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Journal of Computer-Aided Molecular Design

, Volume 33, Issue 2, pp 205–264 | Cite as

Force field development phase II: Relaxation of physics-based criteria… or inclusion of more rigorous physics into the representation of molecular energetics

  • A. T. HaglerEmail author
Perspective

Abstract

In the previous paper, we reviewed the origins of energy based calculations, and the early science of FF development. The initial efforts spanning the period from roughly the early 1970s to the mid to late 1990s saw the development of methodologies and philosophies of the derivation of FFs. The use of Cartesian coordinates, derivation of the H-bond potential, different functional forms including diagonal quadratic expressions, coupled valence FFs, functional form of combination rules, and out of plane angles, were all investigated in this period. The use of conformational energetics, vibrational frequencies, crystal structure and energetics, liquid properties, and ab initio data were all described to one degree or another in deriving and validating both the FF functional forms and force constants. Here we discuss the advances made since in improving the rigor and robustness of these initial FFs. The inability of the simple quadratic diagonal FF to accurately describe biomolecular energetics over a large domain of molecular structure, and intermolecular configurations, was pointed out in numerous studies. Two main approaches have been taken to overcome this problem. The first involves the introduction of error functions, either exploiting torsion terms or introducing explicit 2-D error correction grids. The results and remaining challenges of these functional forms is examined. The second approach has been to improve the representation of the physics of intra and intermolecular interactions. The latter involves including descriptions of polarizability, charge flux aka geometry dependent charges, more accurate representations of spatial electron density such as multipole moments, anisotropic nonbond potentials, nonbond and polarization flux, among others. These effects, though not as extensively studied, likely hold the key to achieving the rigorous reproduction of structural and energetic properties long sought in biomolecular simulations, and are surveyed here. In addition, the quality of training and validation observables are evaluated. The necessity of including an ample set of energetic and crystal observables is emphasized, and the inadequacy of free energy as a criterion for FF reliability discussed. Finally, in light of the results of applications of the two approaches to FF development, we propose a “recipe” of terms describing the physics of inter and intramolecular interactions whose inclusion in FFs would significantly improve our understanding of the energetics and dynamics of biomolecular systems resulting from molecular dynamics and other energy based simulations.

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 Anisotropic nonbond potentials 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

AUE

Absoluter unsigned error

BCC

Bond charge correction

BNS

Ben Naim–Stillinger

C22

CHARMM22

CASP

Critical assessment of protein structure prediction

CFF

Consistent force field

CHARMM

Chemistry at HARvard Macromolecular Mechanics

CHELPG

Charges from electrostatic potentials using a grid-based method

CHEQ

Charge equilibration method

CMAP

Grid based energy correction map

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

DMA

Distributed multipole analysis

DZVP

Valence double-zeta plus polarization

ECEPP

Empirical conformational energy program for peptides

EHT

Extended Hückel theory

ESP

Electrostatic potential

EVB

Empirical valence bond

FEP

Free energy perturbation

FF

Force field

FQ

Fluctuating charges

FRET

Forster resonance energy transfer

GAFF

General AMBER force field

Gly

Glycine

GROMOS

GROningen MOlecular Simulation

hCatL

human Cathepsin L

HF-SCF

Hartree–Fock self-consistent-field

Hyp

Hydroxyproline

IDP

Intrinsically disordered protein

LCAO

Linear combination of atomic orbitals

LJ

Lennard-Jones

LP

Oxygen lone pair

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

MEP

Molecular electrostatic potentials

MM

Molecular mechanics

MMFF

Merck molecular force field

NMA

N-methylacetamide

OPLS

Optimized potential for liquid simulations

OPLS-AA

OPLS all atom

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)

PMF

Potential of mean force

POL3

Polarizable water model (3)

PPII

Polyproline II conformation

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

RMSE

Root mean square error

SAMPL

Statistical assessment of the modeling of proteins and ligands (competition)

SAXS

Small angle X-ray scattering

SCF-LCAO-MO

Self-consistent field-linear combination of atomic–molecular orbital

SDFF

Spectroscopically determined force fields (for macromolecules)

SIBFA

Sum of interactions between fragments ab initio (computed)

SPC

Simple point charge (water model)

ST2

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

STO

Slater-type atomic orbitals

SWM4-NDP

Simple water model with negative Drude polarization

TIP3P

Transferable intermolecular potential three point

TTBM

Tri-tert-butylmethane

TZVP

Triple-zeta plus valence polarization (basis set)

UB

Urey–Bradley

UBFF

Urey Bradley force field

VDW

Van der Waals

VFF

Valence force field

WH

Waldman–Hagler

Notes

Acknowledgements

We would like to thank Drs. Mike Gilson, Sam Krimm, Alex MacKerell, Benoit Roux, Pengyu Ren, Jay Ponder, Ken Dill, Kim Palmo, Pnina Dauber-Osguthorpe, for reading parts of manuscript and helpful discussions and Dr. Ruth Sharon for reading and help with editing. We also thank Eitan Hagler for help with the figures, Martha Obermeier for help with proofing and referee 1 who made many helpful suggestions including the addition of the effect of methodology in FF derivation. 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.Valis PharmaSan DiegoUSA

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