Subject: Summary:Interaction energy in host-guest complexes

From: "Dr. Paolo Mencarelli" <[email-masked]>
Date: Tue, 5 Mar 1996 04:14:10 -0500 (EST)

Dear CClers,

Some time ago I posted a question about the interaction energy in host-guest
complexes. Here are the answers I got:

============================================================================
=========
My original question:

Hi all,

I am an organic chemist interested in host-guest chemistry and I have a
question on a computational aspect of this topic.

The interaction energy (Delta E) of the host and the guest in a given
complex may be defined as:

Delta E = Esteric(complex) - Esteric(host) - Esteric(guest) 

where the steric energies may be evaluated by the molecular mechanics
approach.(For the time being I am neglecting the entropic and solvation
effects which are not taken into account by a molecular mechanics simulation
in the gas phase).
The interaction energies are useful in comparing the relative stabilities of
different conformations of the complex, for example different orientations
of the guest with respect to the host. 
Now comes my question: given two different complexes of the same host with
two different guests (or two hosts with the same guest), is it correct to
compare the interaction energies of the two complexes in order to find out
which is the better guest (or the better host)?
I am not sure that this is correct since, when the two guests (or the two
hosts) are not stereoisomers or not even isomers, the two complexes have
different chemical compositions.
Thanks to all who reply. I will summarize.

Paolo

===============================================================================

Date: Fri, 23 Feb 96 10:18:25 +0100
From: [email-masked] (Leif Norskov)
To: [email-masked]
Subject: Re: CCL:Interaction energy in host-guest complex

You asked:

  > is it correct to compare the interaction energies
  > of the two complexes in order to find out which
  > is the better guest ?

Only if you correct for the difference in "Esteric(guest)".
Cubane (CH)8 has a higher internal strain energy than methane,
and hence will most likely have a higher Esteric(complex),
yet it may have a better fit (interaction) with a host.

Regards,

Leif Norskov
Novo Nordisk A/S
Copenhagen
Denmark
[email-masked]
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Date: Fri, 23 Feb 1996 10:43:12 +0100
From: Per-Ola Norrby <[email-masked]>
To: "Dr. Paolo Mencarelli" <[email-masked]>
Cc: [email-masked]
Subject: Re: CCL:Interaction energy in host-guest complex

        Dear Paolo,

        The comparison you want to make is correct, as long as no new
covalent bonds are formed between the guest and host.  The bond-specific
enthalpy contributions will all cancel out.  As you stated, you will only
get the steric component in the gas phase from this comparison (closely
related, but not identical to the enthalpic component).  My gut feeling in
this is that the most serious error in this would be the neglect of
solvation.  However, you should also be aware of the risk of
entropy-enthalpy compensation:  To make it short, the entropy difference
will probably give a significant contribution OPPOSITE to that of the
enthalpy.  For a short summary on this subject, see: J.D.Dunitz, Chemistry
& Biology, 2(11), 709-712, 1995.
        If you are comparing to experimental enthalpies, you mainly have to
worry about the solvation part (there are several good computational
approaches), but if you are trying to correlate binding constants at one
temperature, you will definitely have to take a look at the above article.
The really bad part of this is that it's pretty hard to estimate the
entropy contribution from a weak interaction computationally.

        PeO Norrby

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
 *  Per-Ola Norrby
 *  The Royal Danish School of Pharmacy, Dept. of Med. Chem.
 *  Universitetsparken 2, DK 2100 Copenhagen, Denmark
 *  tel. +45-35376777-506, +45-35370850    fax +45-35372209
 *  Internet: [email-masked], http://compchem.dfh.dk:/
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Date: Fri, 23 Feb 96 2:12:19 PST
From: Thomas Fox <[email-masked]>
To: "Dr. Paolo Mencarelli" <[email-masked]>
Subject: Re: CCL:Interaction energy in host-guest complex

> 
> Now comes my question: given two different complexes of the same host with
> two different guests (or two hosts with the same guest), is it correct to
> compare the interaction energies of the two complexes in order to find out
> which is the better guest (or the better host)?
> I am not sure that this is correct since, when the two guests (or the two
> hosts) are not stereoisomers or not even isomers, the two complexes have
> different chemical compositions.
> Thanks to all who reply. I will summarize.
> 
Ciao Paolo,

I guess what you really want to know if you want to investigate the
relative binding of different guests to the same host (or vice versa) 
is the relative free energy of binding \Delta\Delta G. If you draw a 
free energy cycle:

                    \Delta G1
     Guest1 + Host ------------>   Guest1 in Host
         |                               |
         |                               |
         |                               |
         | \Delta G3                     |  \Delta G4
         |                               |
         |                               |
         |                               |
         |                               |
         v          \Delta G2            v
     Guest2 + Host ------------>   Guest2 in Host

the total free energy when you go around in this cycle

          \Delta G1 + \Delta G4 -\Delta G2 -  \Delta G3 =0

Or, rearranged:
        \Delta G1  - \Delta G2 = \Delta G3 -\Delta G4 = \Delta\Delta G

\Delta G1 and \Delta G2 are the experimentally available results (very
often only in form of the relative free energy of binding, i.e.
\Delta G1  - \Delta G2), whereas from a calculation of whatever sort you
get sth. that involves both \Delta G3 and \Delta G4.

