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     

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.     

Metabolic regulation in bacterial continuous cultures: II

The transient behavior of a continuous culture of Klebsiella pneumoniae with mixed feed of glucose and xylose arising from step-up and step-down in dilution rates and from a feed-switching experiment is presented. he organism gradually switches from simultaneous utilization of the substrates at low growth rates to preferred utilization of the faster substrate (i.e, supporting a higher growth rate) at high dilution rates. The metabolic lags following a step increase in dilution rate and a significant accumulation of the slower substrate during the transient period result from the effects of metabolic regulation. The cybernetic modeling approach that successfully described the foregoing situations with single-substrate feeds is employed to describe mixed substrate behavior. The parameters in the mixed-substrate (glucose and xylose) model are the same as those in the single-substrate models with the singular exception of the rate constant for the xylose growth enzyme synthesis. The reason for this discrepancy is discussed in detail. It appears that the constitutive rate of enzyme synthesis for growth on a given substrate may be related to the past history of the organism in regard to whether or not the organism has been exposed to the particular substrate. Thus, the results further demonstrate the ability of the framework to effectively describe metabolic regulation in batch, fedbatch, and continuous microbial cultures.     

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.     

Synthesizing cellular intelligence and artificial intelligence for bioprocesses

Microbial processes operated under realistic conditions are difficult to describe by mechanistic models, thereby limiting their optimization and control. Responses of living cells to their environment suggest that they possess some "innate intelligence". Such responses have been modeled by a cybernetic approach. Furthermore, the overall behavior of a bioreactor containing a population of cells may be described and controlled through artificial intelligence methods. Therefore, it seems logical to combine cybernetic models with artificial intelligence to evolve an integrated intelligence-based strategy that is physiologically more faithful than the current approaches. This possibility is discussed, together with practical considerations favoring a hybrid approach that includes some mathematical modeling.     

Integrating cybernetic modeling with pathway analysis provides a dynamic, systems-level description of metabolic control

Cybernetic modeling strives to uncover the inbuilt regulatory programs of biological systems and leverage them toward computational prediction of metabolic dynamics. Because of its focus on incorporating the global aims of metabolism, cybernetic modeling provides a systems-oriented approach for describing regulatory inputs and inferring the impact of regulation within biochemical networks. Combining cybernetic control laws with concepts from metabolic pathway analysis has culminated in a systematic strategy for constructing cybernetic models, which was previously lacking. The newly devised framework relies upon the simultaneous application of local controls that maximize the net flux through each elementary flux mode and global controls that modulate the activities of these modes to optimize the overall nutritional state of the cell. The modeling concepts are illustrated using a simple linear pathway and a larger network representing anaerobic E. coli central metabolism. The E. coli model successfully describes the metabolic shift that occurs upon deleting the pta-ackA operon that is responsible for fermentative acetate production. The model also furnishes predictions that are consistent with experimental results obtained from additional knockout strains as well as strains expressing heterologous genes. Because of the stabilizing influence of the included control variables, the resulting cybernetic models are more robust and reliable than their predecessors in simulating the network response to imposed genetic and environmental perturbations.     

Metabolic modeling of Saccharomyces cerevisiae using the optimal control of homeostasis: a cybernetic model definition

A model is presented to describe the observed behavior of microorganisms that aim at metabolic homeostasis while growing and adapting to their environment in an optimal way. The cellular metabolism is seen as a network with a multiple controller system with both feedback and feedforward control, i.e., a model based on a dynamic optimal metabolic control. The dynamic network consists of aggregated pathways, each having a control setpoint for the metabolic states at a given growth rate. This set of strategies of the cell forms a true cybernetic model with a minimal number of assumptions. The cellular strategies and constraints were derived from metabolic flux analysis using an identified, biochemically relevant, stoichiometry matrix derived from experimental data on the cellular composition of continuous cultures of Saccharomyces cerevisiae. Based on these data a cybernetic model was developed to study its dynamic behavior. The growth rate of the cell is determined by the structural compounds and fluxes of compounds related to central metabolism. In contrast to many other cybernetic models, the minimal model does not consist of any assumed internal kinetic parameters or interactions. This necessitates the use of a stepwise integration with an optimization of the fluxes at every time interval. Some examples of the behavior of this model are given with respect to steady states and pulse responses. This model is very suitable for describing semiquantitatively dynamics of global cellular metabolism and may form a useful framework for including structured and more detailed kinetic models.     

