The dynamics of single-substrate continuous cultures: the role of ribosomes

When a chemostat is perturbed from its steady state, it displays complex dynamics. For instance, if the identity of the growth-limiting substrate is switched abruptly, the substrate concentration and cell density undergo a pronounced excursion from the steady state that can last several days. These dynamics occur because certain physiological variables respond slowly. In the literature, several physiological variables have been postulated as potential sources of the slow response. These include transport enzymes, biosynthetic enzymes, and ribosomes. We have been addressing this problem by systematically exploring the role of these variables. In previous work Shoemaker et al. (J. Theor. Biol., 222 (2003) 307-322), we studied the role of transport enzymes, and we showed that transients starting from low transport enzyme levels could be quantitatively captured by a model taking due account of transport enzyme synthesis. However, there is some experimental data indicating that slow responses occur even if the initial enzyme levels are high. Here, we analyse this data to show that in these cases, the sluggish response is most probably due to slow adjustment of the ribosome levels. To test this hypothesis, we extend our previous model by accounting for the evolution of both the transport enzyme and the ribosomes. Based on a kinetic analysis of the data in the literature, we assume that the specific protein synthesis rate is proportional to the ribosome level, and the specific ribosome synthesis rate is autocatalytic. Simulations of the model show remarkable agreement with experimentally observed steady states and the transients. Specifically, the model predictions are in good agreement with (1) the steady-state profiles of the cell density, substrate concentration, RNA, proteins, and transport enzymes, (2) the instantaneous specific substrate uptake, growth, and respiration rates in response to a continuous-to-batch shift, and (3) the transient profiles of the cell density, substrate concentration, and RNA in response to feed switches and dilution rate shifts. Time-scale analysis of the model reveals that every transient response is a combination of two fundamental (and simpler) dynamics, namely, substrate-sufficient batch dynamics and cell-sufficient fed-batch dynamics. We obtain further insight into the transient response by analysing the equations describing these fundamental dynamics. The analysis reveals that in feed switches or dilution rate shift-ups, the transport enzyme reaches a maximum before RNA achieves its maximum, and in dilution rate shift-downs the cell density reaches a maximum before RNA achieves a minimum.     

Behaviour of dictyostelium discoideum amoebae and Escherichia coli grown together in chemostat culture

When Dictyostelium discoideum amoebae and Escherichia coli were grown together in chemostat culture damped oscillations in the popullation densities of the organisms occurred followed by a sudden increase in bacterial numbers and a concommitant decrease in the number of amoebae. After the system had come to equilibrium altering the dilution rate resulted in a monotonic change in the experimental variables to new steady state levels. A square wave increase in the concentration of limiting nutrient in the feed medium during the oscillatory phase of culture produced a sinusoidal response indistinguishable from that prior to the perturbation. The results are more complicated than those predicted by simple models of microbial predator-prey dynamics although they correspond most nearly to models which incorporate saturation kinetics.     

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.     

Complex responses to culture conditions in Pseudomonas syringae pv. tomato DC3000 continuous cultures: The role of iron in cell growth and virulence factor induction

The growth of a model plant pathogen, Pseudomonas syringae pv. tomato DC3000, was investigated using a chemostat culture system to examine environmentally regulated responses. Using minimal medium with iron as the limiting nutrient, four different types of responses were obtained in a customized continuous culture system: (1) stable steady state, (2) damped oscillation, (3) normal washout due to high dilution rates exceeding the maximum growth rate, and (4) washout at low dilution rates due to negative growth rates. The type of response was determined by a combination of initial cell mass and dilution rate. Stable steady states were obtained with dilution rates ranging from 0.059 to 0.086 h^?1 with an initial cell mass of less than 0.6 OD₆₀₀. Damped oscillations and negative growth rates are unusual observations for bacterial systems. We have observed these responses at values of initial cell mass of 0.9 OD₆₀₀ or higher, or at low dilution rates (<0.05 h^?1) irrespectively of initial cell mass. This response suggests complex dynamics including the possibility of multiple steady states. Iron, which was reported earlier as a growth limiting nutrient in a widely used minimal medium, enhances both growth and virulence factor induction in iron‐supplemented cultures compared to unsupplemented controls. Intracellular iron concentration is correlated to the early induction (6 h) of virulence factors in both batch and chemostat cultures. A reduction in aconitase activity (a TCA cycle enzyme) and ATP levels in iron‐limited chemostat cultures was observed compared to iron‐supplemented chemostat cultures, indicating that iron affects central metabolic pathways. We conclude that DC3000 cultures are particularly dependent on the environment and iron is likely a key nutrient in determining physiology. Biotechnol. Bioeng. 2010;105: 955–964. © 2009 Wiley Periodicals, Inc.     

