Are Microbes Optimal Strategists?

Sulfur and methane oxidation by a single microorganism

Wetlands are the major natural source of methane, an important greenhouse gas. The sulfur and methane cycles in wetlands are linked—e.g., a strong sulfur cycle can inhibit methanogenesis. Although there has historically been a clear distinction drawn between methane and sulfur oxidizers, here, we isolated a methanotroph that also performed respiratory oxidization of sulfur compounds. We experimentally demonstrated that thiotrophy and methanotrophy are metabolically compatible, and both metabolisms could be expressed simultaneously in a single microorganism. These findings suggest that mixotrophic methane/sulfur-oxidizing bacteria are a previously overlooked component of environmental methane and sulfur cycles. This creates a framework for a better understanding of these redox cycles in natural and engineered wetlands.

Natural and anthropogenic wetlands are major sources of the atmospheric greenhouse gas methane. Methane emissions from wetlands are mitigated by methanotrophic bacteria at the oxic–anoxic interface, a zone of intense redox cycling of carbon, sulfur, and nitrogen compounds. Here, we report on the isolation of an aerobic methanotrophic bacterium, ‘Methylovirgula thiovorans' strain HY1, which possesses metabolic capabilities never before found in any methanotroph. Most notably, strain HY1 is the first bacterium shown to aerobically oxidize both methane and reduced sulfur compounds for growth. Genomic and proteomic analyses showed that soluble methane monooxygenase and XoxF-type alcohol dehydrogenases are responsible for methane and methanol oxidation, respectively. Various pathways for respiratory sulfur oxidation were present, including the Sox–rDsr pathway and the S₄I system. Strain HY1 employed the Calvin–Benson–Bassham cycle for CO₂ fixation during chemolithoautotrophic growth on reduced sulfur compounds. Proteomic and microrespirometry analyses showed that the metabolic pathways for methane and thiosulfate oxidation were induced in the presence of the respective substrates. Methane and thiosulfate could therefore be independently or simultaneously oxidized. The discovery of this versatile bacterium demonstrates that methanotrophy and thiotrophy are compatible in a single microorganism and underpins the intimate interactions of methane and sulfur cycles in oxic–anoxic interface environments.

Pseudomonad reverse carbon catabolite repression, interspecies metabolite exchange, and consortial division of labor

Microorganisms acquire energy and nutrients from dynamic environments, where substrates vary in both type and abundance. The regulatory system responsible for prioritizing preferred substrates is known as carbon catabolite repression (CCR). Two broad classes of CCR have been documented in the literature. The best described CCR strategy, referred to here as classic CCR (cCCR), has been experimentally and theoretically studied using model organisms such as Escherichia coli. cCCR phenotypes are often used to generalize universal strategies for fitness, sometimes incorrectly. For instance, extremely competitive microorganisms, such as Pseudomonads, which arguably have broader global distributions than E. coli, have achieved their success using metabolic strategies that are nearly opposite of cCCR. These organisms utilize a CCR strategy termed 'reverse CCR' (rCCR), because the order of preferred substrates is nearly reverse that of cCCR. rCCR phenotypes prefer organic acids over glucose, may or may not select preferred substrates to optimize growth rates, and do not allocate intracellular resources in a manner that produces an overflow metabolism. cCCR and rCCR have traditionally been interpreted from the perspective of monocultures, even though most microorganisms live in consortia. Here, we review the basic tenets of the two CCR strategies and consider these phenotypes from the perspective of resource acquisition in consortia, a scenario that surely influenced the evolution of cCCR and rCCR. For instance, cCCR and rCCR metabolism are near mirror images of each other; when considered from a consortium basis, the complementary properties of the two strategies can mitigate direct competition for energy and nutrients and instead establish cooperative division of labor.

