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Herbert M Sauro HSauro at fssc.demon.co.uk
Thu May 11 14:14:08 EST 2000


May 2000

Here is the new FAQ for the Metabolic-Reg group. Hopefully it
will expand in future editions, contributions and comments will be very
welcome. Omissions, reports of errors, bad formatting etc. to be sent to the
maintainer.

FAQ maintainer:

Herbert Sauro
HSauro at fssc.demon.co.uk


-------------------------------------------------------------------------
[1] About bionet.metabolic-reg FAQ
------------------------------------------------------------------------


This is an updated ASCII version of a html FAQ originally posted by Athel
Cornish-Bowden on his web site (and still available at
http://ir2lcb.cnrs-mrs.fr/~athel/mcafaq.htm). Many thanks to Athel for
allowing us to use his FAQ as the basis for the bionet-metabolic-reg
newsgroup FAQ.

Readers will discover that this FAQ is currently biased towards questions
about metabolic control analysis (MCA) and computational aspect of metabolic
systems. However contributions relating to specific regulatory behaviour of
metabolic
systems are also very welcome including of course interesting FAQs
relating to experimental work. Contributions are welcome !!

This FAQ is maintained by Herbert Sauro <HSauro at fssc.demon.co.uk>. The
foundation for the FAQ was provided by Athel Cornish-Bowden's Web-site FAQ.

***** See http://ir2lcb.cnrs-mrs.fr/~athel/mcafaq.htm


Copyright (c) 1998-2000 Herbert Sauro and Athel Cornish-Bowden. This FAQ may
be posted to any USENET newsgroup, on-line service, or BBS as long as it is
posted in its entirety and includes this copyright statement. This FAQ may
not be
distributed for financial gain. This FAQ may not be included in commercial
collections or compilations without express permission from the author.


**************************
[1.1] What's New?

May 2000

This text version is new and has numerous new additions and amendments to
the original Web FAQ.


------------------------------------------------------------------------
[1] About Bionet.Metabolic-Reg FAQ
[1.1] What's New?


[2] Basic Theory of MCA
[2.1] So what's the big deal?
[2.2] What is Metabolic Control Analysis?
[2.3] How is metabolic control analysis related to sensitivity analysis?
[2.4] What is a sensitivity?
[2.5] What is a control strength?
[2.6] What are the main questions that metabolic control analysis sets out
to answer?


[3] Other approaches
[3.1] What is flux-oriented theory?
[3.2] What is biochemical systems theory?


[4] Fundamental Concepts of MCA
[4.1] What is an elasticity?
[4.2] What is an elasticity coefficient?
[4.3] What is a control coefficient?
[4.4] What is a response coefficient?
[4.5] What are local and system properties?
[4.6] What are the theorems of Metabolic Control Analysis?
[4.7] What are the summation relationships?
[4.8] What is the connectivity relationship?
[4.9] Why "elasticity" (rather than, say, "order of reaction")?
[4.10] How is metabolic control analysis related to classical ideas of
metabolic regulation?
[4.11] The Two Fundamental Equations of Metabolic Control Analysis
[4.12] Why does metabolic control analysis appear to ignore enzyme
mechanisms?
[4.13] What is the partitioned response relationship?


[5] Specific Metabolic Concepts
[5.1] How does feedback inhibition affect the distribution of flux control
in a pathway?
[5.2] How can yields of metabolic processes be improved for
biotechnological purposes?
[5.2] Why isn't Phosphofructokinase rate-limiting?
[5.3] Supply and Demand Theory of Metabolic Systems
[5.4] TurboCharging
[5.5] How does channelling affect the summation relationships?
[5.6] What is a controllability coefficient?
[5.7] Is it true that metabolic control analysis assumes that enzymes
are regulated solely by changing their concentrations (or V values)?
[5.8] How does metabolic control analysis explain the fact that most
mutations in diploid organisms are recessive?
[5.9] How does metabolic control analysis aid in understanding
mitochondrial myopathies and other metabolic diseases?
[5.10] Competitive and UnCompetitive inhibition


[6] Real-World Metabolic Models


[7] Computational Resources
[7.1] What programs are available for metabolic modelling?
[7.2] Where can I find information on algorithms for metabolic analysis?
[7.3] What advantages does modelling have over algebraic analysis?


