Kinetics of the H-ATPase in chromatophores from Rhodospirillum rubrum: Effect of the electrical transmembrane potential on the rate constants

The effect of the electrical potential on the H⁺-ATPase of Rhodospirillum rubrum is examined. It is shown that the forward reaction rate (ATP synthesis) is increased by a factor of 10 during illumination while the reversed rate is only slightly decreased. This indicates that the electrical potential across the membrane affects the rate constants mainly by increasing the forward rate constants rather than decreasing the reversed rate constants in order to go from net hydrolysis to net synthesis.     

Evolutionary optimization of the catalytic efficiency of enzymes.

1. The rate equation for a generalized Michaelian type of enzymic reaction mechanism has been analyzed in order to establish how the mechanism should be kinetically designed in order to optimize the catalytic efficiency of the enzyme for a given average magnitude of true and apparent first-order rate constants in the mechanism at given concentrations of enzyme, substrate and product. 2. As long as on-velocity constants for substrate and product binding to the enzyme have not reached the limiting value for a diffusion-controlled association process, the optimal state of enzyme operation will be characterized by forward (true and apparent) first-order rate constants of equal magnitude and reverse rate constants of equal magnitude. The drop in free energy driving the catalysed reaction will occur to an equal extent for each reaction step in the mechanism. All internal equilibrium constants will be of equal magnitude and reflect only the closeness of the catalysed reaction to equilibrium conditions. 3. When magnitudes of on-velocity constants for substrate and product binding have reached their upper limits, the optimal kinetic design of the reaction mechanism becomes more complex and has to be established by numerical methods. Numerical solutions, calculated for triosephosphate isomerase, indicate that this particular enzyme may or may not be considered to exhibit close to maximal efficiency, depending on what value is assigned to the upper limit for a ligand association rate constant. 4. Arguments are presented to show that no useful information on the evolutionary optimization of the catalytic efficiency of enzymes can be obtained by previously taken approaches that are based on the application of linear free-energy relationships for rate and equilibrium constants in the reaction mechanism.     

Relationship between the oxidation potential of the bacteriochlorophyll dimer and electron transfer in photosynthetic reaction centers

The primary electron donor in the photosynthetic reaction center from purple bacteria is a bacteriochlorophyll dimer containing four conjugated carbonyl groups that may form hydrogen bonds with amino acid residues. Spectroscopic analyses of a set of mutant reaction centers confirm that hydrogen bonds can be formed between each of these carbonyl groups and histidine residues in the reaction center subunits. The addition of each hydrogen bond is correlated with an increase in the oxidation potential of the dimer, resulting in a 355-mV range in the midpoint potential. The resulting changes in the free-energy differences for several reactions involving the dimer are related to the electron transfer rates using the Marcus theory. These reactions include electron transfer from cytochrome c₂ to the oxidized dimer, charge recombination from the primary electron acceptor quinone, and the initial forward electron transfer.     

Phi-value analysis of a linear, sequential reaction mechanism: theory and application to ion channel gating

We derive the analytical form of a rate-equilibrium free-energy relationship (with slope Phi) for a bounded, linear chain of coupled reactions having arbitrary connecting rate constants. The results confirm previous simulation studies showing that Phi-values reflect the position of the perturbed reaction within the chain, with reactions occurring earlier in the sequence producing higher Phi-values than those occurring later in the sequence. The derivation includes an expression for the transmission coefficients of the overall reaction based on the rate constants of an arbitrary, discrete, finite Markov chain. The results indicate that experimental Phi-values can be used to calculate the relative heights of the energy barriers between intermediate states of the chain but provide no information about the energies of the wells along the reaction path. Application of the equations to the case of diliganded acetylcholine receptor channel gating suggests that the transition-state ensemble for this reaction is nearly flat. Although this mechanism accounts for many of the basic features of diliganded and unliganded acetylcholine receptor channel gating, the experimental rate-equilibrium free-energy relationships appear to be more linear than those predicted by the theory.     

