Viscophoresis leads to accumulation of particles.

(A) Particle distribution at various timesteps of a simulation with a step-like lower-diffusivity region. (B) Particle distribution at various timesteps for a simulation with a diffusivity gradient. (C) Steady-state particle distribution for the simulation in (A). (D) Steady-state particle distribution for the simulation in (B).

Interaction-driven clustering is modulated by viscophoresis.

(A) Progress of a simulation comprising particles possessing weak interactions (k = 0.04 is the interaction strength; see Methods), initialized with a uniform concentration of particles. (B) Progress of a simulation comprising particles possessing strong interactions (k = 0.01), initialized with a uniform concentration of particles.

Inhomogeneous diffusivity can manifest as anomalous diffusion.

(A) MSD versus time for homogeneous diffusion of 10,000 particles in a 5 mm x 5 mm simulation region. (B) Same as (A) for homogeneous diffusion in a more tightly bounded simulation region (1 μm x 0.45 μm). (C) MSD versus time for inhomogeneous diffusion in a diffusivity gradient versus homogeneous diffusion in the extreme diffusivity cases (simulation region size: 1 μm x 0.45 μm). Inset: zoomed region showing differential saturation of the MSD. (D) MSD versus time for inhomogeneous diffusion due to a stepwise viscosity distribution with viscosity ratio relative to the bulk (simulation region size: 1 μm x 0.45 μm). In all cases, n = 10,000 particles for MSD calculation (error bars denote SEM).

An increase in granule viscosity, radius, or packing density slows down mesoscale dynamics.

(A) Simulated FRAP t1/2 as a function of granule:bulk viscosity ratio (r = 0.01 μm, ϕ = 0.6). (B) Simulated FRAP t1/2 as a function of granule radius (, ϕ = 0.6). (C) Simulated FRAP t1/2 as a function of granule packing density (, r = 0.01 μm). (D) Simulated FRAP t1/2 for homogeneous and inhomogeneous viscosity setups realizing the same effective viscosities (, r = 0.01 μm). In all cases, n = 3 ROIs were chosen for the simulated photobleaching (error bars denote SEM).

Itô convention leads to Fokker-Planck diffusion, contrasting canonical (“Fickian”) homogenization.

(A) Agent-based modeling of particle dynamics used in this study. Choosing the diffusivity at the start point of a particle hop is in line with the Itô interpretation. (B) Numerical solutions for drift-less Fokker-Planck equations with an inhomogeneous diffusion coefficient, for the Itô, Stratonovich and isothermal conventions.

Particle clustering at different strengths in homogeneous versus heterogeneous diffusivity environments.

(A) Progress of a simulation comprising particles possessing weak interactions (k = 0.04), initialized with a uniform concentration of particles; no diffusivity gradient used here. (B) Progress of a simulation comprising particles possessing weak interactions (k = 0.1), initialized with a uniform concentration of particles; no diffusivity gradient used here. (C) Mean local density versus time for particles possessing weak interaction strength. (D) Mean local density versus time for particles possessing strong interaction strength. For (C) and (D), n = 1000 particles for mean local density calculation (error bars denote SEM).

Magnitude and distribution of inhomogeneity in viscosity affects diffusive lensing.

(A) Analysis of simulation trajectories via in silico microrheology. (B) Increasing viscophoretic extent due to variation of the zone viscosity in a chamber comprising a viscous end. (C) Mean squared displacement after transition to normal diffusion (saturation MSD) depends both on the magnitude of viscosity difference and the location of the zone itself. n = 10,000 particles for MSD calculation (error bars denote SEM). (D) Histogram ‖ X ‖2 of at the end of the run for the cases of the 4x viscous zone located at the simulation region edge versus the center.

Dwell times for particles in viscous granules dictate FRAP kinetics.

(A) The in silico implementation of FRAP used in this study. (B) Methodology for determining mean dwell time of particles in viscous granules, from a set of simulation trajectories. (C) Steady-states of systems in the variation of granule viscosity, before commencing in silico FRAP. (D) Steady-states of systems in the variation of granule radius, before commencing in silico FRAP. (E) Steady-states of systems in the variation of granule packing density, before commencing in silico FRAP. (F) Mean dwell time fraction variation as a function of granule:bulk viscosity. (G) Mean dwell time fraction variation as a function of granule radius. (H) Mean dwell time fraction variation as a function of granule packing density. For (F)-(H), n = 10,000 particles used for calculation (error bars denote SEM).