Quantitative determination of the steady-state kinetics of multienzyme reactions using the algebraic rate equations for the component single-enzyme reactions.

Methods are given whereby the steady-state kinetic characteristics of multienzyme reactions consisting of individual single-enzyme reactions linked by freely diffusible intermediates can be determined quantitatively from the experimentally determined complete algebraic rate equations for the individual reactions. The approach is based on the fact that a valid steady-state rate equation for such a multienzyme reaction, in terms of the rate equations for the individual reactions, can be obtained simply from knowledge of the relative rates of the individual reactions when the multienzyme reaction is in the steady state. A number of model multienzyme reactions, which differ as to structural arrangement of the individual reactions, are examined by this approach. Simple mathematical methods which are applicable to most of these models are given for direct calculation of dependent variables. It is either pointed out or demonstrated with Mathematica that the rate equations for all of these models can be handled very easily with the aid of a personal computer equipped with appropriate equation-solving software. Since the approach permits evaluation of all dependent variables for any specific combination of values for the kinetic parameters and independent variables, numerical values for the flux control coefficients of the individual enzymes can be obtained by direct calculation for a wide variety of conditions and can be compared with those obtained according to the methods of Metabolic Control Analysis. Several such comparisons have been made and in all cases identical results were obtained. The intuitive notion that the individual enzymes of a multienzyme reaction would be equally rate limiting if the total amount of enzyme were being used with maximum efficiency is tested and shown to be incorrect. In the course of this test the flux control coefficient for the individual enzymes were found to be appropriate indicators of relative rate limitation or control by the enzymes and to account properly for differences in specific activity among the enzymes.

An investigation of the relationships between rate and driving force in simple uncatalysed and enzyme-catalysed reactions with applications of the findings to chemiosmotic reactions.

Both the rate and the driving force of a reaction can be expressed in terms of the concentrations of the reactants and products. Consequently, rate and driving force can be expressed as a function of each other. This has been done for a single-reactant, single-product, uncatalysed reaction and its enzyme-catalysed equivalent using the van't Hoff reaction isotherm and Haldane's generalized Michaelis-Menten rate equation, the primary objective being explanation of the exponential and sigmoidal relationships between reaction rate and delta mu H+ commonly observed in studies on chemiosmotic reactions. Acquisition of a purely thermodynamic rate vs. driving-force relationship requires recognition of the intensive and extensive variables and maintenance of the extensive variables constant. This relationship is identical for the two reactions and is hyperbolic or sigmoidal, depending on whether the equilibrium constant is smaller or larger than unity. In the case of the catalysed reaction, acquisition of the purely thermodynamic relationship requires the assumption that the enzyme be equally effective in catalysing the forward and backward reactions. If this condition is not met, the relationship is modified by the enzyme in a manner which can be determined from the ratio of the Michaelis constants of the reactant and product. Under conditions of enzyme saturation in respect to reactant+product, the rate vs. driving-force relationship is determined exclusively by the thermodynamics of the reaction and a single kinetic parameter, the magnitude of which is determined by the relative effectiveness of the enzyme in catalysing the forward and backward reactions. In view of this finding, it is pointed out that, since the catalytic components of chemiosmotic reactions appear to be saturated with respect to the reactant-product pair that is varied in experimental rate vs. delta mu H+ determinations, and that, since many complex enzymic reactions conform to the simple Michaelis-Menten equation with respect to a single reactant-product pair when the concentrations of all other reactants and products are maintained constant, one might expect to be capable of simulating the experimental relationships simply from knowledge of the thermodynamics of the reaction and the relative effectiveness of the catalytic component in catalysing the forward and backward reactions using the simple Michaelis-Menten equation. That this expectation appears to be largely correct is demonstrated with model reactions.(ABSTRACT TRUNCATED AT 400 WORDS)

Determination of the P/2e- stoichiometries at the individual coupling sites in mitochondrial oxidative phosphorylation. Evidence for maximum values of 1.0, 0.5, and 1.0 at sites 1, 2, and 3.