Prediction of metabolic fluxes from gene expression data with Huber penalty convex optimization function

As one of the critical parameters of a metabolic pathway, the metabolic flux in a metabolic network serves as an essential role in physiology and pathology. Constraint-based metabolic models are the widely used frameworks for predicting metabolic fluxes in genome-scale metabolic networks. Integrating the transcriptomic data into the constraint-based metabolic models can effectively predict context-specific fluxes across different conditions. However, these methods always need user-defined thresholds to identify the expression levels of metabolic genes or restrain the rate of biomass production, and the predictive results are sensitive to the thresholds. In this work, we present the Huber penalty convex optimization function (HPCOF) combined with the flux minimization principle to predict metabolic fluxes. Our HPCOF method integrates gene expression profiles into the genome-scale metabolic models (GEMs) to reduce the sensitivity to outliers, and uses continuous expression data to avoid selection of arbitrary threshold parameters. In the case studies of Saccharomyces cerevisiae (S. cerevisiae) and Escherichia coli (E. coli) strains under different conditions, the results show that our HPCOF method has a better fit to the experimentally measured values, and has a higher Pearson correlation coefficient, a smaller P-value and a lower sum of squared error than other methods. The HPCOF code can be freely downloaded from for academic users.

Catabolite repression in Campylobacter jejuni correlates with intracellular succinate levels

Bacteria have evolved different mechanisms to catabolize carbon sources from nutrient mixtures. They first consume their preferred carbon source, before others are used. Regulatory mechanisms adapt the metabolism accordingly to maximize growth and to outcompete other organisms. The human pathogen Campylobacter jejuni is an asaccharolytic Gram-negative bacterium that catabolizes amino acids and organic acids for growth. It prefers serine and aspartate as carbon sources, however it lacks all regulators known to be involved in regulating carbon source utilization in other organisms. In which manner C. jejuni adapts its metabolism towards the presence or absence of preferred carbon sources is unknown. In this study, we show with transcriptomic analysis and enzyme assays how C. jejuni adapts its metabolism in response to its preferred carbon sources. In the presence of serine as well as lactate and pyruvate C. jejuni inhibits the utilization of other carbon sources, by repressing the expression of a number of central metabolic enzymes. The regulatory proteins RacR, Cj1000 and CsrA play a role in the regulation of these metabolic enzymes. This metabolism dependent transcriptional repression correlates with an accumulation of intracellular succinate. Hence, we propose a demand-based catabolite repression mechanism in C. jejuni, depended on intracellular succinate levels.

Regulation-Structured Dynamic Metabolic Model Provides a Potential Mechanism for Delayed Enzyme Response in Denitrification Process

In a recent study of denitrification dynamics in hyporheic zone sediments, we observed a significant time lag (up to several days) in enzymatic response to the changes in substrate concentration. To explore an underlying mechanism and understand the interactive dynamics between enzymes and nutrients, we developed a trait-based model that associates a community's traits with functional enzymes, instead of typically used species guilds (or functional guilds). This enzyme-based formulation allows to collectively describe biogeochemical functions of microbial communities without directly parameterizing the dynamics of species guilds, therefore being scalable to complex communities. As a key component of modeling, we accounted for microbial regulation occurring through transcriptional and translational processes, the dynamics of which was parameterized based on the temporal profiles of enzyme concentrations measured using a new signature peptide-based method. The simulation results using the resulting model showed several days of a time lag in enzymatic responses as observed in experiments. Further, the model showed that the delayed enzymatic reactions could be primarily controlled by transcriptional responses and that the dynamics of transcripts and enzymes are closely correlated. The developed model can serve as a useful tool for predicting biogeochemical processes in natural environments, either independently or through integration with hydrologic flow simulators.

On-line identification of fermentation processes for ethanol production

A strategy for monitoring fermentation processes, specifically, simultaneous saccharification and fermentation (SSF) of corn mash, was developed. The strategy covered the development and use of first principles, semimechanistic and unstructured process model based on major kinetic phenomena, along with mass and energy balances. The model was then used as a reference model within an identification procedure capable of running on-line. The on-line identification procedure consists on updating the reference model through the estimation of corrective parameters for certain reaction rates using the most recent process measurements. The strategy makes use of standard laboratory measurements for sugars quantification and in situ temperature and liquid level data. The model, along with the on-line identification procedure, has been tested against real industrial data and have been able to accurately predict the main variables of operational interest, i.e., state variables and its dynamics, and key process indicators. The results demonstrate that the strategy is capable of monitoring, in real time, this complex industrial biomass fermentation. This new tool provides a great support for decision-making and opens a new range of opportunities for industrial optimization.

