Stereochemical control of yeast reductions. 2. Quantitative treatment of the kinetics of competing enzyme systems for a single substrate

Quantitative expressions have been developed for systems such as yeast reductions where competing enzymes act on one substrate to yield two enantiomeric products. These expressions relate the observed stereochemical variables, the extent of conversion (C), the optical purity expressed as enantiomeric excess (ee), and the initial substrate concentration (A₀) to the kinetic parameters K_R and K_S (apparent Michaelis constants) and y ($\text{V}{}_{\mathrm{R}}\text{V}{}_{\mathrm{S}}$, the ratio of maximal velocities) of such competing enzymes. The expressions have been experimentally verified using a purified competing enzyme system of l- and d-lactic dehydrogenases. Furthermore, the enantioselective reduction of β-keto esters by intact yeast cells has been examined by means of this kinetic analysis.     

Lactose transport in Escherichia coli cells Dependence of kinetic parameters on the transmembrane electrical potential difference

We determine the kinetic parameters $\text{V}$ and $\text{K}{}_{\mathrm{<mtext>T</mtext>}}$ of lactose transport in Escherichia coli cells as a function of the electrical potential difference (Δψ) at pH 7.3 and $\text{Δ}\text{pH}\text{= 0}$. We report that transport occurs simultaneously via two components: a component which exhibits a high $\text{K}{}_{\mathrm{<mtext>T</mtext>}}$ (larger than 10 mM) and whose contribution is independent of Δψ, a component which exhibits a low $\text{K}{}_{\mathrm{<mtext>T</mtext>}}$ independent of Δψ (0.5 mM) but whose $\text{V}$ increases drastically with increasing Δψ. We associate these components of lactose transport with facilitated diffusion and active transport, respectively. We analyze the dependence upon Δψ of $\text{K}{}_{\mathrm{<mtext>T</mtext>}}$ and $\text{V}$ of the active transport component in terms of a mathematical kinetic model developed by Geck and Heinz (Geck, P. and Heinz, E. (1976) Biochim. Biophys. Acta 443, 49–63). We show that within the framework of this model, the analysis of our data indicates that active transport of lactose takes place with a H⁺/lactose stoichiometry greater than 1, and that the lac carrier in the absence of bound solutes (lactose and proton(s)) is electrically neutral. On the other hand, our data relative to facilitated diffusion tend to indicate that lactose transport via this mechanism is accompanied by a H⁺/lactose stoichiometry smaller than that of active transport. We discuss various implications which result from the existence of H⁺/lactose stoichiometry different for active transport and facilitated diffusion.     

Determination of the kinetic constants of fructose transport and phosphorylation in the perfused rat liver

The kinetics of fructose uptake was determined in perfused rat liver during steady-state fructose elimination. On the basis of the corresponding values of fructose concentration in the affluent and in the effluent medium, and the fructose and ATP concentration in biopsies, the kinetics of membrane transport and intracellular phosphorylation in the intact organ was calculated according to a model system. Carrier-mediated fructose transport has a high $\text{K}{}_{\mathrm{<mtext>m</mtext>}}$ (67 mM) and $\text{V}$ (30 μmoles · min^?1 ·g^?1). The calculated kinetic constants of the intracellular phosphorylation were compared with values obtained with an acid-treated rat liver high speed supernatant (values given in parentheses). $\text{K}{}_{\mathrm{<mtext>m</mtext>}}$ with fructose 1.0 mM (0.7 mM), $\text{K}{}_{\mathrm{<mtext>m</mtext>}}$ with ATP 0.54 mM (0.37 mM), $\text{V}$ 10.3 μmoles · min^?1 · g^?1 (10.1 μmoles · min^?1 · g^?1, calculated on the basis of the highest measured rate of fructose uptake correcting the ATP concentration to saturating values). The kinetics of fructose uptake reveals that at Physiological fructose concentrations the membrane transport limits the rate of fructose uptake, thus protecting the liver from severe depletion of adenine nucleotides.     

Malate dehydrogenase. Kinetic studies with meso-tartrate and 2-keto-3-hydroxysuccinate, comparison of the mitochondrial and supernatant pig heart enzymes.