[8] People and References
[8.1] Where can I find more detailed information in the printed literature?
[8.2] How do I contact people working on metabolic control analysis?
[8.3] Where can I find information about meetings related to metabolic
control analysis?
[8.4] References
[8.5] Are there any books devoted to metabolic control analysis?
[8.6] Why is the question that interests me not listed?
[8.7] Where can I find more detailed information on the web?

[9] Acknowledgments



[2] Basic Theory
------------------------------------------------------------------------


[2.1] So what's the big deal?

Cellular systems such as gene networks, signal transduction schemes and the
traditional metabolic pathways are some of the main elements that constitute
the insides of cells; they make cells complicated and difficult to
understand. The standard biochemistry and molecular biology text books
abound with
colourful diagrams of how the things we find in cells are connected to one
another, how one reaction step follows another or how signals are
transmitted along
cascades of proteins.

Whereas physics and chemistry and in fact all the other related sciences
rely heavily on quantitative methods and strict mathematical theory,
biochemistry
and particularly molecular biology stand-out as some of the few sciences
that have either rejected the quantitative approach or have yet to embrace
it.
This newsgroup and by implication this FAQ attempts to answer questions
concerning quantitative approaches to describing cellular systems. This is
an important
new field; if we are ever to find truly rational ways
at finding new drug targets or improving commercially important products of
living systems then our current obsessive fixation on genes and gene
sequences
rather that what actually goes on downstream of gene expression will have to
change. I mean, I don't think it requires a rocket scientist to realise
where most
therapeutic drugs act and if you want to improve ethanol production in yeast
where
should one look, in the nucleus or the cytoplasm? No prizes for the correct
answer.


[2.2] What is metabolic control analysis?

Metabolic control analysis is a method for analysing how the control of
fluxes and intermediate concentrations in a metabolic pathway is distributed
among
the different enzymes that constitute the pathway. Instead of assuming the
existence of a unique rate-limiting step, it assumes that there is a
definite amount of flux control and that this is spread quantitatively among
the
component enzymes. Metabolic control analysis was formerly (and is sometimes
still) known as metabolic control theory, and is closely related to the
engineering discipline known as sensitivity analysis. Alternative approaches
to studying the kinetic behaviour of multi-enzyme systems are flux-oriented
theory and biochemical systems theory.

Metabolic Control Analysis can be divided into a number of related areas:

a) Structural Analysis
b) Perturbation Analysis
c) Response Analysis
d) Regulation Analysis
e) Heuristic Theorem Analysis

These areas of study will be expanded in future FAQ releases.

**************************
[2.3] What is metabolic control theory (and is it different from
metabolic control analysis)?

Metabolic control theory is an older term for metabolic control analysis. It
is still used by some authors, but started to fall into disuse at the end of
the 1980s when some authors began to emphasize that metabolic control
analysis
is more a method for analysing how control is distributed than a body of
theory
as such.


**************************
[2.4] How is metabolic control analysis related to sensitivity analysis?

Sensitivity analysis is a technique in engineering that shares much of the
mathematics and concepts of metabolic control analysis. The control
coefficients of metabolic control analysis are, in effect, sensitivities as
understood by engineers.


**************************
[2.5] What is a sensitivity?

Sensitivity was the term used originally for what is now called a control
coefficient, and it underlines the fact that metabolic control analysis is a
form of sensitivity analysis.


**************************
[2.6] What is a control strength?

Control strength is an older term for what is now called a control
coefficient.


**************************
[2.7] What are the main questions that metabolic control analysis
sets out to answer?

Metabolic control analysis begins by recognizing that flux control is not a
unique property of one "rate-limiting" enzyme in a pathway but is a
distributed property shared among all of the enzymes. It then sets out to
quantify the distribution. Similar considerations apply to concentrations of
the intermediate metabolites in a pathway, and other variables whose values
are set by the properties of the system. Such variables include the transit
time
(how long does it take on average for a molecule to traverse a system?) and
other times, but these have received less attention than fluxes and
concentrations.


[3] Other Approaches
------------------------------------------------------------------------


[3.1] What is flux-oriented theory?

Flux-oriented theory is an approach developed by E. A. Newsholme, B.
Crabtree and their associates that can regarded as an alternative to
metabolic
control analysis for formalizing control relationships in metabolism.
Although it
has some similarities with metabolic control analysis it differs in
important
respects. In particular, it incorporates the concept of partially external
regulators, whose concentrations are partially variable and partially
constant.


