Anion and ionic strength effects upon the oxidation of cytochrome c by cytochrome c oxidase

Citrate and other polyanion binding to ferricytochrome c partially blocks reduction by ascorbate, but at constant ionic strength the citrate-cytochrome c complex remains reducible; reduction by TMPD is unaffected. At a constant high ionic strength citrate inhibits the cytochrome c oxidase reaction competitively with respect to cytochrome c, indicating that ferrocytochrome c also binds citrate, and that the citrateferrocytochrome c complex is rejected by the binding site at high ionic strength. At lower ionic strengths, citrate and other polyanions change the kinetic pattern of ferrocytochrome c oxidation from first-order towards zero-order, indicating preferential binding of the ferric species, followed by its exclusion from the binding site. The turnover at low cytochrome c concentrations is diminished by citrate but not the K_m (apparent non-competitive inhibition) or the rate of cytochrome a reduction by bound cytochrome c. Small effects of anions are seen in direct measurements of binding to the primary site on the enzyme, and larger effects upon secondary site binding. It is concluded that anion-cytochrome c complexes may be catalytically competent but that the redox potentials and/or intramolecular behaviour of such complexes may be affected when enzyme-bound. Increasing ionic strength diminishes cytochrome c binding not only by decreasing the ‘association’ rate but also by increasing the ‘dissociation’ rate for bound cytochrome c converting the ‘primary’ (T) site at high salt concentrations into a site similar kinetically to the ‘secondary’ (L) site at low ionic strength. A finite K_m of 170 μM at very high ionic strength indicates a ratio of $\text{K}{}^{\mathrm{\infty }}{}_{\mathrm{<mtext>M</mtext>}}\text{K}{}^0{}_{\mathrm{<mtext>M</mtext>}}$ of about 5000. It is proposed that anions either modify the E¹₀ of cytochrome c bound at the primary (T) site or that they perturb an equilibrium between two forms of bound c in favour of a less active form.     

Thermodynamics and kinetics of co-operative protein-nucleic acid binding: II. Studies on the binding between protamine and calf thymus DNA

Unspecific binding of a protamine, namely fluorescein-labelled clupeine Z, to double-stranded calf thymus DNA was studied using fluorescence titration methods and chemical relaxation techniques. Both equilibrium and kinetic data have been analysed using general theoretical approaches discussed in the accompanying paper. The results agree well with the predictions made on the basis of a standard co-operative binding model.Basic parameters evaluated are the co-operative binding constant (K), the coefficient measuring co-operative interaction between nearest neighbours (q), the number of nucleotides occupied by one protamine molecule (n) and the rate constant of dissociation at the ends of bound ligand sequences (K_D). Values obtained at 20 °C, pH 7.5 and 0.4 m-NaCl were K = 5.8 × 10⁷m^?1, q = 1700, n = 20 and K_D = 0.29 s^?1. They have been found to be sensitive to the concentration of added salt (NaCl). This effect apparently reflects the essentially electrostatic nature of the binding process. The results can be satisfactorily described in terms of competitive binding of sodium ions.     

The effect of sodium on inorganic phosphate- and p-nitrophenyl phosphate-facilitated ouabain binding to (Na+ + K+)-activated ATPase

The effect of the hydrolysis product P_i and the artificial substrate p-nitrophenyl phosphate (p-nitrophenyl-P) on ouabain binding to (Na⁺ + K⁺)-activated ATPase was investigated.The hypothesis that (Mg²⁺ + p-nitrophenyl-P)-supported ouabain binding might be due to P_i release and thus (Mg²⁺ + P_i)-supported could not be confirmed.The enzyme · ouabain complexes obtained with different substrates were characterized according to their dissociation rates after removal of the ligands facilitating binding. The character of the enzyme · ouabain complex is determined primarily by the monovalent ion present during ouabain binding, but, qualitatively at least, it is immaterial whether binding was obtained with p-nitrophenyl phosphate or P_i.The presence or absence of Na⁺ during binding has a special influence upon the character of the enzyme · ouabain complex. Without Na⁺ and in the presence of Tris ions the complex obtained with (Mg²⁺ + P_i) and that obtained with (Mg²⁺ + p-nitrophenyl-P) behaved in a nearly identical manner, both exhibiting a slow decay. High Na⁺ concentration diminished the level of P_i-supported ouabain binding, having almost no effect on p-nitrophenyl phosphate-supported binding. Both enzyme · ouabain complexes, however, now resembled the form obtained with (Na⁺ + ATP), as judged from their dissociation rates and the K⁺ sensitivity of their decay. The complexes obtained at a high Na⁺ concentration underwent a very fast decay which could be slowed considerably after adding a low concentration of K⁺ to the resuspension medium. The most stable enzyme · ouabain complex was obtained in the presence of Tris ions only, irrespective of whether p-nitrophenyl phosphate or P_i facilitated complex formation. The presence of K⁺ gave rise to a complex whose dissociation rate was intermediate between those of the complexes obtained in the presence of Tris and a high Na⁺ concentration.It is proposed that the different ouabain dissociation rates reflect different reactive state of the enzyme. The resemblance between the observations obtained in phosphorylation and ouabain binding experiments is pointed out.     

