TY - JOUR AB - Using the geodesic distance on the n-dimensional sphere, we study the expected radius function of the Delaunay mosaic of a random set of points. Specifically, we consider the partition of the mosaic into intervals of the radius function and determine the expected number of intervals whose radii are less than or equal to a given threshold. We find that the expectations are essentially the same as for the Poisson–Delaunay mosaic in n-dimensional Euclidean space. Assuming the points are not contained in a hemisphere, the Delaunay mosaic is isomorphic to the boundary complex of the convex hull in Rn+1, so we also get the expected number of faces of a random inscribed polytope. As proved in Antonelli et al. [Adv. in Appl. Probab. 9–12 (1977–1980)], an orthant section of the n-sphere is isometric to the standard n-simplex equipped with the Fisher information metric. It follows that the latter space has similar stochastic properties as the n-dimensional Euclidean space. Our results are therefore relevant in information geometry and in population genetics. AU - Edelsbrunner, Herbert AU - Nikitenko, Anton ID - 87 IS - 5 JF - Annals of Applied Probability TI - Random inscribed polytopes have similar radius functions as Poisson-Delaunay mosaics VL - 28 ER - TY - JOUR AB - The phytohormone auxin is the information carrier in a plethora of developmental and physiological processes in plants(1). It has been firmly established that canonical, nuclear auxin signalling acts through regulation of gene transcription(2). Here, we combined microfluidics, live imaging, genetic engineering and computational modelling to reanalyse the classical case of root growth inhibition(3) by auxin. We show that Arabidopsis roots react to addition and removal of auxin by extremely rapid adaptation of growth rate. This process requires intracellular auxin perception but not transcriptional reprogramming. The formation of the canonical TIR1/AFB-Aux/IAA co-receptor complex is required for the growth regulation, hinting to a novel, non-transcriptional branch of this signalling pathway. Our results challenge the current understanding of root growth regulation by auxin and suggest another, presumably non-transcriptional, signalling output of the canonical auxin pathway. AU - Fendrych, Matyas AU - Akhmanova, Maria AU - Merrin, Jack AU - Glanc, Matous AU - Hagihara, Shinya AU - Takahashi, Koji AU - Uchida, Naoyuki AU - Torii, Keiko U AU - Friml, Jirí ID - 192 IS - 7 JF - Nature Plants TI - Rapid and reversible root growth inhibition by TIR1 auxin signalling VL - 4 ER - TY - JOUR AB - The intercellular transport of auxin is driven by PIN-formed (PIN) auxin efflux carriers. PINs are localized at the plasma membrane (PM) and on constitutively recycling endomembrane vesicles. Therefore, PINs can mediate auxin transport either by direct translocation across the PM or by pumping auxin into secretory vesicles (SVs), leading to its secretory release upon fusion with the PM. Which of these two mechanisms dominates is a matter of debate. Here, we addressed the issue with a mathematical modeling approach. We demonstrate that the efficiency of secretory transport depends on SV size, half-life of PINs on the PM, pH, exocytosis frequency and PIN density. 3D structured illumination microscopy (SIM) was used to determine PIN density on the PM. Combining this data with published values of the other parameters, we show that the transport activity of PINs in SVs would have to be at least 1000× greater than on the PM in order to produce a comparable macroscopic auxin transport. If both transport mechanisms operated simultaneously and PINs were equally active on SVs and PM, the contribution of secretion to the total auxin flux would be negligible. In conclusion, while secretory vesicle-mediated transport of auxin is an intriguing and theoretically possible model, it is unlikely to be a major mechanism of auxin transport inplanta. AU - Hille, Sander AU - Akhmanova, Maria AU - Glanc, Matous AU - Johnson, Alexander J AU - Friml, Jirí ID - 14 IS - 11 JF - International Journal of Molecular Sciences TI - Relative contribution of PIN-containing secretory vesicles and plasma membrane PINs to the directed auxin transport: Theoretical estimation VL - 19 ER - TY - JOUR AB - We study how a block of genome with a large number of weakly selected loci introgresses under directional selection into a genetically homogeneous population. We derive exact expressions for the expected rate of growth of any fragment of the introduced block during the initial phase of introgression, and show that the growth rate of a single-locus variant is largely insensitive to its own additive effect, but depends instead on the combined effect of all loci within a characteristic linkage scale. The expected growth rate of a fragment is highly correlated with its long-term introgression probability in populations of moderate size, and can hence identify variants that are likely to introgress across replicate populations. We clarify how the introgression probability of an individual variant is determined by the interplay between hitchhiking with relatively large fragments during the early phase of introgression and selection on fine-scale variation within these, which at longer times results in differential introgression probabilities for beneficial and deleterious loci within successful fragments. By simulating individuals, we also investigate how introgression probabilities at individual loci depend on the variance of fitness effects, the net fitness of the introduced block, and the size of the recipient population, and how this shapes the net advance under selection. Our work suggests that even highly replicable substitutions may be associated with a range of selective effects, which makes it challenging to fine map the causal loci that underlie polygenic adaptation. AU - Sachdeva, Himani AU - Barton, Nicholas H ID - 39 IS - 4 JF - Genetics SN - 00166731 TI - Replicability of introgression under linked, polygenic selection VL - 210 ER - TY - JOUR AB - We analyze the theoretical derivation of the beyond-mean-field equation of state for two-dimensional gas of dilute, ultracold alkali-metal atoms in the Bardeen–Cooper–Schrieffer (BCS) to Bose–Einstein condensate (BEC) crossover. We show that at zero temperature our theory — considering Gaussian fluctuations on top of the mean-field equation of state — is in very good agreement with experimental data. Subsequently, we investigate the superfluid density at finite temperature and its renormalization due to the proliferation of vortex–antivortex pairs. By doing so, we determine the Berezinskii–Kosterlitz–Thouless (BKT) critical temperature — at which the renormalized superfluid density jumps to zero — as a function of the inter-atomic potential strength. We find that the Nelson–Kosterlitz criterion overestimates the BKT temperature with respect to the renormalization group equations, this effect being particularly relevant in the intermediate regime of the crossover. AU - Bighin, Giacomo AU - Salasnich, Luca ID - 420 IS - 17 JF - International Journal of Modern Physics B TI - Renormalization of the superfluid density in the two-dimensional BCS-BEC crossover VL - 32 ER -