Homotropic effects in aspartate transcarbamoylase

J. Mol. Biol. (1985) 186, 175-184

Homotropic

Effects in Aspartate Transcarbamoylase

What Happens when the Enzyme Binds a Single Molecule of the Bisubstrate Analog iV-Phosphonacetyl-L-Aspartate? Jefferson Foote and H. K. Schachman Departments of Biochemistry and Molecular Biology and the Virus Laboratory, Wendell M. Stanley Hall liniversity of Californ&z Berkeley, CA 94720, U.S.A. (Received 29 January,

1985, and in revised form

IO June 1985)

The active sites of aspartate transcarbamoylase from Escherichia coli were titrated by measuring the decrease in the enzyme-catalyzed arsenolysis of N-carbamoyl-L-aspartate caused by the addition of the tight-binding inhibitor, Kphosphonacetyl-L-aspartate. Because the enzyme is a poor catalyst for this non-physiological reaction. high concentrations are required for the assays (more than lOOO-fold the dissociation constant’ of the reversibly bound inhibitor) and, therefore, virtually all of t,he bisubst,rate analog is bound. From the endpoint of the titration, 5.7 active sites were calculated, in excellent agreement’ with the number, six, based on the structure of the enzyme. Simple inhibition was observed only when the molar ratio of inhibitor to enzyme exceeded five; under these conditions, as shown in earlier physical chemical studies, t,he R-conformational state of the enzyme is the sole or predominant species. At low ratios of inhibitor to enzyme. the a,ddition of inhibitor caused an increase in activity which is attributable to the conversion of the enzyme from the low-activity T-state to the much more active R-state. Comparison of the linear increase in activity as a function of inhibitor concentration at the low molar ratio (0.01, i.e. 1 inhibitor/600 active sites) with the activity lost’ at the high ratio provided a direct value for the mean number of active sites converted from the T-state to the R-state as a result of the binding of one bisubstrate analog to an enzyme molecule. This number was four with Mg . ATP or carbamoyl phosphate present and 4.7 for the enzyme in t)he presence of Mg . PP,, values approaching or identical to the theoretical maximum, 4.7, for a concerted transition with all of the active sites of the molecule changing from the T- t’o Rstate upon the formation of a binary complex of hexameric enzyme with a single inhibitor. With the enzyme in the absence of effecters or with Mg . CTP present, the titrations showed that an average of t’wo and one sites, respectively, of 4.7 possible, changed conforma,tion upon ligand binding. These results were interpreted as a manifestation of an equilibrium between a suh-population of T- and R-&ate enzyme complexes containing one bound inhibitor molecule. The R-state species would represent 40:), of the population for aspart’ate transcarbamoylase in the absence of ext,raneous ligands. The effect,s of Mg . ATP and Mg . CTP in increasing and decreasing, respectively, the apparent yield of R-state active sites when the enzyme binds one bisubstrate analog molecule are in accord wit’h previous findings of the preferential binding of ATP to the R-state and CTP t)o the T-state.

1. Introduction Twenty years have elapsed since the description by Monod et al. (1965) of a two-state model aimed at accounting for the co-operativity exhibited by allosteric proteins such as aspartate transcarbamoylase. Although the model has been shown to account satisfactorily for a host of observations, ~K)P2~S836/85/ZlOlT.i-10

$03.00/O

two of its basic tenets have been refractory to direct experimental validation. Vital to this model is the existence of an equilibrium between two conformational states of a protein; in most systems, the equilibrium in the absence of ligands, If it exists, lies so far in t,he direction of one species that, the other species is undetectable. Equally necessary to t~his two-st’atr model is a symmetry constraint: all

175

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188.5 Academic

Press Inc. (London)

Ltd

176

J. Foote and H. K. Schachman

subunits in an oligomeric protein must have the same tertiary structure, regardless of whether ligand is absent, saturating, or non-saturating. ATCase? from Escherichia coli is a well-known allosteric enzyme. It is an oligomer consisting of six catalytic polypeptide chains and six regulatory chains constrained by D, symmetry (Gerhart & Schachman, 1965; Wiley & Lipscomb, 1968; Weber, pyrimidine biosynthetic 1968). Within the pathway, ATCase functions at a control point, catalyzing the initial synthesis of N-carbamoyl-I,aspartate from L-aspartate and carbamoyl phosphate (Reichard & Hanshoff, 1956). Its allosteric nature was manifest in early studies in which sigmoidal substrate saturation kinetics and heterotropic activation and inhibition by nucleotides were discovered (Gerhart & Pardee, 1962). A comprehensive set of experiments was reported in which both enzyme kinetics and the results of several physical probes of conformational changes were analyzed in terms of a two-state model (Howlett & Schachman, 1977; Blackburn & Schachman, 1977; Howlett et aE., 1977). An internally consistent set of parameters resulted, including the equilibrium constant for interconversion of the two conformational states and the relative affinities of ligands for the binding sites of these two states. self-consistency does not provide However, sufficient evidence that the underlying assumptions of the model are free from error. Most kinetic studies of homotropic effects in ATCase have focused on the enzyme’s sigmoidal saturation curves. An alternative substrate of activation by approach is the analysis “inhibitors”. In the initial demonstration of this phenomenon (Gerhart & Pardee, 1962), addition of low concentrations of maleate, an unreactive aspartate analog, caused a twofold increase in the velocit’y of the enzymic reaction conducted at subsaturating levels of aspartate. This activation indicated that the binding of an inhibitor to an active site improved the catalytic activity of neighboring sites, to such an extent that enzyme molecules with one or a few blocked active sites processed substrates at a, faster rate than those enzyme molecules with a full complement of active sites. Similar results have been seen with other inhibitors, including the bisubstrate analog PALA (Collins & Stark, 197 1). Complete analysis of activation/inhibition curves within the two-state framework is quite complex, and many assumptions are needed in order to fit the data in terms of the two-&ate model of Monod et al. (1965). In a study of the reverse reaction catalyzed by ATCase (Foote & Lipscomb, 1981), the activation of the holoenzyme by PALA was found to be almost l&fold.