**************************
[3.2] What is biochemical systems theory?

Biochemical systems theory is an approach developed by M. A. Savageau and
his associates, who regard it as a general theory of metabolic control that
includes metabolic control analysis and flux-oriented theory as special
cases. It places much more emphasis on predicting how systems will behave
when the
conditions are changed than on understanding in physical terms how they are
controlled.



[4] Fundamental Concepts
------------------------------------------------------------------------


[4.1] What is an elasticity?

An elasticity is a local property of an isolated enzyme that expresses how
its rate varies with the concentration of any metabolite that affects it:
this can be
its substrate, product, or any other metabolite. An elasticity of, say, 0.5
with
respect to a substrate means that a 2% increase in substrate concentration
would increase the rate of the reaction catalysed by the enzyme by 1%,
i.e. by 0.5 times 2%. Strictly speaking the definition applies to the limit
at infinitesimally small changes, but it applies with reasonable accuracy
for
small changes, say up to 10 or 20%. It follows that substrate elasticities
are
positive (except under conditions of substrate inhibition), product
elasticities are
negative (except in the very rare case of product activation), activator
elasticities are positive, and inhibitor elasticities are negative.
Simple algebra shows that for an enzyme obeying Michaelis-Menten kinetics
under irreversible conditions the substrate elasticity varies from 1 at very
low
concentrations down to zero at saturation. As this is exactly the behaviour
attributed to the order of reaction (or kinetic order) with respect to
substrate, one may wonder whether elasticity is just an obscure name for
order of
reaction: this is discussed elsewhere.

Although substrate elasticities are normally between 0 and 1 (and are always
numerically small) for irreversible reactions, it is crucial to realize that
reversible reactions are very different. Substrate elasticities approach
infinity for reactions close to equilibrium, and the passage from positive
to negative as a substrate becomes a product when the reaction passes from
one
side of equilibrium to the other involves crossing infinity, not zero. This
property means that it is essential to treat all reactions as reversible in
computer simulations of metabolism unless it is absolutely certain that the
reverse reaction is completely negligible under all circumstances simulated.


**************************
[4.2] What is an elasticity coefficient?

An elasticity coefficient is exactly the same as an elasticity; both terms
are used.


**************************
[4.3] What is a control coefficient?

A control coefficient is the system property of an enzyme that expresses how
some systemic variable, usually a flux or a metabolite concentration,
depends on
the activity of the enzyme. If some perturbation of an enzyme activity
increases
the rate of the isolated reaction by 5%, whereas the same perturbation of
the
same enzyme when it is embedded in a metabolic system increases the flux by
2%,
the enzyme is said to have a flux control coefficient of 2/5, or 0.4. If the
same perturbation causes the concentration of the substrate of the enzyme to
decrease by 10%, the enzyme has a concentration control coefficient for that
metabolite of -10/5, or -2. Notice that there is no mention of the
concentration of the
enzyme when the control coefficients are defined in this way. However, the
rate of
an enzyme-catalysed reaction is often found to be directly proportional to
the
enzyme concentration: if (and only if) this is the case the anonymous
"perturbation" referred to in the definition can be a change in the enzyme
concentration.
This then allows a less abstract and apparently simpler definition of a
control
coefficient, and such a definition was widely used for a number of years. It
is, however, falling into disuse, both because it is not always valid, and
because even when it is valid it can encourage the wholly erroneous
misconception
that metabolic control analysis deals only with effects brought about by
changes
in enzyme concentration or limiting activity.

In the older literature control coefficients were known as sensitivities or
control strengths.


**************************
[4.4] What is a response coefficient?

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.


**************************
[4.5] What are local and system properties?

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.


**************************
[4.6] What are the theorems of Metabolic Control Analysis?


Indeed, what are they? Waiting for a contribution, but try this one:

Briefly: The theorems of MCA represent special algebraic relationships
between the coefficients of MCA. They originate from the unique structural
and
kinematic properties of the underlying metabolic system. For this reason
they have important heuristic value for gaining insight into the nature and
properties of metabolic systems. The theorems are also one of the
distinguishing aspects of MCA and makes MCA more that just traditional
sensitivity analysis, moreover the theorems are experimentally verifiable
properties which makes MCA a credible scientific theory of cellular systems.

