Reaction path of phosphofructo-1-kinase is altered by mutagenesis and alternative substrates

Escherichia coli phosphofructokinase (PFK) has been proposed to have a random, nonrapid equilibrium mechanism that produces nonallosteric ATP inhibition as a result of substrate antagonism. The consequences of such a mechanism have been investigated by employing alternative substrates and mutants of the enzyme that produce a variety of nonallosteric kinetic patterns demonstrating substrate inhibition and sigmoid velocity curves. Mutations of a methionine residue in the sugar phosphate binding site produced apparent cooperativity in the interaction of fructose 6-phosphate. Cooperativity could also be seen with native enzyme using a poorly binding substrate, fructose 1-phosphate. With an alternative nucleotide, 1-carboxymethyl-ATP, coupled with a mutation that introduced a negative charge in the nucleotide binding site, one could observe substrate inhibition by fructose 6-phosphate and apparent cooperativity in the interaction with nucleotide. Furthermore, the use of a phosphoryl donor, gamma-thiol-ATP, which greatly reduced the catalytic rate, apparently facilitated the equilibration of all binding reactions and eliminated ATP inhibition. These unusual kinetic patterns could be interpreted within the random, steady-state model as reflecting changes in the rates of particular binding and catalytic events.     

Role of nutrient supply on cell growth in bioreactor design for tissue engineering of hematopoietic cells

In the present study, a dynamic mathematical model for the growth of granulocyte progenitor cells in the hematopoietic process is developed based on the principles of diffusion and chemical reaction. This model simulates granulocyte progenitor cell growth and oxygen consumption in a three-dimensional (3-D) perfusion bioreactor. Material balances on cells are coupled to the nutrient balances in 3-D matrices to determine the effects of transport limitations on cell growth. The method of volume averaging is used to formulate the material balances for the cells and the nutrients in the porous matrix containing the cells. All model parameters are obtained from the literature. The maximum cell volume fraction reached when oxygen is depleted in the cell layer at 15 days and is nearly 0.63, corresponding to a cell density of 2.25 x 10(8) cells/mL. The substrate inhibition kinetics for cell growth lead to complex effects with respect to the roles of oxygen concentration and supply by convection and diffusion on cell growth. Variation in the height of the liquid layer above the cell matrix where nutrient supply is introduced affected the relative and absolute amounts of oxygen supply by hydrodynamic flow and by diffusion across a gas permeable FEP membrane. Mass transfer restrictions of the FEP membrane are considerable, and the supply of oxygen by convection is essential to achieve higher levels of cell growth. A maximum growth rate occurs at a specific flow rate. For flow rates higher than this optimal, the high oxygen concentration led to growth inhibition and for lower flow rates growth limitations occur due to insufficient oxygen supply. Because of the nonlinear effects of the autocatalytic substrate inhibition growth kinetics coupled to the convective transport, the rate of growth at this optimal flow rate is higher than that in a corresponding well-mixed reactor where oxygen concentration is set at the maximum indicated by the inhibitory kinetics.     

Time-dependent elimination of substrates flowing through the liver or kidney

Established steady-state models of elimination of flowing substrates by Michaelis-Menten kinetics in the intact liver and kidney are extended to time-dependent situations. It is shown how time-dependent distributions of substrate concentration can be calculated using steady-state results and a knowledge of the motion of fluid through the organs. The result is simplest when time-dependence is due to changes in substrate concentrations at the inlet, for example following injection or infusion. The case of the liver is treated in greater detail, and includes an evaluation of the instantaneous overall elimination rate.     

