Applying Tensile and Compressive Force to Xenopus Animal Cap Tissue

Relaxation and Noise-Driven Oscillations in a Model of Mitotic Spindle Dynamics

During cell division, the mitotic spindle moves dynamically through the cell to position the chromosomes and determine the ultimate spatial position of the two daughter cells. These movements have been attributed to the action of cortical force generators which pull on the astral microtubules to position the spindle, as well as pushing events by these same microtubules against the cell cortex and plasma membrane. Attachment and detachment of cortical force generators working antagonistically against centring forces of microtubules have been modelled previously (Grill et al. in Phys Rev Lett 94:108104, 2005) via stochastic simulations and mean-field Fokker-Planck equations (describing random motion of force generators) to predict oscillations of a spindle pole in one spatial dimension. Using systematic asymptotic methods, we reduce the Fokker-Planck system to a set of ordinary differential equations (ODEs), consistent with a set proposed by Grill et al., which can provide accurate predictions of the conditions for the Fokker-Planck system to exhibit oscillations. In the limit of small restoring forces, we derive an algebraic prediction of the amplitude of spindle-pole oscillations and demonstrate the relaxation structure of nonlinear oscillations. We also show how noise-induced oscillations can arise in stochastic simulations for conditions in which the mean-field Fokker-Planck system predicts stability, but for which the period can be estimated directly by the ODE model and the amplitude by a related stochastic differential equation that incorporates random binding kinetics.

The Use of Xenopus for Cell Biology Applications

Problems of cell biology and the molecular controls underpinning them have been studied in the remarkably versatile Xenopus systems for many years. This versatility is showcased in several accompanying protocols, which are introduced here. One protocol demonstrates how the Xenopus embryonic ectoderm can be used to study the effects of mechanical cell deformation; another illustrates how the developing eye can be used as a platform for determining cell-cycle length. Two protocols show how extracts from Xenopus embryos can be exploited to characterize the behavior of specific intracellular proteins-specifically, to determine protein phosphorylation status and the ability to bind to chromatin. Finally, because specific antibodies to Xenopus proteins are pivotal reagents for cell biology and biochemistry applications, four protocols describing how to generate, purify, and assay the specificity of antibodies raised against Xenopus proteins are included in hopes of stimulating the expansion of these critical resources across the Xenopus community.