Biomolecular force fields: where have we been, where are we now, where do we need to go and how do we get there?

Abstract

In this perspective, we review the theory and methodology of the derivation of force fields (FFs), and their validity, for molecular simulations, from their inception in the second half of the twentieth century to the improved representations at the end of the century. We examine the representations of the physics embodied in various force fields, their accuracy and deficiencies. The early days in the 1950s and 60s saw FFs first introduced to analyze vibrational spectra. The advent of computers was soon followed by the first molecular mechanics machine calculations. From the very first papers it was recognized that the accuracy with which the FFs represented the physics was critical if meaningful calculated structural and thermodynamic properties were to be achieved. We discuss the rigorous methodology formulated by Lifson, and later Allinger to derive molecular FFs, not only obtain optimal parameters but also uncover deficiencies in the representation of the physics and improve the functional form to account for this physics. In this context, the known coupling between valence coordinates and the importance of coupling terms to describe the physics of this coupling is evaluated. Early simplified, truncated FFs introduced to allow simulations of macromolecular systems are reviewed and their subsequent improvement assessed. We examine in some depth: the basis of the reformulation of the H-bond to its current description; the early introduction of QM in FF development methodology to calculate partial charges and rotational barriers; the powerful and abundant information provided by crystal structure and energetic observables to derive and test all aspects of a FF including both nonbond and intramolecular functional forms; the combined use of QM, along with crystallography and lattice energy calculations to derive rotational barriers about ɸ and ψ; the development and results of methodologies to derive "QM FFs" by sampling the QM energy surface, either by calculating energies at hundreds of configurations, or by describing the energy surface by energies, first and second derivatives sampled over the surface; and the use of the latter to probe the validity of the representations of the physics, reveal flaws and assess improved functional forms. Research demonstrating significant effects of the flaws in the use of the improper torsion angle to represent out of plane deformations, and the standard Lorentz-Berthelot combining rules for nonbonded interactions, and the more accurate descriptions presented are also reviewed. Finally, we discuss the thorough studies involved in deriving the 2nd generation all-atom versions of the CHARMm, AMBER and OPLS FFs, and how the extensive set of observables used in these studies allowed, in the spirit of Lifson, a characterization of both the abilities, but more importantly the deficiencies in the diagonal 12-6-1 FFs used. The significant contribution made by the extensive set of observables compiled in these papers as a basis to test improved forms is noted. In the following paper, we discuss the progress in improving the FFs and representations of the physics that have been investigated in the years following the research described above.