Fig 1.
A rigid-body (RB) based model is used to study the interaction between ligands and receptors (a). Each domain or subunit of a ligand is simplified as a spherical rigid body with radius ri. Each receptor is simplified as a cylinder with radius rj and height hj. A functional site is placed on the surface of each rigid body. The distance between functional sites dij and their relative orientation ωij need to be below cutoff values to trigger binding reaction between these two molecules. Three scenarios were designed to test the relation between the binding avidity of a multi-specific ligand and the affinity of its individual binding site. In the first scenario, receptors A (red) and C (yellow) are placed on cell surface. Ligands B (green) and D (blue) are separately placed in the 3D extracellular region as monomers (b). In the second scenario, ligand B and D are spatially tethered (referred as BD) in the extracellular region (c). In the third scenario, higher-order assembly of a multi-specific ligand is formed, which contains two ligands B and two ligands D (referred as B2D2) (d).
Fig 2.
To evaluate how spatial organization of a multi-specific ligand affects its binding with receptors, we fixed the binding affinity between receptor C and ligand D as -9kT.
The affinity between receptor A and ligand B were changed from -5kT (black), -7kT (red) to -9kT (blue). The simulation results for the first scenario are shown in (a) and (b); the simulation results for the second scenario are shown in (c) and (d); and the simulation results for the third scenario are shown in (e) and (f). The figure indicates that when ligands B and D are tethered, the interaction between receptor C and ligand D can be affected by the interaction between receptor A and ligand B, although the CD affinity remains unchanged.
Fig 3.
We systematically changed both AB binding affinity and CD binding affinity simultaneously.
The overall testing results are plotted as two-dimensional contour profiles. The AB binding affinity is indexed along x axis, while the CD binding affinity is indexed along y axis. The color index of the contours indicates the number of interactions, as shown on the right side of the figure. The numbers of AB interactions formed in the first scenario are illustrated in (a) under all combinations of AB and CD affinities, while the numbers of CD interactions are given in (b). For the second scenario, the numbers of AB and CD interactions are recorded in (c) and (d), respectively. Finally, the numbers of AB interactions formed in the third scenario are plotted in (e) and the numbers of CD interactions are plotted in (f).
Fig 4.
We changed the relative concentrations of two receptors on cell surfaces.
The second scenario was applied, in which the total number of receptor A was fixed and the total number of receptor C was changed from 0 to 100. We first fixed both AB and CD binding affinities (a). The figure shows that higher surface densities of receptors C lead to more interactions between receptor A and its ligand. In the second test (b), we changed the affinity between receptor A and ligand B from -7kT to -11kT. The x index of the figure is the number of receptors C on cell surfaces. The relative increment of AB interactions between 0 and a given concentration of receptors C is recorded in the y axis. The simulation results of the figure demonstrate that the ligands with reduced affinity have higher specificity to distinguish different types of cells based on the concentrations of their receptors.
Fig 5.
In order to investigate the functional role of binding site organization, four different topologies were designed.
Each topology includes two ligands B and two ligands D, as shown in the bottom row. The binding of all four types of topology were simulated. The average numbers of interactions between ligands and receptors are plotted as striped bars, while the deviations in total number of interactions are plotted as black bars. The first two topologies show similar average and deviation. Moreover, the fourth model has higher deviations than the third model, although they have very close average number of interactions.
Fig 6.
The internal flexibility of multi-specific ligands was incorporated in the simulations.
Comparing a simulation in which flexibility was incorporated (red) with a simulation without flexibility (black), we found that flexibility not only leads to more interactions on average, but also causes larger fluctuations in the number of interactions along simulation time (a). We further changed the maximal ranges of translational and rotational perturbations in each simulation step to adjust the spatial variability between different binding sites in a multi-specific ligand. The overall testing results are plotted in (b) as a three-dimensional histogram. The maximal ranges of translational and rotational fluctuations are indexed along the x and y directions. The figure suggests that the overall binding of ligands is promoted by the intramolecular flexibility within an appropriate range. However, binding will be negatively affected when molecules are over flexible.