Computer model for glucose-limited growth of a single cell of Escherichia coli B/r-A

A computer model is described which is capable of predicting changes in cell composition, cell size, cell shape, and the timing of chromosome synthesis in response to changes in external glucose limitation. The model is constructed primarily from information on unrestricted growth in glucose minimal medium. The ability of the model to make reasonable quantitative predictions under glucose-limitation is a test of the plausibility of the basic biochemical mechanisms included in the model. Such a model should be of use in differentiating among competing hypotheses for biological mechanisms and in suggesting as yet unobserved phenomena. The last two points are illustrated with the testing of a mechanism for the control of the initiation of DNA synthesis and predictions on cellwidth variations during the division cycle.     

Kinetic study of hybridoma cell growth in continuous culture. I. A model for non-producing cells

The kinetic behavior of a nonproducing hybridoma clone AFP-27-NP was investigated in continuous culture under glucose-limited conditions. A total of more than 21, 000 h of cultures were operated at dilution rates ranging from 0.01 to 0.06 h(-1). The viable cell concentrations, dead cell concentrations, and cell volumes all varied with the dilution rate. A steady-state model was developed based on the biomass concentration and the glucose concentration. The specific growth rate as a function of glucose concentration is described by a model similar to the Monod model with a threshold glucose concentration and a minimum specific growth rate incorporated; the model is meaningful only at glucose concentrations and specific growth rates above these levels. A death rate is included in the model which is described by an inverted Monod-type function of glucose concentration. The yield coefficient based on glucose is constant in the lower range of specific growth rates and changes to a new constant value in the upper region of specific growth rates. No maintenance term for glucose consumption was needed; in the plot of specific glucose consumption rate vs. specific growth rate, the line intercepted the specific growth rate axis at a value close to the minimum growth rate. The values for the model parameters were determined from regression analysis of the steady-state data. The model predictions and experimental results fit very well.     

Simulation of CFSTR through development of a mathematical model for anaerobic growth of Escherichia coli cell population

A computer model is described that simulates a population of Escherichia coli B/r-A cells growing under anaerobic conditions. This population model is an ensemble of single-cell models. The ability of the model of predict the dynamic response of a cell population in a CFSTR to a change in feed flowrates or concentrations was investigated. With glucose as the limiting nutrient the feed concentration of glucose was shifted from 1.0 to 1.88 g/L. With a fixed concentration of glucose (1.0 g/L) step changes in residence time (4.1-1.95 h) were examined. The predicted changes of cell size distribution, substrate concentration, RNA content, and cell dry weight during the transition period compared reasonably well to those observed experiementally. We believe this model is the only model currently available that can make such predictions on an a priori basis.     

A finite representation model for an asynchronous culture of E. coli

A computer model is described which models an asynchronous population of E. coli by using a large, but finite number of representative single cells. Asynchrony generation and maintenance occurs at the single cell level by modulating the activity of an enzyme responsible for septum formation. Such modulation introduces cycle time imprecision and does not require the introduction of any new parameters into the single-cell model. Based on comparisons to experiment, reasonable predictions are possible for changes of cellular dry weight during exponential growth and turbidostat washout, and overall chemostat cell yields and changes in cell number, glucose concentration, and cell size distribution for a chemostat subject to a step change in dilution rate. Additionally, a correlation between cell RNA content and size is predicted as is an inertial effect when chemostat residence time is decreased under conditions of initially high glucose concentrations. Limitations imposed by the model's finite nature and their solutions are discussed.     

Modeling of poly(3-hydroxybutyrate) production by high cell density fed-batch culture of R<Emphasis Type="Italic">alstonia eutropha</Emphasis>

High cell density culturing has been conducted for the production of poly(3-hydroxybutyrate) fed-batch cultures ofRalstonia eutropha with phosphate limitation. It was found that a high glucose concentration inhibited the synthesis of P(3HB) in the high cell density culture ofR. eutropha. Although a low glucose concentration can trigger the synthesis of P(3HB) in a manner similar to that of phosphate limitation, it also limited both the P(3HB) synthesis and the cell growth, and led to a low P(3HB) productivity because glucose is the sole carbon source in this reaction. An unstructured model was proposed for predicting the cell growth and P(3HB) synthesis in high cell density cultures ofR. eutropha, where the phosphate concentration played a key role in the accumulation of P(3HB) and in cell growth. Good agreements were found between the experimental data and model predictions. The results of simulation showed that the final P(3HB) concentration would decrease more than 25% when the glucose was concentration increased to 40 g/L, and indicated that the optimal glucose concentration for P(3HB) production by high cell density cultures ofR. eutropha was around 9 g/L.     

