Steady state kinetic model for the binding of substrates and allosteric effectors to Escherichia coli phosphoribosyl-diphosphate synthase

A steady state kinetic investigation of the P(i) activation of 5-phospho-d-ribosyl alpha-1-diphosphate synthase from Escherichia coli suggests that P(i) can bind randomly to the enzyme either before or after an ordered addition of free Mg(2+) and substrates. Unsaturation with ribose 5-phosphate increased the apparent cooperativity of P(i) activation. At unsaturating P(i) concentrations partial substrate inhibition by ribose 5-phosphate was observed. Together these results suggest that saturation of the enzyme with P(i) directs the subsequent ordered binding of Mg(2+) and substrates via a fast pathway, whereas saturation with ribose 5-phosphate leads to the binding of Mg(2+) and substrates via a slow pathway where P(i) binds to the enzyme last. The random mechanism for P(i) binding was further supported by studies with competitive inhibitors of Mg(2+), MgATP, and ribose 5-phosphate that all appeared noncompetitive when varying P(i) at either saturating or unsaturating ribose 5-phosphate concentrations. Furthermore, none of the inhibitors induced inhibition at increasing P(i) concentrations. Results from ADP inhibition of P(i) activation suggest that these effectors compete for binding to a common regulatory site.     

Steady state model for evaluation of external and internal mass transfer effects in an immobilized biofilm

A steady model for the evaluation of external liquid film diffusion and internal pore diffusion effects in an immobilized biofilm system under continuous mode of operation was developed. The model takes into account, substrate diffusion through external liquid film and biofilm. Average rate of substrate consumption in the biofilm was considered. The overall efficiency of the biofilm was mathematically represented by considering the combined effects of substrate penetration and substrate utilization in the biofilm. The model was illustrated using a case study of pyridine biodegradation in a rotating biological contactor immobilized with pyridine degrading microbial film. The model is able to effectively predict both internal and external mass transfer effects in an immobilized biofilm system.     

Dynamics of Fst for the island model

F(st) is a measure of genetic differentiation in a subdivided population. Sewall Wright observed that F(st)=1/1+2Nm in a haploid diallelic infinite island model, where N is the effective population size of each deme and m is the migration rate. In demonstrating this result, Wright relied on the infinite size of the population. Natural populations are not infinite and therefore they change over time due to genetic drift. In a finite population, F(st) becomes a random variable that evolves over time. In this work we ask, given an initial population state, what are the dynamics of the mean and variance of F(st) under the finite island model? In application both of these quantities are critical in the evaluation of F(st) data. We show that after a time of order N generations the mean of F(st) is slightly biased below 1/1+2Nm. Further we show that the variance of F(st) is of order 1/d where d is the number of demes in the population. We introduce several new mathematical techniques to analyze coalescent genealogies in a dynamic setting.     

Exacting predictions by cybernetic model confirmed experimentally: Steady state multiplicity in the chemostat

We demonstrate strong experimental support for the cybernetic model based on maximizing carbon uptake rate in describing the microorganism's regulatory behavior by verifying exacting predictions of steady state multiplicity in a chemostat. Experiments with a feed mixture of glucose and pyruvate show multiple steady state behavior as predicted by the cybernetic model. When multiplicity occurs at a dilution (growth) rate, it results in hysteretic behavior following switches in dilution rate from above and below. This phenomenon is caused by transient paths leading to different steady states through dynamic maximization of the carbon uptake rate. Thus steady state multiplicity is a manifestation of the nonlinearity arising from cybernetic mechanisms rather than of the nonlinear kinetics. The predicted metabolic multiplicity would extend to intracellular states such as enzyme levels and fluxes to be verified in future experiments. © 2012 American Institute of Chemical Engineers Biotechnol. Prog., 2012     

Steady state terrestrial ecosystems and the global carbon cycle

The assumption that landscapes dominated by mature vegetation are presently in carbon steady state with the atmosphere is challenged. Evidence suggests that the vegetation and soils of these landscapes are frequently disturbed and over short time periods (<300 yr) slowly sequester atmospheric carbon. The critical consideration in this argument is the time interval used to evaluate a steady state. Current models of carbon flux through the terrestrial biota limit their time considerations to 120 yr, a short and inadequate time interval for realistic assumptions about steady state in the carbon cycle of vegetation.Research performed under subcontract 19B-07762C with S. Brown and 19X-43326C with the Center for Energy and Environment Research of the University of Puerto Rico (A. E. Lugo) under Martin Marietta Energy Systems, Inc., contract DE-AC05-840R21400 with the U.S. Department of Energy.     

