Optimizing the sensitivity of enzyme systems to perturbations from equilibrium

Algebraic derivations and numerical examples illustrate how metabolite pool sizes and enzyme rate constants influence the rate at which a multireactant enzyme system, initially poised in a near-equilibrium steady state, responds to small perturbations in the concentrations of the reactants. Certain enzymes, such as those employing the ordered bi bi catalytic mechanism, become relatively insensitive to perturbations when the reactants are all present at high concentrations. Other enzymes, such as those employing the ping-pong bi bi mechanism, are most sensitive to perturbations at high reactant concentrations. The ratio of the reactant concentrations to one another significantly alters sensitivity to perturbations; equations are presented for calculation of the reactant concentrations yielding maximal sensitivity to perturbations. Natural selection could choose metabolite pool sizes and enzyme rate constants which would optimize the performance of these systems, but changing metabolic loads (naturally or experimentally imposed) constantly alter the sensitivity of these systems to perturbations, changing the relative strengths of various connections in metabolic control networks.     

Kinetic coupling between protein folding and prolyl isomerization. I. Theoretical models.

Kinetic models were developed to describe the influence of prolyl peptide bond isomerization on the kinetics of reversible protein folding for cases in which structural intermediates do not occur. In the simulations, the number of prolyl residues and the relative rates of folding and isomerization were varied. The experimentally observed rate constants were found to be identical with the intrinsic rate constants of folding and isomerization only when folding remains much faster than prolyl isomerization throughout the transition region. When the rate of folding becomes similar to or lower than the rate of isomerization, the observed kinetic parameters are complex functions of all microscopic rate constants. In particular, the observed folding rates in the transition region decrease with the number of prolyl residues. Pseudo two-state kinetics with single folding and unfolding reactions are observed in several cases, although the apparent folding rates depend strongly on prolyl isomerization reactions in the unfolded chain. This virtual simplicity can easily lead to misinterpretation of kinetic data. Additional phases can be resolved when refolding is started from the fast-folding species (UF). The coupling between folding and prolyl peptide bond isomerization also modifies the dependence on denaturant concentration of the apparent rate constants of folding. We suggest several tests to detect and characterize the contributions of folding and isomerization steps to the observed folding kinetics.     

Slow,Reversible, Coupled Folding and Binding of the Spectrin Tetramerization Domain

Many intrinsically disordered proteins (IDPs) are significantly unstructured under physiological conditions. A number of these IDPs have been shown to undergo coupled folding and binding reactions whereby they can gain structure upon association with an appropriate partner protein. In general, these systems display weaker binding affinities than do systems with association between completely structured domains, with micromolar K_d values appearing typical. One such system is the association between α- and β-spectrin, where two partially structured, incomplete domains associate to form a fully structured, three-helix bundle, the spectrin tetramerization domain. Here, we use this model system to demonstrate a method for fitting association and dissociation kinetic traces where, using typical biophysical concentrations, the association reactions are expected to be highly reversible. We elucidate the unusually slow, two-state kinetics of spectrin assembly in solution. The advantages of studying kinetics in this regime include the potential for gaining equilibrium constants as well as rate constants, and for performing experiments with low protein concentrations. We suggest that this approach would be particularly appropriate for high-throughput mutational analysis of two-state reversible binding processes.     

Determination of thermodynamics and kinetics of RNA reactions by force

Single-molecule methods have made it possible to apply force to an individual RNA molecule. Two beads are attached to the RNA; one is on a micropipette, the other is in a laser trap. The force on the RNA and the distance between the beads are measured. Force can change the equilibrium and the rate of any reaction in which the product has a different extension from the reactant. This review describes use of laser tweezers to measure thermodynamics and kinetics of unfolding/refolding RNA. For a reversible reaction the work directly provides the free energy; for irreversible reactions the free energy is obtained from the distribution of work values. The rate constants for the folding and unfolding reactions can be measured by several methods. The effect of pulling rate on the distribution of force-unfolding values leads to rate constants for unfolding. Hopping of the RNA between folded and unfolded states at constant force provides both unfolding and folding rates. Force-jumps and force-drops, similar to the temperature jump method, provide direct measurement of reaction rates over a wide range of forces. The advantages of applying force and using single-molecule methods are discussed. These methods, for example, allow reactions to be studied in non-denaturing solvents at physiological temperatures; they also simplify analysis of kinetic mechanisms because only one intermediate at a time is present. Unfolding of RNA in biological cells by helicases, or ribosomes, has similarities to unfolding by force.     

