Radio Planetary Nebulae in the Small Magellanic Cloud

We present ten new radio continuum (RC) detections at catalogued planetary nebula (PN) positions in the Small Magellanic Cloud (SMC): SMPS6, LIN 41, LIN 142, SMP S13, SMP S14, SMP S16, J18, SMP S18, SMP S19 and SMP S22. Additionally, six SMC radio PNe previously detected, LIN 45, SMP S11, SMPS17, LIN321, LIN339 and SMPS24 are also investigated (re-observed) here making up a population of 16 radio detections of catalogued PNe in the SMC. These 16 radio detections represent ~15 % of the total catalogued PN population in the SMC. We show that six of these objects have characteristics that suggest that they are PN mimics: LIN 41, LIN 45, SMP S11, LIN 142, LIN 321 and LIN 339. We also present our results for the surface brightness - PN radius relation ({\Sigma}-D) of the SMC radio PN population. These are consistent with previous SMC and LMC PN measurements of the ({\Sigma}-D) relation.Comment: Accepted for publication in Astrophysics and Space Scienc

Evolutionary Conservation of the Heterochronic Pathway in C. elegans and C. briggsae

Heterochronic genes control the sequence and timing of developmental events during four larval stages of Caenorhabitis nematodes. Mutations in these genes may cause skipping or reiteration of developmental events. C. briggsae is a close relative of C. elegans. These species have similar morphology and share the same ecological niche. C. briggsae undergoes the same developmental pathway consisting of four larval stages before reaching adulthood. It also has the same set of heterochronic genes. Lin-28 is one of the heterochronic genes that also exists in other animals from flies to humans. It conservatively blocks the maturation of let-7 miRNA, the process is generally associated with the stem cell state. lin-28 is silenced as cells differentiate. C. elegans mutants of lin-28 have a reduced number of seam cells and precocious alae. Despite the highly conserved protein sequence, C. briggsae develop a distinct phenotype when its lin 28 is disrupted. Worms did not have a characteristic vulval development defect, they also became lethargic and had a reduced fertility. This observation led to a question of how conserved the heterochronic pathway is in close species

C. elegans LRP-2 functions in vulval precursor cell polarity

The C. elegans vulva is formed from divisions of three vulval precursor cells (VPCs) – P5.p, P6.p, and P7.p – arranged along the anteroposterior axis in the ventral epithelium (Sulston and Horvitz, 1977). Previous analyses show the orientation of P5.p and P7.p descendants is determined by the interaction of multiple Wnt signals. Specifically, in the absence of all Wnts, the VPCs display a randomized orientation, which is likely the default (Green et al., 2008; Minor et al. 2013). Two separate Wnts from the anchor cell, LIN-44 and MOM-2 acting through receptors LIN-17/Frizzled and LIN-18/Ryk, respectively, regulate P7.p orientation (Ferguson et al., 1987; Sternberg and Horvitz, 1988; Sawa et al., 1996; Inoue et al., 2004; Gleason et al., 2006). In the absence of these signals the orientation of the progeny of P7.p mimic those of P5.p and face toward the posterior of the worm, a phenotype referred to as posterior-reversed vulval lineage (P-Rvl). This posterior orientation is dependent on the instructive signal EGL-20, a Wnt expressed in the tail acting through CAM-1/ROR and VANG-1/Van Gogh, and is referred to as “ground polarity” (Green et al., 2008). Here we examine the role of a low-density lipoprotein receptor, lrp-2, and its role in controlling the orientation of P7.p daughter cells. To investigate this interaction double mutants were constructed with both alleles of lrp-2 and lin-17(n671) (Table 1). Much like cam-1(gm122) and vang-1(ok1142), both alleles of lrp-2 suppress the lin-17(n671) phenotype from 74 to approximately 50% P-Rvl leading us to hypothesize that lrp-2 functions in the same pathway as cam-1 and vang-1. Furthering this hypothesis we have shown that, like cam-1 and vang-1, lrp-2 controls the localization of SYS-1/b-catenin (Minor and Sternberg, 2019). To ensure that this phenotype was a result of loss of lrp-2 function as opposed to background effects we injected a fosmid (WRM0617cA02) containing the full-length sequence of lrp-2 and found that it does rescue the double mutant phenotype of lin-17(n671); lrp-2(gk272) from 55 to 73%. In order to better test this hypothesis a triple mutant was constructed between lin-17(n671), lrp-2(gk272), and cam-1(gm122) (Table 1). This triple mutant displays the same P-Rvl penetrance as both the lin-17(n671); lrp-2(gk272) and lin-17(n671); cam-1(gm122) double mutants confirming that lrp-2 functions in the same pathway as cam-1

