A linear framework for time-scale separation in nonlinear biochemical systems.
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This has yielded familiar formulas such as those of Michaelis-Menten in enzyme kinetics, Monod-Wyman-Changeux in allostery and Ackers-Johnson-Shea in gene regulation.We show that elimination of internal complexity is feasible when the relevant graph is strongly connected.The framework provides a new methodology with the potential to subdue combinatorial explosion at the molecular level.
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PubMed Central - PubMed
Affiliation: Department of Systems Biology, Harvard Medical School, Boston, Massachusetts, United States of America. jeremy@hms.harvard.edu
ABSTRACT
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Cellular physiology is implemented by formidably complex biochemical systems with highly nonlinear dynamics, presenting a challenge for both experiment and theory. Time-scale separation has been one of the few theoretical methods for distilling general principles from such complexity. It has provided essential insights in areas such as enzyme kinetics, allosteric enzymes, G-protein coupled receptors, ion channels, gene regulation and post-translational modification. In each case, internal molecular complexity has been eliminated, leading to rational algebraic expressions among the remaining components. This has yielded familiar formulas such as those of Michaelis-Menten in enzyme kinetics, Monod-Wyman-Changeux in allostery and Ackers-Johnson-Shea in gene regulation. Here we show that these calculations are all instances of a single graph-theoretic framework. Despite the biochemical nonlinearity to which it is applied, this framework is entirely linear, yet requires no approximation. We show that elimination of internal complexity is feasible when the relevant graph is strongly connected. The framework provides a new methodology with the potential to subdue combinatorial explosion at the molecular level. Related in: MedlinePlus |
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Mentions: We start from a graph, G, consisting of vertices, , with labelled, directed edges, , and no self loops, (Figure 2A). The vertices represent components of a system, on which a dynamics is defined by treating each edge as if it were a chemical reaction under mass-action kinetics, with the label as rate constant. We can imagine that an amount (or, equivalently, a concentration) of each component is placed on the corresponding vertex and that these amounts are transported across the edges in the direction of the arrows at rates that are proportional to the amounts on the source vertices. The constant of proportionality is the label on the edge. For instance, if the amounts of the components are denoted , then the edge in Figure 2A contributes to the amount of component 1 at a rate , and so on. Since each edge has only one source vertex, the reactions are all first-order and the dynamics are therefore linear. |
View Article: PubMed Central - PubMed
Affiliation: Department of Systems Biology, Harvard Medical School, Boston, Massachusetts, United States of America. jeremy@hms.harvard.edu