Influence of oxygen and substrate concentrations on the ideal film thickness and the maximum overall substrate uptake rate in microbial film fermenters

The criterion for the oxygen limitation of substrate uptake in microbial film fermenters is expressed in terms of diffusion coefficients, utilization coefficients, and the free solution concentrations of substrate and oxygen. It is proposed that the ideal film thickness in such fermenters is equal to the penetration depth of the limiting substrate. The ideal film thickness is calculated, in terms of the parameters contained in the criterion for oxygen limitation, for three separate kinetic rate expressions. It is found that for the air–glucose–microbe system a simplified kinetic rate expression can be used and the region of dependence on two substrates is shown to be very limited. This is not true for other systems. Maximum uptake rates are calculated for a range of concentrations. Finally, it is shown that the procedure used can be generalized to determine the limiting substrate in a multisubstrate system and to calculate ideal film thickness and uptake rates for any pair of substrates where the kinetics of substrate uptake are known for the individual microorganism.     

Multiple steady-state phenomena within enzyme reactors: The enzyme reaction with two substrates

The theoretical dynamic characteristics of an isothermal continuous flow stirred tank enzyme reactor (CFSTER) operating on two substrates are investigated. Under certain conditions multiple steady states are possible; namely, with an enzyme which binds with the two substrates sequentially. The occurrence of multiple steady states is found to be primarily dictated by three dimensionless parameters which incorporate rate law constants. The global stability of certain steady states is examined by numerically solving the transient material balance on the CFSTER. The effect of recycle on the dynamics of an isothermal plug flow enzyme reactor (PFER) is also studied. A general conclusion indicated by this work is that any open isothermal reaction system wherein the reaction rate law passes through a maximum with increasing substrate concentration and where back mixing occurs with exhibit multiple steady-state behavior in some operating range.     

Requirements for Rapid Plasmid ColE1 Copy Number Adjustments: A Mathematical Model of Inhibition Modes and RNA Turnover Rates

The random distribution of ColE1 plasmids between the daughter cells at cell division introduces large copy number variations. Statistic variation associated with limited copy number in single cells also causes fluctuations to emerge spontaneously during the cell cycle. Efficient replication control out of steady state is therefore important to tame such stochastic effects of small numbers. In the present model, the dynamic features of copy number control are divided into two parts: first, how sharply the replication frequency per plasmid responds to changes in the concentration of the plasmid-coded inhibitor, RNA I, and second, how tightly RNA I and plasmid concentrations are coupled. Single (hyperbolic)- and multiple (exponential)-step inhibition mechanisms are compared out of steady state and it is shown how the response in replication frequency depends on the mode of inhibition. For both mechanisms, sensitivity of inhibition is “bought” at the expense of a rapid turnover of a replication preprimer, RNA II. Conventional, single-step, inhibition kinetics gives a sloppy replication control even at high RNA II turnover rates, whereas multiple-step inhibition has the potential of working with unlimited precision. When plasmid concentration changes rapidly, RNA I must be degraded rapidly to be “up to date” with the change. Adjustment to steady state is drastically impaired when the turnover rate constants of RNA I decrease below certain thresholds, but is basically unaffected for a corresponding increase. Several features of copy number control that are shown to be crucial for the understanding of ColE1-type plasmids still remain to be experimentally characterized. It is shown how steady-state properties reflect dynamics at the heart of regulation and therefore can be used to discriminate between fundamentally different copy number control mechanisms. The experimental tests of the predictions made require carefully planned assays, and some suggestions for suitable experiments arise naturally from the present work. It is also discussed how the presence of the Rom protein may affect dynamic qualities of copy number control.     

Redox potential dependence of photophosphorylation and electron transfer in continuous illumination of Rhodopseudomonas sphaeroides chromatophores