Analysis of the rate-limiting step in a ligand-cell receptor interaction: the immunoglobulin E system

Theory predicts that the kinetics of simple interactions between a ligand and a receptor bound on the surface of a cell will be affected by the occupancy of receptors on the same cell. In a diffusion-limited reaction the effect will be on the rate of dissociation but not on the rate of association until the cell is virtually saturated with ligand. If the rate of reaction is not diffusion limited, then the opposite holds; i.e., the forward velocities will be proportional to the concentration of vacant receptors, but the reverse reactions will not be. We examined the kinetics of reaction between immunoglobulin E (IgE) and its receptor and clearly demonstrated that the reaction is not diffusion controlled. The substantial (congruent to 30-fold) increase in the forward rate constant observed for the reaction of IgE with solubilized receptors as opposed to cell-bound receptors is therefore not an artifact of calculation. Since the reverse rate constants show little difference, we postulate that the presence of other surface components (rather than conformational differences in the receptor) affects the reaction with the cells. As an aid to the analysis, the theory has been extended so that not only the rate constants but also the entire course of the reaction of ligand with cell receptors can be predicted for diffusion-limited vs. non-diffusion-limited interactions.     

Integrated steady state rate equations and the determination of individual rate constants.

Integrated steady state rate equations have been used to determine the kinetic constants (Vs, Ks, Vp, and Kp) and rate constants (k1, k2, k3, and k4) of the reversible enzyme mechanism: (see article). The fumarase reaction has been used as a model to illustrate the procedures for determining these constants. In contrast to initial velocity studies, the values of the constants have been obtained by examining the enzyme reaction in only one direction rather than in both forward and reverse directions. To accomplish this, a new procedure is described for fitting data to integrated rate equations which eliminates problems encountered when data are analyzed graphically. The advantages of examining on enzyme reaction in one direction with these new procedures allow this method to be extended to the examination of enzymes with simple mechanisms where initial velocities are difficult to measure because either the substrate or product is not readily available, or because the reaction is not readily reversible.     

Radical-pair energetics and decay mechanisms in reaction centers containing anthraquinones, naphthoquinones or benzoquinones in place of ubiquinone

In reaction centers from Rhodobacter sphaeroides (formerly called Rhodopseudomonas sphaeroides), light causes an electron-transfer reaction that forms the radical pair state (P+I-, or PF) from the initial excited singlet state (P) of a bacteriochlorophyll dimer (P). Subsequent electron transfer to a quinone (Q) produces the state P+Q-. Back electron transfer can regenerate P from P+Q-, giving rise to 'delayed' fluorescence that decays with approximately the same lifetime as P+Q-. The free-energy difference between P+Q- and P can be determined from the initial amplitude of the delayed fluorescence. In the present work, we extracted the native quinone (ubiquinone) from Rps. sphaeroides reaction centers, and replaced it by various anthraquinones, naphthoquinones, and benzoquinones. We found a rough correlation between the halfwave reduction potential (E1/2) of the quinone used for reconstitution (as measured polarographically in dimethylformamide) and the apparent free energy of the state P+Q- relatively to P. As the E1/2 of the quinone becomes more negative, the standard free-energy gap between P+Q- and P decreases. However, the correlation is quantitatively weak. Apparently, the effective midpoint potentials (Em) of the quinones in situ depend subtly on interactions with the protein environment in the reaction center. Using the value of the Em for ubiquinone determined in native reaction centers as a reference, and the standard free energies determined for P+Q- in reaction centers reconstituted with other quinones, the effective Em values of 12 different quinones in situ are estimated. In native reaction centers, or in reaction centers reconstituted with quinones that give a standard free-energy gap of more than about 0.8 eV between P+Q- and P*, charge recombination from P+Q- to the ground state (PQ) occurs almost exclusively by a temperature-insensitive mechanism, presumably electron tunneling. When reaction centers are reconstituted with quinones that give a free-energy gap between P+Q- and P* of less than 0.8 with quinones that give a free-energy gap between P+Q- and P* of less than 0.8 eV, part or all of the decay proceeds through a thermally accessible intermediate. There is a linear relationship between the log of the rate constant for the decay of P+Q- via the intermediate state and the standard free energy of P+Q-. The higher the free energy, the faster the decay. The kinetic and thermodynamic properties of the intermediate appear not to depend strongly on the quinone used for reconstitution, indicating that the intermediate is probably not simply an activated form of P+Q-.(ABSTRACT TRUNCATED AT 400 WORDS)     

