5 structure. Although nearly all TBPY-5 structures in the PDB database show small but distinct distortions of the Berry and anti-Berry types some exhibit a greater degree of distortion. To explore the structures on the path between the tetrahedral vanadium toward the Berry type distortion we show in Fig. 4 a plot of structures in which the VO4X group is bereft of the ligand at longest distance, be it X or an oxido ligand. In such a plot we can observe how the geometries (often VO4) evolve from a tetrahedron (abbreviated as T-4) to a TBPY-5 that has lost a ligand (abbreviated as vTBPY-4). Such a plot allows us to visualize how these structures describe a reaction coordinate for a ligand association reaction to

Please cite this article as: I. Sánchez-Lombardo, et al., Evaluating transition state structures of vanadium–phosphatase protein complexes using shape analysis, J. Inorg. Biochem. (2015), http://dx.doi.org/10.1016/j.jinorgbio.2015.04.005

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Table 2 Comparison of active site geometries as described by the authors, by the τ-parameter and by CShM analysis. Name

Nua

PDB ID

Author assignment

τ

Acid phosphatase Glucosyl-3-phosphoglycerate phosphatase Glucosyl-3-phosphoglycerate phosphatase YopH protein tyrosine phosphatase Small molecule Bact KDN-9P Alkaline phosphatase Phosphatase PhoE (fka YhfR)

His His

1rpt 4qih_a

TBPY-5

His

4qih_b

Cys

2i42 ebigif 3e81_c 1b8j_b 1h2f_a

Not TBPY-5 SPY-5 Almost ideal TBPY-5 Distorted TBPY-5

1h2f_b

Tetrahedral

1j9l_a 2gso_a 2d1g_a 2rbk

Distorted square pyramid TBPY-5 Distorted TBPY-5 Distorted TBPY-5 Distorted tetrahedral Distorted TBPY-5 Distorted TBPY-5 Distorted TBPY-5 TBPY-5 Distorted TBPY-5 Near TBPY-5 Near TBPY-5 Distorted tetrahedral Distorted TBPY-5 Nearly perfect TBPY-5

Survival protein E (SurE) NPP Acid phosphatase A (AcpA) HPP wild type

Asp Ser His, Glu covalent His, Glu covalent – Thr Ser Asp

HPP D10A mutant Mannosyl-3-phosphoglycerate Mannosyl-3-phosphoglycerate N-acylneuraminate-9-phosphatase Low Mr PTP Phosphoacetate hydrolase RPTPγ RPTPγ RPTPγ HPTP-b-CD PTP1B PTP1B PTP1B W179F W354F PTPase

Asp Asp Asp Asp Cys Thr Cys Cys Cys Cys Cys Cys Cys O

W354F PTPase SSu72 phosphatase PTP10D

Cys Cys –

2rar 3zx5_b 3zwk 4knw_a 1z12 3t00 3qcc_b 3qcd 2hy3_a 2i4e_a 3i80 3i7z 3qkq 3f9b_b (O) 3f9b_c (S) 3omx_a 3s3f

VHZ — short PTP Alkaline phosphatase Phox Purple acid phosphatase

Cys O OEt

4erc 3zwu_b 4kkz_d

Phosphatase PhoE (fka YhfR)

a b

TBPY-5 SPY-5 TBPY-5 TBPY-5 Tetrahedral + long dist Cys Not TBPY-5

S(TBPY-5)

CShM shape, distortion

Agreeb Ref.