Sexual dimorphism in canine shape among extant great apes

There have been numerous attempts to sex fossil specimens using the canine dentition. Whether focused on canine size or canine shape, most of these efforts share two deficiencies: lack of quantification of male-female differences in the adopted criteria and a failure to adequately explore among extant species the discriminatory power of these criteria. Here, canine shape indices relating to relative canine height, upper canine root/crown proportionality, and relative length of the lower canine mesial ridge were calculated for males and females of all species and subspecies of extant great apes and two species of gibbons. The accuracy of these indices for identifying the sex of the extant ape specimens was investigated through discriminant analysis and the use of bivariate plots of the two upper and two lower canine indices. The indices were found to be highly accurate in identifying the sex of great ape individuals, not only in single-species and subspecies samples but in mixed-species samples as well; assignment error rates were mostly between 0 and 4%. Accuracy was lowest in Pan (error rates as high as 15%) and highest in Pongo (one error). In most cases, error rates were lower in the upper canines. The effectiveness of these shape indices for sexing might be related to the degree of absolute canine size dimorphism; the indices did not effectively segregate males and females among minimally canine-dimorphic gibbons. The mixed-species results reveal that same-sex index values are remarkably concordant across great ape species, as are the patterns of spatial segregation of males and females in the bivariate plots. Results suggest that, while the indices can be used with some confidence to sex individual fossil specimens, their greatest utility will be for identifying the sex of groups of canines united by size and morphology. © 1995 Wiley-Liss, Inc.     

Kinetic and equilibrium studies of the reactions of heme-substituted horse heart myoglobins with oxygen and carbon monoxide.

In order to study the effects of chemical modifications of the vinyl groups of heme on oxygen and carbon monoxide binding to myoglobin, apomyoglobins from horse heart were reconstituted with six different hemins with various side chains. Laser flash photolysis experiments of these reconstituted myoglobins showed that the combination rate constants for oxygen (k') and carbon monoxide (l') were closely related to the electron-attractive properties of the side chains. The k' values obtained in 0.1 M potassium phosphate buffer, pH 7.0, at 20 degrees were 0.83 (meso-), 2.4 (deutero-), 1.1 (reconstituted proto-), 1.2 (native proto-), 1.5 (2-formyl-4-vinyl-), 1.9 (2-vinyl-4-formyl-), and 2.7 X 10(7) M-1 S-1 (2,4-diformylmyoglobins), and the corresponding l' values were 2.8, 18, 4.8, 5.1, 7.1, 15, and 35 X 10(5) M-1 S-1, respectively. These rate constants tend to increase as the electron-withdrawing power of the side chains increases, indicating that reduced electron density of the iron atom of heme in myoglobin favors the combination reaction for both oxygen and carbon monoxide. Equilibrium constants (L) between carbon monoxide and various myoglobins were also determined by measuring the partition coefficients (M) between oxygen and carbon monoxide for the myoglobins, and were also found to be closely related to the electronic properties (pK3 of porphyrin) of the heme side chains. The equilibrium association constants for carbon monoxide thus obtained increased with a decrease in pK3 value of the porphyrin. This order was completely opposite to the case of the oxygen binding reaction. The dissociation rate constants for oxygen (k) and carbon monoxide (l) were calculated from the equilibrium and the combination rate constants. The dissociation rate constants showed a similar characteristic to the combination rate constants and increased with the increase in electron attractivity of heme side chains. The concomitant increase in both the combination and dissociation rate constants with increase in electronegativity of the iron atom suggests that these reactions have different rate determining steps, although such a reaction process is contradictory to the generally accepted concept that in a reversible reaction, both on and off reactions proceed through the same transition state. In the on reaction sigma bond formation appears to be dominant, while in the off reaction eta bond break-up is more important.     

On the Specificity of Allopurinol and Oxypurinol as Inhibitors of Xanthine Oxidase. A Pulse Radiolysis Determination of Rate Constants for Reaction of Allopurinol and Oxypurinol with Hydroxyl Radicals

Allopurinol has been employed as a “specific” inhihitor of xanthine oxidase in studies of hypoxic/ reoxygenation injury. Pulse radiolysis was used to establish rate constants for the reactions of allopurinol and its major metabolite oxypurinol with hydroxyl radicals: values were (1.45 ± 0.241 × 10⁹ M^-1 s^-1 for allopurinol and (4.95 ± 0.84) × 10⁹ M^-1 s^-1 for oxypurinol. These rate constants show that, in view of the amounts of allopurinol that have been used in animal studies. hydroxyl radical scavenging by this molecule could contribute to its biological actions. especially if animals are pre-treated with allopurinol. so allowing oxypurinol to form. The ability of allopurinol to protect tissues not containing xanthine oxidase against reoxygenation injury may be related to radical scavenging by allopurinol and oxypurinol.     

