Portal de Periódicos da CAPES

Pre-steady State Quantification of the Allosteric Influence ofEscherichia coli Phosphofructokinase

2001; Elsevier BV; Volume: 276; Issue: 37 Linguagem: Inglês

10.1074/jbc.m102785200

1083-351X

Audrey S. Pham, Gregory D. Reinhart,

Cancer, Hypoxia, and Metabolism

Stopped-flow kinetics was utilized to determine how allosteric activators and inhibitors of wild-type Escherichia coli phosphofructokinase influenced the kinetic rate and equilibrium constants of the binding of substrate fructose 6-phosphate. Monitoring pre-steady state fluorescence intensity emission changes upon an addition of a ligand to the enzyme was possible by a unique tryptophan per subunit of the enzyme. Binding of fructose 6-phosphate to the enzyme displayed a two-step process, with a fast complex formation step followed by a relatively slower isomerization step. Systematic addition of fructose 6-phosphate to phosphofructokinase in the absence and presence of several fixed concentrations of phosphoenolpyruvate indicated that the inhibitor binds to the enzyme concurrently with the substrate, forming a ternary complex and inducing a conformational change, rather than a displacement of the equilibrium as predicted by the classical two-state model (Monod, J., Wyman, J., and Changeux, J. P. (1965) J. Mol. Biol. 12, 88–118). The activator, MgADP, also altered the affinity of fructose 6-phosphate to the enzyme by forming a ternary complex. Furthermore, both phosphoenolpyruvate and MgADP act by influencing the fast complex formation step while leaving the slower enzyme isomerization step essentially unchanged. Stopped-flow kinetics was utilized to determine how allosteric activators and inhibitors of wild-type Escherichia coli phosphofructokinase influenced the kinetic rate and equilibrium constants of the binding of substrate fructose 6-phosphate. Monitoring pre-steady state fluorescence intensity emission changes upon an addition of a ligand to the enzyme was possible by a unique tryptophan per subunit of the enzyme. Binding of fructose 6-phosphate to the enzyme displayed a two-step process, with a fast complex formation step followed by a relatively slower isomerization step. Systematic addition of fructose 6-phosphate to phosphofructokinase in the absence and presence of several fixed concentrations of phosphoenolpyruvate indicated that the inhibitor binds to the enzyme concurrently with the substrate, forming a ternary complex and inducing a conformational change, rather than a displacement of the equilibrium as predicted by the classical two-state model (Monod, J., Wyman, J., and Changeux, J. P. (1965) J. Mol. Biol. 12, 88–118). The activator, MgADP, also altered the affinity of fructose 6-phosphate to the enzyme by forming a ternary complex. Furthermore, both phosphoenolpyruvate and MgADP act by influencing the fast complex formation step while leaving the slower enzyme isomerization step essentially unchanged. phosphofructokinase fructose 6-phosphate phosphoenolpyruvate Monod-Wyman-Changeux Phosphofructokinase (PFK)1 catalyzes the phosphorylation of fructose 6-phosphate (Fru-6-P) from MgATP to form fructose 1,6-bisphosphate and MgADP. Allosteric mechanism is one of the regulation strategies used by PFK to control catalysis in this first committed and highly regulated step of glycolysis. Allostery is defined as effector ligand(s) binding to a remote site (allosteric site) and influences the binding affinity of substrate(s) to the active site. Activators increase, whereas inhibitors decrease, substrate binding affinity. In Escherichia coli PFK, phosphoenolpyruvate (PEP) is a potent inhibitor of Fru-6-P binding, whereas MgADP is a weak activator (1Blangy D. Buc H. Monod J. J. Mol. Biol. 1968; 31: 13-35Crossref PubMed Scopus (305) Google Scholar). The allosteric properties of E. coli PFK have been studied extensively using steady state enzyme kinetics (1Blangy D. Buc H. Monod J. J. Mol. Biol. 1968; 31: 13-35Crossref PubMed Scopus (305) Google Scholar, 2Monod J. Wyman J. Changeux J.P. J. Mol. Biol. 1965; 12: 88-118Crossref PubMed Scopus (6184) Google Scholar, 3Deville-Bonne D. Garel J.-R. Biochemistry. 1992; 31: 1695-1700Crossref PubMed Scopus (23) Google Scholar, 4Auzat I. Le Bras G. Garel J.-R. J. Mol. Biol. 1995; 246: 248-253Crossref PubMed Scopus (11) Google Scholar, 5Deville-Bonne D. Bourgain F. Garel J.-R. Biochemistry. 1991; 30: 5750-5754Crossref PubMed Scopus (29) Google Scholar, 6Johnson J.L. Reinhart G.D. Biochemistry. 1992; 31: 11510-11518Crossref PubMed Scopus (38) Google Scholar, 7Johnson J.L. Reinhart G.D. Biochemistry. 1994; 33: 2635-2643Crossref PubMed Scopus (25) Google Scholar, 8Deville-Bonne D. Laine R. Garel J.-R. FEBS Lett. 1991; 290: 173-176Crossref PubMed Scopus (24) Google Scholar, 9Auzat I. Garel J.-R. Protein Sci. 1992; 1: 254-258Crossref PubMed Scopus (13) Google Scholar, 10Serre M.-C. Garel J.-R. Eur. J. Biochem. 1990; 189: 487-492Crossref PubMed Scopus (4) Google Scholar) and fluorescence emission (7Johnson J.L. Reinhart G.D. Biochemistry. 