From:	"PSI%SURFNET.1412007::MOIRA::groot" %! at !% caos.caos.kun.nl
Date:	Mon, 28 Jun 1993 09:56:28 METDST
Subject:	interaction function

Dear Netters,

Last week I posted the following question to the Comp-Chem-List:

>I have a series of noncovalently bound enzyme-inhibitor complexes for which
>the 3D-structures have been determined/modelled.
>I am trying to find computational methods that will allow me to estimate
>the binding between the enzyme and these inhibitors. In other words: does
>somebody know of A VALIDATED (published) INTERACTION FUNCTION ? Are
>there papers in which experimentally determined binding data are correlated
>with calculated interaction energies?
>Since I am interested in both a large number and a wide variety of inhibitor
>structures I don't think free energy perturbation methods will help me with
>respect to this.

About 10 persons responded to my question (many thanks!) or expressed
their interest in the answers I would get. From the various responses I got
I would say that:
* the problem is very much alive both in industry and at academia
* a number of people are collecting the combination of experimental
  structures and binding data in order to test methodology
* systems under study vary from enzyme-inhibitor to antigen-antibody complexes
* some scientists report successes with "simple" methods (neglect of
  solvation, conformation, entropy, etc) while others prefer working
  with more sophisticated methodologies.
* nobody claimed to have found the ultimate answer or as Bruce Bush (one of the
  respondents) said "So the problem is by no means solved even at the crudest
  level."

If this mailing results in more reactions, I will again try to summarise
them and mail them to the Comp-Chem-List.

Peter
Grootenhuis
(grootenhuis \\at// akzo.akzo.400net.nl)


                        ========================
                        SUMMARY OF THE RESPONSES
                        ========================


Kate Holloway (kate.holloway;at;merck.com):
=======================================
        I am in the process of writing up some work on HIV protease inhibitors
which is directly applicable to the question you ask.  I too had too many
inhibitors to use a technique as time-consuming as FEP, so I tried other more
simpler methods and found that, at least for HIV protease inhibitors, there
was a very good correlation (R2 of about 0.8) between the molecular mechanics
intermolecular energy component and the measured IC50 (and this was with the
enzyme held fixed, only the inhibitor moving!).  However, this was only true
with our in-house force field MM2X (developed by Tom Halgren), not with CHARMm
(R2 of about 0.5).  I have not tried AMBER.
      Using the correlation equation we derived for a set of between 30 and 60
inhibitors we were able to make fairly accurate predictions of inhibitor
activity prior to synthesis.  Unfortunately, when we tried to improve the
accuracy of our calculations by including enzyme flexibility, solvation, etc.,
we were not successful, but that work is not completed.

Arne Elofsson (arne-0at0-mango.mef.ki.se):
====================================
There was a paper by M. Levitt in science last year/.
Where he correlated between binding strength and energy.
This paper has been challenged by van Gunsteren & Marks
IN (JMB) i think this year

==> W.F. van Gunsteren and A.E.Mark, J. Mol. Biol. 227 (1192) 389-395.
==> C.Lee and M.Levitt, Nature 352 (1991) 448-451
==> (added by PG)

Jerome Gabriel (gabriel (+ at +) jg1.bchem.temple.edu):
=============================================
...I start off by minimising the energy of an inhibitor-gp120 complex.
Then I calculate the potential energy of the inhibitor alone and
of gp120 alone.  From this data I can calculate what I call the
interaction potential: E(cmplx) - { E(gp120 alone) + E(inhibitor) } .
We have plotted the interaction energy versus apparent Kd for
several known inhibitor and get a very nice linear relationship...