Hierarchical amino acid utilization and its influence on fermentation dynamics: rifamycin B fermentation using Amycolatopsis mediterranei S699, a case study

Background  

Industrial fermentation typically uses complex nitrogen substrates which consist of mixture of amino acids. The uptake of amino acids is known to be mediated by several amino acid transporters with certain preferences. However, models to predict this preferential uptake are not available. We present the stoichiometry for the utilization of amino acids as a sole carbon and nitrogen substrate or along with glucose as an additional carbon source. In the former case, the excess nitrogen provided by the amino acids is excreted by the organism in the form of ammonia. We have developed a cybernetic model to predict the sequence and kinetics of uptake of amino acids. The model is based on the assumption that the growth on a specific substrate is dependent on key enzyme(s) responsible for the uptake and assimilation of the substrates. These enzymes may be regulated by mechanisms of nitrogen catabolite repression. The model hypothesizes that the organism is an optimal strategist and invests resources for the uptake of a substrate that are proportional to the returns.     

Regulatory design in a simple system integrating membrane potential generation and metabolic ATP consumption. Robustness and the role of energy dissipating processes

Bacterial physiological responses integrate energy-coupling processes at the membrane level with metabolic energy demand. The regulatory design behind these responses remains largely unexplored. Propionigenium modestum is an adequate organism to study these responses because it presents the simplest scheme known integrating membrane potential generation and metabolic ATP consumption. A hypothetical sodium leak is added to the scheme as the sole regulatory site. Allosteric regulation is assumed to be absent. Information of the rate equations is not available. However, relevant features of the patterns of responses may be obtained using Metabolic Control Analysis (MCA) and Metabolic Control Design (MCD). With these tools, we show that membrane potential disturbances can be compensated by adjusting the leak flux, without significant perturbations of ATP consumption. Perturbations of membrane potential by ATP demand are inevitable and also require compensatory changes in the leak. Numerical simulations were performed with a kinetic model exhibiting the responses for small changes obtained with MCA and MCD. A modest leak (10% of input) was assumed for the reference state. We found that disturbances in membrane potential and ATP consumption, produced by environmental perturbations of the cation concentration, may be reverted to the reference state adjusting the leak. Leak changes can also compensate for undesirable effects on membrane potential produced by changes in nutrient availability or ATP demand, in a wide range of values. The system is highly robust to parameter fluctuations. The regulatory role of energy dissipating processes and the trade-off between energetic efficiency and regulatory capacity are discussed.     

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.     

On the matching and proportional laws of cybernetic models

The Matching and Proportional Laws are heuristic control policies that have found widespread use in cybernetic models of biological systems. Within this context, the laws serve as optimization surrogates for predicting the response of metabolic control circuits that modulate enzyme levels and activities. The key result of the current contribution is to demonstrate clearly the optimality properties of these laws and the assumptions that underlie their development. In doing so, we arrive at generalized versions of the Matching and Proportional Laws that are shown to collapse to the forms originally derived by Kompala et al. (Biotechnol. Bioeng. 1986, 28, 1044-1055) when certain simplifications are applied. As a further line of investigation, we show how Kompala et al.'s cybernetic laws compare with alternative control policies in their ability to describe diauxic growth behavior of microbial cultures. We find that Kompala et al.'s model describes the experimental observations more accurately than other limiting-case models that are either too aggressive or too passive in capturing the mixed-substrate growth rates and intermediate lag periods. Monte Carlo analysis of computational growth experiments in which strains obeying different regulatory policies directly compete for available nutrients reveals that the Matching and Proportional Law policy does not maximize the average growth rate of the culture. However, it allocates metabolic resources more frugally than other policies that outperform it and may be more realistic in reflecting the cell's true fitness-to-cost tradeoff as judged by its agreement with experimental growth data.     