0.91 0.85

0.17 0.18

TBPY-5, 12% anti-Berry TBPY-5, 18% Berry

✓

0.81

1.67

Umbrella, 56% TBPY-5

0.3 0.17 0.95 0.77

3.34

5+2 TBPY-5 anti-Berry 58% TBPY-5, 21% Berry TBPY-5, semi-Berry Tetrahedral, 28% umbrella

✘ ✓ ✓

[91] [98] [80] [83] [95]

Tetrahedral, 21% umbrella

✓

[95]

Flattened tetrahedron TBPY-5, 36% anti-Berry Umbrella, 58% TBPY-5 TBPY-5, semi-Berry +

✘ ✓ ✓ ✓

[94] [13] [88] [87]

✓ ✘ ✘ ✘ ✓ ✘ ✘ ✘ ✓ ✓ ✓ ✓ ✘

[87] [86] [86] [92] [82] [90] [89] [89] [93] [81] [47] [47] [48] [79]

✓ ✓ ✓

[79] [84] [96]

0.43 0.55 0.76 0.78

0.25 0.82

8.28 (10.55) 1.56 1.43 0.78

0.89 0.97 0.56 5.74 1.07 3.43 0.88 0.48 0.83 2.42 0.98 2.64 0.91 2.09 0.76 4.66 0.82 0.27 0.9 0.08 0.83 0.13 0.88 0.1 0.07 (SP = 4.26)

umbrella Umbrella, 55% TBPY-5 Umbrella, 43% TBPY-5 Trigonal planar Tetrahedral, 6% TBPY-5 TBPY-5, semi-Anti-Berry Tetrahedral, 33% TBPY-5 Tetrahedral, 22% TBPY-5 Tetrahedral, 37% TBPY-5 Tetrahedral, 26% umbrella TBPY-5, 22% Berry TBPY-5 TBPY-5, 11% anti-Berry TBPY-5, 9% anti-Berry Vacant pentagonal PY

0.78 0.73 0.88

TBPY-5, 20% Berry TBPY-5, 28% anti-Berry Tetrahedral, 5% TBPY-5

0.35 0.84 0.83

0.9 0.91

0.85 0.2

Umbrella, 46% TBPY-5 Umbrella, 57% TBPY-5 TBPY-5

[77] [78] [78]

[97] [85] [76]

Nu = nucleophile. This column indicates whether there is an agreement between the τ-value and the shape analysis ([√]) or not ([X]).

Fig. 4. Shape map for the VO4 fragments when one ignores the long V⋯X in the VO4X centers (where X is everything but an O or a N atom) in vanadate–phosphatase complexes that conform approximately to the umbrella distortion path that goes from the tetrahedron (T-4) to the axially vacant trigonal bipyramid (vTBPY-4). The structures are assigned one of the two extreme ideal shapes if they are within 40% along the path, or an intermediate umbrella shape if they are in the middle region of the map.

vanadium forming a TBPY-5 geometry, and proceeding to complete an SN2 substitution reaction arriving at the T-4 geometry by losing a ligand and deviating from the TBPY-5 with a vacant site (Scheme 2). The plot in Fig. 4 identified three regimes of the structures. The first regime with distortions of the TBP-5 characterized as “tetrahedron” in Fig. 4, are those structures that appear as four-coordinate with a fifth weakly coordinated atom as expected when a fifth ligand is approaching a phosphate in the initial attack during phosphate ester hydrolysis. When the fifth ligand distance is particularly long, that structure may deviate from others, and this atom in the axial position be ignored and result in parameters that are inconsistent with a TBPY-5 geometry. These structures can be described as a geometry of a 4-coordinate tetrahedral vanadium with an incoming fifth ligand, and thus represent a structure early in the reaction pathway (Scheme 2). The group of structures that exhibit umbrella distortions covers a broad range of structures and distortions. The second regime located in the middle of the figure and labeled “umbrella” represents structures that are distorted along a pathway in which one ligand is stretched away from the incoming ligand and thus now structurally is reflecting a departing ligand. The geometry shown in Scheme 2 formed along the pathway of T-4 converting to the distorted TBPY-5. Specific examples include the cases of glucosyl-3-phosphoglycerate phosphatase (PDB ID 4qih_b) [78] and mannosyl-3-phosphoglycerate (PDB ID 3zx5_a) [86], where one of the oxido ligands has been practically replaced by a donor atom from the protein, in a nearly tetrahedral complex. These umbrella-distorted TBPY-5 geometries are approaching