Thermodynamic and kinetic studies of a stoichiometric model of energetic metabolism under starvation conditions

Abstract A stoichiometric model of anaerobic glycolysis is presented and the influence on its dynamics by the ATP-consuming membrane transport processes and substrate input rate are studied. The model is represented by a system of four ODE (ordinary differential equations), mass conservation equations and functions of state variables, such as thermodynamic efficiency. A low substrate input rate provokes damped oscillations while a high enrgy load determines sustained oscillations in all the metabolites and in thermodynamic efficiency. Due to the lack of linearity between fluxes and forces in the oscillatory region it may be stated that oscillations appear when the system is kinetically controlled.     

Dynamics of chemostat in which one microbial population grows on multiple complementary nutrients

The equations of a chemostat in which one microbial population grows on multiple rate-limiting nutrients are formulated. The dynamics of a chemostat involving growth on complementary nutrients is studied through stability analysis of the system of equations. Some conditions are derived that relate the dynamic behavior of the chemostat to its operating conditions and can be applied to any model for the specific growth rate of the population. It is shown that, if maintenance of the population is neglected, the system exhibits no sustained or damped oscillations. If maintenance of the population is considered, damped oscillations are observed for some operating conditions.     

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     

Transient behavior of a continuous stirred tank biological reactor utilizing phenol as an inhibitory substrate

Transient experiments were conducted on a Pseudomomas utilizing phenol in a continuous culture by disturbing the influent substrate concentration and dilution rate. Two stable steady states existed for some ranges of the parameters. Highly damped oscillations were observed in approaching a new high conversion steady state or in returning to a new high conversion steady state following a small disturbance. When a large disturbance was applied there was a smooth (overdamped) approach to a new low conversion steady state. The observed oscillatory behavior for small disturbances was predicted by a modified Powell-Ierusalemskii bottleneck model, but could not be predicted by a Monod-Haldane model; neither model was accurate for predicting the effect of large disturbances. A constant wall growth factor was used to account for microbial film activity, and the existence of two stable states was directly due to the presence of the film.     

pH modulation of transient state kinetics of enzymes. I. Simple theoretical models

The effect of proton concentration on pre-steady-state kinetics has been investigated theoretically for enzyme reactions involving the breaking of one substrate into two products. Even for the simple double-intermediate mechanism the approach to the steady state may exhibit a rather complex kinetics, which is pH-dependent. This process may even exhibit damped oscillations. A change of pH may completely change this transient kinetics and even suppresses the oscillatory regime. A simple method is presented which allows estimation of the values of the rate and ionization constants. This procedure allows one to distinguish the simple double-intermediate mechanism from a more complex process where the 'fast' binding of the substrate induces a 'slow' conformation change of the enzyme.     

Long-Term Changes in Chemostat Cultures of Cytophaga johnsonae

Long-term studies with a gliding, heterotrophic bacterium, Cytophaga johnsonae, were conducted in a glucose-limited chemostat at a high and a low dilution rate. To test the stability of the steady state during long-term experiments the following parameters were monitored: optical density, glucose concentration, glucose uptake potential, ATP content of the cells, and plate counts on two different agar media. Biomass remained relatively constant, although the observed changes could have been possible in both directions. During all steady states, glucose uptake showed a stepwise increase and the glucose concentration showed a corresponding decrease. Glucose uptake potential and glucose concentration in the chemostat were inversely proportional. The ATP content of the cells varied up to 33% during the steady state, but did not show a general trend. After long cultivation in all chemostats, plate counts on both agars dropped to values less than 20% of the original steady-state level. These decreases were due to an inability of the cells to grow on agar plates, not to a lack of vitality of the cells in the chemostat. This study showed that even during shorter chemostat runs, e.g., 1 week, changes in important parameters with the steady state must be expected, especially in the uptake potential and the concentration of the limiting substrate.     

A dynamic mathematical model of the chemostat

A number of experimental studies on the dynamic, behavior of the chemostat have shown that the specific growth rate does not, instantaneously adjust to changes in the concentration of limiting substrate in the chemostat following disturbances in the steady state input limiting substrate concentration or in the steady state dilution rate. Instead of an instantaneous response, as would be predicted by the Monod equation, experimental studies have shown that the specific growth rate experiences a dynamic lag in responding to the changes in the concentration of limiting substrate in the culture vessel. The observed dynamic lag has been recognized by researchers in such terms as an inertial phenomenon and as a hysteresis effect, but as yet a systems engineering approach has not been applied to the observed data. The present paper criticizes the use of the Monod equation as a dynamic relationship and offers as an alternative a dynamic equation relating specific growth rate to the limiting substrate concentration in the chemostat. Following the development of equations, experimental methods of evaluating parameters are discussed. Dynamic responses of analog simulations (incorporating the newly derived equations) are compared with the dynamic responses predicted by the Monod equation and with the dynamic responses of experimental chemostats.     