1994; 33: 2635-2643Crossref PubMed Scopus (25) Google Scholar, 11Valdez B.C. French B.A. Younathan E.S. Chang S.H. J. Biol. Chem. 1989; 264: 131-135Abstract Full Text PDF PubMed Google Scholar, 12Berger S.A. Evans P.R. Biochemistry. 1991; 30: 8477-8480Crossref PubMed Scopus (29) Google Scholar, 13Johnson J.L. Reinhart G.D. Biochemistry. 1997; 36: 12814-12822Crossref PubMed Scopus (32) Google Scholar, 14Teschner W. Garel J.-R. Biochemistry. 1989; 28: 1912-1916Crossref PubMed Scopus (16) Google Scholar, 15Le Bras G. Teschner W. Deville-Bonne D. Garel J.-R. Biochemistry. 1989; 28: 6836-6841Crossref PubMed Scopus (32) Google Scholar, 16Teschner W. Serre M.C. Garel J.-R. Biochimie (Paris). 1990; 72: 403-406Crossref PubMed Scopus (1) Google Scholar, 17Johnson M. Methods Enzymol. 1997; 278: 570-583Crossref PubMed Scopus (6) Google Scholar, 18Pham A.S. Janiack-Spens F. Reinhart G.D. Biochemistry. 2001; 40: 4140-4149Crossref PubMed Scopus (9) Google Scholar, 19Pham A.S. Reinhart G.D. Biochemistry. 2001; 40 (4148): 4150Crossref PubMed Scopus (5) Google Scholar, 20Koshland Jr., D.E. Nemethy G. Filmer D. Biochemistry. 1966; 5: 365-385Crossref PubMed Scopus (2208) Google Scholar, 21Pham T.C. Thermodynamic, fluorescence dynamic, and kinetic characterization of the E187A mutant of Escherichia coli phosphofructokinase.Ph.D. thesis. Texas A & M University, 1999Google Scholar). These steady state techniques have provided useful insight into ligand interactions with the application of linkage analysis (6Johnson J.L. Reinhart G.D. Biochemistry. 1992; 31: 11510-11518Crossref PubMed Scopus (38) Google Scholar, 7Johnson J.L. Reinhart G.D. Biochemistry. 1994; 33: 2635-2643Crossref PubMed Scopus (25) Google Scholar, 13Johnson J.L. Reinhart G.D. Biochemistry. 1997; 36: 12814-12822Crossref PubMed Scopus (32) Google Scholar, 18Pham A.S. Janiack-Spens F. Reinhart G.D. Biochemistry. 2001; 40: 4140-4149Crossref PubMed Scopus (9) Google Scholar, 19Pham A.S. Reinhart G.D. Biochemistry. 2001; 40 (4148): 4150Crossref PubMed Scopus (5) Google Scholar, 20Koshland Jr., D.E. Nemethy G. Filmer D. Biochemistry. 1966; 5: 365-385Crossref PubMed Scopus (2208) Google Scholar, 21Pham T.C. Thermodynamic, fluorescence dynamic, and kinetic characterization of the E187A mutant of Escherichia coli phosphofructokinase.Ph.D. thesis. Texas A & M University, 1999Google Scholar). Linkage is defined as a reciprocity of effects between an allosteric ligand and a substrate interacting to an enzyme. The nature (i.e. whether activating or inhibiting) and potency of change resulting from an interaction is the same regardless of whether an allosteric ligand or a substrate binds to the enzyme first. This linkage phenomenon is a convenient method to derive rate and equilibrium constants from reaction steps that are not readily discernible by physical techniques. Linkage effects can be quantified by a coupling constant Q, where Q above 1 denotes an activating coupling interaction and Q below 1 denotes an inhibiting interaction, between two or more ligands (22Reinhart G.D. Biophys. Chem. 1988; 30: 159-172Crossref PubMed Scopus (48) Google Scholar, 23Braxton B.L. Tlapak-Simmons V.L. Reinhart G.D. J. Biol. Chem. 1994; 269: 47-50Abstract Full Text PDF PubMed Google Scholar). InE. coli PFK, the binding affinity of Fru-6-P is 90-fold reduced in the presence of saturating concentration of phosphoenolpyruvate (PEP) (Q = ∼0.011), regardless of whether PEP or Fru-6-P binds first (13Johnson J.L. Reinhart G.D. Biochemistry. 1997; 36: 12814-12822Crossref PubMed Scopus (32) Google Scholar). The binding affinity of Fru-6-P is 6 times higher in the presence than in the absence of MgADP (Q = 5.6). 2A. S. Pham and G. D. Reinhart, submitted for publication. To date, we understand little of how linkage is manifested under pre-steady state and non-steady state conditions. Few reports have addressed allosteric phenomena in the pre-steady state time scale (24Auzat I. Gawlita E. Garel J.-R. J. Mol. Biol. 1995; 249: 478-492Crossref PubMed Scopus (14) Google Scholar,25Brzovic P.S. Ngo K. Dunn M.F. Biochemistry. 1992; 31: 3831-3839Crossref PubMed Scopus (100) Google Scholar). Only recently, Auzat et al. (24Auzat I. Gawlita E. Garel J.-R. J. Mol. Biol. 1995; 249: 478-492Crossref PubMed Scopus (14) Google Scholar) reported the intrinsic rate constants, as determined by stopped-flow kinetics, associated with the binding of Fru-6-P, PEP, and MgADP to E. coli PFK. By using several concentrations of effectors and substrates, the authors clarified some aspects of the allosteric properties of PFK by examining the interactions between substrates, enzymes, and effectors. Changes in the rate constants for the interaction between Fru-6-P and PFK in the presence of effectors were inferred to be due to a conformational transition between an equilibrium of R (relax, high affinity, high activity) and T (taut, low affinity, low activity) conformational states (2Monod J. Wyman J. Changeux J.P. J. Mol. Biol. 1965; 12: 88-118Crossref PubMed Scopus (6184) Google Scholar). The Monod-Wyman-Changeux (MWC) two-state model relates these mutually exclusive pre-existing conformational states to enzymatic activities (2Monod J. Wyman J. Changeux J.P. J. Mol. Biol. 1965; 12: 88-118Crossref PubMed Scopus (6184) Google Scholar). Modifications to the MWC model were made as necessary, by supplementing new states such as the Rf, Ra, and “not genuine T” states, to characterize kinetically distinct processes (24Auzat I. Gawlita E. Garel J.