Binding Thermodynamics and Kinetics Calculations Using Chemical Host and Guest: A Comprehensive Picture of Molecular Recognition

Abstract

Understanding the fine balance between changes of entropy and enthalpy and the competition between a guest and water molecules in molecular binding is crucial in fundamental studies and practical applications. Experiments provide measurements. However, illustrating the binding/unbinding processes gives a complete picture of molecular recognition not directly available from experiments, and computational methods bridge the gaps. Here, we investigated guest association/dissociation with β-cyclodextrin (β-CD) by using microsecond-time-scale molecular dynamics (MD) simulations, postanalysis and numerical calculations. We computed association and dissociation rate constants, enthalpy, and solvent and solute entropy of binding. All the computed values of k_on, k_off, ΔH, ΔS, and ΔG using GAFF-CD and q4MD-CD force fields for β-CD could be compared with experimental data directly and agreed reasonably with experiment findings. In addition, our study further interprets experiments. Both force fields resulted in similar computed ΔG from independently computed kinetics rates, ΔG = -RT ln(k_on·C⁰/k_off), and thermodynamics properties, ΔG = ΔH - TΔS. The water entropy calculations show that the entropy gain of desolvating water molecules are a major driving force, and both force fields have the same strength of nonpolar attractions between solutes and β-CD as well. Water molecules play a crucial role in guest binding to β-CD. However, collective water/β-CD motions could contribute to different computed k_on and ΔH values by different force fields, mainly because the parameters of β-CD provide different motions of β-CD, hydrogen-bond networks of water molecules in the cavity of free β-CD, and strength of desolvation penalty. As a result, q4MD-CD suggests that guest binding is mostly driven by enthalpy, while GAFF-CD shows that gaining entropy is the major driving force of binding. The study deepens our understanding of ligand-receptor recognition and suggests strategies for force field parametrization for accurately modeling molecular systems.

Figure 1

Structure of β-cyclodextrin (β-CD) and the 7 guest molecules. In the structure of β-CD, hydrogen atoms are not shown. For the β-CD internal (vibrational/conformational) entropy calculation, the 14 dihedral angles used to define the conformations of β-CD are in blue.

Figure 2

Correlations between ΔG_Comp1, ΔG_Comp2, and experimental values. Results from GAFF-CD are shown in blue triangles, and results from q4MD-CD are shown in orange rectangles. Experimental values are shown in black circles. Correlations are labeled correspondingly.

Figure 3

Hydrogen-bond (H-bond) patterns of representative free β-CD conformations with GAFF-CD and q4MD-CD. With GAFF-CD, there are 18 water molecules forming H bonds with β-CD, 24 H bonds with water (blue dotted lines), and 1 intramolecular H bond (orange dotted lines). With q4MD-CD, there are 11 water molecules forming H bonds with β-CD, 16 H bonds with water, and 5 intramolecular H bonds.

Figure 4

RMSD plots and representative conformations of β-CD for free β-CD, β-CD-2-naphthyl ethanol complex, and β-CD-tert-butanol complex with GAFF-CD and q4MD-CD. RMSD (Å) are computed against the crystal structure by using conformations chosen every 100 ps from all conformations of free β-CD and bound-state conformations of complexes. Representative conformations are shown near the labels (a–d) and circles on the plots. In the representative conformations, ligands are in green.

Figure 5

Water entropy decompositions of pure water and in the vicinities of free β-CD, free 2-naphthyl ethanol, and β-CD-2-naphthyl ethanol complex in GAFF-CD. From top to bottom are pure water (A), free β-CD (B), free 2-naphthyl ethanol (C), and β-CD-2-naphthyl ethanol complex (D). Plane of the spatial grid in the figures is shown in green in the first column. From left to right are total entropy (1, S_Water), translational entropy (2, S_{Water Trans}), rotational entropy (3, S_{Water Rot}), and conformational entropy (4, S_{Water Conf}). Each column has a separate color bar (values in kcal/mol). Red areas are regions occupied by the solute molecules, and water entropy cannot be calculated.