as compared

to only a threefold

activation

TAbbreviations used: ATCase, aspartate t’ranscarbamoylase (carbamoyl phosphate: L-aspartate carbamoyltransferase, EC 2.1.3.2); PALA,

N-phosphonacetyl-L-aspartate.

for the physiological direction. Several findings of that study suggest circumstances under which t,he molecular events underlying homotropic activation might be observed without t,he experimental difficulties and reliance on unvalidated assumptions currently inherent in a two-state simulation. The absence of kinetically detectable R-state, even at high substrate concentratioq, obviates consideration of the allosteric equilibrium constant as a necessary parameter. Use of enzyme concenbrations lOOO-fold higher than the dissociation constant, of PALA. made necessary by the low enzyme activit) in the reverse reaction, allows the approximation that virtually all of the PALA added to an enzyme solution will be bound. The considerably greater magnitude of the activation of the reverse react,ion. compared to t,he forward react,ion. expands the sensitivity of the scale over which the a&ion of the activator may be observed. A method exploit’ing these advantages of the reverse reaction is proposed and tested, and the results provide st,rong evidence that all symmetry-related regions in an ATCase molecule undergo a concerted transition when t’he enzyme is converted from the T-&ate t’o the R-conformation.

2. Experimental Design The effect of PALA in promot,ing the conversion of ATCase from a low-activity conformation to a form with much greater activity can be analyzed in quantitative terms from a simple steady-stat’e experiment. Only a few * priori kinetics are required for the theoretical assumptions treatment. It is assumed that an act,ive site in ATCase can be in either of two conformational states, T or R,. an R-site being the more catalytically active. Although this nomenclature is reminiscent of the model of Monod et al. (1965), t’he remaining postulates of that model are not necessary for the proposed analysis. No symmetry constraints are assumed: whether T-sites and R-sites co-exist on t’he same molecule or exclusively on separat,e molecules is without influence. What is critical is that under given conditions of substrate concentration, PH. temperature, et’c.. an R-site will turn over substrates many times faster than a T-site. Because of this marked difference in the activity of the two types of site. it, is possible to measure quantitatlively the PALA-promoted conversion of T-sites into R-sites. The cat’alyt,ic activit,y of a T-site is measured in an assay of the reverse reaction. Tn a series of otherwise ident,ical assays of enzymt’ solutions cont’aining high, but sub-sat,uratmg. concentrations of PALA. it is possible to measurts the catalytic act,ivitp of an R,-site. Wit,h these cat,alytic activities of both T- and R-sites. the number of R-sites formed upon the binding of one PALA

molecule

to ATCase

is deduced

from

t,he

measured increase in velocity in an additional series of assays with trace amounts of P,4T,A present. In the absence of substrates and effect#ors. a

Homotropic EJfects in Aspartate Transcarbamoylase population of ATCase molecules is entirely or predominantly in the T-conformational state. Lower catalytic efficiency (Gerhart & Pardee, 1962) and distinct physical properties (Gerhart & Schachman, 1968) distinguish this state from the R-state, which is predominant when ATCase is saturated with PALA or aspartate and carbamoyl phosphate (Howlett et al., 1977). It, has been shown that, unlike the latter two compounds, the substrates of the reverse reaction do not promote a conformational change in ATCase from the T-state to the R-state (Foote & Lipscomb, 1981). These substrates do not prevent PALA from promoting this change; indeed, adding moderate amounts of PALA to a reverse reaction assay can engender a 40.fold increase in velocihy. If the ATCase concentration is high in such an assay, and a very small amount of PALA is added, virtually all of the PALA will bind to enzyme, but it will be improbable that a given enzyme molecule will bind more than one PALA molecule. The small change in velocity observed under these circumstances is attributable to two processes. First., each molecule of PALA added blocks one T-site which previously had been convertming substrate to product, with a turnover of t per second. On a macroscopic scale, this process will cause a decrease in the observed velocity equal to t x [PALA]. Second, each PALA molecule bound will cause conversion of a certain number. n, of the remaining unblocked sites from T-state to R-state, with each R-site having a new specific activity, r. The parameter n, which applies to an event involving one enzyme molecule, will necessarily be an integer. Various allosteric models may disallow certain n values. A concerted mechanism for ATCase, for example, constrains n to be either 0 or 5. By contrast, the population average, ?i, may be defined and measured regardless of which allosteric model is postulated. This conversion of n sites from the T-state to R-state per PALA molecule added changes the observed velocity by fi(r- t)[PALA]. The overall change in velocity resulting from these two effect,s can be written as: Avelocity

= %(r- t)[PALA]

- L[PALA].

