There and back again: bridging meso- and nano-scales to understand lipid vesicle patterning.

We describe a complete methodology to bridge the scales between nanoscale molecular dynamics and (micrometer) mesoscale Monte Carlo simulations in lipid membranes and vesicles undergoing phase separation, in which curving molecular species are furthermore embedded. To go from the molecular to the mesoscale, we notably appeal to physical renormalization arguments enabling us to rigorously infer the mesoscale interaction parameters from its molecular counterpart. We also explain how to deal with the physical timescales at stake at the mesoscale.

Boundary fluctuation dynamics of a phase-separated domain in planar geometry.

Using phase-ordering kinetics and of renormalization group theories, we derive analytically the relaxation times of the long wavelength fluctuations of a phase-separated domain boundary in the vicinity of (and below) the critical temperature in the planar Ising universality class. For a conserved order parameter, the relaxation time grows like Λ^{3} at wavelength Λ and can be expressed in terms of parameters relevant at the microscopic scale: lattice spacing, bulk diffusion coefficient of the minority phase, and temperature. These results are supported by numerical simulations of 2D Ising models, enabling in addition calculating the nonuniversal numerical prefactor.