Kinetic parameters of enzymatic reactions in states of maximal activity; an evolutionary approach

A theoretical investigation is presented which allows the calculation of states of maximal reaction rates for single enzymes and for unbranched enzymatic chains. As an extension to previous papers (Heinrich & Holzhütter, 1985, Biomed. biochim. Acta 44, 959-969; Heinrich et al., 1987, Bull. math. Biol. 49, 539-595) a detailed enzymatic mechanism was taken into consideration. Conclusions are drawn for the optimal values of the microscopic rate constants as well as of the maximal activities and Michaelis constants. Ten solutions are found which depend on the equilibrium constant as well as on the concentrations of substrates and products. It is shown that for high equilibrium constants one of the solutions applies to a very large range of the concentrations of the outer reactants. This solution is characterized by maximal values of the rate constants of all forward reactions and by non-maximal values of the rate constants of all backward reactions. In contrast to previous assumptions (Albery & Knowles, 1976b, Biochemistry 15, 5631-5640; Burbaum et al., 1989, Biochemistry 28, 9293-9305) states of maximal reaction rate are not always characterized by the highest possible values of the second-order rate constants which are related to the diffusion of the substrate and the product to the active site of the enzyme. Predictions are made concerning the ratios of maximal activities in optimal states as well as for the adaptation of the Michaelis constants to the concentrations of the outer reactants. Using metabolic control analysis it is shown that the solutions obtained for single enzymes may also be applied in multi-enzyme systems.     

Study of the photocycle and charge motions of the bacteriorhodopsin mutant D96N.

Absorption kinetic and electric measurements were performed on oriented purple membranes of D96N bacteriorhodopsin mutant embedded in polyacrylamide gel and the kinetic parameters of the photointermediates determined. The rate constants, obtained from fits to time-dependent concentrations, were used to calculate the relative electrogenicity of the intermediates. The signals were analyzed on the basis of different photocycle models. The preferred model is the sequential one with reversible reaction. To improve the quality of the fits the necessity of introducing a second L intermediate arose. We also attempted to interpret our data in the view of reversible reactions containing two parallel photocycles, but the pH dependencies of the rate constants and electrogenicities favored the model containing sequential reversible transitions. A fast equilibrium for the L2<==>M1 transition and a strong pH dependence of the M2 electrogenicity was found, indicating that the M1 to M2 transition involves complex charge motions, as is expected in a conformational change of the protein.     

Interrelationship among specific rates of cell growth,substrate consumption,and metabolite formation in some simple microbial reactions producing primary metabolites

Applying the carbon balance principle, the interrelationship between ν = μ/Y + m (μ is the specific growth rate of microorganism, v is the specific substrate consumption rate) and π = Aμ B (Luedeking–Piret eqyuation, π is the specific metabolite formation rate) has been established for three types of simple microbial reactions. Equations for the kinetic parameters A and B have been proposed for each of the three types of microbial reactions, Expresses in terms of γ_x, γ_s and γ_p (carbon contents of dry cell, mass, major carbon energy source, and metabolite) as well as the parameters Y and m. Values of both A and B calculated from the proposed equations were compared with their experimental data for lactic acid fragmentation, aerobic SCP production, and alcohol fermentation. The estimated values agreed with the observed ones with reasonably small deviations.     

Kinetic studies of reactions of iron(IV)-oxo porphyrin radical cations with organic reductants

