This page is the third of four containing a list of frequently asked questions (FAQ) about metabolic control analysis.
A response coefficient defines the sensitivity of any system variable to any perturbation. For example, if increasing the concentration of an external inhibitor by 10% causes the flux through a pathway to decrease by 5% one may say that the response coefficient of the flux with respect to the inhibitor concentration is -5/10, or -0.5.
The relatively small number of enzymes that are expressed by mitochondrial genes
behave differently from enzymes expressed by nuclear genes when mutations are
present. This is because heterogeneity of the mitochondrial population and
variations in the numbers of mitochondria in each cell allow the activity of an
enzyme present in both normal and mutant forms to vary over the range 0-100%
with many intermediate values possible (not just 50%, as for the case of a
heterozygote in a diploid organism for an enzyme expressed by a nuclear gene).
As with all enzymes, mitochondrial enzymes typically have small flux
control coefficients for any given flux, but these increase
as the enzyme activity decreases. The point at which any given enzyme becomes
important
in the sense that variations in activity produce obvious phenotypic
effects varies with the enzyme. Thus some mitochondrial enzymes can fall to
quite low levels of activity before medical problems arise, whereas others
cannot.
A major objective of metabolic control analysis is to treat systems as systems,
rather than just as collections of components. Nonetheless, the properties of a
system are determined by the properties of its components, and one needs a
clear way of distinguishing between the two. It is important to understand that
both the system and its components are matters of definition. In introductory
accounts of metabolic control analysis one usual takes the system to be a
pathway of four or five enzymes and the enzyme-catalysed reactions as its
components. However, one may later want to expand the system to encompass a
larger part of cell metabolism, and then the simpler system may be regarded as
a component of the larger one. Moreover, the linear algebra that underlies the
mathematical treatment of control analysis means that blocks of reactions
behave in the same way as individual reactions. (This is the basis of
top-down analysis
, which allows larger systems to be
analysed by treating blocks of reactions as if they were single reactions).
Thus glycolysis, for example, may be regarded as a complete system in one
analysis but as a component of carbohydrate metabolism in another. None of this
complicates matters as long as the terms used in an analysis are clearly
defined, and one of the main criticisms of flux-oriented
theory is that it does not define the limits of the system under study with
sufficient precision and consequently allows potentially confusing concepts
such as partially externally regulators
.
Once the limits of the system are decided it is appropriate to consider
system properties that apply complete system in the presence of all its
components, whereas local properties are those of the isolated components.
Study of isolated enzymes has been the major activity in kinetic investigations
for most of this century, but there are important differences between kinetic
measurements designed to reveal mechanistic information and those intended to
aid in understanding system behaviour. In mechanistic studies one normally
tries to make the reaction mixture as simple as possible to minimize
ambiguities in the interpretation, and one often creates conditions very
different from those in the cell (such as extreme concentrations of effectors)
in order to illuminate differences between mechanisms that would be difficult
to recognize under more physiological conditions. Neither of these is appropriate
for considering the local properties of the component of a system:
here the ideal is to mimic the conditions that exist in the complete system as
exactly as possible, except that no other catalysts are present. Thus the
isolated enzyme should see
exactly the same concentrations of its substrates,
products and any other metabolites that interact with it as it would see in the
complete system.
The flux control coefficients for any given flux, summed over all the enzymes in the system, add up to 1. In an unbranched system there is only one flux, because in the steady state the rate through every reaction is the same. However, in a branched pathway there can be, and normally are, different fluxes in the different branches. In this case it is important that all of the flux control coefficients in the summation refer to the same flux, and that all of the enzymes in the pathway are included, regardless of whether they occur in the particular branch considered.
A similar relationship applies to the concentration control coefficients for any given metabolite. However, in this case the values add up to 0.
There are other summation relationships for other system variables. For example, one can define transit time control coefficients for the time required on average for mass to pass through a system, and these control coefficients add up to -1.
Before metabolic control analysis existed modelling of metabolic systems in the computer was the only realistic way that a biochemist could get any idea of how a complex metabolic system might behave in different conditions. However, it was very demanding, in terms both of computer expertise and indeed of hardware, and as a result its use was confined to a few experts and the insights that came from it were very little diffused in the biochemical world.
The situation has now completely changed in that a number of powerful programs are widely available for use on common computer systems without particular expertise in computational or modelling techniques. The question arises, however, of why one might want to model metabolic systems now that metabolic control analysis provides much insight into how they behave, which is valid in general without reference to particular systems. In fact there are several reasons why most people active in control analysis continue to use both analysis and modelling. The most obvious is that it is usually very much faster and easier to obtain specific numerical information about a metabolic system by computer modelling than by algebra, and one can easily set up quite complicated models and ask and answer complicated questions about them. Even if the answers may subsequently be generalized as theorems of metabolic control analysis the insights that allow the algebraic analysis often come in the first place from modelling.
elasticity(rather than, say,
order of reaction)?
The term elasticity
comes from the science of econometrics, where one may
say, for example, that if the demand for cars decreases by 6% when the price of
cars increases by 3% then there is a demand-price elasticity for cars of 2 (=
6/3). In metabolic control analysis one says that there is a substrate
elasticity of 2 if the rate of a reaction increases
by 6% when the substrate concentration increases by 3%. Note two differences:
there is change of sign, so that the econometric elasticity would be -2, not 2,
if the conventions of metabolic control analysis applied; second, econometric
elasticities are usually greater than 1, whereas in control analysis
elasticities in irreversible processes are usually (though not
always) between -1 and 1.
Given that most biochemists are more familiar with chemistry (in which the
order of reaction has much in common with an elasticity) than with
econometrics, one may wonder why the less familiar term is retained in
metabolic control analysis, especially as biochemical systems
theory uses the term kinetic order
for the corresponding quantity. There
are in fact two reasons, though neither is very persuasive.
Strictly speaking a chemical order of reaction ought to be an integer, whereas
an elasticity is rarely an integer; nonetheless, the use of the order of
reaction
for a non-integral quantity is widespread in biochemistry, and
normally causes no problems. Perhaps more important, a kinetic order in
biochemical systems theory is a parameter in a power-law
equation, and as such must be constant over the range of validity of the
equation (because a law has to be expressed in terms of constants if it is to be
meaningful). By contrast, metabolic control analysis never assumes that
elasticities are constant, and in understanding how systems behave it is
important to realize that elasticities (and control
coefficients) vary with the conditions. For this reason there may be some
merit in retaining a distinct term.
The ISGSB (International Study Group for Systems Biology (formerly BTK: BioThermoKinetics) maintains a regular programme
of meetings (at two-year intervals) with a substantial content of metabolic
control analysis. The 14th ISGSB
meeting was in Vladimir, Russia, in September 2010. The next meeting is likely to be in 2012.