Multiconformational MMGBSA Rescoring; Advancing On Mount Free Energy

Blogging has been a little slow lately mainly because there have been exciting new developments with one of the projects I have been involved in and I was in meetings related to this. One of the topics that was discussed at the conference I was at last week was the accurate prediction of free energies of binding, one of the holy grails of drug discovery. Free-energy perturbation (FEP) still remains the gold standard to get relative free energies of binding, but the procedure is very computer intensive and therefore can be carried out only with small changes in congeneric series of inhibitors. The goal remains elusive and extremely challenging.

A poor man's way of quickly obtaining such ∆Gs is MMGBSA (Molecular Mechanics Generalized Born Surface Area). The GBSA model is well-established as a continuum solvation model for taking solvation into account. What MMGBSA does is take a docked ligand structure and then calculate the free energy of binding as the difference between the bound and unbound states using a force field, including implicit solvation.

Therefore, it calculates

∆G (binding) = ∆G (protein-ligand complex) - ∆G (protein) - ∆G (ligand)

Clearly it has to calculate the energies of the free ligand and free protein. Much of the challenge lies in these two terms. For starters, one has to calculate the strain energy penalty that the protein has to pay in order to bind the ligand. The binding energy that we see experimentally emerges after the protein has paid this strain penalty. How much this strain energy can be has been a controversial topic recently and I will get into it in another post. Suffice it to say that it's a challenging calculation that is not always handled well by MMGBSA. This is because in calculating the ligand free energy, MMGBSA essentially uses a force field to relax the ligand from the bound conformation to the nearest local energy minimum. However, a complex ligand exists in several local energy minima in solution and this force field local minimum may not correspond to any of them. Thus, one has to consider the global strain penalty that the protein has to pay. For this the method also has to consider the multiple conformations that a ligand adopts in solution. Sadly there are very few techniques that will deconvolute the Boltzmann population of a ligand's real conformations in solution and give us the global minimum. This problem in calculating strain energies remains an important drawback of the method.

Calculating ∆G (protein) is also not a trivial matter. We need to consider the entropy of the protein. One can get this from time-consuming MD simulations but it's not certain if the force field is parametrized well and if conformational space has been sampled comprehensively. Another uncertain factor is the induced fit effects involved in binding. A lot of these effects can be subtle and may extend to second shell amino acid residues.

Given these drawbacks, MMGBSA has nonetheless been quite successful in improving agreement with experiment. One of the reasons it works so well is that when you are dealing with congeneric series of ligands for a given target, many of the terms like conformational entropy and protein reorganization energy are the same or very similar and cancel, although there can be surprises. It seems now that at least one of the problems in MMGBSA- not considering the multiple conformations of the ligand in solution- can be tackled. A simple way to get multiple conformations of a ligand in solution is to do a conformational search. Assuming that the search is "complete", one can then calculate the conformational entropy penalty that the ligand has to pay in order to sacrifice all conformations except one in which it binds to the protein. There has been an implicit way to take this into account- many docking programs include a penalty of 0.65 kcal/mol per frozen rotatable bond. But clearly this penalty may be quite less if there are hundreds of conformations in solution that would lead to a large conformational penalty.

Now a group from Amgen has done such multi-conformational MMGBSA rescoring for four important targets and their ligands- CDK2, Thrombin, Factor Xa and HIV-RT. They compare scores obtained with Schrodinger's GlideXP routine with experimental binding affinities. Then they compare scores obtained with MMGBSA rescoring either with a single ligand conformer representation or with a multiple conformer representation that takes ligand conformational entropy into account. The comparison between single and multiple conformers gives somewhat mixed results and sometimes the single conformer representation also does fairly well; however, one thing is strikingly clear, that MMGBSA rescoring can radically improve correlation with experimental affinities compared to simple GlideXP scoring. In some cases the correlation coefficient jumps from essentially 0.00 to a whopping (by current standards) 0.75. There is a lot of interesting methodology described in the paper worth taking a look at. But it's quite clear how including some of the explicit physical effects involved in protein-ligand binding can substantially improve correlation with experiment. In this case the extra effort expended is a fraction of the cost involved in FEP calculations and the methods can also tackle more diverse ligands.

