  The cytoskeleton -- a composite network of biopolymers, molecular motors, and
associated binding proteins -- is a paradigmatic example of active matter.
Particle transport through the cytoskeleton can range from anomalous and
heterogeneous subdiffusion to superdiffusion and advection. Yet, recapitulating
and understanding these properties -- ubiquitous to the cytoskeleton and other
out-of-equilibrium soft matter systems -- remains challenging. Here, we combine
light sheet microscopy with differential dynamic microscopy and single-particle
tracking to elucidate anomalous and advective transport in
actomyosin-microtubule composites. We show that particles exhibit multi-mode
transport that transitions from pronounced subdiffusion to superdiffusion at
tunable crossover timescales. Surprisingly, while higher actomyosin content
enhances superdiffusivity, it also markedly increases the degree of
subdiffusion at short timescales and generally slows transport. Corresponding
displacement distributions display unique combinations of non-Gaussianity,
asymmetry, and non-zero modes, indicative of directed advection coupled with
caged diffusion and hopping. At larger spatiotemporal scales, particles undergo
superdiffusion which generally increases with actomyosin content, in contrast
to normal, yet faster, diffusion without actomyosin. Our specific results shed
important new light on the interplay between non-equilibrium processes,
crowding and heterogeneity in active cytoskeletal systems. More generally, our
approach is broadly applicable to active matter systems to elucidate transport
and dynamics across scales.
