Re: modelling metabolism

[Judith Rosen <***>]

Hi Jannie,

I was fascinated by your statement that all of metabolism can be modelled. Would you say 
this is true for all organisms or only for single celled organisms? I ask because I don't 
see how any set of models could ever completely encompass the metabolic system of a 
multicellular organism: the feedback relationships with the rest of the organism are too 
integral to be left out of the model and that means the organism itself must be part of 
the model. Even in a single celled organism, I have trouble accepting that the model of 
metabolism can actually be complete.

I wish I had my reference materials here, I must say! Without them, I cannot answer my 
own questions, which revolve around this: Is metabolism itself a complex system in an 
organism? At what point in modelling complex systems do the incomplete models begin to 
impact the results in a practical/serious way? Is there always a threshold whereby 
incomplete models (ie; models of complex systems) will be mostly accurate below the 
threshold and mostly inaccurate above it? Are there different categories of models such 
that one category may work better to model the behavior of a complex system than another 
category?

Most of us who are not scientists who use modelling have some experience with this issue: 
Weather forecasting. I know that meteorologists use several different models because they 
often say, "Some of the models tell us the storm will take this general track, but other 
models say it will do THIS, instead..." Does anyone on the list know whether one model is 
proving to be more accurate consistently? If one is more accurate, it would be worth 
talking to the people who developed that model and learning what their approach was-- how 
did it differ from the approach used by all the others? If none of the meteorological 
models are more accurate than any others, then perhaps the modelling approach itself is 
what needs to change in modelling complex systems.

Judith
PS: Jannie, I found your discussion of the work you are doing to be extremely 
interesting. Thanks for posting that! I personally look forward to the discussions that 
may help develop your ideas in whatever way you need.

-----Original Message-----
From: Jannie Hofmeyr <***>
Sent: Feb 27, 2004 12:36 AM
To: ***
Subject: Re: [ROSEN] Triple-J ; OnLine Cell Modelling (JWS)

James asked about the online cellular systems modelling efforts of the
Triple-J group, which are most visible through our website
http://jjj.biochem.sun.ac.za/.

The Triple-J Group for Molecular Cell Physiology consists of myself, Jacky
Snoep and Johann Rohwer, all members of the Biochemistry department of the
University of Stellenbosch (a university town situated in the heart of the
Cape winelands about 50 km from Cape Town in South Africa). As our name
indicates we are interested in understanding cellular processes from a
systems point of view: the physiology of cellular processes. We approach
this by using theory (especially metabolic control analysis), computer
modelling and experiment (mostly with single cell organisms such as
bacteria and yeast). From a bioinformatics point of view we are doing
computational systems biology.

What we are doing at present is purely within the Newtonian realm. We
construct models of metabolic pathways (networks of coupled enzyme
catalysed reactions) as systems of differential equations and solve them
numerically in order to study both the time-dependent and steady-state
behaviour of the system. We also use control analyis to understand the
control and regulation of such systems --- control analysis is a
sensitivity analysis: one perturbs a step in the system through, say,
altering the concentration of the enzyme that catalyses that step and
calculating how it affects, say, the steady-state material fluxes through
the system or the steady-state concentration of some chemical species
(metabolite). Our website is at present the only one where one can do
online modelling: one chooses a model to study, sets the parameters to the
required values and requests a calculation. This opens a Mathematica
kernel in the background which does the calculation and sends a graph of
the results to the webpage. Besides being a research tool, it has been
used extensively all over the world for teaching. Two journals (The
European Journal of Biochemistry, and Microbiology) use it as a review
tool. Authors that submit a paper that describes a model are invited to
allow us to construct and put the model on our website where reviewers can
access and assess the model. If the paper is published the model becomes
public. Just as an interesting aside: we have not encountered one model,
either submitted or coded from the literature that did not contain errors,
so purely as a validation process this is already useful.

>The standard "flow chart" of arrowed molecules leading to
>next molecular-forms doesn't tell the rules for getting from
>any one chemicalform to any others.  The historical approach
>has been to simply identify molecules present and then sort of
>jury-rig a taxonomy of patterned placements.

The typical metabolic map shows metabolites as names or structures and the
enzyme-catalysed reactions that interconvert them as arrows. If you open
any model on our website (e.g. the first one: Detailed glycolytic model in
Lactococcus lactis) you can see a representation of such a map. The
structure (or topology, if you like) of such a pathway is captured in what
we call a stoichiometric matrix, a table in which each row represents a
metabolite and each column a reaction. An entry c_ij in the matrix
represents the number of molecules of metabolite_i that participates in
reaction_j (>0 if it is a product, <0 if a substrate, =0 if it does not
participate in that reaction). All this to emphasise that the map is
simply a useful pictorial representation: mathematically the structure is
a matrix.

OK, while this at least tells us the routes through which material can
flow through the network, it says nothing about how much, how fast, etc.
For this one needs a local mathematical "rule" for each reaction that
describes the rate at which that reaction proceeds. These so-called rate
equations in our models can be viewed by clicking any of the red circles
that identify a reaction. Such a rate equation thus captures the kinetic
and thermodynamic properties of each reaction. So, James, there are the
rules you were looking for.

>Your general groups of researchers seem to be developing
>a strong interactional modality of analysis and I was
>wondering if you've chosen a dynamic criteria for
>the charting; or several dynamics, possibly, co-integrated
>and weighted.

The overall dynamical behaviour of such a pathway is then described by a
set of differential equations that contain both the pathway topology and
kinetics. In fact, the description is simple and elegant:

ds/dt = N.v

where s is the vector of all the variable metabolite concentrations, N is
the stoichiometric matrix, and v is the vector of rate equations.

All of this is pretty standard stuff, also described by Rosen, who was of
course perfectly happy with such models of parts of a living system. The
whole of the M part of an (M,R)-system can be captured in such a model
(and this is what we and many other groups in the world are attempting to
do). However, these models at present do not contain the R part, although
it is possible to do this partially by allowing the enzyme concentrations
(which are usually fixed) to become variables. The R part can of course be
modelled on its own, so can any other cell process. It is when you want to
stick them all together that the fun starts... or the depression begins...
and, of course, where Robert Rosen enters the picture.

James, I hope this answers your question. I would be very happy to expand
on anything.

It is of course because I want to stick everything together that I have
developed such a deep interest in Robert Rosen and his ideas. I also
believe the time is ripe to start building on his ideas instead of just
analysing and explaining them (not that this is unimportant). I am
presently on a year-long sabbatical in Europe where I at long last have
the freedom to consolidate my ideas and I would very much like to test
them on this list.

Till later
Jannie


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