The theorems of MCA can be classified into two main groups (other less
known groups also exist):

The summation theorems, which include the 'classical' summation theorems
and the branch theorems;

and the all important connectivity theorems which connect local to
system properties.


**************************
[4.7] What are the summation relationships?

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.


**************************
[4.8] What is the connectivity relationship?

For any metabolite and any flux in a system, one can multiply the flux
control coefficient of an enzyme by its elasticity with respect to the
metabolite
concerned. If one does this for all of the enzymes in the system and adds
all the resulting products, they give a sum of zero. This is the general
form of
the connectivity relationship. For metabolites that have non-zero
elasticities for numerous enzymes (i.e. for metabolites that influence the
activities of
numerous enzymes) the resulting sum contains many terms and is not
particularly useful. However, if a metabolite influences only two enzymes,
as for example
the enzyme that produces it and the enzyme that consumes it, it will have
only two non-zero elasticities, and the sum will contain only two terms,
each of
which must then be minus the other. In this case the connectivity
relationship becomes much more useful, as it provides a way of calculating
an unknown
control coefficient from a known one, provided the relevant elasticities are
also known.


**************************
[4.9] Why "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.


**************************
[4.10] How is metabolic control analysis related to classical ideas of
metabolic regulation?

Because of the abstraction of mechanistic details into the elasticities of
metabolic control analysis, the classical concepts of feedback inhibition of
the first committed step of a pathway, cooperativity, etc., can seem to be
forgotten about, or at least hidden as mathematical details. However, their
effects on the distribution of control have been well understood (albeit not
much emphasized) since the original paper of Kacser and Burns (1973).


**************************
[4.11] The Two Fundamental Equations of Metabolic Control Analysis

MCA can boast two fundamental equations that summarise the main ideas of
MCA, the first equation is the relationship between the local properties of
a
system and its global behaviour, in matrix form this equation is:

C = inv (E)

where C is the matrix of control coefficients and E the matrix of elasticity
coefficients (modified with network structural information).

The second fundamental equation of MCA is the response relationship, this
relates the three most important quantitative measures in MCA into one
relation, that is the control coefficient, the response coefficient and the
system boundary elasticities.

R = C E


**************************
[4.12] Why does metabolic control analysis appear to ignore enzyme
mechanisms?

Metabolic control analysis tends to treat the kinetic properties of the
component enzymes as a black box. Some authors have been very critical of
this, suggesting that shedding light on mechanism is the only reason for
studying
kinetics in the first place. However, in reality it is the usual kind of
abstraction one finds (and needs) at all level of science. Although wave
mechanics is at the basis of all chemistry, it is hardly possible to present
a list of typical reactions of aldehydes, for example, in terms of wave
equations. Even if it were possible it would not be helpful because it would
hide the points of immediate interest in a lot of algebra. At another level,
all interactions between living organisms are dependent on the laws of
chemistry, but again, it would be neither possible nor, if it were possible,
helpful to discuss the political relationships between countries in terms of
chemical reactions. Studies of biochemical kinetics have been dominated for
nearly a century by an interest in molecular mechanisms, but for
understanding how whole pathways behave it has been found useful to decrease
the emphasis
on mechanism. Thus mechanisms such as cooperative feedback inhibition are
not
ignored in metabolic control analysis, but they are given less emphasis than
in classical studies of metabolic regulation.


**************************
[4.13] What is the partitioned response relationship?

If an external parameter, such as the concentration of an inhibitor, acts on
only one enzyme in a system, the response coefficient for any system
variable can be obtained by multiplying the appropriate control coefficient
for the
enzyme acted on by the elasticity of the same enzyme with respect to the
external parameter. (If the external parameter acts on more than one enzyme
the response coefficient is the sum of several such terms, one for each
affected
enzyme. However, this case is inconvenient to apply, and experimentally one
normally tries to avoid it by using specific effectors.)


[5] Specific Metabolic Concepts
------------------------------------------------------------------------


[5.1] How does feedback inhibition affect the distribution of flux control
in a pathway?

The effect of feedback inhibition by an end-product of the first committed
step in its biosynthesis is to transfer flux control away from that step in
order
to increase the share of control residing in the reactions that consume the
end-product. This can be seen as a means of transferring flux control from
supply to demand.


