Báo cáo khoa học: Weak oligomerization of low-molecular-weight protein tyrosine phosphatase is conserved from mammals to bacteria pot

Chemical shift data and NMR relaxation confirm that dimerization takes place through the enzyme’s active site, and is fully equivalent to the dimerization previously characterized in a eu

tyrosine phosphatase is conserved from mammals to

bacteria

Jascha Blobel1, Pau Bernado´1, Huimin Xu2, Changwen Jin2and Miquel Pons1,3

1 Laboratory of Biomolecular NMR, Institute for Research in Biomedicine, Barcelona, Spain

2 Beijing Nuclear Magnetic Resonance Center, College of Life Sciences, College of Chemistry and Molecular Engineering, Peking University, Beijing, China

3 Departament de Quı´mica Orga`nica, Universitat de Barcelona, Spain

Introduction

Low-molecular-weight protein tyrosine phosphatases

(lmwPTPs) constitute one of the four families of protein

tyrosine phosphatases [1] In eukaryotic cells, lmwPTPs

participate in platelet-derived growth factor

(PDGF)-induced mitogenesis [2] and insulin-mediated mitotic signaling [3] Dephosphorylation of different substrates, such as the ephrin [4] or fibroblast growth factor receptor, resulting in cell proliferation [5], has also been

Keywords

low-molecular-weight protein tyrosine

phosphatase (lmwPTP); phosphatase

regulation; protein oligomerization; signaling

pathways; supramolecular proenzyme

Correspondence

M Pons, Laboratory of Biomolecular NMR,

Institute for Research in Biomedicine,

Parc Cientı´fic de Barcelona, Baldiri Reixac,

10, 08028 Barcelona, Spain

Fax: +34934039976

Tel: +34934034683

E-mail: mpons@ub.edu

(Received 13 April 2009, revised 5 June

2009, accepted 9 June 2009)

doi:10.1111/j.1742-4658.2009.07139.x

The well-characterized self-association of a mammalian low-molecular-weight protein tyrosine phosphatase (lmwPTP) produces inactive oligomers that are in equilibrium with active monomers A role of the inactive oligo-mers as supramolecular proenzymes has been suggested The oligomeriza-tion equilibrium of YwlE, a lmwPTP from Bacillus subtilis, was studied by NMR Chemical shift data and NMR relaxation confirm that dimerization takes place through the enzyme’s active site, and is fully equivalent to the dimerization previously characterized in a eukaryotic low-molecular-weight phosphatase, with similarly large dissociation constants The similarity between the oligomerization of prokaryotic and eukaryotic phosphatases extends beyond the dimer and involves higher order oligomers detected by NMR relaxation analysis at high protein concentrations The conservation across different kingdoms of life suggests a physiological role for lmwPTP oligomerization in spite of the weak association observed in vitro Struc-tural data suggest that substrate modulation of the oligomerization equilib-rium could be a regulatory mechanism leading to the generation of signaling pulses The presence of a phenylalanine residue in the dimeriza-tion site of YwlE, replacing a tyrosine residue conserved in all eukaryotic lmwPTPs, demonstrates that lmwPTP regulation by oligomerization can be independent from tyrosine phosphorylation

Structured digital abstract

l MINT-7148507 : ywle (uniprotkb: P39155 ) and YwlE (uniprotkb: P39155 ) bind ( MI:0407 ) by nuclear magnetic resonance ( MI:0077 )

Abbreviations

AIR, ambiguous interaction restraints; BPTP, Bos taurus protein tyrosine phosphatase; BR, best representative; EM, energy minimization; HSQC, heteronuclear single-quantum correlation; lmwPTP, low-molecular-weight protein tyrosine phosphatase; PDGF, platelet-derived growth factor; SAXS, small-angle X-ray scattering; YwlE, Bacillus subtilis protein tyrosine phosphatase.

suggested The regulation of lmwPTPs is not completely

understood and different mechanisms have been

described [6] Reversible inactivation by oxidation of

the catalytic cysteine of phosphatases has been shown

to provide a regulation mechanism [7] In the case of

lmwPTP, the presence of an additional cysteine results

in the reversible formation of a disulfide bond [8]

