Improvements in the OPLS3 Force Field
Realistic atomistic simulation of complex molecular systems is contingent upon the availability of an accurate and reliable molecular mechanics force field. The treatment of systems of interest in biology and materials science typically requires models on the order of thousands to millions of atoms, and timescales from nanoseconds to seconds; even at the low end of both of these ranges, purely quantum mechanical dynamics is extremely expensive (and not necessarily more accurate, as quantum chemical methods that are tractable for systems of this size have deficiencies of their own). Hence, molecular mechanics force field development has been a central goal of computational chemistry for the past four decades.
OPLS (optimized potentials for liquid simulations) first developed by Jorgensen and coworkers,1,2 was one of the first models in which parameters were extensively optimized to reproduce liquid state thermodynamic properties for a variety of small organic molecules. This effort yielded a core set of nonbonded (van der Waals) parameters, which still remain at the heart of OPLS development. OPLS33 represents a next generation model that builds upon this OPLS framework with the following key improvements:
A. Valence and Torsion Parameters
Extensive use of high-quality quantum chemical calculations to generate more accurate valence and torsional parameterizations. The OPLS3 model contains nearly two orders of magnitude more explicitly fit torsional parameters than alternative small molecule force fields leading to greater accuracy in modeling small molecule conformational barriers and propensities:
Table 1. Distribution of RMS error with respect to QM over the 11845 torsion profiles.
|Model||%<1.0 kcal/mol||%>1.0 and <2.0 kcal/mol||%>2.0 kcal/mol|
B. Parameterization of Bond Charge Correction Terms (BCC)
The OPLS3 force field employs a CM1A-BCC based charge model based on a combination of Cramer-Truhlar CM1A charges1 with an extensive parameterization of bond charge correction terms (BCC). In OPLS3, we also introduce virtual (off-atom centered) sites to better represent lone pair and sigma hole charge distributions. Overall, these improvements improve the modeling of key interactions (Figure 1) and are reflected in the observed high level of accuracy seen across an expansive set of aqueous solvation free energies.2,3
Figure 1. Interaction energy between aryl chloride and carbonyl oxygen comparing QM to OPLS2.1 and OPLS3. The halogen bond gives ride to an attractive interaction at close distances which is captured with the addition of a virtual charge site for the aryl chloride in OPLS3.
Table 2. Error summary for hydration free energy results for 239 small molecules.
% > 2 kcal/mol
aValues for ChelpG/CHARMM and AM1-BCC/GAFF, OPLS_2005 and OPLS2.0/2.1 are those reported in Shivakumar et al.
C. Quantum Chemical and Training Simulation Data
For predictive biomolecular simulation, the protein force field must be refined to a very high degree of accuracy and stability. Small errors in, for example, the torsional potential of the protein dihedral angles, can translate into significant disagreements with experiment, ranging from discrepancies in the prediction of NMR spectra to incorrect prediction of the stability of proteins and peptides. OPLS3 incorporates a greatly increased amount of quantum chemical data, and training to simulation data as compared with experiment, leading to significant improvements in the representation of secondary structure elements in simulated peptides and native structure stability over a number of proteins.
Table 3. Average RMS difference with respect to X-ray or NMR structure.
D. Protein-Ligand Binding
Together, the improvements made to both the small molecule and protein force field lead to a high level of accuracy in predicting protein-ligand binding measured over a wide range of targets and ligands (less than 1 kcal/mol RMS error) representing a 30% improvement over earlier variants of the OPLS force field.
Table 4. Relative binding free energy results.a
|Weighted Average||1.28 +/- 0.06||1.11 +/- 0.05||0.95 +/- 0.04|
aIncludes root mean square error (RMSE) reported in kcal/mol and square of the correlation coefficient (R2). Uncertainty in weighted average RMSE calculated based on bootstrapping method.
Case Study 1: Impact of an Improved Protein Force Field on Protein-Ligand Binding
Experimental versus FEP-predicted binding free energies over 6 BACE ligands distinguished by their R1 substituent. Left panel shows the binding mode of the methoxy derivative indicating the position of the functional group varied across the series. Binding affinities as a function of the R1 functional group shown in the middle panel. At right, representative structures, taken from simulations of OPLS2.1 and OPLS3, of the Ala396 residue and its associated helix, which enclose the S3 pocket of the BACE1 binding site.
Case Study 2: Impact of an Improved Charge Model on Protein-Ligand Binding
Sub-set of FXA series ligands illustrating electron rich receptor environment from the carboxylate of Asp189 and the backbone carbonyl of Gly219 coordinating aryl nitrogen lone pairs of 17i and 17h. Binding free energies relative to 17d are tabulated in Table.
Table 5. Experimental and predicted relative binding free energies for FXA ligands.a
|17d → 17i||3.9||0.5||2.1|
|17d → 17h||4.9||1.0||3.9|
aFree energies are in kcal/mol. Specified ligands are illustrated in Figure 8. Ligand names are taken from Chan et al.71
- Jorgensen, W. L.; Maxwell, D. S.; Tirado-Rives, J., Development and testing of the OPLS all-atom force field on conformational energetics and properties of organic liquids. J. Am. Chem. Soc., 1996, 118, 11225-11236.
- Harder, E. et al., OPLS3: A Force Field Providing Broad Coverage of Drug-like Small Molecules and Proteins. J. Chem. Theory Comput., 2016, 12(1), 281–296.
- Storer, J. W.; Giesen, D. J.; Cramer, C. J.; Truhlar, D. G., Class IV charge models: a new semiempirical approach in quantum chemistry. J. Comput. Aided. Mol. Des., 1995, 9(1), 87-110.
- Shivakumar, D.; Harder, E.; Damm, W.; Friesner, R. A.; Sherman, W. J., Improving the Prediction of Absolute Solvation Free Energies Using the Next Generation OPLS Force Field. J. Chem. Theory Comput., 2012, 8, 2553–2558.