NMR-based stable isotope resolved metabolomics in systems biochemistry

An important goal of metabolomics is to characterize the changes in metabolic networks in cells or various tissues of an organism in response to external perturbations or pathologies. The profiling of metabolites and their steady state concentrations does not directly provide information regarding the architecture and fluxes through metabolic networks. This requires tracer approaches. NMR is especially powerful as it can be used not only to identify and quantify metabolites in an unfractionated mixture such as biofluids or crude cell/tissue extracts, but also determine the positional isotopomer distributions of metabolites derived from a precursor enriched in stable isotopes such as (13)C and (15)N via metabolic transformations. In this article we demonstrate the application of a variety of 2-D NMR editing experiments to define the positional isotopomers of compounds present in polar and non-polar extracts of human lung cancer cells grown in either [U-(13)C]-glucose or [U-(13)C,(15)N]-glutamine as source tracers. The information provided by such experiments enabled unambiguous reconstruction of metabolic pathways, which is the foundation for further metabolic flux modeling.     

Growth of microbial populations in nonminimal media: some considerations for modeling

Ramkrishna and his co-workers have developed so-called cybernetic models which purport to describe, among other things, how microorganisms make choices when presented with two or more functionally equivalent, or substitutable, nutrients that are sources of carbon and available energy. In general, however, organisms are presented with choices not just between nutrients that are substitutable for one another, but also between sets of nutrients some of which are by no means substitutable for one another. It is postulated herein that the main ideas of cybernetic modeling apply to these more general choices as they seem to apply to the choices considered by Ramkrishna and his co-workers. Some consequences of the postulate are worked out for steady-state growth situations where two, or in one case three, nutrients limit or potentially limit growth rate. If predicted phenomena are observed experimentally so as to verify the postulate, a significantly improved basis for understanding growth of microorganisms in practical fermentation media as well as in natural situations will be provided by this application of cybernetic modeling ideas.     

From the sequence to cell modeling: comprehensive functional genomics in Escherichia coli

As a result of the enormous amount of information that has been collected with E. coli over the past half century (e.g. genome sequence, mutant phenotypes, metabolic and regulatory networks, etc.), we now have detailed knowledge about gene regulation, protein activity, several hundred enzyme reactions, metabolic pathways, macromolecular machines, and regulatory interactions for this model organism. However, understanding how all these processes interact to form a living cell will require further characterization, quantification, data integration, and mathematical modeling, systems biology. No organism can rival E. coli with respect to the amount of available basic information and experimental tractability for the technologies needed for this undertaking. A focused, systematic effort to understand the E. coli cell will accelerate the development of new post-genomic technologies, including both experimental and computational tools. It will also lead to new technologies that will be applicable to other organisms, from microbes to plants, animals, and humans. E. coli is not only the best studied free-living model organism, but is also an extensively used microbe for industrial applications, especially for the production of small molecules of interest. It is an excellent representative of Gram-negative commensal bacteria. E. coli may represent a perfect model organism for systems biology that is aimed at elucidating both its free-living and commensal life-styles, which should open the door to whole-cell modeling and simulation.     

Modeling of the metabolic energy dissipation for restricted tumor growth

Energy dissipation mostly represents unwanted outcome but in the biochemical processes it may alter the biochemical pathways. However, it is rarely considered in the literature although energy dissipation and its alteration due to the changes in cell microenvironment may improve methods for guiding chemical and biochemical processes in the desired directions. Deeper insight into the changes of metabolic activity of tumor cells exposed to osmotic stress or irradiation may offer the possibility of tumor growth reduction. In this work effects of the osmotic stress and irradiation on the thermodynamical affinity of tumor cells and their damping effects on metabolic energy dissipation were investigated and modeled. Although many various models were applied to consider the tumor restrictive growth they have not considered the metabolic energy dissipation. In this work a pseudo rheological model in the form of “the metabolic spring-pot element” is formulated to describe theoretically the metabolic susceptibility of tumor spheroid. This analog model relates the thermodynamical affinity of cell growth with the volume expansion of tumor spheroid under isotropic loading conditions. Spheroid relaxation induces anomalous nature of the metabolic energy dissipation which causes the damping effects on cell growth. The proposed model can be used for determining the metabolic energy “structure” in the context of restrictive cell growth as well as for predicting optimal doses for cancer curing in order to tailor the clinical treatment for each person and each type of cancer.     

