Analytical methods for cytoplasmic streaming in elongated cells

Cytoplasmic streaming, the coherent flow of cytoplasm, plays a critical role in transport and mixing over large scales in eukaryotic cells. In many large cells, this process is driven by active forces at the cell boundary, such as cortical cytoskeletal contractions in Drosophila and C. elegans embryos, or intracellular cargo transport in plant cells. These cytoplasmic flows are approximately Newtonian and governed by the Stokes equations. In this paper, we use lubrication theory - a powerful technique for simplifying the fluid mechanics equations in elongated geometries - to derive a general solution for boundary-driven cytoplasmic flows. We apply this framework to predict cytoplasmic fluid dynamics and cortical stresses in four systems of biological significance: the Drosophila and C. elegans embryos (including pseudocleavage furrow formation), the pollen tube of seed plants, and plant root hair cells. Our results showcase the elegance and accuracy of asymptotic solutions in capturing the complex flows and stress patterns in diverse biological contexts, reinforcing its utility as a robust tool for cellular biophysics.