Wildebeest herds on rolling hills: Flocking on arbitrary curved surfaces.

The collective behavior of active agents, whether herds of wildebeest or microscopic actin filaments propelled by molecular motors, is an exciting frontier in biological and soft matter physics. Almost three decades ago, Toner and Tu developed a continuum theory of the collective action of flocks, or herds, that helped launch the modern field of active matter. One challenge faced when applying continuum active matter theories to living phenomena is the complex geometric structure of biological environments. Both macroscopic and microscopic herds move on asymmetric curved surfaces, like undulating grass plains or the surface layers of cells or embryos, which can render problems analytically intractable. In this paper, we present a formulation of the Toner-Tu flocking theory that uses the finite element method to solve the governing equations on arbitrary curved surfaces. First, we test the developed formalism and its numerical implementation in channel flow with scattering obstacles and on cylindrical and spherical surfaces, comparing our results to analytical solutions. We then progress to surfaces with arbitrary curvature, moving beyond previously accessible problems to explore herding behavior on a variety of landscapes. This approach allows the investigation of transients and dynamic solutions not revealed by analytic methods. It also enables versatile incorporation of new geometries and boundary conditions and efficient sweeps of parameter space. Looking forward, the paper presented here lays the groundwork for a dialogue between Toner-Tu theory and data on collective motion in biologically relevant geometries, from drone footage of migrating animal herds to movies of microscopic cytoskeletal flows within cells.

Fundamental limits on the rate of bacterial growth and their influence on proteomic composition.

Despite abundant measurements of bacterial growth rate, cell size, and protein content, we lack a rigorous understanding of what sets the scale of these quantities and when protein abundances should (or should not) depend on growth rate. Here, we estimate the basic requirements and physical constraints on steady-state growth by considering key processes in cellular physiology across a collection of Escherichia coli proteomic data covering ≈4,000 proteins and 36 growth rates. Our analysis suggests that cells are predominantly tuned for the task of cell doubling across a continuum of growth rates; specific processes do not limit growth rate or dictate cell size. We present a model of proteomic regulation as a function of nutrient supply that reconciles observed interdependences between protein synthesis, cell size, and growth rate and propose that a theoretical inability to parallelize ribosomal synthesis places a firm limit on the achievable growth rate. A record of this paper's transparent peer review process is included in the supplemental information.

Characterization of the interaction between ß-catenin and sorting nexin 27: contribution of the type I PDZ-binding motif to Wnt signaling.

BACKGROUND: Sorting Nexin 27 (SNX27) is a 62-kDa protein localized to early endosomes and known to regulate the intracellular trafficking of ion channels and receptors. In addition to a PX domain common among all of the sorting nexin family, SNX27 is the only sorting family member that contains a PDZ domain. To identify novel SNX27-PDZ binding partners, we performed a proteomic screen in mouse principal kidney cortical collecting duct cells (mpkCCD) using a GST-SNX27 fusion construct as bait. We found that the C-terminal type I PDZ binding motif (DTDL) of ß-catenin, an adherens junction scaffolding protein and transcriptional co-activator, interacts directly with SNX27. Using biochemical and immunofluorescent techniques, ß-catenin was identified in endosomal compartments where co-localization with SNX27 was observed. Furthermore, E-cadherin, but not Axin, GSK3 or Lef-1 was located in SNX27 protein complexes. While overexpression of wild-type ß-catenin protein increased TCF-LEF dependent transcriptional activity, an enhanced transcriptional activity was not observed in cells expressing ß-Catenin ΔFDTDL or diminished SNX27 expression. These results imply importance of the C-terminal PDZ binding motif for the transcriptional activity of ß-catenin and propose that SNX27 might be involved in the assembly of ß-catenin complexes in the endosome.

Microtubule End-Clustering Maintains a Steady-State Spindle Shape.

