Local, Smooth, and Consistent Jacobi Set Simplification

The relation between two Morse functions defined on a common domain can be studied in terms of their Jacobi set. The Jacobi set contains points in the domain where the gradients of the functions are aligned. Both the Jacobi set itself as well as the segmentation of the domain it induces have shown to be useful in various applications. Unfortunately, in practice functions often contain noise and discretization artifacts causing their Jacobi set to become unmanageably large and complex. While there exist techniques to simplify Jacobi sets, these are unsuitable for most applications as they lack fine-grained control over the process and heavily restrict the type of simplifications possible. In this paper, we introduce a new framework that generalizes critical point cancellations in scalar functions to Jacobi sets in two dimensions. We focus on simplifications that can be realized by smooth approximations of the corresponding functions and show how this implies simultaneously simplifying contiguous subsets of the Jacobi set. These extended cancellations form the atomic operations in our framework, and we introduce an algorithm to successively cancel subsets of the Jacobi set with minimal modifications according to some user-defined metric. We prove that the algorithm is correct and terminates only once no more local, smooth and consistent simplifications are possible. We disprove a previous claim on the minimal Jacobi set for manifolds with arbitrary genus and show that for simply connected domains, our algorithm reduces a given Jacobi set to its simplest configuration.Comment: 24 pages, 19 figure

IglE is an outer membrane-associated lipoprotein essential for intracellular survival and murine virulence of type A Francisella tularensis

IglE is a small, hypothetical protein encoded by the duplicated Francisella pathogenicity island (FPI). Inactivation of both copies of iglE rendered Francisella tularensis subsp. tularensis Schu S4 avirulent and incapable of intracellular replication, owing to an inability to escape the phagosome. This defect was fully reversed following single-copy expression of iglE in trans from attTn7 under the control of the Francisella rpsL promoter, thereby establishing that the loss of iglE, and not polar effects on downstream vgrG gene expression, was responsible for the defect. IglE is exported to the Francisella outer membrane as an ∼13.9-kDa lipoprotein, determined on the basis of a combination of selective Triton X-114 solubilization, radiolabeling with [(3)H]palmitic acid, and sucrose density gradient membrane partitioning studies. Lastly, a genetic screen using the iglE-null live vaccine strain resulted in the identification of key regions in the carboxyl terminus of IglE that are required for intracellular replication of Francisella tularensis in J774A.1 macrophages. Thus, IglE is essential for Francisella tularensis virulence. Our data support a model that likely includes protein-protein interactions at or near the bacterial cell surface that are unknown at present

FTT0831c/FTL_0325 contributes to Francisella tularensis cell division, maintenance of cell shape, and structural integrity

The Francisella FTT0831c/FTL_0325 gene encodes amino acid motifs to suggest it is a lipoprotein and that it may interact with the bacterial cell wall as a member of the OmpA-like protein family. Previous studies have suggested that FTT0831c is surface exposed and required for virulence of Francisella tularensis by subverting the host innate immune response (M. Mahawar et al., J. Biol. Chem. 287:25216-25229, 2012). We also found that FTT0831c is required for murine pathogenesis and intramacrophage growth of Schu S4, but we propose a different model to account for the proinflammatory nature of the resultant mutants. First, inactivation of FTL_0325 from live vaccine strain (LVS) or FTT0831c from Schu S4 resulted in temperature-dependent defects in cell viability and morphology. Loss of FTT0831c was also associated with an unusual defect in lipopolysaccharide O-antigen synthesis, but loss of FTL_0325 was not. Full restoration of these properties was observed in complemented strains expressing FTT0831c in trans, but not in strains lacking the OmpA motif, suggesting that cell wall contact is required. Finally, growth of the LVS FTL_0325 mutant in Mueller-Hinton broth at 37°C resulted in the appearance of membrane blebs at the poles and midpoint, prior to the formation of enlarged round cells that showed evidence of compromised cellular membranes. Taken together, these data are more consistent with the known structural role of OmpA-like proteins in linking the OM to the cell wall and, as such, maintenance of structural integrity preventing altered surface exposure or release of Toll-like receptor 2 agonists during rapid growth of Francisella in vitro and in vivo

A Multiplex Human Syndrome Implicates a Key Role for Intestinal Cell Kinase in Development of Central Nervous, Skeletal, and Endocrine Systems

Six infants in an Old Order Amish pedigree were observed to be affected with endocrine-cerebro-osteodysplasia (ECO). ECO is a previously unidentified neonatal lethal recessive disorder with multiple anomalies involving the endocrine, cerebral, and skeletal systems. Autozygosity mapping and sequencing identified a previously unknown missense mutation, R272Q, in ICK, encoding intestinal cell kinase (ICK). Our results established that R272 is conserved across species and among ethnicities, and three-dimensional analysis of the protein structure suggests protein instability due to the R272Q mutation. We also demonstrate that the R272Q mutant fails to localize at the nucleus and has diminished kinase activity. These findings suggest that ICK plays a key role in the development of multiple organ systems