Subject: Rigid body minimization, summary

From: [email-masked] (judson richard s)
Date: Mon, 13 Mar 1995 12:49:11 -0800 (PST)

Sometime back, I posted the following query, and got a number
of responses, which are included below. Thanks all!

-------------------------------------------------------------

We are starting to look at rigid body gradient optimization
of ligands inside protein cavities. I am looking for information
on what the best methods and implementations are. For instance
have people used truncated Newton methods vs. CG methods?
Are implementations in one commercial package superior to
those in another? Does converting to all internal coordinates
work much better than using cartesians plus Lagrange multiplier
constraints?

Any information is useful. I will summarize if there is interest.

 -----------------------------------------------
| Richard Judson				|
| Center for Computational Engineering, MS 9214	|
| Sandia National Laboratories			|
| Livermore, CA 94551-0969			|
| (510)294-1438					|
| (510)294-2234 (FAX)				|
| email: [email-masked]			|
|						|
 -----------------------------------------------

Dear Richard,

If you are talking about rigid ligand and rigid enzyme, you will
have only 6 variables: 3 translation and 3 rotation. In that case,
quasy-newton methods (e.g. BFGS) are superior CG or truncated
Newton. I used 2 approaches: (i) rigid coordinates, R, Theta, Phi,
A, B, C - where (R, Theta, Phi) determine position of the
center mass of ligand relative to enzyme's center mass and A, B and C
are rotational angles. (ii) internal coordinates. In my experience,
internal coordinates of ligand are better for optimization. Using
this coordinates, it is also easy to add flexibility to the ligand. 
Internal coordinates are also help, when doing simulated annealing
(or any random based search), because it easy to add constrains to
the length of ligand - enzyme bond. Otherwise, ligand, sometimes,
has a tendency to fly away from the active site. 

Andrey

I forgot to add: I would certainly be interested in what other
people have to say on this subject.

-------------------------------------------------------------------------------
Konrad Hinsen                     | E-Mail: [email-masked]
Departement de Chimie             | Tel.: +1-514-343-6111 ext. 3953
Universite de Montreal            | Fax:  +1-514-343-7586
C.P. 6128, succ. A                | Deutsch/Esperanto/English/Nederlands/
Montreal (QC) H3C 3J7             | Francais (phase experimentale)
-------------------------------------------------------------------------------

   those in another? Does converting to all internal coordinates
   work much better than using cartesians plus Lagrange multiplier
   constraints?

I would expect that. First of all, I must say that I have no experience
at all with minimization, but I do have with dynamics. However,
the two problems are sufficiently similar.

Using Lagrange multipliers in a straightforward way will not satisfy
the constraints well over many time steps, due to the accumulation of
numerical errors. The common solution for dynamics is an algorithm
calles SHAKE, which uses an iterative method to satisfy the constraints
exactly after each step. This works well for some types of constraints,
but badly or not at all for others, as the convergence of the iterative
algorithm can become very bad. Some problems - like keeping more than
three particles in a plane - cannot be handled at all in this way.

Another problem with Lagrange multipliers is that you have to be
careful in the choice of constraints. You could define a rigid
body by keeping the distances between all atom pairs fixed, but for
more than three particles this will lead to redundant constraints.
You must then select exactly the right number of constraints to
get the right number of degrees of freedom, and of course not
all possible choices will be equally good in terms of convergence.

A description of how to do dynamics in internal coordinates and
avoiding all these problems can be found in
  G.R. Kneller & K. Hinsen
  Phys. Rev. E 50, 1559 (1994)
Another paper on an implementation and application of this method 
is in preparation.

-------------------------------------------------------------------------------
Konrad Hinsen                     | E-Mail: [email-masked]
Departement de Chimie             | Tel.: +1-514-343-6111 ext. 3953
Universite de Montreal            | Fax:  +1-514-343-7586
C.P. 6128, succ. A                | Deutsch/Esperanto/English/Nederlands/
Montreal (QC) H3C 3J7             | Francais (phase experimentale)
-------------------------------------------------------------------------------

[ On Mon, 23 Jan 1995 17:44:35 -0800 (PST) ]
[ [email-masked] (judson richard s) wrote: ]
[ ... ]

Judson> Any information is useful. I will summarize if there is interest.