Metabolic Fluxes Between [14C]2-Deoxy-D-Glucose and [14C]2-Deoxy-D-Glucose-6-Phosphate in Brain In Vivo

The rates of the phosphorylation and dephosphorylation of 2-deoxyglucose were measured in rat brain in vivo using tracer kinetic techniques. The rate constant for each reaction was estimated from two separate experiments with different protocols for tracer administration. Tracer amounts of [1-14C]2-deoxyglucose (1 microCi) were injected through the internal carotid artery (intraarterial experiment), or through the atrium (intravenous experiment). Brains were sampled by freeze-blowing at various times after the injection. In the intraarterial experiment, the rate constant for the forward reaction from 2-deoxyglucose to 2-deoxyglucose phosphate was calculated by dividing the initial rate of 2-deoxyglucose phosphate production by the 2-deoxyglucose content in brain. The rate constant for the reverse reaction from 2-deoxyglucose phosphate to 2-deoxyglucose was calculated from the decay constant of 2-deoxyglucose phosphate. The rate constants estimated were 10.1 +/- 1.4%/min (SD) and 3.00 +/- 0.01%/min (SD), respectively, for the forward and reverse reactions. In the intravenous experiment, rate constants for both reactions were estimated by compartmental analysis. By fitting data to program SAAM-27, the rate constants for the forward and reverse reactions were estimated as 11.4 +/- 0.4%/min (SD) and 5.1 +/- 0.4%/min (SD), respectively. The rate constants determined were compared to those for the reactions between glucose and glucose-6-phosphate, estimated previously from labeled glucoses. It is concluded that the rate of glucose utilization measured by the 2-deoxyglucose method reflects the rate of the hexokinase reaction and not the rate of glucose utilization or brain energy utilization.     

P+HA- charge recombination reaction rate constant in Rhodobacter sphaeroides reaction centers is independent of the P/P+ midpoint potential.

The kinetics of the P+HA- (oxidized donor, reduced bacteriopheophytin acceptor) recombination reaction was measured in a series of reaction center mutants of Rhodobacter sphaeroides with altered P/P+ midpoint potentials between 410 and 765 mV. The time constant for P+HA- recombination was found to range between 14 and 26 ns and was essentially independent of P/P+ midpoint potential. Previous work has shown that the time constant for initial electron transfer in these mutants at room temperature is also only weakly dependent on the P/P+ midpoint potential, ranging from about 2.5 ps to about 50 ps. These results, taken together, imply that heterogeneity in the P/P+ midpoint potential within the reaction center population is not likely the dominant cause of the substantial kinetic complexity observed in the decay of the excited singlet state of P on the picosecond to nanosecond time scale. In addition, the pathway of P+HA- decay appears to be direct or via P+BA- rather than proceeding back through P, even in the highest-potential mutant, as is evident from the fact that the rate of P+HA- recombination is unaltered by pushing P+HA- much closer to P in energy. Finally, the midpoint potential independence of the P+HA- recombination rate constant suggests that the slow rate of P+HA- recombination arises from an inherent limitation in the maximum rate of this process rather than because it occurs in the inverted region of a classical Marcus rate vs free energy curve.     

Mechanism of the hexamer-dodecamer reaction of lobster hemocyanin.

The overall forward and reverse rate constants for the hexamer-dodecamer reaction of lobster hemocyanin have been determined in 0.1 ionic strength glycine buffers at pH 9.6, at free calcium ion levels from 0.0031 to 0.0053 molar, at 25 degrees C. Concentration-jump relaxation experiments in a stopped-flow apparatus were monitored by light scattered at 90 degrees. The reaction is pseudobimolecular, and the overall forward rate constant bears virtually all of the calcium ion concentration-dependence, while the overall reverse rate constant is truly unimolecular. Four calcium ions appear to participate in the reaction between two hexameric molecules, and appear to become an integral part of the structure of the dodecameric molecule under these conditions.     

Pumping capacity of bacterial reaction centers and backpressure regulation of energy transduction.