P/2e- stoichiometries in six assay systems spanning different portions of the respiratory chain were estimated by direct determinations of Pi uptake in suspensions of bovine heart mitochondria containing a hexokinase trap. The electron donors were malate + pyruvate, succinate, and ascorbate + N,N,N',N'-tetramethyl-p-phenylenediamine, and the electron acceptors were ferricyanide (Site 1, Site 2, and Sites 1 + 2) and O2 (Sites 1 + 2 + 3, Sites 2 + 3, and Site 3). A major objective was to find conditions in which the six systems yield results in sufficiently good agreement to allow confidence as to their reliability. This objective was achieved, and maximum values of 1.1, 0.5, and 1.0 were observed in the Sites 1, 2, and 3 systems, respectively. This required that the energy-conserving reactions be relatively nonlimiting and that the P/2e- ratios be estimated from the slopes of plots of respiration rate versus phosphorylation rate obtained by inhibiting oxidative phosphorylation with respiratory chain inhibitors. The latter requirement allows avoidance of the effect of an apparent endogenous uncoupler and is based on the observation (Tsou, C. S., and Van Dam, K. (1969) Biochim. Biophys. Acta 172, 174-176) that uncoupling agents at low concentrations decrease the rate of phosphorylation nearly as much in absolute amount at low rates of respiration as at high rates. The maximum P/2e- stoichiometry at Site 1 is considered to be 1.0, and the value observed in the Site 1 system is suggested to be higher as a result of H+ ejection at the transhydrogenase level. Respiratory control due to carboxyatractyloside inhibition was examined and found to differ greatly among the systems. It is pointed out that this observation is not consistent with the lack of complete control being due primarily to ion cycling and that, in view of this, the relatively meager control at Site 3 is not consistent with O2 being reduced on the matrix side of the coupling membrane.

Steady-state kinetics of the overall oxidative phosphorylation reaction in heart mitochondria. Evidence for linkage of the energy-yielding and energy-consuming steps by freely diffusible intermediates and for an allosteric mechanism of respiratory control at coupling site 2.

The three coupling segments of the respiratory chain of bovine heart mitochondria were examined individually by steady-state kinetic methods to determine whether or not freely diffusible intermediates occur between the energy-yielding and energy-consuming steps involved in the oxidative phosphorylation of extramitochondrial ADP. The principal method employed was the dual inhibitor technique, for which an appropriate model is provided. The results indicate that in accordance with the chemiosmotic theory the intermediate reactants that link the energy-yielding rotenone-sensitive (Site 1), cytochrome bc1 (Site 2), and cytochrome aa3 (Site 3) reactions of the respiratory chain to the energy-consuming ATP synthetase, AdN transport, and Pi transport reactions are freely diffusible (delocalized). Site 2 was found to differ from the others in regard to the mechanism by which the energy-linked respiratory chain reaction is controlled by the energy-consuming steps. Whereas the Site 1 and Site 3 respiratory chain reactions are controlled primarily by the thermodynamic mechanism of reaction reversal, the Site 2 respiratory reaction is controlled primarily by a kinetic mechanism in which an intermediate that links it to the energy-consuming steps inhibits it allosterically. From the effects of nigericin and valinomycin the allosteric intermediate appears to be the electrical component of the protonmotive force.

Steady-state kinetics of the overall oxidative phosphorylation reaction in heart mitochondria. Determination of the coupling relationships between the respiratory reactions and miscellaneous observations concerning rate-limiting steps.