Phosphorylation of a tandem repeat of tyrosine residues

(YY-loop) lining the active site [9] has also been

suggested as a possible regulation mechanism leading to

either activation or inactivation, depending on the

substrate involved [9–12] Dimerization of Bos taurus

lmwPTP (BPTP) has been observed in crystals [13] and

has also been shown to take place in solution [14], and

the protein evolves further into higher molecular weight

species which stand in fast equilibrium with the

mono-mer and dimono-mer [15] Dimono-merization involves the tyrosines

of the YY-loop and residues of the active site, leading

to an intrinsically inactive species It has been suggested

that lmwPTP oligomerization could be an additional

regulation mechanism, although its physiological

relevance remains unproven [13] A major objection is

the high dissociation constant of the lmwPTP dimer

in vitro, although crowding conditions inside the

cytoplasm may enhance oligomerization [16,17]

Prokaryotic lmwPTPs have recently been identified

and have been far less studied than eukaryotic

lmwPTPs [18] Some prokaryotic lmwPTPs are

viru-lence factors that mimic eukaryotic phosphatases and

dephosphorylate eukaryotic proteins, thereby

interfer-ing with the host defense response An example is a

phosphatase from Mycobacterium tuberculosis released

into the extracellular medium, from which it is

proba-bly translocated into macrophages, interfering with the

host signaling pathways [19]

Endogenous prokaryotic lmwPTPs participate in the

regulation of bacterial metabolism [20] They can be

divided into two types on the basis of their sequence and

biological characteristics [21] The first type binds and

dephosphorylates endogenous kinases (BY-kinases),

with which they often appear to be co-regulated in a

single operon [22–24] They control the biosynthesis

and transport of virulence factors, such as exo- and

capsular polysaccharides [25–28] One member is Wzb

from Escherichia coli, which acts with the kinase Wzc

in the regulation of colanic acid production [29–31]

The second type has been found in Gram-positive

bacteria [32] Although little is known about their

function to date, one representative, YwlE from

Bacil-lus subtilis, has been identified as the cognate

phosp-hotyrosine-phosphatase of McsB, McsA and CtsR

[33] It has been suggested that they are essential in

certain processes, such as bacterial stress resistance

Comparison of lmwPTPs from phylogenetically dis-tant species (endogenous prokaryotic and eukaryotic forms) is expected to identify conserved features that may shed light on the intrinsic regulation mechanisms

of this class of phosphatases

Prokaryotic and eukaryotic lmwPTPs show low sequence homology (less than 30% sequence identity) [20], but a comparison of the presently available X-ray [33–38] and NMR [20,39] structures shows a well-conserved tertiary structure exhibiting a Rossman fold [40]

It has been proposed that substrate specificity is mainly determined by the residues lining the active site Eukaryotic and prokaryotic lmwPTPs acting on eukaryotic substrates as virulence factors show high similarity in these residues [34–37]

Endogenous prokaryotic lmwPTPs acting on pro-karyotic substrates have different specificities and correspondingly different residues lining the active site Wzb, the only representative of type one prokaryotic lmwPTPs with an available experimental structure [20], possesses mainly hydrophobic residues GAL-VGKGA (38–45), compared with polar and aromatic residues in the case of eukaryotes The B taurus and human forms share the sequence SDWNVGRSP (47–55), forming the so-called W-loop lining the active site The second type of endogenous lmwPTP, repre-sented by YwlE [39], has a loop with the sequence FASPNGKA(40–47), containing both polar and hydrophobic residues In both types of endogenous lmwPTP, W49, suggested to be important for eukary-otic substrate recognition, is missing [20]

The YY-loop is the second flexible loop that appears over the active site in all lmwPTPs The name comes from the two consecutive tyrosine resi-dues found in eukaryotic lmwPTPs All known eukaryotic and prokaryotic lmwPTPs bear at least one tyrosine in this region, with the exception of YwlE, which possesses a nonphosphorylatable phen-ylalanine (F120) Thus, although phosphorylation and dimerization could be related regulatory events

in most lmwPTPs, phosphorylation cannot be a regu-latory mechanism of YwlE However, dimerization,

as shown below, is conserved The dimerization of both eukaryotic and prokaryotic lmwPTPs involves the active site, and the best docking model of the prokaryotic dimer is very similar to the crystal struc-ture of the eukaryotic dimer Furthermore, both phosphatases evolve to similar higher order oligo-mers, as detected by NMR relaxation The evolution-ary conservation of the oligomerization process strongly suggests a functional role in spite of the large dissociation constants measured in vitro

