Dear Francois,

To my knowledge, there is no any equation that can represent the number of conformers in a molecule. This is because of the existence of many factors which affect the number of conformation. For example, in conformational analysis, the study of the energetics between different rotamers, there is a significant consideration to the spatial orientation and through-space interactions of substituents which is difficult to be included in an equation from only considering the dihedral angles in a molecule.

Hoping this will be helpful,

Rafik

Hi,

No and in-fact there can't be. The conformations of a particular molecule depends upon the rotation along the single bonds and angle of rotation cannot be fixed. Therefore, N- number of confomers are possible for a particular molecule along rotatable bonds.

Dear Mohsin,

Would you please give us an equation that can give the number of conformation in one or two examples such as taxol and doxorubicin?

Thanks,

Rafik

Dear Sir (Rafik),

I think you have misread my answer and in-fact I haven't mentioned in the text that one can calculate the number of confomers or any equation is documented in the literature that can be employed for the calculation.

This is an interesting question. If you are using a torsional scanning method  you should be able to derive a formula based on the number of rotatable bonds and the number of torsional local minima that each rotatable bond has (generally 1, 2 or 3).  However a torsional scanning method will generate many useless conformers where there is bad atom clash. The proportion of useful conformers to useless conformers will not generally be constant, between any two given molecules, so such a formula may not be as useful as might appear at first sight..

   Many conformer generating programs use a user-defined energy cut-off to weed out useless conformers. Some programs then allow conformers to be clustered by similarity and representative conformers selected from each cluster. Using this method no formula for deciding how many conformers to save is needed, as the number of conformers returned is proportional to the number of local minima in the torsional energy landscape, as it should be (note: for highly flexible ligands you may stiillneed to set an upper limit).  It is a matter of debate where you should set the energy cut-off, depending on the maximum strain energy you think a protein will impose on a ligand (my opinion is "not much", but others might disagree).

As we are aware of the fact that the default cut-off for the conformer generation is 20 kcal/mol above the global minima. One can tune the upper limit but, how can one fix the same? Isn't it different for the different class of inhibitors and different for same inhibitor with the different target? 

Where you should set a default cut-off for the conformer generation is also a very interesting question. There are papers, even quite recent ones, that claim that strain energy of > 20kcal/mol can be present in a bound ligand conformation.  I am sure this is not correct and my feeling is that the figure for the most strain energy that should be accommodated by a small bound ligand is about 3-4kcal/mol (there are publications that suggest this too).  Does that mean you should set a default cut-off of 4kcal/mol when generating conformers ?  No, not really, because the conformer generator will not calculate conformer energies perfectly and you want to make allowance for that and so use a higher cut-off to avoid losing reasonable conformations. 

Mohsin suggests that in theory the cut-off should be different for different molecules. I think this is right. The larger the inhibitor, the more binding energy can in principle be achieved through optimal contact with the protein active site. Therefore more strain energy can be allowed in a bound conformation. So you should perhaps allow a higher cut-off with larger molecules. Unfortunately, though, if your large molecule is highly flexible, a high cut-off might lead to too many conformers being generated, for you to comfortably handle.

One more query I would like to highlight is; What is the standard with respect to which we are setting the upper limit though it is documented above the global minima. Is it possible to allocate global minima for proteins and in fact, we are not the running frequency calculations to testify the same. 

I'm not quite sure I understand your query. I don't know if a standard such as you describe exists. however I look at it this way. A 4 kcal/mol change in Free Energy of binding equates to a 1000 fold in change in the binding constant. So if you bind a molecule which has a strain energy of binding of 4kcal/mol you are taking a theoretical hit of 1000 fold, against the affinity of similar sized molecule making the same interactions but with no strain energy. That is quite a big hit and is about the most I'd be willing to accept, before looking for a better, strain reduced, solution. So my inclination is to set the cut-off at slightly above 4kcal, say 5kcal/mol, for the reasons I gave previously regarding the uncertainty in the energy calculation. If it is a very large molecule (>500MW), maybe I'd go to 6-7kcal/mol.

On to your second point, I think it is very important that we try to properly quantify how much strain a potent ligand has when it binds to the protein. Unfortunately such studies are very difficult to do well. Some of the best carried out studies (in my view) do suggest a figure of 3-5kcal/mol, as the maximum expected for a druglike molecule.

I've been following the discussion generated by this question. My interest is in which conformations a molecule will adopt in its crystal structure and we performed a study a couple of years ago that might have some relevant results for the docking problem. We only looked at a fairly small set of molecules, but collected some statistics on the energy of crystalline conformations relative to the gas phase global minimum. We found that, in the absence of possible intramolecular dydrogen bonds, drug-like molecules crystallise with conformers up to 25 kJ/mol (6 kcal/mol) above the global mimimum. In case it's of interest, the paper is here:

“Which conformations make stable crystal structures? Mapping crystalline molecular geometries to the conformational energy landscape” Chemical Science, 5, 3173-3182 (2014). http://pubs.rsc.org/en/content/articlelanding/2014/sc/c4sc01132e

Graeme shares some very interesting work. The figure of 6 kcal/mol as a maximum strain energy in small molecules is consistent with , though slightly higher than the figure of 3-5 kcal/mol I quoted earlier. This begs the question of whether more strain energy is allowed in a small molecule crystal structure than in the ligand of a protein. Two factors of difference are 1) Ligands are rarely fully enclosed by proteins so not all the ligand surface is involved in productive binding, whereas in the small molecule crystal the molecule is usually completely surrounded. 2) there are no symmetry considerations such as are described in Graeme's nice paper, to worry about in protein ligand complexes, that might lead to high strain energy. I think both these factors would tend to lead to lower strain energy, on the whole, in ligands in proteins, but it is not clear cut.