-R. J. Mol. Biol. 1995; 249: 478-492Crossref PubMed Scopus (14) Google Scholar). These conformational state assignments if not confusing, were ambiguous as it became increasingly apparent that the two-state model provides a limited framework for interpreting allosteric properties (4Auzat I. Le Bras G. Garel J.-R. J. Mol. Biol. 1995; 246: 248-253Crossref PubMed Scopus (11) Google Scholar, 5Deville-Bonne D. Bourgain F. Garel J.-R. Biochemistry. 1991; 30: 5750-5754Crossref PubMed Scopus (29) Google Scholar, 26Lau F.T.-K. Fersht A.R. Nature. 1987; 326: 811-812Crossref PubMed Scopus (53) Google Scholar). In the first place, the formation of a possible ternary complex between substrate, inhibitor, and protein, which has been substantiated (13Johnson J.L. Reinhart G.D. Biochemistry. 1997; 36: 12814-12822Crossref PubMed Scopus (32) Google Scholar), was not considered. Second, when a model appears to mathematically explain a phenomenon so well, regardless of whether it has any biophysical basis, it is tempting to design experiments by sampling only a few representative effector concentrations to conform to its guiding principles. When the rate constant for a substrate in the presence of an inhibitor differs from that in the presence of an activator, the disparity is attributed to the shifting of the enzyme between differing conformational states. Saturation plateaus were not often observed when only few effector concentrations were examined, and ligand interactions appeared to be competitive. By systematically varying the Fru-6-P concentration in a wide range of constant effector ligand concentrations (or vice versa) to explore a complete two-dimensional array of substrate and effector concentrations, we can examine comprehensively the processes involved in ligand-influenced binding events. All reagents used in experiments were of analytical grade and were purchased from either Sigma or Fisher. The purification protocol and steady state kinetics were performed as described previously (18Pham A.S. Janiack-Spens F. Reinhart G.D. Biochemistry. 2001; 40: 4140-4149Crossref PubMed Scopus (9) Google Scholar, 19Pham A.S. Reinhart G.D. Biochemistry. 2001; 40 (4148): 4150Crossref PubMed Scopus (5) Google Scholar). The pre-steady state kinetic experiments were performed using an Applied Photophysics SX18.MV model stopped-flow spectrofluorometer connected to an Acorn Archimedes 420/1 operating system. The instrument was set with a 2-mm path length cell and an excitation band pass of <10 nm (slit width = 1 or 2 mm). In most cases, the sample was subjected to excitation at 295 nm with a 150-watt xenon arc lamp, and emission intensity was monitored through a WG-335 (Schott) cut-on filter between the sample cell and the detector. The dead time of the instrument (i.e. the period between the trigger of the flow and the start of data collection) was estimated (27Peterman B.F. Laidler K.J. Biochim. Biophys. Acta. 1979; 577: 314-323Crossref PubMed Scopus (11) Google Scholar) at 1.4 ms, which gives an upper rate limit of ∼700 s−1. Pseudo-first order conditions were maintained in which the protein concentration (0.5–2 μm, 0.02–0.07 mg/ml) was at least 10 times less than that of the ligand concentrations. No dependence of the observed rate constant on PFK concentration was detected within this concentration range. Data were collected within a pre-selected time range, and data points within the first 2 ms were discarded when fitting the data. To improve the signal-to-noise ratio, all rate constants were determined from an average of six runs, with each run consisting of 400 data points. In the coupling experiment between a substrate and an effector ligand, PFK was combined with an appropriate ligand concentration in one syringe, and a second ligand was introduced via another syringe to initiate the reaction. Nonlinear regression analyses were performed using Kaleidagraph software (Synergy). Decays profiles were fit to a single exponential equation, yielding the observed rate constant (kobs). Values of kobs as a function of ligand concentrations were then fit to the rate-dependent mechanisms described below. As with steady state conditions, experiments were performed with enzyme and ligand species in EPPS buffer (pH 8, KOH), 10 mmMgCl2, 100 mm KCl, and 0.1 mmEDTA. The steady state rate equation describing the interaction of substrate A and allosteric ligandX with the enzyme E is shown (28Reinhart G.D. Arch. Biochem. Biophys. 