Concentration-dependent chemical shifts and

docking calculations

Figure 1A compares the 15N–1H heteronuclear

single-quantum correlation (HSQC) spectra of YwlE

recorded at protein concentrations of 0.05 and 1.0 mm

Although most of the peaks remain unperturbed,

sev-eral cross-peaks show unequivocal

concentration-dependent chemical shifts suggesting oligomerization

(Fig 1A) The combined 1H and 15N chemical shift

changes are shown in Fig 1B The residues showing the largest variations are located in the neighboring region of the active site (Fig 1C) Residues V39–A51, forming what would be the W-loop in eukaryotic lmwPTPs, as well as residue T84, facing the W-loop

on the opposite site of the active site crevice, are among the most affected Residues N10 and S14, located in the crevice of the active site, also show chemical shift changes Furthermore, the aromatic resi-dues Y127 and F120 around the YY-loop, just outside the active site, are also affected Only one perturbed residue (V32) is placed in a remote position from the

A

B

D

C

Fig 1 Concentration-dependent chemical shifts (A) Overlay of expanded regions of15N–1H HSQC spectra of 0.05 m M (black) and 1.0 m M (blue) YwlE (B) Combined 15 N and 1 H chemical shift changes (C) Chemical shift mapping Residues showing changes above the threshold, indicated by the black broken line in (B), are highlighted on the structure of YwlE (1zgg) The W- and YY-loops are shown in blue and red, respectively The active site residues are shown in yellow (D) Sequence alignment of YwlE and BPTP (adapted from Lescop et al [19]) Residues showing the largest concentration-dependent chemical shift changes are highlighted in green The active site of BPTP is highlighted in yellow.

active site A similar set of residues was perturbed by

concentration changes of eukaryotic BPTP [14]

Figure 1D compares the chemical shift differences

associated with the same concentration changes

superimposed onto the aligned sequences of YwlE and

BPTP

The oligomerization of BPTP has been characterized

extensively by NMR chemical shifts [14], NMR

relaxa-tion [15], 129Xe-NMR [41], analytical

ultracentrifuga-tion [13], X-ray [13] and small-angle X-ray scattering

(SAXS) [42] At low concentrations (< 0.25 mm), only

monomeric and dimeric forms are detectable At

higher concentrations, NMR relaxation, 129Xe-NMR

and SAXS experiments detect the formation of larger

oligomers NMR relaxation data can be explained by

the presence of an additional species which is

compati-ble with a tetramer, although more complex

oligomeri-zation processes cannot be ruled out

Chemical shift and ultracentrifugation data of BPTP

have been analyzed previously as a two-state

mono-mer–dimer equilibrium, and this was shown to be a

correct approximation up to a concentration of

0.5 mm Assuming that the monomer–dimer

equilib-rium is also the dominant oligomerization process in

YwlE, we used the chemical shift restraints to model

the structure of the dimer using the molecular docking

program haddock 2.0 [43] The NMR structure of

YwlE (1zgg) was used as the model for the monomeric

form The docking protocol and the definition of

active and passive restraints are described in Materials

and methods

The 200 best solutions clustered into five families

The five families are related by the relative rotation of

the two lmwPTP monomers around an axis going

through their active sites The RMSD values, buried

surface, energy components, haddock scoring of all

families (Table S1) and Ramachandran map analysis

of the best family (Table S2) are given as Supporting

information The most populated family (containing

more than 50% of the solutions) includes the two

structures with the best haddock scoring terms

(Ehaddock=)107.8 and )101.0 kcalÆmol)1)

Consi-dering the average of the 10 best structures in each

family, the same family also shows the largest buried

surface area (1278 ± 135 A˚2) and the largest

desolva-tion energy ()38.3 ± 5.6 kcalÆmol)1)

The best representative (BR) of the most populated

family, sharing an RMSD with all other family

mem-bers of 3.8 ± 1.1 A˚, shows very good agreement with

the crystallographic dimer of BPTP [13] The resulting

superposition of both dimers is shown in Fig 2A

In the docking model of the YwlE dimer, the

flex-ible loops around the active site (W- and YY-loops)

are involved in the stabilization of the dimer, in full agreement with the crystallographic dimer of BPTP Other structural similarities between the prokaryotic model and the eukaryotic dimer are the aromatic residue F120 and the catalytically active C7 of YwlE, which occupy the positions of Y131 and C12

of BPTP The second residue defining the active site motif of all phosphatases, namely the arginine placed six residues after the catalytic cysteine, is also located in equivalent positions in both prokaryotic and eukaryotic dimeric lmwPTPs (Fig 2B) Residue W49 of BPTP, after which the eukaryotic W-loop is named, is replaced by F40 in the prokaryotic form (Fig 2B)

