Metabolic control analysis
MCA quantifies how variables, such as fluxes and species concentrations, depend on network parameters.
MCA has sometimes also been referred to as Metabolic Control Theory, but this terminology was rather strongly opposed by Henrik Kacser, one of the founders[citation needed].
More recent work[4] has shown that MCA can be mapped directly on to classical control theory and are as such equivalent.
Biochemical systems theory[5] (BST) is a similar formalism, though with rather different objectives.
Both are evolutions of an earlier theoretical analysis by Joseph Higgins.
[6] Chemical reaction network theory is another theoretical framework that has overlap with both MCA and BST but is considerably more mathematically formal in its approach.
[7] Its emphasis is primarily on dynamic stability criteria[8] and related theorems associated with mass-action networks.
In more recent years the field has also developed [9] a sensitivity analysis which is similar if not identical to MCA and BST.
A control coefficient[10] [11][12] measures the relative steady state change in a system variable, e.g. pathway flux (J) or metabolite concentration (S), in response to a relative change in a parameter, e.g. enzyme activity or the steady-state rate (
The elasticity coefficient measures the local response of an enzyme or other chemical reaction to changes in its environment.
Such changes include factors such as substrates, products, or effector concentrations.
The connectivity theorems[10][11] are specific relationships between elasticities and control coefficients.
Two basic sets of theorems exists, one for flux and another for concentrations.
The concentration connectivity theorems are divided again depending on whether the system species
Kacser and Burns[10] introduced an additional coefficient that described how a biochemical pathway would respond the external environment.
and 2) How well do modifications of the target influence the phenotype by transmission of the perturbation to the rest of the network.
For example, a drug might be very effective at changing the activity of its target protein, however if that perturbation in protein activity is unable to be transmitted to the final phenotype then the effectiveness of the drug is greatly diminished.
are fixed boundary species so that the pathway can reach a steady state.
Focusing on the flux control coefficients, we can write one summation and one connectivity theorem for this simple pathway: Using these two equations we can solve for the flux control coefficients to yield Using these equations we can look at some simple extreme behaviors.
This situation represents the classic rate-limiting step that is frequently mentioned in textbooks.
The effect is however dependent on the complete insensitivity of the first step to its product.
In fact the classic rate limiting step has almost never been observed experimentally.
Control equations can also be derived by considering the effect of perturbations on the system.
This is often of importance to metabolic engineers who are interested in increasing rates of production.
At steady state the reaction rates are often called the fluxes and abbreviated to
In metabolic control analysis the key parameters are the enzyme concentrations.
[17] A detailed discussion of this approach can be found in Heinrich & Schuster[18] and Hofmeyr.
[19] A linear biochemical pathway is a chain of enzyme-catalyzed reaction steps.
The only difference was that metabolic control analysis was confined to zero frequency responses when cast in the frequency domain whereas classical control theory imposes no such restriction.
The other significant difference is that classical control theory[27] has no notion of stoichiometry and conservation of mass which makes it more cumbersome to use but also means it fails to recognize the structural properties inherent in stoichiometric networks which provide useful biological insights.