Hierarchy of non-glucose sugars in Escherichia coli

BACKGROUND

Understanding how cells make decisions, and why they make the decisions they make, is of fundamental interest in systems biology. To address this, we study the decisions made by E. coli on which genes to express when presented with two different sugars. It is well-known that glucose, E. coli's preferred carbon source, represses the uptake of other sugars by means of global and gene-specific mechanisms. However, less is known about the utilization of glucose-free sugar mixtures which are found in the natural environment of E. coli and in biotechnology.

RESULTS

Here, we combine experiment and theory to map the choices of E. coli among 6 different non-glucose carbon sources. We used robotic assays and fluorescence reporter strains to make precise measurements of promoter activity and growth rate in all pairs of these sugars. We find that the sugars can be ranked in a hierarchy: in a mixture of a higher and a lower sugar, the lower sugar system shows reduced promoter activity. The hierarchy corresponds to the growth rate supported by each sugar- the faster the growth rate, the higher the sugar on the hierarchy. The hierarchy is 'soft' in the sense that the lower sugar promoters are not completely repressed. Measurement of the activity of the master regulator CRP-cAMP shows that the hierarchy can be quantitatively explained based on differential activation of the promoters by CRP-cAMP. Comparing sugar system activation as a function of time in sugar pair mixtures at sub-saturating concentrations, we find cases of sequential activation, and also cases of simultaneous expression of both systems. Such simultaneous expression is not predicted by simple models of growth rate optimization, which predict only sequential activation. We extend these models by suggesting multi-objective optimization for both growing rapidly now and preparing the cell for future growth on the poorer sugar.

CONCLUSION

We find a defined hierarchy of sugar utilization, which can be quantitatively explained by differential activation by the master regulator cAMP-CRP. The present approach can be used to understand cell decisions when presented with mixtures of conditions.

Prediction of metabolic flux distribution from gene expression data based on the flux minimization principle

Prediction of possible flux distributions in a metabolic network provides detailed phenotypic information that links metabolism to cellular physiology. To estimate metabolic steady-state fluxes, the most common approach is to solve a set of macroscopic mass balance equations subjected to stoichiometric constraints while attempting to optimize an assumed optimal objective function. This assumption is justifiable in specific cases but may be invalid when tested across different conditions, cell populations, or other organisms. With an aim to providing a more consistent and reliable prediction of flux distributions over a wide range of conditions, in this article we propose a framework that uses the flux minimization principle to predict active metabolic pathways from mRNA expression data. The proposed algorithm minimizes a weighted sum of flux magnitudes, while biomass production can be bounded to fit an ample range from very low to very high values according to the analyzed context. We have formulated the flux weights as a function of the corresponding enzyme reaction's gene expression value, enabling the creation of context-specific fluxes based on a generic metabolic network. In case studies of wild-type Saccharomyces cerevisiae, and wild-type and mutant Escherichia coli strains, our method achieved high prediction accuracy, as gauged by correlation coefficients and sums of squared error, with respect to the experimentally measured values. In contrast to other approaches, our method was able to provide quantitative predictions for both model organisms under a variety of conditions. Our approach requires no prior knowledge or assumption of a context-specific metabolic functionality and does not require trial-and-error parameter adjustments. Thus, our framework is of general applicability for modeling the transcription-dependent metabolism of bacteria and yeasts.

Optimization-based metabolic control analysis

In this work, a novel optimization-based metabolic control analysis (OMCA) method is introduced for reducing data requirement for metabolic control analysis (MCA). It is postulated that using the optimal control approach, the fluxes in a metabolic network are correlated to metabolite concentrations and enzyme activities as a state-feedback control system that is optimal with respect to a homeostasis objective. It is then shown that the optimal feedback gains are directly related to the elasticity coefficients (ECs) of MCA. This approach requires determination of the relative "importance" of metabolites and fluxes for the system, which is possible with significantly reduced experimental data, as compared with typical MCA requirements. The OMCA approach is applied to a top-down control model of glycolysis in hepatocytes. It is statistically demonstrated that the OMCA model is capable of predicting the ECs observed experimentally with few exceptions. Further, an OMCA-based model reconciliation study shows that the modification of four assumed stoichiometric coefficients in the model can explain most of the discrepancies, with the exception of elasticities with respect to the NADH/NAD ratio.

