Courant Institute of Mathematical Sciences, NYU
Title: Rolling versus sliding: the relative dynamics of DNA-coated colloids
Abstract: A versatile way to make microscale particles (colloids) with programmable interactions is to coat them with single-stranded DNA, which causes particles to stick together when their DNA comes close enough to hybridize. By choosing different DNA base pair codes, such particles can assemble into a variety of ordered structures, but, critically, only if they can rearrange on each other's surfaces while their DNA remains in contact. How do they do this? We create a simplified model that illustrates the effect of the DNA on the particles' coarse-grained dynamics, and predicts the magnitude of this effect to be large, about 100 times larger than the effect of hydrodynamics for certain systems. The model also predicts that DNA-coated particles should prefer to roll on each other's surfaces, not slide, and we describe a beautiful but unsolved math problem regarding the stochastic dynamics of rolling particles. Finally, we discuss some attempts to connect the model to ongoing experiments, and point out connections to similar processes in biology, such as models of muscle friction, blood cell dynamics, and transport through the nuclear pore complex.
Biography: Miranda Holmes-Cerfon is an applied mathematician, who uses and develops tools to address problems in science and engineering. Her mathematical work draws on many areas of pure and applied mathematics, but areas of particular interest include stochastic analysis, statistical mechanics, computational geometry, and rigidity theory. Her scientific work focuses mainly on modeling physical systems, including those in materials science, fluid dynamics, soft-matter physics, geophysics, and oceanography.