Tom Hendrickson (hendrick' at \`humbert.agouron.com):
==============================================
... Here at Agouron, we have many crystal structures of enzyme-inhibitor
complexes. The study that we did involved the enzyme thymidylate synthase and
about 31 inhibitors complexed to it. The method used was minimization of a
substructure of the protein with the program MacroModel, developed at
Columbia University. There is an implicit solvation potential in the force
field which has been shown to work quite well with small organic molecules.
This work was presented by me at the Molecular Graphics meeting in
Interlaken, Switzerland this past month. I will probably write the work
up shortly for publication.
The overall method is quite simple, but a bit lengthly to explain.
The resultant "binding energy" is not the absolute binding free energy,
but the difference can be rationalized in terms of misssing consderations of
loss of configurational entropy associated with translation and rotation and
conformational entropy of the side chains of the protein and torsional
rotations of the free ligand.  We have shown that on can get results
equivalent to free energy perturbation calculations if the changes  primarily
involve the enthalpy in the free energy.
In general, the method may be good for evaluating the output from 3D
searches of databases or for evaluating small changes to a known inhibitor
structure. Since it is essentialy a minimization technique, it runs fairly
quickly...

Richard Judson (rsjuds ( ( at ) ) california.sandia.gov):
=============================================
...	There are no refs in what follows which include the works of
	Art Olson (at Scripps) but I am familiar with the work and will
	dig some more and send you the ref. Also there is something
	called HINT which purports to do something like docking into a
	FIELD of properties. Peter Goodford's GRID has long done stuff
	like that. Of course there is LUDI from BIOSYM now. That helps
	construct molecules in a cavity . We saw it and it looks like
	it has some potential but we are evaluating it at present.
	Finally there is the CAVEAT (from Paul Bartlett) program that
	lets you find molecules whose stored conformers (in the CSD)
	match some set of vectors so that you can use them as templates
	for building the 3D functionality constellation that you want...

 Author    BL Stoddard, DE Koshland
 Title     Molecular Recognition Analyzed by Docking Simulations
           - The Aspartate Receptor and Isocitrate Dehydrogenase
           from Escherichia-Coli
 Source    Proceedings of the National Academy of Sciences of the
           United States of America 90: 4 (FEB 15 1993)
 Page(s)   1146-1153
 Keywords  Protein Docking; Drug Design; Energy Minimization;
           Substrate Binding; Receptor Signaling
 KeyWords+ PROTEIN-PROTEIN-INTERACTION; MALTOSE-BINDING;
           PHOSPHORYLATION; ENZYME; COMPLEMENTARITY;
           CHEMORECEPTOR; SPECIFICITY; CHEMOTAXIS; LIGAND; SITE
           Berkeley, CA 94720

 Author    SH Rotstein, MA Murcko
 Title     GenStar - A Method for Denovo Drug Design
 Source    Journal of Computer - Aided Molecular Design 7: 1
            (FEB 1993)
 Page(s)   23-43
 Keywords  Drug Design; Protein Structure; Drug Ligand
           Interactions; HIV Protease Inhibitors; Carbonic
           Anhydrase Inhibitors; Ligand Design; Protein Active
           Site; Enzyme Inhibitors; FKBP-12 Inhibitors
 KeyWords+ HUMAN IMMUNODEFICIENCY VIRUS-1; PRIMARY STRUCTURE
           GENERATION; ASSISTED MOLECULAR DESIGN; HIV-PROTEINASE-
           INHIBITORS; HYDROGEN-BONDING REGIONS; FAVORABLE
           BINDING-SITES; CARBONIC ANHYDRASE-II; CAVITY SURFACE-
           AREA; HYDROPHOBIC INTERACTIONS; ABINITIO CALCULATIONS

 Author    J Cherfils, S Duquerroy, J Janin
 Title     Protein-Protein Recognition Analyzed by Docking
           Simulation
 Source    Proteins - Structure Function and Genetics 11: 4
            (1991)
 Page(s)   271-280
 Keywords  Antigen Antibody Recognition; Protease-Inhibitor
           Complexes; Simulated Annealing; Energy Refinement;
           Docking Algorithm
 KeyWords+ PANCREATIC TRYPSIN-INHIBITOR; ANTIBODY-ANTIGEN
           COMPLEX; ACCESSIBLE SURFACE-AREA; 3-DIMENSIONAL
           STRUCTURE; CRYSTAL-STRUCTURE; SHAPE COMPLEMENTARITY;
           ENZYME-INHIBITOR; BOVINE TRYPSIN; BINDING-ENERGY;
           LYSOZYME