Initial rate, product inhibition, and isotope rate kinetic studies of pig heart mitochondrial and supernatant malate dehydrogenases, acting upon the nonphysiological substrates, meso-tartrate and 2-keto-3-hydroxysuccinate, are reported. The measured spontaneous keto-enol equilibrium for 2-keto-3-hydroxysuccinate in 0.05 m Tris-acetate (pH 8.0) at 25 °C favors the enol form, dihydroxyfumarate, with an apparent equilibrium constant of 0.036. The enzyme-catalyzed reaction favors meso-tartrate with an apparent equilibrium constant of 1.25 × 10^?6, M^?1 at pH 8.0. The mechanism apparently remains ordered bi bi for both enzymes when these nonphysiological substrates are used, and the chemical-converting hydride transfer step becomes more rate limiting for both enzymes. This conclusion is supported by $\text{V}{}_{\mathrm{<mtext>H</mtext>}}\text{V}{}_{\mathrm{<mtext>D</mtext>}}$ and $\text{(}\text{V}{}_{\mathrm{<mtext>H</mtext>}}\text{K}{}_{\mathrm{<mtext>H</mtext>}}\text{)}\text{V}{}_{\mathrm{<mtext>D</mtext>}}\text{K}{}_{\mathrm{<mtext>D</mtext>}}$ values of 2.6 and 3.1, respectively, for the mitochondrial enzyme and 1.9 and 2.9, respectively, for the supernatant enzyme.     

Breaks in arrhenius plots of reactions involving membrane-bound and solubilized sialyltransferases,due to temperature dependence of kinetic parameters

Temperature dependence of asialomucin-sialyltransferase ($\text{CMP}\text{-N-}\text{acetylneuraminate:}\text{D}\text{-galactosyl-glyco-protein}$) N-acetylneuraminyltransferase, EC 2.4.99.1) activity is investigated. Discontinuities in Arrhenius plots are observed, whether the enzyme is membrane-associated or solubilized. These discontinuities cannot be firmly correlated with the phase-transition temperatures of either endogenous or exogenous phospholipids. Arrhenius plots of the kinetic parameters also exhibit sharp discontinuities, so that it is concluded that a significant change in K_m and V_max values occurs with varying temperature. Our results suggest that the biphasic behavior of Arrhenius plots may be attributed to the temperature dependence of the kinetic parameters for both membrane-associated and solubilized sialyltransferase activities.     

Neutral salt effects on the velocity and activation volume of the lactate dehydrogenase reaction: Evidence for enzyme hydration changes during catalysis

The effects of different neutral salts on the maximal velocity (V) and activation volume ($\text{Δ}\text{V3}$) of the M₄-lactate dehydrogenase reaction were studied to determine the mechanistic basis of the inhibitory effects of these salts. For salting-in salts (which increase protein group solubility), increasing salt concentrations led to reductions in V and increases in $\text{Δ}\text{V3}$, with the order of salt effectiveness following the Hofmeister (lyotropic) series: KSCN > KI > KBr. A 50% reduction in V was associated with an approximately 17 cm³ mol^?1 increase in $\text{Δ}\text{V3}$ for different concentrations of the same salt and for equal concentrations of different salting-in salts. Salting-out salts were also inhibitory, but no uniform correlation between changes in V and $\text{Δ}\text{V3}$ was observed. The strongly salting-out salt KF decreased $\text{Δ}\text{V3}$ at all concentrations. The weaker salting-out salt K₂SO₄ increased $\text{Δ}\text{V3}$ at concentrations below 0.1 m and decreased $\text{Δ}\text{V3}$ at higher concentrations. KCl increased $\text{Δ}\text{V3}$ as the salt concentration was raised to approximately 0.2 m; further increases in KCl concentration were without effect on $\text{Δ}\text{V3}$. The rate and volume effects of these neutral salts, especially the highly regular covariation in V and $\text{Δ}\text{V3}$ found for salting-in salts, seem difficult to explain in terms of salt-induced changes in the geometry of the active site. We propose instead that these salt effects can all be explained in terms of the energy and volume changes which accompany transfers of protein groups (amino acid side chains and peptide backbone linkages) between the hydrophobic interior of the enzyme and the enzyme-water interface during catalytic conformational changes.     