Iron(IV)-oxo porphyrin radical cations are observed intermediates in peroxidase and catalase enzymes, where they are known as Compound I species, and the putative oxidizing species in cytochrome P450 enzymes. In this work, we report kinetic studies of reactions of iron(IV)-oxo porphyrin radical cations that can be compared to reactions of other metal-oxo species. The iron(IV)-oxo radical cations studied were those produced from 5,10,15,20-tetramesitylporphryinato-iron(III) perchlorate (1), 5,10,15,20-tetramesitylporphryinato-iron(III) chloride (2), both in CH(3)CN solvent, and that from 5,10,15,20-tetrakis(pentafluorophenyl)porphyrinato-iron(III) perchlorate (3) in CH(2)Cl(2) solvent. The substrates studied were alkenes and activated hydrocarbons diphenylmethane and ethylbenzene. For a given organic reductant, various iron(IV)-oxo porphyrin radical cations react in a relatively narrow kinetic range; typically the second-order rate constants vary by less than 1 order of magnitude for the oxidants studied here and the related oxidant 5,10,15,20-tetrakis(pentafluorophenyl)porphyrinato-iron(IV)-oxo porphyrin radical cation in CH(3)CN solvent. Charge transfer in the transition states for epoxidation reactions of substituted styrenes by oxidants 1 and 2, rho(+) values of -1.9 and -0.9, respectively, mirrors results found previously for related species. Competition kinetic reactions with a catalytic amount of porphyrin iron(III) species and a terminal oxidant give relative rate constants for oxidations of competing substrates that are somewhat smaller than the ratios of absolute rate constants. Water in CH(3)CN solutions has an apparent modest stabilizing effect on oxidant 1 as indicated in slightly reduced rate constants for oxidation reactions. The iron(IV)-oxo porphyrin radical cations are orders of magnitude less reactive than porphyrin-manganese(V)-oxo cations and a corrole-iron(V)-oxo species. The small environment effects found here suggest that high energy demanding hydrocarbon oxidation reactions catalyzed by cytochrome P450 enzymes might require highly reactive iron(V)-oxo transients as oxidants instead of the more stable, isomeric iron(IV)-oxo porphyrin radical cations.     

喀斯特天然林植物多样性指数和土壤理化指标的相关性

植物多样性的土壤生态系统功能是喀斯特生态学研究的热点之一。在贵州省茂兰国家级自然保护区不同功能区(干扰等级)内采用野外样地调查和实验室分析相结合的方法,分析了41个喀斯特森林样地的植物多样性指数和土壤理化指标值的变化规律与相关性。结果表明:(1)依据乔木层物种重要值聚类法划分的5个喀斯特森林类型包括小叶栾树-青冈栎林、香叶树-枫香林、香椿-香叶树林、灯台-小花梾木林和檵木-马尾松林,由核心区、缓冲区、实验区至外缘区,乔木层植物多样性指数、林地岩石裸露率、土壤蓄水量、肥力及养分指标呈降低趋势。(2)因子分析表明不同层片植物多样性和不同土层土壤理化因子的相关趋势性各异。相关显著的因子对数量率呈乔木灌木草本的趋势,乔木植物多样性因子起主导作用。(3)喀斯特森林乔木层植物多样性指数和土壤理化指标的相关性分3种类型。直线型是植物多样性指数和土壤理化指标值相关性中较普遍的一类,相应指标对数量率为39.84%;曲线型是植物多样性指数和土壤理化指标值相关性中机理较复杂的一类,相应指标对数量率为46.10%,其中植物多样性指数有拐点值无生态意义的指标对数量率为11.72%,有拐点值有生态意义且呈先降后升、或先升后降趋势的指标对数量率分别为17.19%;无关型是植物多样性指数和土壤理化指标值相关性不显著,相应指标对数量率为54.69%。(4)喀斯特地区水土资源管理为目标的营林措施中,天然林乔木层植物多样性指数对土壤物理、肥力和养分指标响应的拐点值可成为人工造林中物种数量与株数比例选择的参考依据之一。     

Oxygen dependence of the kinetics of nonenzymatic lipid peroxidation

Kinetics of lipid peroxidation was considered theoretically taking into account a reversible pattern of peroxide radical formation. It has been shown that at reasonable values of the reactions rate constants discrepancy between oxygen absorption and the expenditure of polyunsaturated fatty acids can be explained. The PL equation system was written for an open system, its parametric analysis was carried out and the limit of autooscillation regime existence in relation to the rates of lipids additions and oxygen concentration were found.     