Studies on the stimulation of cytochrome P-450-dependent monooxygenase activity by dilauroylphosphatidylcholine

Steady-state kinetic and deuterium isotope effect studies have been conducted to determine the influence of the phospholipid dilauroylphosphatidylcholine on the catalytic activity of a reconstituted monooxygenase system composed of cytochrome P-450 and NADPH-cytochrome c (P-450) reductase. Addition of this lipid up to a concentration equivalent to its CMC resulted in an increase in V for benzphetamine N-demethylation. Above the CMC, no further change in V was observed. In contrast, the K_m was not affected throughout the entire lipid concentration range. Furthermore, the deuterium isotope effect for 7-ethoxycoumarin O-deethylation was not affected by the lipid concentration indicating that the contribution of the carbon-hydrogen bond cleavage step to V was also not affected. These data are consistent with the mass-action model proposed earlier (G. T. Miwa, S. B. West, M. T. Huang, and A. Y. H. Lu, (1979), J. Biol. Chem.254, 5695–5700) for cytochrome P-450 and NADPH-cytochrome c (P-450) reductase association during catalysis. The lipid concentration, below its CMC, appears to decrease the apparent dissociation constant for the cytochrome P-450-reductase complex thus causing an increase in the steady-state concentration of this catalytically active complex.     

Intracellular Potassium : A Determinant of the Sodium-Potassium Pump Rate

Normal human red cells which have had their intracellular sodium (Na_c) reduced have a diminished Na-K pump rate, but only if intracellular potassium (K_c) is high. If most of the K_c is replaced by tetramethylammonium or choline, both ouabain-sensitive Na efflux and K influx are significantly increased even with Na_c below normal. Cells with reduced Na_c and high K_c have an unchanged Na efflux if external potassium (K_ext) is removed. In contrast, low-Na, low-K cells have a large ouabain-sensitive Na efflux which shows a normal response to removal of K_ext. Neither low-K nor high-K cells have an altered ouabain-sensitive K efflux. Measurement at constant low Na_c and varying K_c shows the pump Na efflux to be an inverse function of K_c. Thus, in low-Na cells, K_c appears to act as an inhibitor of the pump. Inhibition by high K_c can be seen even when Na_c is normal. The effects attributed to K_c are distinguished experimentally from other variables such as cell volume, adenosine triphosphate concentration, effects of the replacement cations, and the method used to alter intracellular cation concentrations. A role is proposed for K_c, in cooperation with Na_c, in regulating the pump rate of normal human red cells.     

The interaction of myosine S1 with phosphorothioates of ADP: An 18O exchange study by 31P NMR

The ¹⁸O exchange reaction which labeled P_i undergoes in the presence of complexes of myosin subfragment 1, MgCl₂, and the different phosphorothioates of ADP has been observed by ³¹P NMR. From these experiments it can be concluded that ADP and ADP (α-S) (A) on the one hand and ADP (β-S) and ADP (α-S) (B) on the other hand form similar complexes as far as the number of reversals of the nucleoside triphosphate formation step from the nucleoside diphosphate and P_i, is concerned. In addition, the same seems to hold for the rate constant k_?2, which describes the binding step of free P_i, to the subfragment 1 nucleoside diphosphate complex. These observations support former kinetic experiments which yielded the same similarities for the rate parameters describing association and dissociation of the subfragment 1 nucleotide complexes.     