Activation of the β-galactoside transport system in escherichia coli ML-308 by n-alkanols. Modification of lipid-protein interaction by a change in bilayer fluidity

The net rate of transport of $\text{o-}\text{nitrophenyl}\text{-β-}\text{d}\text{-}\text{galactopyranoside}$ by Escherichia coli ML-308 is increased at temperatures below the apparent phase transition of the lipid bilayer in the presence of n-alkanols. The degree of activation produced is determined both by the concentration and chain length of the n-alkanol used. At low concentrations n-alkanols “activate” transport, but do not cause either cell lysis or denaturation of β-galactosidase.Arrhenius plots of the kinetic constants for transport indicate the K_m shows discontinuity with increasing temperature, while the slope for V changes only gradually. The presence of 10.5 mM n-hexanol increases the value of both K_m and V at low temperature. A comparison of these data to those obtained at a single substrate concentration (1.85 mM o-nitrophenyl-β-d-galactopyranoside) suggests the biphasic behavior of Arrhenius plots at that concentration may be attributed to changes in the K_m for the transport process.     

Foundations of the use of an enzyme-kinetic analogy in cell-mediated cytotoxicity

A mathematical model of the ⁵¹Cr-release microcytotoxicity assay is utilized to find conditions under which the kinetics of this assay resemble the kinetics of a classical enzyme-substrate reaction. Assuming a steady-state approximation, that “bystander” effector cells do not bind markedly better than the cytotoxic effector cells, and that the programming of the target cells for lysis is irreversible, it is shown that the velocity of label release is v = v_maxT_T/(K_{$\text{1}\text{2}$}+T_T), where both V_max and K_{$\text{1}\text{2}$} are linear functions of the effector-cell population and T_T is the initial target-cell population. Moreover, the expressions for K_{$\text{1}\text{2}$} and V_max are expressed in terms of natural kinetic parameters of the process and attributes of the noncytotoxic bystanders.     

Human complex-forming glycoprotein, heterogeneous in charge: the primary structure around the cysteine residues and characterization of a disulfide bridge

L-929 cell surface membranes have been assayed in vitro and found to contain significant protein kinase activity. A steady-state kinetic analysis indicated that at least two distinct protein kinases were present. Plots of reaction velocity (v) against substrate (ATP) concentration were distinctly biphasic, as were Lineweaver-Burk plots of $\text{1}\text{v}$ versus $\text{1}\text{ATP}$. Michaelis constants of the two enzymes were calculated to be 22 and 173 μm, respectively. Sodium dodecyl sulfate polyacrylamide gel analysis of the phosphorylated membrane proteins provided additional support for the existence of more than one protein kinase. Different endogenous proteins were phosphorylated at 1 μm ATP compared to 1 μm ATP. Further studies of the low K_m (22 μm) enzyme suggested that it is a typical cyclic 3′,5′-AMP-independent protein kinase. Its activity was dependent on the presence of Mg²⁺, but it was not affected by cyclic 3′,5′-AMP, cyclic 3′,5′-GMP, or the heat-stable inhibitor of cyclic 3′,5′-AMP-dependent protein kinases. ATP and GTP, but not other nucleoside triphosphates, could serve as phosphoryl donor and maximum kinase activity was expressed at pH 7.0. Phosvitin and casein were superior to histones as exogenous substrates for the low K_m enzyme.     

