Inhibition and activation of enzymes. The effect of a modifier on the reaction rate and on kinetic parameters

A combined analysis of enzyme inhibition and activation is presented, based on a rapid equilibrium model assumption in which one molecule of enzyme binds one molecule of substrate (S) and/or one molecule of a modifier X. The modifier acts as activator (essential or non-essential), as inhibitor (total or partial), or has no effect on the reaction rate (v), depending on the values of the equilibrium constants, the rate constants of the limiting velocity steps, and the concentration of substrate ([S]). Different possibilities have been analyzed from an equation written to emphasize that v = f([X]) is, in general and at a fixed [S], a hyperbolic function. Formulas for Su (the value of [S], different from zero, at which v is unaffected by the modifier) and v(su) (v at that particular [S]) were deduced. In Lineweaver-Burk plots, the straight lines related to different [X] generally cross in a point (P) with coordinates (Su, v(su)). In certain cases, point P is located in the first quadrant which implies that X acts as activator, as inhibitor, or has no effect, depending on [S]. Furthermore, we discuss: (1) the apparent Vmax and Km displayed by the enzyme in different situations; (2) the degree of effect (inhibition or activation) observed at different concentrations of substrate and modifier; (3) the concept of Ke, a parameter that depends on the concentration of substrate and helps to evaluate the effect of the modifier: it equals the value of [X] at which the increase or decrease in the reaction rate is half of that achieved at saturating [X]. Equations were deduced for the general case and for particular situations, and used to obtain computer-drawn graphs that are presented and discussed. Formulas for apparent Vmax, Km and Ke have been written in a way making it evident that these parameters can be expressed as pondered means.     

Kinetic study of the inhibition of the amidolytic activity of thrombin by benzamidine and N-dansyl-(p-guanidino)-phenylalanine-piperidide (I-2581)

1. v([I]) data were obtained for the hydrolysis of the chromogenic substrate H-D-Phe-L-Pip-L-Arg-pNA (S-2238) by native human thrombin in the presence of the synthetic inhibitors Benzamidine and N-dansyl-(p-guanidino)-phenylalanine-piperidide (I-2581). v([S]) data were also obtained in the absence and presence of fixed concentrations of each of the inhibitors. 2. Analysis of the kinetic data was based on the numerical fitting to rate equations of the polynomial quotient type of degree n:m using nonlinear regression methods. The discrimination between rate equations with different degrees was performed by application of the statistical F test. 3. Of eight v([I]) curves fitted, in six cases it was found that degree 1:2 was significantly better than degree 1:1 at a confidence level of 95% or higher; in no case was a significant improvement found with rate equations with a higher number of parameters. For the v([S]) data, of eleven curves fitted it was found that in nine cases degree 2:2 significantly improved degree 1:1 at confidence levels 99% and in one case at a level of 95%; no significant improvement was found with rate equations of higher degree for these data either. 4. Our findings allow us to propose that inhibition of the amidolytic activity of native human thrombin by benzamidine and I-2581 may be accounted for by mechanisms whose v([I]) rate equation will be a minimum of degree 1:2, thus implying a pure inhibition.(ABSTRACT TRUNCATED AT 250 WORDS)     

The interpretation of non-hyperbolic rate curves for two-substrate enzymes. A possible mechanism for phosphofructokinase

1. A theoretical appraisal of the alternative pathway mechanism for a two-substrate enzyme shows that this mechanism is capable of giving rise to apparent substrate inhibition or substrate activation (Dalziel, 1958). It has now been shown that these phenomena may occur simultaneously in the following ways. With certain relationships between the kinetic parameters and the constant concentration of one substrate, A, the plot of initial rate, v, against the concentration of the other substrate, B, may show substrate ;activation' at low concentrations of B and substrate ;inhibition' at high concentrations of B. In other circumstances the plot of v against [B], with [A] constant, may be sigmoid (substrate activation), whereas the plot of v against [A], with [B] constant, may pass through a maximum (substrate inhibition). 2. Kinetic data for phosphofructokinase are of the latter type and it is suggested that the mechanism of this enzyme may involve a kinetically preferred pathway. It is emphasized that the phenomena of substrate inhibition and activation need not necessarily involve more than one binding site for each substrate on the enzyme molecule, nor more than one monomer per molecule.     

The kinetic properties and reaction mechanism of histamine methyltransferase from human skin.

