Building a More Predictive Protein Force Field: A Systematic and Reproducible Route to AMBER-FB15

Abstract

The increasing availability of high-quality experimental data and first-principles calculations creates opportunities for developing more accurate empirical force fields for simulation of proteins. We developed the AMBER-FB15 protein force field by building a high-quality quantum chemical data set consisting of comprehensive potential energy scans and employing the ForceBalance software package for parameter optimization. The optimized potential surface allows for more significant thermodynamic fluctuations away from local minima. In validation studies where simulation results are compared to experimental measurements, AMBER-FB15 in combination with the updated TIP3P-FB water model predicts equilibrium properties with equivalent accuracy, and temperature dependent properties with significantly improved accuracy, in comparison with published models. We also discuss the effect of changing the protein force field and water model on the simulation results.

Figure 1.

Plot of the potential energy in alanine dipeptide calculated for energy-minimized structures at the MP2/aug-cc-pVTZ level with the (φ,ψ) dihedral angles constrained. Color indicates the relative potential energy with respect to the minimum.

Figure 2.

MM vs. QM potential energies for MM-optimized geometries of threonine dipeptide. Each data point corresponds to a local energy minimum predicted by the force field. The Cycle 1 parameters were fitted to QM data from the torsion scans only. The QM data points at the local minima of Cycle 1 are added to the optimization of the Cycle 2 parameters. Cycle 3 is the final parameter set. The spurious MM energy minima (points far below the diagonal line) are eliminated in later cycles.

Figure 3.

Time series of RMSD to the experimental crystal structure for three proteins and four simulations. The right panels show Gaussian kernel density estimates of the RMSD values. The diamond markers indicate the RMSD to the crystal structure using the Cartesian-averaged protein backbone conformations over the whole simulation.

Figure 4.

Lipari-Szabo S² order parameters and error residuals compared to experimental NMR measurements. The root-mean-squared error (RMSE) and mean signed error (MSE) of the simulated observables with respect to experiment are given in the legends. The background of the error residual plots are colored according to secondary structure as determined by DSSP analysis (white, helix; light gray, coil; dark gray, strand).

Figure 5.

Scatter plots of experimental vs. calculated NMR three-bond scalar couplings. Two proteins are shown (left: bacteriophage lysozyme, PDB ID 1AM7, right: GB3, PDB ID 1IGD) and three models (top, AMBER99SB-ildn/TIP3P; middle, AMBER99SB-nmr/TIP3P; bottom, AMBER-FB15/TIP3P-FB from this work.) Symbols represent the atom pair involved in the coupling, and colors represent the position of the residue in the protein sequence.

Figure 6.

Temperature dependence of secondary structure for two small peptides as a function of temperature and several force field / water model combinations. The performance of the AMBER-FB15 / TIP3P-FB model combination is the dark blue trace in the middle row. Left column: The helical fraction of Ac-(AAQAA)₃-NH₂. Right column: The fraction folded of CLN025. Top row: Comparison of multiple protein force fields using TIP3P water model. Middle row: Same comparison using TIP3P-FB water model. Bottom row: Comparison of four water models using AMBER-FB15 protein force field.

Figure 7.

Correlation between average protein-water interaction energy and fraction of secondary structure. Left: AAQAA simulated with A99SB-V (left). Right: CLN025 simulated with AMBER-FB15 (right). Each plot contains four simulations with four water models. Error bars represent one standard error.