A mathematical model for the growth of a single cell of E. coli on a glucose/glutamine/ammonium medium

Extension of a single cell model of E. coli B/r to make predictions of culture response to variations in glutamine/glucose/ammonium ion concentrations is described. A biphasic glutamine transport system, a nitrogen metabolism scheme that includes glutamate dehydrogenase (GDH), glutamine synthetase/glutamate synthase (GS/GOGAT), the glutaminase routes, and a transaminase mechanism for glutamine carbon usage are added to the prototype model. The predictions of the extended model with regard to nutrient concentrations and cell size compare well with the experimental data and the prototype model predictions, demonstrating the capability of the integrated kinetic model to illustrate important enzymological interactions in a biological system. The discrepancies between the experimental data and the model predictions on growth yield suggest that a more detailed regulatory system of the TCA cycle is required for a more accurate energy budget.     

Cellular levels, excretion, and synthesis rates of cyclic AMP in Escherichia coli grown in continuous culture.

Changes in dilution rate did not elicit large and systematic changes in cellular cyclic AMP levels in Escherichia coli grown in a chemostat under carbon or phosphate limitation. However, the technical difficulties of measuring low levels of cellular cyclic AMP in the presence of a large background of extracellular cyclic AMP precluded firm conclusions in this point. The net rate of cyclic AMP synthesis increased exponentially with increasing dilution rate through either the entire range of dilution rates examined (phosphate limitation) or a substantial part of the range (lactose and glucose limitations). Thus, it is probable that growth rate regulates the synthesis of adenylate cyclase. The maximum rate of net cyclic AMP synthesis was greater under lactose than under glucose limitation, which is consistent with the notion that the uptake of phosphotransferase sugars is more inhibitory to adenylate cyclase than the uptake of other carbon substrates. Phosphate-limited cultures exhibited the lowest rate of net cyclic AMP synthesis, which could be due to the role of phosphorylated metabolites in the regulation of adenylate cyclase activity. Under all growth conditions examined, greater than 99.9% of the cyclic AMP synthesized was found in the culture medium. The function of this excretion, which consumed up to 9% of the total energy available to the cell and which evidently resulted from elaborate regulatory mechanisms, remains entirely unknown.     

Nutrient utilization by bovine articular chondrocytes: a combined experimental and theoretical approach

A combined experimental-numerical approach was adopted to characterize glucose and oxygen uptake and lactate production by bovine articular chondrocytes in a model system. For a wide range of cell concentrations, cells in agarose were supplemented with either low or high glucose medium. During an initial culture phase of 48 h, oxygen was monitored noninvasively using a biosensor system. Glucose and lactate were determined by medium sampling. In order to quantify glucose and oxygen uptake, a finite element approach was adopted to describe diffusion and uptake in the experimental model. Numerical predictions of lactate, based on simple relations for cell metabolism, were found to agree well for low glucose, but not for high glucose medium. Oxygen did not play a role in either case. Given the close association between chondrocyte energy metabolism and matrix synthesis, a quantifiable prediction of utilization can present a valuable contribution in the optimization of tissue engineering conditions.     

Metabolism of H2-CO2, methanol, and glucose by Butyribacterium methylotrophicum.

