Scaffold Hopping Transformations Using Auxiliary Restraints for Calculating Accurate Relative Binding Free Energies

Abstract

In silico screening of drug-target interactions is a key part of the drug discovery process. Changes in the drug scaffold via contraction or expansion of rings, the breaking of rings, and the introduction of cyclic structures from acyclic structures are commonly applied by medicinal chemists to improve binding affinity and enhance favorable properties of candidate compounds. These processes, commonly referred to as scaffold hopping, are challenging to model computationally. Although relative binding free energy (RBFE) calculations have shown success in predicting binding affinity changes caused by perturbing R-groups attached to a common scaffold, applications of RBFE calculations to modeling scaffold hopping are relatively limited. Scaffold hopping inevitably involves breaking and forming bond interactions of quadratic functional forms, which is highly challenging. A novel method for handling ring opening/closure/contraction/expansion and linker contraction/expansion is presented here. To the best of our knowledge, RBFE calculations on linker contraction/expansion have not been previously reported. The method uses auxiliary restraints to hold the atoms at the ends of a bond in place during the breaking and forming of the bonds. The broad applicability of the method was demonstrated by examining perturbations involving small-molecule macrocycles and mutations of proline in proteins. High accuracy was obtained using the method for most of the perturbations studied. The rigor of the method was isolated from the force field by validating the method using relative and absolute hydration free energy calculations compared to standard simulation results. Unlike other methods that rely on λ-dependent functional forms for bond interactions, the method presented here can be employed using modern molecular dynamics software without modification of codes or force field functions.

Figure 1.. An illustration of the process of ring breaking.

A 6-membered ring with a lightning bolt indicating the bond to be broken and red clips indicating the dihedrals to be restrained is shown.

Figure 2.. A thermodynamic cycle for a sample ring opening transformation.

ΔG₁, ΔG₂, ΔG₃ and ΔG₄ are the free energy changes of applying the auxiliary restraints, breaking the covalent bond, releasing the auxiliary restraints and completing any remaining chemical differences, respectively. ΔG_total = ΔG₁ + ΔG₂ + ΔG₃ + ΔG₄.

Figure 3.. Illustration of the concept of A) ring and B) linker contraction transformations using auxiliary restraints.

ΔG₁ represents the free energy change of removing the non-bonded interaction of atoms a2 and H. ΔG₂ represents the free energy change of applying the restraints listed in Table 1. Atoms shown in red are dummy atoms with no nonbonded interactions. The blue lines indicate the auxiliary bond restraints applied on a1-a2 and H-a2. The dashed arcs indicate the auxiliary angle restraints applied on a1-a2-a3 and H-a2-a1.

Figure 4.

A) An example of the ring opening transformation between ligands 20 and 17 of Chk1. The red lightning bolt indicates the bond being broken during the ring opening transformation, and the red clips indicate the auxiliary dihedral restraints. B) Distance distribution between atoms C and O at the ends of the breaking bond under dihedral restraints of k= 10 kcal/mol at different λ values. C) Distance distribution between atoms C and O at the ends of the breaking bond under no dihedral restraint at different λ values. The bond interaction is scaled linearly by λ.

Figure 5.

An example illustrating the ring contraction transformation from Erα ligands 3b to 2d studied using the auxiliary restraints method. The atom to be removed from the ring (a2) is indicated by a red circle, and the bond to be formed (a1-a3) is indicated by a blue dashed line. The blue lines indicate the auxiliary bond restraints applied on a1-a2 and H-a2. The dashed arcs indicate the auxiliary angle restraints applied on a1-a2-a3 and H-a2-a1. Chirality is indicated using the wedge-dash notation. Further changes are required in addition to the ring contraction.

Figure 6.

An example illustrating the linker contraction transformation from CatS ligands 35 to 132 studied using the auxiliary restraints method. Atom (a2) to be removed from the linker is indicated by the red circle and the bond (a1-a3) to be formed is indicated by the blue dashed line. The blue lines indicate the auxiliary bond restraints applied on a1-a2 and H-a2. The dashed arcs indicate the auxiliary angle restraints applied on a1-a2-a3 and H-a2-a1. Chirality is indicated using the wedge-dash notation. Units: kcal/mol.

Figure 7.

A) The ring opening transformation between macrocycles CK2 2 and 1. The red lightning bolt indicates the bond broken during ring opening transformation. B) Distance distribution between atoms C and C at the ends of the breaking bond under dihedral restraints of k= 10 kcal/mol. C) Distance distribution between atoms C and C at the ends of the breaking bond under no dihedral restraint. Bond interaction is scaled linearly by λ.

Figure 8.

Comparison of the calculated and experimental ΔΔG for the ring opening/closure transformations (blue dots), the linker and chain contraction/expansion transformations (red dots). A total of 44 transformations were studied. Calculated values used the auxiliary restraints method. Units: kcal/mol.

Figure 9.

A) Cartoon representation of the SGPB/OMTKY3-L18P complex (PDB code 2sgp). The red box indicates the enlarged area shown in panel B. B) The binding complex of OMTKY3-L18P and SGPB. SGPB is shown as a surface. OMTKY3 is shown as licorice, with P18 in the center. Carbon, Nitrogen, Oxygen and Sulfur atoms are shown in white, blue, red and yellow respectively. The backbone φ/ψ dihedrals are indicated by yellow bars and their values are shown in white. Hydrogen atoms and water are omitted.

Figure 10.

Comparison of the calculated and experimental ΔΔG for the Leu18-to-Pro mutations in OMTKY3 complexes. Units: kcal/mol.

Figure 11.

The thermodynamic cycle for validating free energy calculations. ΔG₁ and ΔG₂ are the free energy changes calculated using ring opening transformations in water and in vacuum, respectively. ΔG₃ and ΔG₄ are the free energy changes calculated by transferring the whole molecules from water to vacuum without breaking bonds.