Steve Bougerolle steveb at
Fri Jun 21 05:58:14 PDT 2002

On Fri, 2002-06-21 at 16:52, Björn Lindberg wrote:

> One cell contains thousands of different substances (enzymes, proteins,
> etc) that interact with each other. Many of them are not yet known, and
> to model their interactions give rise to massive nonlinear equation
> systems. Even if we managed to correctly model this, it would still be a
> very coarse model. So I wonder why you think that an atom is more
> difficult to understand? I am not really a physicist, which is why I'm
> asking.

The basic problem is to predict the position (or probability
distribution along r, theta and phi) of particles inside an atom.  For
practically all cases this is known to be impossible to do precisely,
because we can't solve the equations of motion for a system with more
than two bodies.  So, a hydrogen atom is the only one where we can do
anything like an exact explanation (and even that breaks down if you
look at it truly closely).  That, by the way, is why all atomic
structure models begin with studying hydrogen atoms.

So, however complex a cell is to study, it can't possibly be more
difficult than an atom because we KNOW we can't solve the equations of
motion for an atom at all.

Nevertheless, we do study atoms and nuclei despite that hurdle, by
simplifying.  For atoms we treat nuclei as single particles and come up
with various sorts of mathematical models to predict the orbital
perturbation of the electrons because of forces from other electrons
(and even from other atoms).

The problem is actually much more difficult for nuclei because most of
the time there aren't any really convenient simplifications.  For really
large nuclei you can model any one particle as being in a potential
sphere created by all the others.  Nevertheless, we do try various
simplifications and models, and do get numerical results out of them.

A cell has a lot of different structures, and more things to consider
than in an atom.  On the other hand, it also looks to me like you have a
very large amount of scope to simplify any one particular problem you
might want to study related to a cell.  We don't have that advantage in
atomic or nuclear physics;  all there is to do is predict the motion and
we run starkly up against the theoretical difficulties.

In any case, if all you can come up with is a coarse model this is still
a whole lot better than arguing that critical evolution steps "could
happen" because there is no logical proof otherwise.  I have found a few
simulations related to this sort of thing, so it appears at least some
people in biology agree with me on this...

Steve Bougerolle
Creek & Cowley Consulting

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