1983; 224: 389-401Crossref PubMed Scopus (75) Google Scholar) in Equation1. vET=VoKixo[A]+VoQaxWax[A][X]KiaoKixo+Kixo[A]+Kiao[X]+Qax[A][X]Equation 1 where v is the observed rate, V ois the maximal rate in the absence of allosteric ligand, andWax is the coupling constant reflecting theVmax influence between A andX. Qax is the coupling constant describing the binding affinities of A andX to the enzyme. K iao and K ixo are the dissociation constants for A and X, respectively, in the absence of all other ligands. Since ET = [E] + [EA] + [EX] + [AEX], the concentration of the ternary complex can be calculated using the following expression: [AEX]=Qax[A][X]KiaoKixo+Kixo[A]+Kiao[X]+Qax[A][X]Equation 2 By using Equation 2, we determined that at least 60 mm Fru-6-P and 200 mm PEP are needed to obtain 90% of the fractional component from which the ternary complexAEX predominates. Thus, to characterize fully a coupling interaction between two ligands, a wide concentration range of each ligand was needed to capture the various ligand complex states. This finding is the basis of our rationale for performing the experiments at extremely high ligand concentrations. For data exhibiting a linear observed rate dependence as a function of ligand concentration, the simplest model to describe the binding of a ligand to an enzyme is a one-step mechanism, E+X ⇌koffkon E−X. SCHEME IThis model predicts that a single first order rate constant will be observed and related to kon andkoff by the expression,kobs = kon[X] + koff, wherekon is the rate constant for the bimolecular association of a ligand to an enzyme, and koffis the unimolecular dissociation rate constant (29Johnson, K. A., The Enzymes, 3rd Ed., Sigman, D. S., 20, 1992, 1, 61, Academic Press, San DiegoGoogle Scholar). However, a hyperbolic dependence of the observed rate constant as a function of ligand concentration requires minimally a two-step mechanism, where one step is concentration-independent. The mechanism that best describes the rate dependence pattern for the binding of Fru-6-P to PFK is given by Scheme II (24Auzat I. Gawlita E. Garel J.-R. J. Mol. Biol. 1995; 249: 478-492Crossref PubMed Scopus (14) Google Scholar,30Hiromi K. Kinetics of Fast Reactions. Halsted Press, New York1979: 255-283Google Scholar), E+X ⇌K1 EX ⇌k4k3 E′X SCHEME IIThe ligand binding process is defined byK1, an equilibrium constant (K1 =k2/k1), and by a relatively slow unimolecular isomerization process that is represented by the forward (k3) and reverse (k4) steps. The isomerization step can be detected spectroscopically, and the rate dependence pattern is expressed by Equation 3, kobs=k3[X]K1+[X]+k4Equation 3 where kobs is the observed rate constant. For the mechanism shown in Scheme II, the apparent overall dissociation constant (K) is determined by Equation 4 (24Auzat I. Gawlita E. Garel J.-R. J. Mol. Biol. 1995; 249: 478-492Crossref PubMed Scopus (14) Google Scholar, 30Hiromi K. Kinetics of Fast Reactions. Halsted Press, New York1979: 255-283Google Scholar), K=[E][X][EX]+[E′X]=K11+(1/K2)=K11+k3/k4Equation 4 where K1 is the equilibrium constant for the fast complexation step of EX; K2is the equilibrium constant for the isomerization process between theEX and E′X forms (K2 =k4/k3), andk3 and k4 are the unimolecular forward and reverse isomerization rate constants, respectively. For the coupling constant determination, the rate Equation 1 can be simplified to (22Reinhart G.D. Biophys. Chem. 1988; 30: 159-172Crossref PubMed Scopus (48) Google Scholar, 28Reinhart G.D. Arch. Biochem. Biophys. 1983; 224: 389-401Crossref PubMed Scopus (75) Google Scholar) Equation 5, Kia=KiaoKixo+[X]Kixo+Qax[X]Equation 5 where Kia represents an apparent dissociation constant determined from steady state measurements and K iao is the dissociation constant in the absence of other ligand. To determine the maximum relative fluorescence change and the fraction of the total fluorescence change occurring within the dead time of the instrument at a particular concentration of the substrate, we used the following Equation 6 (31Tanaka A. Ohnishi M. Hiromi K. Biochemistry. 1982; 21: 107-113Crossref PubMed Scopus (30) Google Scholar), ΔFa=ΔFo(1−e−kobsdt)Equation 6 where ΔFo is the observed fluorescence change; dt is the dead time of the instrument, and ΔFa is the actual change in fluorescence with a dead time of 0. Congruency between ΔFa and the fluorescence changes derived from equilibrium measurements indicates that the total contributions of amplitude changes are fully accounted by the observed changes derived from pre-steady state techniques. The dependence of the observed rate constant (kobs) for the binding of Fru-6-P to the enzyme exhibited a hyperbolic pattern that approached saturation at Fru-6-P concentrations above 1 mm (Fig.1). Introducing Fru-6-P at the lowest concentration allowable by the detection system to the free PFK yielded a rate constant of 100 s−1; binding approached an apparent upper rate constant of ∼400 s−1 at Fru-6-P concentrations greater than 1 mm. This pattern is well described by a two-step sequential mechanism shown in Scheme II, wherein the second process is the fluorescence detection step. These data are fully consistent with those reported by Auzat et al. (24Auzat I. Gawlita E. Garel J.