**************************
[5.2] How can yields of metabolic processes be improved for biotechnological
purposes?

Since it became possible (around 1980) to identify the genes responsible for
the synthesis of enzymes and to overexpress them in mutant organisms, a
major objective of biotechnology has been to identify the rate-limiting
enzymes in
pathways that lead to commercially important products, so that they can been
overexpressed in the hope of increasing the yields of the desired products.
Despite enormous financial investment around the world these efforts have
been wholly unsuccessful, at least to the present, no examples of successes
from
them being known. Metabolic control analysis leads one to believe that
rate-limiting enzymes as classically conceived do not exist and that
therefore one cannot expect any successes in the future from an approach
that is
fundamentally misconceived. If it is accepted (i) that regulatory mechanisms
evolved to serve the needs of the organisms that possess them, and (ii) that
their major effect in practice is to transfer flux control away from the
regulated enzyme, then it follows that they can be expected to oppose,
probably with great efficiency, any attempt to force more material through a
pathway.
This not only explains why the naive approach is unlikely to work; it also
suggests two strategies that may work better: either to select mutants in
which the feedback loops are suppressed, or to subvert the feedback loops to
biotechnological ends by artificially stimulating demand, e.g. by
engineering a leak of the desired product into the medium.


**************************
[5.2] Why isn't Phosphofructokinase (PFK) rate-limiting?

What? You mean it isn't? Refer to any undergrad text book and you can almost
guarantee that PFK will be referred to as *the* rate-limiting step. However
ample experimental evidence now shows us that PFK is anything but
rate-limiting.

Waiting for someone to write a short summary to fill in the details.


**************************
[5.3] Supply and Demand Theory of Metabolic Systems

Waiting for someone to write a short summary


**************************
[5.4] TurboCharging

Interesting property of glycolysis.

Waiting for someone to write a short summary


**************************
[5.5] How does channelling affect the summation relationships?


The term channelling refers to mechanisms in which the product of one enzyme
is transferred directly to an enzyme that uses it as substrate without
necessarily passing through the free solution. This implies the existence of
a complex
between the two (or more) enzymes involved, a static complex if it has a
long life time and exists independently of whether the reaction is
proceeding, or
a dynamic complex if it is formed transiently during the catalysis. In
either
case increasing the concentration of one component enzyme of the complex
affects the concentrations both of the free component and those of any
complexes that it forms with other enzymes. As these various different
species may have different kinetic constants for the reactions in which they
are
involved the rate of the reaction catalysed by the enzyme whose total
concentration is varied will not be proportional to that concentration.

As long as the summation relationships are expressed in terms of control
coefficients that refer to the independent catalysts, in accordance with
modern practice, they are not affected by channelling. As it is no longer
true that
the individual rates are proportional to the concentrations of the
individual enzymes, however, the summation relationships no longer apply if
the control
coefficients refer to enzyme concentrations rather than catalytic
activities. With static complexes the deviations may be large, but with
dynamic
complexes they still usually apply approximately.



**************************
[5.6] What is a controllability coefficient?

Controllability coefficient was the term used originally for the elasticity
to a parameter (rather than to an intermediate metabolite). Not all authors
find it useful to make this distinction. Those who do sometimes use the term
"kappa elasticity" or "-elasticity" for the old controllability coefficient.

What is the top-down approach to metabolic control analysis?

In the top-down approach developed by Brown, Hafner and Brand one seeks to
allow the analysis of complex metabolic systems by grouping reactions into
blocks, which are then treated as if they were single enzymes.


**************************
[5.7] Is it true that metabolic control analysis assumes that enzymes are
regulated
solely by changing their concentrations (or V values)?

No! This is a serious misconception that has bedevilled understanding of
metabolic control analysis for years. It arose from the once-common practice
of defining control coefficients in terms of changes of enzyme
concentration.
However, the modern practice is to regard "control coefficients" defined in
this way as response coefficients (for response to changes in enzyme
concentration) that may happen to be numerically equal to control
coefficients only because the relevant elasticities are equal to 1. In any
case, the
partitioned response property means that the magnitude of the response of a
system to any effector is determined by the elasticity of the enzyme acted
on by the effector with respect to that effector multiplied by the control
coefficient for that enzyme.


**************************
[5.8] How does metabolic control analysis explain the fact that most
mutations in diploid organisms are recessive?

