alpha-helix signals -> protein folding

Rob Miller rmiller at bsm.biochemistry.ucl.ac.uk
Sun Jul 17 05:53:33 EST 1994

N.T. Gladd said :

> Subject: Re: QUESTIONS: alpha-helix "signals" in proteins
> From: ntgladd at langmuir.EECS.Berkeley.EDU (Tom Gladd)
> Date: 12 Jul 1994 03:37:14 GMT
> Organization: Plasma Theory and Simulation Group
> I have followed this discussion with interest.   I hope I can impose on 
> the group to make an argument from a physicist's perspective.  
> Given some initial unfolded protein state, the various components will 
> feel unbalanced electrical forces and dynamically respond, tracing out 
> some path in the multidimensional phase space whose coordinates 
> characterize the protein. 
> ...
> When the protein finds a point in phase space about which 
> the variation of all  its variables become periodic it can be said to be 
> metastable.  Not only has the protein found a local energy minimum, but 
> each of its components is rocking or rotating back and forth  in its own 
> potential well.  I say metastable because such a system would 
> constitute a highly complex nonlinear oscillator in which resonances 
> could develop that would knock one or more components out of their 
> local well and thus destabilize the system.
> For most proteins, then, the 
> native state corresponds to a local energy minimum with such a large 
> basin of attraction that almost any initial conditions will follow a path to 
> that minimum.
> I'm not sure what this picture means for a predictive theory of folding  -- 
> unless, perhaps, one could mathematically demonstrate that certain 
> sequences of amino acids are likely to lead to large phase space 
> attraction basins for certain secondary structures.
> N. T. Gladd 
> Berkeley Research Associates
> ntgladd at langmuir.eecs.berkeley.edu

 I was saddened that this thread did not seem to get picked up on; perhaps the
respondents did not say `Distribution: world'.  In any event, this model is
basically identical to one I have developed through seven years of (U.S.) grad
school in biochem and computer science, specifically studying protein 
structure and folding.  My initial ideas are due to a draft paper by 
Edward Fredkin on Digital Information Mechanics (later shortened to Digital
Mechanics for publication -- certainly a better acronym :-), and I can 
add some thoughts about `what this picture means for a predictive theory 
of folding' :

(1) Let us say that an amino acid sequence specifies a `program' for the 
folding of the protein.  This is consistent with the described model 
when one recognizes that it is possible to build a network of cellular 
automata (CA) capable of `computation' in the sense that it can perform the 
basic operations recognized by Turing.  In other words, for both the CA
network and the protein, the system processes it's input (the environment) 
and eventually outputs a `final' structure.  The Halting Problem states that,
given a description of a machine and a program with input to run on it, it 
is not possible to determine a priori even the simplest characteristic of 
the program's results, such as whether the program + input will end up in
an infinite loop.  The only way to find out for certain is to actually 
run (or simulate) the program and see -- and even then you don't know 
if it was about to halt before you killed it (in the real world, you use a 
debugger or slap a logic analyzer on that puppy and figure it out, but 
that's another story).  The `metastable state' described above for a
protein is actually a particular infinite loop for the computation 
(machine + program + input) defined by the amino acid sequence and it's
environment.  Computer science _suggests_, therefore, that you can't 
be certain of the final folded structure without at least some simulation 
of _a_potential_ kinetic pathway.  (See Robert Leopold, Proceedings of 
Hawaii International Conference on System Sciences 26 (Jan. 93) for a 
paper on the simulation of multiple folding pathways leading to one or 
a few final structures.)  For myself, these ideas have led to the 
continuing development of predictive models based on the simulation of 
`amino acid computation' in the (ludicrous ?) hope that (a) the computation
is relatively simple, given the _right_representation_ (see F.P. Brooks
III), and (b) the `basins of attraction' for folding are large enough
to really make this work out in a reasonable amount of time.

(2) Does this mean that the `protein threading' idea, where one evaluates
the folding of an (unknown structure) amino acid sequence as a given
structural motif shouldn't work ?  Certainly it does seem to work in 
many cases (D.T. Jones, et al), and I am employed to be extending that
work.  The key is that there appear to be a finite number of folds 
(metastable structure results) so that, like part of the proof of 
NP-completeness, we can `nondeterministically _guess_' an answer and see
if it looks correct.  Whether the library of folds is sufficient to always
be able to guess the right final structure remains to be seen, and the 
potential energy / fitness functions used to evaluate sequence-structure
pairs are not yet infallible.  The question of kinetic vs. thermodynamic
control here becomes whether we'll be able to find a sequence that gives a 
good score for one fold, but for which the structural `basin of attraction'
leads to a different fold; I doubt we'll find such a beast soon.

Comments and criticisms *please*, posted or e-mailed direct; also
interested in any literature references along these lines.

Peace and a long and enjoyable life to you; I have not wished to 
offend or step on any toes.


Rob Miller, Ph.D.  `On an Errand out of the wilderness'

Biomolecular Structure and Modelling Unit (BSM),
Department of Biochemistry and Molecular Biology,
University College / Gower Street / London WC1E 6BT.
United Kingdom.

Tel: 44 71387 7050 x2303 
Fax: 44 71380 7193
home: 44 442 65092
Internet: rmiller at bsm.bioc.ucl.ac.uk

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