Modeling oscillatory Microtubule--Polymerization

Polymerization of microtubules is ubiquitous in biological cells and under certain conditions it becomes oscillatory in time. Here simple reaction models are analyzed that capture such oscillations as well as the length distribution of microtubules. We assume reaction conditions that are stationary over many oscillation periods, and it is a Hopf bifurcation that leads to a persistent oscillatory microtubule polymerization in these models. Analytical expressions are derived for the threshold of the bifurcation and the oscillation frequency in terms of reaction rates as well as typical trends of their parameter dependence are presented. Both, a catastrophe rate that depends on the density of {\it guanosine triphosphate} (GTP) liganded tubulin dimers and a delay reaction, such as the depolymerization of shrinking microtubules or the decay of oligomers, support oscillations. For a tubulin dimer concentration below the threshold oscillatory microtubule polymerization occurs transiently on the route to a stationary state, as shown by numerical solutions of the model equations. Close to threshold a so--called amplitude equation is derived and it is shown that the bifurcation to microtubule oscillations is supercritical.Comment: 21 pages and 12 figure

Active Brownian Particles. From Individual to Collective Stochastic Dynamics

We review theoretical models of individual motility as well as collective dynamics and pattern formation of active particles. We focus on simple models of active dynamics with a particular emphasis on nonlinear and stochastic dynamics of such self-propelled entities in the framework of statistical mechanics. Examples of such active units in complex physico-chemical and biological systems are chemically powered nano-rods, localized patterns in reaction-diffusion system, motile cells or macroscopic animals. Based on the description of individual motion of point-like active particles by stochastic differential equations, we discuss different velocity-dependent friction functions, the impact of various types of fluctuations and calculate characteristic observables such as stationary velocity distributions or diffusion coefficients. Finally, we consider not only the free and confined individual active dynamics but also different types of interaction between active particles. The resulting collective dynamical behavior of large assemblies and aggregates of active units is discussed and an overview over some recent results on spatiotemporal pattern formation in such systems is given.Comment: 161 pages, Review, Eur Phys J Special-Topics, accepte

Microtubule Flux and Sliding in Mitotic Spindles of Drosophila Embryos

We proposed that spindle morphogenesis in Drosophila embryos involves progression through four transient isometric structures in which a constant spacing of the spindle poles is maintained by a balance of forces generated by multiple microtubule (MT) motors and that tipping this balance drives pole-pole separation. Here we used fluorescent speckle microscopy to evaluate the influence of MT dynamics on the isometric state that persists through metaphase and anaphase A and on pole-pole separation in anaphase B. During metaphase and anaphase A, fluorescent punctae on kinetochore and interpolar MTs flux toward the poles at 0.03 μm/s, too slow to drive chromatid-to-pole motion at 0.11 μm/s, and during anaphase B, fluorescent punctae on interpolar MTs move away from the spindle equator at the same rate as the poles, consistent with MT-MT sliding. Loss of Ncd, a candidate flux motor or brake, did not affect flux in the metaphase/anaphase A isometric state or MT sliding in anaphase B but decreased the duration of the isometric state. Our results suggest that, throughout this isometric state, an outward force exerted on the spindle poles by MT sliding motors is balanced by flux, and that suppression of flux could tip the balance of forces at the onset of anaphase B, allowing MT sliding and polymerization to push the poles apart

Resonant microchannel volume and mass measurements show that suspended cells swell during mitosis

Osmotic regulation of intracellular water during mitosis is poorly understood because methods for monitoring relevant cellular physical properties with sufficient precision have been limited. Here we use a suspended microchannel resonator to monitor the volume and density of single cells in suspension with a precision of 1% and 0.03%, respectively. We find that for transformed murine lymphocytic leukemia and mouse pro–B cell lymphoid cell lines, mitotic cells reversibly increase their volume by more than 10% and decrease their density by 0.4% over a 20-min period. This response is correlated with the mitotic cell cycle but is not coupled to nuclear osmolytes released by nuclear envelope breakdown, chromatin condensation, or cytokinesis and does not result from endocytosis of the surrounding fluid. Inhibiting Na-H exchange eliminates the response. Although mitotic rounding of adherent cells is necessary for proper cell division, our observations that suspended cells undergo reversible swelling during mitosis suggest that regulation of intracellular water may be a more general component of mitosis than previously appreciated.National Cancer Institute (U.S.). Physical Sciences-Oncology Center (MIT, (U54CA143874))National Cancer Institute (U.S.) (Koch Institute Support (core) grant P30-CA14051)Samsung Scholarship Foundatio

Bipolarization and Poleward Flux Correlate during Xenopus Extract Spindle Assembly

We investigated the mechanism by which meiotic spindles become bipolar and the correlation between bipolarity and poleward flux, using Xenopus egg extracts. By speckle microscopy and computational alignment, we find that monopolar sperm asters do not show evidence for flux, partially contradicting previous work. We account for the discrepancy by describing spontaneous bipolarization of sperm asters that was missed previously. During spontaneous bipolarization, onset of flux correlated with onset of bipolarity, implying that antiparallel microtubule organization may be required for flux. Using a probe for TPX2 in addition to tubulin, we describe two pathways that lead to spontaneous bipolarization, new pole assembly near chromatin, and pole splitting. By inhibiting the Ran pathway with excess importin-alpha, we establish a role for chromatin-derived, antiparallel overlap bundles in generating the sliding force for flux, and we examine these bundles by electron microscopy. Our results highlight the importance of two processes, chromatin-initiated microtubule nucleation, and sliding forces generated between antiparallel microtubules, in self-organization of spindle bipolarity and poleward flux