The fermentative metabolism of Butyribacterium methylotrophicum grown on either H2-CO2, methanol, glucose, or CO is described. The following reaction stoichiometries were obtained: 1.00 H2 + 0.52 CO2 leads to 0.22 acetate + 0.06 cell C; 1 methanol + 0.18 CO2 + 0.01 acetate leads to 0.24 butyrate + 0.29 cell C; and 1.00 glucose leads to 0.31 CO2 + 1.59 acetate + 0.21 butyrate + 0.13 H2 + 1.58 cell C. Cell yields of 1.7 g (dry weight) per mol of H2, 8.2 g (dry weight) per mol of methanol, 42.7 g (dry weight) per mol of glucose, and 3.0 g (dry weight) per mol of CO were obtained from linear plots of cell synthesis and substrate consumption. Doubling times of 9.0, 9.0, and 3 to 4 h were observed during batch growth on H2-CO2, methanol, and glucose, respectively. Indicative of a growth factor limitation, glucose fermentation in defined medium displayed a lower cell synthesis efficiency than when yeast extract (0.05%) was present. B. methylotrophicum fermentation displayed atypically high substrate/cell carbon synthesis conversion ratios for an anaerobe, as greater than 24% of the carbon was assimilated into cells during growth on methanol or glucose. The data indicate that B. methylotrophicum conserves carbon-bound electrons during growth on single-carbon or multicarbon substrates.     

Translational control of insulin biosynthesis. Evidence for regulation of elongation, initiation and signal-recognition-particle-mediated translational arrest by glucose.

The biosynthesis of insulin in the islets of Langerhans is strongly controlled at the translational level by glucose. We have used a variety of experimental approaches in efforts to dissect the mechanisms underlying the stimulatory effect of glucose. To assess its effects on rates of peptide-chain elongation, isolated rat islets were labelled with [3H]leucine at different glucose concentrations in the presence or absence of low concentrations of cycloheximide. Under these conditions, at glucose concentrations up to 5.6 mM, endogenous insulin mRNA did not become rate-limiting for the synthesis of insulin, whereas stimulation of non-insulin protein synthesis was abolished by cycloheximide at all glucose concentrations, indicating either that insulin synthesis is selectively regulated at the level of elongation at glucose concentrations up to 5.6 mM, or that at these concentrations inactive insulin mRNA is transferred to an actively translating pool. Glucose-induced changes in the intracellular distribution of insulin mRNA in cultured islets were assessed by subcellular fractionation and blot-hybridization using insulin cDNA probes. At glucose concentrations above 3.3 mM, cytoplasmic insulin mRNA was increasingly transferred to fractions co-sedimenting with ribosomes, and relatively more of the ribosome-associated insulin mRNA became membrane-associated, consistent with effects of glucose above 3.3 mM on both the initiation of insulin mRNA and SRP (signal recognition particle)-mediated transfer of cytosolic nascent preproinsulin to the endoplasmic reticulum. When freshly isolated islets were homogenized and incubated with 125I-Tyr-tRNA, run-off incorporation of 125I into preproinsulin was increased by prior incubation of the islets at 16.7 mM-glucose. The addition of purified SRP receptor increased the run-off incorporation of [125I]iodotyrosine into preproinsulin, especially when the islets had been preincubated at 16.7 mM-glucose. These findings taken together suggest that glucose may stimulate elongation rates of nascent preproinsulin at concentrations up to 5.6 mM, stimulates initiation of protein synthesis involving both insulin and non-insulin mRNA at concentrations above 3.3 mM, and increases the transfer of initiated insulin mRNA molecules from the cytoplasm to microsomal membranes by an SRP-mediated mechanism that involves the modification of interactions between SRP and its receptor.     

Evidence for new factors in the coordinate regulation of energy metabolism in Escherichia coli. Effects of hypoxia, chloramphenicol succinate, and 2,4-dinitrophenol on glucose utilization, glycogen synthesis, adenylate energy charge, and hexose phosphates during the first two periods of nitrogen starvation.