The rate of ethanol elimination in fed and fasted rats can be predicted based on the liver content of alcohol dehydrogenase (EC 1.1.1.1), the steady-state rate equation, and the concentrations of substrates and products in liver during ethanol metabolism. The specific activity, kinetic constants, and multiplicity of enzyme forms are similar in fed and fasted rats, although the liver content of alcohol dehydrogenase falls 40% with fasting. The two major forms of the enzyme were separated and found to have very similar kinetic properties. The rat alcohol dehydrogenase is subject to substrate inhibition by ethanol at concentrations above 10 mM and follows a Theorell-Chance mechanism. The steady-state rate equation for this mechanism predicts that the in vivo activity of the enzyme is limited by NADH product inhibition at low ethanol concentrations and by both NADH inhibition and substrate inhibition at high ethanol concentrations. When the steady-state rate equation and the measured concentrations of substrates and products in freeze-clamped liver of fed and fasted rats metabolizing alcohol are employed to calculate alcohol oxidation rates, the values agree very well with the actual rates of ethanol elimination determined in vivo.     

Mutating away from your enemies: The evolution of mutation rate in a host–parasite system

The rate at which mutations occur in nature is itself under natural selection. While a general reduction of mutation rates is advantageous for species inhabiting constant environments, higher mutation rates can be advantageous for those inhabiting fluctuating environments that impose on-going directional selection. Analogously, species involved in antagonistic co-evolutionary arms races, such as hosts and parasites, can also benefit from higher mutation rates. We use modifier theory, combined with simulations, to investigate the evolution of mutation rate in such a host–parasite system. We derive an expression for the evolutionary stable mutation rate between two alleles, each of whose fitness depends on the current genetic composition of the other species. Recombination has been shown to weaken the strength of selection acting on mutation modifiers, and accordingly, we find that the evolutionarily attracting mutation rate is lower when recombination between the selected and the modifier locus is high. Cyclical dynamics are potentially commonplace for loci governing antagonistic species interactions. We characterize the parameter space where such cyclical dynamics occur and show that the evolution of large mutation rates tends to inhibit cycling and thus eliminates further selection on modifiers of the mutation rate. We then find using computer simulations that stochastic fluctuations in finite populations can increase the size of the region where cycles occur, creating selection for higher mutation rates. We finally use simulations to investigate the model behaviour when there are more than two alleles, finding that the region where cycling occurs becomes smaller and the evolutionarily attracting mutation rate lower when there are more alleles.     

Stochastic environmental fluctuations drive epidemiology in experimental host–parasite metapopulations

Environmental fluctuations are important for parasite spread and persistence. However, the effects of the spatial and temporal structure of environmental fluctuations on host–parasite dynamics are not well understood. Temporal fluctuations can be random but positively autocorrelated, such that the environment is similar to the recent past (red noise), or random and uncorrelated with the past (white noise). We imposed red or white temporal temperature fluctuations on experimental metapopulations of Paramecium caudatum, experiencing an epidemic of the bacterial parasite Holospora undulata. Metapopulations (two subpopulations linked by migration) experienced fluctuations between stressful (5°C) and permissive (23°C) conditions following red or white temporal sequences. Spatial variation in temperature fluctuations was implemented by exposing subpopulations to the same (synchronous temperatures) or different (asynchronous temperatures) temporal sequences. Red noise, compared with white noise, enhanced parasite persistence. Despite this, red noise coupled with asynchronous temperatures allowed infected host populations to maintain sizes equivalent to uninfected populations. It is likely that this occurs because subpopulations in permissive conditions rescue declining subpopulations in stressful conditions. We show how patterns of temporal and spatial environmental fluctuations can impact parasite spread and host population abundance. We conclude that accurate prediction of parasite epidemics may require realistic models of environmental noise.     

Vitamin K-dependent carboxylase from calf liver: studies on the steady-state kinetic mechanism

The steady-state kinetic mechanism of vitamin K-dependent carboxylase from calf liver has been investigated by initial-velocity measurements with varying concentrations of two carboxylase substrates and constant, nonsaturating concentrations of the other two substrates. With all combinations of the varied substrates tested linear kinetics were obtained with lines intersecting on the left side of the 1/v axis in double-reciprocal plots. Thus the carboxylase has a sequential reaction mechanism which includes the quinternary complex of the enzyme with its four substrates. A mechanism with the ordered steady-state addition of all substrates to the enzyme accords well with the results. A totally random mechanism was excluded but the alternative possibility remained that part of the substrates are added in a rapid-equilibrium random reaction. Experiments with saturating constant concentrations of sodium bicarbonate and varying concentrations of the other substrates suggest that bicarbonate (CO2) is either the first or, more probably, the last substrate bound to the enzyme.     