The substrate kinetic properties of histamine methyltransferase from human skin were studied at limiting concentrations of both histamine and S-adenosylmethionine. Substrate inhibition by histamine was observed at concentrations above 10 microM. Primary plots showed evidence of a sequential reaction mechanism. The Michaelis constants were derived from secondary plots of slopes from the primary plots ([S]/v versus [S]) versus reciprocal of the second substrate concentration. The mean Km values for histamine and S-adenosylmethionine were 4.2 and 1.8 microM respectively. Histamine in concentrations of 25-100 microM inhibited enzyme activity uncompetitively with respect to S-adenosylmethionine. No substrate inhibition was observed with S-adenosylmethionine. To elucidate the reaction mechanism further, inhibition by the two products, S-adenosylhomocysteine and 1-methylhistamine, was studied. S-Adenosylhomocysteine inhibited non-competitively with respect to histamine and competitively with respect to S-adenosylmethionine. 1-Methylhistamine inhibited non-competitively with respect to histamine and to S-adenosylmethionine. These results are interpreted as providing evidence for an ordered sequential Bi Bi reaction mechanism, with the methyl-group donor S-adenosylmethionine as the first substrate that adds to the enzyme and histamine as the second substrate. 1-Methylhistamine is the first product to leave the enzyme and S-adenosylhomocysteine is the second. The results are discussed in terms of the possible role that this enzyme could play in the modulation of histamine-mediated reactions in skin.     

On the mechanistic origin of damped oscillations in biochemical reaction systems

A generalized reaction scheme for the kinetic interaction of two reactants in a metabolic pathway has been examined in order to establish what minimal mechanistic patterns are required to support a damped oscillatory transient-state kinetic behaviour of such a two-component system when operating near a steady state. All potentially oscillating sub-systems inherent in this scheme are listed and briefly characterized. The list includes several mechanistic patterns that may be frequently encountered in biological system (e.g. involving feedback inhibition, feed-forward activation, substrate inhibition or product activation), but also draw attention to some hitherto unforeseen mechanisms by which the kinetic interaction of two metabolites may trigger damped oscillations. The results can be used to identify possible sources of oscillations in metabolic pathways without detailed knowledge about the explicit rate equations that apply.     

Isomerase activity of the C-terminal fructose-6-phosphate binding domain of glucosamine-6-phosphate synthase from Escherichia coli

The isomerase activity of the C-terminal fructose-6P binding domain (residues 241-608) of glucosamine-6-phosphate synthase from Escherichia coli has been studied. The equilibrium constant of the C-terminal domain k(eq) ([glucose-6P]/[fructose-6-P]) = 5.0. A non-competitive product inhibition of the isomerase activity by the reaction product glucose-6-P has been detected. The existence of more than one binding and reaction sites for the substrate fructose-6P on the molecule of glucosamine-6-phosphate synthase can be expected. The fructose-6P binding domain possibly includes a regulatory site, different from the catalytic center of the enzyme.     

Hysteresis, multiplicity of stationary states and auto-oscillations in the reversible flow-through reaction]

A mathematical model has been investigated of a reversible flow-through reaction S1 reversible S2 catalyzed by an olygomeric enzyme E(R,T) the protomers of which undergo concerted conformational transitions R reversible T. The isosteric activation of olygomer E by product S2 binding preferably to protomer active sites in conformation R is shown to be a possible cause of hysteresis in the quasi-stationary input characteristic of the reaction, v (s2). The latter determines the rate law of the reaction, provided the concentration of S2 is a quasi-stationary one. The hysteresis of the characteristic v (s1) gives rise to multiple steady states and self-oscillations in the reaction.     

Dynamics and stability analysis of the growth and astaxanthin production system of Haematococcus pluvialis

This paper investigated high cell density cultivation of Haematococcus pluvialis for astaxanthin production in 3.7-L bioreactors. A biomass concentration of 2.74 g L⁻¹and an astaxanthin yield of 64.4 mg L⁻¹ were obtained. Based on the experimental results, a new and simple dynamic model is proposed, differing from Monod kinetics, to describe cell growth, product formation and substrate consumption. Good agreement was found between the model predictions and experimental data. The model revealed that there was cell growth inhibition on product formation and product feedback compensation for substrate consumption, but no substrate inhibition or product inhibition of cell growth. Stability analysis demonstrated that no multiplicity of steady states was observed; the unique positive steady state was locally asymptotically stable; and the effect of dilution rate on steady states was greater than that of the initial substrate concentration. Received 23 February 1999/ Accepted in revised form 08 June 1999     