Study of the dynamic behavior of the chemostat system

This paper deals with a theoretical study on the dynamic, character of the chemostat system. It. is primarily based on the Monod model for growth limitation, although certain more complex models are considered. Since the Monod model is described in terms of two variables, an analysis by use of a phase plane plot will show the various possible types of behavior theoretically expected for transient conditions of the system. In this paper it will be shown that the chemostat system might show an overshoot (or an underswing) with respect to changes in cell and substrate concentrations, depending on the extent to which the system might be disturbed from steady-slate conditions. Other types of transient behavior ran also be expected when one of the system parameters such as dilution rate or input substrate concentration is disturbed in a stepwise manner. The simple Monod chemostat model was found never to oscillate in either a damped or a sustained manner as has been experimentally reported. Discussion is included about the transient behavior of other chemostat models such as that involving a variable yield coefficient, i.e., including the effect of cell maintenance requirements.     

pH modulation of transient state kinetics of enzymes. II. Transient state kinetics of plant cell wall acid phosphatase

The pre-steady-state kinetics of plant cell wall acid phosphatase has been investigated at different pH values. The approach of the steady stale lasts about 1 or 2 s and may be fitted with two exponential terms. For certain pH values the approach to the steady state exhibits damped oscillations. Plotting the sum and the product of the two time constants of these exponentials as a function of substrate concentration yields two straight lines. From the slopes and intercepts of these lines one may determine the values of rate and ionization constants involved in the reaction scheme. The results obtained are consistent with the view that the binding of the substrate to the enzyme does not induce a 'slow' conformation change of the enzyme. The enzyme reacts with its substrate while being mostly in its ionized form. Release of p-nitrophenol is also favoured by this ionized form of the enzyme. However, the hydrolysis of the phosphoryl-enzyme complex mostly occurs from the protonated form of the enzyme. The ionization constants of the free enzyme and of the various enzyme-ligand complexes are very similar.     

Continuous cultivation of Saccharomyces cerevisiae. II. Growth on ethanol under transient-state conditions

Growth of Saccharomyces cerevisiae LBG H 1022 on ethanol under transient-state conditions was studied. As a cultivation device, an aerated Chemap fermentor combined with continuously working gas analyzers for oxygen and carbon dioxide was used. Yeast cell dry matter, substrate concentration, specific oxygen uptake, specific carbon dioxide release, and respiration quotient were measured during the different transient states. Depending on which range of the dilution rate the initial steady state was found, we obtain different responses to the shift experiment. For the lower range, up to D = 0.07, we deal with damped oscillations ranging above and below the steady-state values. For the higher specific growth rates, the rate of damping is strongly enhanced and the shape of the curves becomes an asymptotic approach to the final steady states.     

The ideal free distribution and bacterial growth on two substrates

A population dynamical model describing growth of bacteria on two substrates is analyzed. The model assumes that bacteria choose substrates in order to maximize their per capita population growth rate. For batch bacterial growth, the model predicts that as the concentration of the preferred substrate decreases there will be a time at which both substrates provide bacteria with the same fitness and both substrates will be used simultaneously thereafter. Preferences for either substrate are computed as a function of substrate concentrations. The predicted time of switching is calculated for some experimental data given in the literature and it is shown that the fit between predicted and observed values is good. For bacterial growth in the chemostat, the model predicts that at low dilution rates bacteria should feed on both substrates while at higher dilution rates bacteria should feed on the preferred substrate only. Adaptive use of substrates permits bacteria to survive in the chemostat at higher dilution rates when compared with non-adaptive bacteria.     

Oscillatory behavior of Saccharomyces cerevisiae in continuous culture: I. Effects of pH and nitrogen levels

The appearance of sustained oscillations in bioreactor variables (biomass and nutrient concentrations) in continuous cultures of Saccharomyces cerevisiae indicates the complex nature of microbial systems, the inadequacy of current growth kinetic models, and the difficulties which may arise in bioprocess control and optimization. In this study we investigate continuous bioreactor behavior over a range of operating conditions (dilution rate, feed glucose concentration, feed ammonium concentration, dissolved oxygen, and pH) to determine the process requirements which lead to oscillatory behavior. We present new results which indicate that high feed ammonium concentrations may eliminate oscillations and that under oscillatory conditions ammonium levels are generally low and oscillatory as well. The effects of pH are complex and oscillations were only observed at pH values 5.5 and 6.5; no oscillations were observed at a pH of 4.5. Under our nominal operating conditions (feed glucose concentration 10 g/L, dilution rate 0.145 h(-1), feed ammonium concentration 0.0303M, dissolved oxygen level 50%, pH 5.5, and T = 30 degrees C) we found two possible final bioreactor states depending on the transient used to reach the nominal operating conditions. One of the states was oscillatory and characteristic of oxidative metabolism and the other was nonoscillatory and fermentative.     