Cultivation of Escherichia coli with mixtures of 3-phenylpropionic acid and glucose: steady-state growth kinetics.

The fate of pollutants in the environment is affected by the presence of easily degradable carbon sources. As a step towards understanding these complex interactions, a model system was explored: the degradation of mixtures of glucose (i.e., an easily degradable substrate) and 3-phenylpropionic acid (3ppa) (a model pollutant) by Escherichia coli ML 30 was studied systematically in carbon-limited continuous culture. The two substrates were always consumed simultaneously regardless of the dilution rate applied. Even at dilution rates higher than the maximum specific growth rate for 3ppa (0.35 +/- 0.05 h-1), the two carbon substrates were utilized together. When cells were grown at a constant dilution rate with different mixtures of 3ppa and glucose, in which 3ppa contributed between 5 and 90% of carbon substrate in the feed medium, the steady-state concentrations of 3ppa and glucose were approximately proportional to the ratio of the two substrates in the feed medium. When cells were cultivated at different dilution rates with a 1:1 mixture (based on carbon) of glucose and 3ppa, an overall maximum specific growth rate of 0.90 +/- 0.05 h-1 and a Monod substrate saturation constant for 3ppa (Ks) of 600 to 700 micrograms liter-1, similar to that measured during growth with 3ppa alone, fitted the experimentally determined steady-state 3ppa concentrations. However, due to the highly differing substrate affinity constants for 3ppa and glucose (Ks approximately 30 to 70 micrograms liter-1), the total steady-state carbon concentration in the culture at a constant dilution rate was determined mainly by the steady-state 3ppa carbon concentration, and it increased with increasing proportions of 3ppa in the feed medium.     

Shared kinase fluctuations between two enzymatic reactions

Kinases serve crucial roles in many cellular signaling pathways that process and transfer information. When signaling kinases phosphorylate two targets, these can serve as branch points that distribute information among two pathways. Responses to stimuli transmitted by activated kinases show high levels of cell-to-cell variation that influence cellular function. We ask how fluctuations around a steady state, due to kinase fluctuations and intrinsic noise, are distributed between two reactions with substrates phosphorylated by a shared kinase. We develop the formalism to answer this question and, for a realistic set of biological constants, we illustrate various features of fluctuations and relaxation times to a steady state. We find that the steady-state response determines the size and range in enzyme concentration of phosphorylated substrate fluctuations, and that the choice of an operating point can have a large impact on how shared kinase noise is distributed among two available pathways.     

Kinetic properties of Cellulomonas sp. purine nucleoside phosphorylase with typical and non-typical substrates: implications for the reaction mechanism

Phosphorolysis catalyzed by Cellulomonas sp. PNP with typical nucleoside substrate, inosine (Ino), and non-typical 7-methylguanosine (m7Guo), with either nucleoside or phosphate (Pd) as the varied substrate, kinetics of the reverse synthetic reaction with guanine (Gua) and ribose-1-phosphate (R1P) as the varied substrates, and product inhibition patterns of synthetic and phosphorolytic reaction pathways were studied by steady-state kinetic methods. It is concluded that, like for mammalian trimeric PNP, complex kinetic characteristics observed for Cellulomonas enzyme results from simultaneous occurrence of three phenomena. These are sequential but random, not ordered binding of substrates, tight binding of one substrate purine bases, leading to the circumstances that for such substrates (products) rapid-equilibrium assumptions do not hold, and a dual role of Pi, a substrate, and also a reaction modifier that helps to release a tightly bound purine base.     

