Absolute and Relative Binding Free Energy Calculations of Nucleotides to Multiple Protein Classes

Abstract

Polyphosphate nucleotides, such as ATP, ADP, GTP, and GDP, play a crucial role in modulating protein functions through binding and/or catalytically activating proteins (enzymes). However, accurately calculating the binding free energies for these charged and flexible ligands poses challenges due to slow conformational relaxation and the limitations of force fields. In this study, we examine the accuracy and reliability of alchemical free energy simulations with fixed-charge force fields for the binding of four nucleotides to nine proteins of various classes, including kinases, ATPases, and GTPases. Our results indicate that the alchemical simulations effectively reproduce experimental binding free energies for all proteins that do not undergo significant conformational changes between their triphosphate nucleotide-bound and diphosphate nucleotide-bound states, with 87.5% (7 out of 8) of the absolute binding free energy results for 4 proteins within ±2 kcal/mol of experimental values and 88.9% (8 out of 9) of the relative binding free energy results for 9 proteins within ±3 kcal/mol of experimental values. However, our calculations show significant inaccuracies when divalent ions are included, suggesting that nonpolarizable force fields may not accurately capture interactions involving these ions. Additionally, the presence of highly charged and flexible ligands necessitates extensive conformational sampling to account for the long relaxation times associated with long-range electrostatic interactions. The simulation strategy presented here, along with its demonstrated accuracy across multiple protein classes, will be valuable for predicting the binding of nucleotides or their analogs to protein targets.

Figure 1.

Comparison of experimental and alchemical relative binding free energies of nucleotides (i.e. ATP → ADP or GTP → GDP transformation) to multiple classes of proteins using fixed-charge force fields and without the presence of magnesium ions during simulations. The varying symbols represent the RBFE values for the nine proteins considered in this study. The dashed line corresponds to $y=x$, while the dotted and the dash-dotted lines correspond to $y=x\pm 2$ and $y=x\pm 4$ kcal/mol, respectively.

Figure 2.

Alchemical simulation results of complex and ligand legs for ATP → ADP or GTP → GDP transformation in the presence of a magnesium ion coordinating the nucleotide. The unusually high variation across both ligand and complex legs for all protein-nucleotide complexes makes it challenging to reliably predict binding free energies with traditional 12–6 force fields for interactions involving magnesium ions.

Figure 3.

Experimental and alchemical RBFE results for nucleotides binding to multiple proteins in the presence of a magnesium ion coordinating the nucleotide. Black symbols represent the free energies obtained using the magnesium ion parametrization by Allner et. al. with weak distance restraints between the magnesium ion and the nucleotide. Red symbols correspond to parametrization by Li et. al. with no restraints between the magnesium ion and the nucleotide. Green symbols correspond to parametrization by Li et. al. with strong restraints between the magnesium ion and the nucleotide. The dashed line indicates $y=x$, while the dotted and dash-dotted lines correspond to $y=x\pm 2$ and $y=x\pm 4$ kcal/mol, respectively.

Figure 4.

Comparison of the experimental and alchemical absolute binding free energies for nucleotides binding to four proteins, without the presence of magnesium ions coordinating the nucleotides during simulations. Black symbols represent the ABFE values for ATP binding to the four proteins, while red symbols represent the ABFE values of ADP binding to the same proteins. The dashed line indicates $y=x$, and the dotted and dash-dotted lines correspond to $y=x\pm 2$ and $y=x\pm 4$ kcal/mol, respectively.