Revealing noncovalent interactions

Abstract

Molecular structure does not easily identify the intricate noncovalent interactions that govern many areas of biology and chemistry, including design of new materials and drugs. We develop an approach to detect noncovalent interactions in real space, based on the electron density and its derivatives. Our approach reveals the underlying chemistry that compliments the covalent structure. It provides a rich representation of van der Waals interactions, hydrogen bonds, and steric repulsion in small molecules, molecular complexes, and solids. Most importantly, the method, requiring only knowledge of the atomic coordinates, is efficient and applicable to large systems, such as proteins or DNA. Across these applications, a view of nonbonded interactions emerges as continuous surfaces rather than close contacts between atom pairs, offering rich insight into the design of new and improved ligands.

Figure 1

Plots of the electron density and its reduced gradient for methane, water, branched octane, bicyclo[2,2,2]octene, and the homomolecular dimers of methane, benzene, water, and formic acid. The data was obtained by evaluating B3LYP/631G* density and gradient values on cuboid grids.

Figure 2

Plots of the reduced density gradient versus the electron density mulitplied by the sign of the second Hessian eigenvalue. Results are shown for bicyclo[2,2,2]octene, methane dimer, and water dimer. The data was obtained by evaluating B3LYP/631G* density (a) or promolecular density (b) and gradient values on cuboid grids.

Figure 3

Gradient isosurfaces (s = 0.5 au) for (a) bicyclo[2,2,2]octene, (b) branched octane, and the homomolecular dimers of (c) benzene, (d) methane, (e) water, and (f) formic acid. Gradient isosurfaces are also shown for cuboid sections of (g) diamond and (h) graphite. The surfaces are colored on a blue-green-red scale according to values of sign(λ₂)ρ, ranging from −0.04 to 0.02 au. Blue indicates strong attractive interactions and red indicates strong non-bonded overlap.

Figure 4

Gradient isosurfaces (s^pro = 0.35) for cuboid sections of the (a) β-sheet and (b) α-helix polypeptides. Gradient isosurfaces (s^pro = 0.25) are also shown for the (c) B-form of DNA, and the (d) A-T and (e) C-G base pairs. The surfaces are colored on a blue-green-red scale according to values of sign(λ₂) ρ, ranging from −0.06 to 0.05 au. Blue indicates strong attractive interactions and red indicates strong non-bonded overlap.

Figure 5

Gradient isosurfaces (s^pro = 0.35) for interaction between the tetR protein and tetracy-cline inhibitor. The surfaces are colored on a blue-green-red scale according to values of sign(λ₂)ρ, ranging from −0.06 to 0.05 au. Blue indicates strong attractive interactions and red indicates strong non-bonded overlap.