Sucrose transport by Streptococcus mutans. Evidence for multiple transport systems

The transport of sucrose by selected mutant and wild-type cells of Streptococcus mutans was studied using washed cocci harvested at appropriate phases of growth, incubated in the presence of fluoride and appropriately labelled substrates. The rapid sucrose uptake observed cannot be ascribed to possible extracellular formation of hexoses from sucrose and their subsequent transport, formation of intracellular glycogen-like polysaccharide, or binding of sucrose or extracellular glucans to the cocci. Rather, there are at least three discrete transport systems for sucrose, two of which are $\text{phospho}\text{enol}\text{pyruvate-dependent}$ phosphotransferases with relatively low apparent $\text{K}{}_{\mathrm{<mtext>m</mtext>}}$ values and the other a non-phosphotransferase (non-PTS) third transport system (termed TTS) with a relatively high apparent $\text{K}{}_{\mathrm{<mtext>m</mtext>}}$. For strain 6715-13 mutant 33, the $\text{K}{}_{\mathrm{<mtext>m</mtext>}}$ values are 6.25·10^?5 M, 2.4·10^?4 M, and 3.0·10^?3 M, respectively; for strain NCTC-10449, the $\text{K}{}_{\mathrm{<mtext>m</mtext>}}$ values are 7.1·10^?5 M, 2.5·10^?4 M and 3.3·10^?3 M, respectively. The two lower $\text{K}{}_{\mathrm{<mtext>m</mtext>}}$ systems could not be demonstrated in mid-log phase glucose-adapted cocci, a condition known to repress sucrose-specific phosphotransferase activity, but under these conditions the highest $\text{K}{}_{\mathrm{<mtext>m</mtext>}}$ system persists. Also, a mutant devoid of sucrose-specific phosphotransferase activity fails to evidence the two high affinity (low apparent $\text{K}{}_{\mathrm{<mtext>m</mtext>}}$) systems, but still has the lowest affinity (highest $\text{K}{}_{\mathrm{<mtext>m</mtext>}}$) system. There was essentially no uptake at 4°C indicating these processes are energy dependent. The third transport system, whose nature is unknown, appears to function under conditions of sucrose abundance and rapid growth which are known to repress $\text{phospho}\text{enol}\text{pyruvate-dependent}$ sucrose-specific phosphotransferase activity in S. mutans. These multiple transport systems seem well-adapted to S. mutans which is faced with fluctuating supplies of sucrose in its natural habitat on the surfaces of teeth.     

Interrelations between pH and temperature for the catalytic rate of the M4 lsozyme of lactate dehydrogenase (EC 1.1.1.27) from goldfish (Carassius auratus L.).

A kinetic study of the rate of pyruvate reduction by goldfish LDH-M₄ (the homotetrameric form of lactate dehydrogenase which predominates in skeletal muscle) provided an analysis of the effects of pH and temperature on v (reaction velocity) and estimates of how temperature might affect catalysis in vivo, where the physiological pH regulation imposes a temperature coefficient of ?0.015 to ?0.020 pH unit/ °C. Consistent with published data for other LDHs, (i) V (maximum reaction velocity) was pH insensitive over a physiological pH range, (ii) the K_m for pyruvate, K_P, was sensitive to both pH and temperature, and (iii) the K_m for NADH and the dissociation constant for NADH were both sensitive to temperature, but not to pH. V approximately doubled with each 10 °C (E_a = 11.7 kcal/mol). The effects of pH and temperature on K_P were consistent with two enthalpic contributions, an ionization enthalpy (ΔH_i^°) of 7.2 kcal/mol (probably a histidine imidazole), and an enthalpy (ΔH_SO) of 5.8 kcal/mol for the combination of pyruvate with the nonionized (pH ? pK′) LDH-NADH complex. When the pH was varied according to the physiological temperature coefficient, v was more sensitive to temperature than for conditions of constant pH, the usual design of kinetic experiments. This effect was due to the decreased temperature sensitivity of K_P caused by partial concellation of the ΔH_i^° effect by the pH regulation: $\text{d}\text{pH}\text{dT}\text{?}\text{d}\text{p}\text{K′}\text{dT}$. At constant pH, on the other hand, K_P increased strongly with temperature and had the effect of offsetting (especially at higher pH values) the large increases in V. It was suggested that the magnitudes of ΔH_i^° and ΔH_SO might have been important in the evolution of LDHs and other enzymes of cold-blooded animals.     

pH kinetic studies of the N-demethylation of N,N-dimethylaniline catalyzed by chloroperoxidase

