Cybernetic modeling of growth in mixed, substitutable substrate environments: Preferential and simultaneous utilization

Growth of microorganisms on substitutable substrate mixtures display diverse growth dynamics characterized by simultaneous or preferential uptake of carbon sources. This article shows that cybernetic modeling concepts which were successful in predicting diauxic growth patterns can be extended to describe simultaneous consumption of substrates. Thus the growth of Escherichia coli on mixtures of glucose and organic acids such as pyruvate, fumarate, and succinate has been described successfully by the cybernetic model presented here showing both diauxic and simultaneous uptake when observed. The model also describes the changes in utilization patterns that occur under changing dilution rates, substrate concentrations, and models of preculturing. The model recognizes the importance of the synthesis of biosynthetic precursors in cell growth through a kinetic structure that is quite general for any mixture of carbon-energy sources. (c) 1996 John Wiley & Sons, Inc.     

Complex growth dynamics in batch cultures: experiments and cybernetic models

The cybernetic framework developed by Ramkrishna and co-workers is shown to encompass the regulation of nutrient transport processes as well as the effect of nutrient transport on the biotic phase. A structured model which accounts for both an abiotic or environmental phase and a biotic or cellular phase is proposed to describe bacterial growth on lactose as the limiting carbon and energy source. In the presence of lactose, competing uptake mechanisms are proposed. At low lactose concentrations, an energy-requiring transport process is the preferred uptake mechanism. The coupling between cellular energetics and nutrient uptake results in an interesting intermittent growth phenomenon. As the concentration of lactose increases, a nonenergetic transport process is preferred and cellular growth ceases to be intermittent. Model simulations are compared with previously reported experimental results and exhibit good agreement over the entire range of initial lactose concentrations.     

Cybernetic modeling of bacteriol cultures at low growth rates: single-substrate systems

The cybernetic framework developed by Ramkrishna and co-workers has been expanded to include the effects of cellular maintenance energy requirements on biomass levels in slow-growing, carbon-substrate-limited cultures. A simple structured model, based on the existence of distinct key enzymes for growth and maintenance functions, is presented. Comparisons of the model with experimental data for the growth of Klebsiella oxytoca in constant fed-batch culture on glucose, fructose, arabinose, and xylose show good agreement. In addition, perturbed fed-batch culture experiments indicate that slow-growing cultures respond less rapidly to a removal of the growth limitation than do faster-growing ones. The possibility of a growth-rate dependent "critical resource" is discussed.     

Cybernetic modeling of iron-limited growth and siderophore production

The cybernetic modeling framework developed by Ramkrishna and co-workers has been applied to a case of bacterial metabolite production, namely the production of siderophores (iron-chelating agents) associated with iron-limiting fermentation conditions. Experimental growth data showed that, even though final biomass levels were controlled by exhaustion of the carbon source, iron-limiting conditions also affected the biomass yield. A structured model which includes the process of an iron-limiting energy resource production was able to quantitatively account for this apparent dual-substrate limitation over a wide range of batch and continuous operating conditions. The experiments data also showed quite large difference in iron uptake over the wide range of operating condition and iron levels investigated. The inclusion in the model of the processes of low and high (siderophore-mediated) affinity iron transport, and siderophore production led to simulation results that were in good quantitative agreement with the siderophore, medium and cell iron levels, in both batch and steady-state continuous culture operating conditions.     

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.     

Prediction of dynamic behavior of mutant strains from limited wild-type data

Metabolic engineering is the field of introducing genetic changes in organisms so as to modify their function towards synthesizing new products of high impact to society. However, engineered cells frequently have impaired growth rates thus seriously limiting the rate at which such products are made. The problem is attributable to inadequate understanding of how a metabolic network functions in a dynamic sense. Predictions of mutant strain behavior in the past have been based on steady state theories such as flux balance analysis (FBA), minimization of metabolic adjustment (MOMA), and regulatory on/off minimization (ROOM). Such predictions are restricted to product yields and cannot address productivity, which is of focal interest to applications. We demonstrate that our framework ( [Song and Ramkrishna, 2010] and [Song and Ramkrishna, 2011]), based on a “cybernetic” view of metabolic systems, makes predictions of the dynamic behavior of mutant strains of Escherichia coli from a limited amount of data obtained from the wild-type. Dynamic frameworks must necessarily address the issue of metabolic regulation, which the cybernetic approach does by postulating that metabolism is an optimal dynamic response of the organism to the environment in driving reactions towards ensuring survival. The predictions made in this paper are without parallel in the literature and lay the foundation for rational metabolic engineering.     

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.     

