Coupling of Active Motion and Advection Shapes Intracellular Cargo Transport

Intracellular cargo transport can arise from passive diffusion, active motor-driven transport along cytoskeletal filament networks, and passive advection by fluid flows entrained by such motor/cargo motion. Active and advective transport are thus intrinsically coupled as related, yet different representations of the same underlying network structure. A reaction-advection-diffusion system is used here to show that this coupling affects the transport and localization of a passive tracer in a confined geometry. For sufficiently low diffusion, cargo localization to a target zone is optimized either by low reaction kinetics and decoupling of bound and unbound states, or by a mostly disordered cytoskeletal network with only weak directional bias. These generic results may help to rationalize subtle features of cytoskeletal networks, for example as observed for microtubules in fly oocytes.Comment: revtex, 5 pages, 5 figures, to appear in PRL (http://prl.aps.org/

Polarization of PAR Proteins by Advective Triggering of a Pattern-Forming System

In the Caenorhabditis elegans zygote, a conserved network of partitioning-defective (PAR) polarity proteins segregates into an anterior and a posterior domain, facilitated by flows of the cortical actomyosin meshwork. The physical mechanisms by which stable asymmetric PAR distributions arise from transient cortical flows remain unclear. We present evidence that PAR polarity arises from coupling of advective transport by the flowing cell cortex to a multistable PAR reaction-diffusion system. By inducing transient PAR segregation, advection serves as a mechanical trigger for the formation of a PAR pattern within an otherwise stably unpolarized system. We suggest that passive advective transport in an active and flowing material may be a general mechanism for mechanochemical pattern formation in developmental systems

Localised dynactin protects growing microtubules to deliver oskar mRNA to the posterior cortex of the Drosophila oocyte.

The localisation of oskar mRNA to the posterior of the Drosophila oocyte defines where the abdomen and germ cells form in the embryo. Kinesin 1 transports oskar mRNA to the oocyte posterior along a polarised microtubule cytoskeleton that grows from non-centrosomal microtubule organising centres (ncMTOCs) along the anterior/lateral cortex. Here, we show that the formation of this polarised microtubule network also requires the posterior regulation of microtubule growth. A missense mutation in the dynactin Arp1 subunit causes most oskar mRNA to localise in the posterior cytoplasm rather than cortically. oskar mRNA transport and anchoring are normal in this mutant, but the microtubules fail to reach the posterior pole. Thus, dynactin acts as an anti-catastrophe factor that extends microtubule growth posteriorly. Kinesin 1 transports dynactin to the oocyte posterior, creating a positive feedback loop that increases the length and persistence of the posterior microtubules that deliver oskar mRNA to the cortex

Parameter-space topology of models for cell polarity

Reaction-diffusion systems have been widely successful in the theoretical description of biological patterning phenomena, giving rise to numerous models based on differing mechanisms, mathematical implementations and parameter choices. However, even for models with common design features, the diversity of mathematical realizations may hinder the identification of common behavior. Here, we analyze three different reaction-diffusion models for cell polarity that feature conservation of mass, rapid cytoplasmic diffusion and bistability via a cusp bifurcation of uniform states. In all three models, the nonuniform polar states are front solutions, and growth of domains ceases through stalling of a propagating front. For these three models we find a characteristic parameter space topology, comprising a region of linear instability that loops around the cusp point and that is enclosed by a 'comet-shaped' region of nonuniform domain states. We propose a minimal model based on the cusp bifurcation normal form that includes essential characteristics of all cell polarity models considered. For this minimal model, we provide a complete analytical description of the parameter space topology, and find that the instability loop appears as a generic property of the cusp bifurcation. This topological analysis provides a unifying understanding of earlier mathematically distinct models and is suitable to classify future models. © 2014 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.SWG acknowledges funding from the European Research Council/ERC Grant agreement no 281903.Peer Reviewe

Polarization of PAR proteins by advective triggering of a pattern-forming system

In the Caenorhabditis elegans zygote, a conserved network of partitioning-defective (PAR) polarity proteins segregates into an anterior and a posterior domain, facilitated by flows of the cortical actomyosin meshwork. The physical mechanisms by which stable asymmetric PAR distributions arise from transient cortical flows remain unclear. We present evidence that PAR polarity arises from coupling of advective transport by the flowing cell cortex to a multistable PAR reaction-diffusion system. By inducing transient PAR segregation, advection serves as a mechanical trigger for the formation of a PAR pattern within an otherwise stably unpolarized system. We suggest that passive advective transport in an active and flowing material may be a general mechanism for mechanochemical pattern formation in developmental systems.Peer Reviewe

Dynamics of a Volvox

Spherical embryos of the algal genus $Volvox$ must turn themselves inside out to complete their embryogenesis. This `inversion', which shares important features with morphological events such as gastrulation in animals, is perhaps the simplest example of a topological transition in developmental biology. Waves of cell shape changes are believed to play a major role in the process, but quantification of the dynamics and formulation of a mathematical description of the process have been lacking. Here, we use selective plane illumination microscopy on $V. globator$ to obtain the first quantitative three-dimensional visualizations of inversion $in~vivo$. A theory is formulated for inversion based on local variations of intrinsic curvature and stretching of an elastic shell, and for the mechanics of an elastic snap-through resisted by the surrounding fluid.Comment: 5 pages, 4 figures, video available on request to [email protected]