Physical limits on kinesin-5–mediated chromosome congression in the smallest mitotic spindles

A characteristic feature of mitotic spindles is the congression of chromosomes near the spindle equator, a process mediated by dynamic kinetochore microtubules. A major challenge is to understand how precise, submicrometer-scale control of kinetochore micro­tubule dynamics is achieved in the smallest mitotic spindles, where the noisiness of microtubule assembly/disassembly will potentially act to overwhelm the spatial information that controls microtubule plus end–tip positioning to mediate congression. To better understand this fundamental limit, we conducted an integrated live fluorescence, electron microscopy, and modeling analysis of the polymorphic fungal pathogen Candida albicans, which contains one of the smallest known mitotic spindles (<1 μm). Previously, ScCin8p (kinesin-5 in Saccharomyces cerevisiae) was shown to mediate chromosome congression by promoting catastrophe of long kinetochore microtubules (kMTs). Using C. albicans yeast and hyphal kinesin-5 (Kip1p) heterozygotes (KIP1/kip1∆), we found that mutant spindles have longer kMTs than wild-type spindles, consistent with a less-organized spindle. By contrast, kinesin-8 heterozygous mutant (KIP3/kip3∆) spindles exhibited the same spindle organization as wild type. Of interest, spindle organization in the yeast and hyphal states was indistinguishable, even though yeast and hyphal cell lengths differ by two- to fivefold, demonstrating that spindle length regulation and chromosome congression are intrinsic to the spindle and largely independent of cell size. Together these results are consistent with a kinesin-5–mediated, length-dependent depolymerase activity that organizes chromosomes at the spindle equator in C. albicans to overcome fundamental noisiness in microtubule self-assembly. More generally, we define a dimensionless number that sets a fundamental physical limit for maintaining congression in small spindles in the face of assembly noise and find that C. albicans operates very close to this limit, which may explain why it has the smallest known mitotic spindle that still manifests the classic congression architecture.     

Mathematical Modelling of Anaerobic Reactors Treating Domestic Wastewater: Rational Criteria for Model Use

Anaerobic digestion modelling is an established method for assessing anaerobic wastewater treatment for design, systems analysis, operational analysis, and control. Anaerobic treatment of domestic wastewater is a relatively new, but rapidly maturing technology, especially in developing countries, where the combination of low cost, and moderate-good performance are particularly attractive. The key emerging technology is high-rate anaerobic treatment, particularly UASB reactors. Systems modelling can potentially offer a number of advantages to this field, and the key motivations for modelling have been identified as operational analysis, technology development, and model-based design. Design is particularly important, as it determines capital cost, a key motivation for implementers. Published modelling studies for anaerobic domestic sewage treatment are limited in number, but well directed at specific issues. Most have a low structural complexity, with first order kinetics, as compared to the more commonly used Monod kinetics. This review addresses the use of anaerobic models in general, application of models to domestic sewage systems, and evaluates future requirements for models that need to address the key motivations of operational analysis, technology development, and model-based design. For operational analysis and technology development, a complex model such as the ADM1 is recommended, with further extensions as required to address factors such as sulphate reduction. For design, the critical issSues are hydraulics and particles (i.e., biomass and solid substrate) modelling. Therefore, the kinetic structure should be relatively simple (at least two-step), but the hydraulic and particulate model should be relatively complex.     

Where to Dig for Fossils: Combining Climate-Envelope,Taphonomy and Discovery Models

Fossils represent invaluable data to reconstruct the past history of life, yet fossil-rich sites are often rare and difficult to find. The traditional fossil-hunting approach focuses on small areas and has not yet taken advantage of modelling techniques commonly used in ecology to account for an organism’s past distributions. We propose a new method to assist finding fossils at continental scales based on modelling the past distribution of species, the geological suitability of fossil preservation and the likelihood of fossil discovery in the field, and apply it to several genera of Australian megafauna that went extinct in the Late Quaternary. Our models predicted higher fossil potentials for independent sites than for randomly selected locations (mean Kolmogorov-Smirnov statistic = 0.66). We demonstrate the utility of accounting for the distribution history of fossil taxa when trying to find the most suitable areas to look for fossils. For some genera, the probability of finding fossils based on simple climate-envelope models was higher than the probability based on models incorporating current conditions associated with fossil preservation and discovery as predictors. However, combining the outputs from climate-envelope, preservation, and discovery models resulted in the most accurate predictions of potential fossil sites at a continental scale. We proposed potential areas to discover new fossils of Diprotodon, Zygomaturus, Protemnodon, Thylacoleo, and Genyornis, and provide guidelines on how to apply our approach to assist fossil hunting in other continents and geological settings.     

Variances of selection differentials in normal samples.

Standardized variances of selection differentials are defined in general and then considered in detail for the case of directional selection on the basis of normally distributed test scores. Symmetry properties, bounds and asymptotic values for the variances are derived. The results are used to investigate the variance of response to selection.