A biochemically structured model for Saccharomyces cerevisiae.

A biochemically structured model for the aerobic growth of Saccharomyces cerevisiae on glucose and ethanol is presented. The model focuses on the pyruvate and acetaldehyde branch points where overflow metabolism occurs when the growth changes from oxidative to oxido-reductive. The model is designed to describe the onset of aerobic alcoholic fermentation during steady-state as well as under dynamical conditions, by triggering an increase in the glycolytic flux using a key signalling component which is assumed to be closely related to acetaldehyde. An investigation of the modelled process dynamics in a continuous cultivation revealed multiple steady states in a region of dilution rates around the transition between oxidative and oxido-reductive growth. A bifurcation analysis using the two external variables, the dilution rate, D, and the inlet concentration of glucose, S(f), as parameters, showed that a fold bifurcation occurs close to the critical dilution rate resulting in multiple steady-states. The region of dilution rates within which multiple steady states may occur depends strongly on the substrate feed concentration. Consequently a single steady state may prevail at low feed concentrations, whereas multiple steady states may occur over a relatively wide range of dilution rates at higher feed concentrations.     

The endonuclease Hje catalyses rapid, multiple turnover resolution of Holliday junctions

Holliday junction-resolving enzymes are ubiquitous, structure-specific endonucleases that resolve four-way DNA junctions by the introduction of paired nicks in opposing strands, and are required for homologous recombination, double-strand break repair, recombination-dependent restart of stalled or collapsed DNA replication forks, and phage DNA processing. Here, we present the first steady-state kinetic characterisation of a junction-resolving enzyme; the Hje endonuclease from Sulfolobus solfataricus. We demonstrate that substrate turnover by Hje is sequence-independent and limited largely by the rate of cleavage of the phosphodiester bonds of the bound Holliday junction substrate, rather than substrate association or product dissociation. Reaction rates under multiple turnover conditions compare favourably with type II restriction enzymes. These properties, coupled with a high level of specificity for four-way junctions over all other DNA substrates, make Hje a suitable enzyme for applications requiring the detection and cleavage of Holliday junctions in vitro.     

Differential, structure-dependent susceptibility of poly(A) and RNA to monomeric and dimeric pancreatic ribonuclease A.

Cross-linked dimers of bovine RNAase A are definitely more efficient than monomers at degrading polyadenylic acid under conditions of ionic strength and pH, where the polymer assumes either a double-helical or an ordered single-stranded, base-stacked structure. The opposite occurs, i.e., monomers of RNAase A are definitely more active than dimers,when poly(A) is digested by the two enzyme species under conditions where the conformation of the polymer is essentially that of a random coil. The same pattern of events occurs when total RNA from Escherichia coli or single-stranded RNA of f2 sus11 bacteriophage are used as substrates under opposite ionic-strength conditions. In the presence of high salt concentrations, favouring the formation and the stability of a secondary structure in self-complementary sequences of RNA, the ribonucleic acids are degraded at a higher rate by dimers than by monomers of bovine RNAase A. The opposite occurs in the presence of very low salt concentrations, i.e. when the RNAs are in solution presumably as random coils. These observations are discussed in the light of a hypothesis already advanced to understand the mechanism of enzymic degradation of secondary structures of polyribonucleotides.     

Mechanism of ketol acid reductoisomerase--steady-state analysis and metal ion requirement