Population dynamics and competition in chemostat models with adaptive nutrient uptake

 The standard Monod model for microbial population dynamics in the chemostat is modified to take into consideration that cells can adapt to the change of nutrient concentration in the chemostat by switching between fast and slow nutrient uptake and growing modes with asymmetric thresholds for transition from one mode to another. This is a generalization of a modified Monod model which considers adaptation by transition between active growing and quiescent cells. Global analysis of the model equations is obtained using the theory of asymptotically autonomous systems. Transient oscillatory population density and hysteresis growth pattern observed experimentally, which do not occur for the standard Monod model, can be explained by such adaptive mechanism of the cells. Competition between two species that can switch between fast and slow nutrient uptake and growing modes is also considered. It is shown that generically there is no coexistence steady state, and only one steady state, corresponding to the survival of at most one species in the chemostat, is a local attractor. Numerical simulations reproduce the qualitative feature of some experimental data which show that the population density of the winning species approaches a positive steady state via transient oscillations while that of the losing species approaches the zero steady state monotonically. Received 4 August 1995; received in revised form 15 December 1995     

Inhibition Kinetics of Phenol Degradation by Pseudomonas aeruginosa from Continuous Culture and Washout Data

Steady states of a continuous culture with an inhibitory substrate were used to estimate kinetic parameters under substrate limitation (chemostat operation). Pure cultures of an indigenous Pseudomonas aeruginosa were grown in continuous culture on phenol, the sole source of carbon and energy, at dilution rates of 0.010 to 0.20 h^{- 1}. Using different dilution rates, several steady states were investigated and the specific phenol consumption rates were calculated. In addition, phenol degradation was investigated by increasing the dilution rate above the critical dilution rate (washout cultivation). The results showed that the specific phenol consumption rate increased with increased dilution rate at steady state and that the degradation by Pseudomonas aeruginosa can be described by simple substrate inhibition kinetics under substrate limitation but cannot be described by simple substrate inhibition kinetics under washout cultivation. Fitting of the steady-state data from continuous cultivation to various inhibition models resulted in the best fit for the Yano and Koga kinetic inhibition model. The r_{s max} value of 0.278 mg/mg/h obtained from the Yano and Koga equation was comparable to the experimentally calculated r_{s max} value of 0.283 mg/mg/h obtained under washout cultivation.     

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.     

Time-dependent kinetic complexities in cholinesterase-catalyzed reactions

Cholinesterases (ChEs) display a hysteretic behavior with certain substrates and inhibitors. Kinetic cooperativity in hysteresis of ChE-catalyzed reactions is characterized by a lag or burst phase in the approach to steady state. With some substrates damped oscillations are shown to superimpose on hysteretic lags. These time dependent peculiarities are observed for both butyrylcholinesterase and acetylcholinesterase from different sources. Hysteresis in ChE-catalyzed reactions can be interpreted in terms of slow transitions between two enzyme conformers E and E′. Substrate can bind to E and/or E′, both Michaelian complexes ES and E’s can be catalytically competent, or only one of them can make products. The formal reaction pathway depends on both the chemical structure of the substrate and the type of enzyme. In particular, damped oscillations develop when substrate exists in different, slowly interconvertible, conformational, and/or micellar forms, of which only the minor form is capable of binding and reacting with the enzyme. Biphasic pseudo-first-order progressive inhibition of ChEs by certain carbamates and organophosphates also fits with a slow equilibrium between two reactive enzyme forms. Hysteresis can be modulated by medium parameters (pH, chaotropic and kosmotropic salts, organic solvents, temperature, osmotic pressure, and hydrostatic pressure). These studies showed that water structure plays a role in hysteretic behavior of ChEs. Attempts to provide a molecular mechanism for ChE hysteresis from mutagenesis studies or crystallographic studies failed so far. In fact, several lines of evidence suggest that hysteresis is controlled by the conformation of His438, a key residue in the catalytic triad of cholinesterases. Induction time may depend on the probability of His438 to adopt the operative conformation in the catalytic triad. The functional significance of ChE hysteresis is puzzling. However, the accepted view that proteins are in equilibrium between preexisting functional and non-functional conformers, and that binding of a ligand to the functional form shifts equilibrium towards the functional conformation, suggests that slow equilibrium between two conformational states of these enzymes may have a regulatory function in damping out the response to certain ligands and irreversible inhibitors. This is particularly true for immobilized (membrane bound) enzymes where the local substrate and/or inhibitor concentrations depend on influx in crowded organellar systems, e.g. cholinergic synaptic clefts. Therefore, physiological or toxicological relevance of the hysteretic behavior and damped oscillations in ChE-catalyzed reactions and inhibition cannot be ruled out.