Reactions of mercaptans with cytochrome c oxidase and cytochrome c

1. The steady-state oxidation of ferrocytochrome c by dioxygen catalyzed by cytochrome c oxidase, is inhibited non-competitively towards cytochrome c by methanethiol, ethanethiol, 1-propanethiol and 1-butanethiol with K_i values of 4.5, 91, 200 and 330 μM, respectively.2. The inhibition constant K_i of ethanethiol is found to be constant between pH 5 and 8, which suggests that only the neutral form of the thiol inhibits the enzyme.3. The absorption spectrum of oxidized cytochrome c oxidase in the Soret region shows rapid absorbance changes upon addition of ethanethiol to the enzyme. This process is followed by a very slow reduction of the enzyme. The fast reaction, which represents a binding reaction of ethanethiol to cytochrome c oxidase, has a k₁ of 33 M^?1 · s^?1 and dissociation constant K_d of 3.9 mM.4. Ethanethiol induces fast spectral changes in the absorption spectrum of cytochrome c, which are followed by a very slow reduction of the heme. The rate constant for the fast ethanethiol reaction representing a bimolecular binding step is 50 M^?1 · s^?1 and the dissociation constant is about 2 mM. Addition of up to 25 mM ethanethiol to ferrocytochrome c does not cause spectral changes.5. EPR (electron paramagnetic resonance) spectra of cytochrome c oxidase, incubated with methanethiol or ethanethiol in the presence of cytochrome c and ascorbate, show the formation of low-spin cytochrome a₃-mercaptide compounds with g values of 2.39, 2.23, 1.93 and of 2.43, 2.24, 1.91, respectively.     

Ubiquinol-cytochrome c reductase (EC 1.10.2.2). Isolation in Triton X-100 by hydroxyapatite and gel chromatography. Structural and functional properties

1. A method for the isolation of a monodisperse ubiquinol-cytochrome c reductase (complex III) from beef heart mitochondria has been developed. The procedure consists of an enzyme solubilization in Triton X-100 followed by hydroxyapatite and gel chromatography.2. The minimum unit of the isolated complex is composed of 9 polypeptide subunits with M_r of 49000, 47000, 30000, 25000, 12000, 11000 and 6000. It contains 8 μmol of cytochrome b, 4 μmol of cytochrome c₁ 7–8 μmol of nonheme iron, corresponding to 3.5–4 μmol of the Rieske iron-sulfur protein, less than 1.0 μmol of ubiquinone and about 60 μmol of phospholipids, per g of protein. The specific detergent binding amounts to 0.2 g of Triton X-100 per g protein.3. Cytochrome b exhibits an α-absorbance maximum at 562 nm. In redox titrations it reveals two half-reduction potentials, i.e. ?10 and +100 mV, at pH 7.0. The absorbance maximum of cytochrome c₁ lies at 553 nm and its half-reduction potential amounts to +250 mV.4. The reductase reveals electron-transferring activity with ubiquinol-1, -2, -3, and -9 as donor and cytochrome c as acceptor. The activity with ubiquinol-9 was analyzed according to the surface dilution scheme developed for the action of phospholipases. The molecular activity amounts to 75 mol of cytochrome c reduced per s at 20°C.5. A dissociation constant K′_s of 5.5 mM has been determined for the Triton-solubilized enzyme: ubiquinol-containing micelle association. In this case the total concentration of ubiquinol plus Triton X-100 has been substituted for the concentration of binding areas on the ubiquinol-containing micelles. This substitution makes the reasonable assumption that the sum of ubiquinol concentration plus Triton X-100 is proportional to the number of available binding areas.6. A K′_m value of 0.025 was found for ubiquinol-9. This is an analog to the Michaelis constant and is expressed as mol fraction of ubiquinol in the ubiquinol-Triton micelle.     

Analysis of multitemperature isothermal titration calorimetry data at very low c: Global beats van't Hoff

Isothermal titration calorimetry data for very low c (≡K[M]₀) must normally be analyzed with the stoichiometry parameter n fixed — at its known value or at any reasonable value if the system is not well characterized. In the latter case, ΔH° (and hence n) can be estimated from the T-dependence of the binding constant K, using the van't Hoff (vH) relation. An alternative is global or simultaneous fitting of data at multiple temperatures. In this Note, global analysis of low-c data at two temperatures is shown to estimate ΔH° and n with double the precision of the vH method.     