(1)

Solving for r?;leads t’o: g=

Avelocit,y/[PALA] (r-t)

177

The measurement of t relies on the evidence obtained in a previous study of the reverse reaction catalyzed by ATCase (Foote & Lipscomb, 1981). Both the enzyme kinetics with N-carbamoyl-naspartate and phosphate or arsenate and the physical chemical properties of the enzyme in the absence or presence of these ligands indicated that ATCase was predominantly in the T-state. Hence the measured turnover number divided bv six (or more correctly, the number of active sites per enzyme molecule) yields directly the value of t. A determination of r requires measurement of the turnover rate for active sites in the R-state. This can be evaluated from the kinetics of the reverse reaction catalyzed by ATCase in the presence of sufficient, PALA to convert the enzyme quantitatively to the R-state. As shown by a variety of chemical and physical techniques (Howlett & Schachman, 1977; Blackburn & Schachman, 1977; Johnson & Schachman, 1980; Wang et al., 1981), ATCase is converted quantitatively to the R-state at a mean stoichiometry of five PALA molecules per enzyme. The value of r can be measured, in principle, by assaying a sample at, a ratio of five PALA/ATCase and equating r with t.he observed velocity divided by the enzyme concentration. This approach entails the assumptions that all of the added PALA is bound and that an average of one active site per enzyme molecule is accessible to the substrates. A more certain approach, used below, obviates these assumptions. The molar ratio of PALA to ATCase is varied bet,ween five and six and the system is treated as a non-allosteric enzyme undergoing inhibition by a tight-binding inhibitor.

3. Materials and Methods (a) Materials

ATCase was prepared by the met’hod of Gerhart & Holoubek (1967) from an E. coEi strain harboring a multicopy plasmid bearing the pyrB-pyrl operon (Pauza et al., 1982). Mitochondrial glutamate-oxaloacetate transaminase (L-aspartate: 2-oxoglutarate aminotransferase, EC 2.6.1.1) was purified to homogeneity from ten 0.7 kg pig hearts by the method of Barra et al. (1976). PALA was prepared as described (Kempe et al., 1976) and recrystallized from ethanol/acetone as the analytically pure tri(cyclohexylammonium) salt. A-Carbamoyl-n-

aspartate was synthesized by reaction of L-aspartate and

+t .

(2)

Equation (2) indicates that ?i. the average number of active sites converting from T- to R-state when ATCase binds one PALA molecule: can be calculated if, in addit’ion to the experimental considerations listed above, the catalytic activities t and r of a T-site and an R-site can be measured. (The parameters t and r are turnover rates per active sit,e, typically in units of s- ‘, observed at the uniform substrate concentrations selected for the experiment. They are not. the turnover numbers observed under conditions of complete saturation by subst’rates.)

KCNO in alkaline solution (Nyc & Mitchell. 1947). The product was converted to the free acid by passage through Dowex 5OW-X8, H’ form, neutralized with cyclohexylamine, and recrystallized from water/acetone as the di(cyclohexylammonium) salt. Additional materials were from commercial sources. (b) Enzyme assays transaminase/ malate The glutamate-oxaloacetate dehydrogenase coupled-enzyme assay for the ATCase reverse reaction (Foote & Lipscomb, 1981) was used in this work with one significant modification: the mitochondrial transaminase was used, rather than the commercially available cytoplasmic isozyme. owing to a 20-fold higher V,,,,,/K, value for aspartate at pH 7.0. As

J. Foote and H. K. Schachmn

178

discussed by McClure (1969), a factor of 20 increase in V,,,,,/Km of a rate-limiting auxiliary enzyme will yield a 20-fold shortening of the initial lag encountered in coupled-enzyme assays. Standard assay mixtures included the following components: 4 pg malate dehydrogenase/ml, glutamate-oxaloacetate transaminase at an A 280 of 0.04, 05 mw-2-oxoglutarate, 0.16 mM-NADH, 30 mM-triethanolamine acetate (pH 7.0). Reaction mixtures were pre-warmed to the desired temperature (30°C unless otherwise stated) and reaction progress was followed at 340 nm in a Cary 14 spectrophotometer equipped with a thermostatted cuvette holder. In experiments in which temperature was a variable, 50 mMbuffer was used, and the pH of stock solutions was adjusted at the temperature intended. Before use, stock solutions dialyzed into ATCase were 50 rnMtriethanolamine acetate (pH 7.0), 10 mM-2-mercaptoethanol, 0.2 mM-ethylenediamine tetraacetate, and spun for 5 min in an Eppendorf centrifuge to remove any precipitate. Substrate concentrations in most reaction mixtures were 5 mM-N-carbamoyl-L-aspartate and 2 or 3 mirr-arsenate, concentrations well below saturating. The substitution of arsenate for phosphate in reverse reaction assays has been discussed (Foote & Lipscomb. 1981).

Most data points were obtained in triplicate. Velocities observed at extremely low PALA concentrations for purposes of determining the initial slope of an activation curve. were fit to a straight line by least-squares. The standard error of the slope was usually about 10%. The loss in activity at high PALA concentrations was fit to an equation describing tight-binding inhibition with a finite dissociation constant for the inhibitor: 1’ = (42) {[~%-,,a,

-

PALAl

-

Km,,

+

~Wl,o,a,+ PALAl + K,,d* -4[El,,,,,P~4LAJ 1. (3) where J’ is the initial reaction velocity observed under steady-state conditions, [E],,,,l is the total concentration of active sites. K,,,, is the dissociation constant for PALA binding to an R-site in ATCase, and r is as defined above. (For the derivation of a similar equation, see, e.g. Segel (1975).) A non-linear least-squares program written in Fortran 77 was used for fitting, taking as starting parameters an extremely low dissociation constant and preliminary experimental estimates of r and [E],,t,,. A4s pointed out in Experimental Design. this treatment relies on the approximation of homogeneous, R-state enzyme. Because data at the lower PALA concentrations are t,he most likely to present a deviation from this approximation, fits were also done on truncated data sets. If inclusion of lower-concentration data significant,ly and systematically changed the final parameter set of the fitting routine, all point.s at these concentrations were rejected. Standard errors of the parameters were usually around 19;) for [E],,t,,, loo/, for r, and 10 to 3O”i, for

K PALA.