Multiplicity and stability analysis of microorganisms in continuous culture: effects of metabolic overflow and growth inhibition

Metabolic overflow (enhanced uptake of substrate and secretion of intermediates) is a phenomenon often observed for cells grown under substrate excess. Growth inhibition by substrate and/or product is also normally found for this kind of culture. An effort is made in this work to analyze the dynamic behavior of a continuous culture subject to metabolic overflow and growth inhibition by substrate and/or product. Analysis of a model system shows that in a certain range of operating conditions three nonwashout steady state solutions are possible. Local stability analysis indicates that only two of them are stable thus leading to multiplicity and hysteresis. Further analysis of the intrinsic effects of different terms describing the metabolic overflow and growth inhibitions reveals that for the model system and the parameters considered, the combined effects of product inhibition and an enhanced formation rate of product under substrate excess cause the multiplicity and hysteresis. Growth inhibition by substrate and/or an enhanced substrate uptake appear not to be necessary conditions. The combined effects of enhanced product formation and product inhibition can also lead to unusual dynamic behavior such as a prolonged time period to reach a steady state, oscillatory transition from one steady state to another, and sustained oscillations. Using the occurrence of multiplicity and oscillation as criteria, the operating regime of a continuous culture can be divided into four domains: one with multiplicity and oscillation, one with unique steady state but possible oscillatory behavior, the other two with unique and stable steady state. The model predictions are in accordance with recent experimental results. The results presented in this work may be used as guidelines for choosing proper operating conditions of similar culture systems to avoid undesired instability and multiplicity. Copyright 1998 John Wiley & Sons, Inc.     

Kinetic consequences of a slow substrate binding step in group transferases. Interpretation of product inhibition experiments.

The steady state kinetic properties of a simple model for an enzyme catalyzed group transfer reaction between two substrates have been calculated. One substrate is assumed to bind slowly and the other rapidly to the enzyme. Apparent substrate inhibition or substrate activation by the rapidly binding substrate may result if the slowly binding substrate binds at unequal rates to the free enzyme and to the complex between the enzyme and the rapidly binding substrate. Competitive inhibition by each product with respect to its structurally analogous substrate is to be expected if both substrates are in rapid equilibrium with their enzyme-substrate complexes. This product inhibition pattern, however, may also be observed when one substrate binds slowly. Noncompetitive inhibition with respect to the rapidly binding substrate by its structurally analogous product may result if the slowly binding substrate binds more slowly to the enzyme-product complex than to the free enzyme. Inhibition by substrate analogs which are not products should follow the same rules as inhibition by products. Thus substrate analog inhibition experiments are not particularly informative. The form of inhibition by "transition state analog" inhibitors should reveal which substrate binds slowly. There is no sharp conceptual distinction between ordered and random "kinetic mechanisms". I therefore suggest that the use of these concepts should be abandoned.     

Reaction mechanism of 21S dynein ATPase from sea urchin sperm. I. Kinetic properties in the steady state

21S Dynein ATPase [EC 3.6.1.3] from axonemes of a Japanese sea urchin, Pseudocentrotus depressus, and its subunit fractions were studied to determine their kinetic properties in the steady state, using [gamma-32P]ATP at various concentrations, 5 mM divalent cations, and 20 mM imidazole at pH 7.0 and 0 degrees C. The following results were obtained. 1. 21S Dynein had a latent ATPase activity of about 0.63 mumol Pi/(mg . min) in 1 mM ATP, 100 mM KCl, 4 mM MgSO4, 0.5 mM EDTA, and 30 mM Tris-HCl at pH 8.0 and 25 degrees C. Its exposure to 0.1% Triton X-100 for 5 min at 25 degrees C induced an increase in the ATPase activity to about 3.75 mumol Pi/(mg . min) and treatment at 40 degrees C for 5 min also induced a similar activation. 2. The double-reciprocal plot for the ATPase activity of dynein activated by the treatment at 40 degrees C consisted of two straight lines, while that of nonactivated 21S dynein fitted a single straight line. 3. In low ionic strength solution, the Mg- and Mn-ATPase of 21S dynein showed substrate inhibition at ATP concentrations above 0.1 mM; the inhibition decreased with increasing ionic strength. Ca- and Sr-ATPase showed no substrate inhibition. 4. Both the Vmax and Km values of dynein ATPase decreased reversibly upon addition of about 40% (v/v) glycerol. In the presence of glycerol, the dynein ATPase showed an initial burst of Pi liberation. The apparent Pi-burst size was 1.0 mol/(10(6) g protein) and the true size was calculated to be 1.6 mol/1,250 K after correcting for the effect of Pi liberation in the steady state and the purity of our preparation. 5. One of the subunit fractions of 21S dynein which was obtained by the method of Tang et al. showed substrate inhibition and an initial burst of Pi liberation of 1.4 mol/(10(6) g protein) in the presence of 54% (v/v) glycerol.     