Even if we are not close to conquering the free energy fort, at least we seem to be getting concrete footholds on it.

Guimaraes, C.R., Cardozo, M. (2008). MM-GB/SA Rescoring of Docking Poses in Structure-Based Lead Optimization. Journal of Chemical Information and Modeling, 48(5), 958-970. DOI: 10.1021/ci800004w

Computational modeling of GPCRs: not too bad

GPCRs constitute one of the most important family of proteins in our body, both for their innate importance in signal transduction and neurotransmission, and as important targets for drugs. Many of the important drugs on the market today target GPCRs. And yet there is an unusual gap between knowledge and application when it comes to this important family. That's because only two crystal structures of GPCRs are known. And one of them was derived last year, so there's been a real dearth of structural information about GPCRs for a long time.

We do know something about many GPCRs, however. We know that they are 7-TM receptor-spanning proteins. And the two structures we do know about shed valuable insight on GPCR function. One is rhodopsin which has been around for a while. Then there was big news last year about the second important GPCR whose structure was determined- the ß-2 adrenergic receptor.

Given the paucity of structural information and the availability of two structures, a logical question is whether computational modeling can teach us something new about GPCRs whose structure is unknown. To this end, Stefano Costanzi at the NIH did a nice set of experiments which he published in J. Med. Chem. He attempted to build a homology model of the adrenergic receptor based on the sequence and structure of rhodopsin. Since we now have a crystal structure of the adrenergic GPCR, we have something concrete to compare modeled structures and ligand orientations to.

Costanzi was particularly interested in knowing how a small molecule-carazolol- binds to the modeled GPCR. This is important both from a structural and functional drug-discovery point of view. His results indicate that we can do pretty well. In essence, he built two models of the receptor, one of them de novo. While the models were similar to rhodopsin in the conserved regions, the important differences were with respect to a loop that flaps on top of the protein. In one model the loop was buried inside the binding pocket, and in the other one it was open. Docking of carazolol into the buriled-loop model using the Glide program from Schrodinger gave a binding pose in which the ligand was, not surprisingly, buried deeper into the cavity compared to the crystal structure. This was naturally the effect of the loop blocking part of the pocket. The other model in which the loop was not buried gave much better results. Curiously, the ligand was buried a little deep in the pocket even in this model, even though it was much less buried compared to the previous one. It still misaligned considerably with the experimental pose. Inspection revealed that there was a Phe in the pocket which was anti in the model but +gauche in the crystal structure. Since the corresponding residue in rhodopsin was Ala, there was no way this unusual conformation could have been predicted ab initio. Fixing the conformation of this residue to +gauche suddenly gave excellent alignment with the ligand orientation in the crystal structure.

An instructive piece of work that shows that homology modeling and docking of ligands into GPCRs of unknown structure can be fruitful. However, it also indicates caveats like the Phe conformation which are hard to account for de novo. However, since structures of members in this important family of proteins are unavailable anyway, even some predictive ability might be welcome in this area.

Costanzi, S. (2008). On the Applicability of GPCR Homology Models to Computer-Aided Drug Discovery: A Comparison between In Silico and Crystal Structures of the ß2-Adrenergic Receptor. Journal of Medicinal Chemistry DOI: 10.1021/jm800044k

A relatively rare example of docking-based virtual screening

Many studies published in the last few years have demonstrated that in general, ligand-based methods are better for virtual screening compared to structure-based docking methods. For example, a 2007 Merck study showed that 2-D similarity searching methods are quite good for finding similar leads, while 3-D methods can do some scaffold hopping and find new families of structures. Both methods are generally superior to docking. One of the reasons for this is that docking is not really designed for virtual screening; docking is much more valuable for prediction of crystallographic conformations and most importantly, predicting binding affinity, which is the holy grail of the industry. The latter task is still extremely challenging, although dents have been made in tackling it.