A

B

Fig 2 (A) Best YwlE dimeric docking model (green) superimposed onto the crystallographic BPTP dimer (gray) (B) Expansion of the active site of YwlE (green) displaying functionally important side-chains (colored by atom type) superimposed with the equivalent side-chains of BPTP (gray) The labels show the structurally equiva-lent YwlE ⁄ BPTP residues C7 ⁄ C12 and R13 ⁄ R18 participate in the catalytic activity, and F40 ⁄ W49 and F120 ⁄ Y131 are involved in dimerization.

Self-association monitored by NMR relaxation

The concentration-dependent chemical shift changes in

YwlE are smaller in magnitude than those observed

for BPTP.15N-NMR relaxation rates are very sensitive

to self-association equilibria as they strongly depend

on the rotational correlation time of all the species in

solution Therefore, we used longitudinal (R1) and

transverse (R2)15N-NMR relaxation rates measured at

different protein concentrations to analyze the

oligo-merization of lmwPTP Figure 3 shows the average

R2⁄ R1 values (<R2⁄ R1>) of all measured residues

at different YwlE concentrations The increase in

<R2⁄ R1> at higher concentrations confirms the

self-association of YwlE

When multiple species coexist in fast exchange in

solution, the measured 15N-NMR relaxation rates are

the concentration-weighted averages of the individual

relaxation rates of each species In NMR relaxation

experiments, all residues in the protein are sensing the

changes in the correlation time associated with the

for-mation of higher molecular weight species, whereas

only residues in the interface of the dimer show

changes in chemical shifts The 15N-NMR relaxation

approach makes use of a large number of independent

measurements (approximately the number of residues

times the number of concentrations), giving the

possi-bility to distinguish between different oligomerization

models However, the structure of the monomer and

dimer are required to analyze the data

The combined use of NMR spin relaxation and

hydrodynamic calculations has previously been shown

to be a powerful tool for the characterization of weak

protein–protein interactions in solution [15, 41, 44–48]

This approach assumes that the lifetime of the

differ-ent oligomeric species is significantly longer than their

rotational correlation times, but the exchange is still

fast on the chemical shift time-scale Under these

conditions, the measured relaxation rates are inter-preted as the weighted average of the relaxation rates

of the coexisting individual species [48]

A detailed analysis of the oligomerization process was carried out by comparing the residue-specific relaxation rates obtained experimentally with those derived from hydrodynamic calculations of the experi-mental monomer structure and the haddock model for the dimer, as described below

The theoretical relaxation data of the monomer and the haddock model of the dimer were computed using HydroNMR [49,50], and the dissociation constant of the dimer (Kd), giving the relative populations of monomer and dimer at different concentrations, was fitted to reproduce the experimental R2⁄ R1 values of the individual residues (see Materials and methods) This approach gives a well-defined minimum (v2= 1.128) with a Kdvalue of 5.20 ± 0.20 mm The experi-mental and fitted R2⁄ R1 values for all four relaxation datasets are shown in Fig 4A–D The residue-specific residuals are given in Fig S1

Good agreement was observed at the lower protein concentrations, but the calculated R2⁄ R1 values at higher lmwPTP concentrations were systematically lower than the experimental values (Fig 4A) A statis-tically significant better fit was obtained by the inclu-sion of an additional species (an isotropic tetramer) in the equilibrium, as observed previously in the case of BPTP [15,41,42]

As described previously for BPTP, we modeled the higher oligomers of YwlE as a single isotropic tetra-mer, i.e with the same relaxation rates, R1T= 0.689 and R2T= 42.4 s)1, for all residues (see Materials and methods) This procedure provided a much better agreement with the experimental relaxation data (v2= 0.921), as shown in Fig 4F–I,, yielding thermo-dynamic constants of Kd= 7.59 ± 0.73 mm and

Kt= 0.27 ± 0.10 mm The improvement derives mainly from the better reproduction of the high-concentration data (cf Fig 4E, J) The reported uncer-tainties were obtained from a Monte-Carlo analysis of the model as described in Materials and methods The improvement in the figure of merit v2 from 1.128 to 0.921 is statistically significant according to the F-test (P < 10)10), indicating that the YwlE oligomerization equilibrium involves at least three species An equiva-lent situation has been demonstrated previously in the case of BPTP [15] The dependence of the dissociation constants on the assumed values of R1T and R2T was checked by testing values diverging by ± 20% from the initial estimates The variations in Kdand Ktwere 0.23 mm and 0.11 mm, respectively, centered around the initially estimated dissociation constants

Fig 3 Average R 2 ⁄ R 1 (<R 2 ⁄ R 1 >) values measured at different

YwlE concentrations.