The effect of pH on the kinetic parameters for the chloroperoxidase-catalyzed N-demethylation of N,N-dimethylaniline supported by ethyl hydroperoxide was investigated from pH 3.0 to 7.0. Chloroperoxidase was found to be stable throughout the pH range studied. Initial rate conditions were determined throughout the pH range. The V_max for the demethylation reaction exhibited a pH optimum at approximately 4.5. The K_m for N,N-dimethylaniline increased with decreasing pH, while the K_m for ethyl hydroperoxide varied in a manner paralleling V_max. Comparison of the $\text{V}{}_{\mathrm{<mtext>max</mtext>}}\text{K}{}_{\mathrm{m}}$ values for N,N-dimethylaniline and ethyl hydroperoxide indicated that the interaction of N,N-dimethylaniline with chloroperoxidase compound I was rate-limiting below pH 4.5, while compound I formation was rate-limiting above pH 4.5. The log of the $\text{V}{}_{\mathrm{<mtext>max</mtext>}}\text{K}{}_{\mathrm{m}}$ for ethyl hydroperoxide was independent of pH, indicating that chloroperoxidase compound I formation is not affected by ionizations in this pH range. The plot of the log of the $\text{V}{}_{\mathrm{<mtext>max</mtext>}}\text{K}{}_{\mathrm{m}}$ for N,N-dimethylaniline versus pH indicated an ionization on compound I with a pK of approximately 6.8. The plot of the log of the V_max versus pH indicated an ionization on the compound I-N,N-dimethylaniline complex, with a pK of approximately 3.1. The results show that chloroperoxidase can demethylate both the protonated and neutral forms of N,N-dimethylaniline (pK approximately 5.0), suggesting that hydrophobic binding of the arylamine substrate is more important in catalysis than ionic bonding of the amine moiety. For optimal catalysis, a residue in the chloroperoxidase compound I-N,N-dimethylaniline complex with a pK of approximately 3.1 must be deprotonated, while a residue in compound I with a pK of approximately 6.8 must be protonated.     

The concept of high- and low-affinity reactions in bovine cytochrome c oxidase steady-state kinetics

(1) Analysis of the data from steady-state kinetic studies shows that two reactions between cytochrome c and cytochrome c oxidase sufficed to describe the concave Eadie-Hofstee plots ($\text{K}{}_{\mathrm{<mtext>m</mtext>}}\text{? 1 · 10}{}^{\mathrm{?8}}\text{M}$ and $\text{K}{}_{\mathrm{<mtext>m</mtext>}}\text{? 2 · 10}{}^{\mathrm{?5}}\text{M}$). It is not necessary to postulate a third reaction of $\text{K}{}_{\mathrm{<mtext>m</mtext>}}\text{? 10}{}^{\mathrm{?6}}\text{M}$. (2) Change of temperature, type of detergent and type of cytochrome c affected both reactions to the same extent. The presence of only a single catalytic cytochrome c interaction site on the oxidase could explain the kinetic data. (3) Our experiments support the notion that, at least under our conditions (pH 7.8, low-ionic strength), the dissociation of ferricytochrome c from cytochrome c oxidase is the rate-limiting step in the steady-state kinetics. (4) A series of models, proposed to describe the observed steady-state kinetics, is discussed.     

Derivation of the equations that describe the effects of unstirred water layers on the kinetic parameters of active transport processes in the intestine

Unidirectional flux of solutes into the intestinal mucosal cells is determined by the rate of movement of these molecules across both an unstirred water layer and the microvillus membrane of the epithelial cell. Therefore, an equation is derived in this paper that describes the velocity of active transport as a function of the characteristics of both the transport carrier in the membrane and the resistance of the overlying unstirred water layer. Using this equation a series of curves are presented that depict the effect on the kinetics of active transport of varying the thickness (d) or surface area (S_w) of the unstirred water layer, the free diffusion coefficient (D) of the solute, the distribution of active transport sites along the villus ($\text{?}{}_{\mathrm{<mtext>n</mtext>}}$), the maximal transport velocity (J^m_d) and the true Michaelis constant (K_m). These theoretical curves illustrate the serious limitations inherent in interpretation of previously published data dealing with active transport processes in the intestine.     