-R. J. Mol. Biol. 1995; 249: 478-492Crossref PubMed Scopus (14) Google Scholar). To determine how allosteric ligands affect the rate constant for binding, we monitored Fru-6-P binding in a range of fixed concentrations of PEP preincubated with the enzyme. The rate dependence for the binding of Fru-6-P to the PEP·PFK complex also displayed hyperbolic profiles that are well modeled by the two-step mechanism shown in Scheme II. Thekobs for Fru-6-P interaction as a function of PEP displayed several distinct transitions, and Fig.2 shows these transitions using several concentrations of PEP. In the absent of PEP, thekobs for Fru-6-P is between ∼100 and 400 s−1. In PEP concentrations of <0.5 mm, thekobs for Fru-6-P decreased drastically, displaying an overall downward shift in the trend. At 0.5 mm PEP, the kobs was generally 15 times lower, whereas the overall trend appeared to parallel that of thekobs pattern for Fru-6-P binding to free enzyme form. At PEP concentrations greater than 0.5 mm,kobs increased, with regions at both extreme Fru-6-P concentrations shifting upward. In PEP concentrations of 30 mm, the kobs at 100 mm Fru-6-P is comparable to kobsvalues extrapolated for saturating Fru-6-P concentrations interacting with free PFK. In addition, the mid-transitions, corresponding to theK1 value, become progressively steeper with increasing PEP concentrations. The kobs data for the Fru-6-P/PEP interactions were fit to Equation 3, and the derived dependence of rate and equilibrium constants are depicted in Fig.3. From the initial value of ∼300 s−1, the forward isomerization rate constant,k3, decreased dramatically with increasing effector concentrations up to 1 mm PEP and then rose gradually with increasing PEP concentrations up to 60 mm(Fig. 3 A). The midpoint of the downward transition appeared to be a PEP concentration of ∼0.3 mm, a value that is comparable the dissociation constant for PEP determined from equilibrium measurements. No further increase ink3 was observed at PEP concentrations above 15 mm. The trend exhibited by the k3values was clearly multiphasic, with only a minor difference in the values between low and high concentrations of PEP. The rate constant for the reverse isomerization step, k4, displayed a dependence on PEP concentration similar to that ofk3. The value of k4 was ∼90 s−1 in the absence of PEP, decreased to 5 s−1 at 1 mm PEP, and then increased gradually to 20 s−1 at a PEP concentration of 60 mm(Fig. 3 B). The difference of the k4value in the absence of PEP and that of saturating PEP concentrations was 4-fold. The influence of PEP on the interaction of Fru-6-P and PFK was largely exhibited in the complex formation step, as indicated by the higher equilibrium constants (K1) with increasing effector concentrations (Fig. 3 C). K1value initiated at 0.3 mm in the absence of PEP and approached a plateau of ∼60 mm at a PEP concentration of 30 mm. The K1 values approached at high PEP concentrations are consistent with the hypothesis of the formation of the PEP·PFK·Fru-6-P ternary complex. Thus, PEP appeared to act by affecting the ligand-encountered complex rather than by inducing a shift in subsequent conformation-change equilibrium. The overall dissociation constants obtained from pre-steady state measurements (K) were compared with those obtained from equilibrium fluorescence measurements (Kia) to determine whether these techniques fully account for the processes involved in binding. Each equilibrium value for Fru-6-P was derived as a function of a fixed PEP concentration. The K andKia data points overlap at the mid-range PEP concentrations (0.2–10 mm) but diverge at both extreme regions of PEP concentrations (data not shown). The K values initiated at 0.1 mm in the absence of PEP and decreased to 0.01 mm with increasing PEP concentrations of up to 0.25 mm; K values increased with PEP concentrations higher than 0.25 mm. The dip in the low PEP concentration range terminated coincidentally at the PEP concentration that corresponded to its dissociation constant (0.24 mm). The initial Kia value was determined to be 0.01 mm, in the absence of PEP, and increased in a sigmoidal pattern to 0.7 mm, in saturating PEP concentrations. The plateau region, indicating an approach of binding saturation, was 3 times lower for Kia than for K. Comparing the fluorescence amplitude trends determined by equilibrium measurements and those determined by stopped flow may provide insight to the discrepancy observed betweenK and Kia. Fig.4 shows the trends in the fluorescence amplitude change as a function of Fru-6-P concentration. The fluorescence signals for Fru-6-P determined by stopped-flow measurements only decreased by ∼10%, whereas the signals determined by steady state fluorescence decreased by a total of 30%. In both measurement types, the fluorescence signals for Fru-6-P in the presence of PEP was progressively smaller with increasing concentrations. The rate dependence pattern for the binding of allosteric ligands to the free enzyme in each case yielded a linear relationship in whichkobs is proportional to ligand concentration. The slope of each curve represents the second-order apparent rate constant for the loading of the ligand onto the enzyme, and the ordinate represents a first-order apparent rate constant for the unloading of the ligand from the enzyme. The observed rate for the binding of MgADP to PFK yielded a kon of 22 ± 0.8 mm−1 s−1 and for PEP to PFK yielded a kon of 3.0 ± 0.4 mm−1 s−1 and akoff of 5.7 ± 0.3 s−1. These values are fully consistent with those obtained by Auzat et al. (24Auzat I. Gawlita E. Garel J.