 Author    SH Northrup, HP Erickson
 Title     Kinetics of Protein-Protein Association Explained by
           Brownian Dynamics Computer Simulation
 Source    Proceedings of the National Academy of Sciences of the
           United States of America 89: 8 (APR 15 1992)
 Page(s)   3338-3342
 Keywords  Diffusion Controlled Reactions; Antibody Antigen
           Complexation; Self-Assembly; Lengthy Collisions
 KeyWords+ CYTOCHROME-C PEROXIDASE; ORIENTATION CONSTRAINTS;
           ROTATIONAL DIFFUSION; BINDING; DISSOCIATION; DOMAINS;
           ACTIN; RATES; MODEL

 Author    L Banci, S Schroder, PA Kollman
 Title     Molecular Dynamics Characterization of the Active
           Cavity of Carboxypeptidase-A and Some of Its
           Inhibitor Adducts
 Source    Proteins - Structure Function and Genetics 13: 4
            (AUG 1992)
 Page(s)   288-305
 KeyWords  Molecular Dynamics; Catalysis Carboxypeptidase;
           Ligand Binding
 KeyWords+ REFINED CRYSTAL-STRUCTURE; D-PHENYLALANINE; GROUND-
           STATES; NUCLEIC-ACIDS; FORCE-FIELD; COMPLEX;
           SIMULATION; BINDING; RESOLUTION; PROTEINS

Here is the Olson Reference:

Title: AUTOMATED  at.at DOCKING at.at  OF SUBSTRATES TO PROTEINS BY SIMULATED
       ANNEALING
Author(s): GOODSELL DS; ()at()OLSON AJ()at()
Corporate Source: SCRIPPS CLIN & RES FDN,RES INST,DEPT MOLEC
       BIOL,10666 N TORREY PINES RD/LA JOLLA//CA/92037; SCRIPPS CLIN &
       RES FDN,RES INST,DEPT MOLEC BIOL,10666 N TORREY PINES RD/LA
       JOLLA//CA/92037
Journal: PROTEINS-STRUCTURE FUNCTION AND GENETICS, 1990, V8, N3, P 195-202

George Seibel (seibelgl "-at-" smithkline.com):
=======================================
... The most interesting thing that I know of
right now is Hans Bohm's Ludi potential.  In my notes from the York
meeting, I have it as 6 kJ/mole for each hydrogen bond, and 100
J/mol*Angstrom**2 for everything that is not involved in a hydrogen
bond.  As far as I know it doesn't have any sort of penalty for
hydrogen bonds *not* made... but I'm not sure about that.  He had a
paper in JCAMD within the last year or so, which I don't have here
right now.  He may or may not have discussed the potential there.  We
have a postdoc here named Jonathan Keske who is working on this very
problem.  He has gathered a huge database of complex structures from
the PDB, and looked up binding constants for all of them.  He's now
working on developing an interaction potential based on this data...
...I think that the Ludi potential or something like it is probably the
way to go here for now.  Bohm didn't say anything about the functional
form, i.e. the distance dependence.  I would guess that "hydrogen bond"
is probably any donor-acceptor distance of less than about 3.2 Angstroms
or so, and they all get the same energy.  He showed a graph of his potential
against Ki for a number of complexes (like maybe 20 or 30 unidentified
receptor/ligand systems) and it was pretty linear.  Let me know if you
hear about any good papers along these lines...

Herman van Vlijmen (vlijmen[ AT ]tammy.harvard.edu):
==============================================
... Two papers that are of interest are:
J. Novotny et al. On the attribution of binding energy in antigen-antibody
complexes McPC603, D1.3, and HyHel-5. Biochemistry, 28:4735-4749, 1989.
G. Klebe and U. Abraham. On the prediction of binding properties of drug
molecules by comparative molecular field analysis.
In addition, I can tell you that Amedeo Caflisch, with us at the Karplus
lab, has improved the Novotny-type calculation considerably, by using
Poisson-Boltzmann electrostatics, and a more accurate estimation of the
conformational entropy loss.

