Concentration control coefficient, metabolic

As mentioned, there are other summation relationships that can be derived in a similar way. For example, in arriving at the result above, we deduced that a 1% increase in the activity of every enzyme would produce not only a 1% change in flux but also a zero change in the concentration of any metabolite. It follows from this sort of consideration that if we define concentration control coefficients for any particular metabolite, they will sum to zero. These other relationships have, in general, received less attention than the flux summation theorem, which is now regarded as being fundamental to the understanding of metabolic control. 

Metabolic control analysis (MCA) is a specialized theory that is concerned with particular sensitivity coefficients, elasticity coefficients and control coefficients. These coefficients tell us how a steady state of a biochemical system shifts in response to perturbation in enzyme activities or external (clamped) substrate concentration [53, 209],... 

The metabolic control analysis determines quantitatively the effects of various metabolic pathway reactions on flows and on metabolic concentrations. The analysis defines two coefficients (i) the control coefficients, which characterize the response of the system flows, concentrations, and other variables after parameter perturbations and (ii) the elasticity coefficients, which quantify the changes of reaction rates after perturbations of substrate concentrations or kinetic parameters under specified conditions. 

Steady-state metabolic flows./ depend on the total concentrations of the enzymes Ek, and flow control coefficients ( jj are defined by... 

Control coefficients are properties of a metabolic pathway as a whole. The kinetic properties of individual enzymes that are relevant for control are expressed in terms of their elasticity coefficients. An elasticity coefficient ef quantifies how strongly a metabolite concentration Xj affects an enzyme rate V directly, at constant concentrations of all other metabolite concentrations ... 

Connectivity theorems allow to relate the control coefficients (systemic properties) to the elasticity coefficients (properties of the network s enzymes individually as if in isolation) (Westerhoff and Van Dam 1987 Heinrich and Schuster 1996 Fell 1997). The connectivity theorems have given us a strong insight into the functioning of metabolic pathways. For example, it follows directly from these theorems that enzymes that are very sensitive to the concentrations of metabolites, such as substrates, products and allosteric effectors, tend to have little control over the flux. This is illustrated by overproduction of phosphofructokinase in bakers yeast, an enzyme often referred to textbooks as rate-limiting. Yet, overproduction of phosphofructokinase does not lead to a significant flux increase, since the cell compensates by lowering the level of its allosteric effector fructose 2,6-bisphosphate (Schaaff et al. 1989 Davies and Brindle 1992). 

The methods of FBA and elementary flux modes study interactions between different routes in a metabolic network and the quantification of flux distributions but do not evaluate how fluxes are controlled. In Metabolic Control Analysis (MCA), the control exerted by the rate of a reaction over a substrate flux or any other system parameter (e.g., metabolite concentration or cell proliferation) can be described quantitatively as a control coefficient. The control coefficient is a relative measure of how much a perturbation affects a system variable and is defined as the fractional change in the system property over the fractional change in the reaction rate [e.g., Bums et al. 1985],... 

Those of us that have done basic research have tended to look at enzyme activity, pathway activity, hormone and receptor concentrations and the like. That is fine, and we have learned from that, but in many oases we did not consider the underlying controls (transcription rates, enzyme synthesis rates) or did not fully relate the cellular information to the animal production level in any systematic mathematical formalism. The former is difficult to do, expensive, and in many ways not necessary to our purposes in animal agriculture. The latter is easy to do, inexpensive and in fact an absolute requirement for our purposes what are the true biological controls, at the level at which control is exerted, that drive animal production. A description of metabolic control theory and control coefficients is beyond the purpose of this article, but readers are at least encouraged to read some of Kacser, Carson and Cobelli and Comish-Bowden to understand this (Comish-Bowden, 2005). I will go into more detail with references on multiple regressions to study the relationship of basic metabolic control, transcriptomics and animal production below. 

If 02 consumption were indeed zero order for a particular plant species, then it would appear that any phytoproduction process involving that species would require only that a minimum dissolved 02 concentration be maintained any concentration increase beyond that would be irrelevant. In the case of tobacco cells, any concentration greater than 15 % of air saturation would yield the same metabolic rate and, presumably, the same productivity of all metabolites. If, on the other hand, consumption is first order in the concentration range achievable in a practical bioreactor (equivalently, if Kf is comparable to working concentrations), then its concentration is an important control parameter in the bioreactor. However, Kobayashi et al. studied berberine production by suspended and immobilized cells of Thalictrum minus [50]. They assert that 02 uptake is a zero-order process but observed that berberine production depended on 02 availability. They controlled that availability by adjusting the speed of shaking of the culture flasks, thus varying the mass transfer coefficient for absorption of 02. 

As briefly outlined in Section 6.3, one of the theoretical frameworks in quantitative analysis of metabolic networks is metabolic control analysis. In metabolic control analysis, the enzyme elasticity coefficients provide empirical constraints between the metabolites concentrations and the reaction fluxes. These constraints can be considered in concert with the interdependencies in the J and c spaces that are imposed by the network stoichiometry. If the coefficients elk = (c / Ji)dJi/dck are known, then these values bind the fluxes and concentrations to a hyperplane in the (J, c) space. 

Early studies of vitamin Be requirements used the development of abnormalities of tryptophan or methionine metabolism during depletion, and normalization during repletion with graded intakes of the vitamin. Although tryptophan and methionine load tests are unreliable as indices of vitamin Be status in epidemiological studies (Section 9.5.4 and Section 9.5.5), under the controlled conditions of depletion/repletion studies they do give a useful indication of the state of vitamin Be nutrition. More recent studies have used more sensitive indices of status, including the plasma concentration of pyridoxal phosphate, urinary excretion of 4-pyridoxic acid, and erythrocyte transaminase activation coefficient. 

The vial equilibration method is the most common in vitro method for determining partition coefficients for volatile or semivolatile materials and has been used most successfully for volatile organic solvents (Gargas et al., 1988). Tissues are harvested from the species of interest and incubated with the test compoxmd imtil equilibrium is reached between the tissue and the headspace in the vial. The blood/air or tissue/air partition coefficients are given by the ratio of the concentrations of the chemical in the blood or tissue relative to its concentration in the headspace. Tissue-blood partition coefficients are calculated from the respective tissue/air and blood/air values. A number of operational equations have been derived to calculate these ratios xmder specific experimental conditions. Time to steady state is critical and should be optimized for the test compoxmd. Metabolism of the compound in exposed tissue samples must be controlled. Analysis is performed by gas chromatography in a verified linear range. Human tissues can be obtained from tissue bank organizations to provide species specificity to models developed with human data. To estimate... 

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