A kinetic characterization of the rabbit plasmin isozymes.

Steady-state and presteady-state kinetic parameters for plasmins derived from the two rabbit plasminogen isozymes have been determined. Steady-state kinetic experiments with N-α-tosyl-l-arginine methyl ester indicate that each isozyme has a similar V. Plasmin isozyme 2 has a higher K_m value for this substrate as well as a higher K_i, for the competitive inhibitor, benzamidine-HCl. Presteady-state kinetic experiments, using the p-nitrophenyl esters of p-(methylethylsulfoniummethyl)benzoate, p-(pyridiniummethyl) benzoate, p-(thiouroniummethyl)benzoate and p-(guanidinium)benzoate, indicate that each plasmin has similar rate constants of acylation (k₂). However, values of the dissociation constant (K_S) indicate that plasmin isozyme 1 has a greater binding affinity for these substrates than does isozyme 2. The magnitude of this difference varies with the substrate and is the greatest for those containing analogs of the guanidino moiety of l-arginine.     

Cyanide-linked dimer-monomer equilibrium of Chromatium vinosum ferric cytochrome c′

Cyanide binding to Chromatium vinosum ferricytochrome c′ has been studied to further investigate possible allosteric interactions between the subunits of this dimeric protein. Cyanide binding to C. vinosum cytochrome c′ appears to be cooperative. However, the cyanide binding reaction is unusual in that the overall affinity of cyanide increases as the concentration of cytochrome c′ decreases and that cyanide binding causes the ligated dimer to dissociate to monomers as shown by gel-filtration chromatography. Therefore, the cyanide binding properties of C. vinosum ferricytochrome c′ are complicated by a cyanide-linked dimer to monomer dissociation equilibrium of the complexed protein. The dimer to monomer dissociation constant is 20-fold smaller than that for CO linked dissociation constant of ferrocytochrome c′. Furthermore, the pH dependence of both the intrinsic equilibrium binding constant and the dimer to monomer equilibrium dissociation constant was investigated over the pH range of 7.0 to 9.2 to examine the effect of any ionizable groups. The equilibrium constants did not exhibit a significant pH dependence over this pH range.     

Rat brain hexokinase: glucose and glucose-6-phosphate binding sites and C-terminal amino acid of the purified enzyme

The binding of glucose and glucose-6-P by pure rat brain hexokinase has been studied by using an ultrafiltration procedure [H. Paulus (1969) Anal. Biochem. 32, 91–100]. Each mole of enzyme (molecular weight 98,000) binds 1 mole of glucose or 1 mole of glucose-6-P. The dissociation constant for the enzyme-glucose complex (0.04 mm) is in excellent agreement with the kinetically determined K_m for this substrate. The dissociation constant for the enzyme-glucose-6-P complex was estimated to be 1.3 μm, substantially lower than values of 7–8 μm obtained by alternative methods. This discrepancy appears to be due to retardation of the passage of the charged glucose-6-P through the ultrafiltration membrane, resulting in an effective increase in the ligand concentration at the membrane surface and thereby a decrease in the apparent dissociation constant. No appreciable retardation of the passage of the uncharged glucose molecule was observed.The binding of glucose-6-P (but not glucose) is prevented in the presence of P_i. This is in accord with a previously suggested model in which binding of P_i is considered to stabilize the enzyme in a conformation having little, if any, affinity for glucose-6-P.Serine was found as a C-terminal amino acid. The method used would not have detected C-terminal proline or tryptophan residues, and thus these cannot be excluded by the present experiments. However, in view of other results indicating that rat brain hexokinase consists of a single polypeptide chain, it seems probable that serine is indeed the only C-terminal amino acid in the molecule.     

