Metabolic control analysis

You don't need to be Editor-In-Chief to add or edit content to WikiDoc. You can begin to add to or edit text on this WikiDoc page by clicking on the edit button at the top of this page. Next enter or edit the information that you would like to appear here. Once you are done editing, scroll down and click the Save page button at the bottom of the page.

Jump to: navigation, search

Metabolic control analysis (MCA) is a mathematical framework for describing metabolic, signaling and genetic pathways. MCA quantifies how variables, such as fluxes and species concentrations, depend on network parameters. In particular it is able to describe how network dependent properties, called control coefficients, depend on local properties called elasticities.[1][1][1]

MCA was originally developed to describe the control in metabolic pathways but was subsequently extended to describe signaling and genetic networks. 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.

More recent work [1] has shown that MCA can be mapped directly on to classical control theory and are as such equivalent.

Biochemical systems theory [1] is a similar formalism, though with a rather different objectives. Both are evolutions of an earlier theoretical analysis by Joseph Higgins [1].


Control Coefficients

A control coefficient [1] [1][1] measures the relative steady state change in a system variable (e.g. fluxes or concentrations) in response to a relative change in a parameter (eg enzyme activity). The two main control coefficients are the flux and concentration control coefficients. Flux control coefficients are defined by:

C^J_{v_i} = \left( \frac{dJ}{dp} \frac{p}{J} \right) \bigg/ \left( \frac{dv_i}{dp}\frac{p}{v_i} \right) = \frac{d\ln J}{d\ln v_i}

and concentration control coefficients by:

C^S_{v_i} = \left( \frac{dS}{dp} \frac{p}{S} \right) \bigg/ \left( \frac{dv_i}{dp}\frac{p}{v_i} \right) = \frac{d\ln S}{d\ln v_i}

Summation Theorems

The flux control summation theorem was stated and proven by Kacser and Burns and it is one of the most fundamental discoveries of metabolic control analysis. The flux control summation theorem implies that metabolic fluxes are systemic properties and that their control is shared by all reactions in the system. When a single reaction changes its control of the flux this is compensated by changes in the control of the same flux by all other reactions.

\sum_i C^J_{v_i} = 1

\sum_i C^S_{v_i} = 0

Elasticity Coefficients

The rate of a chemical reaction is influenced by many different factors, such as temperature, pH, reactant and product concentrations and other effectors. The degree to which these factors change the reaction rate is described by the elasticity coefficient.

\varepsilon^v_S = \frac{\partial v}{\partial S} \frac{S}{v} = \frac{\partial \ln v}{\partial \ln S}

Connectivity Theorems

The connectivity theorems are specific relationships between elasticities and control coefficients. They are useful because they highlight the close relationship between the kinetic properties of individual reactions and the system properties of a pathway. 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 Sn is different from the local species Sm.


\sum_i C^J_i \varepsilon^i_S = 0

\sum_i C^{S_n}_i \varepsilon^i_{S_m} = 0 \quad n \neq m

\sum_i C^{S_n}_i \varepsilon^i_{S_m} = -1 \quad n = m

It is possible to combine the summation with the connectivity theorems to obtain closed expressions that relate the control coefficients to the elasticity coefficients. For example, consider the simplest non-trivial pathway:

X_o \rightarrow S \rightarrow X_1

We assume that Xo and X1 are fixed boundary species so that the pathway can reach a steady state. Let the first step have a rate v1 and the second step v2. Focusing on the flux control coefficients, we can write one summation and one connectivity theorem for this simple pathway:

C^J_{v_1} + C^J_{v_2} = 1

C^J_{v_1} \varepsilon^{v_1}_S + C^J_{v_2} \varepsilon^{v_2}_S = 0

Using these two equations we can solve for the flux control coefficients to yield:

C^J_{v_1} = \frac{\varepsilon^{2}_S}{\varepsilon^{2}_S - \varepsilon^{1}_S}

C^J_{v_2} = \frac{-\varepsilon^{1}_S}{\varepsilon^{2}_S - \varepsilon^{1}_S}

Using these equations we can look at some simple extreme behaviors. For example, let us assume that the first step is completely insensitive to its product, S, then \varepsilon^{v_1}_S = 0 . In this case, the control coefficients reduce to:

C^J_{v_1} = 1

C^J_{v_2} = 0


That is all the control (or sensitivity) is on the first step. This situation represents the classic rate-limiting step that is frequently mentioned in text books. The flux through the pathway is completely dependent on the first step. Under these conditions, no other step in the pathway can affect the flux. The effect is however dependent on the complete insensitivity of the first step to its product. Such a situation is likely to be rare in real pathways. In fact the classic rate limiting step has almost never been observed experimentally. Instead, a range of limitingness is observed, with some steps having higher control than others.

References


External links

 This biochemistry article is a stub. You can help WikiDoc by expanding it.
de:Metabolic Control Analysis

Acknowledgement and Attribution Regarding Sources of Content

Some of the initial content on this page may be incorporated in part from copyleft sources in the public domain including wikis such as Wikipedia and AskDrWiki. Drug information for patients came from the The National Library of Medicine. Infectious disease information may have come from the Centers for Disease Control (CDC). Differential Diagnoses are drawn from clinicians as well as an amalgamation of 3 sources: 1.The Disease Database; 2. Kahan, Scott, Smith, Ellen G. In A Page: Signs and Symptoms. Malden, Massachusetts: Blackwell Publishing, 2004:3; 3. Sailer, Christian, Wasner, Susanne. Differential Diagnosis Pocket. Hermosa Beach, CA: Borm Bruckmeir Publishing LLC, 2002:7 .

Retrieved from "http://en.wikidoc.org/index.php/Metabolic_control_analysis"
Personal tools