Molecular Mythology 


Behavior of proteins is detemined by structure and thermondynamics,
not by structure alone.




Scientists, like everyone else, need myths to live by. Without the simplicity of myths, the 
complexity can discourage analysis. So molecular dynamics, to grow, needed
its myths. I write because some of the myths stand in the way of further growth,
at least in my view.

The reality is that most proteins work on a macroscopic scale, 
involving thermodynamic variables like concentration, average electrical
and electrochemical potential, flux and current flow, on the time scales
of milliseconds and longer.

The myth is that calculations in atomic detail can in themselves deal with
these macroscopic variables.

Consider the messenger molecules that control
so many proteins and work in concentrations of micro to picomolar. The 
concentration of these molecules must be controlled in experiments and
so simulations must include enough molecules to estimate concentration
without too much random error, let's say 10%. In simple cases, that means
100 messenger molecules. Let's say the messenger binding constant is 0.1 
micromolar. An atomic simulation must then include a staggering number of
water molecules, 100 times 55 moles of water for each 0.1 micromole
of messenger, making 100 x 55 x 10^8 molecules of water, about 5 x 10^11,
500 billion. 

It seems obvious that a calculation involving 500 billion water molecules 
is impractical.

Consider ionic solutions. A large range of biological function depends on
gradients of electrochemical potential, gradients of concentration and
average electrical potential. All channels depend sensitively on these
gradients, which are the energy source for their function. Indeed, errors
of only 10 millivolts in the electrochemical potential are not acceptable 
in the laboratory because they lead to misidenification of the type of 
the selectivity and thus type of channel.

Salt solutions in biology are around 0.3 molar and in these concentrations
the concentration of ions does not provide an accurate representation of their
chemical potential. Salt solutions are not ideal. Their free energy per mole
(which is the appropriate thermodynamic generalization of concentration)
is not that of an ideal gas of (uncharged) particles. It rather contains a 
large excess term which must be included in laboratory calculations if
channels are to be correctly identified by their "equilibrium" potential
(Hodgkin and Huxley's name for the gradient of chemical potential).

This excess term depends on the concentration of all ions in the system,
 not just the ion in question, and so dealing with it is complex, subtle, and
 in general a (minor) nightmare for the biologist interested in channels.
 
 The excess term was a nightmare for the founders of molecular dynamics
 for that reason too. If they had tried to calibrate their force fields in realistic
 salt concentrations, they would have needed a different force field for eah
  type and concentration of salt surrounding the protein, and their caculations
  would have been impossible.
  
  So molecular dynamics used a myth to develop their force fields. The myth
  was that proteins could function in the solutions in which force fields were
  calibrated, namely in infinitely dilute salt solutions, commonly called distilled
  water.
  
  The myth was necessary I repeat and no criticism should be made of those
  who created it. Without the myth, molecular dynamics as we know it could
  not be done. No one could use pairwise force fields (that compute the force
  between two atoms ignoring other atoms) if the force field had to include 
  the type and concentration of every ionic species in a normal Ringer solution.
  
  The myth was not believed by its founders in general, and I know it was not
  in particular from private conversations with a few of them, but like most
  myths, it is believed ever more strongly as it is passed down, generation 
  to genration.
  
  The myth needs now to be seen for what it is, a serious impediment to
  understanding how proteins work, because molecular dynamics has grown
  so successful. It now deals with macroscopic size systems, whole proteins
  and their functions. But molecular dynamics cannot deal with the function
  of these systems unless it can deal with the ions that surround and energize
  most of them.
  
   The concentrations (i.e., number density to be precise) of ions in the interesting
   part of proteins, near their active sites, or in their channels, are very very high,
   typically 10 molar, often much more (pure water is 55 molar). These ions do 
   not behave anything like ideal gases of uncharged particles. Their free energy
   per mole is largely nonideal, determined by the size of the ions, the size of
   the confining space, and the electric field. None of these variables have any
   effect on the free energy per mole of an ideal solution.
   
   So the challenge is to incorporate this reality into the myths of molecular
   dynamics so calculations can be done on atomic detailed structures, using
   the thermodynamic variables that drive the function of these structures,
   and to do that on the biological time scale.
 channels and near active sites