Kinetic indication for multiple sites of ubiquinol-1 interaction in ubiquinol-cytochrome c reductase in bovine heart mitochondria

We have assayed the ubiquinol-cytochrome c reductase activity either in situ or in different mitochondrial fractions, including the isolated bc₁ complex, employing ubiquinol-1 and exogenous cytochrome c as substrates. A clear biphasic behavior of both the time courses and the initial rates of cytochrome c reduction have been observed. Two K_m values have been found, one of 1–7 × 10^?6m ubiquinol-1, and another varying from 0.6 to 4.6 × 10^?5m ubiquinol-1, depending on the cytochrome c concentration and the type of mitochondrial fraction used. Either the kinetic phase with the lower K_m or the kinetic phase with the higher K_m exhibits an almost identical antimycin sensitivity. We have also monitored the rapid reduction of endogenous b cytochromes in the presence of antimycin, and the initial rates are again biphasic as a function of ubiquinol-1 concentration. These findings indicate that the steps conferring the biphasic kinetics to the ubiquinol-cytochrome c reductase activity involve the redox equilibria between exogenous ubiquinol-1 and the b cytochromes, and suggest that two redox pathways may be present in the electron transfer from ubiquinol to cytochrome c through the bc₁ segment of the mammalian respiratory chain.     

Inhibition of the acidogenic dissimilation of glucose in anaerobic continuous cultures by free butyric acid

Summary In anaerobic wastewater treatment the separation of fermentative and methanogenic bacteria is aimed at an increased performance of the total digestion process. It is known that the attainable growth rate of the acidogenic population in continuous culture decreases at increasing influent concentrations of glucose. To account for this phenomenon, a new kinetic model was developed that combines substrate and product inhibition. In the present research product inhibition was investigated quantitatively in a continuous culture fermenting 50 mmol/l glucose. Extra acetate and butyrate were added up to 200 mmol/l at different pH values, and it turned out that only free butyric acid inhibited growth. The lower attainable growth rates of cultures producing comparable amounts of butyrate when fed with concentrated influents, strongly indicated substrate inhibition. Evidence is presented that transitions to low-conversion steady states predicted by the kinetic model, play a role and decrease the stability of the culture.Nomenclature D dilution rate, h^-1 - D_att highest D using certain experimental procedure h^-1 - K_i substrate inhibition constant, mol·m^-3 - K_p product inhibition constant mol·m^-3 - K_s substrate saturation constant, mol·m^-3 - P concentration inhibitory product mol·m^-3 - S substrate concentration, mol·m^-3 - S_o influent substrate concentration, mol·m^-3 - S _max ^c substrate concentration at _max ^c , mol·m^-3 - S _max ^h substrate concentration at _max ^h , mol·m^-3 - specific growth rate, h^-1 - experimental realization of at D_att, h^-1 - _max maximum specific growth rate, h^-1 - _max ^c maximum attainable specific growth rate according to combined substrate/product inhibition model, h^-1 - _h ⁰ specific growth rate at S₀ according to Haldane kinetics, h^-1 - _max ^c maximum attainable specific growth rate according to Haldane kinetics, h^-1 - Y_p yield inhibitory product, mol·mol^-1 - Y_x yield biomass, kg dry weight·kg^-1 - bio biomass - EtOH ethanol - gluc glucose - HAc acetate - HBt butyrate - HCap caproate - HFo formate - HPr propionate - HVal valerate - prod produced - lact lactate     

Electron transfer between horse heart and Candida krusei cytochromes c in the free and bound states

Electron transfer between horse heart and Candida krusei cytochromes c in the free and phosvitin-bound states was examined by difference spectrum and stopped-flow methods. The difference spectra in the wavelength range of 540–560 nm demonstrated that electrons are exchangeable between the cytochromes c of the two species. The equilibrium constants of the electron transfer reaction for the free and phosvitin-bound forms, estimated from these difference spectra, were close to unity at 20°C in 20 mM Tris-HCl buffer (pH 7.4). The electron transfer rate for free cytochrome c was (2–3) · 10⁴ M^?1 · s^?1 under the same conditions. The transfer rate for the bound form increased with increase in the binding ratio at ratios below half the maximum, and was almost constant at higher ratios up to the maximum. The maximum electron exchange rate was about 2 · 10⁶ M^?1 · s^?1, which is 60–70 times that for the free form at a given concentration of cytochrome c. The activation energy of the reaction for the bound cytochrome c was equal to that for the free form, being about 10 kcal/mol. The dependence of the exchange rate on temperature, cytochrome c concentration and solvent viscosity suggests that enhancement of the electron transfer rate between cytochromes c on binding to phosvitin is due to increase in the collision frequency between cytochromes c concentrated on the phosvitin molecule.     