Metabolic engineering from a cybernetic perspective: aspartate family of amino acids

Using the modular cybernetic framework developed by Varner and Ramkrishna (Varner and Ramkrishna; 1998a, b) a cybernetic model is formulated that describes the time evolution of the aspartate family of amino acids in Corynebacterium lactofermentum ATCC 21799. The network model formulation is employed in the role of a diagnostic tool for the overproduction of threonine. More precisely, having determined a parameter set that describes the time evolution of a base strain (lysine producer), the model predicted response to genetic perturbations, designed to enhance the level of threonine, are simulated using an appropriately modified cybernetic model and compared with the experimental results of Stephanopoulos and Sinskey (Colón et al., 1995a, Appl. Environ. Microbiol. 61, 74-78) for identical genetic perturbations. It is found that the model predicted response to enzymatic over-expression in the aspartate pathway agrees, for the most part, with experimental observations within the experimental error bounds. This result lends credence to the hypothesis that cybernetic models can be employed to predict the local response of a metabolic network to genetic perturbation, thereby, affording cognizance of the potential pitfalls of a particular genetic alteration strategy a priori.     

Cybernetic modeling and regulation of metabolic pathways in multiple steady states of hybridoma cells

Hybridoma cells utilize a pair of complementary and partially substitutable substrates, glucose and glutamine, for growth. It has been shown that cellular metabolism shifts under different culture conditions. When those cultures at different metabolic states are switched to a continuous mode, they reach different steady states under the same operating conditions. A cybernetic model was constructed to describe the complementary and partial substitutable nature of substrate utilization. The model successfully predicted the metabolic shift and multiple steady-state behavior. The results are consistent with the experimental observation that the history of the culture affects the resulting steady state.     

Microbial Metabolism as an Evolutionary Response: The Cybernetic Approach to Modeling

ABSTRACT:?

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.

IMTECH communication no.001/2001     

Cybernetic models based on lumped elementary modes accurately predict strain‐specific metabolic function

In a recent article, Song and Ramkrishna (Song and Ramkrishna [2010]. Biotechnol Bioeng 106(2):271–284) proposed a lumped hybrid cybernetic model (L‐HCM) towards extracting maximum information about metabolic function from a minimum of data. This approach views the total uptake flux as distributed among lumped elementary modes (L‐EMs) so as to maximize a prescribed metabolic objective such as growth or uptake rate. L‐EM is computed as a weighted average of EMs where the weights are related to the yields of vital products (i.e., biomass and ATP). In this article, we further enhance the predictive power of L‐HCMs through modifications in lumping weights with additional parameters that can be tuned with data viewed to be critical. The resulting model is able to make predictions of diverse metabolic behaviors varying greatly with strain types as evidenced from case studies of anaerobic growth of various Escherichia coli strains. Incorporation of the new lumping formula into L‐HCM remarkably improves model predictions with a few critical data, thus presenting L‐HCM as a dynamic tool as being not only qualitatively correct but also quantitatively accurate. Biotechnol. Bioeng. 2011; 108:127–140. © 2010 Wiley Periodicals, Inc.     

Are microbes intelligent beings?: An assessment of cybernetic modeling

Microorganisms growing in a multi-substrate medium have different and varying preferences for the various components of the medium. The preferences depend on the operating conditions and the substrates may be utilized sequentially or simultaneously. Sometimes an organism may change its preferences among substrates and/or switch between sequential and simultaneous utilization. These aspects are difficult to describe through models based on chemical and physical laws alone. Cybernetic modeling ascribes to microorganisms the ability to perceive their environment (i.e. the growth medium) and make 'intelligent' choices regarding substrate utilization to maximize an objective, which is usually the growth rate. This article reviews the development of cybernetic modeling since it began in 1982. Different workers have suggested different perspectives of how microbes make optimal use of their resources. These are discussed and future directions for improvement are indicated.     

Modeling Microbially Induced Carbon Degradation in Redox-Stratified Subsurface Environments: Concepts and Open Questions

The degradation of organic matter, including organic contaminants, in subsurface environments is controlled by the abundances and functional capabilities of the resident microorganisms. As a consequence, modeling approaches simulating the fate of organics and related changes in redox conditions have to account for the effects of microbial activity on the degradation kinetics, as well as for the spatial and temporal distributions of the chemical species (e.g., terminal electron acceptors, nutrients or toxic substances) that control microbial activity. The present paper reviews the principal modeling approaches that are used to simulate the degradation of organic matter in water-saturated porous media. Special attention is devoted to modeling the bioavailability of chemical substrates of microbial reactions, and the sequential occurrence of terminal electron accepting pathways. While the various model approaches found in the literature are capable of reproducing field data sets from various environmental settings, they are rarely compared in terms of performance and predictive ability. Most approaches incorporate simplifications or empirical rate laws, which limit their range of application. Thus, there remains a need for further development of more general, process-based modeling concepts to represent microbially mediated reactive processes.     

Unified kinetic treatment for growth on dual nutrients

This paper presents a new formulation for the analysis of growth kinetics on multiple nutrients. The baseline for the theory is the concept that a noninteractive growth process occurs among perfectly substitutable nutrients if the locus of points of the substrate concentrations producing equal growth rate is linear. A deviation function is then defined with respect to this base case, and several models for this function are suggested. The underlying theory is taken by analogy with mixture thermodynamics. The proposed formulation is tested against data in the literature on growth under substitutable and complementary substrate mixtures. (c) 1994 John Wiley & Sons, Inc.     

