Pedro Mendes wrote:
>In a previous message I was writing about control analysis and
>channelling. I mentioned one way in which MCA can be applied to
>channelling without any problems in terms of the summation theorem.
>This is the method developed by Boris Kholodenko and Hans Westerhoff
>that uses the elementary reactions of the enzymatic mechanisms.
....
>The papers by Boris and Hans were the first to describe a systematic
>way of applying control analyis to channelling mechanisms using the
>elementary reactions.
....
>As far as I am aware, the other way to apply MCA to channelling (i.e.
>seeing the two reactions as a single one) that I suggested has never
>been applied. I would be grateful if anyone knows anything to the
>contrary (I reply to Danny Kohl's points about this in a separate
>message)
There is an experimental example of a dynamically channelled system where
MCA has been applied simultaneously in two different ways. In the first
way, the flux control coefficients were measured directly as response
coefficients to changes in the concentrations of components. In the second
way, flux control coefficients were measured by dividing the system
response to a specific inhibitor by the local response to that inhibitor.
In this case there was some grouping of individual reactions to make them a
smaller number of more complex reactions.
The dynamically channelled pathway is the uncoupled mitochondrial electron
transport chain, where electron transport is a group-transfer reaction
between successive pairs of electron carriers.
Experimentally, the sum of the flux control coefficients was 2 when the
coefficients were calculated by varying catalyst concentrations directly,
but 1 when calculated from the ratio of system responses to local responses
(as predicted by van Dam, Kholodenko and Westerhoff). The two calculations
used essentially the same data set. The first method uses the classical
definition of control coefficients in terms of catalyst concentrations, the
second method is equivalent to considering elementary reactions.
This is published:
Brand, M.D., Vallis, B.P.S. and Kesseler, A (1994) The sum of flux control
coefficients in the electron-transport chain of mitochondria. Eur. J.
Biochem. 226, 819-829
In the same way, calculation of flux control coefficients from elasticities
of grouped reactions in the top-down approach circumvents the problem of
channelling by grouping the channelled reactions together. Thus, even
though the electron transport chain is dynamically channelled, measuring
its overall (group) elasticity to its product allows calculation of its
flux control coefficient without any complications due to channelling -
equivalent to measurement from elementary rates.
see:
Brand, M.D. (1996) Top down metabolic control analysis. J. Theor. Biol.
182, 351-360
Hafner, R.P., Brown, G.C. and Brand, M.D. (1990) Analysis of the control
of respiration rate, phosphorylation rate, proton leak rate and
protonmotive force in isolated mitochondria using the 'top-down' approach
of metabolic control theory. Eur. J. Biochem. 188, 313-319
Brown, G.C., Hafner, R.P. and Brand, M.D. (1990) A 'top-down' approach to
the determination of control coefficients in metabolic control theory.
Eur. J. Biochem. 188, 321-325
The classic measurements of the flux control coefficients in the electron
transport chain using inhibitors (Groen et al (1982) J Biol Chem 257,
2754-2757, and many papers from several groups using the same approach
susequently) are confounded by this dynamic channelling, and the expected
sum of flux control coefficients would be between 1 and 2, not 1 as assumed
generally and in these papers. However, since the flux control by the chain
components is only a small proportion of the total flux control for the
relatively extensive systems people have looked at, the error is not very
great (the sum is not much more than 1). As pointed out by van Dam,
Kholodenko and Westerhoff, the difference between the sum of response
coefficients to concentrations of catalysts and the sum of the elementary
flux control coefficients for this case of dynamic channelling and for
other cases of static channelling should provide a very powerful
experimental tool to prove or diprove channelling within a cell. I don't
think it has been used this way yet.
Martin Brand
Martin D. Brand
Department of Biochemistry, University of Cambridge
Tennis Court Road, Cambridge CB2 1QW UK
phone: +44 1223 333648, fax: +44 1223 333345
Internet: http://www.bio.cam.ac.uk/dept/biochem/brand/