The linear sequence of steps involved in the oxidation of extramitochondrial succinate by O2 in bovine heart mitochondria was examined by a steady-state kinetic method to determine whether or not freely diffusible intermediates occur between the various inhibitor-sensitive steps. The kinetic method is based on the facts (1) that if two inhibitor-sensitive steps within a sequence are linked by a freely diffusible intermediate, inhibition of one will make the other less rate limiting in the overall reaction and thus will increase the amount of inhibitor of the other step required for half-maximal inhibition of the overall reaction, and (2) that if the two steps are not linked in this manner, inhibition of one will make the other more rate limiting and thus will decrease the amount of inhibitor of the other required for half-maximal inhibition. These two types of "coupling relationships" between steps were designated as "sequential" and "fixed," respectively. The results indicate the existence of freely diffusible intermediates (sequential coupling relationships) between the succinate transport and succinate dehydrogenase reactions, between the succinate dehydrogenase and cytochrome bc1 reactions, and between the cytochromes bc1 and aa3 reactions. Uncoupling respiration from phosphorylation results in the coupling relationship between the bc1 and aa3 reactions becoming partially fixed. This change is accompanied by marked decreases in the degrees to which the bc1 and aa3 reactions limit the overall reaction and appears to account for the large uncoupler-induced releases of inhibition at the levels of the bc1 and aa3 reactions observed previously by others. It is suggested that cytochrome c is the freely diffusible intermediate between the bc1 and aa3 reactions and that the uncoupler-induced changes occur as a result of formation of functional and highly efficient supercomplexes between cytochrome c and the cytochromes bc1 and aa3 complexes.

Swelling and contraction of heart mitochondria suspended in ammonium phosphate.

Bovine heart mitochondria which have been allowed to swell in isotonic NH4+ phosphate contract in response to initiation of oxidative phosphorylation. The contraction occurs optimally at pH 6.0 and appears from inhibition studies to result from Pi uptake being slower than removal of internal Pi via phosphorylation of external ADP. Similar results are obtained when K+ + nigericin is substituted for NH4+. Mersalyl inhibition of Pi transport in respiring, nonphosphorylating mitochondria which have been allowed to swell in NH4+ phosphate reveals a contractile process having an alkaline pH optimum. This contraction resembles closely the contraction observed in salts of strong acids and presumably occurs by electrophoretic ejection of Pi anions driven by electrogenic H+ ejection.

Magnesium-induced inner membrane aggregation in heart mitochondria.

Mg(2+) at an optimal concentration of 2mM (ph 6.5) induces large increases (up to 30 percent) in the optical density of bovine heart mitochondria incubated under conditions of low ionic strength (< approx. 0.01). The increases are associated with aggregation (sticking together) of the inner membranes and are little affected by changes in the energy status of the mitochondria. Virtually all of a number of other polyvalent cations tested and Ag(+) induce increases in mitochondrial optical density similar to those induced by Mg(2+), their approximate order of concentration effectiveness in respect to Mg(2+) being: La(3+) > Pb(2+) = Cu(2+) > Cd(2+) > Zn(2+) > Ag(+) > Mn(2+) > Ca(2+) > Mg(2+). With the exception of Mg(2+), all of these cations appear to induce swelling of the mitochondria concomitant with inner membrane aggregation. The inhibitors of the adenine nucleotide transport reaction carboxyatratyloside and bongkrekic acid are capable of preventing and reversing Mg(2+)-induced aggregation at the same low concentration required for complete inhibition of phosphorylating respiration, suggesting that they inhibit the aggregation by binding to the adenine nucleotide carrier. The findings are interpreted to indicate (a) that the inner mitochondrial membrane is normally prevented from aggregating by virtue of its net negative outer surface change, (b) that the cations induce the membrane to aggregate by binding at its outer surface, decreasing the net negative charge, and (c) that carboxyatractyloside and bongkrekic acid inhibit the aggregation by binding to the outer surface of the membrane, increasing the net negative charge.

Adenine nucleotide-induced contraction of the inner mitochondrial membrane. I. General characterization.

The inner membranes of isolated bovine heart mitochondria undergo pronounced contraction upon being exposed to exogenous adenosine diphosphate (ADP), adenosine triphosphate (ATP), and certain other high-energy phosphate compounds. Contraction results in decrease of inner membrane expanse which in turn results in decrease of intracristal space and increase of mitochondrial optical density (OD). The magnitude of the OD change appears to be proportional to the degree of contraction Half-maximal contraction can be achieved with ADP or ATP at concentrations as low as about 0 3 microM. Atractyloside at concentrations as low as about 1.2 nmol/mg mitochondrial protein completely inhibits the contraction. It is concluded from these and other observations that inner membrane contraction occurs as a result of adenine nucleotide binding to the carrier involved in the exchange of adenine nucleotides across the inner mitochondrial membrane.