In a diploid organism the usual possibilities for the degree of expression
of an enzyme are 100% (normal homozygote), 50% (heterozygote) and 0%
(abnormal
homozygote) of the activity in the normal homozygote. However, the flux
control
coefficients of most enzymes are close to zero, and although they increase
if the enzyme
activity is decreased they rarely increase to significant levels if the
activity
decrease is 50% or less. Thus heterozygotes, with only 50% activity of the
affected
enzyme, can maintain essentially the same metabolic fluxes as individuals
with 100%
activity. However, if an enzyme activity falls to zero its flux control
coefficient for the flux through its own reaction becomes 1, as the capacity
to supply
flux through the pathway in question vanishes. Thus although heterozygotes
typically display little or no phenotypic difference from normal
homozygotes, abnormal
homozygotes display the phenotype characteristic of the complete loss of a
metabolic pathway.


**************************
[5.9] How does metabolic control analysis aid in understanding mitochondrial
myopathies and other metabolic diseases?

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.


**************************
[5.10] Competitive and UnCompetitive inhibition

Waiting for someone to write a short summary


[6] Real-World Metabolic Models
------------------------------------------------------------------------

Yes, there are some, but currently waiting for someone to write a short
summary


[7] Computational Resources
------------------------------------------------------------------------

[7.1] What programs are available for metabolic modelling?

There are currently two software packages that are the preferred tools for
modelling metabolic systems, these are Gepasi and Scamp (now being updated
to Scamp II - Jarnac). Both systems run under Windows 95/98/NT, Gepasi and
Scamp II are currently available free of charge.

MetaModel* runs on MS-DOS with very basic hardware requirements (i.e. it
will run on any PC-type computer from the past ten years or so). Brief
descriptions of these and other programs may be found elsewhere*. I believe
there is one
metabolic simulation package for the Macintosh, I think it's called KinCyte
but I can't find a web site for it.

More details of other simulation packages to follow. Contributions here are
very welcome especially from the authors of other software packages!


**************************
[7.2] Where can I find information on computational algorithms for metabolic
analysis?

Information on computational algorithms used in metabolic analysis is not
readily available on the net. There is only one site which currently has any
information on algorithms (and not too much either) used in metabolic
analysis and that is the site at:

http://fssc.demon.co.uk under the biotech page


**************************
[7.3] What advantages does modelling have over algebraic analysis?

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.


[8] People and References
------------------------------------------------------------------------


[8.1] Where can I find more detailed information in the printed literature?

The two classic papers that introduced metabolic control analysis are those
of Kacser and Burns (1973) and Heinrich and Rapoport (1974). The former has
recently been reissued in a revised form (Kacser, Burns and Fell, 1995) that
is probably more appropriate for the modern reader, both because it is more
easily accessible and because it is expressed in the terminology currently
in use.
Two recent monographs mainly concerned with metabolic control analysis are
those
of Fell (1996) and Heinrich and Schuster (1996), of which the former is
fairly
elementary and the latter fairly advanced. (I have reviewed* both of these.)
Chapter 10 of the book on enzyme kinetics by Cornish-Bowden (1995a) is
concerned with metabolic control analysis, and is now available as
hypertext*.

A multiauthor book edited by Cornish-Bowden and Cárdenas (1990) contains an
almost complete picture of metabolic control analysis as it was in 1989 (as
well as some chapters on biochemical systems theory and a brief account of
flux-oriented theory).

The issue of the Journal of Theoretical Biology for 7th October 1996 is a
special issue in memory of Henrik Kacser, and contains many contributions
concerned with current applications of metabolic control analysis.
Abstracts* of all of the contributions are available on the web.

Two recent reviews of metabolic control analysis are those of Fell (1992)
and Cornish-Bowden (1995b).

A collection of references to reviews on channelling and related topics is
available on the web.


**************************
[8.2] How do I contact people working on metabolic control analysis?

There is a list on this web-site http://ir2lcb.cnrs-mrs.fr/~athel of names,
addresses, telephone and fax numbers, e-mail addresses and URLs of
web-sites, for people who are or have been active in the field.


**************************
[8.3] Where can I find information about meetings related to metabolic
control analysis?

There is a web page (http://ir2lcb.cnrs-mrs.fr/~athel) with general
information about forthcoming meetings, mainly ones with some relationship
with
metabolic control analysis. Suggestions for additions to this page are
always welcome.
The BTK (BioThermoKinetics group) maintains a regular programme of meetings
(at two-year intervals) with a substantial content of metabolic control
analysis. The 9th BTK meeting will be at Stellenbosch (South Africa) in
April 2000.