Transduction of free-energy by Rhodobacter sphaeroides reaction-center-light-harvesting-complex-1 (RCLH1) was quantified. RCLH1 complexes were reconstituted into liposomal membranes. The capacity of the RCLH1 complex to build up a proton motive force was examined at a range of incident light intensities, and induced proton permeabilities, in the presence of artificial electron donors and acceptors. Experiments were also performed with RCLH1 complexes in which the midpoint potential of the reaction center primary donor was modified over an 85-mV range by replacement of the tyrosine residue at the M210 position of the reaction center protein by histidine, phenylalanine, leucine or tryptophan. The intrinsic driving force with which the reaction center pumped protons tended to decrease as the midpoint potential of the primary donor was increased. This observation is discussed in terms of the control of the energetics of the first steps in light-driven electron transfer on the thermodynamic efficiency of the bacterial photosynthetic process. The light intensity at which half of the maximal proton motive force was generated, increased with increasing proton permeability of the membrane. This presents the first direct evidence for so-called backpressure control exerted by the proton motive force on steady-state cyclic electron transfer through and coupled proton pumping by the bacterial reaction center.     

Kinetic studies on human lactate dehydrogenase isoenzyme-catalyzed lactate-to-pyruvate reaction

In order to evaluate the functional differences that may exist in human lactate dehydrogenase (LDH) isoenzymes widely used for clinical examination the kinetic and thermodynamic properties of the lactate to pyruvate reaction that they catalize were examined. Small but significant differences in the kinetic properties of the three isoenzymes were observed. The difference in the rate constants might affect the activity measurement of the individual isoenzyme as the initial velocity for the L-P reaction catalyzed will not be the same for an equal amount of enzyme. Equilibrium constants for the overall reaction in the presence and absence of pyruvate have been determined. On the basis of transition-state theory, the standard enthalpy and free-energy changes for formation of ternary activated complex were positive, while the standard entropy change was negative. Although the standard free-energy change was the same for activation by the three isoenzymes, the enthalpy and entropy changes for the LDH-3-catalyzed reaction were different from the respective values for others. A large positive value for the free-energy change and a negative value for the entropy change indicated unfavorable production of the activated complex (K _infeq. ^sup╪ =1.89×10^-16). The enzyme appears to stabilize and retain the activated complex until it dissociates into the products.     

Manganese oxidation by modified reaction centers from Rhodobacter sphaeroides

The transfer of an electron from exogenous manganese (II) ions to the bacteriochlorophyll dimer, P, of bacterial reaction centers was characterized for a series of mutants that have P/P(+) midpoint potentials ranging from 585 to 765 mV compared to 505 mV for wild type. Light-induced changes in optical and EPR spectra of the mutants were measured to monitor the disappearance of the oxidized dimer upon electron donation by manganese in the presence of bicarbonate. The extent of electron transfer was strongly dependent upon the P/P(+) midpoint potential. The midpoint potential of the Mn(2+)/Mn(3+) couple was calculated to decrease linearly from 751 to 623 mV as the pH was raised from 8 to 10, indicating the involvement of a proton. The electron donation had a second order rate constant of approximately 9 x 10(4) M(-1) s(-1), determined from the linear increase in rate for Mn(2+) concentrations up to 200 microM. Weak dissociation constants of 100-200 microM were found. Quantitative EPR analysis of the six-line free Mn(2+) signal revealed that up to seven manganese ions were associated with the reaction centers at a 1 mM concentration of manganese. The association and the electron transfer between manganese and the reaction centers could be inhibited by Ca(2+) and Na(+) ions. The ability of reaction centers with high potentials to oxidize manganese suggests that manganese oxidation could have preceded water oxidation in the evolutionary development of photosystem II.     

Asymmetry and free energy transduction in biology

This paper is an extension of our earlier theoretical studies on the relationship between kinetic asymmetry and free-energy transductions in biological systems induced by external fluctuations. In the first part of the paper, the asymmetry conditions necessary for external-noise-induced free-energy transductions to occur are derived for a special cyclic, four-state model in which only one reaction step is perturbed by the fluctuations. The results can be used to explain the earlier findings that asymmetry in rate constants was not required in the uphill transport of ligands induced by externally fluctuating the ligand concentrations. In the second part of the paper, the coupling between two enzyme systems through direct enzyme-enzyme inter-actions is studied. The existence of kinetic asymmetry in both the driving and the driven enzyme systems is found necessary for coupling and free-energy transductions to occur.     