Please cite this article as: I. Sánchez-Lombardo, et al., Evaluating transition state structures of vanadium–phosphatase protein complexes using shape analysis, J. Inorg. Biochem. (2015), http://dx.doi.org/10.1016/j.jinorgbio.2015.04.005

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Scheme 2. Umbrella distortions in vanadium–phosphatase complexes along the pathway of phosphate ester hydrolysis.

the structure of the first and second transition states/intermediates on the phosphate ester hydrolysis path. These geometries all show a bond to a fifth ligand which can be viewed as an incoming nucleophile attacking a central “phosphate group”, and is the structure most directly representing the first TBPY-5-transition state on the energy surface. This TBPY-5 umbrella distortion is also shown in Scheme 2, which shows the key distortions that take place along the phosphate ester hydrolysis pathway, and eventually going on to complete the SN2 substitution reaction. Whereas most of the structures can be explained by the shapes and distortion pathways discussed so far, there are some that represent linear combinations of such modes, or other types of distortions. For instance, we have chosen to apply the labels semi-Berry or semi-antiBerry for those distortions in which only one of the two axial ligands is displaced from the trigonal symmetry axis, either toward an equatorial edge (semi-Berry, Fig. S1f) or vertex (semi-anti-Berry, Fig. S1g). As shown in Fig. 4 when plotting the parameters, the geometries appear close to the umbrella pathway and away from the ideal trigonal bipyramid geometry, reflecting that this type of distortion is quite common. However, the third and last regime in Fig. 4 is referred to as “trigonal bipyramid”. There is only one point on this part of the curve and it is on the axis reflecting the pure vacant trigonal bipyramidal vTBPY-4 geometry of vanadium in this phosphatase complex. This structure mimics the products in the reaction pathway at the end of the phosphate ester hydrolysis. 3.4. Exploring the phosphate ester hydrolysis catalytic cycle for PTP1B Vanadate and vanadium compounds are known to exert an insulin enhancing effect [51,54,99–112], and the mode of action is generally

attributed to inhibition of regulatory protein phosphatases [50,54, 113–116]. Because the PTP1B is generally attributed to be responsible for many of the observed effects of vanadate and vanadium compounds when using these materials to normalize the elevated blood glucose levels in diabetes [50–54,117], the mechanism for the phosphorylation reaction of this enzyme is particularly important [118,119]. The application of X-ray crystallographic data to map out the structures of the geometries in the active site along the energy surface of the phosphate ester hydrolysis has been described. Specifically, Hengge et al. [47] collected the structures available to investigate the reaction pathway for PTP1B and these structures identified are shown in Fig. 5 and using the CShM method the coordination chemistries could be calculated and are shown in Table 3. Finally, as shown in Fig. 6 they were able to propose the catalytic cycle from these structures. Briefly, the enzyme begins the enzyme reaction (Fig. 5) or catalytic cycle (Fig. 6) as a free cysteine in the protein (PDB ID: 2cm2) [65]. This is a wildtype apoenzyme. After binding the substrate analog in the form of a phosphorylated amino acid Tyr in the peptide DADEpYL the Michaelis complex forms are shown in Figs. 5b–6b containing a long bond (3.285 Å) from the cysteine group (PDB ID: 1ptu) [66] to the phosphate. The structure labeled (c) contains a “TPBY-5”-type vanadium with a very long bond (2.648 Å) to the cysteine group (3i7z) [47]. This is the first 5-coordinate transition state on the pathway and vanadium is in the TPBY-5 geometry. The structure labeled (d) contains phosphorylated cysteine (1a5y) [67] with the phosphate group near tetrahedral. The structure labeled (e) contains a vanadium bound to a cysteine group in a TBPY-5 geometry (3i80) [47] and represents the second 5-coordinate transition state on the phosphoryl group reaction pathway. The final structure labeled (f) contains cysteine with a long bond to a tungstate (2hnq) [68]. The tungstate in this structure mimics

