Modeling the relative dynamics of DNA-coated colloids

Abstract

We construct a theoretical model for the dynamics of a microscale colloidal particle, modeled as an interval, moving horizontally on a DNA-coated surface, modelled as a line coated with springs that can stick to the interval. Averaging over the fast DNA dynamics leads to an evolution equation for the particle in isolation, which contains both friction and diffusion. The DNA-induced friction coefficient depends on the physical properties of the DNA, and substituting parameter values typical of a 1µm colloid coated densely with weakly interacting DNA gives a coefficient about 100 times larger than the corresponding coefficient of hydrodynamic friction. We use a mean-field extension of the model to higher dimensions to estimate the friction tensor for a disc rotating and translating horizontally along a line. When the DNA strands are very stiff and short, the friction coefficient for the disc rolling approaches zero while the friction for the disc sliding remains large. Together, these results could have significant implications for the dynamics of DNA-coated colloids or other ligand-receptor systems, implying that DNA-induced friction between colloids can be stronger than hydrodynamic friction and should be incorporated into simulations, and that it depends nontrivially on the type of relative motion, possibly causing the particles to assemble into out-of-equilibrium metastable states governed by the pathways with the least friction.

Programmable interactions with biomimetic DNA linkers at fluid membranes and interfaces

“…The reaction kinetics is specified by on and of f rates of forming a possible type of bond (e.g. αβ) that are calculated as follows [114,116,128,204,210] k on = k 0 on exp[−β∆G conf αβ ({r})] k off = ρ 0 k 0 on exp[β∆G 0 αβ ],…”

Self-assembly of photonic crystals by controlling the nucleation and growth of DNA-coated colloids

“…When a particle from the gas phase attaches to a crystalline nucleus, it must first “roll” on the surface of the cluster before settling at a metastable position within the emerging lattice. This process can be slowed dramatically by the transient formation and rupture of DNA linkages ( 13 , 20 , 21 ). We model this effect by introducing an unstable intermediate state in which a colloidal particle is adsorbed onto the nucleus but not yet maximally coordinated in the emerging crystalline lattice (see SI Appendix , section 6B for details).…”

“…On the one hand, colloidal particles can be thought of as “model atoms” that interact via an effective interaction potential that is averaged over all of the molecular degrees of freedom ( 19 ). On the other hand, the effective interaction arises from the transient formation and rupture of very real DNA duplexes that link neighboring particles together, whose kinetics may dramatically influence the rates of local rearrangements within a colloidal assembly ( 13 , 20 , 21 ). Such dynamical considerations are crucially important, as numerous examples of colloidal self-assembly have shown that the thermodynamically stable phase that one would predict on the basis of the effective interactions alone is not always accessible, and that these systems are prone to becoming arrested as a colloidal gel instead ( 22 , 23 ).…”

Programming Self-Assembled Materials With DNA-Coated Colloids

“…Rogers et al believed that for particles with fewer strands that bind strongly, the lifetime of the DNA bonds may be large to slow down the rotational diffusion of the particles [23]. Theoretical works have been recently developed to rationalize the experiment findings [64,68,69]. For example, by using a simulation method that tracks the single binding and unbinding between complementary linkers, Mognetti et al proved that particles could move relative to each other while being cross-linked.…”