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

Particles with ligand-receptor contacts span the nano to micro scales in biology and artificial systems. Such "nanoscale caterpillars" bind and unbind fluctuating "legs" to surfaces, whose fluctuations cause the nanocaterpillar to diffuse over long timescales. Quantifying this diffusion is a challenge, since binding events often occur on very short time and length scales. Here we present a robust analytic framework, validated by simulations, to coarse-grain these fast dynamics and obtain the long time diffusion coefficient of a nanocaterpillar in one dimension. We verify our theory experimentally, by measuring diffusion coefficients of DNA-coated colloids on DNA-coated surfaces. We furthermore compare our model to a range of other models and assumptions found in the literature,and find ours is the most general, encapsulating others as special limits. Finally, we use our model to ask: when does a nanocaterpillar prefer to move by sliding, where one leg is always linked to the surface, or by hopping, which requires all legs to unbind simultaneously? We classify a range of nanocaterpillar systems (viruses, molecular motors, white blood cells, protein cargos in the nuclear pore complex, bacteria such as Escherichia coli, and DNA-coated colloids) according to whether they prefer to hop or slide, and present guidelines for materials design.