Some remarks.
 - just looking at MM energy might get you some idea, but you really want
   to look at *free energies* instead. Maybe, very maybe if you two
   extremely similar hosts and/or guests you might get away by looking 
  only at energy contributions and neglecting entropy. Just imagine a 
   guest that is a little bigger than the other which might prohibit 
   some crucial movement inside the host...
   Only if you - as you obviously have done - have the same guest in
   different conformations/orientations the approach of looking only at
   MM energies has some chance to yield meaningful numbers.

 - be sure to include solvent contribution in some way. I have had
   situations where my free energy calculations indicated a \Delta G4 
   that was more or less =0. So the experimentally observed binding 
   energy difference was entirely due to different solvation of my two 
   guests (40 atom haptens to a catalytic antibody that only differed 
   in a CH2 vs a S in a side chain).

 - my very personal opinion (no flames please): if you cant or dont want to
  address these two points (*free* energies and solvation), you might as
   well use your intuition and not bother doing calculations at all. Yes, I
  know too well that free energy calculaions are expensive and not always
   feasible due to time constraints...but as usual you only get what you
   pay for.
   As I said already above, if you use the same guest in different
    conformations you might get away
   with only using the steric energy that you get out of some MM program -
   after all, the solvation energy is the same, and the entropic
   contributions are probably almost the same, but when you look at
   chemically
   different guests or hosts this approximation is not longer valid.

You may want to look at some of the papers from the Gunsteren, Karplus etc
group, or also from our group (Kollman) that deal with free energy
calculations for protein-ligand binding and host-guest systems. There is a
nice book, if I remember right its called Biomolecular Simulations in
Liquids or sth. like that, edited by van Gunsteren, that sums up a lot of 
these questions quite nicely. I think there is also a review by Peter
Kollman in the 1993 or 1994 Chemical Reviews that addresses these
problems.

Ciao and feel free to contact me if you have further questions,

Th.

--

Thomas Fox                          
Dept. of Pharmaceutical Chemistry   
University of California            e-mail: [email-masked]
San Francisco, CA 94143-0446        http://www.amber.ucsf.edu/~fox/index.html

				 ,,,  
                                (o o)
-----------------------------ooo-(^)-ooo-------------------------------------
                                  U  
         Wer Kleinstweich Produkte kauft oder in Umlauf bringt 
        wird mit Abhaengigkeit nicht unter zehn Jahren bestraft.
-----------------------------------------------------------------------------
#include '../.disclaimer'
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Date: Fri, 23 Feb 1996 11:46:07 +0000 (GMT)
From: Paddy Kane <[email-masked]>
To: [email-masked]
Subject: Re: CCL:Interaction energy in host-guest complex

 Hi Paolo,

 I model the interaction of calixarenes with various types of hosts - neutral
and ionic - with molecular mechanics. The nature of molecular mechanics is such
that the difference in energies between two conformational isomers is relevant
but that the greater the chemical difference in the two molecules being
compared the less relevant is the energy difference.

 Regards,
 Paddy.

 Paddy Kane
 School of Chemical Sciences
 Dublin City University
 Dublin 9
 Ireland
 [email-masked]

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Date: Fri, 23 Feb 96 15:18:10 +0300
From: Igor V. Pletnev <[email-masked]>
To: [email-masked]
Subject: Re: CCL:Interaction energy in host-guest complex

Hi Paolo

it's undoubtedly correct if you
(i) compare deltas not Es (and you do so), and
(ii) explicitly say that you are evaluating and comparing not interaction
energies but "strain which the complexation costs" or "steric contribution
into energy".

For many reasons, mol.mech's kilocalories or kiloJoules are not those
as in experiment (or even in other computational scheme); however, the former
may be in nice, sometimes even linear, correlation with the last. Naturally,
you have good chances for such a correlation only if the same binding scheme
is operative.

Many examples are in the field of host-guest with inorganic guests
(e.g., crowns-potassium: Hay et al., JACS, 1993, 11158.)

