## Tuesday, June 7, 2011

### Metabolic Control Analyis 101: Part 1

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## What is Metabolic Control Analysis?

Broadly speaking, Metabolic Control Analysis is a mathematical approach that allows us to understand and quantify how perturbations to a biochemical pathway propagate out from the disturbance to the rest of the system.

Metabolic Control Analysis (MCA) was born in an era when work on metabolism was in full swing. Since then, protein signaling and gene regulatory network have largely taken the limelight. Renewed interest in topics such biofuels, metabolism may be making a comeback. Since the development of MCA, we now know that it is much more general and applies to any kind of biochemical network be it metabolic, signal or gene regulatory. Therefore the first thing I’m going to do is stop called Metabolic Control Analysis, Metabolic Control Analysis. Instead, to indicate its generality, I will call it Biochemical Control Analysis (BCA).

BCA quantifies how variables, such as fluxes and species concentrations, depend on the system’s parameters. In particular it is able to describe how network dependent properties, called control coefficients, depend on local properties called elasticities.This will be the first in a series of short articles on the basic ideas embodied in BCA.

In this first article I will clarify the meaning of a couple of words used in BCA:

#### Variable

A variable, also called a dependent variable or state variable is a measurable characteristic of a system that can only be changed by an observer through changes to a suitable parameter. Variables are by definition determined by the system. Examples of possible variables include the pathway flux and species concentrations, such as metabolites or proteins.

#### Parameter

A parameter is a measurable characteristic of a system that can in principle be controlled by the observer. Parameters are also often called independent variables. By definition, a parameter cannot be changed by the system itself, if it can then it is called a variable. Examples of parameters include external concentrations such as glucose fed to a culture or externally added drug compounds, internal parameters such as kinetic constants, and depending on the system under study, enzyme concentrations.

#### Control

The term control has a special meaning in control analysis. Control refers to the ability of a system parameter to affect a system variable. For example, changes to the external glucose concentration in a microbial culture will most likely change the culture’s growth rate. The concentration of glucose therefore has ‘control’ over the growth rate. Engineering an enzyme in pathway so that its kcat is larger will result in changes to the pathways flux and metabolite concentrations. Changes to the promoter consensus sequence of a particular gene will result in changes to the concentration of the expressed protein and any other variables that depends on that protein. It is possible to quantify control by either measuring or computing control coefficients.

#### Regulation

Regulation may be defined as the capacity to achieve control. Such control may involve homeostasis or ability to move from one state to another in a particular manner.

#### Flux

The flux is the steady state flow of mass through a pathway.