Dynamics of a biological fixed film for phenol degradation in a fluidized-bed bioreactor

Experimental and modeling studies were conducted to analyze the dynamic response behavior of a phenol-oxidizing fixed film using a differential, fluidized-bed bioreactor in a recycle loop with a well-mixed reservoir. With the bioreactor at steady state, a pulse of phenol was added to perturb the system, and the phenol concentration was monitored continuously until steady state was again achieved.The experimental dynamics were compared with a dynamic mathematical model based on diffusion and reaction within the biofilm, liquid mixing, and biofilm growth. Constant-pH experiments could be adequately described using an unstructured, double-Monod kinetic expression with substrate inhibition by phenol.However, in dynamic experiments without pH control, the pH of the liquid phase dropped, and damped oscillations were observed in the phenol concentration and reaction rate trajectories. Oscillatory solutions could not be induced in the model, even when product inhibition was included, and a linear stability analysis did not reveal tendencies toward instability. The cause of the experimental oscillations remains unknown.     

Kinetics of enzymes subject to very strong product inhibition: Analysis using simplified integrated rate equations and average velocities

Enzymes which catalyze energetically unfavorable reactions in the physiological direction are likely to be strongly inhibited by the reaction products. (Some energetically favorable reactions may also display strong "product inhibition" when assayed in the reverse direction.) In some cases, the inhibition caused by an accumulating product is so potent that true initial velocities cannot be directly determined using conventional assay methods. Continuous removal of the inhibitory product may be mitigated against by the nature of the assay or the unavailability of the appropriate coupling enzyme. It can be shown that if (a) only one inhibitory product is allowed to accumulate and (b) the substrate concentrations remain essentially constant over the assay period (i.e. Kproduct less than or equal to 10(-2)Ksubstrate, so that the decreasing reaction rate stems only from progressive product inhibition), then plots of reciprocal average (apparent) velocity (i.e. 1/v = t/[P]) versus [P] are linear and extrapolate to 1/v0, the reciprocal of the initial uninhibited velocity at the fixed substrate concentrations. Intercept replots give the usual initial velocity reciprocal plot patterns and permit Vmax and the substrate Km's to be determined. Slope replots are diagnostic of the type of inhibition exerted by the accumulating product and permit the inhibition constants to be determined. If all the appropriate coupling enzymes are available, some kinetic mechanisms can be diagnosed using data derived from the reaction progress curves in the presence of one accumulating product at a time.     

Biphasic kinetic behavior of rat cytochrome P-4501A1-dependent monooxygenation in recombinant yeast microsomes

Rat cytochrome P-4501A1-dependent monooxygenase activities were examined in detail using recombinant yeast microsomes containing rat cytochrome P-4501A1 and yeast NADPH-P-450 reductase. On 7-ethoxycoumarin, which is one of the most popular substrates of P-4501A1, the relationship between the initial velocity (v) and the substrate concentration ([S]) exhibited non-linear Michaelis-Menten kinetics. Hanes-Woolf plots ([S]/v vs. [S]) clearly showed a biphasic kinetic behavior. Aminopyrine N-demethylation also showed a biphasic kinetics. The regression analyses on the basis of the two-substrate binding model proposed by Korzekwa et al. (Biochemistry 37 (1998) 4137-4147) strongly suggest the presence of the two substrate-binding sites in P-4501A1 molecules for those substrates. An Arrhenius plot with high 7-ethoxycoumarin concentration showed a breakpoint at around 28 degrees C probably due to the change of the rate-limiting step of P-4501A1-dependent 7-ethoxycoumarin O-deethylation. However, the addition of 30% glycerol to the reaction mixture prevented observation of the breakpoint. The methanol used as a solvent of 7-ethoxycoumarin was found to be a non-competitive inhibitor. Based on the inhibition kinetics, the real V(max) value in the absence of methanol was calculated. These results strongly suggest that the recombinant yeast microsomal membrane containing a single P-450 isoform and yeast NADPH-P-450 reductase is quite useful for kinetic studies on P-450-dependent monooxygenation including an exact evaluation of inhibitory effects of organic solvents.     