Regards,
Igor

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Date: Fri, 23 Feb 1996 08:56:49 -0500
From: Trevor Creamer <[email-masked]>
To: "Dr. Paolo Mencarelli" <[email-masked]>
Subject: Re: CCL:Interaction energy in host-guest complex

On Feb 23,  3:13am, Dr. Paolo Mencarelli wrote:
> Subject: CCL:Interaction energy in host-guest complex
> Hi all,

Hi Paolo,

> Now comes my question: given two different complexes of the same host with
> two different guests (or two hosts with the same guest), is it correct to
> compare the interaction energies of the two complexes in order to find out
> which is the better guest (or the better host)?

I think perhaps you could come to very erroneous conclusions doing this.
Neglecting entropy and solvation effects can lead to serious errors unless the
two different guests are very, very similar in size, shape, flexibility and
chemical composition (I'll focus on guests, but the same applies to hosts). Let
me illustrate with two simple examples:

(i) Entropy -
Imagine you have a hypothetical host that binds n-pentane. The energy of
binding is dE(n-pentane). When bound the pentane is held rigidly in a fairly
extended conformation. It has lost all of its configurational entropy. The
configurational entropy for rotation about a single C-C bond is roughly 0.7
kcal/mol. Now let's imagine the same host binding 2-pentene. The energy of
binding, dE(2-pentene) is going to be very close to that of dE(n-pentane) since
they are chemically very similar (at least to a molecular mechanics calculation
they are). The solvation component will also be very similar. However, rotation
about the double bond is obviously much harder than rotation about a single
bond. So, roughly, we can say that rotation about C=C has a configurational
entropy of about 0.0 kcal/mol. So the 2-pentene will lose 0.7 kcal/mol less
entropy upon binding, which is enough to make it a better guest than n-pentane,
but you won't see that if you ignore entropy in your calculations.

(ii) Solvation -
This one's a little harder to find a clear example for. Ignore entropic effects
for the moment. This time imagine a hypothetical host that binds the hydroxyl
group of an alcohol. The binding site is deep inside the host. The host will
bind 1-pentanol and cyclo-pentanol. When bound, both of these guests are
completely shielded from solvent (that way we only have to think about solvent
effects on the unbound guests). In water, the 1-pentanol is flexible and, on
average, will adopt a relatively extended conformation. Thus, much of the
molecule is in contact with solvent. The cyclo-pentanol is much more restrained
and, since it is a ring, buries much of its surface against itself (i.e. the
inside of the ring is not accessible to solvent). So you can expect the cyclic
molecule to have less aliphatic surface area exposed to the water. This would
argue that binding the 1-pentanol (removing it from water) should be more
favorable (if you ignore entropy). But you won't necessarily see that from a
molecular mechanics calculation.

I hope this makes sense (I've just got into work and haven't had a coffee yet).
Good luck !
Cheers,
        Trevor

-- 
________________________________________________________________________

 Trevor P. Creamer                          Dept. of Biophysics
 Email  - [email-masked]           & Biophysical Chemistry
 Phone  - (410) 614 3972                    Johns Hopkins University
 Fax    - (410) 614 3971                       School of Medicine
				            Baltimore, MD 21205
                                            U.S.A.
________________________________________________________________________

--------------------------------------------------------------------------------
Date: 23 Feb 1996 09:25:58 -0800
From: Tom Hendrickson <[email-masked]>
To: "Dr. Paolo Mencarelli" <[email-masked]>
Subject: Re: CCL-Interaction energy i

        Reply to:   RE>CCL:Interaction energy in host-guest complex

I will be discussing this topic at the upcoming meeting in Erice, Scicily in
May, "Experimental and Computational Approaches to Structure Based Drug
Design"
In general, the answer is no   because binding may be driven by any number of
thermodynamic factors and unless you have a "comprehensive" function you
cannot be correct with every case. Also, you are only looking at half the
binding equation in detail.
This said, however, we have done both molecular dynamics and molecular
mechanics minimization and have looked at interaction energies beween protein
and ligand. As always, with ligands whose binding is driven primarily by the
same physics , correlations can be found between ,for example, between the
binding free energies of a series of ligands to FKBP and the average
proterin/ligand interaction energies as derived from MD simulations. However,
these simulations were not done in the gas phase, where electrostatic effects
in solution are poorly modelled.

Regards,
Tom Hendrickson
Agouron Pharmaceuticals,Inc.
San Diego, Ca
------------------------------------------------------------------------------
Date: Fri, 23 Feb 96 12:40:02 EST
From: Igor Shamovsky <[email-masked]>
To: [email-masked]
Subject: Host-guest complexes.