Bruce Bush (Bruce_Bush()at()merck.com):
==================================
   Bruce L. Bush, Molecular Systems / Biophysical Chemistry,
   Merck Research Labs, Rahway NJ 07065 USA    (908) 594-6758

In general,  binding (L+R -> LR) in solution can be regarded as
proceeding in three steps:  removing species L and R  from
water (i.e. desolvating each species); letting them interact in vacuum
(L + R -> LR, whose energy is given by standard empirical energy functions
such as Lennard-Jones + Coulomb);  and then resolvating LR, thus partly
reversing the desolvation of L and R separately.

As this scheme indicates, one way to get at binding energy in solution is
to find the solvation (desolvation) free energy of each species separately.
Barry Honig and his group (Kim Sharp, Michael Gilson,
Anthony Nicholls) have published many papers in Biochemistry, Proteins, etc.
on estimating these energies.  Their approach is to divide the solvation
free energy into a charge-dependent or "dielectric" solvation energy, and a
non-charge-dependent, cavity-formation, or "hydrophobic" energy.
Adding all of these to the in vacuo energy gives, in principle, the full
binding energy in solvent. The DelPhi program (Biosym Technologies, inc.);
produced by Honig et al calculates the dielectric part alone.
The POLARIS program (Molecular Simulations, Inc.) of Arieh Warshel and his
group makes a similar decomposition of the energy but represents the "water"
as a grid of dipoles rather than as a continuum.

Another approach is to create an effective potential, usually a pairwise
potential, which somehow incorporates effects of solvent.  Scheraga's
ECEPP program takes this approach.  Note however that
 ** An interaction function which claims to reproduce binding energy in an
  aqueous medium is *necessarily* non-additive. **
Thus the function cannot simply be a sum over atom pairs (i,j) of some
f(distance(i,j)).  At the very least, the interaction function
may involve calculating some  property p(i) of each atom (such as
its surface exposure) which is not additive over atom pairs, and using this
p(i) to modulate a pairwise interaction (for example, p(i)*f(distance(i,j))).

The BATCHMIN or MACROMODEL energy function, described in publications by
Clark Still's group, is a pairwise effective potential which is non-
additive in this sense.  Still claims that this function produces good
results for free energy of aqeuous solvation of organic molecules and
ions -- a necessary but not sufficient condition for giving binding energies.

You want to compare widely different ligands or binding geometries.
This is an extremely difficult problem which calls for very SIMPLE and
rough estimates.  One study which did produce a regression (rather than a
first-principles calculation) of measured binding affinities, involving 9
crystallographic structures of thermolysin-inhibitor complexes, is:

TI: Definition and display of steric, hydrophobic, and hydrogen-bonding
properties of ligand binding sites in proteins using Lee and Richards
accessible surface: validation of a high-resolution graphical tool for drug
design.
AU: Bohacek-RS; McMartin-C
AD: Pharmaceuticals Division, CIBA-GEIGY Corporation, Summit, New Jersey
  07901.
SO: J-Med-Chem. 1992 May 15; 35(10): 1671-84

Of course, a regression is not a prediction, and it is not clear whether the
"explanatory" factors (numbers of polar / nonpolar atoms involved in the
interface, etc.) are really explanatory for other systems.  In fact, the
reported r-square of 0.99 becomes far worse (? 0.4 ?) if one additional
thermolysin inhibitor is included in the fit.  So the problem is by no
means solved even at the crudest level.

--------------------------------------------------------------------------------
E-mail address: grootenhuis $#at#$ akzo.akzo.400net.nl

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Phone: 31-4120-61920 --- Fax: 31-4120-62539
--------------------------------------------------------------------------------


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