Causality, Complexity and Computers
21
It will be noted that the value of the coefficient varies over the whole range
of enzyme activities because of the non-linearity. This means that the
response of the system to the same fractional change will be different at
different absolute values of the enzyme.
We can now see clearly what meaning can be attached to the term
'controlling' enzyme or 'master reaction'. Obviously this must be the one
whose coefficient is numerically equal to 1, that is, a reaction where, say,
a 1 % change in the enzyme produces a 1 % change in the dependent flux.
The same enzyme may be rate-controlling at the lower end of its range but
quite insensitive at high values. The non-linearity is the result of all the
interactions of the system and hence depends, in general, on the values of
all the other components. The coefficient is therefore a systemic property
depending not only on the one enzyme but on all others, as well as on
certain external parameters such as fixed substrate sources. What applies
to one enzyme applies to all others. The coefficients of all enzymes therefore depend on each other and will change if anyone of them changes (by
e.g. a movement to a new position). It is therefore seen that many enzymes
contribute to the flux and to its control. In a simple pathway, for example,
no single enzyme may have a coefficient of 1 but all may have small values
and therefore none of them will be master reactions (compare Fig. 5). Flux
control is therefore seen to be dependent not simply on the enzyme itself,
nor on its structural position nor on the structure as a whole. The absolute
and relative values of all parameters are equally important. It is a truly
systemic property, being the response characteristic of the whole system
at one point of its phase space.
Coefficients can be determined for a large number of properties with
respect to any changes in the parameters under experimental control. Thus
F·
it is possible to determine the coefficient C x~ of a certain flux Pi with
J
respect to a controlled food source J0. In general all systemic properties,
i.e. dependent variables, have coefficients with respect to all independent
parameters, C~. In principle all such coefficients are determinable and a
matrix of these displays in quantitative terms the role each element plays
when acting within the system. Although these are 'properties' of the
elements, they are dependent (and sometimes critically dependent) on
other elements. We shall therefore find that this property may change,
(change in the value of the coefficient) if e.g. the organism is exposed to
different environments (change in 'external' parameters) or if the genetic
background ('internal' parameters) is changed. The element, e.g. an
enzyme, having undergone no change is nevertheless seen to have altered
its role. Although by no means restricted to biological systems, it is in
organisms that these concepts are essential to our understanding.
21
It will be noted that the value of the coefficient varies over the whole range
of enzyme activities because of the non-linearity. This means that the
response of the system to the same fractional change will be different at
different absolute values of the enzyme.
We can now see clearly what meaning can be attached to the term
'controlling' enzyme or 'master reaction'. Obviously this must be the one
whose coefficient is numerically equal to 1, that is, a reaction where, say,
a 1 % change in the enzyme produces a 1 % change in the dependent flux.
The same enzyme may be rate-controlling at the lower end of its range but
quite insensitive at high values. The non-linearity is the result of all the
interactions of the system and hence depends, in general, on the values of
all the other components. The coefficient is therefore a systemic property
depending not only on the one enzyme but on all others, as well as on
certain external parameters such as fixed substrate sources. What applies
to one enzyme applies to all others. The coefficients of all enzymes therefore depend on each other and will change if anyone of them changes (by
e.g. a movement to a new position). It is therefore seen that many enzymes
contribute to the flux and to its control. In a simple pathway, for example,
no single enzyme may have a coefficient of 1 but all may have small values
and therefore none of them will be master reactions (compare Fig. 5). Flux
control is therefore seen to be dependent not simply on the enzyme itself,
nor on its structural position nor on the structure as a whole. The absolute
and relative values of all parameters are equally important. It is a truly
systemic property, being the response characteristic of the whole system
at one point of its phase space.
Coefficients can be determined for a large number of properties with
respect to any changes in the parameters under experimental control. Thus
F·
it is possible to determine the coefficient C x~ of a certain flux Pi with
J
respect to a controlled food source J0. In general all systemic properties,
i.e. dependent variables, have coefficients with respect to all independent
parameters, C~. In principle all such coefficients are determinable and a
matrix of these displays in quantitative terms the role each element plays
when acting within the system. Although these are 'properties' of the
elements, they are dependent (and sometimes critically dependent) on
other elements. We shall therefore find that this property may change,
(change in the value of the coefficient) if e.g. the organism is exposed to
different environments (change in 'external' parameters) or if the genetic
background ('internal' parameters) is changed. The element, e.g. an
enzyme, having undergone no change is nevertheless seen to have altered
its role. Although by no means restricted to biological systems, it is in
organisms that these concepts are essential to our understanding.