Adenine nucleotide regulation in pancreatic beta-cells: modeling of ATP/ADP-Ca2+ interactions

Glucose metabolism stimulates insulin secretion in pancreatic beta-cells. A consequence of metabolism is an increase in the ratio of ATP to ADP ([ATP]/[ADP]) that contributes to depolarization of the plasma membrane via inhibition of ATP-sensitive K+ (K(ATP)) channels. The subsequent activation of calcium channels and increased intracellular calcium leads to insulin exocytosis. Here we evaluate new data and review the literature on nucleotide pool regulation to determine the utility and predictive value of a new mathematical model of ion and metabolic flux regulation in beta-cells. The model relates glucose consumption, nucleotide pool concentration, respiration, Ca2+ flux, and K(ATP) channel activity. The results support the hypothesis that beta-cells maintain a relatively high [ATP]/[ADP] value even in low glucose and that dramatically decreased free ADP with only modestly increased ATP follows from glucose metabolism. We suggest that the mechanism in beta-cells that leads to this result can simply involve keeping the total adenine nucleotide concentration unchanged during a glucose elevation if a high [ATP]/[ADP] ratio exits even at low glucose levels. Furthermore, modeling shows that independent glucose-induced oscillations of intracellular calcium can lead to slow oscillations in nucleotide concentrations, further predicting an influence of calcium flux on other metabolic oscillations. The results demonstrate the utility of comprehensive mathematical modeling in understanding the ramifications of potential defects in beta-cell function in diabetes.     

Role of substrate inhibition kinetics in enzymatic chemical oscillations.

Two chemical kinetic models are investigated using standard nonlinear dynamics techniques to determine the conditions under which substrate inhibition kinetics can lead to oscillations. The first model is a classical substrate inhibition scheme based on Michaelis-Menten kinetics and involves a single substrate. Only when this reaction takes place in a flow reactor (i.e., both substrate and product are taken to follow reversible flow terms) are oscillations observed; however, the range of parameter values over which such oscillations occur is so narrow it is experimentally unobservable. A second model based on a general mechanism applied to the kinetics of many pH-dependent enzymes is also studied. This second model includes both substrate inhibition kinetics as well as autocatalysis through the activation of the enzyme by hydrogen ion. We find that it is the autocatalysis that is always responsible for oscillatory behavior in this scheme. The substrate inhibition terms affect the steady-state behavior but do not lead to oscillations unless product inhibition or multiple substrates are present; this is a general conclusion we can draw from our studies of both the classical substrate inhibition scheme and the pH-dependent enzyme mechanism. Finally, an analysis of the nullclines for these two models allows us to prove that the nullcline slopes must have a negative value for oscillatory behavior to exist; this proof can explain our results. From our analysis, we conclude with a brief discussion of other enzymes that might be expected to produce oscillatory behavior based on a pH-dependent substrate inhibition mechanism.     

Effectiveness factors for substrate and product inhibition

The transformation technique of Na and Na (Math. Biosci., 6 , 25, 1970) is extended to convert boundary-value problems involving the steady-state diffusion equation for spherical immobilized enzyme particles exhibiting substrate and product inhibition to initial-value problems. This allows a study of the influence of external mass transfer resistances on the effectiveness factors. It also considerably reduces the number of calculations required to investigate the effect of changes in the kinetic parameters on the overall rate of reaction. The existence of multiple steady states for substrate inhibition kinetics in spherical catalyst particles is illustrated and a criterion for uniqueness of steady states is developed. Effectiveness factors for competitive and noncompetitive product inhibition increase with increasing value of the Sherwood number for the substrate and increasing value of the ratio of substrate to product effective diffusivities within the particle.     

