Using multicanonical Metropolis simulations we estimate phase transition properties of 3D Potts models for q = 4 to 10: The transition temperatures, latent heats, entropy gaps, normalized entropies at the disordered and ordered endpoints, interfacial tensions, and spinodal endpoints.

Obligate biotrophic pathogens like the pea powdery mildew (PM) Erysiphe pisi establish long-term feeding relationships with their host, during which they siphon sugars from host cells through haustoria. Plants in turn deploy sugar transporters to restrict carbon allocation toward pathogens, as a defense mechanism. Studies in Arabidopsis have shown that sugar transport protein 13 (STP13), a proton-hexose symporter involved in apoplasmic hexose retrieval, contributes to bacterial and necrotrophic fungal resistance by limiting sugar flux toward these pathogens. By contrast, expression of Lr67res, a transport-deficient wheat STP13 variant harboring two amino acid substitutions (G144R and V387L), conferred resistance against biotrophic fungi in wheat and barley, indicating its broad applicability in disease management. Here, we investigated the role of STP13 and STP13G144R in legume–PM interactions. We show that Medicago truncatula STP13.1 is a proton-hexose symporter involved in basal resistance against PM and indirectly show that Lr67res-mediated PM resistance, so far reported only in monocots, is transferable to legumes. Among the 30 MtSTPs, STP13.1 exhibited the highest fold induction in PM-challenged leaves and was also responsive to chitosan, ABA and sugar treatment. Functional assays in yeast showed that introduction of the G144R mutation but not V388L abolished MtSTP13.1’s hexose uptake ability. Virus-induced gene silencing of MtSTP13 repressed pathogenesis-related (PR) gene expression and enhanced PM susceptibility in M. truncatula whereas transient overexpression of MtSTP13.1 or MtSTP13.1G144R in pea induced PR and isoflavonoid pathway genes and enhanced PM resistance. We propose a model in which STP13.1-mediated sugar signaling triggers defense responses against PM in legumes.

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We study the Kolmogorov-Johnson-Mehl-Avrami theory of phase conversion in finite volumes. For the conversion time we find the relationship tau(con)=tau(nu)[1+f(d)(q)]. Here d is the space dimension, tau(nu) the nucleation time in the volume V, and f(d)(q) a scaling function. Its dimensionless argument is q=tau(ex)/tau(nu), where tau(ex) is an expansion time, defined to be proportional to the diameter of the volume divided by expansion speed. We calculate f(d)(q) in one, two, and three dimensions. The often considered limits of phase conversion via either nucleation or spinodal decomposition are found to be volume-size dependent concepts, governed by simple power laws for f(d)(q).