On the active transport of organic acids (fluorescein) in the choroid plexus of the rabbit

The kinetics of active transport of an organic acid (fluorescein) through the membranes of the choroid plexus from the lateral ventricules of the brain of rabbit was studied both morphologically and functionally. It was shown that fluorescein is actively translocated through the apical and basal membrane of the epithelium and is accumulated in blood capillaries at a concentration exceeding one order of magnitude that in the incubation medium. The kinetic curves displaying saturation and the demonstration of inhibition by other acids shows that a specific carrier is involved in the transfer across the membrane. The active transport of fluorescein at 20°C was found to be sodium independent. Total exclusion of sodium from the incubation medium does not change the Michaelis constant ($\text{K}{}_{\mathrm{<mtext>m</mtext>}}$) and maximal velocity ($\text{V}$). The active transport depends on the operation of (Na⁺ + K⁺)-ATPase as energy source but obviously no specific complexes with the participation of sodium are involved.     

Studies of the kinetics of Na+ gradient-coupled glucose transport as found in brush-border membrane vesicles from rabbit jejunum

The Na⁺-dependent d-glucose transport reaction in rabbit jejunal brush-border vesicles was studied. Initial rate data were obtained by fitting a polynomial equation to progress curves at different d-glucose concentrations and extracting the slope of the tangent at zero-time. Kinetic replots of the initial rate values produced biphasic Hofstee patterns indicative of two pathways for transport distinguished by their $\text{K}{}_{\mathrm{<mtext>m</mtext>}}$ values for glucose. Neither was dependent on the presence of a membrane potential. Both were dependent on Na⁺ and both were inhibited by phlorizin. Increasing external sodium was found to elevate the apparent $\text{V}{}_{\mathrm{<mtext>max</mtext>}}$ for both pathways. Internal sodium was inhibitory. Pulsed progress curve analysis indicated that the effect of internal sodium was best characterized as carrier sequestration by a sodium-carrier binary complex. Inhibition by internal sodium was completely reversed by the presence, internally, of d-glucose. The presence of two pathways and the kinetic constants for these pathways do not agree with the conclusions of Hopfer and Groseclose (1980) J. Biol. Chem. 255, 4453–4462). Experiments are presented which bear on the reason for the disagreement.     

A simple model for a regulatory enzyme

A simple model for a regulatory enzyme is described which leads to relationships between the initial velocity of the catalysed reaction and the varied concentration of a substrate that are of the non-inflected or sigmoidal varieties without a maximum. The model assumes that the most relevant measure of protein configuration (itself determining the kinetic behaviour of the enzyme) is the apparent association constant, α_i, measured for the given fractional saturation of the ligand under investigation. It is further assumed that the original state of the protein in solution, α₀, is destabilized by an increment of energy, ΔG_p⁰, that is proportional to the fractional saturation of the enzyme by ligand so that the formation of a new configurational state, a,, can be represented by ?ΔG_p⁰ = RT ln $\text{α}{}_1\text{α}{}_0$. The rate or fractional saturation equation that can be derived from this model predicts both positive and negative cooperativity. Either equation can be transformed for linear representation, provided the maximum velocity or its equivalent maximum saturation is known, and estimates of α₀ and α_i (the apparent association constants at zero and complete saturation) can be obtained thereby. A procedure is also described by which an initial estimate of the maximum velocity or saturation can be improved. The model is tested by application to a range of data in the literature and it is shown to give fits to the data comparable in quality to those provided by the model of Monod, Wyman &; Changeux (1965).     

Determination of enzyme kinetic parameters by continuous addition of substrate to a single reaction mixture and analysis by a tangent-slope procedure: I. Analysis of the method using computed progress curves

