Metabolic control analysis

Metabolic control analysis (MCA) is a mathematical framework for describingmetabolic, 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. C v 1 J + C v 2 J = 1 {displaystyle C_{v_{1}}^{J}+C_{v_{2}}^{J}=1} C v 1 J = ε S 2 ε S 2 − ε S 1 {displaystyle C_{v_{1}}^{J}={frac {varepsilon _{S}^{2}}{varepsilon _{S}^{2}-varepsilon _{S}^{1}}}} C v 1 J = 1 {displaystyle C_{v_{1}}^{J}=1} C v 1 S = 1 ε S 2 − ε S 1 {displaystyle C_{v_{1}}^{S}={frac {1}{varepsilon _{S}^{2}-varepsilon _{S}^{1}}}} Metabolic control analysis (MCA) is a mathematical framework for describingmetabolic, 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. MCA was originally developed to describe the control in metabolic pathwaysbut 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 has shown that MCA can be mapped directly on to classical control theory and are as such equivalent. Biochemical systems theory is a similar formalism, though with a rather different objectives. Both are evolutions of an earlier theoretical analysis by Joseph Higgins. A control coefficient 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 ( v i {displaystyle v_{i}} ) of step i. The two main control coefficients are the flux and concentration control coefficients. Flux control coefficients are defined by: C v i J = ( d J d p p J ) / ( ∂ v i ∂ p p v i ) = d ln ⁡ J d ln ⁡ v i {displaystyle C_{v_{i}}^{J}=left({frac {dJ}{dp}}{frac {p}{J}} ight){igg /}left({frac {partial v_{i}}{partial p}}{frac {p}{v_{i}}} ight)={frac {dln J}{dln v_{i}}}}