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(Im)Perfect robustness and adaptation of metabolic networks subject to metabolic and gene-expression regulation: marrying control engineering with metabolic control analysis.

He F, Fromion V, Westerhoff HV - BMC Syst Biol (2013)

Bottom Line: This study then focuses on robustness against and adaptation to perturbations of process activities in the network, which could result from environmental perturbations, mutations or slow noise.In particular, the new approach enables one to address the issue whether the intracellular biochemical networks that have been and are being identified by genomics and systems biology, correspond to the 'perfect' regulatory structures designed by control engineering vis-à-vis optimal functions such as robustness.To the extent that they are not, the analyses suggest how they may become so and this in turn should facilitate synthetic biology and metabolic engineering.

View Article: PubMed Central - HTML - PubMed

Affiliation: The Manchester Centre for Integrative Systems Biology, Manchester Interdisciplinary Biocentre, University of Manchester, Manchester M1 7DN, UK. hans.westerhoff@manchester.ac.uk.

ABSTRACT

Background: Metabolic control analysis (MCA) and supply-demand theory have led to appreciable understanding of the systems properties of metabolic networks that are subject exclusively to metabolic regulation. Supply-demand theory has not yet considered gene-expression regulation explicitly whilst a variant of MCA, i.e. Hierarchical Control Analysis (HCA), has done so. Existing analyses based on control engineering approaches have not been very explicit about whether metabolic or gene-expression regulation would be involved, but designed different ways in which regulation could be organized, with the potential of causing adaptation to be perfect.

Results: This study integrates control engineering and classical MCA augmented with supply-demand theory and HCA. Because gene-expression regulation involves time integration, it is identified as a natural instantiation of the 'integral control' (or near integral control) known in control engineering. This study then focuses on robustness against and adaptation to perturbations of process activities in the network, which could result from environmental perturbations, mutations or slow noise. It is shown however that this type of 'integral control' should rarely be expected to lead to the 'perfect adaptation': although the gene-expression regulation increases the robustness of important metabolite concentrations, it rarely makes them infinitely robust. For perfect adaptation to occur, the protein degradation reactions should be zero order in the concentration of the protein, which may be rare biologically for cells growing steadily.

Conclusions: A proposed new framework integrating the methodologies of control engineering and metabolic and hierarchical control analysis, improves the understanding of biological systems that are regulated both metabolically and by gene expression. In particular, the new approach enables one to address the issue whether the intracellular biochemical networks that have been and are being identified by genomics and systems biology, correspond to the 'perfect' regulatory structures designed by control engineering vis-à-vis optimal functions such as robustness. To the extent that they are not, the analyses suggest how they may become so and this in turn should facilitate synthetic biology and metabolic engineering.

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The closed-loop control structure of a metabolic pathway subject to various types of regulation. There are three types of feedback control mechanisms: i) proportional or nonlinear control that is related to the substrate or allosteric effects; ii) derivative control that can be related with signalling, e.g. phyosphocreatine buffering; and iii) integral control introduced by gene-expression regulation because protein synthesis requires time integration. The former two control loops i) and ii) are often modelled together with the dynamics of the metabolic process. Here, metabolite concentration X is the output of a metabolic process and is the controlled variable of different control loops. Reaction rates v(X,E) are the manipulated variables because they are functions of both enzyme concentration E, i.e. the output of integral control loop (gene-expression regulation), and metabolic process (f(X)), i.e. the outputs of proportional/nonlinear and derivative control loops (metabolic regulation or signalling). Here, the integral control input q(t) is a function of the controlled variable (q(t) = φ(X(t)) or the difference (or error) between the controlled variable and a reference signal (r).
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Figure 6: The closed-loop control structure of a metabolic pathway subject to various types of regulation. There are three types of feedback control mechanisms: i) proportional or nonlinear control that is related to the substrate or allosteric effects; ii) derivative control that can be related with signalling, e.g. phyosphocreatine buffering; and iii) integral control introduced by gene-expression regulation because protein synthesis requires time integration. The former two control loops i) and ii) are often modelled together with the dynamics of the metabolic process. Here, metabolite concentration X is the output of a metabolic process and is the controlled variable of different control loops. Reaction rates v(X,E) are the manipulated variables because they are functions of both enzyme concentration E, i.e. the output of integral control loop (gene-expression regulation), and metabolic process (f(X)), i.e. the outputs of proportional/nonlinear and derivative control loops (metabolic regulation or signalling). Here, the integral control input q(t) is a function of the controlled variable (q(t) = φ(X(t)) or the difference (or error) between the controlled variable and a reference signal (r).

Mentions: N is the stoichiometry matrix. E is a diagonal matrix with the concentrations of the enzymes that catalyse the various reactions along its diagonal. f(X) is a vector function of the concentrations of the metabolites and kinetic parameter values. The regulated metabolic pathway can be described in terms of a closed-loop feedback control system, as indicated in Figure 6, in which kp, ki and kd are the PID control parameters. We here note that Figure 6 and subsequent figures refrain from biochemical detail. This is because the analysis in the present paper aims at obtaining a set of conclusions with general significance. Being specific in the schemes we use as illustrations would detract from this aim.