   Hi Paolo:

   Yes, you can definitely do that, of course, if you take
into account geometric relaxation of both host and guest,
and calculate their specific mutual orientations.

Dr. Igor Shamovsky
Chemistry Department
Queen's University
Kingston, Ontario
Canada K7L 3N6

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Date: Fri, 23 Feb 1996 10:27:51 -0800
From: Ben Burke <[email-masked]>
To: "Dr. Paolo Mencarelli" <[email-masked]>
Cc: [email-masked]
Subject: + 3336 CCL:Interaction energy in host-guest comple [40] Per-Ola Norrby 

On 23 Feb 1996 02:38:14 Dr. Paolo Mencarelli wrote:
> The interaction energy (Delta E) of the host and the guest in a given
> complex may be defined as:

> Delta E = Esteric(complex) - Esteric(host) - Esteric(guest)

> where the steric energies may be evaluated by the molecular mechanics
> approach.(For the time being I am neglecting the entropic and solvation
> effects which are not taken into account by a molecular mechanics simulation
> in the gas phase).

Paolo,
Do not forget the contributions from (1) electrostatics, and
(2) intramolecular "strain" energy.  The electrostatics will
necessarily have to be balanced by solvation.  The "strain"
energy will be the intramolecular energy difference between
an estimate of the global energy minimum and the energy of
the conformer which is bound.  This strain terms includes
stretch, bend, torsional, electrostatic, solvation and steric
terms.  For a large guest (such as a protein), I suggest
constrained minimization to a local energy minima as the
"estimate" of the global energy minimum; for smaller systems,
many methods have been described to search conformational
space reliably.

Best to you,
--Ben

-- 

---------------------------------------------------------------------------
Benjamin J. Burke          Agouron Pharmaceuticals      [email-masked]
Research Scientist         3565 General Atomics Ct      Tel: (619) 622-3018
Computational Chemistry    San Diego, CA     92121      FAX: (619) 622-3299
---------------------------------------------------------------------------

----------------------------------------------------------------------------
----Date: Mon, 26 Feb 96 14:26
From: Jonathan Baell <[email-masked]>
To: Paolo <[email-masked]>
Subject: host-guest complexes

Dear Paolo

Your measurement of shape complementarity is a good place to start to 
estimate likely affinities of various hosts for various guests, since a 
steric mismatch is energetically very expensive (I think proportional to 
the sixth power of distance; I'd check this, though) and if "it don't 
fit, it won't bind" no matter how favourable the other factors.

If the synthetic targets are readily accessible/available (unlikely 
perhaps) your binding data of sterically-matched compounds might be very 
useful in seeing not only how well theoretical calculations can account 
for your observations, but in developing better theory.  However, I would 
be concerned if you use your method in a predictive sense for 
synthetically complicated molecules as one might well find that, if 
you're looking at binding in aqueous solution, the binding is entropy 
driven.

You may indirectly model entropy effects by inclusion of hydrophobic 
parameters in your molecular mechanics calculations.  When combined with 
steric/Van der Waals (did the net ever decide whether it was "van" or 
"Van"?; I cannot remember the conclusion) and electrostatic/H-bonding 
interactions calculations (with charges preferably calculated 
semiempirically in the complex also, in case of high polarizability, and 
at least using a solvent continuum model), you might be on safer ground.  
The program HINT is a good one to look at with respect to its 
consideration of hydrophobicity (there is a URL for this), and I think 
attempts are being made to correlate a HINT score with binding constants, 
and to introduce the capability of calculating and incorporating 
potential energies in the case of conformationally flexible ligands. 

In any case, it seems to me that you need not worry about the point of 
structural dissimilarity, because you are most interested in the energy 
penalty involved in your particular compound assuming the binding 
conformation, compared with its calculated global minimum in the absence 
of host.  This value of energy difference is valid in comparisons between 
structurally dissimilar compounds, but your force field accuracy in 
calculating this value may be the limiting factor.

Thus I would have thought that while you can't directly compare your 
potential energies of your complexes with each other in the case of 
structural difference, you can once you have substracted the potential 
energy of the relevant ligand in its intrinsically lowest energy 
conformation.

Sincerely 

Jonathan Baell

===============================================================================

Regards, 

Paolo

*********************************************************
*   Dr. Paolo Mencarelli                                *
*   Dipartimento di Chimica  - Universita' La Sapienza  *
*   P.le Aldo Moro, 2  00185 Roma - ITALY               *
*   tel 06-49913697 fax 06-490631                       *
*   E-Mail [email-masked]                       * 
*********************************************************