4. Kinetic

Active-site

Titration

A complete activation/inhibition curve which serves as the basis for the kinetic act,ive-site titration method is illustrated in Figure 1. Upon the addition of PALA there is a large increase in

I

I

I

I

I

2

3

4

---

5

6

PALA/ATCase

Figure 1. Kinet’ic active-site titration: activation and inhibition of ATCase reverse reaction. A series of assays at fixed enzyme and substrate concentrat’ions of I 1.6 PwATCase. 3 mm-arsenate, and 5 mw,2’-carbamoylr,-aspartate. wit’h the concentration of PALA varied. gave t,he velocit.ies shown. The maximum activity is 17-fold of higher t)han the velocity observed in the absenre PALA. In view of the very high enzyme concentration relat,ivr t,o the dissociation constant of PALA. the ratio scale along the abscissa reflects not) merely the quotient of total eoncenbrations of PAL.4 and ATCase, but t)he average number of PAL.4 molecules bound per enzyme molecule. (This approximation is not strictly true in t,he rrgion between 5 and 6 P.4LAiATCasr.)

catalytic activity, amounting t’o a 1li-fold enhancement, even though an average of’ three of the sis active sites are occupied hy the inhibitor. Figure 1 also shows that further additions of PAl,A cause ii marked loss in activity. with the velocity of thr catalyzed react’ion approaching zero at a ratio of’ about six PALAjATCase molecule+. The experimental turnover rates per act’ive site. r and f. and the quantit’y. Aveloc~itvl[PALill. are readily rvahat)ed from different of the wtivc regions tionlinhibition curve. Expansion of the right-hand part of E‘igurr 1 yields the inhibition curve shown in Figure ?(a.). The curva,ture indicates clearly that. despite thca high concent#ration of :l’I’C’ase (about 10 ELM) ;mtl equivalent, amount’s of PALA. some of the inhibitor is not hound. Therefore. a small amount of csatalytic activity persists even at a molar ratio of about six

t Experiments with different preparations of isolated catalyt,ic subunits werp condurtrd in order to test t,he reliability of the titration method for determining the number of active sit,es. In all of these studies t,hr observed number of active sites was systematically lower than 3. the value expected for the trimeric subunit,s. FOI some prrparations only 1.7 ac%ive sitesltrimer were found and the highest value was 2.2. All of the prrparationa involved dissociation of the holoenzyme with a mercurial, followed by separation of the cat#alytica trimers from t,he mrrcaptide complexes of thr regulator) subunits.

Homotropic Eflects in Aspartate Transcarbamoylase

I.5 Tn : -

I-0

t 5 8

0.5

1

5.2

5.6

54

58

6.0

PALA / ATCase (a)

O.,i

x z 2 5 ’

O.I-

0

I 0.01

I 0.02

I 0.03

0.04

PALA / ATCase (b)

Figure 2. Analysis of the inhibition and activation of ATCase by PALA. (a) Region of “pure inhibition.” The portion of the data in Fig. 1 lying between 5 and 6 PALA/ATCase is plotted on an expanded scale. As discussed in the text, at this high ratio the ATCase is all in the R-state, and can be treated as a non-allosteric enzyme undergoing inhibition by a tight-binding ligand. Least-squares analysis showed 5.7 active sites present/enzyme, a typical value for the enzyme preparations used in this work. (b) Region of “pure Data points at the extreme left of Fig. 1, activation.”

plus others not shown in that Figure, are plotted on a greatly expanded abscissa scale. Values on this scale, as in (a), are PALA molecules added/enzyme, not per active site. Wit#h such a vast excess of ATCase over PALA, in

t,his region of the activation/inhibition species wit,h multiple

curve, enzyme

PALA bound will be rare.

PALA/ATCase. Accordingly, the data in Figure 2(a) were fit, to an equation describing tight-binding inhibition (eqn (3)) by an iterative procedure so as to obtain the catalytic activity of an uninhibited active site (r), the total concentration of active sites, and t,he dissociation constant of PALA from

179

the ATCase-PALA complexes. An excellent fit was obtained; the curve in Figure 2(a) was calculated from the fitted parameters with 5.7 fully functional active sites per ATCase molecule, r equal to e qual to 25 nM. This value for 0.19 s- ‘, and K,,,, K PALA is in good agreement with Ki determined by Collins & Stark (1971). Precise values were obtained for r and the average number of active sites, but the precision of the fitted value of KPALA was limited by the narrow concentration range (58 to 69 PM) over which PALA was varied. The observation that the theoretical curve fits the inhibition data so well supports the assumption in the Experimental Design that in this range of PALA/ATCase ratios the population of ATCase molecules is virtually completely in the R-state. The activation of ATCase at very low molar ratios of PALA to enzyme is illustrated in Figure 2(b). Even at a molar ratio of 0.01 (i.e. one PALA molecule/600 active sites), the increase in activity (about 24%) was measurable with good accuracy. Moreover, the velocity varied in a linear fashion as a function of PALA-ATCase. Such a linear dependence would be expected if the frequency of multiple binding events was negligible. The value at zero PALA per ATCase divided by the total concentration of active sites gives 3.2 x 10m3 s- ’ for t, the rate at which an uninhibited T-site converts substrates into products. The slope of the line in Figure 2(b), corresponding to Avelocity/PALA, was 0.39 s- ‘. Substitution of these two values and that for r (0.19 s-l) into equation (2) gives 2.1 for fi, the average number of R-sites formed as the result of binding one PALA molecule to an ATCase molecule. Some ambiguity exists in ascribing the reaction velocity in the absence of PALA to t, because some of the catalytic activity might be due to trace amounts of R-state ATCase in the population of uninhibited enzyme molecules. Previous estimates of the allosteric equilibrium constant, L = [T]/[R], for the unliganded enzyme yielded a value of about’ lo2 (Howlett et al., 1977). Thus, a small fraction of the unliganded enzyme may be in the R-state and the interpretation of the activity (3.2 x 1O-3 s- ‘) as attributable to T-state enzyme yields a. maximum value of t. However, the finding t’hat t is so much smaller than either r or Avelocity/PALA indicates that any uncertainty in the actual value of t has little influence on the calculation of n from equation (2). A premise of the active site titration described by equation (2) is that 5 reflects the behaviour of a of one PALA complex comprised molecular molecule

and one ATCase

molecule.