Figure 5 compares the concentration dependence of

the molar fractions of the different oligomers of YwlE

and BPTP calculated from the dissociation constants

determined by NMR

Discussion

Evolutionary conservation of specific sequence or structural features in homologous proteins is consid-ered to be a relevant criterion for their physiological significance Intermolecular interactions are also vali-dated by their conservation in phylogenetically distant species In this work, we show that similar oligomeri-zation processes are conserved in eukaryotic and pro-karyotic lmwPTPs

Previous studies of lmwPTP from B taurus have demonstrated the formation of oligomers in solution [13–15,41,42] A dimer showing intermolecular contacts involving the active site and tyrosine residues in the YY-loop was observed in crystals [13] and was con-firmed to exist in solution [14] As the active site is closed by the second molecule on dimer formation, this species is intrinsically inactive Higher order oligomers were also detected by concentration-dependent NMR relaxation rate measurements [15], 129Xe-NMR [41] and SAXS [42] The oligomerization processes were found to correspond to weak interactions in vitro, with

A

B

C

D

E

F

G

H

I

J

Fig 4 R 2 ⁄ R 1 values of individual residues measured at the four YwlE concentrations (m M ) of 1.00 [(A) and (F) in blue], 0.50 [(B) and (G) in green], 0.25 [(C) and (H) in dark yellow] and 0.10 [(D) and (I) in red] Calculated values using the best-fitted parameters for the monomer– dimer (A–D) and monomer–dimer–tetramer (F–I) models are shown in black The contribution of the highest concentration experiments to the fitting error of individual residues is shown in (E) for the monomer–dimer model and in (J) for the monomer–dimer–tetramer model The individual contributions from all the concentrations are given as Supporting information.

Fig 5 Molar fractions of the different species present in the YwlE

(full lines) and BPTP (broken lines) oligomerization equilibria

Mono-mers are shown in red, diMono-mers in green and tetraMono-mers in blue.

Points and circles represent the experimental points with their

uncertainties.