Nitric Oxide Binds to the Proximal Heme Coordination Site of the Ferrocytochrome c/Cardiolipin Complex: FORMATION MECHANISM AND DYNAMICS*

Mammalian mitochondrial cytochrome c interacts with cardiolipin to form a complex (cyt. c/CL) important in apoptosis. Here we show that this interaction leads to structural changes in ferrocytochrome c that leads to an open coordinate site on the central iron, resulting from the dissociation of the intrinsic methionine residue, where NO can rapidly bind (k = 1.2 × 10⁷ m⁻¹ s⁻¹). Accompanying NO binding, the proximal histidine dissociates leaving the heme pentacoordinate, in contrast to the hexacoordinate nitrosyl adducts of native ferrocytochrome c or of the protein in which the coordinating methionine is removed by chemical modification or mutation. We present the results of stopped-flow and photolysis experiments that show that following initial NO binding to the heme, there ensues an unusually complex set of kinetic steps. The spectral changes associated with these kinetic transitions, together with their dependence on NO concentration, have been determined and lead us to conclude that NO binding to cyt. c/CL takes place via an overall scheme comparable to that described for cytochrome c′ and guanylate cyclase, the final product being one in which NO resides on the proximal side of the heme. In addition, novel features not observed before in other heme proteins forming pentacoordinate nitrosyl species, include a high yield of NO escape after dissociation, rapid (<1 ms) dissociation of proximal histidine upon NO binding and its very fast binding (60 ps) after NO dissociation, and the formation of a hexacoordinate intermediate. These features all point at a remarkable mobility of the proximal heme environment induced by cardiolipin.     

On the acquisition and analysis of microscale thermophoresis data

A comprehensive understanding of the molecular mechanisms underpinning cellular functions is dependent on a detailed characterization of the energetics of macromolecular binding, often quantified by the equilibrium dissociation constant, K_D. While many biophysical methods may be used to obtain K_D, the focus of this report is a relatively new method called microscale thermophoresis (MST). In an MST experiment, a capillary tube filled with a solution containing a dye-labeled solute is illuminated with an infrared laser, rapidly creating a temperature gradient. Molecules will migrate along this gradient, causing changes in the observed fluorescence. Because the net migration of the labeled molecules will depend on their liganded state, a binding curve as a function of ligand concentration can be constructed from MST data and analyzed to determine K_D. Herein, simulations demonstrate the limits of K_D that can be measured in current instrumentation. They also show that binding kinetics is a major concern in planning and executing MST experiments. Additionally, studies of two protein–protein interactions illustrate challenges encountered in acquiring and analyzing MST data. Combined, these approaches indicate a set of best practices for performing and analyzing MST experiments. Software for rigorous data analysis is also introduced.     

Urea-induced modification of cytochrome c flexibility as probed by cyanide binding

Cyanide binding to cytochrome c was monitored by absorption spectroscopy from neutral to acidic pH in the presence of urea. These results were compared with acid-induced unfolding at corresponding urea concentration monitored by absorption spectroscopy and circular dichroism. The association rate constant k_a increased 20-fold when the concentration of urea was raised from 0 M to 6 M at neutral pH. However, the secondary structure of the protein was not affected, i.e. there was no striking conformational change in these urea concentrations at neutral pH. At the pH that was very close to the pK of acid-induced unfolding, the k_a value reached its maximum (k_a,max) in all urea concentrations. Interestingly, the k_a,max value increased exponentially with increasing urea concentrations. These results are interpreted in terms of a change in the flexibility of the least stable part of the cyt c structure that is responsible for the Fe–S(Met80) bond disruption and for ligand binding to heme iron.     

Interaction of the regulatory gene product with the operator site in the l-arabinose operon of Escherichia coli

The DNA binding properties of the araC protein in the absence of l-arabinose have been studied in Escherichia coli using the nitrocellulose membrane filter technique. Equilibrium competition experiments demonstrate that the araC protein binds specifically to the ara operator. The apparent K_m of the interaction is 1 × 10^?12m at 20 °C. The rates of association and dissociation of the complex have also been determined. A k_a of 2 × 10⁹m^?1 s^?1at 20 °C is calculated assuming binding to a single site. The half-life of the complex is three minutes. The equilibrium constant calculated from the ratio of k_a to k_d is 2.8 × 10^?12m at 20 °C. The good agreement between the equilibrium and kinetic determinations of the equilibrium constant suggest that the kinetic studies are providing true rate constants. It is calculated that about 1% of the purified araC protein is active with respect to operator binding activity.