From the Frenkel-Kontorova model to Josephson junction arrays - the Aubry's transition as a jamming-glass transition -

The Frenkel Kontorova (FK) model is known to exhibit the so called Aubry's transition which is a jamming or frictional transition at zero temperature. Recently we found similar transition at zero and finite temperatures in a super-conducting Josephson junction array (JJA) on a square lattice under external magnetic field. In the present paper we discuss how these problems are related.Comment: 19 pages, 6 figures. To appear in the proceedings of YKIS2009 Frontiers in Nonequilibrium Physics, Progress in Theoretical Physics supplement 2010

The role of negative regulators in coordination of the Myxococcus xanthus developmental program

Myxococcus xanthus is a prokaryote that has a complex life cycle distinguished by multicellular behaviors and cell differentiation. Upon starvation, Myxococcus xanthus cells enter a developmental program wherein cells have different developmental fates: the majority of cells undergo programmed cell death (PCD), and the remaining cells either migrate into fruiting bodies and then differentiate into spores or do not aggregate and remain as peripheral rods. This developmental program is controlled by a cascade of positive developmental regulators whose expression is subject to positive autoregulation. Several histidine kinase (HK) homologs (espA, espC, red and todK) have been described that are necessary for appropriate progression through the developmental program. Mutants in these genes aggregate and sporulate earlier than wild type, producing disorganized fruiting bodies and spores outside of the fruiting bodies. These observations suggest that these kinases act as negative regulators (NRs) to repress the developmental program, but it is not clear if they function in one or more signaling pathways, how they mediate repression of the developmental program, and what ultimate advantage they provide to the developmental program. Using genetic epistasis analysis, we demonstrate that these NRs are organized into three distinct signaling systems comprised of 1) EspA/EspC, 2) TodK and 3) Red. Consistently, analysis of the accumulation patterns of several developmental regulatory proteins in each NR mutant demonstrated three distinct patterns: 1) in espA and espC mutants most developmental regulators accumulate earlier than in wild type, but the ordered cascade of production is maintained, 2) in red mutants most developmental marker proteins are under accumulated and the ordered cascade of production is not maintained, 3) in todK mutants certain developmental marker proteins are produced earlier than in wild type and the ordered cascade of production is perturbed. Phenotypic analysis of single, double, triple and quadruple NR mutants demonstrated that there is a strong negative correlation between the rate of progression through the developmental program and coordinated fruiting body formation. Loss of coordinated fruiting body formation appeared to be the result of uncoordinated developmental subpopulations. To determine whether the perturbation in the ordered cascade of developmental regulators in the red and todK mutants was due to misregulation of the developmental subpopulations, we first set out to define the temporal proportion of the different cell subpopulations and then examined the accumulation of key developmental regulator proteins in the two developmental subpopulations. Our analyses indicate that the cell population doubles over the course of 24 hours followed by a sudden burst programmed cell death (PCD). The aggregating and non-aggregating subpopulations displayed distinct accumulation patterns of components involved in Type IV pilus-mediated motility, and spore structural proteins. Most key developmental regulator proteins were shown to first gradually accumulate in the non-aggregating cell fraction and then to rapidly accumulate in the aggregating cell fraction. Using a similar approach to analyze the red and todK NR mutants, we demonstrate that both mutants do not increase their population to the same extent as wild type, likely because PCD is induced earlier than wild type. Furthermore, in both mutants, developmental regulatory proteins are induced inappropriately rapidly in the non-aggregating cell fraction, and subsequently fail to accumulate appropriately in the aggregating cell fraction. Consequently, many cells are induced to sporulate before they have completed aggregation, and coordinated fruiting body formation is perturbed. These results strongly suggest that TodK and Red mediate the gradual accumulation of one or more developmental coordinators during the aggregation phase of the developmental program. These results suggest that coordination of developmental subpopulations requires negative regulatory signaling systems that quench the positive autoregulatory loops that ensure coupling of sporulation and aggregation