**************************
[8.4] References

Only sources specifically referred to are listed here. A longer list is
given with the web version of Chapter 10 of Fundamentals of Enzyme Kinetics,
and
another one forms part of the MCA Web, and other references may be found in
the articles listed.

G. C. Brown, R. Hafner and M. D. Brand (1990) A 'top-down' approach to the
determination of control coefficients in metabolic control theory. Eur. J.
Biochem. 188, 321-325 [@]
A. Cornish-Bowden (1995a) Fundamentals of Enzyme Kinetics (2nd edn.), pp.
239-270, Portland Press, London [@]
A. Cornish-Bowden (1995b) Metabolic control analysis in theory and practice.
Adv. Mol. Cell. Biol. 11, 21-64 [@]
A. Cornish-Bowden and M. L. Cárdenas, eds. (1990) Control of Metabolic
Processes, Plenum Press, New York [@]
B. Crabtree and E. A. Newsholme (1987) The derivation and interpretation of
control coefficients. Biochem. J. 247, 113-120 [@]
D. A. Fell (1992) Metabolic control analysis: a survey of its theoretical
and experimental development. Biochem. J. 286, 313-330 [@]
D. A. Fell (1996) Understanding the Control of Metabolism, Portand Press,
London [@]
R. Heinrich and T. A. Rapoport (1974) A linear steady-state treatment of
enzymatic chains. Critique of the crossover theorem and a general procedure
to identify interaction sites with an effector. Eur. J. Biochem. 42, 89-95
[@]
R. Heinrich and S. Schuster (1996) The Regulation of Cellular Systems,
Chapman and Hall, New York [@]
H. Kacser and J. A. Burns (1973) The control of flux. Symp. Soc. Exp. Biol.
27, 65-104 [@]
H. Kacser, J. A. Burns and D. A. Fell (1995) The control of flux. Biochem.
Soc. Trans. 23, 341-391 [@]
M. A. Savageau (1976) Biochemical Systems Analysis: a Study of Function and
Design in Molecular Biology, Addison-Wesley, Reading, Massachusetts. [@]


**************************
[8.5] Are there any books devoted to metabolic control analysis?

There are two recent books that deal extensively with metabolic control
analysis. One is elementary: Understanding the Control of Metabolism, by
David Fell, Portland Press, London, 1997.

The other is much more advanced: The Regulation of Cellular Systems, by
Reinhart Heinrich and Stefan Schuster, Chapman and Hall, New York, 1996.


**************************
[8.6] Why is the question that interests me not listed?

There are three possible reasons:

No one has asked before.

The question is not really relevant to metabolic control analysis, or is too
specific (e.g. questions like "which enzyme has the highest flux control
coefficient in glycolysis in well-fed rats?" are not sufficiently general
for this page: they would be better addressed to the BTK-MCA Newsgroup
Archive).

I don't know the answer.

If your question belongs in category 1, or if it belongs in category 3 and
you have an answer to suggest, please send me a message, in which you:

Specify the question you would like included, and (if you like)

Suggest an answer.


**************************
[8.7] Where can I find more detailed information on the web?

Some possibilities are as follows:

Athel Cornish-Bowden's Web FAQ at
http://ir2lcb.cnrs-mrs.fr/~athel/mcafaq.htm

Pedro Mendes' MCA Web <http://gepasi.dbs.aber.ac.uk/metab/mca_hime_htm>

The web version of Chapter 10 of Fundamentals of Enzyme Kinetics,
<http://ir2lcb.cnrs-mrs.fr/~athel/mcai.htm>

Douglas Kell's Canon of reviews on metabolic organization, channelling and
control. <http://gepasi.dbs.aber.ac.uk/metab/mca_home.htm>

Herbert Sauro's Biotechnology site at
http://members.tripod.co.uk/sauro/biotech.htm



[9] Acknowledgments
------------------------------------------------------------------------


Many thanks to Athel Cornish-Bowden for permitting me to redistribute and
modify his Web-site FAQ for the bionet.metabolic-reg newsgroup.

Any errors in this document are the sole responsibility of the maintainer.












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