Engineering substrate preference in subtilisin: structural and kinetic analysis of a specificity mutant

Bacillus subtilisin has been a popular model protein for engineering altered substrate specificity. Although some studies have succeeded in increasing the specificity of subtilisin, they also demonstrate that high specificity is difficult to achieve solely by engineering selective substrate binding. In this paper, we analyze the structure and transient state kinetic behavior of Sbt160, a subtilisin engineered to strongly prefer substrates with phenylalanine or tyrosine at the P4 position. As in previous studies, we measure improvements in substrate affinity and overall specificity. Structural analysis of an inactive version of Sbt160 in complex with its cognate substrate reveals improved interactions at the S4 subsite with a P4 tyrosine. Comparison of transient state kinetic behavior against an optimal sequence (DFKAM) and a similar, but suboptimal, sequence (DVRAF) reveals the kinetic and thermodynamic basis for increased specificity, as well as the limitations of this approach. While highly selective substrate binding is achieved in Sbt160, several factors cause sequence specificity to fall short of that observed with natural processing subtilisins. First, for substrate sequences which are nearly optimal, the acylation reaction becomes faster than substrate dissociation. As a result, the level of discrimination among these substrates diminishes due to the coupling between substrate binding and the first chemical step (acylation). Second, although Sbt160 has 24-fold higher substrate affinity for the optimal substrate DFKAM than for DVRAF, the increased substrate binding energy is not translated into improved transition state stabilization of the acylation reaction. Finally, as interactions at subsites become stronger, the rate-determining step in peptide hydrolysis changes from acylation to product release. Thus, the release of the product becomes sluggish and leads to a low k(cat) for the reaction. This also leads to strong product inhibition of substrate turnover as the reaction progresses. The structural and kinetic analysis reveals that differences in the binding modes at subsites for substrates, transition states, and products are subtle and difficult to manipulate via straightforward protein engineering. These findings suggest several new strategies for engineering highly sequence selective enzymes.     

Bistability in the isocitrate dehydrogenase reaction: an experimentally based theoretical study.

The enzyme isocitrate dehydrogenase (IDH, EC 1.1.1.42) can exhibit activation by one of its products, NADPH. This activation is competitively inhibited by the substrate NADP+, whereas NADPH competes with NADP+ for the catalytic site. Experimental observations briefly presented here have shown that if IDH is coupled to another enzyme, diaphorase (EC 1.8.1.4), which transforms NADPH into NADP+, the system can attain either one of two stable states, corresponding to a low and a high NADPH concentration. The evolution toward either one of these stable states depends on the time of addition of diaphorase to the medium containing IDH and its substrate NADP+. We present a theoretical and numerical analysis of a model for the IDH-diaphorase bienzymatic system, based on the regulatory properties of IDH. The results confirm the occurrence of bistability for parameter values derived from the experiments. Depending on the total concentration of NADP+ plus NADPH and the concentration of IDH, the system can either admit a single steady state or display bistability. We obtain an expression for the critical time t*, before which diaphorase addition leads to the lower steady state and after which addition of the enzyme leads to the upper steady state of NADPH. The analysis is extended to the case where the second substrate of IDH, isocitrate, is consumed in the course of the reaction without being regenerated. Bistability occurs only as a transient phenomenon in these conditions.     

Application of the metabolic control theory to the study of the dynamics of substrate cycles

Substrate cycles are ubiquitous structures of the cellular metabolism (e.g. Krebs cycle, fatty acids -oxydation cycles, etc... ). Moiety-conserved cycles (e.g. adenine nucleotides and NADH/NAD, etc...) are also important.The role played by such cycles in the metabolism and its regulation is not clearly understood so far. However, it was shown that these cycles can generate multistationarity (bistability), irreversible transitions, enhancement of sensitivity, temporal oscillations and chaotic motions (Hervagault & Canu, 1987; Hervagault & Cimino, 1989; Reich & Sel'kov, 1981; Ricard & Soulié, 1982). Fig. 1: Scheme of the open binary substrate cycle under study. The substrate S is converted into P with a net rate v₂. Substrate P is converted in turn into S with a net rate v₃. Step v₂ is inhibited by excess of the substrate, S. In addition, the cycle operates under open conditions, that is zero-order input of S at rates \ga₀(v₁) and first order outputs of S and P at rates \gaS and \gaP(v₄), respectively.The metabolic control theory (see also Fell, 1990), which shows how a metabolic network reacts to small perturbations in the vicinity of a steady state, and is formulated with the so-called control coefficients, was applied to such a cycle in order to get a better knowledge on the importance of each step at the regulatory point of view.The behaviour of a binary substrate cycle (fig. 1) in which one of the enzymes may be subjected to inhibition by excess of its substrate (v₂) was studied theoretically. The flux and concentration control coefficients were calculated for various steady states of the system. The evolution of the different control coefficients is compared to the evolution of the steady states. We mainly focused our study on situations for which the steady states are stable.