dissociation constants in the millimolar range, and, in

spite of the putative regulatory role that can be

associ-ated with an interaction that changes the phosphatase

activity reversibly, the large dissociation constants shed

some doubt on the physiological relevance of this

mechanism

YwlE from B subtilis is a prokaryotic lmwPTP

involved in the regulation of endogenous bacterial

meta-bolic processes [33], not influenced, like prokaryotic

virulence factors, by the interaction of bacteria with

eukaryotic hosts As such, the comparison with BPTP is

expected to genuinely display the effects of evolution in

lmwPTPs of two phylogenetically distant organisms

The very similar fold of YwlE and eukaryotic lmwPTP

monomers provides a strong case for a common

evolu-tionary origin, in spite of only a modest sequence

homol-ogy Low sequence homology is expected between

homologous proteins from very distant species, and

stresses the relevance of the conservation of specific

resi-dues or residue classes in particular sites Here, we have

analyzed the oligomerization of YwlE using NMR

chemical shift and 15N-NMR relaxation measurements

at different protein concentrations in order to compare it

with the previously reported oligomerization of BPTP

The structure of the YwlE dimer was modeled by

computational docking of two monomers using

experi-mental NMR chemical shifts as constraints The BR of

the family with the highest average haddock score,

which is also the most populated, shows the highest

similarity to the crystal structure of dimeric BPTP A

detailed comparison of the specific residues forming

the dimer interface confirmed that the dimers formed

by eukaryotic and prokaryotic lmwPTP are, indeed,

homologous structures Two pairs of aromatic residues

seem to play equivalent roles in the formation of the

dimer in YwlE and BPTP: F120⁄ Y131 and F40 ⁄ W49

from the prokaryotic and eukaryotic lmwPTPs,

respec-tively F120 and Y131 occupy similar positions in the

interaction surface, close to the active site cysteines C7

and C12 of YwlE and BPTP, respectively Tyrosines

131 and 132 are highly conserved in all eukaryotic

lmwPTPs and are phosphorylation sites implicated in

lmwPTP regulation

The other pair of aromatic residues involves the

highly conserved tryptophan, which is present in nearly

all eukaryotic lmwPTPs and gives the name to the

W-loop This flexible loop shows maximal variations

between eukaryotic and endogenous prokaryotic

lmwPTPs, in agreement with the different

characteris-tics of their respective substrates W49 is missing in

prokaryotic lmwPTP, whereas the role of its indole

side-chain in the stabilization of the dimer seems to be

taken on by the phenyl group of F40 of YwlE

Residues N44 in YwlE and R53 in BPTP, both located in the W-loop, seem to play equivalent roles in the stabilization of the dimers by interacting with their related residues N44 and R43 of the second molecule

of the dimer

The physical characteristics of the residue pairs F40⁄ W49, N44 ⁄ R53 and F120 ⁄ Y131 of YwlE and BPTP are conserved in PtpB, a lmwPTP from the Gram-negative bacterium Salmonella aureus (F36 and N40) [51], and Etp from E coli (H42 and K46) Escherichia coli Wzb, a member of the first type of endogenous lmwPTPs, does not have the aromatic homolog to F40⁄ W49 in the substrate recognition loop However, concentration-dependent 15N-NMR relaxation data for this protein point to the formation

of higher molecular weight species [20] The apparent correlation time increases from 9.95 ns (0.1 mm) to 10.7 ns (0.3 mm) and, compared with the theoretical value for the monomer (9.21 ns) predicted from its NMR structure (2fek) using HydroNMR [49,50], sug-gests a weak self-association mechanism, similar to that observed for YwlE and BPTP

The similarity of the lmwPTP dimers of the prokary-otic and eukaryotic forms, involving structurally related, although not identical, residues, strongly sug-gests that the conserved feature is, indeed, the forma-tion of a dimer, and rules out the alternative explanation that dimer formation is a necessary side-effect of the conservation of the active site and sur-rounding substrate recognition and regulation loops Phosphorylation of the adjacent tyrosine residues Y131 and Y132 in eukaryotic lmwPTP is considered to

be a regulation mechanism Interestingly, the crystal structure of the BPTP dimer, with a bound phosphate and the tyrosine side-chain pointing to the active site

of the second molecule, is reminiscent of the expected reaction product of a dephosphorylation reaction, although dimerization does not require the previous phosphorylation of the tyrosine The observation of dimeric YwlE having a phenylalanine residue in the dimer interface in place of a tyrosine confirms that lmwPTP dimerization is independent of phosphoryla-tion However, the structure of the YwlE dimer sug-gests that the active site of each molecule is occupied

by the residues of the other molecule forming the dimer, and therefore the dimer is an inactive species Modulation of the monomer–dimer equilibrium could therefore provide a mechanism to modulate phospha-tase activity

The formation of higher oligomers also seems to

be conserved between eukaryotic and prokaryotic lmwPTPs Higher oligomers formed by the interac-tion of dimers are also expected to be enzymatically

inactive The W49G BPTP mutant, in which

dimeri-zation is prevented, shows a much lower tendency to

oligomerize (results not shown) Larger oligomers are

known to be preferentially stabilized by crowding

con-ditions as found inside the cell [16,52] Crowding is

expected to decrease the effective dissociation constant

of a lmwPTP tetramer (72 kDa) by a factor of

101–102 Larger aggregates or aggregates of higher

molecular weight can give reductions of 103–105 in the

dissociation constants inside the cell relative to the

values that would be determined in vitro [53] A

moderate decrease in the dissociation constants of

BPTP oligomers has been observed in vitro in the

presence of a low-molecular-weight crowder [41]