Steady state osmotic adaptation inUlva lactuca

The effects of hyper- and hypo-saline stresses on the levels of various inorganic and organic solutes inUlva lactuca have been recorded. Hypoosmotic stress decreased the tissue concentration of K⁺, Na⁺ and Cl^- while hyper-osmotic stress caused a transient increase in Na⁺ and a stable accumulation of K⁺ and Cl^-. The tissue content of -dimethylsulphoniopropionate (-dimethylpropiothetin) responded to changes in salinity. The time course of hypersaline stress showed the -dimethylsulophoniopropionate concentration rose as the Na⁺ level fell. The levels of free sugars and amino acids, including proline, were relatively low in this alga and did not appear to be important in osmotic adjustment. The possibility that tertiary sulphonium dipolar ions have an analogous role in some algae to glycinebetaine and possibly other quaternary nitrogen compounds in higher plants as cytoplasmic osmotica is discussed briefly.Abbreviations DMSP -dimenthylsulphomiopropionate - AFT apparent free space - TLE thin layer electrophoresis - NPS ninhydrin positive substances - TLC thin layer chromatography     

Steady state and transient growth of autotrophic nitrifying bacteria

Growth of the autotrophic nitrifying bacteria Nitrosomonas europaea and Nitrobacter sp. was studied in continuous culture. Steady state growth kinetics of both organisms conformed with that predicted by chemostat theory, modified to account for maintenance energy requirement. Steady state data were used to calculate the maximum specific growth rate, the saturation constant for growth, the true growth yield and the maintenance coefficient. Transient growth was studied by imposing step changes in dilution rate. Step increases resulted in overshoots and oscillations in substrate concentration before establishment of a new steady state while step decreases in dilution rate were followed by monotonic changes in substrate concentration. The size of overshoots in substrate concentration following step increases in dilution rate was dependent on both the magnitude of the increase and of the dilution rate prior to the change.     

Steady state multiplicity and stability of enzymatic reaction systems

Several techniques for investigating the multiplicity and stability of open isothermal enzymatic reactors are discussed and some of the pitfalls in previous thinking pointed out. The example which is used to illustrate these methods exhibits several interesting features. Among these is the existence of a stable oscillatory state which surrounds a unique steady state which is asymptotically stable to certain finite disturbances.     

Steady state enzyme kinetics for systems with three enzyme-binding species

The steady state enzyme kinetics of those systems are discussed, which involve three species binding to enzymes. Two specific systems are considered. In one system, all three species bind only once to the enzyme. In the other system, two species bind once and one binds twice to the enzyme. The species are labeled S, A and B. The general case is considered, in which all possible complexes involving enzyme E and species S generate product P. Species A and B may become co-substrates, activators or inhibitors. The steady state enzyme kinetic equations for the general case for both systems are presented. These equations are further discussed for a number of special cases, which may be of interest to enzymologists and others using enzymes.     

Steady state and pre-steady state kinetic properties of rat liver selenium-glutathione peroxidase.

The kinetic properties of partially purified rat liver selenium-glutathione peroxidase were studied under various conditions. Steady state kinetic measurements show sigmoidal saturation curves, parabolic double reciprocal plots, and Hill coefficients greater than unity. Although these kinetic results appear to show cooperative interactions between subunits, they more reflect the presence of several oxidation-reduction forms of the catalytic site. A substrate-induced transition between enzyme forms was evidence by the occurrence of a lag in the attainment of the final steady state velocity under certain preincubation conditions. This hysteretic behavior was evident only when the enzyme was incubated in the absence of reduced glutathione, the donor substrate. Thus, reduced glutathione induces the transition to the fully active form of the enzyme, a slow process requiring about 0.5 min after addition of glutathione, depending on conditions. The length, tau, of the lag period is dependent on the concentrations of enzyme and glutathione, but to a first approximation, this lag period is independent of the concentration of the hydroperoxide acceptor substrate. The lag period is also relatively independent of the nature of the hydroperoxide species. A model for the transition process that is compatible with these observations and with the possible oxidation-reduction properties of the selenium moiety of the enzyme is suggested.     

