CIRSE: a solvation energy estimator compatible with flexible protein docking and design applications

Abstract

We present the Coordinate Internal Representation of Solvation Energy (CIRSE) for computing the solvation energy of protein configurations in terms of pairwise interactions between their atoms with analytic derivatives. Currently, CIRSE is trained to a Poisson/surface-area benchmark, but CIRSE is not meant to fit this benchmark exclusively. CIRSE predicts the overall solvation energy of protein structures from 331 NMR ensembles with 0.951+/-0.047 correlation and predicts relative solvation energy changes between members of individual ensembles with an accuracy of 15.8+/-9.6 kcal/mol. The energy of individual atoms in any of CIRSE's 17 types is predicted with at least 0.98 correlation. We apply the model in energy minimization, rotamer optimization, protein design, and protein docking applications. The CIRSE model shows some propensity to accumulate errors in energy minimization as well as rotamer optimization, but these errors are consistent enough that CIRSE correctly identifies the relative solvation energies of designed sequences as well as putative docked complexes. We analyze the errors accumulated by the CIRSE model during each type of simulation and suggest means of improving the model to be generally useful for all-atom simulations.

Figure 1.

CIRSE predictions of total solvation energy (Y-axis, kilocalories per mole) for structures in 331 NMR ensembles plotted against the P/SA benchmark energy (X-axis, kilocalories per mole). Aggregate results are shown in the top left panel with a 1:1 trendline; results for five individual ensembles are shown in other panels.

Figure 2.

CIRSE predictions of atomistic solvation energy (X-axis, kilocalories per mole) compared to the P/SA benchmark (Y-axis, kilocalories per mole) for four atom types. The names depicted in each subplot correspond to the first of one or more AMBER atom types enumerated in Table 1. Data in this figure comprise one structure of each of the 331 NMR ensembles used to validate CIRSE.

Figure 3.

Energy minimization of three proteins using the CIRSE potential in conjunction with AMBER ff99. The P/SA benchmark solvation energy is plotted on the X-axis and the CIRSE estimate on the Y-axis. All units are kilocalories per mole. The CIRSE energy was observed to decrease steadily over the course of each minimization (solid line), although more rapidly than the actual benchmark solvation energy (dashed line indicates X = Y).

Figure 4.

Rotamer optimization of six native structures using the CIRSE potential in conjunction with AMBER ff99. The P/SA benchmark solvation energy is plotted on the X-axis and the CIRSE estimate on the Y-axis. All units are kilocalories per mole. Concentric circles indicate the original structure; native side-chain configurations were removed. The solid black line traces global refinement followed by 50 patch refinements; the final segment, bracketed by separate circles, corresponds to energy minimization of the re-packed structure. The PDB ID of each structure is given in the top left corner of each subplot.

Figure 5.

Total energy of six systems (Y-axis, kilocalories per mole) according to the AMBERgp + CIRSE potential during the course of rotamer optimization and energy minimization (X-axis, step 1 → 2 being global refinement, steps 2 → 3, …, 51 → 52 patch refinement, 52 → 53 unconstrained energy minimization). The PDB ID of each system is listed in its subplot. (Solid line) CIRSE + AMBERgp energy, (dashed line) P/SA + AMBERgp energy, (+ line segment) energy of the state obtained after the final patch refinement minimized with a fixed backbone, (• line segment) CIRSE + AMBERgp energy of the NMR structure minimized according to the same potential, (○ line segment) CIRSE + AMBERgp energy of the NMR structure minimized with a fixed backbone.

Figure 6.

CIRSE estimates (X-axis, kilocalories per mole) of the energy of hundreds of random amino acid sequences plotted against the P/SA benchmark energy (Y-axis,kilocalories per mole). As in Figure 4, the label at the top left corner of each subplot denotes the PDB ID of the template.

Figure 7.

AMBERgp + CIRSE estimates of the energy of 1000 docked complexes as well as the native complex (circled) for bound coordinates of each of nine interacting protein pairs (Y-axis, kilocalories per mole) plotted against RMSD from the crystal structure (X-axis, Å).

Figure 8.

Degree of buried SASA (Y-axis, Ų) of 1000 docked complexes as well as the native complex (circled) for bound coordinates of each of nine interacting protein pairs (Y-axis, kilocalories per mole) plotted against RMSD from the crystal structure (X-axis, Å).