We studied the effects of decreased aeration, chloramphenicol succinate, and 2,4-dinitrophenol on the cellular rates of glycogen synthesis and glucose utilization and on the cellular concentrations of adenine nucleotides, glucose 6-phosphate, fructose 1,6-diphosphate, and phosphoenolpyruvate during the first two periods of nitrogen starvation of Escherichia coli W4597(K). A quantitative relationship between the changes in the rates and the accompanying changes in the hexose phosphates is demonstrated. However, the relationship for glycogen synthesis is different in different sets of metabolic conditions. We suggest that this difference reflects a change in the steady state level of a previously unknown effector of ADP-glucose synthetase (glucose 1-phosphate adenylyltransferase, EC 2.7.7.27) the rate-limiting enzyme of bacterial glycogen synthesis. We show that the properties of the hypothetical in vivo effector are consistent with the inhibitory effects of ppGpp (guanosine 3'-diphosphate 5'-diphosphate) and pppGpp (guanosine 3'-diphosphate 5'-triphosphate) on this enzyme in vitro. In addition, tetracycline, an inhibitor of the synthesis of these nucleotides, apparently prevents the change in the quantitative relationship. The relationship between glucose utilization and the hexose phosphates is altered at the transition to Period II of nitrogen starvation. We propose that this change reflects the alteration of the cellular steady state level of an unknown effector of the glucose phosphotransferase system. In contrast to the ATP-hexose phosphate system of shared regulatory effects, the specific effects of the unknown effectors allow the rates of glucose utilization and glycogen synthesis to be altered independently of each other and independently of changes in the rate of glycolysis. This independence allows a greater latitude of response for the individual pathways in more severe metabolic stress or in accommodating the metabolic changes necessary for long term survival.     

Mathematical modeling for mixed culture growth of two bacterial populations with opposite substrate preferences

An unstructured mathematical model is proposed for mixed culture growth of two different bacterial species that exhibit "opposite" substrate preferences in response to the "same" environmental conditions. The model incorporates enzymatic control mechanisms such as induction, repression, and inhibition in the microorganisms as manifested in their preferential utilization of substrates and microbial interactions such as amensalism and competition. The model predicts cell mass, substrate concentrations, dissolved oxygen tension, as well as key enzyme levels. The predictions of the model are compared with experimental data for pure culture growth and for mixed culture growth on two substrates, glucose and citrate, in a batch reactor.     

Reduction in lactate accumulation correlates with differentiation-induced terminal cell division of leukemia cells.

Lactate accumulation in the medium and glucose utilization decreased during the induction of in vitro differentiation of mouse erythroleukemia (MEL) and human myeloid leukemia (HL-60) cells. The decrease in lactate accumulation occurred as early as 24 h after inducer treatment was initiated and occurred prior to the decrease in glucose utilization. The decrease in lactate accumulation was greater than that predicted by the decrease in glucose utilization, i.e., the ratio of glucose used glycolytically, as measured by lactate accumulation, to glucose used in other pathways ('glycolytic ratio') markedly decreased during differentiation in these cell lines. Differentiation correlated with the abrogation of the high levels of lactate accumulation first described by Warburg as characteristic of some transformed and neoplastic cells. Studies on both parental and differentiation-resistant variant MEL cell lines indicated that the changes in lactate accumulation were not dependent on the changes in glucose utilization and could be dissociated from them. Moreover, the changes in lactate accumulation only occurred in cells able to undergo differentiation-induced terminal cell division. This regulatable expression of lactate accumulation in MEL and HL-60 cells in vitro may make them useful model systems for the elucidation of the molecular mechanisms controlling lactate formation in malignant cells.     

Restricted amino acid nutrition induces attachment to glass and spreading of Ehrlich ascites tumour cells

Ehrlich ascites tumour (EAT) cells were cultured in vitro in Eagle's MEM and Medium 199 with a lowered amino-acid content. Under these conditions EAT cells lose their rounded shape typical of highly malignant cancer cells, and begin to spread on the substratum. The changes in EAT cell morphology are preceded by a decrease in the rate of protein synthesis. These changes were maintained for three days after returning the cells to Eagle's MEM with a normal amino-acid content, but the return to control media did not cause reasumption of growth in the once spread cells. The increase in glucose content (up to five-fold) or the presence of inhibitors of DNA synthesis did not prevent the attachment and flattening of EAT cells in media with a lowered amino acid content. Several possible mechanisms of the influence of restricted amino-acid availability on the changes in EAT cell surface properties are pointed out and the need for study of cancer cell responses to restricted nutrition is discussed.     

