The equilibrium constants of trans and cis dimerization of membrane bound (2D) and freely moving (3D) adhesion receptors are expressed and compared using elementary statistical-thermodynamics. Both processes are mediated by the binding of extracellular subdomains whose range of motion in the 2D environment is reduced upon dimerization, defining a thin reaction shell where dimer formation and dissociation take place. We show that the ratio between the 2D and 3D equilibrium constants can be expressed as a product of individual factors describing, respectively, the spatial ranges of motions of the adhesive domains, and their rotational freedom within the reaction shell. The results predicted by the theory are compared to those obtained from a novel, to our knowledge, dynamical simulations methodology, whereby pairs of receptors perform realistic translational, internal, and rotational motions in 2D and 3D. We use cadherins as our model system. The theory and simulations explain how the strength of cis and trans interactions of adhesive receptors are affected both by their presence in the constrained intermembrane space and by the 2D environment of membrane surfaces. Our work provides fundamental insights as to the mechanism of lateral clustering of adhesion receptors after cell-cell contact and, more generally, to the formation of lateral microclusters of proteins on cell surfaces.
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