Oligomer formation, therefore, could be a requirement

to ensure that the effective dissociation constants

match the protein concentrations in vivo

One can speculate on the hypothetical advantages

of a regulation mechanism based on the equilibrium

between active monomers and an inactive dimer, in

which the active site is also the dimerization site

Pro-vided that the stability of the dimer is only moderate,

increasing the concentration of possible substrates

would cause an increase in the concentration of active

monomers, as substrate binding would compete with

dimerization This suggests that oligomeric lmwPTP

would provide a latent reservoir of phosphatase

(equivalent to a proenzyme form) that could be

acti-vated by phosphorylated substrates, and would return

to the inactive form after the substrate has been

exhausted by the activity of the phosphatase This

self-regulating mechanism would allow for the

genera-tion of ‘phosphorylagenera-tion pulses’ following kinase

activity

Materials and methods

Protein preparation and NMR experiments

Sample preparation and NMR measurements, including

described elsewhere [39] Briefly, reducing conditions were

ensured by the presence of 30 mm dithiothreitol in solution

made up of 50 mm Tris⁄ HCl buffer at pH 7.5, 50 mm NaCl

experiments were performed at 25C on a 600 MHz

15

N-NMR relaxation rates R1and R2were measured at 0.1,

0.25, 0.5 and 1.0 mm total protein concentrations Changes

in chemical shift were monitored by comparing

measure-ments at 0.05 and 1.00 mm lmwPTP The combined

changes in chemical shift (Dd) were calculated using the

relationship

Dd¼ ½Dd2

observed in the1H and15N dimensions, respectively

Generation of a dimeric model by computational docking

Models of potential lmwPTP dimers were generated from the first model of the NMR structure 1zgg using haddock 2.0 [46] This approach is implemented in cns [55] (cns Version 1.2 used here) and takes advantage of experimen-tally measured data reporting on perturbations in the

chemical shifts, as detected by HSQC experiments, were used As suggested by the authors of haddock, residues showing strong chemical shift changes in combination with

a solvent accessibility of greater than 50% were chosen as

‘active’ ambiguous interaction restraints (AIRs) These included the three residues F40, N44 and F120 A second group of residues serving as a less restrictive type of restraint, generally referred to as ‘passive’ AIRs, was made

up of residues showing strong chemical shift changes and also their direct neighbors, both of which had to exhibit a surface accessibility of greater than 30% The 13 residues G9, N31, N33, S42, P43, G45, T49, H50, T84, H85, G121, I126 and K128 passed the restriction criteria for passive AIRs The solvent accessibility of all residues was deter-mined by the program naccess [56] from the monomer

of the program, whereas python scripts derived from aria [57] were used to analyze all results and automate the pro-cess The process consists of two docking stages: a rigid body energy minimization (EM) and a semi-rigid simulated annealing in torsion angle space It should be noted that, during the rigid body EM, a 180 rotated model was gener-ated from each rigid-docked structure to amplify the diver-sity amongst dimeric models In the second stage, all residues making intermolecular contacts within a 5 A˚ cut-off were considered as flexible No symmetry restraints were enforced The full electrostatic binding energy was pre-served throughout the protocol In the scoring of the final dimeric models, the contributions from van der Waals’ and electrostatic interactions, AIR distance restraints and desol-vation energies, as well as buried surface area terms, were scaled and summed in the haddock scoring term (Ehaddock) as suggested by the authors haddock 2.0 gener-ated 1000 dimers during hard docking The best 200 dimers were retained for the semi-flexible simulated annealing step The refined final 200 dimers were sorted into families using the program cluster_struc, a part of the haddock program package, using a maximum RMSD difference of 12 A˚ amongst the family members in combination with a mini-mum family size of five structures The BR of a family is

the structure that has the lowest average RMSD to all the

remaining members The BR of the most populated family,

which has the highest average haddock score, as well as

the largest average buried surface area and the highest

des-olvation energy amongst the 10 best members (Fig S1),

was chosen as the model of the YwlE dimer

Hydrodynamic calculations

15

N-NMR relaxation rates for monomer and dimer were

calculated using the program HydroNMR [49] Hydrogens

were added to the dimer using a program from the WHAT

IF server (http://swift.cmbi.ru.nl/servers/html/index.html)