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.

Systematic development of hybrid cybernetic models: application to recombinant yeast co-consuming glucose and xylose

The hybrid cybernetic modeling approach of Kim et al. (Kim et al. [2008] Biotechnol. Prog., in press) views the substrate uptake flux in microorganisms as being distributed in a regulated way among different elementary modes (EMs) of a metabolic network, which intracellular fluxes related to the uptake rates by the pseudo-steady-state approximation on intracellular metabolites. While the conceptual development has been demonstrated by Kim et al. (Kim et al. [2008] Biotechnol. Prog., in press) using a rather simple example (i.e., Escherichia coli metabolizing a single substrate), its extension to a larger scale network involving multiple substrates results in serious overparameterization (which implies an excessive number of parameters relative to the measurements available to determine them). Through the case study of recombinant Saccharomyces yeast co-consuming glucose and xylose, we present a systematic way of formulating a minimal order hybrid cybernetic model (HCM) for a general metabolic network. The overparameterization problem mostly arising from a large number of EMs is avoided using a model reduction technique developed by Song and Ramkrishna (Song and Ramkrishna [2009a] Biotechnol. Bioeng. 102(2):554-568) where an original set of EMs is condensed to a much smaller subset. Detailed discussions follow on the issue of determining the minimal set of active modes needed for the description of the simultaneous consumption of multiple substrates. The developed HCM is compared with other metabolic models: macroscopic bioreaction models (Provost et al. [2006] Bioprocess Biosyt. Eng. 29(5-6):349-366), and dynamic flux balance analysis. It is shown that the HCM outperforms the other two as validated using various sets of fermentation data. The difference among the models is more dramatic in a situation such as the sequential utilization of glucose and xylose, which is observed under realistic fermentation conditions.

Spontaneous reaction silencing in metabolic optimization

Metabolic reactions of single-cell organisms are routinely observed to become dispensable or even incapable of carrying activity under certain circumstances. Yet, the mechanisms as well as the range of conditions and phenotypes associated with this behavior remain very poorly understood. Here we predict computationally and analytically that any organism evolving to maximize growth rate, ATP production, or any other linear function of metabolic fluxes tends to significantly reduce the number of active metabolic reactions compared to typical nonoptimal states. The reduced number appears to be constant across the microbial species studied and just slightly larger than the minimum number required for the organism to grow at all. We show that this massive spontaneous reaction silencing is triggered by the irreversibility of a large fraction of the metabolic reactions and propagates through the network as a cascade of inactivity. Our results help explain existing experimental data on intracellular flux measurements and the usage of latent pathways, shedding new light on microbial evolution, robustness, and versatility for the execution of specific biochemical tasks. In particular, the identification of optimal reaction activity provides rigorous ground for an intriguing knockout-based method recently proposed for the synthetic recovery of metabolic function.

Cellular growth and other integrated metabolic functions are manifestations of the coordinated interconversion of a large number of chemical compounds. But what is the relation between such whole-cell behaviors and the activity pattern of the individual biochemical reactions? In this study, we have used flux balance-based methods and reconstructed networks of Helicobacter pylori, Staphylococcus aureus, Escherichia coli, and Saccharomyces cerevisiae to show that a cell seeking to optimize a metabolic objective, such as growth, has a tendency to spontaneously inactivate a significant number of its metabolic reactions, while all such reactions are recruited for use in typical suboptimal states. The mechanisms governing this behavior not only provide insights into why numerous genes can often be disabled without affecting optimal growth but also lay a foundation for the recently proposed synthetic rescue of metabolic function in which the performance of suboptimally operating cells can be enhanced by disabling specific metabolic reactions. Our findings also offer explanation for another experimentally observed behavior, in which some inactive reactions are temporarily activated following a genetic or environmental perturbation. The latter is of utmost importance given that nonoptimal and transient metabolic behaviors are arguably common in natural environments.

