Ligand binding in a spherical region randomly crowded by receptors

Abstract

This paper reports on some results concerning the binding of diffusing ligands in a spherical 3D region randomly filled by free receptors. It is shown that commonly accepted mean-field theory which is successfully used for bulk diffusion-controlled reactions cannot describe the behavior of ligand concentration in the diffusion layer close to the region boundary. To eliminate this drawback of the theory, we introduce a new complementary diffusion equation in the boundary layer with an appropriate matching condition. Using this equation, we find the characteristic ligand penetration length and total time-dependent flux of ligand binding to free receptors randomly distributed in a spherical region.

Diffusion to Capture and the Concept of Diffusive Interactions

“…A surprising finding emerges if we plug realistic figures in Eq. (10). The typical size of a cell is around 10 µm, while the typical size of a receptor is of the order of 1.5 nm.…”

“…Combining Eq. (10) and Eq. ( 12), we can compute the ratio between the steric factor f u corresponding to a sparse uniform configuration of the M receptors and that of the cluster configuration, f c , namely…”

“…paracrine delivery), 5 where confinement, crowding (excluded-volume) effects 6,7 and non-specific interactions among diffusing species and with all sorts of cellular structures 8 make it very difficult to elaborate quantitative models for the calculation of diffusive encounter rates. [9][10][11][12][13] Among all the possible effects on diffusion-influenced encounters and reactions arising in non-ideal conditions, in this short review we shall concentrate on the so-called diffusive interactions (DI). As we shall see in the following, these describe a fundamental mechanism of competition among different reactive boundaries, competing for the same diffusive molecular flux.…”

Point-particle method to compute diffusion-limited cellular uptake

“…(B4) (dashed curves). Inset: Penetration length ξ obtained from the fit of the radial profile (filled circles) and theoretical prediction given by ξ = R/ √ 3φ [44] (dashed line). The average is performed over 5 − 20 independent realizations.…”

Diffusion toward non-overlapping partially reactive spherical traps: fresh insights onto classic problems

“…Various arrangments of traps may account for spatial heterogeneities and help to elucidate the role of disorder onto reaction kinetics, in particular, onto the reaction rate [17][18][19][20][21][22][23] . More generally, reactive traps and passive spherical obstacles can be used as elementary "bricks" to build up model geometrical structures of porous media or macromolecules such as enzymes or proteins [24][25][26][27][28][29][30][31] .…”