The Nanocaterpillar's Random Walk: Diffusion With Ligand-Receptor Contacts

TL;DR

This paper develops an analytical model for the diffusion of ligand-receptor particles, revealing how microscopic parameters influence nanoscale motion and explaining observed variations in diffusion behavior across biological and synthetic systems.

Contribution

The authors derive a validated analytical formula for the long-term diffusion coefficient of ligand-receptor particles, linking microscopic parameters to macroscopic diffusion behavior.

Findings

Diffusion coefficient can be significantly reduced by ligand-receptor interactions.

Temperature variations cause rapid changes in diffusion behavior.

The model explains experimental data on DNA-coated colloids and other biological systems.

Abstract

Particles with ligand-receptor contacts bind and unbind fluctuating "legs" to surfaces, whose fluctuations cause the particle to diffuse. Quantifying the diffusion of such "nanoscale caterpillars" is a challenge, since binding events often occur on very short time and length scales. Here we derive an analytical formula, validated by simulations, for the long time translational diffusion coefficient of an overdamped nanocaterpillar, under a range of modeling assumptions. We demonstrate that the effective diffusion coefficient, which depends on the microscopic parameters governing the legs, can be orders of magnitude smaller than the background diffusion coefficient. Furthermore it varies rapidly with temperature, and reproduces the striking variations seen in existing data and our own measurements of the diffusion of DNA-coated colloids. Our model gives insight into the mechanism of motion, and allows us to ask: when does a nanocaterpillar prefer to move by sliding, where one leg is always linked to the surface, and when does it prefer to move by hopping, which requires all legs to unbind simultaneously? We compare a range of systems (viruses, molecular motors, white blood cells, protein cargos in the nuclear pore complex, bacteria such as Escherichia coli, and DNA-coated colloids) and present guidelines to control the mode of motion for materials design.