-R. J. Mol. Biol. 1995; 249: 478-492Crossref PubMed Scopus (14) Google Scholar) using slightly different buffer conditions. Introducing PEP to the PFK equilibrium complex containing various concentrations of Fru-6-P in all cases yielded kobs that ranged between the values observed for the binding of either PEP or Fru-6-P alone to the free enzyme. Fig. 5 shows the linear rate dependence pattern for the binding of PEP to PFK in the presence of various fixed concentrations of Fru-6-P. Addition of 30 mm PEP to 10 μm Fru-6-P in complex with PFK produced the kobs of ∼185 s−1, in contrast to the kobs of ∼85 s−1for PEP without Fru-6-P and ∼400 s−1 for Fru-6-P without PEP. At all Fru-6-P concentrations, the observed rate constant for PEP binding showed a linear concentration-dependent pattern, and no additional mechanistic steps were detected. Increasing the Fru-6-P concentrations caused the slope to become more shallow (corresponding to decreasing kon) and the intercept to increase (corresponding to increasingkoff). Decreasing konvalues for PEP were offset by the increase inkoff values. In addition, thekoff values appeared to be affected to a greater extent than the kon values;koff values were 15 times higher in the presence than in the absence of Fru-6-P, whereas konvalues were only 5 times lower. Both trends exhibited an approach of plateaus at Fru-6-P concentrations above 1 mm, providing evidence for a ternary complex of inhibitor, enzyme, and substrate.Figure FSIIIView Large Image Figure ViewerDownload Hi-res image Download (PPT) To compare the values derived from steady state with those from pre-steady state, the “measured” koff values were compared with the “calculated” koff. The calculated koff values were determined fromKia·kon, from whichKia values were derived using Equation 5. The parameters Kix for PEP and Kiafor Fru-6-P and the coupling constant values were obtained from equilibrium measurements reported previously (13Johnson J.L. Reinhart G.D. Biochemistry. 1997; 36: 12814-12822Crossref PubMed Scopus (32) Google Scholar). These calculatedkoff values roughly overlapped those measured values determined at pre-steady state with an approach of the point of saturation by a flattening of the trend apparent at Fru-6-P concentrations above 2 mm. A close correlation of the measured koff and the calculatedkoff rate constants indicated that the one-step mechanism adequately describes this kinetic process. Similar to the results for PEP binding to the PFK·Fru-6-P complex, the observed rate dependence for MgADP binding to the enzyme in the presence of fixed Fru-6-P concentrations (1–50 μm) yielded a linear relationship that was concentration-dependent. However, in contrast to the results for Fru-6-P/PEP binding, the slopes increased (rather than decreased) and the intercepts remained invariant (rather than increased) with higher Fru-6-P concentrations up to 50 μm (Fig. 6 A). As previously noted from experiments performed under equilibrium conditions, Fru-6-P and MgADP each independently produce substantial quenching of the PFK tryptophanyl fluorescence, but quenching is suppressed with increasing of ligand concentrations leading to insignificant changes in the presence of saturating concentrations of both ligands (6Johnson J.L. Reinhart G.D. Biochemistry. 1992; 31: 11510-11518Crossref PubMed Scopus (38) Google Scholar). Thus, rates for MgADP at Fru-6-P concentrations higher than 50 μm are unobtainable, because the changes in fluorescence intensity were insufficient to allow a determination of rate constants pertaining to the ternary complex. Although the results suggest that MgADP modestly influences the rate constant for Fru-6-P binding, however, with such limited Fru-6-P concentration ranges, the trend probably did not reflect the maximum changes possible by the ternary complex (Fig. 6 B). The measured and calculatedkoff values overlapped entirely and probably indicate that the measured rate constants reflect full accountability of the steps involved in the mechanism. When experiments were attempted in which Fru-6-P was introduced to the MgADP·PFK complex, the fluorescence signals were insignificant, and the observed rates cannot be measured reliably. The results indicate that the single-substrate, single-effector thermodynamic box previously described by Reinhart (28Reinhart G.D. Arch. Biochem. Biophys. 