Therefore,

the

value of ii should be independent, of enzyme concentration. Accordingly, experiments similar to that shown in Figure 2 were performed at concentrations of 5, 10 and 18 PM-ATCase. The resulting G values, 2.2. 2.0 and 2.0. respectively, were identical within experimental error. This finding tends to rule out the possibility that in the activation

region

of Figure

2(b). some of the added

J. Foote and H. K. Schachman

180

PALA is not bound, which is an open question in the absence of knowledge of the affinity of a T-site for PALA. Similarly, the independence of the value of 6 on enzyme concentration indicates that the activation is not attributable to enzyme species containing multiply bound PALA molecules, such as ATCase-PALA,. We conclude that the observed lack of change in ?i denotes kinetic significance solely for the bimolecular complex (ATCasePALA,) and the unliganded enzyme. Although a conformational equilibrium between T-state and R-state enzyme molecules in t,he absence of ligands may be questioned, the existence of multiple conformations in the presence of PALA is indisputable. Hence, substrate concentration should have an effect on E, because of preferential binding of substrates to R-sites. Similar effects may be anticipated for buffer salts. hydrogen ions, or other ligands. The extent to which substrate concentration biases the determination of ?i was ascertained in three kinetic titrations in which arsenate and N-carbamoyl-I>-aspartate were present at equal concentrations of 5 mM, 3 mM and 1.5 mbt. Respective 6 values showed a, syst,ematic decline with substrate concentration: 2.5. 2.1 and 1.7. This finding suggests that the 6 value obtained upon extrapolation to zero substrate concentration may deviate somewhat from the 5 value obtained at, a single set of substrate concentrations. No correction was attempted in the comparative studies described below? in which parallel experiments employed uniform substrate and buffer concent’rations.

5. Nucleotide

Effects on ii

A postulate of the model of Monod rt aI. (1965) is that, heterotropic effecters influence the activity of of the R-conforthe enzyme bv stabilization mational state in t’he case of activators, or of the T-state in t’he case of inhibitors. It was of int’erest. therefore, to examine the effects of’ t’he actjivator. ATP. and the inhibitor. (‘TP. on t,hr value of 5. analogous to that Accordingly. kinetic, titrat,ions shown in Figure 1 were conducted on t,he enzyme in the presence of @.5rnM Mg. (‘TF’ or 2 m&lMg . ATP. As seen in Figure 3. the ac%ivation ot ATCase caused hv PALA is subst,antially increased when Mg. .\TP ‘is present. and. conversely. thr activation is reduced markedly for the enzyme in the presence of Mg .CTP. The values oft. r and r/ in

the various experiments

are summarized

Mg . ATP (‘auses a significant

in

Table I.

increase in t compared

to the control. whereas Mg .(‘TP causes it (VI‘responding decrease. In all experiments f is very much smaller t)han r, the value of which is hardl! affected by t)he presenc*ca of either Mg . ATT’ or Mg . (‘TP. Thr predominant r&cl of hot h nucleotides was on Avelocity/PALA. resulting in a marked

increase

in fi when

Mg. ATF’

was present

and a large decrease itr ri; for the enzytnr in the, presence of Mg CTP. Table 1 also summa,rizes t)hr rrsult,s of active-sites titrations of AT&se in t,he presence of Mg PPi and of carbamoyl phosphat,et. Both f and r were reduced when &her of thesr ligands was prrsrnt due presumably to t’heir being bound at active sites not occupied by PALA. The form of the ac*t,iv;ltion/inhibition curve remained similar to that ill Figure I. In part,icular. retention of quantit,at.ivch binding of PALA, necessary for a, valid titration procedure. was demon&rated by the sharp titration endpoints seen in these experiments. A more subtle effect of these liga,nds was on the ease with which the R-PALA complex was formed. The value, G = 4.7, for the enzyme

in the presence of Mg.PP,.

is part,icularly striking because the endpoint, of thr t,itration (Fig. 2(a)) shows that there are only 5.7 active sites per enzyme molecule. Therefore. the addition of one PALA molecule per AT(lase molecule in t’hc presence of Mg . PP, (*aused the conversion of all the remaining active sites in that 0

I

2

3

4

5

6

PALA /ATCose

Figure 3. Kucleotide effects on the activation, inhibition curve. (m) Reaction with 2 mM-Mg ATP; (A) reactions with 0.5 mM-Mg . CTP; (0) reactions without effecters. The titration shown in Fig. 1 was repeated with ident,ical enzyme concentrations and with the added presence of the allosteric activator, Mg . ATP. or the inhibitor, Mg CTP. The large differences in velocity in the central region of the 3 curves are obvious. The maximum of the Mg ATP curve is shifted to lower PALA. and that of the Mg. CTP curve toward higher. relative to the control without effecters. At the extreme left of the graph, the curves are seen to have very different slopes, whereas between 5 and 6 PALA/ATCasc. the 3 converge.