Perspectives in the Modeling and Optimization of PHB Production by Pure and Mixed Cultures

Poly(beta-hydroxybutyrate) or PHB is an important member of the family of polyhydroxyalkanoates with properties that make it potentially competitive with synthetic polymers. In addition, PHB is biodegradable. While the biochemistry of PHB synthesis by microorganisms is well known, improvement of large-scale productivity requires good fermentation modeling and optimization. The latter aspect is reviewed here. Current models are of two types: (i) mechanistic and (ii) cybernetic. The models may be unstructured or structured, and they have been applied to single cultures and co-cultures. However, neither class of models expresses adequately all the important features of large-scale non-ideal fermentations. Model-independent neural networks provide faithful representations of observations, but they can be difficult to design. So hybrid models, combining mechanistic, cybernetic and neural models, offer a useful compromise. All three kinds of basic models are discussed with applications and directions toward hybrid model development.

Investigation of metabolic objectives in cultured hepatocytes

Using optimization based methods to predict fluxes in metabolic flux balance models has been a successful approach for some microorganisms, enabling construction of in silico models and even inference of some regulatory motifs. However, this success has not been translated to mammalian cells. The lack of knowledge about metabolic objectives in mammalian cells is a major obstacle that prevents utilization of various metabolic engineering tools and methods for tissue engineering and biomedical purposes. In this work, we investigate and identify possible metabolic objectives for hepatocytes cultured in vitro. To achieve this goal, we present a special data-mining procedure for identifying metabolic objective functions in mammalian cells. This multi-level optimization based algorithm enables identifying the major fluxes in the metabolic objective from MFA data in the absence of information about critical active constraints of the system. Further, once the objective is determined, active flux constraints can also be identified and analyzed. This information can be potentially used in a predictive manner to improve cell culture results or clinical metabolic outcomes. As a result of the application of this method, it was found that in vitro cultured hepatocytes maximize oxygen uptake, coupling of urea and TCA cycles, and synthesis of serine and urea. Selection of these fluxes as the metabolic objective enables accurate prediction of the flux distribution in the system given a limited amount of flux data; thus presenting a workable in silico model for cultured hepatocytes. It is observed that an overall homeostasis picture is also emergent in the findings.

Hybrid filtering of feed stream noise from oscillating yeast cultures by combined Kalman and neural network configurations

Large continuous flow bioreactors are often under the influence of noise in the feed stream(s). Prior removal of noise is done by filters based either on specific algorithms or on artificial intelligence. Neither method is perfect. Hybrid filters combine both methods and thereby capitalize on their strengths while minimizing their weaknesses. In this study, a number of hybrid models have been compared for their ability to recover nearly noise-free stable oscillations of continuous flow Saccharomyces cerevisiae cultures from aberrant behavior caused by noise in the feed stream. Each hybrid filter had a different neural network in conjunction with an extended Kalman filter (EKF). The choice of the best configuration depended on the performance index. All hybrid filters were superior to both the EKF and purely neural filters. Along with previous studies of monotonic fermentations, the present results establish the suitability of hybrid neural filters for noise-affected bioreactors.

A method for estimation of elasticities in metabolic networks using steady state and dynamic metabolomics data and linlog kinetics

Background

Dynamic modeling of metabolic reaction networks under in vivo conditions is a crucial step in order to obtain a better understanding of the (dis)functioning of living cells. So far dynamic metabolic models generally have been based on mechanistic rate equations which often contain so many parameters that their identifiability from experimental data forms a serious problem. Recently, approximative rate equations, based on the linear logarithmic (linlog) format have been proposed as a suitable alternative with fewer parameters.

Results

In this paper we present a method for estimation of the kinetic model parameters, which are equal to the elasticities defined in Metabolic Control Analysis, from metabolite data obtained from dynamic as well as steady state perturbations, using the linlog kinetic format. Additionally, we address the question of parameter identifiability from dynamic perturbation data in the presence of noise. The method is illustrated using metabolite data generated with a dynamic model of the glycolytic pathway of Saccharomyces cerevisiae based on mechanistic rate equations. Elasticities are estimated from the generated data, which define the complete linlog kinetic model of the glycolysis. The effect of data noise on the accuracy of the estimated elasticities is presented. Finally, identifiable subset of parameters is determined using information on the standard deviations of the estimated elasticities through Monte Carlo (MC) simulations.

Conclusion

The parameter estimation within the linlog kinetic framework as presented here allows the determination of the elasticities directly from experimental data from typical dynamic and/or steady state experiments. These elasticities allow the reconstruction of the full kinetic model of Saccharomyces cerevisiae, and the determination of the control coefficients. MC simulations revealed that certain elasticities are potentially unidentifiable from dynamic data only. Addition of steady state perturbation of enzyme activities solved this problem.