Steady state bifurcation analysis of reaction-diffusion equations-A critique

This note supplies missing details and corrects some mathematical errors in the recent significant paper by Auchmuty and Nicolis (1975).     

Steady state proline levels in salt-shocked barley leaves

Excised barley (Hordeum vulgare var Larker) leaves were treated with salt solutions or wilted. After the treatment period, the leaves were allowed to recover in a 50 millimolar sucrose and 1 millimolar glutamate solution, and proline, Na⁺, and K⁺ were measured at intervals. Na⁺ and K⁺ concentrations stayed at a constant high level after the salt treatments, and proline increased to a steady state concentration in response. The relationship between the maximum rate of proline accumulation and the Na⁺ concentration reached in each experiment was linear. The final steady state proline concentration reached was also directly proportional to the Na⁺ concentration. For a given Na⁺ concentration in the leaves, the steady state proline level was greater when 410 millimolar NaCl was added to the leaves than when 205 millimolar NaCl was added. These results are consistent with proline acting as a compatible cytoplasmic solute, balancing an accumulation of salts outside of the cytoplasm.

In contrast to the proline levels in salt-shocked leaves, the concentrations in wilted leaves decreased to near control levels within 24 hours of relief of stress.

     

Steady state kinetics of pyruvate kinase from muscle]

The dependence of the forward pyruvate kinase reaction on the concentrations of ADP and Mg2+ was studied. It was shown that high total ADP concentrations (2-15 mM) exceeding total Mg2+ concentration in the medium lead to the inhibition of the pyruvate kinase reaction, whereas relatively high Mg2+ concentrations (up to 15 mM) do not cause any inhibition. The kinetics of the reaction can be described in the best way by a scheme incorporating the active PEP . E . Mg2+ . Mg . ADP complex and dead-end complexes containing free ADP. An analysis of the experimental data allows to determine all coefficients of the rate equation and to calculate the values of all kinetic parameters. The values of the constants obtained were used for mathematical simulation of the reaction on the basis of the kinetic scheme given. The mathematical model obtained describes satisfactorily the experimentally determined dependences, which is indicative of the correctness of the model.     

Steady state analysis of metabolic pathways using Petri nets

Computer assisted analysis and simulation of biochemical pathways can improve the understanding of the structure and the dynamics of cell processes considerably. The construction and quantitative analysis of kinetic models is often impeded by the lack of reliable data. However, as the topological structure of biochemical systems can be regarded to remain constant in time, a qualitative analysis of a pathway model was shown to be quite promising as it can render a lot of useful knowledge, e. g., about its structural invariants. The topic of this paper are pathways whose substances have reached a dynamic concentration equilibrium (steady state). It is argued that appreciated tools from biochemistry and also low-level Petri nets can yield only part of the desired results, whereas executable high-level net models lead to a number of valuable additional insights by combining symbolic analysis and simulation.     

Human hypoxanthine-guanine phosphoribosyltransferase. Steady state kinetics of the forward and reverse reactions

A steady state kinetic study of the hypoxanthine-guanine phosphoribosyltransferase-catalyzed reaction in the forward and the reverse directions was carried out. The results obtained favor a sequential mechanism where the monomagnesium complexes of IMP and PPi bind to the enzyme in a rapid equilibrium random fashion while products must dissociate from the enzyme in ordered sequence, first the purine base and then the magnesium complex(es) of P-Rib-PP.     

A generalized model of island biogeography

MacArthur and Wilson’s equilibrium theory is one of the most influential theories in ecology. Although evolution on islands is to be important to island biodiversity, speciation has not been well integrated into island biogeography models. By incorporating speciation and factors influencing it into the MacArthur-Wilson model, we propose a generalized model unifying ecological and evolutionary processes and island features. Intra-island speciation may play an important role in both island species richness and endemism, and the contribution of speciation to local species diversity may eventually be greater than that of immigration under certain conditions. Those conditions are related to the per species speciation rate, per species extinction rate, and island features, and they are independent of immigration rate. The model predicts that large islands will have a high, though not the highest, proportional endemism when other parameters are fixed. Based on the generalized model, changes in species richness and endemism on an oceanic island over time were predicted to be similar to empirical observations. Our model provides an ideal starting point for re-evaluating the role of speciation and re-analyzing available data on island species diversity, especially those biased by the MacArthur-Wilson model.