Application of hybrid cybernetic model in simulating myeloma cell culture co-consuming glucose and glutamine with mixed consumption patterns

A dynamic model called hybrid cybernetic model (HCM) based on structured metabolic network is established for simulating mammalian cell metabolism featured with partially substitutable and partially complementary consumption patterns of two substrates, glucose and glutamine. Benefiting from the application of elementary mode analysis (EMA), the complicated metabolic network is decomposed into elementary modes (EMs) facilitating the employment of the hybrid cybernetic framework to investigate the external and internal flux distribution and the regulation mechanism among them. According to different substrate combination, two groups of EMs are obtained, i.e., EMs associated with glucose uptake and simultaneous uptake of glucose and glutamine. Uptake fluxes through various EMs are coupled together via cybernetic variables to maximize substrate uptake. External fluxes and internal fluxes could be calculated and estimated respectively, by the combination of the stoichiometrics of metabolic networks and fluxes through regulated EMs. The model performance is well validated via three sets of experimental data. Through parameter identification of limited number of experimental data, other external metabolites are precisely predicted. The obtained kinetic parameters of three experimental cultures have similar values, which indicates the robustness of the model. Furthermore, the prediction performance of the model is successfully validated based on identified parameters.     

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.     

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.     

A complex systems theory of teleology

Part I [sections 2–4] draws out the conceptual links between modern conceptions of teleology and their Aristotelian predecessor, briefly outlines the mode of functional analysis employed to explicate teleology, and develops the notion of cybernetic organisation in order to distinguish teleonomic and teleomatic systems. Part II is concerned with arriving at a coherent notion of intentional control. Section 5 argues that intentionality is to be understood in terms of the representational properties of cybernetic systems. Following from this, section 6 argues that intentional control needs to be seen as a particular type of relationship between the system and its environment.I would like to gratefully acknowledge the large guiding input of Professor C. A. Hooker, who supervised the development of this paper from its inception. Bill herfel also provided valuable criticism of late drafts.     

A simple structured model describing the growth of Streptomyces lividans

The growth of Streptomyces lividans in defined media was modeled using a simple structured growth model. Conventional unstructured models like Monod kinetics, substrate inhibition kinetics, and the logistic equation were also used in an attempt to fit the data, but the results were all unsatisfactory. The main reason for failure in applying simple unstructured models is that they cannot describe the long lag phases sometimes observed during growth of S. lividans. The simple structured growth model was derived along similar principles to cybernetic growth models. This model quite accurately describes the growth of S. lividans. It assumes that the rate of assimilation of a substrate depends on the concentration of a specific key enzyme. This key enzyme is only produced in the presence of the substrate, and it is broken down at a steady rate. An enzyme synthesis allocation variable, w, similar to the cybernetic variable, u, described in cybernetic growth models, is proposed to control enzyme synthesis. Until the key enzyme concentration approaches its maximum level, very little substrate is consumed. And consequently, the lag phase is sustained.     

Application of cybernetic models to metabolic engineering: investigation of storage pathways

A cybernetic model is proposed to examine generic features of storage pathways. This model is capable of describing synthesis of carbon and non-carbon storage polymers. The effect of environmental conditions is evaluated using storage polymer level as a fraction of total biomass as a gauge of pathway performance. The base wild-type pathway is then analyzed to determine the effect of genetic alterations upon system performance. Proposed modifications are tested using the cybernetic model as a diagnostic tool to ascertain the ramifications of potential genetic alterations. A methodology is developed within the cybernetic framework to describe alterations of enzyme activity and over-expression of pathway enzymes. Copyright 1998 John Wiley & Sons, Inc.     

A simultaneous saccharification and fermentation model for dynamic growth environments

Many mathematical models by researchers have been formulated for Saccharomyces cerevisiae which is the common yeast strain used in modern distilleries. A cybernetic model that can account for varying concentrations of glucose, ethanol and organic acids on yeast cell growth dynamics does not exist. A cybernetic model, consisting of 4 reactions and 11 metabolites simulating yeast metabolism, was developed. The effects of variables such as temperature, pH, organic acids, initial inoculum levels and initial glucose concentration were incorporated into the model. Further, substrate and product inhibitions were included. The model simulations over a range of variables agreed with hypothesized trends and to observations from other researchers. Simulations converged to expected results and exhibited continuity in predictions for all ranges of variables simulated. The cybernetic model did not exhibit instability under any conditions simulated.     