Hybrid filtering to rescue stable oscillations from noise-induced chaos in continuous cultures of budding yeast

In large-scale fermentations with oscillating microbial cultures, noise is commonly present in the feed stream(s). As this can destabilize the oscillations and even generate chaotic behavior, noise filters are employed. Here three types of filters were compared by applying them to a noise-affected continuous culture of Saccharomyces cerevisiae with chaotic oscillations. The aim was to restore the original noise-free stable oscillations. An extended Kalman filter was found to be the least efficient, a neural filter was better and a combined hybrid filter was the best. In addition, better filtering of noise was achieved in the dilution rate than in the oxygen mass transfer coefficient. These results suggest the use of hybrid filters with the dilution rate as the manipulated variable for bioreactor control.

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.

Integrated analysis of metabolic phenotypes in Saccharomyces cerevisiae

Background

The yeast Saccharomyces cerevisiae is an important microorganism for both industrial processes and scientific research. Consequently, there have been extensive efforts to characterize its cellular processes. In order to fully understand the relationship between yeast's genome and its physiology, the stockpiles of diverse biological data sets that describe its cellular components and phenotypic behavior must be integrated at the genome-scale. Genome-scale metabolic networks have been reconstructed for several microorganisms, including S. cerevisiae, and the properties of these networks have been successfully analyzed using a variety of constraint-based methods. Phenotypic phase plane analysis is a constraint-based method which provides a global view of how optimal growth rates are affected by changes in two environmental variables such as a carbon and an oxygen uptake rate. Some applications of phenotypic phase plane analysis include the study of optimal growth rates and of network capacity and function.

Results

In this study, the Saccharomyces cerevisiae genome-scale metabolic network was used to formulate a phenotypic phase plane that displays the maximum allowable growth rate and distinct patterns of metabolic pathway utilization for all combinations of glucose and oxygen uptake rates. In silico predictions of growth rate and secretion rates and in vivo data for three separate growth conditions (aerobic glucose-limited, oxidative-fermentative, and microaerobic) were concordant.

Conclusions

Taken together, this study examines the function and capacity of yeast's metabolic machinery and shows that the phenotypic phase plane can be used to accurately predict metabolic phenotypes and to interpret experimental data in the context of a genome-scale model.

Unveiling steady-state multiplicity in hybridoma cultures: the cybernetic approach

Mammalian cells grown in suspension produce waste metabolites such as lactate, alanine, and ammonia, which reduce the yield of cell mass and the desired product on the nutrients supplied. Previous studies (Cruz et al., 1999; Europa et al., 2000; Follstad et al., 1999) have shown that the cells can be made to alter their metabolism by starving them on their nutrients in continuous cultures at low dilution rates or starting the culture as a fed-batch. This leads to multiple steady states in continuous reactors, with some states being more favorable than others. Mathematical models that take into account the metabolic regulation that leads to these multiple steady states are invaluable tools for bioreactor control. In this article we present a cybernetic modeling strategy in which Metabolic Flux Analysis (MFA) is used to guide the cybernetic formulation. The hybridoma model presented as a result of this strategy considers the partially substitutable, partially complementary nature of glucose and glutamine. The choice of competitions within the network is guided by MFA and the model is successful in explaining the three multiple steady states observed. The cybernetic model though identified for the hybridoma experiments of Hu and others (Europa et al., 2000) seem generally applicable to mammalian systems as it captures the pathways that are common to mammalian cells grown in suspension. The model presented here could be used for start-up strategies for continuous reactors and model-based feedback control for maintaining high productivity of the reactor.

Microbial metabolism as an evolutionary response: the cybernetic approach to modeling

The growth and metabolic capabilities of microorganisms depend on their interactions with the culture medium. Many media contain two or more key substrates, and an organism may have different preferences for the components. Microorganisms adjust their preferences according to the prevailing conditions so as to favor their own survival. Cybernetic modeling describes this evolutionary strategy by defining a goal that an organism tries to attain optimally at all times. The goal is often, but not always, maximization of growth, and it may require the cells to manipulate their metabolic processes in response to changing environmental conditions. The cybernetic approach overcomes some of the limitations of metabolic control analysis (MCA), but it does not substitute MCA. Here we review the development of the cybernetic modeling of microbial metabolism, how it may be combined with MCA, and what improvements are needed to make it a viable technique for industrial fermentation processes.