Each time a cell divides, the microtubule cytoskeleton self-organizes into the metaphase spindle: an ellipsoidal steady-state structure that holds its stereotyped geometry despite microtubule turnover and internal stresses [1-6]. Regulation of microtubule dynamics, motor proteins, microtubule crosslinking, and chromatid cohesion can modulate spindle size and shape, and yet modulated spindles reach and hold a new steady state [7-11]. Here, we ask what maintains any spindle steady-state geometry. We report that clustering of microtubule ends by dynein and NuMA is essential for mammalian spindles to hold a steady-state shape. After dynein or NuMA deletion, the mitotic microtubule network is "turbulent"; microtubule bundles extend and bend against the cell cortex, constantly remodeling network shape. We find that spindle turbulence is driven by the homotetrameric kinesin-5 Eg5, and that acute Eg5 inhibition in turbulent spindles recovers spindle geometry and stability. Inspired by in vitro work on active turbulent gels of microtubules and kinesin [12, 13], we explore the kinematics of this in vivo turbulent network. We find that turbulent spindles display decreased nematic order and that motile asters distort the nematic director field. Finally, we see that turbulent spindles can drive both flow of cytoplasmic organelles and whole-cell movement-analogous to the autonomous motility displayed by droplet-encapsulated turbulent gels [12]. Thus, end-clustering by dynein and NuMA is required for mammalian spindles to reach a steady-state geometry, and in their absence Eg5 powers a turbulent microtubule network inside mitotic cells.

Newly synthesized polycystin-1 takes different trafficking pathways to the apical and ciliary membranes.

Mutations in the genes encoding polycystin-1 (PC1) and polycystin 2 (PC2) cause autosomal dominant polycystic kidney disease. These transmembrane proteins colocalize in the primary cilia of renal epithelial cells, where they may participate in sensory processes. PC1 is also found in the apical membrane when expressed in cultured epithelial cells. PC1 undergoes autocatalytic cleavage, producing an extracellular N-terminal fragment that remains noncovalently attached to the transmembrane C-terminus. Exposing cells to alkaline solutions elutes the N-terminal fragment while the C-terminal fragment is retained in the cell membrane. Utilizing this observation, we developed a "strip-recovery" synchronization protocol to study PC1 trafficking in polarized LLC-PK1 renal epithelial cells. Following alkaline strip, a new cohort of PC1 repopulates the cilia within 30 minutes, while apical delivery of PC1 was not detectable until 3 hours. Brefeldin A (BFA) blocked apical PC1 delivery, while ciliary delivery of PC1 was BFA insensitive. Incubating cells at 20°C to block trafficking out of the trans-Golgi network also inhibits apical but not ciliary delivery. These results suggest that newly synthesized PC1 takes distinct pathways to the ciliary and apical membranes. Ciliary PC1 appears to by-pass BFA sensitive Golgi compartments, while apical delivery of PC1 traverses these compartments.

NuMA recruits dynein activity to microtubule minus-ends at mitosis.

To build the spindle at mitosis, motors exert spatially regulated forces on microtubules. We know that dynein pulls on mammalian spindle microtubule minus-ends, and this localized activity at ends is predicted to allow dynein to cluster microtubules into poles. How dynein becomes enriched at minus-ends is not known. Here, we use quantitative imaging and laser ablation to show that NuMA targets dynactin to minus-ends, localizing dynein activity there. NuMA is recruited to new minus-ends independently of dynein and more quickly than dynactin; both NuMA and dynactin display specific, steady-state binding at minus-ends. NuMA localization to minus-ends involves a C-terminal region outside NuMA's canonical microtubule-binding domain and is independent of minus-end binders γ-TuRC, CAMSAP1, and KANSL1/3. Both NuMA's minus-end-binding and dynein-dynactin-binding modules are required to rescue focused, bipolar spindle organization. Thus, NuMA may serve as a mitosis-specific minus-end cargo adaptor, targeting dynein activity to minus-ends to cluster spindle microtubules into poles.

Increased lateral microtubule contact at the cell cortex is sufficient to drive mammalian spindle elongation.