Cybernetic modelling of growth and ethanol production in a recombinant Saccharomyces cerevisiae strain secreting a bifunctional fusion protein

Recombinant Saccharomyces cerevisiae YPB-G strain secreting a fusion protein displaying both BsAAase/GAase activities was grown in 1.5 l YPS media containing single (starch) and mixed carbon sources (glucose+starch) using a 2.5 l New Brunswick BiofloIII fermenter. Ethanol and biomass formation, starch utilisation, secretion of the amylolytic enzymes (-amylase and glucoamylase), accumulation of reducing sugars and glucose were followed during the fermentation of YPB-G under different conditions. Moreover, a model has been developed for the growth of recombinant yeast on substitutable substrates using cybernetic framework principles and incorporating product formation. In the present work, both the biphasic and the diauxic growth patterns observed experimentally in batch culture of recombinant yeast cells were simulated successfully by modifying the cybernetic framework to include ethanol formation and the degradation kinetics of starch which is not directly utilised by yeast. The model can further be expanded to fed-batch systems.     

The concept of multiple-nutrient-limited growth of microorganisms and its application in biotechnological processes

The "law of the minimum" (Liebig's law) states that usually one nutrient restricts the maximum quantity of biomass that can be produced within a system, whereas all other nutrients are in excess. This general rule has been applied also to the growth of microorganisms, e.g., by adjusting the relative concentrations of the individual nutrients in growth media such that one of them, in the case of heterotrophic microbes, usually the carbon source, determines the maximum cell density that can be obtained in a culture. However, experimental data demonstrated that growth of microbial cultures can be limited simultaneously by two or more nutrients. These authors reported that during growth of bacteria and yeasts at a constant dilution rate in the chemostat, three distinct growth regimes were recognised as a function of the C:N ratio in the inflowing medium: (1) a clearly carbon-limited regime with the nitrogen source in excess, (2) a transition ("double-nutrient-limited") growth regime where both the carbon and the nitrogen source were below the detection limit, and (3) a clearly nitrogen-limited growth regime with the carbon source in excess. Subsequent calculations suggested that the extension and position of this double-nutrient-limited zone should be strongly dependent on the imposed growth rate: Whereas it is very narrow at high growth rates it should become very broad during slow growth. This pattern as a function of growth rate has now been confirmed for a number of different organisms. In industrial processes, microbial growth is always in some way controlled by the limited availability of nutrients, and limitation of specific nutrients is frequently used to force microbial cultures into a productive physiological state. This article will discuss what the consequences of multiple-nutrient-limited growth are for industrial processes and how the concept might be applied. Specific examples will be given that demonstrate the advantages and the potential of multiple nutrient-limited growth conditions for industrial production processes.     

Cybernetic modeling based on pathway analysis for Penicillium chrysogenum fed-batch fermentation

A macrokinetic model employing cybernetic methodology is proposed to describe mycelium growth and penicillin production. Based on the primordial and complete metabolic network of Penicillium chrysogenum found in the literature, the modeling procedure is guided by metabolic flux analysis and cybernetic modeling framework. The abstracted cybernetic model describes the transients of the consumption rates of the substrates, the assimilation rates of intermediates, the biomass growth rate, as well as the penicillin formation rate. Combined with the bioreactor model, these reaction rates are linked with the most important state variables, i.e., mycelium, substrate and product concentrations. Simplex method is used to estimate the sensitive parameters of the model. Finally, validation of the model is carried out with 20 batches of industrial-scale penicillin cultivation.     

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.     

Predicting stability of mixed microbial cultures from single species experiments: 1. Phenomenological model

The growth of mixed microbial cultures on mixtures of substrates is a fundamental problem of both theoretical and practical interest. On the one hand, the literature is abundant with experimental studies of mixed-substrate phenomena [T. Egli, The ecological and physiological significance of the growth of heterotrophic microorganisms with mixtures of substrates, Adv. Microbiol. Ecol. 14 (1995) 305-386]. On the other hand, a number of mathematical models of mixed-substrate growth have been analyzed in the last three decades. These models typically assume specific kinetic expressions for substrate uptake and biomass growth rates and their predictions are formulated in terms of parameters of the model. In this work, we formulate and analyze a general mathematical model of mixed microbial growth on mixtures of substitutable substrates. Using this model, we study the effect of mutual inhibition of substrate uptake rates on the stability of the equilibria of the model. Specifically, we address the following question: How much of the dynamics exhibited by two competing species can be inferred from single species data? We provide geometric criteria for stability of various types of equilibria corresponding to non-competitive exclusion, competitive exclusion, and coexistence of two competing species in terms of growth isoclines and consumption curves. A growth isocline is a curve in the plane of substrate concentrations corresponding to the zero net growth of a given species. In [G.T. Reeves, A. Narang, S.S. Pilyugin, Growth of mixed cultures on mixtures of substitutable substrates: The operating diagram for a structured model, J. Theor. Biol. 226 (2004) 143-157], we introduced consumption curves as sets of all possible combinations of substrate concentrations corresponding to balanced growth of a single microbial species. Both types of curves can be obtained in single species experiments.     

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

ABSTRACT

Poly(β-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.