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Journal of Computer-Aided Molecular Design

, Volume 33, Issue 2, pp 133–203 | Cite as

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

  • Pnina Dauber-Osguthorpe
  • A. T. HaglerEmail author
Perspective

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.

Keywords

Force fields: force field derivation Potential functions van der Waals Hydrogen bond: drug discovery Molecular dynamics Molecular mechanics Protein simulation Molecular simulation Nonbond interactions Combination rules Polarizability Charge flux Nonbond flux Polarizability flux Free energy Coupling terms Cross terms AMBER Charmm OPLS GAFF AMOEBA SDFF CFF VFF Consistent force field Electrostatics Multipole moments Quantum derivative fitting QDF 

Abbreviations

AG

Arithmetic–geometric

Ala

Alanine

AMBER

Assisted model building with energy refinement

AMOEBA

Atomic multipole optimized energetics for biomolecular applications

BNS

Ben Naim–Stillinger

CFF

Consistent force field

CHARMM

Chemistry at HARvard Macromolecular Mechanics

CNDO

Complete neglect of differential overlap

COMPASS

Condensed-phase optimized molecular potentials for atomistic simulation studies

CVFF

Consistent valence force field

DFT

Density functional theory

ECEPP

Empirical conformational energy program for peptides

EHT

Extended Huckel theory

FF

Force field

FQ

Fluctuating charges

Gly

Glycine

GROMOS

GROningen MOlecular Simulation

Hyp

Hydroxyproline

LCAO

Linear combination of atomic orbitals

LJ

Lennard-Jones

LSQ

Least squares

MC

Monte Carlo

MCMS FF

Momany, Carruthers, McGuire, and Scheraga Force Field

MCY

Matsuoka–Clementi–Yoshimine

MD

Molecular dynamics

MDDR

MDL drug data report

MDL

Molecular design limited

MM

Molecular mechanics

MMFF

Merck molecular force field

NMA

N-methylacetamide

OPLS

Optimized potential for liquid simulations

OPLS-AA

OPLS-AA/L OPLS all atom FF (L for LMP2)

PCILO

Perturbative configuration interaction using localized orbitals

PDB

Protein data base

PEFC

Potential energy function consortium (Biosym)

QCPE

Quantum chemistry program exchange

QDF

Quantum derivative fitting

QDP

Charge dependent polarizability

QM

Quantum mechanics

RESP

Restrained electrostatic potential

RMS

Root mean square

RMSD

Root mean square deviation

SCF-LCAO-MO

Self-consistent field-linear combination of atomic-molecular orbital (wave function)

SDFF

Spectroscopically determined force fields (for macromolecules)

SPC

Simple point charge (water model)

ST2

Four point water model replacing Ben-Naim Stillinger (BNS) model

STO

Slater-type atomic orbitals

TIP3P

Transferable intermolecular potential (functions for water, alcohols and ethers)

TTBM

Tri-tert-butylmethane

UB

Urey–Bradley

VDW

van der Waals

VFF

Valence force field

WH

Waldman–Hagler

Notes

Acknowledgements

We would like to thank Dr. Mike Gilson, for reading parts of the manuscript and helpful discussions and Dr. Ruth Sharon for reading, discussing and valuable help with editing. We also thank Eitan Hagler for help with the figures. Special thanks to the editor, Dr. Terry Stouch for his invitation to write this perspective, encouragement, and endless patience.

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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of ChemistryUniversity of MassachusettsAmherstUSA
  2. 2.Art Pearl StudiosNewlynUK
  3. 3.Valis PharmaSan DiegoUSA

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