Fig. 5. The structures of the active site complexes in a series of X-ray structures compiled to illustrate the reaction pathway or organic phosphate ester hydrolysis by PTP1B. The structures show (a) the active site cysteine in the resting state of the PTP1B apoenzyme (PDB ID 2cm2) [65]; (b) a Michaelis–Menten complex between the phosphorylated amino acid Tyr in the model peptide DADEpYL and a serine-mutant at the typical cysteine residue C2155 in PTP1B (1ptu) [66]; (c) a “TBPY-5” complex of the first transition state complex from the native PTP1B, vanadate and the amino acid Tyr in the peptide DADEYL (3i7z) [47]; (d) a PO3 fragment coordinated to the sulphur of cysteinate in PTP1B (1a5y) [67]; (e) vanadate coordinated to cysteine forming the second transition state complex between native PTP1B and vanadate (3i80) [47]; (f) tungstate is in the active site of PTP1B forming a long bond to the cysteine mimicking the PTP1B–tungstate product complex (2hnq) [68]. Reproduced with permission from [47].

Please cite this article as: I. Sánchez-Lombardo, et al., Evaluating transition state structures of vanadium–phosphatase protein complexes using shape analysis, J. Inorg. Biochem. (2015), http://dx.doi.org/10.1016/j.jinorgbio.2015.04.005

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Table 3 Parameters for the six structures reported for the hydrolysis of p-nitrophenylphosphate ester by PTP1B, relative to the umbrella pathway that connects the tetrahedron with the trigonal bipyramid. Name

PDB ID

Atom M–X

Apoenzyme Michaelis–Menten comp TSA1 Phospho-enzyme TSA2 Product complex

2cm2 1ptu 3i7z 1a5y 3i80 2hnq

– P V P V W

a

τ

3.285 2.648

0.83

2.514

0.90

S(T-4) 1.27 3.71 0.00 3.40 0.16

S(TBPY-5) 2.82 0.13 0.08

S(vTBP-4)

0.14 3.50 0.04 2.48

S(SPY-5)

4.97 4.36

Path dev.a

Ref

0 48 22 2 7 4

[65] [66] [47] [67] [47] [68]

Deviation from the umbrella distortion pathway (in %).

the product phosphate. The CShM method allowed us to evaluate all the available structures including those that contain vanadium, phosphorus or tungsten in the active sites. The intermediates in the catalytic cycle shown in Fig. 6 for phosphate ester hydrolysis by PTP1B include structures in the tetrahedron regime, structures near the transition states in the umbrella regime (Scheme 2)

and structures near the product with tetrahedral vanadium (Fig. 4). Some of these structures contain vanadium–protein complexes, however, others were obtained with tungstate, phosphate or no additives. Together they describe the catalytic cycle. Using the CShM method these structures were all investigated with regard to possible reaction pathways of the structures of these intermediates. As shown in Table 3 the

Fig. 6. The catalytic cycle supported by X-ray structures of PTP1B at various stages along the pathway. Hydrogen bonding distances are in Å and for clarity the Trp179 has been omitted and only one of the backbone carbonyl groups is shown. Each of the active sites of these structures is shown also in Fig. 5 and described in detail in Fig. 5 caption. Here these structures are placed in context in the catalytic cycle. Reproduced with permission from [47].

Please cite this article as: I. Sánchez-Lombardo, et al., Evaluating transition state structures of vanadium–phosphatase protein complexes using shape analysis, J. Inorg. Biochem. (2015), http://dx.doi.org/10.1016/j.jinorgbio.2015.04.005

