A physical perspective on cytoplasmic streaming

Organisms show a remarkable range of sizes, yet the dimensions of a single cell rarely exceed 100 µm. While the physical and biological origins of this constraint remain poorly understood, exceptions to this rule give valuable insights. A well-known counterexample is the aquatic plant Chara , whose cells can exceed 10 cm in length and 1 mm in diameter. Two spiralling bands of molecular motors at the cell periphery drive the cellular fluid up and down at speeds up to 100 µm s −1 , motion that has been hypothesized to mitigate the slowness of metabolite transport on these scales and to aid in homeostasis. This is the most organized instance of a broad class of continuous motions known as ‘cytoplasmic streaming’, found in a wide range of eukaryotic organisms—algae, plants, amoebae, nematodes and flies—often in unusually large cells. In this overview of the physics of this phenomenon, we examine the interplay between streaming, transport and cell size and discuss the possible role of self-organization phenomena in establishing the observed patterns of streaming.

LINEAR TRANSPORT OF PARTICLES ON NETWORKS

We introduce a model of transport of particles in a network, which is represented by a connected graph with m vertices and n edges. Each edge represents a one-dimensional conductor of particles, whose behavior is described by means of a linear Boltzmann-like equation. In graph vertices, a system of linear boundary conditions is given which takes into account the exchanges of particles between the edges. The well-posedness of the initial value problem is studied into an abstract L1-like setting and the structure of the solution is given for simplest case of pure streaming transport.