C. elegans LRP-2 functions in vulval precursor cell polarity

The C. elegans vulva is formed from divisions of three vulval precursor cells (VPCs) – P5.p, P6.p, and P7.p – arranged along the anteroposterior axis in the ventral epithelium (Sulston and Horvitz, 1977). Previous analyses show the orientation of P5.p and P7.p descendants is determined by the interaction of multiple Wnt signals. Specifically, in the absence of all Wnts, the VPCs display a randomized orientation, which is likely the default (Green et al., 2008; Minor et al. 2013). Two separate Wnts from the anchor cell, LIN-44 and MOM-2 acting through receptors LIN-17/Frizzled and LIN-18/Ryk, respectively, regulate P7.p orientation (Ferguson et al., 1987; Sternberg and Horvitz, 1988; Sawa et al., 1996; Inoue et al., 2004; Gleason et al., 2006). In the absence of these signals the orientation of the progeny of P7.p mimic those of P5.p and face toward the posterior of the worm, a phenotype referred to as posterior-reversed vulval lineage (P-Rvl). This posterior orientation is dependent on the instructive signal EGL-20, a Wnt expressed in the tail acting through CAM-1/ROR and VANG-1/Van Gogh, and is referred to as “ground polarity” (Green et al., 2008). Here we examine the role of a low-density lipoprotein receptor, lrp-2, and its role in controlling the orientation of P7.p daughter cells. To investigate this interaction double mutants were constructed with both alleles of lrp-2 and lin-17(n671) (Table 1). Much like cam-1(gm122) and vang-1(ok1142), both alleles of lrp-2 suppress the lin-17(n671) phenotype from 74 to approximately 50% P-Rvl leading us to hypothesize that lrp-2 functions in the same pathway as cam-1 and vang-1. Furthering this hypothesis we have shown that, like cam-1 and vang-1, lrp-2 controls the localization of SYS-1/b-catenin (Minor and Sternberg, 2019). To ensure that this phenotype was a result of loss of lrp-2 function as opposed to background effects we injected a fosmid (WRM0617cA02) containing the full-length sequence of lrp-2 and found that it does rescue the double mutant phenotype of lin-17(n671); lrp-2(gk272) from 55 to 73%. In order to better test this hypothesis a triple mutant was constructed between lin-17(n671), lrp-2(gk272), and cam-1(gm122) (Table 1). This triple mutant displays the same P-Rvl penetrance as both the lin-17(n671); lrp-2(gk272) and lin-17(n671); cam-1(gm122) double mutants confirming that lrp-2 functions in the same pathway as cam-1

LRP-2 controls the localization of C. elegans SYS-1/beta-catenin

The polarity of the C. elegans P7.p cell divisions is controlled by the Wnt/β-catenin asymmetry pathway (Green et al., 2008; Minor et al., 2013). This pathway includes the β-catenin-like proteins SYS-1 and WRM-1, POP-1/TCF, and the Nemo-like-kinase, LIT-1 (reviewed by Mizumoto and Sawa, 2007). The Wnt/β-catenin asymmetry pathway ensures different ratios of SYS-1 to POP-1, controlling the differential transcription of Wnt target genes between daughters of an asymmetric cell division. Because our genetic data indicate an antagonism between LRP-2 and LIN-17 similar to that between CAM-1 and VANG-1 and LIN-17 (Minor and Sternberg, 2019), we wanted to determine if LRP-2 can control the asymmetric localization of SYS-1 between the daughter cells of P7.p during anaphase of the first cell division. The initial establishment of vulval polarity can be observed through the localization of VENUS::SYS-1 (VNS::SYS-1), localized in a high (P7.pa)/low (P7.pp) pattern in the wild-type worm, reciprocal to the localization of POP-1/TCF (Phillips et al., 2007; Green et al., 2008). It was previously reported (Green et al. 2008) that VNS::SYS-1 asymmetry in P7.p daughter cells is often lost in lin-17(n671) and lin-18(e620) mutants. These mutants display two aberrant patterns of VNS::SYS-1 localization as well as the wild-type pattern, though less frequently. The two deviant localization patterns include one in which both P7.pa and P7.pp express equal amounts of VNS::SYS-1 and a reversed VNS::SYS-1 pattern in which P7.pp is enriched with VNS::SYS-1. By observing VNS::SYS-1 localization in a lin-17(n671); lrp-2(gk272) background we see that the aberrant localization of SYS-1 is suppressed to a similar degree to that of lin-17(n671); cam-1(gm122) and lin-17(n671); vang-1(ok1142). This observation confirms LRP-2 controls vulval cell polarity by antagonizing LIN-17 in a similar fashion to CAM-1 and VANG-1, and that the effect of LRP-2 is at the level of P7.p rather than its progeny