A new method has been developed which provides reliable estimates of enzyme kinetic constants from single reaction progress curves recorded under conditions of continuously increasing substrate concentration. Equally spaced data points simulating such progress curves and containing known amounts of superimposed random noise were fit to the Hill equation by (i) direct nonlinear curve-fitting of raw data, and (ii) a tangent-slope technique in which the raw data are numerically differentiated, transformed into substrate versus velocity data, and then analyzed as linear plots. Both integral and differential procedures provided accurate and precise estimates of the Hill parameters (S_0.5, V, and n) from single reaction mixtures. However, the tangent-slope method was at least 10-fold faster to compute and was not dependent on accurate initial guesses of the Hill parameters or integration of the rate equation. With the tangent-slope method, the optimal number of data points used in calculating tangent slopes was found to be 9 or 11. The reliability of the Hill parameters determined with the tangent-slope method was relatively insensitive to the maximum substrate concentration over a range of $\text{S}{}_{\mathrm{<mtext>max</mtext>}}\text{S}{}_{0.5}$ of 1.5 to 10; the optimal value was 3. Through further analysis of simulated data, it was found that slow enzyme inactivation (<4% loss during the assay), or product competitive inhibition (maximum product concentration < 30% of the inhibitor dissociation constant) does not produce serious errors in the Hill parameters. Methods are presented to detect and distinguish enzyme inactivation and product competitive inhibition. It is suggested that continuous addition methodology combined with tangent-slope analysis provides the basis for a flexible system for kinetic characterization of enzymes which has wider applicability and other advantages over multicuvette or conventional progress curve methodology. A major advantage in contrast to the progress curve approach is that product accumulation and associated product effects are lowest at lower substrate concentrations.     

Study of the interaction of Saccharomyces cerevisiae with glucose by particle microelectrophoresis

Saccharomyces cerevisiae NCYC 239 in the presence of glucose at temperatures under 303 K shows a time-dependent lowering of electrophoreric mobility $\text{υ}$. At temperatures above 303 K, this time-dependent change in $\text{υ}$ is in the direction of increased mobilities. Cells suspended in buffer indicate a surface pK_a of less than 4, whereas for cells suspended in buffered glucose it is impossible to derive a surface pK_a. A kinetic study of the interaction of S. cerevisiae with glucose as a function of temperature allows calculation of an activation energy of 140 kJ·mol^?1 for the combined processes of (i) uptake of glucose onto the cell wall, (ii) transfer through the cell wall and membrane, and (iii) the establishment of a steady glucose flux through the wall and membrane.     

Steady-state kinetics of ADP-arsenate and ATP-synthesis in Rhodospirillum rubrum chromatophores

(1) Rates of ATP synthesis and ADP-arsenate synthesis catalyzed by Rhodospirillum rubrum chromatophores were determined with the firefly luciferase method and by a coupled enzyme assay involving hexokinase and glucose-6-phosphate dehydrogenase. (2) V_m for ADP-arsenate synthesis was about 2-times lower than V_m for ATP-synthesis. With saturating [ADP], K(As_i) was about 20% higher than K(P_i). With saturating [anion], K(ADP) was during arsenylation about 20% lower than during phosphorylation. (3) Plots of $\text{1}\text{v}$ vs. $\text{1}\text{[}\text{substrate}\text{]}$ were non-linear at low concentrations of the fixed substrate. The non-linearity was such as to suggest a positive cooperativity between sites binding the variable substrate, resulting in an increased $\text{V}{}_{\mathrm{<mtext>m</mtext>}}\text{K}{}_{\mathrm{<mtext>m</mtext>}}$ ratio. High concentrations of the fixed substrate cause a similar increase in $\text{V}{}_{\mathrm{<mtext>m</mtext>}}\text{K}{}_{\mathrm{<mtext>m</mtext>}}$, but abolish the cooperativity of the sites binding the variable substrate. (4) Low concentrations of inorganic arsenate (As_i) stimulate ATP synthesis supported by low concentrations of P_i and ADP about 2-fold. (5) At high ADP concentrations, the apparent K_i of As_i for inhibition of ATP-synthesis was 2–3-times higher than the apparent K_m of As_i for arsenylation; the apparent K_i of P_i for inhibition of ADP-arsenate synthesis was about 40% lower than the apparent K_m of P_i for ATP synthesis. (6) The results are discussed in terms of a model in which P_i and As_i compete for binding to a catalytic as well as an allosteric site. The interaction between these sites is modulated by the ADP concentration. At high ADP concentrations, interaction between these sites occurs only when they are occupied with different species of anion.