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deviation from tetrahedral is large when the complex is near transition states, whereas in the Michaelis–Menten complex, the phosphoenzyme and the product analog the deviation is very small. However, most importantly, these complexes are found to be directly on the pathway between the umbrella distorted trigonal bipyramidal structure and the tetrahedral substrate (or products). It therefore follows that the reaction path seems to favor umbrella-like distortions of trigonal bipyramid geometries. Considering that shape analysis is very effective in documenting changes in geometries and readily trace bond breaking and bond forming reactions, this method is ideal for analyzing further the nature of events that take place at the central atoms. The transition state structures are of the umbrella type distortions, and are found to be very near the TBPY-5 geometries. A complex containing vanadium was reported for both formation of the phosphorylprotein intermediate (the first, TSA1) and cleavage of the phosphorylprotein intermediate (the second, TSA2) and represent two important transition state structures in the PTP1B protein. The deviations from the TBPY-5 geometries were found to be small for both TSA1 and TSA2, and furthermore, the TSA2 was found to be near the direct pathway for an umbrella distorted transition state. TSA1 on the other hand, although found to be near the ideal TBPY-5 geometry but the furthest away forms the direct pathway between the tetrahedral and TBPY-5 umbrella geometry. Most of the structures did show that there was some minor deviation from the ideal and “direct” geometries, suggesting that there is some fine tuning going on with the structure of the protein complexes. In Fig. 7 we illustrate these results by showing a plot of the CShM as a function of the reaction coordinate in the PTP1B catalytic cycle. Because we do not know the exact reaction coordinate for each of the points we are focusing on the qualitative appearance of the plot. The solid trace shows the deviations in the geometry of the tetrahedral geometry starting at zero and ending at zero. In contrast if one starts with the vTBPY-4 geometry (for comparison with the 4-coordinate tetrahedral geometry to mimic the 5-coordinate TBPY-5 geometry) the deviation begins high and is the smallest at the transition states. The solid line shows the direct pathway between the umbrella distorted trigonal bipyramid along an umbrella distorted pathway toward the tetrahedron geometry. A striking observation is the experimental points obtained from the CShM analysis of the X-ray structures indicated by full circles and how close they are to the ideal pathway. These results suggest that distortions of the umbrella type are the most favored distortions in the phosphatase catalyzed phosphoryl group transfer reactions. In general no distinction is made in the literature for whether vanadium is inhibiting enzymes that catalyze phosphoryl group transfer

through five-coordinate transition states or through exploded transition states. The results that we show here suggest that such distinction may not be necessary because of the size of vanadium which may result in it catching both types of reactions. This conclusion is arrived at as follows based on the data shown in Fig. 5c. The V\\S bond shown is 2.5 Å and the V\\O bond is 2.1 Å in the transition state V–PTP1B complex. One would expect a bond distance of 2.5 Å from an oxygen nucleophile attacking a phosphoryl group with a very low bond order, that is a weak bond in an explored transition state. The fact that vanadium forms the protein complex with these bond distances would support the possibility that the exploded transition states would be caught. The studies shown here further demonstrate that distortions of the umbrella type of the transition state are particularly favorable and this may be related to the mechanism for phosphatases catalyzing hydrolysis of monoesters where the exploded transition states are more prevalent than for enzymes catalyzing phosphotriester or diester hydrolysis. In the studies shown here we not only use vanadium but also other intermediates along the hydrolysis pathway that have been characterized using X-ray crystallography. Studies with the vanadium compounds and protein phosphatases are not trivial because the cysteine in the active site has the potential to reduce vanadium [52,120–124]. The ability of vanadium to effectively produce a transition state structure is generally believed to be important for the mode of action of vanadium compounds as antidiabetic agents [50,51,54,99,102,103,105, 111,113,125]. These studies demonstrate that vanadium indeed possesses some characteristics that make the V–protein complex particularly stable in a geometry near the mechanistically ideal transition state structure [12]. Because one can make many different vanadium complexes it would be the expectation that compounds could be produced that would be significantly more potent. This problem is nontrivial, because vanadium seems to be extracted from all the different compounds used, and thus the complex found to inhibit remains the simple salt leading to the observation that all vanadium complexes have limited variability in their inhibitory potency [12]. It would however seem possible that one should be able to design a vanadium compound that showed superior stabilization. Such a vanadium compound would stabilize the transition state via an appropriate umbrella distortion and also through additional second sphere interactions with the amino acids, e.g. H-bonding or hydrophobic interactions. Such a complex would have the potential to be a more potent inhibitor and could be favored over losing the ligand by hydrolysis of the coordination complex and binding as vanadate to the phosphatase. 4. Conclusions