The atomic element radius was assigned to be 3.3 A˚ and

the atomic distance (N–H) 1.02 A˚ [50] The temperature

was set to 25C, the viscosity to 8.91 · 10)3P and the

NMR field strength to 14.09 T For the monomer of

B subtilis, a rotational correlation time of scMon= 8.65 ns

(<R2⁄ R1> = 8.36) was calculated, exhibiting an

anisot-ropy of Dpar⁄ Dper= 1.18 The dimer had a scDimvalue of

20.00 ns (<R2⁄ R1> = 43.14) and Dpar⁄ Dper= 1.58, being

clearly the most anisotropic species For the tetramer, no

structure is available, but it is expected to be a compact

globular object When calculating the theoretical relaxation

rates for the tetramer, solvent depletion effects arising from

protein–protein interfaces must be accounted for This can

be achieved using the rotational correlation time of the

dimer (scDim) for the calculation of the rotational

correla-tion time of a solvent-depleted monomer (scDMon) through

the relationship scDmon= scDim⁄ 2.78, giving scDMon=

7.19 ns [58,59] The theoretical rotational correlation time

for the tetramer can then be calculated by scTet= nscDMon,

with n = 4, resulting in scTet= 28.78 ns [15] From scTet,

theoretical R1T and R2T values for a spherical body of

0.689 and 42.4 s)1 (R2⁄ R1= 61.52) are calculated for a

magnetic field of 14.09 T The two relaxation rates are used

for all residues of the tetramer in the fitting protocol of

experimental15N-NMR relaxation data

The rotational correlation time of E coli lmwPTP Wzb

was calculated from the best energy model of the NMR

14.09 T

15N-NMR relaxation data analysis

the fitting as described elsewhere [41] Briefly, data from

individual residues were not used when any of the following

three situations were encountered: (a) heteronuclear

Over-hauser effect < 0.6, (b) large (> 25%) experimental errors

when compared with the relaxation rates R2⁄ R1 and (c)

large disagreement (> 25%) between the experimental and

simulated R2⁄ R1 values using the relevant model, filtering

for residues affected by chemical exchange A total of 95

experimental R2⁄ R1 values were extracted, leaving 313

R2⁄ R1 values spanning the four protein concentrations of 0.10, 0.25, 0.50 and 1.00 mm lmwPTP in the case of the

monomer–dimer–tetramer equilibrium The average relative relaxation rates (<R2⁄ R1>) were calculated for each protein concentration

Experimental R1 and R2 values are the concentration-weighted average of the relaxation rates of all participating species Equation (2) shows the calculation of the relaxation rates for the monomer–dimer–tetramer model, with M being the molar fraction of monomer, D the molar fraction

of dimer and T the molar fraction of tetramer

The relaxation rate Rnof each species is denoted with the

suf-fix corresponding to each species n is equal to 1 and 2 in the case of longitudinal and transverse relaxation, respectively The equilibrium parameters were determined by minimiz-ing the error function defined in Eqn (3)

v2¼ 1=N  ðR

iR

j½ðR2=R1Þexpij  ðR2=R1Þtheoij 2=½EðR2=R1Þexpij 2Þ

ð3Þ where i and j denote different residues (i) at varying protein concentrations (j), and E(R2⁄ R1)exp is the corresponding experimental error N is the number of experimental data used

For the monomer–dimer model, the fitting of the theoret-ical relaxation rates of two species to the experimental values adjusts a single parameter, namely the dissociation

monomer [M] and dimer [D] over all concentration ranges through Eqn (4) The presence of a tetramer, being a dimer of dimers, is accounted for by the dissociation constant Ktgiven by Eqn (5) [T] denotes the concentration

of tetramer

The minimization protocol consists of a grid search for each variable, followed by the minimization of all variables together using the function fmincon as implemented in Matlabª Errors in the calculated parameters are deter-mined using the Monte-Carlo method Thus, a new set of synthetic relaxation rates is calculated from the determined dissociation constants, whereas a further term is added to each relative relaxation rate R2⁄ R1 calculated from the experimental error multiplied by a random chosen value obtained from a Gaussian distribution The newly gener-ated relaxation rate data set is fitted to the applied model The process is repeated 100 times The final error in the dis-sociation constants is equal to the standard deviation of the

100 obtained dissociation constants for each species For

the fitting of the experimental relaxation data to the

mono-mer–dimer–tetramer model, a further type of error

estima-tion is used to prove the validity of the results obtained

using the minimization protocol with Monte-Carlo error

estimation with respect to the relaxation rates of the

tetra-mer (R1T and R2T) Thus, 100 new sets of R1T and R2T

were generated with a variation of 20% from their

theoreti-cally determined values (0.689 and 42.4 s)1) using a

Gauss-ian distribution Each set was used for a new fitting to the

experimental relaxation data using the minimization

proto-col as described above

Acknowledgements

The authors thank Dr Ewen Lescop (ICSN-CNRS) for

useful discussions This work was partially supported

by funds from the Spanish Ministry of Education

(BIO2007-63458 to MP) J.B is a recipient of a

pre-doctoral fellowship from the Spanish Ministerio de

Education y Ciencia P.B holds a Ramo´n y Cajal

con-tract that is partially financed by the Spanish Ministry

of Education and by funds provided to the IRB by the

Generalitat de Catalunya

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