Evaluation of different approaches for modelling individual tree seedling height growth

We compared different approaches for modelling height growth of individual beech seedlings in a controlled factorial experiment as well as in field data from naturally regenerated beech seedlings under the canopy of overstorey mature beech trees. Several competition indices, a model of overstorey fine root density, relative photosynthetically active radiation (PAR) values, and soil water values were used in these approaches. In the factorial experiment relative PAR and soil water content were measured and used for the prediction of seedlings height growth. In the field experiment this was done by using relative PAR and estimated fine root biomass as a surrogate for below ground resource availability. The latter approach was compared with a model where we used various competition indices representing the impact of overstorey trees on beech seedlings. Our results suggested that (1) models which combine resource based growth functions are suitable for the prediction of individual height growth of beech seedlings. Resource based models offer the opportunity to investigate on the independent multiplicative effect of irradiance and water supply and their interactions on tree seedlings. It was (2) shown that a combined model could be used not only to predict individual height growth of beech seedlings in a controlled experiment but also in the field. The model parameters of a pure light response function for the controlled factorial experiment are comparable to those obtained in the field study. The results showed (3) that the precision of predicting beech seedlings height growth is comparable between the model types tested within this study. Approximately half of the observed variation in seedlings relative height growth rate could be explained. However, the simple competition index approach provides no information on the environmental factors constraining tree seedlings growth; whereas the multiplicative combined models can be used to get a better understanding of growth dynamics in the field.     

短花针茅荒漠草原α多样性对绵羊载畜率的响应

以短花针茅(Stipa breviflora)荒漠草原为研究对象,采用巢式样方法分析在不同绵羊载畜率下草地的α多样性以及物种组成的变化,探讨荒漠草原生态系统在放牧利用下α多样性对载畜率的响应。结果表明:物种数和α多样性指数随着载畜率的升高而下降。放牧会减少群落非优势物种的相对多度,非优势物种能够反映α多样性。40 m~2为短花针茅荒漠草原多样性研究的最佳取样面积。种-面积关系以及α多样性指数-面积关系符合对数增长模型:y=aln(x)+b。随着取样面积尺度的增加,α多样性指数沿载畜率梯度差异性逐渐增大,在取样面积为0.16 m~2到0.64 m~2时可以体现中、高载畜率和零、低载畜率水平间的差异性,在160 m~2时可以体现各载畜率水平之间的差异显著性。     

Application of Marcus theory of electron transfer for the reactions between HRP compound I and II and 2,4-disubstituted phenols

Reactions between horseradish peroxidase (HRP) compound I and II and some natural phenolic antioxidants were studied at pH 7. The bimolecular rate constants for these reactions were determined using a sequential mixing stopped-flow spectrometer. The rate constants for the reactions of compound I were found to be two orders of magnitude higher than those for compound II. The phenols under study showed a significant difference in their one-electron reduction potential values. As the rate constants also changed systematically with their one-electron potentials, the Marcus theory of electron transfer was applied to the above determined rate constants and the thermodynamic driving force (deltaG(o)), from which the reorganization energy (lambda) for the electron transfer from phenols to both compound I and II was estimated.     

On the Specificity of Allopurinol and Oxypurinol as Inhibitors of Xanthine Oxidase. A Pulse Radiolysis Determination of Rate Constants for Reaction of Allopurinol and Oxypurinol with Hydroxyl Radicals

Allopurinol has been employed as a “specific” inhihitor of xanthine oxidase in studies of hypoxic/ reoxygenation injury. Pulse radiolysis was used to establish rate constants for the reactions of allopurinol and its major metabolite oxypurinol with hydroxyl radicals: values were (1.45 ± 0.241 × 10⁹ M^-1 s^-1 for allopurinol and (4.95 ± 0.84) × 10⁹ M^-1 s^-1 for oxypurinol. These rate constants show that, in view of the amounts of allopurinol that have been used in animal studies. hydroxyl radical scavenging by this molecule could contribute to its biological actions. especially if animals are pre-treated with allopurinol. so allowing oxypurinol to form. The ability of allopurinol to protect tissues not containing xanthine oxidase against reoxygenation injury may be related to radical scavenging by allopurinol and oxypurinol.     

Nutritional indices in the gypsy moth (Lymantria dispar (L.)) under field conditions and host switching situations