In any case, so this group from Vertex tackled a kinase inhibitor search problem for Pim-1 kinase using docking, and this seems to be one of those cases where docking with Schrodinger's Glide program helped complement and indeed improve upon HTS. The group screened a large database enriched in kinase inhibtors by HTS and got only a 0.3% hit rate. They decided to find out if VS could do better. They used Glide to screen a corporate collection that was less enriched in kinase inhibitors, to avoid bias. They used Glide not in the VS mode but the regular docking mode which takes more time but is more accurate. They used some astute filters to avoid getting false hits from large molecules that fit better in the site. They also used an C-H aromatic hydrogen bond constrain in the docking.

After screening out compounds that were too large and hydrophobic, they got 4 compounds (a 4% hit rate) with activities ranging from 90 nM to 550nM. Two of these could be crystallised and it was confirmed that the experimental conformation was very close to the predicted binding conformation. Glide also picked up the "weak" C-H aromatic hydrogen bond. The authors conjecture that the reason why Glide chose this H-bond is because the traditional hinge region of Pim-1 kinase is more hydrophobic than that in other kinases because of a proline residue. The study demonstrates how VS can serve as a valuable complement to HTS.

Pierce, A.C., Jacobs, M., Stuver-Moody, C. (2008). Docking Study Yields Four Novel Inhibitors of the Protooncogene Pim-1 Kinase. Journal of Medicinal Chemistry DOI: 10.1021/jm701248t

Turning a false-positive into an active

People who deal with molecular recognition are well aware of what difference a small modification to a molecule can make. Just today I was attending a talk by a chemist who binds small molecules to RNA aptamers. He showed an aptamer that binds theophylline with 10,000 fold more affinity by caffeine- a huge difference in binding affinity for a molecule differing by only one methyl.

So it is also for medicinal agents, as demonstrated below for an example from the cited study. People who do screening must always have this nagging doubt about false positives; what if there is only a slight modification to a false positive that will convert it into an active?



Bill Jorgensen's group has done a similar study for an anti-RT HIV inhibitor. He first did similarity searching with the Maybridge library based on six known NNRTI inhibs of RT. Based on this, he found a couple of molecules in the library which he then docked into the active site of RT using the program GLIDE. Along with the six known inhibitors which scored at the top as binders, he also found one from the library. GLIDE had already been benchmarked by reproducing known crystallographic conformations.

However, when they tested this GLIDE ranked molecule against HIV, it was disappointingly inactive. On the other hand, perhaps, since GLIDE had docked it up there with the known actives, there might be a small modification that one could make to it which would inject some activity in it? Jorgensen's group used a program that they have developed named BOMB, which basically docks a molecule in an active site, and then grows appendages to it to see if it would make a difference in the binding affinity. BOMB tried out combinations of different groups on the phenyl ring of the molecule, scored the resulting structures using its energy function, and finally settled on one particular modified structure- also filtered by logP values and other Lipinski considerations- that eventually gave an IC50 of 300 nM. Not a fantastic number, but good enough to pursue as a lead.

Also noteworthy in the paper is a short discussion of another publication where a similar structure was published. According to the authors, the other authors assayed the wrong compound. Heh.

