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

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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.

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Fig. 1

Reproduced with permission from Debiec et al. [58]

Fig. 2

Reproduced with permission from Huang et al. supplementary material [65]

Fig. 3

Reproduced with permission Graphical abstract. Schmollngruber et al. [149]

Fig. 4
Fig. 5

Similar content being viewed by others

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

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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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    Present address: Valis Pharma, San Diego, CA, USA

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  1. Department of Chemistry, University of Massachusetts, Amherst, MA, 01003, USA

    A. T. Hagler

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Hagler, A.T. Force field development phase II: Relaxation of physics-based criteria… or inclusion of more rigorous physics into the representation of molecular energetics. J Comput Aided Mol Des 33, 205–264 (2019). https://doi.org/10.1007/s10822-018-0134-x

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