Has anyone every heard of Schrondinger's equation

Kresten kresten at my-deja.com
Wed Jan 31 11:26:48 EST 2001



> >
> >I think the work by Agard on alpha-lytic protease suggests something
> >like this.
>
> Isn't that the protein whose folding is catalysed by a part of itself,
> the Pro-region? If this is true, then that does not argue against my
> statement. I think that the fold, that the protein adopts, is the
> global minimum of the molecule _with_ its Pro-region. After the
> Pro-region is cleaved, the global minimum is elswhere in the fold
> space, but it is kinetically inaccessible. Thus, the native protein
> does not adopt its global minimum, but it *folds*to* the global
> minimum. From the point of view of someone who wants to do something
> with this protein, you may say that this makes no difference. But from
> the point of view of someone reasoning about the principles of protein
> folding, it does.

I completely agree with all of the above.

What then about plasminogen activator inhibitor, PAI-1. This protein,
AFAIR, has an active (as an inhibitor) state, which is in higher energy
than an inactive latent state. In this case, I think, the protein is
guided to a local minimum, but slowly decays to a nonactive state in
lower energy (again, if I remember correctly!).

My point is that we in many (most) cases will never know where the
energy minimum is (like finding *the* global minimum in an optimization
rutine) and therefore it's difficult to state that proteins fold to the
global minimum. However, we know that they fold to the lowest energy
state that is kinetically accessible.

>
> >Then there's the whole prion/amyloid discussion which is far
> >from being solved.
>
> No, IMHO this is a different issue. The statement, that the native
> fold of a protein is its global minimum, is of course only valid as
> long as it is soluble. The fold that an individual molecule adopts in
> amyloid or other aggregates is surely energetically disfavored
> compared with its native fold, but the fibril as a solid, the "phase
> amyloid", is more stable than the soluble folded form. Again, one
> might say that here the folded form isn't the most stable one. But
> this is just another opportunity to put the statement more precisely:
> The native folded form is the global minimum under certain conditions,
> the "native conditions". (not the most precise term, I admit...)

My point was, do we know whether amyloid fibrils are in a lower energy
state than the native fold? For some (all?) proteins we can make them
form fibrils by destabilizing them, and they will not return to the
native state when we return to native conditions (in most cases anyway,
again as you say, what are the native conditions). So, when fibrils are
formed under some strange conditions (low pH, high/medium temperature,
TFE, medium conc. of urea etc) and subsequently returned to native
conditions, are they stable (thermodynamically) or meta-stable
(unstable thermodynamically, but kinetically stable). I know of no
experiments that have answered this question, but then again I haven't
looked very much either.

I do not understand your distinction between the stability of the
individual molecules in the fibrils and that of the fibril-state. As
far as I see it, the fibrils are stable among other things because the
molecules interact, but I think it is unreasonable to say that this is
seperable from the stability of the "fold". I agree, of course, that if
one takes a single molecule of a protein with a fold like in the native
state, but present as a soluble monomer, this protein is in higher
energy than the soluble, native protein. This was not my point. My
point was, under native conditions, could it be that the total energy
of M protein molecules in the soluble state is higher than the energy
of the same M molecules in an amyloid, but that the amyloid, under
these conditions, in kinetically inaccesible? Or more simply put, under
native conditions, what is the sign of delta_rG for the reaction:

M native-monomers = (amyloid-fold)_M in amyloid state

This is a perfectly acceptable chemical equation, and should therefore
have a well-defined (although unknown and very hard/impossible to
determine) delta_rG.

>
> The point is:
> Nobody has ever argued that proteins wouldn't coagulate, unfold or
> aggregate under certain conditions; but it *has* been argued that the
> folding process is kinetically controlled and ends up in the
> kinetically best accessible minimum, no matter wether this is the
> global one or not. If this where true, it wouldn't make any sense to
> try to compute the native fold in a systematic way, be it calculation
> of the energy of every conformation with semiempirical methods, be it
> the Schrödinger Equation. The only theoretical way to predict a fold
> would be to mimic the *folding*process* in the computer - perhaps even
> the involvement of the ribosome, chaperones etc. And structure
> prediction by homology, without knowing a whole lot about the
> principles of this kinetic control, would also be much less
> succesfull.

Well, again the folding pathway of homologous proteins may be very
similar. For example the papers by Kragelund et al on ACBP suggest
this. So (again playing the devils advocate) even if protein folding
was completely under kinetic control (which I of course agree with you
that it isn't) homology modelling might be very succesfull. Conserved
residues are *not* only conserved due to function, but also due to
folding.

Bye,
Kresten


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