Dynamics of Hydration Water Plays a Key Role in Determining the Binding Thermodynamics of Protein Complexes

Abstract

Interfacial waters are considered to play a crucial role in protein-protein interactions, but in what sense and why are they important? Here, using molecular dynamics simulations and statistical thermodynamic analyses, we demonstrate distinctive dynamic characteristics of the interfacial water and investigate their implications for the binding thermodynamics. We identify the presence of extraordinarily slow (~1,000 times slower than in bulk water) hydrogen-bond rearrangements in interfacial water. We rationalize the slow rearrangements by introducing the "trapping" free energies, characterizing how strongly individual hydration waters are captured by the biomolecular surface, whose magnitude is then traced back to the number of water-protein hydrogen bonds and the strong electrostatic field produced at the binding interface. We also discuss the impact of the slow interfacial waters on the binding thermodynamics. We find that, as expected from their slow dynamics, the conventional approach to the water-mediated interaction, which assumes rapid equilibration of the waters' degrees of freedom, is inadequate. We show instead that an explicit treatment of the extremely slow interfacial waters is critical. Our results shed new light on the role of water in protein-protein interactions, highlighting the need to consider its dynamics to improve our understanding of biomolecular bindings.

Figure 1

Structure of the barnase–barstar complex.

Figure 2

(a) Illustration of single HB, double HB, and bridging waters; dotted lines denote hydrogen bonds. (b) Snapshot of the barnase–barstar complex structure with hydration water, showing the distribution of single HB water (cyan), double HB water (orange), and bridging water (red).

Figure 3

Thermodynamic cycle for obtaining the trapping free energy. Process (1) is the separate solvation processes of the i-th water molecule and the solute u′ (barnase–barstar complex + hydration water − i-th water molecule). Process (2) is the transfer process of the i-th water molecule to a specific position and orientation around the solute u′ in vacuum. Process (3) is the solvation process of the solute u (=solute u′ + i-th water molecule). From the Gibbs free energy changes associated with these processes, the transfer free energy of interest can obtained as −ΔG ₍₁₎ + ΔG ₍₂₎ + ΔG ₍₃₎.

Figure 4

Hydrogen-bond time-correlation functions for bulk water (blue), single HB water (cyan), double HB water (orange), and bridging water (red) versus the logarithmic time axis. Dashed-dotted line denotes the fit by a logarithmic function.

Figure 5

Construction of the thermodynamic–dynamic relationship diagram. Upper panel: Hydrogen-bond time-correlation functions for single HB water (cyan), double HB water (orange), and bridging water (red) taken from Fig. 4, focusing on the time regime where the functions decay from 0.3 to 0.1 (light yellow). Lower panel: Scatter plots of the hydrogen-bond survival times (τ _i) and trapping free energies (${\mathit{G}}_i^{\mathrm{trap}}$) of individual water molecules. Centers of ellipsoids are determined by the averages, and the width and hight are determined by 3.6 σ (where σ is the standard deviation) along each axis.

Figure 6

(a) Schematic representation of the thermodynamic–dynamic relationship diagram of hydration water. Here, the lower panel from Fig. 5 is schematically redrawn for single HB water (cyan), double HB water (orange), and bridging water (red), along with the position for the bulk water (blue). (b) Protein surfaces color-coded with the charge distribution (blue and red for positively and negatively charged regions, respectively).