.-~__--__ t Titrations

were also done with sodium salts of :\TI’

and CTP present in the reaction mixtures. These experiments showed smaller rhanges in ti. compared to the effec%sof magnesium-nucleotides. and large

reductions in t and r. These result,s may be due to binding of free nucleotides at the actjive site in competition with arsenat,e. As metal-nucleot’idr complexes have been shown to bind less tightly to the active sit,e than free nucleotides (Honzat.ko rl al.. 1981). and magnesiun-complexes in particular show enhancpd functions as allosteric effecters (Christopherson & Finch. 1977). titrabions with magnesium-nucleotides are less equivocal than with sodium salts. and only the former are reported.

Homotropic Effects in Aspartate Transcarbamoylase Table 1 Kinetic active-site titrations with and without nucleotides qs- ’ x 103)

Additive No nucleotide Mg ATP Mg CTP Mg PP, Carbamoyl phosphate

T(SK'

3.2 5.6 1.9 0.5 1.5

x 103) 190 220 190 70 20

n. 2.1 4.0 1.1 4.7 3.8

Save for added effecters, the results in this Table arose from titrations conducted under identical conditions, including identical substrate concentrations and nearly identical enzyme concentrations. Hence, values of C, r and t are strictly comparable. Mg. ATP and Mg. PP, were present at 2 mM, Mg (‘TP at 0.5 mM. and Li,-carbamoyl phosphate at 0.2 mM. In experiments involving magnesium-nucleotide complexes, equal amounts of metal and nucleotide were combined. The free concentration of Mg’+ was not ascertained, but may be in the vicinity of 200;, the concentration of the complex (Honzatko et al.. 1981).

molecule to the R-conformation. Carbamoyl phosphate was only slightly less effective than Mg . PP, or Mg . ATP in promoting the’conversion of ATCase from the T-stabe to the R-conformation. 6. Implications as to the Nature of the Allosteric Transition The finding that binding of PALA to unliganded ATCase causes on the average two out of the remaining five active sites to be converted from the T-state to the R-conformation can be interpreted in at least two ways. One possibility is that every time one PALA molecule binds, two sites in each molecule change conformation and three do not, giving hybrid molecules containing unliganded active sites in each of the different conformations. Alternatively, we can assume that some of the ATCase molecules containing one bound PALA change conformation, with all five of the remaining sites being converted to the R-state, and other ATCase--PALA complexes remain in the T-conformation. For ii = 2, the fraction converted would be 4076. With E values of 1 or 2, it is not possible to rule out either of these interpretations; however, the higher 6 values encountered put severe limits on the former interpretation. At, issue is whether the different ii values obtained in the presence or absence of effecters such as Mg. PP,: Mg. ATP, Mg. CTP, or carbamoyl phosphate arise from changes in the stoichiometry of active sites involved in the allosteric transition or from changes in the equilibrium constant for the reaction : IATCase-PALA,],=[ATCase-PALA,],.

(4) The kinetic titration performed with Mg . PP, present’ gave the maximum possible 6 value, 4.7. (The mean number of active sites per molecule, obtained from Fig. 2(a), is 5.7, of which 1 is occupied by PALA.) Similarly, the titration of ATCase in the presence of either Mg . ATP or

181

carbamoyl phosphate leads to ii values approaching limit for a concerted closely the theoretical Unless the assumptions described in transition. Experimental Design are invalid, these results establish the existence of an ATCase species with one active site occupied by PALA, and all five unliganded sites in the R-conformation, a species predicted by the concerted model. The high ii values controvert allosteric models postulating the operation of two or more autonomously regulated subsets of active sites on each ATCase molecule, at least with regard to homotropic effects. Furthermore, the evidence presented here for the concerted transition is fully in accord with previous studies (Gibbons et al., 1976) with various hybrid ATCase molecules composed of mixtures of native and chemically modified chains. In these experiments with molecules containing different arrangements of the active and inactive chains the results indicated that there is no “allosteric unit” smaller than the entire molecule. A sequential allosteric model could be devised involving semi-autonomous allosteric units functionally connected through a network of linkages sensitive to effecters, such t*hat under certain conditions the binding of a ligand to one active site could be communicated to all remaining sites, but such a complex model gives no more adequate an interpretation of the experimental observations than does a concerted allosteric transition. Thus, the variability of E is more simply explained by changes in the equilibrium of equation (4), rather than changes in t,he number of active sites on the same molecule that participate in the allosteric transition. This view is implicit’ in the discussion that follows. The parameter E bears a simple relation to the equilibrium constant for t’he reaction in equation (4). As stated above, the maximum value of fi is equal to the number of active sites per molecule minus 1, for the active site filled by PALA, or slightly less than five. Of the set of molecules with one PALA molecule bound, all ?i molecules in the R-state are matched by (sites- 1) -E molecules in the T-state. The equilibrium constant for equation (4), therefore, is given by:

n Kc, = (sites-1)--G

(5)

The kinetic titration can be considered a method of selective examination of the conformational equilibrium of binary ATCase-PALA complexes. In the absence of nucleotides (G = 2.1), the two species in this population are present in nearly equal amounts (K = 2/3). Addition of Mg . ,4TP shifts the equilibrium toward the R-state (K = 4), providing a differential stabilization corresponding to a free energy change of - 3.6 kJ mol- ‘. Mg . CTP shifts the equilibrium toward the T-state (K = l/4) by + 2.2 kJ mol-‘. These values are in fair agreement with those calculated by the more familiar twostate simulation (with Mg’ + absent ). - 3.3 and +3~?+kJ mol-‘, respectively (Hewlett et al., 1977). An equilibrium constant for the interconversion in

182

J. Foote and H. K. Schachman

equation (4) can be calculated from parameters in the same study, and is only a factor of four lower than the value measured here. The values of r in Table 1 resulting from titrations with Mg . ATP, Mg . CTP, and without effecters are identical within experimental error. By contrast, addition of nucleotides gives rise to large variations in t. This could be attributed to a change in the equilibrium between the T- and R-states of unliganded ATCase, with CTP favoring the T-state, thereby causing an apparent decrease in t, and ATP causing an apparent increase in t because of the preferential stabilization of the R-state. An alternative explanation is that the nucleotides cause changes in the structure of the T-state active site, yielding actual, rather than apparent, changes in t.