The spindle is a dynamic structure that changes its architecture and size in response to biochemical and physical cues. For example, a simple physical change, cell confinement, can trigger centrosome separation and increase spindle steady-state length at metaphase. How this occurs is not understood, and is the question we pose here. We find that metaphase and anaphase spindles elongate at the same rate when confined, suggesting that similar elongation forces can be generated independent of biochemical and spindle structural differences. Furthermore, this elongation does not require bipolar spindle architecture or dynamic microtubules. Rather, confinement increases numbers of astral microtubules laterally contacting the cortex, shifting contact geometry from "end-on" to "side-on." Astral microtubules engage cortically anchored motors along their length, as demonstrated by outward sliding and buckling after ablation-mediated release from the centrosome. We show that dynein is required for confinement-induced spindle elongation, and both chemical and physical centrosome removal demonstrate that astral microtubules are required for such spindle elongation and its maintenance. Together the data suggest that promoting lateral cortex-microtubule contacts increases dynein-mediated force generation and is sufficient to drive spindle elongation. More broadly, changes in microtubule-to-cortex contact geometry could offer a mechanism for translating changes in cell shape into dramatic intracellular remodeling.

Kinesin-5: A Team Is Just the Sum of Its Parts.

How the cell builds a spindle remains an open question. In this issue of Developmental Cell, Shimamoto, Forth, and Kapoor (2015) show that kinesin-5 motor ensembles can exert sliding forces that scale with microtubule overlap length. This behavior could allow microtubule architecture-dependent modulation of force and contribute to spindle self-organization.

Force on spindle microtubule minus ends moves chromosomes.

The spindle is a dynamic self-assembling machine that coordinates mitosis. The spindle's function depends on its ability to organize microtubules into poles and maintain pole structure despite mechanical challenges and component turnover. Although we know that dynein and NuMA mediate pole formation, our understanding of the forces dynamically maintaining poles is limited: we do not know where and how quickly they act or their strength and structural impact. Using laser ablation to cut spindle microtubules, we identify a force that rapidly and robustly pulls severed microtubules and chromosomes poleward, overpowering opposing forces and repairing spindle architecture. Molecular imaging and biophysical analysis suggest that transport is powered by dynein pulling on minus ends of severed microtubules. NuMA and dynein/dynactin are specifically enriched at new minus ends within seconds, reanchoring minus ends to the spindle and delivering them to poles. This force on minus ends represents a newly uncovered chromosome transport mechanism that is independent of plus end forces at kinetochores and is well suited to robustly maintain spindle mechanical integrity.

Sorting nexin 27 (SNX27) associates with zonula occludens-2 (ZO-2) and modulates the epithelial tight junction.

Proteins of the SNX (sorting nexin) superfamily are characterized by the presence of a PX (Phox homology) domain and associate with PtdIns3P (phosphatidylinositol-3-monophosphate)-rich regions of the endosomal system. SNX27 is the only sorting nexin that contains a PDZ domain. In the present study, we used a proteomic approach to identify a novel interaction between SNX27 and ZO-2 [zonula occludens-2; also known as TJP2 (tight junction protein 2)], a component of the epithelial tight junction. The SNX27-ZO-2 interaction requires the PDZ domain of SNX27 and the C-terminal PDZ-binding motif of ZO-2. When tight junctions were perturbed by chelation of extracellular Ca2+, ZO-2 transiently localized to SNX27-positive early endosomes. Depletion of SNX27 in mpkCCD (mouse primary kidney cortical collecting duct) cell monolayers resulted in a decrease in the rate of ZO-2, but not ZO-1, mobility at cell-cell contact regions after photobleaching and an increase in junctional permeability to large solutes. The findings of the present study identify an important new SNX27-binding partner and suggest a role for endocytic pathways in the intracellular trafficking of ZO-2 and possibly other tight junction proteins. Our results also indicate a role for SNX27-ZO-2 interactions in tight junction maintenance and function.