(Im)Perfect robustness and adaptation of metabolic networks subject to metabolic and gene-expression regulation: marrying control engineering with metabolic control analysis.

He F, Fromion V, Westerhoff HV - BMC Syst Biol (2013)

The closed-loop control structure of a metabolic pathway subject to various types of regulation. There are three types of feedback control mechanisms: i) proportional or nonlinear control that is related to the substrate or allosteric effects; ii) derivative control that can be related with signalling, e.g. phyosphocreatine buffering; and iii) integral control introduced by gene-expression regulation because protein synthesis requires time integration. The former two control loops i) and ii) are often modelled together with the dynamics of the metabolic process. Here, metabolite concentration X is the output of a metabolic process and is the controlled variable of different control loops. Reaction rates v(X,E) are the manipulated variables because they are functions of both enzyme concentration E, i.e. the output of integral control loop (gene-expression regulation), and metabolic process (f(X)), i.e. the outputs of proportional/nonlinear and derivative control loops (metabolic regulation or signalling). Here, the integral control input q(t) is a function of the controlled variable (q(t) = φ(X(t)) or the difference (or error) between the controlled variable and a reference signal (r).
© Copyright Policy - open-access
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC4222491&req=5

Figure 6: The closed-loop control structure of a metabolic pathway subject to various types of regulation. There are three types of feedback control mechanisms: i) proportional or nonlinear control that is related to the substrate or allosteric effects; ii) derivative control that can be related with signalling, e.g. phyosphocreatine buffering; and iii) integral control introduced by gene-expression regulation because protein synthesis requires time integration. The former two control loops i) and ii) are often modelled together with the dynamics of the metabolic process. Here, metabolite concentration X is the output of a metabolic process and is the controlled variable of different control loops. Reaction rates v(X,E) are the manipulated variables because they are functions of both enzyme concentration E, i.e. the output of integral control loop (gene-expression regulation), and metabolic process (f(X)), i.e. the outputs of proportional/nonlinear and derivative control loops (metabolic regulation or signalling). Here, the integral control input q(t) is a function of the controlled variable (q(t) = φ(X(t)) or the difference (or error) between the controlled variable and a reference signal (r).
Mentions: N is the stoichiometry matrix. E is a diagonal matrix with the concentrations of the enzymes that catalyse the various reactions along its diagonal. f(X) is a vector function of the concentrations of the metabolites and kinetic parameter values. The regulated metabolic pathway can be described in terms of a closed-loop feedback control system, as indicated in Figure 6, in which kp, ki and kd are the PID control parameters. We here note that Figure 6 and subsequent figures refrain from biochemical detail. This is because the analysis in the present paper aims at obtaining a set of conclusions with general significance. Being specific in the schemes we use as illustrations would detract from this aim.

Bottom Line: This study then focuses on robustness against and adaptation to perturbations of process activities in the network, which could result from environmental perturbations, mutations or slow noise.In particular, the new approach enables one to address the issue whether the intracellular biochemical networks that have been and are being identified by genomics and systems biology, correspond to the 'perfect' regulatory structures designed by control engineering vis-à-vis optimal functions such as robustness.To the extent that they are not, the analyses suggest how they may become so and this in turn should facilitate synthetic biology and metabolic engineering.

View Article: PubMed Central - HTML - PubMed

Affiliation: The Manchester Centre for Integrative Systems Biology, Manchester Interdisciplinary Biocentre, University of Manchester, Manchester M1 7DN, UK. hans.westerhoff@manchester.ac.uk.

ABSTRACT

Background: Metabolic control analysis (MCA) and supply-demand theory have led to appreciable understanding of the systems properties of metabolic networks that are subject exclusively to metabolic regulation. Supply-demand theory has not yet considered gene-expression regulation explicitly whilst a variant of MCA, i.e. Hierarchical Control Analysis (HCA), has done so. Existing analyses based on control engineering approaches have not been very explicit about whether metabolic or gene-expression regulation would be involved, but designed different ways in which regulation could be organized, with the potential of causing adaptation to be perfect.

Results: This study integrates control engineering and classical MCA augmented with supply-demand theory and HCA. Because gene-expression regulation involves time integration, it is identified as a natural instantiation of the 'integral control' (or near integral control) known in control engineering. This study then focuses on robustness against and adaptation to perturbations of process activities in the network, which could result from environmental perturbations, mutations or slow noise. It is shown however that this type of 'integral control' should rarely be expected to lead to the 'perfect adaptation': although the gene-expression regulation increases the robustness of important metabolite concentrations, it rarely makes them infinitely robust. For perfect adaptation to occur, the protein degradation reactions should be zero order in the concentration of the protein, which may be rare biologically for cells growing steadily.

Conclusions: A proposed new framework integrating the methodologies of control engineering and metabolic and hierarchical control analysis, improves the understanding of biological systems that are regulated both metabolically and by gene expression. In particular, the new approach enables one to address the issue whether the intracellular biochemical networks that have been and are being identified by genomics and systems biology, correspond to the 'perfect' regulatory structures designed by control engineering vis-à-vis optimal functions such as robustness. To the extent that they are not, the analyses suggest how they may become so and this in turn should facilitate synthetic biology and metabolic engineering.

Show MeSH