Control analysis of time-dependent metabolic systems†
Metabolic Control Analysis is extended to time dependent systems. It is assumed that the time derivative of the metabolite concentrations can be written as a linear combination of rate laws, each one of first order with respect to the corresponding enzyme concentration. The definitions of the control and elasticity coefficients are extended, and a new type of coefficient (“time coefficient”, “T”) is defined. First, we prove that simultaneous changes in all enzyme concentrations by the same arbitrary factor, is equivalent to a change in the time scale. When infinitesimal changes are considered, these arguments lead to the derivation of general summation theorems that link control and time coefficients. The comparison of two systems with identical rates, that only differ in one metabolite concentration, leads to a method for the construction of general connectivity theorems, that relate control and elasticity coefficients. A mathematical proof in matrix form, of the summation and connectivity relationships, for time dependent systems is given. Those relationships allow one to express the control coefficients in terms of the elasticity and time coefficients for the case of unbranched pathway.
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On paradoxes between optimal growth, metabolic control analysis, and flux balance analysis
2023, BioSystemsIn Microbiology it is often assumed that growth rate is maximal. This may be taken to suggest that the dependence of the growth rate on every enzyme activity is at the top of an inverse-parabolic function, i.e. that all flux control coefficients should equal zero. This might seem to imply that the sum of these flux control coefficients equals zero. According to the summation law of Metabolic Control Analysis (MCA) the sum of flux control coefficients should equal 1 however. And in Flux Balance Analysis (FBA) catabolism is often limited by a hard bound, causing catabolism to fully control the fluxes, again in apparent contrast with a flux control coefficient of zero. Here we resolve these paradoxes (apparent contradictions) in an analysis that uses the ‘Edinburgh pathway’, the ‘Amsterdam pathway’, as well as a generic metabolic network providing the building blocks or Gibbs energy for microbial growth. We review and show that (i) optimization depends on so-called enzyme control coefficients rather than the ‘catalytic control coefficients’ of MCA's summation law, (ii) when optimization occurs at fixed total protein, the former differ from the latter to the extent that they may all become equal to zero in the optimum state, (iii) in more realistic scenarios of optimization where catalytically inert biomass is compensating or maintenance metabolism is taken into consideration, the optimum enzyme concentrations should not be expected to equal those that maximize the specific growth rate, (iv) optimization may be in terms of yield rather than specific growth rate, which resolves the paradox because the sum of catalytic control coefficients on yield equals 0, (v) FBA effectively maximizes growth yield, and for yield the summation law states 0 rather than 1, thereby removing the paradox, (vi) furthermore, FBA then comes more often to a ‘hard optimum’ defined by a maximum catabolic flux and a catabolic-enzyme control coefficient of 1. The trade-off between maintenance metabolism and growth is highlighted as worthy of further analysis.
Dynamic Integration: Dynamics Metabolism
2016, Encyclopedia of Cell BiologyThe sum total of all chemical transformations involved in energy production and the synthesis and storage of small molecules is termed metabolism. The growth of a cell is almost wholly dependent on the careful management of resources made available by metabolic processes. As a result metabolism is highly regulated with significant cross talk between it and other processes such as signaling and gene regulation. Like all biological processes, metabolism is a dynamic process with short- and long-term regulation adjusting supply and demand. Short-term regulation of metabolism is achieved largely through allosteric regulators that create negative feedback loops together with the use of specific network topologies that confer particular regulatory behaviors. In this article the essential operating principles that govern the short-term regulation of metabolism is discussed. Of particular importance is the idea that short-term regulation of metabolism is distributed without any central authority dictating its operation. Dynamics is seen as the end result of all components in a metabolic pathway operating in a concerted manner. Specific pathway examples, termed metabolic motifs, are introduced where their essential properties are discussed. These include linear, branched, and cyclic configurations as well an extended discussion of negative feedback.
Metabolic control analysis indicates a change of strategy in the treatment of cancer
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Sensitivity summation theorems for stochastic biochemical reaction systems
2010, Mathematical BiosciencesWe investigate how stochastic reaction processes are affected by external perturbations. We describe an extension of the deterministic metabolic control analysis (MCA) to the stochastic regime. We introduce stochastic sensitivities for mean and covariance values of reactant concentrations and reaction fluxes and show that there exist MCA-like summation theorems among these sensitivities. The summation theorems for flux variances is shown to depend on the size of the measurement time window (ϵ) within which reaction events are counted for measuring a single flux. It is found that the degree of the ϵ-dependency can become significant for processes involving multi-time-scale dynamics and is estimated by introducing a new measure of time-scale separation. This ϵ-dependency is shown to be closely related to the power-law scaling observed in flux fluctuations in various complex networks.
Dynamic sensitivity analysis of oscillating biochemical systems using modified collocation method
2009, Journal of the Taiwan Institute of Chemical EngineersSensitivity analysis plays an important role in the study of biological systems. Biochemical systems theory (BST) as well as metabolic control analysis (MCA) has had great success in describing the control and regulation of biological systems at steady state. However, there are notable exceptions, such as signal transduction or cell cycle regulation systems where the transient or oscillatory behavior of interest is often found in the temporal response. Some extensions of BST and MCA to non-steady behavior have appeared in the literature. However, there requires to have a unified methodology to efficiently solve biological system models described by the BST or MCA formulation. In this work, the modified collocation method is applied to solve transient responses and its corresponding dynamic sensitivities for the non-linear biological systems described by the GMA formulation. The method could simultaneously compute both solutions and dynamic sensitivities of the system equations element-by-element. Any MCA formulations could be recast into a GMA model so the Jacobian matrix and the partial derivatives with respect to the model parameters could be analytically evaluated while the solution is in progress. In this study, we have presented three biological systems to illustrate the efficiency of the proposed algorithm.
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Part of this study was presented in a condensed version at the Biothermokinetics Workshop of the International Study Group for Biothermokinetics, Aberystwyth, Wales, 26–28 July 1988.