Energetics for oxidation of a bound manganese cofactor in modified bacterial reaction centers

The energetics of a Mn cofactor bound to modified reaction centers were determined, including the oxidation/reduction midpoint potential and free energy differences for electron transfer. To determine these properties, a series of mutants of Rhodobacter sphaeroides were designed that have a metal-ion binding site that binds Mn2+ with a dissociation constant of 1 μM at pH 9.0 (Thielges et al. (2005) Biochemistry 44, 7389-7394). In addition to the Mn binding site, each mutant had changes near the bacteriochlorophyll dimer, P, that resulted in altered P/P+ oxidation/reduction midpoint potentials, which ranged from 480 mV to above 800 mV compared to 505 mV for wild type. The bound Mn2+ is redox active and after light excitation can rapidly reduce the oxidized primary electron donor, P+. The extent of P+ reduction was found to systematically range from a full reduction in the mutants with high P/P+ midpoint potentials to no reduction in the mutant with a potential comparable to wild type. This dependence of the extent of Mn2+ oxidation on the P/P+ midpoint potential can be understood using an equilibrium model and the Nernst equation, yielding a Mn2+/Mn3+ oxidation/reduction midpoint potential of 625 mV at pH 9. In the presence of bicarbonate, the Mn2+/Mn3+ potential was found to be 90 mV lower with a value of 535 mV suggesting that the bicarbonate serves as a ligand to the bound Mn. Measurement of the electron transfer rates yielded rate constants for Mn2+ oxidation ranging from 30 to 120 s(-1) as the P/P+ midpoint potentials increased from 670 mV to approximately 805 mV in the absence of bicarbonate. In the presence of bicarbonate, the rates increased for each mutant with values ranging from 65 to 165 s(-1), reflecting an increase in the free energy difference due to the lower Mn2+/Mn3+ midpoint potential. This dependence of the rate constant on the P/P+ midpoint potential can be understood using a Marcus relationship that yielded limits of at least 150 s(-1) and 290 meV for the maximal rate constant and reorganization energy, respectively. The implications of these results are discussed in terms of the energetics of proteins with redox active Mn cofactors, in particular, the Mn4Ca cofactor of photosystem II.     

The determination of enzyme-substrate dissociation rates by dynamic isotope exchange enhancement experiments

A new method for the determination of dissociation rates of enzyme-substrate complexes has been developed. The rate of exchange of a labeled product back into the substrate is measured during catalysis of the forward reaction when the forward reaction is kept far from equilibrium by the enzymatic removal of the nonexchanging product. The ratio of the exchange rate and the net rate for product formation is then determined at various concentrations of the exchanging product. A plot of this ratio is a diagnostic indication of the kinetic mechanism and the relative rates of product dissociation from the binary and ternary enzyme complexes. This technique has been applied to the reaction catalyzed by bovine liver argininosuccinate lyase. The ratio for the rate of exchange of fumarate into argininosuccinate and the net rate for product formation was found to increase with the concentration of fumarate but to reach a limit of 3.3. The ratio of rates was half-maximal at 36 mM fumarate. The data have been interpreted to indicate the argininosuccinate lyase has a random kinetic mechanism. The calculated lower limit for the rate of release of arginine from the enzyme-fumarate-arginine complex is 0.35 times as fast as the Vmax in the reverse direction. The rate of release of arginine from the enzyme-arginine binary complex is 210 times faster than Vmax in the reverse direction.     

1-p-chlorophenyl-4,4-dimethyl-5-diethylamino-1-penten-3-one hydrobromide, a sulfhydryl-specific compound which reacts irreversibly with protein thiols but reversibly with small molecular weight thiols

1-p-Chlorophenyl-4,4-dimethyl-5-diethylamino-1-penten-3-one hydrobromide (CDDP) has been shown to react selectively with small molecular weight and protein thiols. The reaction of this compound with thiols can be monitored directly owing to the large decrease (approximately 21,000 M-1 cm-1 at 310 nm) in extinction coefficient subsequent to thiol addition. CDDP reacted stoichiometrically with large molecular weight (greater than 11,000) protein thiols. However, with small molecular weight thiols (less than 500) the reaction was less than stoichiometric, indicating a significant degree of back-reaction. The forward and reverse rate constants have been estimated. The fact that the reaction is reversible enables CDDP to be used for the direct monitoring of the oxidation of small molecular weight thiols.     

