Biology Reference
In-Depth Information
3. THE RISE OF SYSTEMS ANALYSIS OF METABOLISM
The occasional criticisms of the rate-limiting step concept made little headway
until various individuals and groups began to explore the properties that would
be expected of metabolic pathways given that they were composed of enzymes
(and transporters) which exhibited nonlinear kinetics with respect to substrates,
products, and effectors. Some approached this through computer simulation of
actual metabolic systems (Chance et al. 1958; Garfinkel & Hess, 1964, Park
& Wright, 1973), though the modest computer power available at the time
and lack of good numerical software for integration of systems of nonlinear
differential equations made this a difficult undertaking. The other approach
was algebraic analysis, often of model metabolic systems, to deduce general
properties that might be expected of connected groups of enzymes, usually under
steady-state conditions. A key concept introduced by Higgins (1963) was to
replace qualitative descriptors such as 'rate-limiting' by sensitivity coefficients
that quantitatively measure the response of the rate of a pathway to a change
in a parameter such as the activity of an enzyme. Sensitivity analysis itself
was not, of course, the innovative step, as it was already used in engineering
and economics, but its application in metabolic biochemistry was. Higgins'
ideas were extended independently by Kacser & Burns (1973) and Heinrich &
Rapoport (1974). Although these two groups initially went about their analyses in
somewhat different ways, they eventually agreed that their ideas were compatible
and unified them under the title of
Metabolic Control Analysis
(Burns et al.,
1985; Cornish-Bowden & Cárdenas, 1990). A key sensitivity coefficient in their
analyses was the flux control coefficient, which measures the relative response
of the metabolic pathway rate (or flux) to a relative change in an enzyme activity.
At about the same time, Savageau (1969, 1976) was developing
Biochemi-
cal Systems Theory
, which included approximations to dynamic behaviour as
well as analysis of metabolic steady states. Crabtree & Newsholme (1985) also
adopted algebraic analysis, by a methodology widely regarded as intermediate
between metabolic control analysis and biochemical systems theory. Both these
approaches also implemented sensitivity analysis.
It can be argued that these developments did not introduce any new theory
into metabolism, but allowed the formulation of a mathematical description;
indeed, Henrik Kacser always insisted on referring to metabolic control analysis
and not metabolic control theory. However, with the new analysis tools, old
principles could be tested and new generalisations about the characteristics of
metabolic systems proposed.
An example of a new generalisation was the flux summation theorem of
Kacser & Burns (1973). They showed that the sum of all flux control coefficients
of the enzymes in a system on a specified metabolic flux would be one. This
surprisingly suggests that there is a limit to the total amount of control that