1983; 224: 389-401Crossref PubMed Scopus (75) Google Scholar) must be expanded to account for the intermediate isomerization step reflecting the interaction of Fru-6-P with the enzyme. A mechanism to describe the Fru-6-P binding to PFK, regardless of whether Fru-6-P binds to the free enzyme form or to the PFK·effector binary complex, is a two-step process that includes a complexation event followed by a slow structural isomerization (Scheme II). K io and K ia∞ describe the first complexation step in the absence and presence of allosteric ligand, respectively. The unimolecular rate constants k3and k4 describe, respectively, the forward and reverse isomerization step in the absence of effector.k9 and k10 correspond to the forward and reverse, respectively, rate constants in saturating concentrations of effector ligand. The binding of an allosteric ligand to free PFK or to the PFK·Fru-6-P complex conforms to a one-step mechanism; k5 and k11describe intrinsic bimolecular association rate constants in the absence of substrate and at the saturating substrate concentration, respectively; k6 and k12describe the unimolecular dissociation rate constants in the absence of Fru-6-P and at the saturating concentration of Fru-6-P, respectively. Table I summarizes these rate and equilibrium constants for the individual and three-way interactions between Fru-6-P, allosteric ligand, and the enzyme. Each overall ligand dissociation constant is then redefined to account for the additional step (Equation 7): Kiao=K1o1+k3/k4,Kia∞=K1∞1+k9/k10,Kixo=k6k5,Kix∞=k12k11Equation 7 The coupling constant (Q) is then defined with respect to rate constants (Equation 8) as follows: Qax=k6k11k5k12=K1o(1+k9/k10)K1∞(1+k3/k4)Equation 8 Table II shows a comparison of the coupling Q values derived from these rate constants with those determined from equilibrium measurements. A comparison ofQ values indicates that the coupling constants determined from pre-steady state kinetics are consistent with those obtained from steady state measurements (7Johnson J.L. Reinhart G.D. Biochemistry. 1994; 33: 2635-2643Crossref PubMed Scopus (25) Google Scholar, 13Johnson J.L. Reinhart G.D. Biochemistry. 1997; 36: 12814-12822Crossref PubMed Scopus (32) Google Scholar).Table IKinetic and equilibrium constants for the binding of ligands to the E. coli phosphofructokinaseInteracting ligandK1o aThe constants are derived as shown in Scheme FSIII and described in the text.k3k4k5k6K1∞k9k10k11k12mms−1mms−1E-Fru-6-P, PEP-E or PEP-E-Fru-6P0.42 ± 0.1329 ± 1289 ± 4.73.0 ± 0.45.7 ± 0.353 ± 5.0482 ± 3322 ± 0.51.7 ± 0.1178 ± 37E-Fru-6-P, MgADP-E or MgADP-E-Fru-6-PbNot all MgADP/Fru-6-P interactions were measurable due to weak fluorescence signals.0.42 ± 0.1329 ± 1289 ± 4.721 ± 0.80.1 ± 0.0354 ± 40.1 ± 0.0a The constants are derived as shown in Scheme FSIII and described in the text.b Not all MgADP/Fru-6-P interactions were measurable due to weak fluorescence signals. Open table in a new tab Table IIComparison of values determined from pre-steady state (ps) and steady state (ss) for the E. coli phosphofructokinaseSpeciesK iao aEquilibrium constants are expressed in mm.K ia∞K ixoK ix∞QpsPEP-E-Fru-6-P0.010.61.91050.017MgADP-E-Fru-6-PbSome values cannot be determined due to weak fluorescence signals.0.010.0052.6ssPEP-E-Fru-6-P0.0060.20.3190.016MgADP-E-Fru-6-P0.0060.0010.0080.0015.6a Equilibrium constants are expressed in mm.b Some values cannot be determined due to weak fluorescence signals. Open table in a new tab The mechanism that drives the interaction of Fru-6-P with PEP/PFK appears to differ from the mechanism that drives the interaction of PEP with Fru-6-P/PFK. Fru-6-P yields a hyperbolic rate dependence mechanism regardless of the liganded state of the enzyme, whether free PFK or a PEP·PFK or MgADP·PFK complex. Conversely, the rate dependence profiles for allosteric effectors yield a one-step mechanism regardless of whether the effector ligand interacts with the free enzyme or with the PFK·Fru-6-P complex. Thus, whereas the observed rate constants for substrate and effector participating in a ternary interaction lie between those for each ligand participating in a binary interaction independently, the rate dependence patterns do not reflect this hybrid characteristic. However, a close examination of both binding events indicates that both ternary interactions followed the same mechanism. Consider the binding of Fru-6-P to the PFK·PEP complex. First, in the presence of low PEP concentrations, Fru-6-P appears to “bump off” PEP and to bind exclusively to the free enzyme. Dramatic decreases in the forward and reverse isomerization rate constants k3 andk4, respectively, suggest that not much Fru-6-P·PFK′·PEP complex is being formed. Second, theK1 value at the low PEP concentrations, which is similar to the K1 value observed for Fru-6-P binding to the free enzyme, suggests that Fru-6-P·PFK is being formed exclusively. The K1 value rises dramatically at PEP concentrations above 1 mm, indicating that PEP is binding directly to the Fru-6-P·PFK complex. A rise ink3 implies the formation of the Fru-6-P·PFK′·PEP complex. The k4 value also increases, but not by more than the k3, possibly indicating that the predominant species in the solution is the Fru-6-P·PFK·PEP complex rather than Fru-6-P·PFK′·PEP. For PEP concentrations above 10 mm, K1levels off to a saturable level, probably reflecting the ternary complex form. These results suggest that the allosteric influence of PEP on the binding of the substrate to the enzyme does not occur predominantly through a subsequent conformational change, as might be expected under the classical allosteric theory (2Monod J. Wyman J. Changeux J.P. J. Mol. Biol. 1965; 12: 88-118Crossref PubMed Scopus (6184) Google Scholar, 20Koshland Jr., D.E. Nemethy G. Filmer D. Biochemistry. 