7. Other Applications (a) Thermodynamic

values

Macroscopic equilibrium constants for t’he conversion of ATCase-PALA, from the T-state to the R-conformation were calculated from equation (5) with experimental values of fi obtained at a series of temperatures ranging from 19°C to 41°C. From these data, the van% Hoff plot in Figure 4 was obtained, along with the values AH = 10 kJ and AS = 31 J mol-’ deg-‘, for the mol-’ conformational transition. These values differ substantially from previous estimates of AH and AS for the T to R transition of the unliganded enzyme (Shrake et al., 1981), but it should be noted that the thermodynamic parameters evaluated from the data in Figure 4 correspond to the isomerization of

O-

-0.1

-

i

-0.2 -

c

-0.3-

0

.

\

!

-0.4-

ATCase-PALA, and not free ATCasr. In contrast, the calorimetric study of Shrake et al. (1981) yielded a value of -25 kJ mol-’ for AH for the T to R conversion of unliganded ATCase. Combination of this value with that of AC: estimated from the twostate model (Howlett et al., 1977) yielded a value of -130 J mol-’ deg- 1 for AS. Another study (Hofman et aZ., 1979) of the thermodynamic values of the conformational change at pH 8.3 yielded -10 kJ mol-’ for AH. (b) State function In their description of the two-state model Monod et al. (1965) defined the state function, i%, as the fraction of the population of enzyme molecules which are in the R-state. As they showed, the value of fi as a function of ligand concentration was related to a variety of parameters describing the two-state model. An alternative formulation with comparable utility invokes the definition of i? as the fraction of free active sites which are in the R-state. Values of this fraction can be determined directly from the experimental data obtained in the kinetic active-site titration with a t,ight-binding inhibitor such as PALA. If all of the added PALA is assumed to be bound (which appears t’o be valid up to a molar ratio of 5 PALA/ATCase), the concentrations of free sites in the T- and R-states can be determined by solving the simultaneous equations:

14 tota,-

IPALA]

= [ &] + [ ET].

W

and (’ = r[&]

+ t[J!&].

(7) In equations (6) and (7). [&I and [ET] are the concentrations of free sites in the R- and T-conformations. respectively, and v is t~heobserved velocity obtained at a given concentration of PALA. With the values of r and t determined a,s described above. it, is possible to calculate the ratio of [&I to the total free sites, FE,]+ [ET], and plot this ratio versus t,he average number of PALA molecules bound per ATCase molecule. Figure 5 shows such plots for ATCase and for the enzyme in the presence of Mg . ATP or Mg . CTP.

0

8. Discussion -0.51 3.1

I 3.2

I 3.3

I 3.4

1 3.5

1000/T

Figure 4. van’t Hoff analysis of the T e R equilibrium for ATCase-PALA,. Kinetic titrations were performed at a series of temperatures from 19°C to 41°C. The equilibrium constant of eqn (5) was extracted from each data set and plotted as shown. The text gives the obtained from the plot. values thermodynamic Considering that the variation in % over the temperature range chosen was not much greater than the experimental error in % (see Materials and Methods), the lack of scatter in the Figure is surprising.

of the extremely large allost~cric Analysis activation and active site-directed inhibition of ATCase as a function of the concentration of th(I

tight-binding

inhibitor

PALA

is shown to yield a

value of %. the average number of active sites per enzyme molecule converted from the low-activit) T-state to bhe highly active R-conformation upon the binding of one PALA molecule. The method is based on assays of the catalytic activity of tZhe non,\‘-carbamoyl-I,-arsenolysis of physiological aspartate and t,he observations (Foote &. I,ipscornb. 1981) that there is no co-operat’ivity with respect to substrates, and t,hat, the enzyme in the K-state is

Homotropic Effects in Aspartate Transcarbamoylase about lo2 more active than in the T-state. Experimental difficulties encountered in using the kinetic active-site titration include the consumption of large amounts of ATCase in the enzyme assays and the demand for accuracy in volumes, concentrations, and velocity measurements to achieve moderately precise estimates of ?i. Why the substrates for t,he reverse reaction, arsenate (or phosphate) and N-carbamoyl-L-aspartate, do not promote the allosteric transition of ATCase from the low-activity to the high-activity conformation is not known. It is worth noting here that the activity of T-state ATCase in catalyzing the physiological reaction (formation of N-carbamoylL-aspartate from carbamoyl phosphate and aspartate) cannot be measured directly by steadystate methods because the substrates, even at low levels, promote the allosteric transition; therefore, measurement’s of enzyme activity for the forward reaction reflect contributions of R-state molecules in the populationt. The procedure for measurement of ti was designed to be independent of a priori assumptions invoked in various models proposed for allosteric proteins. In particular, the postulate of a conformational equilibrium existing in the absence of ligands and all symmetry postulates are avoided. The assumption that individual active sites are “quantized”, existing in either the T or R, but no intermediate, conformational state is retained. The values of 6 for the enzyme in the presence of Mg . PP, or Mg . ATP were found to be close to the theoretical maximum for a concert.ed transition symmetry. This demonstrates the conserving formation of t’he complex R-PALA,, and constitutes strong evidence for the symmetry postulate of the concerted two-state model of Monod et al. (1965), which predicts the existence of such a species. Those experiment’s for ATCase in the absence of ligands or in the presence of Mg . CTP yielded much