Modeling with a view to target identification in metabolic engineering: A critical evaluation of the available tools

The state of the art tools for modeling metabolism, typically used in the domain of metabolic engineering, were reviewed. The tools considered are stoichiometric network analysis (elementary modes and extreme pathways), stoichiometric modeling (metabolic flux analysis, flux balance analysis, and carbon modeling), mechanistic and approximative modeling, cybernetic modeling, and multivariate statistics. In the context of metabolic engineering, one should be aware that the usefulness of these tools to optimize microbial metabolism for overproducing a target compound depends predominantly on the characteristic properties of that compound. Because of their shortcomings not all tools are suitable for every kind of optimization; issues like the dependence of the target compound's synthesis on severe (redox) constraints, the characteristics of its formation pathway, and the achievable/desired flux towards the target compound should play a role when choosing the optimization strategy. © 2010 American Institute of Chemical Engineers Biotechnol. Prog., 2010     

Cybernetic modeling of microbial growth on multiple substrates

The internal regulatory processes, which underlie a variety of behavior in microbial growth on multiple substrates, are viewed as a manifestation of an invariant strategy to optimize some goal of the cells. A goal-seeking or cybernetic model is proposed here, with the optimization obased on a short-term perspective of response to the environment. The model parameters are determined from the growth data on single substrates. The model predicts the entire range of microbial growth behavior on multiple substrates from simultaneous utilization of all sugars to sequential utilization with pronounced diauxic lags. It is shown to predict the many variations of the diauxic phenomenon in different growth conditions. The transients in continuous culture growth on mixed substrates caused by varying the feed strategies are easily simulated by this model. The framework of this model can be applied to batch or continuous culture growth of many bacteria on different combinations of substrates.     

Is metabolic rate a universal ‘pacemaker’ for biological processes?

A common, long‐held belief is that metabolic rate drives the rates of various biological, ecological and evolutionary processes. Although this metabolic pacemaker view (as assumed by the recent, influential ‘metabolic theory of ecology’) may be true in at least some situations (e.g. those involving moderate temperature effects or physiological processes closely linked to metabolism, such as heartbeat and breathing rate), it suffers from several major limitations, including: (i) it is supported chiefly by indirect, correlational evidence (e.g. similarities between the body‐size and temperature scaling of metabolic rate and that of other biological processes, which are not always observed) – direct, mechanistic or experimental support is scarce and much needed; (ii) it is contradicted by abundant evidence showing that various intrinsic and extrinsic factors (e.g. hormonal action and temperature changes) can dissociate the rates of metabolism, growth, development and other biological processes; (iii) there are many examples where metabolic rate appears to respond to, rather than drive the rates of various other biological processes (e.g. ontogenetic growth, food intake and locomotor activity); (iv) there are additional examples where metabolic rate appears to be unrelated to the rate of a biological process (e.g. ageing, circadian rhythms, and molecular evolution); and (v) the theoretical foundation for the metabolic pacemaker view focuses only on the energetic control of biological processes, while ignoring the importance of informational control, as mediated by various genetic, cellular, and neuroendocrine regulatory systems. I argue that a comprehensive understanding of the pace of life must include how biological activities depend on both energy and information and their environmentally sensitive interaction. This conclusion is supported by extensive evidence showing that hormones and other regulatory factors and signalling systems coordinate the processes of growth, metabolism and food intake in adaptive ways that are responsive to an organism's internal and external conditions. Metabolic rate does not merely dictate growth rate, but is coadjusted with it. Energy and information use are intimately intertwined in living systems: biological signalling pathways both control and respond to the energetic state of an organism. This review also reveals that we have much to learn about the temporal structure of the pace of life. Are its component processes highly integrated and synchronized, or are they loosely connected and often discordant? And what causes the level of coordination that we see? These questions are of great theoretical and practical importance.