Fourth expansion and glucose perturbation of the Dictyostelium kinetic model

The kinetic model of carbohydrate metabolism has been expanded to include: (a) the accumulation of alpha and beta-cellulose, insoluble cell-wall glycogen and mucopolysaccharide; (b) the role of RNA turnover as a source of carbon for end-product synthesis and as a buffer regulating the level of uridine nucleotides in this metabolic network; and (c) the role of purine-nucleoside phosphorylase, 5'-AMP nucleotidase, nucleosidediphosphate kinase and polynucleotide phosphorylase. One of many predictions based on this model is that cells differentiating in the presence of glucose will produce sorocarps with an abnormally high trehalose to cellulose ratio. External perturbation of either the model or of developing cells by glucose increases the levels of sorocarp trehalose and glycogen, 5-fold and 6-fold respectively. Evaluation of the experimental data and the simulation analyses have allowed several predictions to be made concerning the compartmentation of metabolites and the permeability of cells to glucose during differentiation.     

The regulatory principles of glycolysis in erythrocytes in vivo and in vitro. A minimal comprehensive model describing steady states, quasi-steady states and time-dependent processes.

A simple mathematical model for glycolysis in erythrocytes is presented which takes into account ATP synthesis and consumption. The system is described by four ordinary differential equations. Conditions in vivo are described by a stable steady state. The model predicts correctly the metabolite concentrations found in vivo. The parameters involved are in agreement with data on the separate steps. The metabolite changes found in pyruvate kinase-deficient erythrocytes and the species variations among erythrocytes from different animals are described satisfactorily. The roles of the enzymes in the control of metabolites and glycolytic flux are expressed in the form of a control matrix and control strengths [R. Heinrich & T.A. Rapoport (1974) Eur. J. Biochem. 42, 89-95] respectively. Erythrocytes from various species are shown to be adapted to a maximal ATP-consumption rate. The calculated eigenvalues reveal the pronounced time-hierarchy of the glycolytic reactions. Owing to the slowness of the 2,3-bisphospho-glycerate phosphatase reaction, quasi-steady states occur during the time-interval of about 0.5-2h incubation, which are defined by perturbed 2,3-bisphosphoglycerate concentrations. The theoretical predictions agree with experimental data. In the quasi-steady state the flux control is exerted almost entirely by the hexokinase-phosphofructokinase system. The model describes satisfactorily the time-dependent changes after addition of glucose to starved erythrocytes. The theoretical consequences are discussed of the conditions in vitro with lactate accumulation and the existence of a time-independent conservation quantity for the oxidized metabolites. Even in this closed system quasi-steady states occur which are characterized by approximately constant concentrations of all glycolytic metabolites except for the accumulation of lactate, fructose 1,6-bisphosphate and triose phosphate.     

The dependence of specific nuclear binding of glucocorticoids by rat thymus cells on cellular ATP levels.

The specific, saturable, nuclear binding of corticosteroids by rat thymus cells has been studied. Both the accumulation and the retention of corticosteroids by the nuclei of rat thymus cells at 37 degrees C were dependent upon the metabolic state of the cells. Treatment of cells with 2,4-dinitrophenol in the absence of glucose inhibited both accumulation and retention in the cell nucleus; these effects could be only partially prevented by the addition of glucose. The presence or absence of glucose also influenced the level of nuclear binding in the absence of 2,4-dinitrophenol, and in all cases the levels of nuclear binding of corticosteroids were correlated with cellular ATP levels. The effects of other reagents on levels of ATP and cyclic AMP also showed that significant changes in the level of nuclear-bound steroid were always accompanied by parallel variations in ATP levels, although there were no such correlations with levels of cyclic AMP. The partial restoration of nuclear binding by glucose in cells previously treated with 2,4-dinitrophenol was unaffected by cycloheximiede although protein synthesis was inhibited. Possible mechanisms by which the corticosteroid receptor is converted to a form capable of binding steroids by a reaction which requires energy but not de nova protein synthesis are discussed.     