The kinetics of glucose-fructose oxidoreductase from Zymomonas mobilis

Glucose-fructose oxidoreductase operates by a classic ping-pong mechanism with a single site for all substrates: glucose, fructose, gluconolactone and sorbitol. The Km values for these substrates were determined. The values of kcat are 200 s-1 and 0.8 s-1 for the forward and reverse directions respectively. The overall catalytic process consists of two half-reactions with alternate reduction of NADP+ and oxidation of NADPH tightly bound to the enzyme. Reduction of enzyme-NADP+ by glucose and oxidation of enzyme-NADPH by gluconolactone involve single first-order processes. The values of the rate constants at saturating substrate are 2100 s-1 and 8 s-1 respectively; deuterium isotope effects indicate that these are for the hydrogen transfer step. Oxidation of enzyme-NADPH by fructose is first order with a limiting rate constant of at least 430 s-1. The reaction of enzyme-NADP+ with sorbitol is biphasic, with rate constants for both phases less than 1 s-1. This behaviour is explained by a mechanism in which the slow cyclisation of the acyclic form of fructose follows its dissociation from the enzyme. The rate-determining steps for the overall reaction are probably dissociation of gluconolactone in the forward direction and hydrogen transfer from sorbitol to enzyme-bound NADP+ in the reverse direction.     

Temperature and pH dependence of the metarhodopsin I-metarhodopsin II kinetics and equilibria in bovine rod disk membrane suspensions

The kinetics of the relaxation of bleached bovine rod disk membrane suspensions from metarhodopsin I into the equilibrium between metarhodopsins I and II were determined at pHs between 5.9 and 8.1 and at temperatures between -1 and 15 degrees C. From these data, thermodynamic equations were generated by two-way linear regression that simultaneously describe the functional dependence on pH and temperature of the pseudo-first-order and true forward rate constants, the reverse and observed rate constants, and the equilibrium constant. Using these equations, we obtained the thermodynamic parameters and the apparent net proton uptake for the transitions from metarhodopsin I to metarhodopsin II and from metarhodopsin I to the activated intermediate. The reversibility of this equilibrium and the effect of aging of the preparation on the measured rate constants were investigated.     

A pulse-radiolysis study of the reduction of flavodoxin from Megasphaera elsdenii by viologen radicals. A conformational change as a possible regulating mechanism

Pulse-radiolysis experiments were performed on solutions containing methyl or benzyl viologen and flavodoxin. Viologen radicals are formed after the pulse. The kinetics of the reaction of these radicals with flavodoxin were studied. The kinetics observed depend strongly on the concentration of oxidized viologen. Therefore one must conclude that a relatively stable intermediate is formed after the reduction of flavodoxin. The midpoint potential of the intermediate state is -(480 +/- 30) mV, and is hardly dependent on the pH between 7 and 9.2. Due to a conformational change (k2 approximately equal to 10(5)S-1) the intermediate state decays to the stable semiquinone form of flavodoxin. The delta G of the conformational change at pH 8 is about 29 kJ mol -1 (0.3 eV). This means that the upper limit for the pK of N-5 in the semiquinone form will be 13. The activation energy of the conformational change is 43 kJ mol -1 (0.45 eV). The reaction between methyl viologen radicals and the semiquinone of flavodoxin can be described by a normal bimolecular reaction. The reaction is diffusion-controlled with a forward rate constant of (7 +/- 1) X 10(8) M -1S -1 (pH 8, I = 55 mM). The midpoint potential of the semiquinone/hydroquinone was found to be -(408 +/- 5) mV. A consequence of the intermediate state is that flavodoxin (Fld) could be reduced by a two-electron process, the midpoint potential of which should be located between -440 mV less than Em (Fld/FldH-) less than -290 mV. The exact value will depend on the delta G of the conformational change between the fully reduced flavodoxin with its structure in the oxidized form and the fully reduced flavodoxin with its structure in the hydroquinone form. The conditions are discussed under which flavodoxin could behave as a two-electron donor.