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.     

Adding artificial feedback to a simple aquatic ecosystem: the cybernetic nature of ecosystems revisited

A cybernetic system can be defined as one controlled by feedback, that is, a system in which input is partially determined by output. I explored the cybernetic properties of a simple planktonic ecosystem by introducing an artificial feedback loop; light energy delivered to the system was linked to the ecosystem's productivity and respiration. Specifically, I programmed a computer to turn lights on and off when dissolved oxygen reached low and high setpoints, respectively. Three treatments were applied that differed in light intensity and in range between high and low setpoints. Experiments were repeated under high and low nutrient conditions. The added feedback did not substantially alter responses to limiting factors from those expected under fixed duration lighting. However, several novel features were observed, including poor coupling between productivity and respiration, similar patterns in energy demand among treatments, and oscillations in primary productivity. These observations can be viewed as support for a holistic, cybernetic view of ecological systems. This view complements the dominant mechanistic-reductionist perspective on causality in ecosystems. The experimental addition of new feedback is apparently a useful means of investigating the self-organizational properties of ecosystems and may also improve our understanding of the consequences of anthropogenically induced feedback in natural and managed systems.     

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.     

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.     

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.     

Prediction of dynamic metabolic behavior of Pediococcus pentosaceus producing lactic acid from lignocellulosic sugars

A dynamic metabolic model is presented for Pediococcus pentosaceus producing lactic acid from lignocellulose-derived mixed sugars including glucose, mannose, galactose, arabinose, and xylose. Depending on the pairs of mixed sugars, P. pentosaceus exhibits diverse (i.e., sequential, simultaneous or mixed) consumption patterns. This regulatory behavior of P. pentosaceus is portrayed using the hybrid cybernetic model (HCM) framework which views elementary modes of the network as metabolic options dynamically modulated. Comprehensive data are collected for model identification and validation through fermentation experiments involving single substrates and various combinations of mixed sugars. Most sugars are metabolized rather sequentially while co-consumption of galactose and arabinose is observed. It is demonstrated that the developed HCM successfully predicts mixed sugar data based on the parameters identified mostly from single substrate data only. Further, we discuss the potential of HCMs as a tool for predicting intracellular flux distribution with comparison with flux balance analysis.     

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.     

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.     

A cybernetic model of growth correlation in young apple trees

Growth correlations among lateral shoots of one-year-old apple treesMalus Mill., were described. The existence of a mechanism was postulated through which small original differences between buds or young shoots are quickly augmented, thus leading to differentiation of long shoots and short shoots. Existing hypotheses do not seem sufficient for explaining correlative phenomena of this type; a cybernetic approach was therefore applied. Studying growth correlations in terms of cybernetic revealed that previous hypotheses concerning correlations do not contradict each other as often thought, but depict different links in a more general chain of events. A cybernetic model points out the importance of root influences in interaction among shoots. It also shows that synergism between auxin, gibberellin and cytokinin in xylem and phloem differentiation and in starch metabolism is very important for understanding correlations in apple trees.     

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 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.     

Cybernetic modeling of the cephalosporin C fermentation process by Cephalosporium acremonium

A cybernetic mathematical model has been developed to describe the production of cephalosporin C. In developing the model, diauxic behavior of substrate consumption, morphological differentiation of cells, and catabolite repression of cephalosporin C production by the preferred substrate, glucose, were considered. The proposed model was tested on the experimental data from the literature and could adequately describe the morphological differentiation of cells, the sequential utilization of carbon sources and the production of cephalosporin C. It could be a useful tool to optimize the production of cephalosporin C by Cephalosporium acremonium in batch, fed-batch or continuous operations.