Brenner, von Neumann and Schrödinger

Erwin Schrödinger's book, "What is Life"?, inspired many scientists like Crick, Watson and Perutz to go into molecular biology. While many of the details in the book were wrong, the book's central message that the time was ripe for a concerted attack on the structure of the genes based on physical principles strongly resonated.

However, influence and importance are two things, and unfortunately the two aren't always correlated. As Sydney Brenner recounts in detail here, the founding script for molecular biology should really have been John von Neumann's 1948 talk at Caltech as part of the Hixon Symposium, titled "The General and Logical Theory of Automata". In retrospect this talk was seminal and far-reaching. Brenner is one of the very few scientists who seems to have appreciated that von Neumann's influence on biology was greater than Schrödinger's and that von Neumann was right and Schrödinger wrong. Part of the reason was that while many biologists like Crick and Watson had read Schrödinger's "What is Life?", almost nobody had read von Neumann's "General and Logical Theory of Automata".

As Brenner puts it, Schrödinger postulated that the machinery for replication (chromosomes) also included the means of reproducing it. Von Neumann realized that the machinery did not include the means themselves but only the *instructions* for those means.

That's a big difference; the instructions are genes, the means are proteins. In fact as Freeman Dyson says in his "Origins of Life", von Neumann was the first to clearly realize the distinction between software (genes) and hardware (proteins). Why? Because as a mathematician and a generalist (and pioneer of computer science), he had a vantage point that was unavailable to specialist biologists and chemists in the field.

Unfortunately abstract generalists are often not recognized as the true originators of an idea. It's worth noting that in his lecture, von Neumann laid out an entire general program for what we now call translation, five years before Watson, Crick, Franklin and others even solved the structure of DNA. The wages of the theoretician are sparse, especially those of the one, as mathematician John Casti put it, who solves "only" the general case.

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

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.