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, 2, 3, 4, 5, 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, 8, 9, 10, 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

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, 2, 3, 4, 5, 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, 8, 9, 10, 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

Fundamental limits on the rate of bacterial growth

Recent years have seen an experimental deluge interrogating the relationship between bacterial growth rate, cell size, and protein content, quantifying the abundance of proteins across growth conditions with unprecedented resolution. However, we still 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 seek to quantitatively understand this relationship across a collection of Escherichia coli proteomic data covering ≈ 4000 proteins and 36 growth rates. We estimate the basic requirements for steady-state growth by considering key processes in nutrient transport, cell envelope biogenesis, energy generation, and the central dogma. From these estimates, ribosome biogenesis emerges as a primary determinant of growth rate. We expand on this assessment by exploring a model of proteomic regulation as a function of the nutrient supply, revealing a mechanism that ties cell size and growth rate to ribosomal content

Fundamental limits on the rate of bacterial growth

Recent years have seen an experimental deluge interrogating the relationship between bacterial growth rate, cell size, and protein content, quantifying the abundance of proteins across growth conditions with unprecedented resolution. However, we still 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 seek to quantitatively understand this relationship across a collection of Escherichia coli proteomic data covering ≈ 4000 proteins and 36 growth rates. We estimate the basic requirements for steady-state growth by considering key processes in nutrient transport, cell envelope biogenesis, energy generation, and the central dogma. From these estimates, ribosome biogenesis emerges as a primary determinant of growth rate. We expand on this assessment by exploring a model of proteomic regulation as a function of the nutrient supply, revealing a mechanism that ties cell size and growth rate to ribosomal content

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 hydrodynamic 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 work, 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. Our 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 work 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.Comment: 46 pages, 16 figures, 4 video

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

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