From: SML108@psuvm.psu.edu
Newsgroups: sci.nanotech
Subject: Re: What computer simulation can't do yet.
Date: 15 Sep 92 21:05:47 GMT
Organization: Penn State University

In article <Sep.9.08.58.33.1992.13696@planchet.rutgers.edu>, ian@inf.ethz.ch
(Ian) says:
>
>In article <Sep.8.15.47.27.1992.733@planchet.rutgers.edu> nickh@CS.CMU.EDU    k
>(Nic
>Haines) writes:
>
><Most deleted>
>
>>
>> Do we have model ribosomes in the quantum biochem simulators?
>>
>
>We don't even have any quantum biochemical simulators to put them in !
>
>You have overestimated the current state of the art with biochemical
>simulation.  We do sometimes do quantum mechanical simulations, they
>are always approximations to limited aspects of well-known systems (eg
>only a few atoms are completely modelled and a few 'broad approximations'
>such as known dipoles are filled in around them; this is typically going to
>produce something like the distribution of electrons between the available
>energy levels in the transition state of a reaction) <Please correct me, I've
>only ever watched other people do this.>.

We can do high level ab initio computations on small molecules, but
since they are of O(n4), they are limited.  There is some very exciting
work going on in Density Functional Theory and with pseudo-spectral
methods that might eventually take this down to O(n3) but no one
has made these methods work reliably yet.

>The far more common class of simulation performed is purely newtonian,
>however.
>Just a masses and forces implementation of the molecular system.  The average
>protein has around 10,000 particles which means that the CPU time required is
>far from trivial, on the order of seconds for each time increment and as each
>increment is typically a femtosecond you'll understand why the longest
>simulations ever performed have only modelled 100's of picoseconds.

Well, not too many people are simulating 10,000 particle systems either...
However, there are now some nansecond simulations of small proteins like
BPTI (see the work of Michael Levitt and Valerie Dagget(sp?)).
Unfortunately, and this might ignite an enormous techie flamewar, the
validity of ANY of our models capable of modeling proteins is questionable
at best.  Numerous groups have shown that the mathematical models used
to represent the energetic states of proteins clearly have serious
problems (ie. the work of Robert Bruccoleri and Jiri Novotny, Moult and
James, and my own work with genetic algorithms).  What we have all
been able to do is demonstrate that the natural state of a protein
is nowhere near the global minimum of the potential function used to
represent its state.  Why does this happen?  Well, some potential
functions first reduce bond stretching and bond angle bending to
a harmonic osciallator rather than a Morse potential.  This isn't all
that problematic, but this is just the beginning.  Bond rotation
terms are represented as truncated Fourier series with the phase
angle stuck at 0 or 180 degrees due to mathematical complications.
High level ab initio calculated torsional profiles are difficult to
reproduce exactly this way and it only gets worse from here...
  Non-bonded interactions which are the interactions between all atoms
that are separated from one another by >3 bonds are treated in a mostly
ad hoc method in order to keep them computationally feasible.  There are
two parts to a non-bond interaction.  The first is the van der Waals
interaction.  This is usually represented by a Lennard Jones repulsive/
attractive potential of the form:
                                             A     B
                                  E       = --- - ---
                                   nonbond   12    6
                                            r     r

where A and B are adjustable constants, and r is the distance between
the two non-bonded atoms.

This part is probably not all that bad, but electrostatic interactions
are handled by considering all atomic charges fixed.  They are also
derived on the assumption that the charges of the atoms in an amino acid
residue are the same whether surrounded by only an alanine on each
side (a terminally blocked peptide) or in a protein.  Numerous results
are beginning to show this is a bad assumption.  An electrostatic
interaction is modeled by a Coulomb potential of the form:


                                              q1 * q2
                             E             = ---------
                              electrostatic   Eps * r

Where q1 and q2 are the charges on the two non-bonded atoms, r is the
distance between them, and Eps is the dielectric constant of the medium
in which the atoms are placed.  It is computationally convenient to
consider Eps = r.  This has been used in many simulations,  Unfortunately,
there is absolutely no physical basis for this.

Enough about the potential functions...  Many groups are working on methods
to remedy these and many other shortcomings, but none of their tricks
are in mass use yet and even then they involve shortcuts, approximations,
and cutoffs which may or may not affect their validity.  We will not
know until they are fully explored...  Even ab initio calculations
incorporate approximations of their own which may or may not cripple
them in the simulation of biological scale systems when this becomes
possible...

What is really amazing is that with these horribly crude potential functions
we have already been able to design several drugs, reasonably rate
relative binding efficiencies of ligands to a protein, derive important
insights into the functions of many proteins and successfully suggest
modifications to improve their stability or kinetic efficiency.  I believe
things WILL get better, but it's going to take time.  I think a lot of
Drexler's timelines are overly optimistic, but I have to respect him
for having the guts to speculate so far...  One final note is that one
of the currently hot topics in protein design, the inverse protein
folding problem, was essentially invented by Drexler in 1982 while
at MIT...

Scott
>As a ribosome is around 100 times larger than a typical enzyme, the answer to
>your question is no, definitely not.
>
>Having said that, we do know a bit about it's mechanism, look in any recent,