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Re: WSN: hidrophobic/Van der Walls interactions energy... (fwd)

Sender: bruce_bush@merck.com (Bruce Bush)
Subject: Re: WSN: hidrophobic/Van der Walls interactions energy...

There have been many arguments in the field of protein
folding over whether "polar" or "nonpolar" or "hydrophobic"
forces cause the folding.  Arguments are wasteful when conclusions come 
from *different* definitions.  Even worse, many analyses are made 
without *any* clear definition of the terms.

The breakdown of energy of folding depends completely on how you
imagine the order of events.  I believe therefore that such a breakdown
of energy into "contributions" is meaningless.

What *is* meaningful is to compare the energies of two similar
processes for two different systems.  For example, two versions (mutants)
of a protein differ at one residue (beta6) which may be nonpolar (Val)
or polar (Glu).  What are the free energies of folding (or aggregation) for the
two different proteins?  If both of the mutants actually fold (or aggregate)
in nearly the same way -- as verified by crystallography, for example --
we can ask about the energy contribution of this mutation to the energy
of folding (or aggregation).  But we CANNOT ask about the total energy
contribution of ALL the polar groups or all the nonpolar groups to the
energy of folding, because if we changed ALL these groups then the
protein wouldn't fold!

At the end I write in more detail about the questions that one can
and cannot ask about the processes of folding.  I hope that these
imaginary experiments are useful to you in deciding what answer 
you need, and what question to ask.

Bruce_Bush@merck.com

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When a protein folds in water (or two solutes come together, or one solute 
changes shape over a high energy barrier, so that the water has a time
to "relax" before another change of shape) there is a free-energy change of
the ENTIRE system (solute molecules plus solvent). There is no single way to
split this total energy among nonpolar groups, the polar groups, and solvent.

It is possible to define and talk about the forces on various solute
groups during folding.  The force on an atom or group is the gradient
of the free energy, that is, the change of the *total* free energy
as the group moves slightly along one of 3 directions.

The forces on the nonpolar groups depend on the polar groups, and
the forces on the polar groups depend on the nonpolar groups.
I do not know any one good way to split such forces into "hydrophobic" and
"polar" contributions.

One sensible attempt to define  "nonpolar" and "polar" contributions
to the free energy of a process is this.  Imagine first that the solute 
groups are not charged at all, or else that they have only certain
polar groups.  For example, one can imagine watching a protein fold
but pretending that all the atoms are carbon (a greasy hydrocarbon)
or that the backbone is a peptide chain but all the sidechains are carbon
(a greasy peptide).  If either "greasy chain" were to fold up in water
into the same shape as the real protein, the energy for this folding 
would probably be very negative (favorable).
Then, as a second step, imagine "bringing charges" or dipole moments
from far-away water into the greasy stuff of the folded protein.  This
second step is very unfavorable.  This argument leads to the conclusion
that the "hydrophobic forces" cause the folding.

But there are two weaknesses to this argument.  First, a greasy carbon
chain would not fold into the same shape as the real protein.  In fact,
the hydrogen bonding peptides at least select which folded shapes are
possible.  It's not fair to "give the hydrophobic interactions credit"
for a process that would not happen at all if there were only
hydrophobic interactions.  

Secondly, the folding process can be imagined as happening in many other
orders.  Each order of events leads to a different breakdown of energy
among the different interactions.  For example:
  step 1: fold up the protein in "air", not in water, but assume that
it folds into the correct protein shape.  The energy for this is negative
and a lot of the negative energy (favorable) belongs to polar (hydrogen
bonding) interactions.  Some of the favorable interaction also belongs
to packing (nonpolar) interactions.  This can be called "nonpolar" but it
cannot be called "hydrophobic" (yet) because there's no 'hydro' (water).
  step 2: push the folded protein into water but let the water flow through
the greasy atoms to come close to the polar groups.  This leads to more
favorable energy.  We can say that this energy also is "polar".
  step 3: "turn on" the interactions between the greasy groups and the
water.  This pushes the water away from the polar groups, and is very
unfavorable.  We can blame the nonpolar groups for this unfavorable process.
This order of events leads to the conclusion that the polar interactions
are favorable to folding but the nonpolar groups lead to unfavorable energies.  

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