Two-fluid dynamics and micron-thin boundary layers shape cytoplasmic flows in early Drosophila embryos

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 Caenorhabiditis elegans embryos, or intracellular cargo transport in plant cells. These cytoplasmic flows are approximately Newtonian and governed by the Stokes equations. In this article, 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.

Developmental Control of Cell Cycle and Signaling

In most species, the earliest stages of embryogenesis are characterized by rapid proliferation, which must be tightly controlled with other cellular processes across the large scale of the embryo. The study of this coordination has recently revealed new mechanisms of regulation of morphogenesis. Here, I discuss progress on how the integration of biochemical and mechanical signals leads to the proper positioning of cellular components, how signaling waves ensure the synchronization of the cell cycle, and how cell cycle transitions are properly timed. Similar concepts are emerging in the control of morphogenesis of other tissues, highlighting both common and unique features of early embryogenesis.

Computational tools for cellular scale biophysics

Mathematical models are indispensable for disentangling the interactions through which biological components work together to generate the forces and flows that position, mix, and distribute proteins, nutrients, and organelles within the cell. To illuminate the ever more specific questions studied at the edge of biological inquiry, such models inevitably become more complex. Solving, simulating, and learning from these more realistic models requires the development of new analytic techniques, numerical methods, and scalable software. In this review, we discuss some recent developments in tools for understanding how large numbers of cytoskeletal filaments, driven by molecular motors and interacting with the cytoplasm and other structures in their environment, generate fluid flows, instabilities, and material deformations which help drive crucial cellular processes.

Long-range formation of the Bicoid gradient requires multiple dynamic modes that spatially vary across the embryo

Morphogen gradients provide essential positional information to gene networks through their spatially heterogeneous distribution, yet how they form is still hotly contested, with multiple models proposed for different systems. Here, we focus on the transcription factor Bicoid (Bcd), a morphogen that forms an exponential gradient across the anterior-posterior (AP) axis of the early Drosophila embryo. Using fluorescence correlation spectroscopy we find there are spatial differences in Bcd diffusivity along the AP axis, with Bcd diffusing more rapidly in the posterior. We establish that such spatially varying differences in Bcd dynamics are sufficient to explain how Bcd can have a steep exponential gradient in the anterior half of the embryo and yet still have an observable fraction of Bcd near the posterior pole. In the nucleus, we demonstrate that Bcd dynamics are impacted by binding to DNA. Addition of the Bcd homeodomain to eGFP::NLS qualitatively replicates the Bcd concentration profile, suggesting this domain regulates Bcd dynamics. Our results reveal how a long-range gradient can form while retaining a steep profile through much of its range.

Cortex-driven cytoplasmic flows in elongated cells: fluid mechanics and application to nuclear transport in Drosophila embryos

The Drosophila melanogaster embryo, an elongated multi-nucleated cell, is a classical model system for eukaryotic development and morphogenesis. Recent work has shown that bulk cytoplasmic flows, driven by cortical contractions along the walls of the embryo, enable the uniform spreading of nuclei along the anterior-posterior axis necessary for proper embryonic development. Here, we propose two mathematical models to characterize cytoplasmic flows driven by tangential cortical contractions in elongated cells. Assuming Newtonian fluid flow at low Reynolds number in a spheroidal cell, we first compute the flow field exactly, thereby bypassing the need for numerical computations. We then apply our results to recent experiments on nuclear transport in cell cycles 4-6 of Drosophila embryo development. By fitting the cortical contractions in our model to measurements, we reveal that experimental cortical flows enable near-optimal axial spreading of nuclei. A second mathematical approach, applicable to general elongated cell geometries, exploits a long-wavelength approximation to produce an even simpler solution, with errors below [Formula: see text] compared with the full model. An application of this long-wavelength result to transport leads to fully analytical solutions for the nuclear concentration that capture the essential physics of the system, including optimal axial spreading of nuclei.