Exacting predictions by cybernetic model confirmed experimentally: Steady state multiplicity in the chemostat

Kim, Sang Hyun; Song, Hyun‐Seob; Sunkara, Sunil R.; Lali, Arvind; Ramkrishna, Doraiswami

doi:10.1002/btpr.1583

Cited by 37 publications

(19 citation statements)

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“…The cybernetic approach hypothesizes that cellular metabolism is optimally regulated to achieve a certain objective function that is related to actual rates rather than yields. Based on optimal control theory, the cybernetic approach then provides accurate predictions of cellular responses to environmental and genetic perturbations, without relying on mechanistic details of regulation (see [44][45][46][47][48][49] for examples of cybernetic modeling).…”

Section: Metabolic Function-based Dynamic Modelingmentioning

confidence: 99%

Mathematical Modeling of Microbial Community Dynamics: A Methodological Review

et al. 2014

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Microorganisms in nature form diverse communities that dynamically change in structure and function in response to environmental variations. As a complex adaptive system, microbial communities show higher-order properties that are not present in individual microbes, but arise from their interactions. Predictive mathematical models not only help to understand the underlying principles of the dynamics and emergent properties of natural and synthetic microbial communities, but also provide key knowledge required for engineering them. In this article, we provide an overview of mathematical tools that include not only current mainstream approaches, but also less traditional approaches that, in our opinion, can be potentially useful. We discuss a broad range of methods ranging from low-resolution supra-organismal to high-resolution individual-based modeling. Particularly, we highlight the integrative approaches that synergistically combine disparate methods. In conclusion, we provide our outlook for the key aspects that should be further developed to move microbial community modeling towards greater predictive power.

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Section: Metabolic Function-based Dynamic Modelingmentioning

confidence: 99%

Mathematical Modeling of Microbial Community Dynamics: A Methodological Review

et al. 2014

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“…Kim et al [16] have provided an experimental verification of the stable steady states for the foregoing two sets of conditions, i.e., at γ = 0.2 and x IN,total = 50, yielding a total of three steady states and five steady states, γ = 0.4 and x IN,total = 25, with a total of five steady states.…”

Section: Experimental Validationmentioning

confidence: 97%

“…Kim et al [16] used the HCM framework to model the anaerobic growth of E. coli GJT001 on glucose and pyruvate. The metabolic network contains 14 reactions (one reversible and 13 irreversible) and 18 metabolites (eight extracellular and 10 intracellular).…”

Section: Hcm For Anaerobic E Coli Growthmentioning

confidence: 99%

“…While these analyses were made using lumped reaction networks, it is possible to consider a detailed network structure using the hybrid cybernetic modeling (HCM) framework [13][14][15]. Recently, Kim et al [16] built an HCM of the anaerobic growth of Escherichia coli on glucose and pyruvate. Using this model, they predicted three and five steady states in a chemostat and experimentally validated them.…”

Section: Introductionmentioning

confidence: 99%

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Complex Nonlinear Behavior in Metabolic Processes: Global Bifurcation Analysis of Escherichia coli Growth on Multiple Substrates

Song

Ramkrishna

2013

Processes

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Abstract:The nonlinear behavior of metabolic systems can arise from at least two different sources. One comes from the nonlinear kinetics of chemical reactions in metabolism and the other from nonlinearity associated with regulatory processes. Consequently, organisms at a constant growth rate (as experienced in a chemostat) could display multiple metabolic states or display complex oscillatory behavior both with potentially serious implications to process operation. This paper explores the nonlinear behavior of a metabolic model of Escherichia coli growth on mixed substrates with sufficient detail to include regulatory features through the cybernetic postulate that metabolic regulation is the consequence of a dynamic objective function ensuring the organism's survival. The chief source of nonlinearity arises from the optimal formulation with the metabolic state determined by a convex combination of reactions contributing to the objective function. The model for anaerobic growth of E. coli was previously examined for multiple steady states in a chemostat fed by a mixture of glucose and pyruvate substrates under very specific conditions and experimentally verified. In this article, we explore the foregoing model for nonlinear behavior over the full range of parameters, γ (the fractional concentration of glucose in the feed mixture) and D (the dilution rate). The observed multiplicity is in the cybernetic variables combining elementary modes. The results show steady-state multiplicity up to seven. No Hopf bifurcation was encountered, however. Bifurcation analysis of cybernetic models is complicated by the non-differentiability of the cybernetic variables for enzyme activities. A methodology is adopted here to overcome this problem, which is applicable to more complicated metabolic networks. OPEN ACCESSProcesses 2013, 1 264

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“…Conversely, highly abstracted kinetic frameworks, such as the cybernetic framework, represented a paradigm shift, viewing cells as growth-optimizing strategists [7]. Cybernetic models have been highly successful at predicting metabolic choice behavior, e.g., diauxie behavior [8], steady-state multiplicity [9], as well as the cellular response to metabolic engineering modifications [10]. Unfortunately, traditional, fully structured cybernetic models also suffer from an identifiability challenge, as both the kinetic parameters and an abstracted model of cellular objectives must be estimated simultaneously.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Modeling of Cell-Free Biochemical Networks Using Effective Kinetic Models

2015

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Abstract:Cell-free systems offer many advantages for the study, manipulation and modeling of metabolism compared to in vivo processes. Many of the challenges confronting genome-scale kinetic modeling can potentially be overcome in a cell-free system. For example, there is no complex transcriptional regulation to consider, transient metabolic measurements are easier to obtain, and we no longer have to consider cell growth. Thus, cell-free operation holds several significant advantages for model development, identification and validation. Theoretically, genome-scale cell-free kinetic models may be possible for industrially important organisms, such as E. coli, if a simple, tractable framework for integrating allosteric regulation with enzyme kinetics can be formulated. Toward this unmet need, we present an effective biochemical network modeling framework for building dynamic cell-free metabolic models. The key innovation of our approach is the integration of simple effective rules encoding complex allosteric regulation with traditional kinetic pathway modeling. We tested our approach by modeling the time evolution of several hypothetical cell-free metabolic networks. We found that simple effective rules, when integrated with traditional enzyme kinetic expressions, captured complex allosteric patterns such as ultrasensitivity or non-competitive inhibition in the absence of mechanistic information. Second, when integrated into network models, these rules captured classic regulatory patterns such as product-induced feedback inhibition. Lastly, we showed, at least for the network architectures considered here, that we could simultaneously estimate kinetic parameters and allosteric connectivity from synthetic data starting from an unbiased collection of possible allosteric structures using particle swarm optimization. However, Processes 2015, 3 139 when starting with an initial population that was heavily enriched with incorrect structures, our particle swarm approach could converge to an incorrect structure. While only an initial proof-of-concept, the framework presented here could be an important first step toward genome-scale cell-free kinetic modeling of the biosynthetic capacity of industrially important organisms.

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Exacting predictions by cybernetic model confirmed experimentally: Steady state multiplicity in the chemostat

Cited by 37 publications

References 38 publications

Mathematical Modeling of Microbial Community Dynamics: A Methodological Review

Mathematical Modeling of Microbial Community Dynamics: A Methodological Review

Complex Nonlinear Behavior in Metabolic Processes: Global Bifurcation Analysis of Escherichia coli Growth on Multiple Substrates

Dynamic Modeling of Cell-Free Biochemical Networks Using Effective Kinetic Models

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