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J. A. BURNS
slight extension enables us to consider enzyme quantity as a variable of the
system thus including such effects as repression and induction. The use of
"net flux" expressions has several advantages:
1) The number of differential equations needed to describe the system
is now only the number of free metabolic pools.
2) High frequency terms, associated mainly with enzyme substrate complexes, have been largely removed from the system which results in a very
large gain in computer efficiency.
3) The steady state and the properties of the steady state will not be
affected and even the "dynamics" should approximate to the true dynamics,
provided enzyme concentrations are several orders of magnitude smaller
than their substrates, which is often the case.
4) Most of the parameters involved in describing an enzyme now have
an intuitive and operational meaning, e.g. Michaelis constant.
Analysis
Routines to carry out the necessary operations of analysis are included
in part B of the program layout among these are:
1) Steady state (x)
This will cause the system to move from its initial position to an exact
steady state, such that all the enzymes are within x per cent of the values
desired for them. For many purposes a steady state close to a given point
in enzyme space is all that is required.
The routine works by integrating the differential equations of the
system, the time required on the computer depending critically on the
ratio of the highest and lowest frequency in the system i.e. the bandwith.
Systems with a large excess of one or more enzymes will have a high
bandwith. If the system has no steady state then the routine will "give up"
after a preset time.
2) Coefficients
This is a routine for calculating the rate controlling effect of any enzyme on any flux in the steady state system.
Let ji be a flux at some point in a steady state system and ej the amount of
any enzyme then if Cj is increased by dCj and the system assumes a neighbouring steady state there will be a change dfi in fi . Let C(i,j) = Limit as
dCj 0 of ((dfilJi)j(dcjjci» or sensitivity coefficient of flux.fi with respect to
enzyme Cj is fractional change in fi divided by fractional change in Cj which
produced it. The routine will calculate and print out the coefficients over
all i,j thus enabling the investigator to study the rate-controlling" effects of
enzymes in his model system.
J. A. BURNS
slight extension enables us to consider enzyme quantity as a variable of the
system thus including such effects as repression and induction. The use of
"net flux" expressions has several advantages:
1) The number of differential equations needed to describe the system
is now only the number of free metabolic pools.
2) High frequency terms, associated mainly with enzyme substrate complexes, have been largely removed from the system which results in a very
large gain in computer efficiency.
3) The steady state and the properties of the steady state will not be
affected and even the "dynamics" should approximate to the true dynamics,
provided enzyme concentrations are several orders of magnitude smaller
than their substrates, which is often the case.
4) Most of the parameters involved in describing an enzyme now have
an intuitive and operational meaning, e.g. Michaelis constant.
Analysis
Routines to carry out the necessary operations of analysis are included
in part B of the program layout among these are:
1) Steady state (x)
This will cause the system to move from its initial position to an exact
steady state, such that all the enzymes are within x per cent of the values
desired for them. For many purposes a steady state close to a given point
in enzyme space is all that is required.
The routine works by integrating the differential equations of the
system, the time required on the computer depending critically on the
ratio of the highest and lowest frequency in the system i.e. the bandwith.
Systems with a large excess of one or more enzymes will have a high
bandwith. If the system has no steady state then the routine will "give up"
after a preset time.
2) Coefficients
This is a routine for calculating the rate controlling effect of any enzyme on any flux in the steady state system.
Let ji be a flux at some point in a steady state system and ej the amount of
any enzyme then if Cj is increased by dCj and the system assumes a neighbouring steady state there will be a change dfi in fi . Let C(i,j) = Limit as
dCj 0 of ((dfilJi)j(dcjjci» or sensitivity coefficient of flux.fi with respect to
enzyme Cj is fractional change in fi divided by fractional change in Cj which
produced it. The routine will calculate and print out the coefficients over
all i,j thus enabling the investigator to study the rate-controlling" effects of
enzymes in his model system.