In response to Guy Brown's question, Herbert wrote:
>Your only option is numerical simulation of specific examples and see
>whether you can work out any generalisations.
In this thread, Herbert wrote:
>But one reason for looking at simple pathways is/was that before the
>advent of BST or MCA people knew hardly anything about how pathways
>worked and what they did think they knew has turned out to be either to
>simplistic or wrong.
And simple simulations can be equally educational.
>And don't stop at steady state, once you've done steady state, move on to
>understanding temproral and spatial phenomena. Simple pathways are not the
>end of the story, just the beginning.
And neither are simple simulations. To me, general theory is most useful
when it is applicable to a wide range of cases. So if one wishes to
consider temporal phenomena, for example, one should first experiment,
either in the real lab or with simulations, on a wide variety of temporal
"problems" to begin elucidating the general truths which span them, then
go to formal theoretical development.
>I see your "specific" results (engineering?) argument, although I'm not
>an engineer I think their agenda is different, *no less important* of
>course, but I think different questions and aims are on the table and is
>probably why we're having this argument.
Well understanding the metabolic causes for a disease is not engineering,
but if one is considering a specific disease then one is looking for
specific results. That's a case where I think it's faster to just build
a simulation model of the pathway and start tinkering with it, than to
start by developing a general theory of which the disease is a specific
case.
>By the way Paul, I (hadn't) know(n) you had worked for Feinberg, I have great
>respect for his work and related work in the chemical engineering field.
[corrections based on a personal e-mail.]
Thanks. I consider myself most fortunate to have had the opportunity.
As I mentioned, I think my work with him to be my best to date, and his
guidance had much to do with that.
[next message from HS]
>...but here's another, with just MCA and no numerical simulation in
>sight, it is easy to show how, why and when cascade structures display
>extreme sensitivity to inputs.
This is where I did "retract" my original statements in a previous post.
This is what I would call a general result. But what gave the inspiration
to ask this question in the first place?
[next message from HS]
>I thought all I needed to do in order to understand metabolism
>was collect all the enzyme data I could lay my hands on, shove it into
>our local ICL 2900 and I'd be able to underatand all about it. As the
>months went by I became more and more disappointed with the results.
When I started working with Jay Bailey, I read the papers from Shuler's
group and by Peretti (sp?) and Bailey which attempted to build whole-cell
models. Jay told me that despite their efforts, the models still failed,
so I realized that this was probably a dead-end without having to spend
so much time. There are definite limits to simulation modeling. Often,
the simpler modelers are the most informative. Still, interpreting
their results is a bit of an art, and this is where engineers may have a
leg up, having been forced to interpret data from entire chemical plants.
This is an example of the "art" of interpreting the output from simulations
(it's in the paper I just sent you, Herbert):
I'm not sure if I mentioned this in a private post or a group post before,
but my Master's advisor had a PhD student who was working on experimental
design to identify parameters. In this case, one should pick conditions
under which the outcome of the experiment is most sensitive to the
parameter of interest. (The idea is that one has a preliminary model,
with initial parameter estimates, with which to perform the design
calculations.) But if you can measure 4 different outputs, and the
sensitivity of #1 is maximal at one time, while that of #2 is at another
time, etc., how does one interpret all the individual sensitivities? His
clever answer was to device something called the "Information Index" (II)
which, in a nutshell, is the weighted sum of squares of the measured
outputs (weighted based on signal/noise for each). Thus, one could look
at a single output from the computer, the II, which was easy to interpret,
and pick the time window and control conditions for which it is maximized.
>The lesson I learned was if you want a computer to pretend to be
>a cell, then simulate, if you want to understand the cell, then do
>theory (or to put it another way: deductive reasoning on the basic
>knowledge biochemists have collected over the years).
But in the previous post you wrote:
>Anyway one of the crazy ideas that one of these
>biochemists had was that there couldn't be any product inhibition in
>metabolism (the killer of rate-limiting steps) because as soon as a
>product is produced by a step it is 'swept' away by the next enzyme
>before it has time to inhibit.
Which goes to show that "the basic 'knowledge' biochemists have collected
over the years" is not always trustworthy.
I'm close to submitting a paper on the regulation of gonadotropin synthesis
and release during the menstrual cycle. I was told by biologists when I
started that the underlying mechanisms were entirely too complex to model,
that even those who have studied the field for years don't completely
understand it, so I shouldn't even start. If I simply took the stated
explanations in the the endocrine literature as given; e.g., "there is
negative feedback at one point in the cycle, and later this switches to
positive feedback," I'd probably agree. But, brazen and stubborn as I am,
I went beyond that to look at the actual data on which these conclusions
where based. Using my understanding of the behavior of dynamical systems,
obtained after many years of simulation, I saw that I could explain much of
the data using a relatively simple model with no "switching." Yes, I have
"lumped" hords of detail to a level that may give the biochemists and
biologists fits, but I have shown that much of the complexity in this
system at least can be explained by "simply" by treatinging synthesis and
release as distinct steps and presuming, for example, that estrogen has a
positive effect on synthesis, but inhibits release. I dare say that my
simple simulation model will shake things up considerably in endocrinology.
(I am rather proud of it. Hubris?)
As I have freely admitted, my original mistake was in forgetting that the
"Sammy" approach can never prove something like the summation theorem, and
these are indeed important results. It can, however, lead one to propose
the theorem in the first place.
But I will close by noting that in many cases, the "Mary" approach can be
viewed as, and shown to be identical to, analysis of the linearization of a
more "global" model. For any "Mary" analysis *of a particular pathway,*
I can build a simulation model for which the results of the analyis are a
special case. And I can do it without being stymied by all the detail around
the edges (I just make the same assumptions as are implicit in the "Mary"
analyis.) Moreover, I don't *need* to work out the general theoretical
principles to calculate any particular sensitivity coefficient for the model.
Later, I may ask if the problem is of sufficient general interest to warrent
theoretical elucidation ... If I have the time.
-Paul
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ON PROBLEM SOLVING
When the only tool you own is a hammer, every problem begins to resemble
a nail.-- Abraham Maslow