Adenine nucleotide-induced contraction on the inner mitochondrial membrane. II. Effect of bongkrekic acid.

In bovine heart mitochondria bongkrekic acid at concentrations as low as about 4 nmol/mg protein (a) completely inhibits phosphorylation of exogenous adenosine diphosphate (ADP) and dephosphorylation of exogenous adenosine triphosphate (ATP), (b) completely reverses atractyloside inhibition of inner membrane contraction induced by exogenous adenine nucleotides, and (c) decreases the amount of adenine nucleotide required to elicit maximal exogenous adenine nucleotide-induced inner membrane contraction to a level which appears to correspond closely with the concentration of contractile, exogenous adenine nucleotide binding sites Bongkrekic acid at concentrations greater than 4 nmol/mg protein induces inner membrane contraction which seems to depend on the presence of endogenous ADP and/or ATP. The findings appear to be consistent with the interpretations (a) that the inner mitochondrial membrane contains two types of contractile, adenine nucleotide binding sites, (b) that the two sites differ markedly with regard to adenine nucleotide affinity, (c) that the high affinity site is identical with the adenine nucleotide exchange carrier, (d) that the low affinity site is accessible exclusively to endogenous adenine nucleotides and is largely unoccupied in the absence of bongkrekic acid, and (e) that bongkrekic acid increases the affinity of both sites in proportion to the amount of the antibiotic bound to the inner membrane.

Osmotically-induced alterations in volume and ultrastructure of mitochondria isolated from rat liver and bovine heart.

Detailed studies correlating changes in mitochondrial optical density, packed volume, and ultrastructure associated with osmotically-induced swelling were performed. Various swelling states were established by incubating mitochondria (isolated in 0.25 M sucrose) at 0 degrees C for 5 min in series of KCl and sucrose solutions ranging in tonicity from 250 to 3 milliosmols. Reversibility of swelling was determined by examining mitochondria exposed to 250 milliosmols media after they had been induced to swell. Swelling induced by lowering the ambient tonicity to approximately 130 (liver mitochondria) and 90 (heart mitochondria) milliosmols involves primarily swelling of the inner compartment within the intact outer membrane. Decreasing the ambient tonicity beyond this level results in rupture of the outer membrane and expansion of the inner compartment through the break. The maximum extent of swelling, corresponding with complete unfolding of the cristae and an increase in over-all mitochondrial volume of approximately 6-fold (liver mitochondria) and 11-fold (heart mitochondria), is reached at approximately 15 (liver mitochondria) and 3 (heart mitochondria) milliosmols. Exposure of liver mitochondria to media of lower tonicity results in irreversibility of inner compartment swelling and escape of matrix material. These changes appear to result from increased inner membrane permeability, possibly due to stretching.

Swelling and contraction of corn mitochondria.

A survey has been made of the properties of corn mitochondria in swelling and contraction. The mitochondria swell spontaneously in KCl but not in sucrose. Aged mitochondria will swell rapidly in sucrose if treated with citrate or EDTA. Swelling does not impair oxidative phosphorylation if bovine serum albumin is present.Contraction can be maintained or initiated with ATP + Mg or an oxidizable substrate, contraction being more rapid with the substrate. Magnesium is not required for substrate powered contraction. Contraction powered by ATP is accompanied by the release of phosphate. Oligomycin inhibits both ATP-powered contraction and the release of phosphate. However, it does not affect substrate-powered contraction. Substrate powered contraction is inhibited by electron-transport inhibitors. The uncoupler, carbonyl cyanide m-chlorophenyl hydrazone, accelerates swelling and inhibits both ATP-and substrate-powered contraction. However, the concentrations required are well in excess of those required to produce uncoupling and to accelerate adenosine triphosphatase; the concentrations required inhibit respiration in a phosphorylating medium.Phosphate is a very effective inhibitor of succinate-powered contraction. Neither oligomycin nor Mg affects the phosphate inhibition. Phosphate is less inhibitory with the ATP-powered contraction.The results are discussed in terms of a hypothesis that contraction is associated with a nonphosphorylated high energy intermediate of oxidative phosphorylation.