The circulatory dynamics of human red blood cell homeostasis: Oxy-deoxy and PIEZO1-triggered changes

The vital function of red blood cells (RBCs) is to mediate the transport of oxygen from lungs to tissues and of CO₂ from tissues to lungs. The gas exchanges occur during capillary transits within fractions of a second. Each oxygenation-deoxygenation and deoxygenation-reoxygenation transition on hemoglobin triggers sharp changes in RBC pH, leading to downstream changes in ion fluxes, membrane potential, and cell volume. The dynamics of these changes during the variable periods between capillary transits in vivo remains a mystery inaccessible to study by current methodologies, a knowledge gap on a fundamental physiological process that is the focus of the present study. The use of a computational model of human RBC homeostasis of tested accreditation enabled a detailed investigation of the expected RBC changes during intercapillary transits, with results advancing novel insights and predictions. The predicted rates of relative RBC volume change on oxygenation-deoxygenation (oxy-deoxy) and deoxygenation-reoxygenation transitions were about 1.5%/min and ?0.9%/min, respectively, far too slow to allow the cells to reach steady states in the intervals between capillary transits. The amplitude of the oxy-deoxy-reoxygenation volume fluctuations varied in proportion with the duration of the intercapillary transit intervals. Upon capillary entry, oxy-deoxy-induced changes occur concurrently with deformation-induced PIEZO1 channel activation, both processes affecting cell pH, membrane potential, and cell volume during intertransit periods. The model showed that the effects were strictly additive as expected from processes operating independently on the cell’s homeostatic fabric. Analysis of the mechanisms behind these predictions revealed, for the first time, the complex interactions between oxy-deoxy and ion transport processes that ensure the long-term homeostatic stability of RBCs for optimal gas transport in physiological conditions and how these may become altered in diseased states. Possible designs of microfluidic devices to test the model predictions are discussed.     

The effects of exogenous glucose, uracil, and inorganic phosphate on differentiation in Dictyostelium discoideum.

The cellular slime mold was exposed to exogenous glucose, uracil, and inorganic phosphate for either 900 or 90 min to determine their effects on the cellular levels of glucose 6-phosphate (glucose-6-P), UDP-glucose, glycogen, trehalose, and cellulose. Glucose, and phosphate to a lesser extent, increase the levels of glucose-6-P and trehalose, whereas glycogen levels are increased only by glucose. Uracil inhibits glucose-6-P and trehalose accumulation, and this inhibition is reversed by glucose or phosphate. Uracil, especially in the presence of glucose, stimulates the accumulation of UDP-glucose and cellulose. In an attempt to understand the dynamics of the biochemical mechanisms underlying these experimental observations, fluxes of the same metabolites were imposed on a kinetic model of this system. The effects of glucose, uracil, and phosphate either singly or in various combinations on the accumulation of glycogen and trehalose can be predicted quantitatively by applying the appropriate external flux(es) of these additives to the model; the predicted effects on glucose-6-P levels are qualitatively consistent with the observations, but are greater in magnitude, suggesting compartmentation of glucose-6-P. Matching the observed and simulated results requires a lower level of additive in the simulated system than in the actual experiment, which is consistent with earlier studies on the cellular permeability of these metabolites.It is concluded that the complex of flux changes induced in the model by the perturbing metabolites may also occur in vivo, and that endogenous glucose availability is a critical variable controlling the rate and cessation of differentiation as well as the relative amounts of the saccharide end products of differentiation.     

Thermodynamic-based computational profiling of cellular regulatory control in hepatocyte metabolism

Thermodynamic-based constraints on biochemical fluxes and concentrations are applied in concert with mass balance of fluxes in glycogenesis and glycogenolysis in a model of hepatic cell metabolism. Constraint-based modeling methods that facilitate predictions of reactant concentrations, reaction potentials, and enzyme activities are introduced to identify putative regulatory and control sites in biological networks by computing the minimal control scheme necessary to switch between metabolic modes. Computational predictions of control sites in glycogenic and glycogenolytic operational modes in the hepatocyte network compare favorably with known regulatory mechanisms. The developed hepatic metabolic model is used to computationally analyze the impairment of glucose production in von Gierke's and Hers' diseases, two metabolic diseases impacting glycogen metabolism. The computational methodology introduced here can be generalized to identify downstream targets of agonists, to systematically probe possible drug targets, and to predict the effects of specific inhibitors (or activators) on integrated network function.