Reference:
From Docking False-Positive to Active Anti-HIV Agent
Gabriela Barreiro, Joseph T. Kim, Cristiano R. W. Guimarães, Christopher M. Bailey, Robert A. Domaoal, Ligong Wang, Karen S. Anderson, and William L. Jorgensen
Web Release Date: 06-Oct-2007; (Article) DOI: 10.1021/jm070683u

The BI guys should have used Glide XP Dock

In the last post, I was wondering why the BI guys did not use any docking to conjecture the binding mode of their new p38 inhibs. While docking is not a foolproof predictor, it can shed light on possible anomalous modes. Particularly interesting was this observation about the benzothiophene sulfur reversing its trans preference to become cis to the adjacent amide oxygen. This counterintuitive observation was later explained by alluding to the glutamate that would have had an unfavourable electrostatic interaction with the sulfur had it been trans to the oxygen. The observation was revealed by the crystal structure. However, before the crystal structure was obtained, they went through the design and synthesis of two compounds based on the reasonable hypothesis that the sulfur would be trans. It was only after their puzzlement with the failure of these designed compounds that the situation became clear through crystallography.

Well, the observation is also revealed by Glide XP docking, and I think this could have saved them some time. I first duplicated the X-ray pose of the earlier BIRB compound in p38 (1KV2 PDB id), and then docked the new compound in. The result; the binding score was still good, if not as good as for BIRB. But the important fact was that all the top 5 docking poses from Glide indicated the sulfur to be cis to the oxygen and away from the Glu, just as in the crystal. In fact, even the fragment docked in the same position as the crystal structure indicated, with the sulfur cis. Not totally surprising if electrostatic interactions are well parametrized and recognised by the scoring function. A further advancement where polarization effects are taken into account during docking would help a lot (This is in the works)

This was one case in which docking could have said basically the same thing that the crystal structure did. In this case, docking could have saved them the design and synthesis of two extra compounds based on a misleading hypothesis, and perhaps additional head-scratching validated by crystallography. On a related note, Glide is pretty well-parametrized on a couple of kinases, including Lck, CDK2, and p38.

Schrodinger's equation

A friend of mine just returned from a conference in New York organised by Schrodinger, and I have to say that Schrodinger really seems to be poised to be the one-stop shop for all things computational.

They already have some great programs in their Maestro suite, including Glide for docking, which you find folks in industry using more and more these days. In their next revisions, they are going to introduce a program named PrimeX for doing crystallography, which will perform analysis similar to CNS, which will be groovy if it brings such analysis to the desktop. They are also going to introduce electron-density fitting for loop refinement in proteins. Right now, loop refinement of, say a 10 residue loop takes forever. But with PrimeX and friends, one can have constraints effected by electron density to restrict conformational searching, thus greatly speeding up the process.

Other products include the very impressive new Glide XP docking protocol. I have been glued to their site ever since they published their admirable paper in 2006. I have already written about the capabilities of GlideXP. This is really the best of computational chemistry applied to docking, where you find chemists trying to include as many experimental parameters as they can in a program. Schrodinger is definitely one company whose chemists have a firm and steady hand on experimental variables.

A very important development is going to be the interfacing of William Jorgensen's MCPRO, a program for doing free energy perturbation (FEP) calculations. FEP calculations are as close as you can come to accurately reproducing experimental binding free energies, one of the holy grails of computational methodology. While GlideXP astoundingly claims to also be able to do that, it would be super to have a GUI and easy operability for a good FEP program at your fingertips. Admittedly, FEP works only for ligand which differ little in their structure (eg. Me vs H). But that's also the phenomenon which we understand the least, how "similar" ligands can have great differences in binding affinity, something which FEP should help us understand.

Other improvements will include better parameters in standard docking, and a new force field, OPLS 2008, which will be "better than MMFF". Considering that the force behind this field is Tom Halgren, the same guy who meticulously crafted MMFF, I would be looking forward to it. There is also talk of a new MD program comparable to Gromacs, AMBER etc. which can do millisecond MD efficiently. That would probably complete the list of capabilities in one program that almost any computational chemist could want.

What I like best about Schrodinger is that it has people at its helm who are among the best that computational chemistry has to offer, most importantly Richard Friesner and Tom Halgren. Looking at their papers, it's clear that like ideal computational chemists, they thoroughly understand experimental data, and clearly know what the limitations of their programs are.