So what exactly are force fields good for?

Sue Storm tries hard to use her favorite force field to counter the 1 kcal/mol barrier



Every once in a while there is a study asking what method X (X = docking, free energy calculations, molecular dynamics, force fields etc.) is good for. Such studies can be useful to take stock of a particular paradigm. So the question that Jonathan Goodman and his group ask in this paper is "Are force fields good for reproducing non-bonded interactions, especially hydrogen bonding, pi-stacking and dispersion?". He and his group compare very high-level quantum chemical ab initio data with data obtained from the most commonly used force fields, namely MM2*, MM3*, MMFFs, OPLS-2005 etc. The ab initio data used is from Pavel Hobza who has almost consummately published on these methods. The question is; how well do the force fields do compared to the gold standard? The answer is necessarily incomplete and complex and again raises many interesting questions about the enigmatic role of hydrogen bonding in chemical and biological systems.

The complexes studied include purely pi-stacked complexes, purely hydrogen bonded complexes and mixed complexes where both interactions play roles. Typical examples include alcohol-amide complexes, water oligomers and of course, the classic stacked and hydrogen bonded DNA nucleoside bases. The parameters that the authors looked at were geometries and energies, both of optimized complexes as well as crystal structures.

The results are perhaps not too surprising; the more recent OPLS-2005 and MMFFs are probably the best in reproducing known geometries and energies while MM2* and MM3* don't perform that well in general. As noted in some other studies, at least some of the results for MMFFs and OPLS compare with those obtained with high-level ab initio calculations, thus indicating the value of these cost-effective methods for geometry optimization and energy determination (let's ignore for a moment that solvation models in ab initio methods make even these less than perfect).

What is more important though is that all the force fields are generally not good for reproducing hydrogen bonded systems compared to systems where dispersion, stacking etc. are the key players. This is partly an indication of the tricky events including long-range solvation which play an important role in h-bond formation. But what is interesting is that the methods underestimate the energetics of hydrogen bonds. While I am a little puzzled by this, one of the explanations that comes to my mind regarding this curious fact is that in real systems, h-bonding is a cooperative interaction. An h-bond can pay for loss of entropy, thus making the overall free energy of the next h-bond more favourable. Of course force fields don't calculate free energy, but to a first approximation we can probably assume that the enthalpy and free energy are similar for these simple systems. To be honest, because of the complex nature of long-range dispersion interactions I would have assumed that the force fields would be worse in modeling these. I frankly don't understand why they work better for such interactions but it's an interesting observation.

But now for some general thoughts; it's always worth remembering that for molecules like proteins which are stabilized by h-bonds, the h-bonds when formed are simply swapped for similar bonds with water, thus making a relatively insubstantial contribution to protein stability. It is the large number of such interactions that can tip the balance for a protein, but the real driving force is now universally recognized as the hydrophobic effect and the burial of non-polar groups. Calculations such as those above indicate that because of the fine-tuning of h-bonds that proteins often use to achieve stability, force fields have some way to go in predicting tiny energy differences. It is still a great challenge to model the sub-angstrom geometry optimization of h-bonds that biopolymers achieve. But force fields are hardly unique in not being able to do this; so are other methods which are still trying to break the 1 kcal/mol barrier. Ironically in this study, the mean unsigned error when the hydrogen-bonded complexes are included is about 1 kcal/mol.

So are force fields good for anything at all? The short answer is yes, exemplified by the massive number of publications that regularly use force fields as well as the substantial number of people in academia and industry studying them. Obviously people think they are important, otherwise so many common programs doing everything from protein folding to drug-protein interactions would not have relied on them. I have had reasonable experience with force fields and have always kept in mind a couple of things about them that are worth reiterating:

1. Force fields are usually good at reproducing geometries, and best for reproducing sterics.
2. Force fields are usually not so good at reproducing energies since energy estimation is a function of the special parameterization and convergence criteria unique to every force field (As the Zen master says, "What the answer is depends on what question you ask"). However, relative conformational energies using a single force field for instance may be useful.
3. As a corollary, force fields can be pretty poor for dealing with molecules having a large number of polar functional groups. While this means that peptides are hard to model, modeling of peptides has also been mitigated by the fact that unlike small molecules, the chemistry to be parameterized is limited.
3. Many times the real problem is not with force fields per se but with the accompanying implicit solvation models. Admirable effort has been expended in developing these models but to be honest we still don't understand enough about that enigmatic solvent named water to do a satisfactory job. We are just scratching the surface when it comes to modeling things like solvent entropy for instance.

If you are following the field's developments, you also see an engaging and ongoing debate that pits the "science first" camp against the "parameterization first" camp. The science first camp disapproves of the other camp's efforts to improve their force fields simply by adding more parameters and optimizing against experiment; to them it is much more important to meticulously improve the methodology by incorporating as much real science as possible. The parameterization first camp argues that statistical methods have their honored place in the annals of science and that getting results fast and efficiently is important for application-oriented scientists like drug discovery people. I believe that as in other matters, both sides are right. It is an uncomfortable feeling when you don't truly understand the science behind a method and yet the method works, but at the same time it is important to have a well-parameterized and tested model that could help you in a practical sense, even if incompletely understood.

As with everything else, finally it is an astute application of force fields that takes into account their strengths and limitations which will lead to productive results. One of the most interesting things about doing science involves weighing the pros and cons of methods, techniques and algorithms and deciding what judicious combination would provide the best answer and why. It may not always work, but it could keep us from getting seduced by the dark side of the force (field)

Paton, R., & Goodman, J. (2009). Hydrogen Bonding and π-Stacking: How Reliable are Force Fields? A Critical Evaluation of Force Field Descriptions of Nonbonded Interactions Journal of Chemical Information and Modeling, 49 (4), 944-955 DOI: 10.1021/ci900009f