Subject: Re: CCL:Rigid body dynamics

From: Konrad Hinsen <[email-masked]>
Date: Fri, 21 Nov 1997 18:58:40 +0100

> > 2. How does it compare with SHAKE type constraint methods:
> >    faster/slower or just different?
> 
> Just different would be a better description, as you constrain the bond
> angles and dihedrals as well (dependent of course, on the way you choose
> your rigid bodies). 
> Second, in the SHAKE approach, each atom still experiences the force due to
> it's interaction with the rest of the  system. In VRDB (as proposed by
> Head-Gordon) , a force/torque acting on a  rigid body is derived from the
> forces acting on it's constitutive atoms. 
> Third, Head-Gordon in her work enforces planarity of the peptide bond by
> turning it into a rigid body. Thus,  your dynamics will differ
> from a plain bond-length SHAKE simulation.

I have no practical experience with VRBD, but with other treatments
of rigid-body and constrained systems, which may be of interest.

First of all it is necessary to distinguish between the consequence of
applying certain constraints and the limitations/efficiency of particular
methods to do so. Obviously keeping a peptide group rigid is a stronger
constraint than fixing just the bond length, but it also comes with a
higher reduction of fast degrees of freedom, which is after all the
reason for applying mechanical constraints. For a discussion and an
explicit comparison for helix dynamics, see

    K. Hinsen, G.R. Kneller
    Influence of constraints on the dynamics of polypeptide chains
    Phys. Rev. E 52, 6868 (1995)

Once you have chosen the constraints you want to apply (that's a
physical choice), you must then pick a method to implement them (that's
an algorithmic choice). In this choice you must consider the limitations
and efficiency criteria for each method. For SHAKE these are

- limitation: no rigid groups of more than three atoms (planar)
  or four atoms (non-planar)  (at least for the commonly implemented
  original version of SHAKE, a generalization has been published,
  but is not in general use)
- efficiency problem: strongly interdependent constraint cause
  a long iteration

For VRBD:

- limitation: no constraints between rigid units
- efficiency consideration: most efficient for large rigid units

Note that many other techniques for implementing constraints have
been proposed and/or tested.

In principle, the results for a given set of constraints should be
identical irrespective of the method used, but I am not aware of any
practical comparison.
-- 
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