During metaphase, forces on kinetochores are exerted by k-fibres, bundles of microtubules that end at the kinetochore. Interestingly, non-kinetochore microtubules have been observed between sister kinetochores, but their function is unknown. Here we show by laser-cutting of a k-fibre in HeLa and PtK1 cells that a bundle of non-kinetochore microtubules, which we term ‘bridging fibre', bridges sister k-fibres and balances the interkinetochore tension. We found PRC1 and EB3 in the bridging fibre, suggesting that it consists of antiparallel dynamic microtubules. By using a theoretical model that includes a bridging fibre, we show that the forces at the pole and at the kinetochore depend on the bridging fibre thickness. Moreover, our theory and experiments show larger relaxation of the interkinetochore distance for cuts closer to kinetochores. We conclude that the bridging fibre, by linking sister k-fibres, withstands the tension between sister kinetochores and enables the spindle to obtain a curved shape.

Theoretical studies have predicted a trade-off between growth rate and yield in heterotrophic organisms. Here we test for the existence of this trade-off by analyzing the growth characteristics of 12 E. coli B populations that evolved for 20,000 generations under a constant selection regime. We performed three different tests. First, we analyzed changes in growth rate and yield over evolutionary time for each population. Second, we tested for a negative correlation between rate and yield across the 12 populations. Finally, we isolated clones from four selected populations and tested for a negative correlation between rate and yield within these populations. We did not find evidence for a trade-off based on the first two tests. However, we did observe a trade-off based on the within-population correlation of yield and rate. Our results indicate that, at least for the populations studied here, an analysis of the within-population diversity might be the most sensitive test for the existence of a trade-off. The observation of a trade-off within, but not between, populations suggests that the populations evolved different genetic solutions for growth in the selective environment, which in turn led to different physiological constraints.

Mitosis relies on forces generated in the spindle, a micro-machine composed of microtubules and associated proteins. Forces are required for the congression of chromosomes to the metaphase plate and their separation in anaphase. However, besides forces, torques may exist in the spindle, yet they have not been investigated. Here we show that the spindle is chiral. Chirality is evident from the finding that microtubule bundles in human spindles follow a left-handed helical path, which cannot be explained by forces but rather by torques. Kinesin-5 (Kif11/Eg5) inactivation abolishes spindle chirality. Our theoretical model predicts that bending and twisting moments may generate curved shapes of bundles. We found that bundles turn by about −2 deg µm−1 around the spindle axis, which we explain by a twisting moment of roughly −10 pNµm. We conclude that torques, in addition to forces, exist in the spindle and determine its chiral architecture.

Biological cells estimate concentration gradients of signaling molecules with a precision that is limited not only by sensing noise, but additionally by the cell’s own stochastic motion. We ask for the theoretical limits of gradient estimation in the presence of both motility and sensing noise. We introduce a minimal model of a stationary chemotactic agent in the plane subject to rotational diffusion with rotational diffusion coefficient D. The agent uses Bayesian estimation to optimally infer the gradient direction relative to itself from noisy concentration measurements. Meanwhile, this direction changes on a time-scale 1/D. We show that the optimal effective measurement time, which characterizes the time interval over which past gradient measurements should be averaged to reduce sensing noise, does not scale with the rotational diffusion time 1/D, but with the square root (rD)−1/2, where r is a rate of information gain defined as a signal-to-noise ratio normalized per unit time. This result for gradient sensing parallels a recent result by Mora et al (2019 Phys. Rev. Lett.) for sensing absolute concentration in time-varying environments.