Speeding up the core algorithm for the dual calculation of minimal cut sets in large metabolic networks

Klamt, Steffen; Mahadevan, Radhakrishnan; Kamp, Axel von

doi:10.1186/s12859-020-03837-3

Cited by 14 publications

(10 citation statements)

References 34 publications

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“…Likewise, one could formulate multiple mixed-integer SOCPs (MISOCP) for finding the IISs of (15). In the MISOCP below, we augment the MILP (14) in [30] with the variables and constraints corresponding to the metabolites and kinetics. (18c)-(18g) are disjunctive constraints that, for sufficiently large γ , either force their left hand sides to be zero or have no effect.…”

Section: Minimal Cut Setsmentioning

confidence: 99%

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Convex representation of metabolic networks with Michaelis-Menten kinetics

Taylor

Rapaport

Dochain

2023

Preprint

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Polyhedral models of metabolic networks are computationally tractable and can predict some cellular functions. A longstanding challenge is incorporating metabolites without losing tractability. In this paper, we do so using a new second-order cone representation of the Michaelis-Menten kinetics. The resulting model consists of linear stoichiometric constraints alongside second-order cone constraints that couple the reaction fluxes to metabolite concentrations. We formulate several new problems around this model: conic flux balance analysis, which augments flux balance analysis with metabolite concentrations; dynamic conic flux balance analysis; and finding minimal cut sets of networks with both reactions and metabolites. The problems are second-order cone or mixed-integer second-order cone programs, which, while not as tractable as their linear counterparts, can nonetheless be solved at practical scales using commercial software.

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Section: Minimal Cut Setsmentioning

confidence: 99%

mentioning

confidence: 99%

Convex representation of metabolic networks with Michaelis-Menten kinetics

Taylor

Rapaport

Dochain

2023

Preprint

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“…Following the contributions to develop dFBA based on both static and dynamic optimization methods [40,141], efforts also focused on the integration of transcriptional regulation [230,231], and the consideration of resource allocations in terms of enzyme production cost [12,232]. Particularly in systems metabolic engineering of strains, rewarding applications of MPA methods fueled continual development of up-to-date mathematical modelling frameworks [233,234], recently finding optimal operating points in two-stage bioprocesses [235]. The challenges associated with the expansion of the CBMs can be related to the biological justification of the underlying assumptions and the efficiency of the computational methods employed to solve the core optimization problems.…”

Section: Perspectives and Challenges Aheadmentioning

confidence: 99%

Modelling Cell Metabolism: A Review on Constraint-Based Steady-State and Kinetic Approaches

Yasemi¹,

Jolicœur²

2021

Processes

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Studying cell metabolism serves a plethora of objectives such as the enhancement of bioprocess performance, and advancement in the understanding of cell biology, of drug target discovery, and in metabolic therapy. Remarkable successes in these fields emerged from heuristics approaches, for instance, with the introduction of effective strategies for genetic modifications, drug developments and optimization of bioprocess management. However, heuristics approaches have showed significant shortcomings, such as to describe regulation of metabolic pathways and to extrapolate experimental conditions. In the specific case of bioprocess management, such shortcomings limit their capacity to increase product quality, while maintaining desirable productivity and reproducibility levels. For instance, since heuristics approaches are not capable of prediction of the cellular functions under varying experimental conditions, they may lead to sub-optimal processes. Also, such approaches used for bioprocess control often fail in regulating a process under unexpected variations of external conditions. Therefore, methodologies inspired by the systematic mathematical formulation of cell metabolism have been used to address such drawbacks and achieve robust reproducible results. Mathematical modelling approaches are effective for both the characterization of the cell physiology, and the estimation of metabolic pathways utilization, thus allowing to characterize a cell population metabolic behavior. In this article, we present a review on methodology used and promising mathematical modelling approaches, focusing primarily to investigate metabolic events and regulation. Proceeding from a topological representation of the metabolic networks, we first present the metabolic modelling approaches that investigate cell metabolism at steady state, complying to the constraints imposed by mass conservation law and thermodynamics of reactions reversibility. Constraint-based models (CBMs) are reviewed highlighting the set of assumed optimality functions for reaction pathways. We explore models simulating cell growth dynamics, by expanding flux balance models developed at steady state. Then, discussing a change of metabolic modelling paradigm, we describe dynamic kinetic models that are based on the mathematical representation of the mechanistic description of nonlinear enzyme activities. In such approaches metabolic pathway regulations are considered explicitly as a function of the activity of other components of metabolic networks and possibly far from the metabolic steady state. We have also assessed the significance of metabolic model parameterization in kinetic models, summarizing a standard parameter estimation procedure frequently employed in kinetic metabolic modelling literature. Finally, some optimization practices used for the parameter estimation are reviewed.

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“…A detailed introduction to the theory of MCS can be found in literature [28,29,40,[44][45][46] and in the Supplementary Text. For the calculation of MCS, it is fundamental to define a set of undesired (target) behaviors and (optionally) a set of desired (protected) behaviors.…”

Section: Using the Mcs Framework To Compute Strain Designs For All Four Coupling Degreesmentioning

confidence: 99%

Systematizing the different notions of growth‐coupled product synthesis and a single framework for computing corresponding strain designs

Schneider

Mahadevan

Klamt

2021

Biotechnology Journal

Self Cite

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A widely used design principle for metabolic engineering of microorganisms aims to introduce interventions that enforce growth-coupled product synthesis such that the product of interest becomes a (mandatory) by-product of growth. However, different variants and partially contradicting notions of growth-coupled production (GCP) exist.Herein, we propose an ontology for the different degrees of GCP and clarify their relationships. Ordered by coupling degree, we distinguish four major classes: potentially, weakly, and directionally growth-coupled production (pGCP, wGCP, dGCP) as well as substrate-uptake coupled production (SUCP). We then extend the framework of Minimal Cut Sets (MCS), previously used to compute dGCP and SUCP strain designs, to allow inclusion of implicit optimality constraints, a feature required to compute pGCP and wGCP designs. This extension closes the gap between MCS-based and bilevelbased strain design approaches and enables computation (and comparison) of designs for all GCP classes within a single framework. By computing GCP strain designs for a range of products, we illustrate the hierarchical relationships between the different coupling degrees. We find that feasibility of coupling is not affected by the chosen GCP degree and that strongest coupling (SUCP) requires often only one or two more interventions than wGCP and dGCP. Finally, we show that the principle of coupling can be generalized to couple product synthesis with other cellular functions than growth, for example, with net ATP formation. This work provides important theoretical results and algorithmic developments and a unified terminology for computational strain design based on GCP.

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Speeding up the core algorithm for the dual calculation of minimal cut sets in large metabolic networks

Cited by 14 publications

References 34 publications

Convex representation of metabolic networks with Michaelis-Menten kinetics

Convex representation of metabolic networks with Michaelis-Menten kinetics

Modelling Cell Metabolism: A Review on Constraint-Based Steady-State and Kinetic Approaches

Systematizing the different notions of growth‐coupled product synthesis and a single framework for computing corresponding strain designs

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