Ketol acid reductoisomerase is an enzyme of the branched-chain amino acid biosynthetic pathway. It catalyzes two separate reactions: an acetoin rearrangement and a reduction. This paper reports on the purification of the enzyme from a recombinant Escherichia coli and on the steady-state kinetics of the enzyme. The kinetics of the reaction were determined for the forward and reverse reaction by using the appropriate chiral substrates. At saturating metal ion concentrations the mechanism follows an ordered pathway where NADPH binds before acetolactate. The product of the rearrangement of acetolactate, 3-hydroxy-3-methyl-2-oxobutyrate, is shown to be kinetically competent as an intermediate in the enzyme-catalyzed reaction. Starting with acetolactate, Mg2+ is the only divalent metal ion that will support enzyme catalysis. For the reduction of 3-hydroxy-3-methyl-2-oxobutyrate, Mn2+ is catalytically active. Product and dead-end inhibition studies indicate that the binding of metal ion and NADPH occurs randomly. In the forward reaction direction, the deuterium kinetic isotope effect on V/K is 1.07 when acetolactate is the substrate and 1.39 when 3-hydroxy-3-methyl-2-oxobutyrate is the substrate.     

Analysis of the mechanism of chloramphenicol acetyltransferase by steady-state kinetics. Evidence for a ternary-complex mechanism.

The mechanism of the enzymic reaction responsible for chloramphenicol resistance in bacteria was examined by steady-state kinetic methods. The forward reaction catalysed by chloramphenicol acetyltransferase leads to inactivation of the antibiotic. Use of alternative acyl donors and acceptors, as well as the natural substrates, has yielded data that favour the view that the reaction proceeds to the formation of a ternary complex by a rapid-equilibrium mechanism wherein the addition of substrates may be random but a preference for acetyl-CoA as the leading substrate can be detected. Chloramphenicol and acetyl-CoA bind independently, but the correlation between directly determined and kinetically derived dissociation constants is imperfect because of an unreliable slope term in the rate equation. The reverse reaction, yielding acetyl-CoA and chloramphenicol, was studied in a coupled assay involving citrate synthase and malate dehydrogenase, and is best described by a rapid-equilibrium mechanism with random addition of substrates. The directly determined dissociation constant for CoA is in agreement with that derived from kinetic measurements under the assumption of an independent-sites model.     

New patterns of mixed-substrate utilization during batch growth of Escherichia coli K12

Microbial growth on mixtures of substrates is of considerable engineering and biological interest. Most of the work until now has dealt with microbial growth on binary mixtures of sugars or polyols. In these cases, it is often found that no matter how the inoculum is precultured, only one of the two substrates is consumed in the first growth phase, leading to the diauxic growth pattern. The goal of the experiments reported here is to investigate growth on mixtures containing at least one organic acid. These experiments show that the substrate utilization patterns in such mixtures are qualitatively different from the diauxic growth pattern. For instance, during growth of Escherichia coli K12 on certain binary mixtures of organic acids, the two substrates are utilized simultaneously, and the mixed-substrate maximum specific growth rate exceeds the single-substrate maximum specific growth rate on either one of the two constituent substrates. Furthermore, the very same mixed-substrate maximum specific growth and substrate uptake rates are observed no matter how the inoculum is precultured. On the other hand, in a mixture of glucose and pyruvate, the maximum specific growth rate seems to depend on the preculturing conditions, thus suggesting the existence of multiple physiological quasi-steady states. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 55: 747-757, 1997.     

Substrate antagonism in the kinetic mechanism of E. coli phosphofructokinase-1.

In the presence of its allosteric activator GDP, the major phosphofructokinase-1 from Escherichia coli K12 follows Michaelis—Menten kinetics. The kinetic behavior observed at steady-state using different concentrations of the substrates ATP and fructose-6-phosphate and the pattern of inhibition by the substrate analogs adenylyl-(β,γ-methylene)-diphosphonate and D-arabinose-5-phosphate are consistent with a random sequential mechanism in rapid equilibrium, rather than with an ordered binding as was suggested earlier. However, ATP and fructose-6-phosphate do not bind independently to the same active site, since the apparent affinity for one substrate is decreased about 20-fold when the other substrate is already bound. The antagonism between ATP and fructose-6-phosphate shows that a negative interaction occurs during the reaction with E. coli phosphofructokinase-1 which must be considered in addition to its allosteric properties.