Taste of sugar at the membrane: thermodynamics and kinetics of the interaction of a disaccharide with lipid bilayers

Abstract

Sugar recognition at the membrane is critical in various physiological processes. Many aspects of sugar-membrane interaction are still unknown. We take an integrated approach by combining conventional molecular-dynamics simulations with enhanced sampling methods and analytical models to understand the thermodynamics and kinetics of a di-mannose molecule in a phospholipid bilayer system. We observe that di-mannose has a slight preference to localize at the water-phospholipid interface. Using umbrella sampling, we show the free energy bias for this preferred location to be just -0.42 kcal/mol, which explains the coexistence of attraction and exclusion mechanisms of sugar-membrane interaction. Accurate estimation of absolute entropy change of water molecules with a two-phase model indicates that the small energy bias is the result of a favorable entropy change of water molecules. Then, we incorporate results from molecular-dynamics simulation in two different ways to an analytical diffusion-reaction model to obtain association and dissociation constants for di-mannose interaction with membrane. Finally, we verify our approach by predicting concentration dependence of di-mannose recognition at the membrane that is consistent with experiment. In conclusion, we provide a combined approach for the thermodynamics and kinetics of a weak ligand-binding system, which has broad implications across many different fields.

Figure 1

(A) Area per lipid (APL) of the POPC and DOPC phospholipid bilayers as a function of time for one 110-ns simulation. (Solid green line) Experimental APL for POPC 66.0 Å²/lipid (47); (solid blue line) experimental APL for DOPC, 67.4 Å²/lipid (48). (B) The deuterium order parameters for the two-acyl chains of POPC and DOPC molecules in the system.

Figure 2

The density profile for the DOPC (A) and POPC (B) systems with 2.5-nm water layer. Water density (red), phospholipid density (black), and the di-mannose density (blue). The di-mannose density is amplified by 50 times to give better clarification. The Z axis is the direction perpendicular to the water-phospholipid interface (XY plane).

Figure 3

Characterization of residence time for di-mannose interaction with phospholipid for all the simulations of the DOPC and POPC systems with 2.5-nm water layer. Residence times are plotted against number of events (Event No.).

Figure 4

Potential of mean force for di-mannose location in the DOPC system. The reaction coordinate is the distance in the z axis between center of masses of di-mannose and the phospholipid bilayer. (Inset) Location of di-mannose in the sugar membrane system at the energy minimum.

Figure 5

Translational and rotational velocity autocorrelation function (A and C) and density of states (B and D) for interface water and bulk water.

Figure 6

Sugar binding to the phospholipid bilayer as a function of sugar concentration. [M]_local and [M]_bulk correspond to the concentration of the dimannose close to the lipid bilayer (local) and in bulk solvent respectively.

Scheme 1

Schematic description of ligand diffusion in a box was used to derive an analytical expression for the binding rate constant for ligand binding with a 2-D surface. The red circle represents the ligand. Z=0 plane is an absorption plane, Z=L_z plane is a reflection plane and periodic boundary condition is applied in the x and y directions.