Fig. 7. Plot of the shape measure as function of the reaction coordinate for the PTP1B catalytic cycle, relative to the umbrella pathway that connects the tetrahedron with the trigonal bipyramid. The continuous line corresponds to the minimal distortion pathway and the circles to the experimental structures in Table 3.

The coordination environment of vanadium–phosphatase protein complexes has been analyzed using the CShM method, which is commonly used in material science. The analysis confirmed that the preference for SPY-5 geometry in small molecules is changed to TBPY-5 when vanadium is found inside a phosphatase. This preference exists even though the protein is providing only one ligand to the vanadium ion and thus not favoring this geometry by steric restrictions. These studies confirm previous analysis using the τ parameter [12,34], although structural diversity upon distortions could be identified better in a quantitative manner using the CShM method. Dogma describes the geometry of vanadium as a TBPY-5 in the ideal phosphatase transition state structure, however, the CShM method analysis shows that many near-ideal TBPY-5 structures, particularly those with umbrella distortions, are very effective. The continuous shape analysis allowed evaluation of vanadium–protein structures and the nature of the structural distortions on the phosphate ester hydrolysis pathway. Specifically, when analyzing the phosphoryl group transfer reaction for PTP1B we found that the geometries between the tetrahedron and the trigonal bipyramid structures were most favored when distorted along the umbrella pathway. Using the continuous shape analysis we have concluded that, based on the calculated shape deviations, structures involving

Please cite this article as: I. Sánchez-Lombardo, et al., Evaluating transition state structures of vanadium–phosphatase protein complexes using shape analysis, J. Inorg. Biochem. (2015), http://dx.doi.org/10.1016/j.jinorgbio.2015.04.005