1966; 5: 365-385Crossref PubMed Scopus (2208) Google Scholar). Rather, differences in signals reflect the changing species population. A parallel argument can be made for the binding of PEP to the Fru-6-P·PFK complex. With increasing Fru-6-P concentrations, the decreasing kon is offset by increasingkoff and could indicate a displacement of PEP and a binding on Fru-6-P. However, the leveling of thekon rate constant observed at Fru-6-P concentrations above 1 mm indicates the formation of a ternary complex. Thus, results derived from either Fru-6-P or PEP binding to the PFK binary complex suggest the same conclusion, the formation of a Fru-6-P·PFK·PEP ternary complex. In addition, the rate constants measured during these processes are fully consistent with the equilibrium values we determined previously for the allosteric effects of PEP on Fru-6-P binding. The displacement model of Auzat et al. (24Auzat I. Gawlita E. Garel J.-R. J. Mol. Biol. 1995; 249: 478-492Crossref PubMed Scopus (14) Google Scholar), which describes the mutually exclusive binding of PEP and Fru-6-P to the enzyme, is not entirely inconsistent with our view. Indeed, our results show evidence for ligand displacement at low Fru-6-P and PEP concentrations. Auzatet al. (24Auzat I. Gawlita E. Garel J.-R. J. Mol. Biol. 1995; 249: 478-492Crossref PubMed Scopus (14) Google Scholar), however, overlooked additional transitions of the Fru-6-P/PEP interactions, because only two concentrations of PEP (0.5 and 2 mm) were used with either 0.025 or 0.1 mm Fru-6-P. Hence, the changes resulting from Fru-6-P/PEP interaction appeared two-state. Equation 2 predicts that high concentrations of both ligands are needed to obtain an appreciable population of the ternary complex. Indeed, this prediction is supported by our experiments, wherein saturation levels were observed for PEP concentrations above 30 mm and for Fru-6-P concentrations above 1 mm. The displacement model of Auzat et al. (24Auzat I. Gawlita E. Garel J.-R. J. Mol. Biol. 1995; 249: 478-492Crossref PubMed Scopus (14) Google Scholar) was based on the MWC prediction that inhibitor and substrate cannot bind to the same enzyme form. Our results show that whereas the MWC two-state model accounts for some aspects of allosteric properties, it is far from a complete and accurate depiction of allosteric influence. The MWC two-state theory presupposes that PEP stabilizes theT form PFK, whereas MgADP and Fru-6-P stabilize theR form. Transitions between the alleged R andT forms would predictably yield the same rate constants for the forward and reverse isomerization steps. However, our data indicate that the rate constants for the presumed R to Ttransition were not the same as those for the T toR transition. On the contrary, each ligand interaction with PFK yields distinct forward and reverse rate constants. Thus, to conserve the working MWC two-state model, other authors (24Auzat I. Gawlita E. Garel J.-R. J. Mol. Biol. 1995; 249: 478-492Crossref PubMed Scopus (14) Google Scholar, 32Lau F.T.-K. Fersht A.R. Biochemistry. 1989; 28: 6841-6847Crossref PubMed Scopus (39) Google Scholar) resort to assigning a sub-classification of the R andT PFK forms for each ligand interaction. For example, it is assumed that Fru-6-P binds to the R form. However, a newRf form is invoked as an attempt to account for the two-state mechanism of the Fru-6-P interaction with PFK. The distinction between the R and Rf states is the high and low fluorescence, where high and low fluorescence states presumably correspond to the increase and decrease, respectively, of fluorescence intensity emission upon the binding of a ligand. This assignment is arbitrary, since the binding of Fru-6-P was not known to cause an increase and then a decrease in fluorescence. Allosteric action can be adequately explained without such a model being invoked. Given that the enzyme reacts to each species specifically, the minimum number of conformations to describe an allosteric action is four as follows: free enzyme, enzyme-substrate, enzyme-effector, and substrate-enzyme-effector, in which an effector may be an inhibitor or an activator. Pre-steady state studies can provide insights into whether the influence of an allosteric ligand on substrate binding affinity necessitates additional intermediate steps unique to each effector ligand or whether allosteric ligand acts through modification of existing rate constants for substrate binding. Our results indicate that activation and inhibition by allosteric ligands occur by essentially the same mechanism; each modifies the existing rate constants and forms the ternary complex.