There is interest, I would appreciate if you could summarize/post your
information.

-- Thank you,
-- Marcel
______________________________________________________________________

	      Marcel TURCOTTE -- Universite de Montreal
	     http://www.IRO.UMontreal.CA/people/turcotte
______________________________________________________________________

Dear Dr Judson

I would appreciate a copy of any summary you put together for the 
above question.

Many thanks

David E. Clark                   | 
Proteus Molecular Design Ltd.,   |  Tel: 01625-500555
Lyme Green Business Park,        |  Fax: 01625-500666
Macclesfield, Cheshire,          |  Email: [email-masked]
SK11 0JL, UK                     |
Dear Richard,

could you keep me informed of the responses you get. I'm very interested 
in this topic since I'm doing similar things, optimising molecules (ions)
in crystaline cavities. Up to now I've used euler angles + gradients to 
do the optimisation but sometimes get into trouble because of 
non-continuous changes in the angles.

many thanks,
kris van alsenoy
[email-masked]

-------------------------------------------------------------------
Please summarize!  Thanks.

Eric Walters

* D. Eric Walters, Ph.D., Associate Professor, Biological Chemistry
* Finch University of Health Sciences/The Chicago Medical School
* 3333 Green Bay Road, North Chicago, IL  60064
* ph 708-578-3000, x-498;fax 708-578-3240; email: [email-masked]
* "A man would do nothing if he waited until he could do it so well that
*  no one would find fault with what he had done." --Cardinal Newman

Dear Dr. Judson

I would like to ask you to send me replies you have got ( or will get).

I am also interested in rigid body dynamics.

Best wishes

		Grzegorz Bakalarski
	grad. stud. in Dep. of Biophys.
		Warsaw University
		Poland

I'm interested...please summarize.

I don't remember if you've ever used it, but the software marketed by a
company I used to work for, BioDesign (now part of MSI), had a function
like this, but I don't know the details of how it worked.  The products
were called Biograf and Polygraf.  I think the rigid body minimization
stuff was designed by Bill Goddard and Marv Goodgame at Caltech.  I can get
in touch with Marv to ask him more details, if you don't get them from
elsewhere.

Wally

========================================================================
Walter E. Reiher III, Ph.D.                            [email-masked]
Consultant in Computational Chemistry
P.O. Box 61056                                        voice 408-720-0240
Sunnyvale, CA 94088                                     fax 408-720-0378

Hi, Richard

   I wrote a rigid-body minimizer for exactly this application back in
1980-81,  while  I  was  at  UCSF.  It was described in my thesis, but
never published (I didn't think anybody  would  be  interested).   The
only publication that refers to it is Kuntz' group at UCSF:

Meng,  E.   C.,  Gschwend,  D.   A.,  Blaney,  J.   M.,  Kuntz, I.  D.
"Orientational  Sampling  and  Rigid-Body  Minimization  in  Molecular
Docking", Proteins 1993, 17, 266-278.

    I'll send you a copy of the paper, and even the program, if you're
interested.  I've never seen anything else that compares  to  it.   My
group at DuPont used it through most of the 80's, so did Scott Dixon's
group  at  Smith  Kline.   I  don't use it much anymore - I do all our
docking work with distance geometry now.  I wrote  it  in  Fortran-77.
This  was my first major program, so the code isn't really pretty, but
it works well.  It works in Euler space  using  numerical  derivatives
with  a DFP minimizer.  Its very fast;  just takes a few seconds to do
a local optimization from a manually docked ligand position.  I  never
worked  on  any  approaches for global optimization with this - I just
wanted it to clean up manual dockings before investing in  full-scale,
all degrees of freedom, optimizations.  

Jeff

Dear Dr. Judson,

Some time ago you posted a question on the compchem newsgroup regarding methods
to perform rigid body optimization of ligands in protein cavities.  I would
very much appreciate a summary of responses.  Thank you.

-- 
-----------------------------

Paul Rejto, Ph.D.
Research Scientist				
Agouron Pharmaceuticals, Inc.
3565 General Atomics Court
San Diego, CA 92121
(619) 622-3149
[email-masked]