A large proportion of gypsy moths (Lymantria dispar (L.)) are likely to experience multiple species diets in the field due to natural wandering and host switching which occurs with these insects. Nutritional indices in fourth and fifth instar gypsy moth larvae were studied in the field for insects that were switched to a second host species when they were fourth instars. The tree species used as hosts were northern pin oak (Quercus ellipsoidalis E. J. Hill), white oak (Q. alba L.), big-tooth aspen (Populus grandidentata Michx.), and trembling aspen (P. tremuloides Michx.). Conclusions of this study include: 1) Insects which fed before the host switch on northern pin oak performed better after the host switch than did insects with other types of early dietary experience. While the northern pin oak-started insects had very low relative food consumption rates on their second host species immediately after the switch, one instar later they had the highest ranked consumption rates. During both instars they had the second highest efficiencies of converting ingested and digested food to body mass. High food consumption rates and relatively high efficiency of food conversion helped these insects to obtain the highest ranked mean relative growth rates in the fifth instar compared to the relative growth rates obtained by insects from any of the other first host species. 2) Among the four host species examined, a second host of trembling aspen was most advantageous for the insects. Feeding on this species after the switch led to higher larval weights and higher relative growth rates for insects than did any of the other second host species. The insects on trembling aspen attained excellent growth despite only mediocre to low food conversion efficiencies. The low efficiencies were offset by high relative food consumption rates. 3) Low food consumption rates often tend to be paired with high efficiency of conversion and vice versa. 4) There is no discernable tendency for the first plant species eaten to cause long-term inductions which affect the ability of gypsy moths to utilize subsequent host plants. Insects did not tend to consume more, grow faster, or be more efficient if their second host plant was either the same as their rearing plant or congeneric to it. Methods are delineated which allow values of nutritional indices to be obtained for insects on intact host plants under field conditions. These methods are useful for the purpose of answering questions about the relative effects that different diet treatments have on insect response.     

An evolutionary approach to enzyme kinetics: Optimization of ordered mechanisms

A theoretical investigation is presented which allows the calculation of rate constants and phenomenological parameters in states of maximal reaction rates for unbranched enzymic reactions. The analysis is based on the assumption that an increase in reaction rates was an important characteristic of the evolution of the kinetic properties of enzymes. The corresponding nonlinear optimization problem is solved taking into account the constraint that the rate constants of the elementary processes do not exceed certain upper limits. One-substrate-one-product reactions with two, three and four steps are treated in detail. Generalizations concern ordered uni-uni-reactions involving an arbitrary number of elementary steps. It could be shown that depending on the substrate and product concentrations different types of solutions can be found which are classified according to the number of rate constants assuming in the optimal state submaximal values. A general rule is derived concerning the number of possible solutions of the given optimization problem. For high values of the equilibrium constant one solution always applies to a very large range of the concentrations of the reactants. This solution is characterized by maximal values of the rate constants of all forward reactions and by non-maximal values of the rate constants of all backward reactions. Optimal kinetic parameters of ordered enzymic mechanisms with two substrates and one product (bi-uni-mechanisms) are calculated for the first time. Depending on the substrate and product concentrations a complete set of solutions is found. In all cases studied the model predicts a matching of the concentrations of the reactants and the corresponding Michaelis constants, which is in good accordance with the experimental data. It is discussed how the model can be applied to the calculation of the optimal kinetic design of real enzymes.     

A novel method for determining rate constants for dehydration of aldehyde hydrates

A method has been developed for calculating rate constants for dehydration of aldehydes that induce ATPase reactions by kinases and where 18O is transferred from the aldehyde or its hydrate to inorganic phosphate during the reaction. The method involves measurement of the fraction of 18O in phosphate by 31P NMR after the ATPase reaction has proceeded for several minutes with zero-order kinetics. The reaction is started by addition of the aldehyde in a small volume of H2 18O, and the speed of washout of 18O by reversible dehydration relative to the rate of the ATPase reaction allows calculation of the rate constants if the hydration equilibrium constant is known from the proton NMR spectrum of the aldehyde. Dehydration rate constants (s-1 at pH 8-8.5, 0.1 M buffer, 25 degrees C) for the following aldehydes (all over 95% hydrated) and kinases used are as follows: D-glyceraldehyde with glycerokinase, 0.03; 2,5-anhydro-D-mannose 6-phosphate with fructose-6-phosphate kinase, 0.025; 2,5-anhydro-D-mannose or 2,5-anhydro-D-talose with fructokinase, 0.029 and 0.017, respectively; D-gluco-hexodialdose with hexokinase, 0.068. With betaine aldehyde and choline kinase or glyoxylate and pyruvate kinase, no 18O was transferred to phosphate during the ATPase reactions. However, the dehydration rate constant for glyoxylate (0.007 s-1 at pH 7 extrapolated to zero buffer concentration and up to 0.11 s-1 at pH 9.0 with 0.3 M buffer) was determined by extrapolating the initial rate of reduction of the free aldehyde catalyzed by lactate dehydrogenase to infinite enzyme levels.(ABSTRACT TRUNCATED AT 250 WORDS)