1‘In previous treatments of the allosteric kinetics of ATCase in catalyzing the forward reaction, no considera.tion was given to the possibility that r,,, for the R-state enzyme differs from that for the T-state (Hoalett et al.. 1977). The experimental results were interpreted in terms of differing affinities (K,) of the 2 conformations for substrates. i.e. “K-system” as described by Monod et al. (1965). In contrast. the data for the reverse reaction thus far have not, provided information regarding possible differences in the relative affinities of T- and R-stat’e enzyme molecules for carbamoyl aspartate. Although a complet~e kinetic study of t)he reverse reaction has not been performed at varying cxarbamoyl aspartate in the presence of sufficient PAL,1 to convert t,he enzyme to the R-state. the limited dat,a presently a.vailable do indicate differences in Vm’,,, between T- and R-stat,e ATCase. For the purposes of the present investigation. differences in K, between T- and R-stat.e molecules are not relevant. but it is entirely possible that the 2 conformations differ in both K, and I’m,, for the subst,rates used in studying the forward and backward reactions.

183

100 a 5 al 2

75

& .c E c In

50

I;:

25

0

I

2

3

4

5

6

PALA /ATCase Figure 5. “State function” describing the percentage of free sites in the R-state. The plot is not of the classical function of state, R, of Monod et al. (1965), but an empirical state function referring to the relative number of active sites which have not been occupied by PALA, but which have converted to the R-state. For each point. the simultaneous eqns (6) and (7) were solved, and the ratio [r]/([r]+[tJ) determined. (A) Points derived from the same data set as in Fig. 1, obtained in the absence of nucleotide effecters; (m) the presence of 2 rnM-Mg. ATP: (0) 0.5 mM-Mg.CTP. Rio ordinate intercept. is shown. owing to the uncertainty of whether R-sites exist in the absence of PALA. The data shown have not been extended beyond 5 PALA/ATCase. due to the complication of incomplete binding of the ligand.

lower values of ii. We interpret the variations in ri. in terms of shifts in the equilibrium for the interconversion of T-stat’e and R-state ATCase complexes containing one bound PALA molecule. The finding that the equilibrium constant for the isomerization reaction; T-PALA, G= R-PALA,, is poised near one may prove experimentally useful, since changes of the equilibrium by fractions of J mole1 will nevertheless efiect conversion of a measurable fraction of the enz! me population. Such precision has not been achieved in estimates of L. the allosteric equilibrium cons! ant for unliganded T- and R-states, which lies ovel,whelmingly in favor of t)he T-stat,e (Hewlett, et al.. 1977). The Hill coefficient may be estimated accurately from substrate saturation curve*;. but) it is an empirical constant without any direct connection to a discrete chemical reaction. Roth L and the Hill coefficient have been used as quantitative measures of cooperativity in ATCase, and its perturbation by nucleotides, mutation, and envi**onment,al factors such as pH. Inasmuch as G may be precisely measured. and its associated eq:iilibrium constant Pertains purely to an allosteric isomerization, this parameter may prove preferable to the ot)her t,wo as an index of homotropic co-operativity. This work was supported by the Vnitrd States Public Health Servirr, research grant (:M 12159 from the

J. Foote and H. K. Schachrnan

184

National Institute of General Medical Sciences aid by the National Science Foundation. research grant PCM8023012.

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Honzatko. R. B.. Lauritzen, A. M. & Lipscomb. IV. X. (1981). Proc. Nat. Acad. Sci., U.S.A. 78, 89&902. Howlett, G. ,I. & Schachman. H. K. (1977). Biochemistry, 16, 5077%5083. Howlett, Q. tJ.. Blackburn, M. N.. Compton, J. (‘:. & Schachman. H. K. (1977). Riochemistry, 16, 5091-5099. Johnson. R. S. & Schachman, H. K. (1980). Proc. %at. Acad. Sci., iJ.S.A. 77, 1995-1999. Kempe, T. D., Swyryd, E. A.. Bruist. M. & Stark. G. K. (1976). Cell, 9, 541-550. McClure. IV. R. (1969). Biochemistry, 8, 8782-8786. Monod, J.. Wyman, .J. & Changeux. J.-P. (1965). J. ‘Vol. Biol. 12, 88--118. Nyc, .J. F. & Mibchell. H. K. (1947). J. Amer. (‘hem. Sot. 69. 1382- 1384. Pauza, C. I).. Karels, M. -1.. Navre. M. & Schachman, H. K. (1982). hoc. Yut. Acud. Ski.. I1.S.A 79. 402+4024. Reichard. I’. & Hanshoff. G. (1956). Acta C:him. &and. 10, 548-566. Segel, I. H. (1975). In Enzyme Kinetics. pp. 73-74. Wiley. New York. Shrake. A.. Ginsburg, A. & Schachman. H. K. (1981). J. Biol. Chem. 256, 5005-5015. Wang, C.-M.. Yang, Y. R.. Hu, C. Y. bt Schachman. H. K. (1981). J. Biol. Chem. 256, 7028-7034. Weber, K. (1968). Nature (London), 218, 111~1119. Wiley. D. (1. & Lipscomb, W. N. (1968). Nature (London). 218, 1119-1121.

Edited by C. R. Cantor