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phosphoryl group transfer favor trigonal bipyramidal geometries distorted in the direction of the umbrella–tetrahedron pathway. Abbreviations CSD Cambridge Structural Database CShM method Continuous shape measures method PDB Protein Data Bank PTP1B protein tyrosine phosphatase 1B SPY-5 square pyramidal TBPY-5 trigonal bipyramidal Acknowledgments DCC and ISL thank the Fulbright Foundation for funding of ISL's fellowship. SA thanks the Spanish Ministerio de Economía y Competitividad for support through project CTQ2011-23862-C02-01. CCM acknowledges the financial support of Illinois State University and DCC thanks Colorado State University. Appendix A. Supplementary data Supplemental data include a figure (Figure S1) showing the geometries of several possible geometric distortions and an expanded Table 1 (Table S1) with more details on the calculated data (shape measures, path deviation functions, and tentative shape assignments). Supplementary data to this article can be found online at http://dx.doi.org/ 10.1016/j.jinorgbio.2015.04.005. References [1] S.C.L. Kamerlin, P.K. Sharma, R.B. Prasad, A. Warshel, Q. Rev. Biophys. 46 (2013) 1–132. [2] F. Duarte, B.A. Amrein, S.C.L. Kamerlin, Phys. Chem. Chem. Phys. 15 (2013) 11160–11177. [3] F. Duarte, J. Åqvist, N.H. Williams, S.C.L. Kamerlin, J. Am. Chem. Soc. 137 (2015) 1081–1093. [4] J.R. Knowles, Annu. Rev. Biochem. 49 (1980) 877–919. [5] S.J. Abbott, S.R. Jones, S.A. Weinman, F.M. Bockhoff, F.W. McLafferty, J.R. Knowles, J. Am. Chem. Soc. 101 (1979) 4323–4332. [6] R.J. He, L.F. Zeng, Y.T. He, S. Zhang, Z.Y. Zhang, FEBS J. 280 (2013) 731–750. [7] A.R. Saltiel, C.R. Kahn, Nature (London) 414 (2001) 799–806. [8] W. Vogel, R. Lammers, J.T. Huang, A. Ullrich, Science 259 (1993) 1611–1614. [9] T. Finkel, J. Cell Biol. 194 (2011) 7–15. [10] T. Hunter, Cell 80 (1995) 225–236. [11] T. Hunter, Cell 100 (2000) 113–127. [12] C.C. McLauchlan, B.J. Peters, G.R. Willsky, D.C. Crans, Coord. Chem. Rev. (2015)http://dx.doi.org/10.1016/j.ccr.2014.12.012 (in press). [13] J.G. Zalatan, T.D. Fenn, A.T. Brunger, D. Herschlag, Biochemistry 45 (2006) 9788–9803. [14] A.J. Kirby, W.P. Jencks, J. Am. Chem. Soc. 87 (1965) 3209–3216. [15] A.J. Kirby, A.G. Varvoglis, J. Am. Chem. Soc. 89 (1967) 415–423. [16] M. Klähn, E. Rosta, A. Warshel, J. Am. Chem. Soc. 128 (2006) 15310–15323. [17] J.G. Zalatan, I. Catrina, R. Mitchell, P.K. Grzyska, P.J. O'Brien, D. Herschlag, A.C. Hengge, J. Am. Chem. Soc. 129 (2007) 9789–9798. [18] R.H. Hoff, A.C. Hengge, J. Labelled Compd Radiopharm. 50 (2007) 1026–1038. [19] D.O. Corona-Martinez, O. Taran, A.K. Yatsimirsky, Org. Biomol. Chem. 8 (2010) 873–880. [20] Y. Ma, G. Lu, Dalton Trans. (2008) 1081–1086. [21] W.O. Wepukhulu, V.L. Smiley, B. Vemulapalli, J.A. Smiley, L.M. Phillips, J.K. Lee, Org. Biomol. Chem. 6 (2008) 4533–4541. [22] A. Alkherraz, S.C.L. Kamerlin, G. Feng, Q.I. Sheikh, A. Warshel, N.H. Williams, Faraday Discuss. 145 (2010) 281–299. [23] F. Duarte, S. Gronert, S.C.L. Kamerlin, J. Org. Chem. 79 (2014) 1280–1288. [24] A.C. O'Donoghue, S.C.L. Kamerlin, Curr. Opin. Chem. Biol. 21 (2014) VIII–X. [25] F. Duarte, T. Geng, G. Marloie, A.O. Al Hussain, N.H. Williams, S.C.L. Kamerlin, J. Org. Chem. 79 (2014) 2816–2828. [26] A.J. Ziegler, J. Florian, M.A. Ballicora, A.W. Herlinger, J. Enzyme Inhib, Med. Chem. 24 (2009) 22–28. [27] H. Krishnamurthy, H.F. Lou, A. Kimple, C. Vieille, R.I. Cukier, Proteins Struct. Funct. Bioinf. 58 (2005) 88–100. [28] C.T. Liu, A.A. Neverov, C.I. Maxwell, R.S. Brown, J. Am. Chem. Soc. 132 (2010) 3561–3573. [29] D. Xu, H. Guo, J. Phys. Chem. B 112 (2008) 4102–4108. [30] S.C.L. Kamerlin, J. Florián, A. Warshel, ChemPhysChem 9 (2008) 1767–1773. [31] J. Åqvist, K. Kolmodin, J. Florian, A. Warshel, Chem. Biol. 6 (1999) R71–R80. [32] M. Welin, L. Wang, S. Eriksson, H. Eklund, J. Mol. Biol. 366 (2007) 1615–1623.

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Please cite this article as: I. Sánchez-Lombardo, et al., Evaluating transition state structures of vanadium–phosphatase protein complexes using shape analysis, J. Inorg. Biochem. (2015), http://dx.doi.org/10.1016/j.jinorgbio.2015.04.005