As it has been already stated here, binding energy calculation of a small molecule to a large protein poses a difficult problem: a method for molecular electrostatic energy calculation should work well both for the protein ligand complex, the protein and the ligand at infinite separation. The protein and the complex are large molecules, whereas the ligand is, by definition, small.
Not every computational approach for the solvation energy calculation is fit for the job though. To elucidate the nature of the problems at hand we performed the following model calculation:
- we prepared a spherical "protein" of a large (but realistic) radius
- we placed a single-atom ligand with a charge at a given distance from the "protein" center (see the Figure)
- we calculated the solvation energy of the system as a function of the ligand distance both when the protein is neutral and charged (in the latter case the protein charge is opposite to that of the "ligand")
We used four different methods for the electrostatic contribution to the solvation energy calculation: Poisson equation solver (in its surface electrostatic incarnation, blue) QUANTUM MGB (cyan) and the two "classic" GB methods, based on the Coulomb approximation: HCT (magenta) and AGBNP (yellow).
The first Figure, corresponding to an overall electrically neutral cluster, shows absolute deficiency of HCT approach deep enough inside the "protein". The problem is caused by unrealistic assumptions with regard to the overlap integrals calculations is occurs pretty frequently in realistic proteins. AGBNP method represents one of the latest GB approaches and is practically free of these difficulties. However, AGBNP is based on Coulomb approximation and thus fails to recover correct behavior of the solvation energy close to the "protein" boundary: AGBNP energy is off by a large number from both QMGB and the exact solution. QMGB and Poisson solutions agree very well everywhere!
The last Figure shows the same calculation for a charged model "protein-ligand" complex. Once again, HCT fails entirely, AGBNP does not work properly at the "protein" boundary and both Poisson solver and QMGB agree very well, though QMGB is about one order of magnitude faster than the Poisson solver!
Practically all this means that QMGB represents a fast and accurate approximation to the Poisson equation solution. QMGB approach does not rely on Coulomb approximation and is shown to work both for small molecules and large molecular clusters involving molecules of very different sizes. Therefore, with QMGB one can find a single transferable set of GB parameters capable of describing large and small molecules on the same footing.
Solvation energy is a major contribution to a ligand binding energy and is the interaction pretty much responsible for binding selectivity. Actual calculation of the solvation energy requires a method valid both for small molecule ligands and large proteins (and protein-ligand complexes).
Calculation of the electrostatic contributions for the binding energies in a continuous solvation energy approach imposes different problems for large and small molecules. Normally people use some kind of Generalized Born (GB) approximation. The latter is only exact for a charge in the center of a spherical cavity and thus can only be valid for a small molecule with most of the charge located within a few atoms.
If the molecule of interest is large, most of the charges are close to the molecular surface, instead. GB approximation in its most commonly accepted form fails next to a molecular surface: the Born radius is missed by a factor of 2. This means that there can be no "classic" GB model working good both for small and large molecules!
Binding affinity calculation requires calculation of differences between the energy of the complex (a large molecule) and the energies of the protein (another large molecule) and the ligand (a small molecule) at infinite separation.
If a GB model is made working by careful adjusting of "bare" Born radii to fit experimental IC50 of complexes, a good sanity check would require reproduction of experimentally known solvation energies of small molecules and ions (and the other way around). The two graphs in this post show, that this is indeed possible. A relatively large error in the small molecules solvation energies shows that although the resulting model is reasonable, the obtained GB parameters are only quantitatively transferable between large and small molecules.
Solvation energy calculation is absolutely crucial for a successful binding free energy (IC50) determination. Quantum Pharmaceuticals develops aqueous solvation models and tests them against available experimental data to validate the theoretical approaches.
The graph on the left represents two types of solvation energy calculations compared with experiments. The first series (small circles) are the energy differences on solvation for a set of molecules without conformational changes taken into account. The second set (large squares) is obtained after a single optimization run.
The correlation with the experiment clearly improves after conformational changes calculations. Apparently this does not only mean that the model is good, it also means that the molecules do change structure when inserted into water from the gas phase.
Traditional opinion is that a good drug must have a high value of the absolute meaning of the binding energy with target protein in order to prevent the thermal dissociation of the drug-protein complex. In this case an essential deformation of protein arises, which has to be taken into account in developing different models of protein-small molecule and protein-protein interaction, and computing affinity constants in drug discovery in-silico methods. The effect of essential perturbation of protein molecule is ignored in standard computational methods of drug design that can contribute a large mistake to results of calculation, to binding energy, for example.
To demonstrate the existence of the ultimate value of the binding energy two models are considered: macroscopic and microscopic, both giving the same conclusions: the critical value of absolute meaning of binding energy is 50-100kJ/M. If the binding energy exceeds this value, then drug essentially perturbs protein configuration. In a microscopic picture this perturbation is a sequence of irreversible conformational transitions in protein body. In a macroscopic one it is an inelastic deformation of a protein substance. Our estimation agrees with the experimental value (50 kJ /M) of the ultimate energy that can be stored in a protein molecule without its destruction.
The existence of the critical value of binding energy should be accounted in structure based drug design methods where protein molecule is considered in an elastic deformation approximation.
Reference: accepted in Russian Journal of Biophysics, 2008
Quantum Pharmaceuticals is a technology based drug discovery company. We develop a unique computational drug discovery platform (QUANTUM), provide drug discovery services, and pursue our own in-house drug discovery projects searching for novel compounds with anti-bacterial, anti-viral and anti-cancer efficacy.
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