Cybernetic model of the growth dynamics of Saccharomyces cerevisiae in batch and continuous cultures

Growth of Saccharomyces cerevisiae on glucose in aerobic batch culture follows the well-documented diauxic pattern of completely fermenting glucose to ethanol during the first exponential growth phase, followed by an intermediate lag phase and a second exponential growth phase consuming ethanol. In continuous cultures over a range of intermediate dilution rates, the yeast bioreactor exhibits sustained oscillations in all the measured concentrations, such as cell mass, glucose, ethanol, and dissolved oxygen, the amounts of intracellular storage carbohydrates, such as glycogen and trehalose, the fraction of budded cells as well as the culture pH. We present here a structured, unsegregated model for the yeast growth dynamics developed from the 'cybernetic' modeling framework, to simulate the dynamic competition between all the available metabolic pathways. This cybernetic model accurately predicts all the key experimentally observed aspects: (i) in batch cultures, duration of the intermediate lag phase, sequential production and consumption of ethanol, and the dynamics of the gaseous exchange rates of oxygen and carbon dioxide; and (ii) in continuous cultures, the spontaneous generation of oscillations as well as the variations in period and amplitude of oscillations when the dilution rate or agitatin rate are changed.

Modelling and analysis of metabolic pathways

Modelling and analysis of metabolic pathways has received an increasing amount of attention over the past few years. Progress has been made in many aspects such as the identification of rate-controlling steps, applications of optimization principles, and stoichiometric analyses. In addition, the scope of modelling has also expanded. These efforts have led to an improved understanding of metabolic pathways and have facilitated their manipulation.

Segregated, structured, distributed models and their role in microbial ecology: A case study based on work done on the filter-feeding ciliateTetrahymena pyriformis

Microbial populations are composed of individual organisms each of which, if environmental circumstances are favorable, is undergoing change of its internal state through the operation of the set of processes that we call the cell cycle. The rate of progression through the cycle is subject to internal controls as well as external influences, and exhibits random as well as deterministic features. Microorganisms of the same species in different stages of the cell cycle have different internal states, and thus, the operation of the cell cycle is by itself sufficient to produce a distribution of states among the individual organisms of a population. In turn, the distribution of states produces distributions of the rates at which the cells of a population carry on their activities. Mathematical models of microbial growth that take the operation of the cell cycle and its consequences into account are more complicated than the kinds of models that are often used in microbial ecology. This paper gives some account of the nature, formulation, and uses of complex growth models. The account is illustrated by work done by the author and his collaborators H. M. Tsuchiya and more recently F. Srienc, as well as by others, on the filter-feeding ciliateTetrahymena pyriformis.

Verification of immune response optimality through cybernetic modeling

An immune response cascade that is T cell independent begins with the stimulation of virgin lymphocytes by antigen to differentiate into large lymphocytes. These immune cells can either replicate themselves or differentiate into plasma cells or memory cells. Plasma cells produce antibody at a specific rate up to two orders of magnitude greater than large lymphocytes. However, plasma cells have short life-spans and cannot replicate. Memory cells produce only surface antibody, but in the event of a subsequent infection by the same antigen, memory cells revert rapidly to large lymphocytes. Immunologic memory is maintained throughout the organism's lifetime. Many immunologists believe that the optimal response strategy calls for large lymphocytes to replicate first, then differentiate into plasma cells and when the antigen has been nearly eliminated, they form memory cells. A mathematical model incorporating the concept of cybernetics has been developed to study the optimality of the immune response. Derived from the matching law of microeconomics, cybernetic variables control the allocation of large lymphocytes to maximize the instantaneous antibody production rate at any time during the response in order to most efficiently inactivate the antigen. A mouse is selected as the model organism and bacteria as the replicating antigen. In addition to verifying the optimal switching strategy, results showing how the immune response is affected by antigen growth rate, initial antigen concentration, and the number of antibodies required to eliminate an antigen are included.