Patterning and polarization of cells by intracellular flows

Abstract

Beginning with Turing's seminal work [1], decades of research have demonstrated the fundamental ability of biochemical networks to generate and sustain the formation of patterns. However, it is increasingly appreciated that biochemical networks also both shape and are shaped by physical and mechanical processes [2, 3, 4]. One such process is fluid flow. In many respects, the cytoplasm, membrane and actin cortex all function as fluids, and as they flow, they drive bulk transport of molecules throughout the cell. By coupling biochemical activity to long-range molecular transport, flows can shape the distributions of molecules in space. Here, we review the various types of flows that exist in cells, with the aim of highlighting recent advances in our understanding of how flows are generated and how they contribute to intracellular patterning processes, such as the establishment of cell polarity.

Keywords: Actomyosin; Advection; Cell polarity; Cortical flow; Membrane flow; Self-organization.

Figure 1

Types of flows (a) Treadmilling driven transport. During Pseudomonas phage infection, tubulin-like filaments (PhuZ, orange) play important roles in centering a nucleus-like structure containing phage DNA, trans port of viral capsids, and their distribution around the nuclear surface. PhuZ polymerization at the cells poles drives treadmilling and flux of subunits, which carry the attached viral capsids (blue) to the cell center. Treadmilling of PhuZ filaments also drives rotation of the phage nucleus (dark blue) to distribute arriving capsids around its surface. (b) Long range cortical flow. In the C. elegans zygote, cortical actomyosin flow is induced by anisotropy of network contractility. This anisotropy is caused by the sperm-donated centriole, which stimulates the local down-regulation of non-muscle myosin II activity (purple foci) at the posterior pole, resulting in anterior directed flow (red arrows) of cortical actin (orange). (c) In migrating cells, a polarized cycle of endo and exocytosis of membrane components, with exocytosis at the leading edge coupled to endocytosis at the cell rear, leads to retrograde flow of material in the bilayer (red arrows). It has been hypothesized that this membrane flow could act as a ‘fluid drive’ to propel the cell forward.

Figure 2

Viscous coupling of fluid layers. (a) Model for reverse fountain flow streaming driven by cortical actomyosin (red). Here flow of the actomyosin cortex (red arrows) generates shear stress, which is transmitted to the overlaying membrane (brown arrows) and adjacent cytoplasm (orange arrows). Motion of the cortex can therefore be coupled to flow of both cytoplasmic components (green arrows) and transmembrane proteins with their surrounding lipids (dark brown arrows, inset). (b) Model of circulatory flow (cyclosis) in a plant cell. Myosin XI (purple, inset) transports large organelles, such as the ER, along oriented cortical actin filaments (purple arrows), inducing flow of the cytoplasm (orange arrows) in which they are moving. The cytoplasm is hydrodynamically coupled to the vacuole interior (green) via the vacuolar membrane. Thus, shear stress originating from Myosin XI motion at the cell cortex propagates throughout the various compartments of the cell, driving the observed pattern of fluid flow.

Figure 3

Flow-induced asymmetry depends on the ratio of diffusive and advective transport. For membrane-associated species subject to advection, asymmetric accumulation by flow will depend on multiple factors: flow velocity, diffusion rates on the membrane and in the cytoplasm, and the rate of exchange between the membrane and cytoplasmic compartments. Here we consider two simplified cases in which flow velocity is held constant and we vary either diffusion or membrane dissociation rates. In (a), we consider a molecule that is stably associated with the membrane (i.e. does not exchange). For a given flow velocity, asymmetry is inversely related to the diffusion coefficient gradients steepen as the diffusion is reduced (i.e. increasing Pe). In (b), we consider the case of varying membrane detachment rates, holding diffusion in the two compartments fixed, in this case (D_mem = 0, D_cyto = 1 μm²/s). Here, asymmetry declines with decreasing lifetime of the bound state, as the time spent being advected is decreased relative to the time spent diffusing (i.e. decreasing Pe). Plots show distributions from a 1-D simulation implementing a graded velocity function across the system where flow velocity u = -0.005 * x (μm/s). Concentration shown in green.

Figure 4

Examples of flow-induced polarity. (a) Kinesin-dependent microtubule streaming (MTs in blue) in the Drosophila stage 10B oocyte drives the mixing of oskar mRNA and RNA-binding proteins (green) allowing it to sample the cell cytoplasm. Inset illustrates myosin V-dependent (purple) entrapment of RNPs at the posterior cortex. (b) In the multi-nucleated fungus Neurospora crassa, hyphal filaments are compartmentalized by septa, perforated by a central pore. Bulk cytoplasm flows unidirectionally (black arrows) through these pores, generating flow vortices known as eddies in the corners of the hyphal compartments. Nuclei and other organelles become trapped in these eddies (yellow), forming aggregates in which the behavior of organelles changes. In particular, confined nuclei engage distinct develop mental programs compared to flowing nuclei (grey) that are associated with the microtubule network (blue), leading to asymmetry within the hyphal compartments. (c) In the C. elegans embryo, clustering of PAR-3 is critical for advective transport by anterior-directed cortical flow. PAR-3 monomers (top inset) are highly diffusive and exchange between the membrane and cytoplasm rapidly, making advection inefficient (low Pe). By contrast, PAR-3 dependent clusters (bottom inset) remain membrane-associated much longer and exhibit reduced diffusion, facilitating long range transport. (d) (i) In migrating cells, retrograde actin flow transports molecules towards the rear end of the cell. The accumulation of molecules at the rear by flow is opposed by turnover at the membrane which allows molecules to be recycled back to the cell front. A fast rate of turnover and recycling coupled to local deposition at the leading edge allows concentration at the cell front (yellow species), while slow turnover (green) drives accumulation at the rear. (ii) Altering turnover in a simple mathematical model of advective transport dramatically alters the concentration profile of molecules across the cell. Here a slowly diffusing molecule on the membrane (D = 0.01 μm²/s) is subject to flow as in Figure 3 and recycled to the cell front at variable rates k_recy.