LRP-2 controls the localization of C. elegans SYS-1/beta-catenin

The polarity of the C. elegans P7.p cell divisions is controlled by the Wnt/β-catenin asymmetry pathway (Green et al., 2008; Minor et al., 2013). This pathway includes the β-catenin-like proteins SYS-1 and WRM-1, POP-1/TCF, and the Nemo-like-kinase, LIT-1 (reviewed by Mizumoto and Sawa, 2007). The Wnt/β-catenin asymmetry pathway ensures different ratios of SYS-1 to POP-1, controlling the differential transcription of Wnt target genes between daughters of an asymmetric cell division. Because our genetic data indicate an antagonism between LRP-2 and LIN-17 similar to that between CAM-1 and VANG-1 and LIN-17 (Minor and Sternberg, 2019), we wanted to determine if LRP-2 can control the asymmetric localization of SYS-1 between the daughter cells of P7.p during anaphase of the first cell division. The initial establishment of vulval polarity can be observed through the localization of VENUS::SYS-1 (VNS::SYS-1), localized in a high (P7.pa)/low (P7.pp) pattern in the wild-type worm, reciprocal to the localization of POP-1/TCF (Phillips et al., 2007; Green et al., 2008). It was previously reported (Green et al. 2008) that VNS::SYS-1 asymmetry in P7.p daughter cells is often lost in lin-17(n671) and lin-18(e620) mutants. These mutants display two aberrant patterns of VNS::SYS-1 localization as well as the wild-type pattern, though less frequently. The two deviant localization patterns include one in which both P7.pa and P7.pp express equal amounts of VNS::SYS-1 and a reversed VNS::SYS-1 pattern in which P7.pp is enriched with VNS::SYS-1. By observing VNS::SYS-1 localization in a lin-17(n671); lrp-2(gk272) background we see that the aberrant localization of SYS-1 is suppressed to a similar degree to that of lin-17(n671); cam-1(gm122) and lin-17(n671); vang-1(ok1142). This observation confirms LRP-2 controls vulval cell polarity by antagonizing LIN-17 in a similar fashion to CAM-1 and VANG-1, and that the effect of LRP-2 is at the level of P7.p rather than its progeny

Simple C*-algebras with locally finite decomposition rank

We introduce the notion of locally finite decomposition rank, a structural property shared by many stably finite nuclear C*-algebras. The concept is particularly relevant for Elliott's program to classify nuclear C*-algebras by K-theory data. We study some of its properties and show that a simple unital C*-algebra, which has locally finite decomposition rank, real rank zero and which absorbs the Jiang-Su algebra Z tensorially, has tracial rank zero in the sense of Lin. As a consequence, any such C*-algebra, if it additionally satisfies the Universal Coefficients Theorem, is approximately homogeneous of topological dimension at most 3. Our result in particular confirms the Elliott conjecture for the class of simple unital Z-stable ASH algebras with real rank zero. Moreover, it implies that simple unital Z-stable AH algebras with real rank zero not only have slow dimension growth in the ASH sense, but even in the AH sense.Comment: 30 pages, no figure

Genetics of intercellular signalling in C. elegans

Cell-cell interactions play a significant role in controlling cell fate during development of the nematode Caenorhabditis elegans. It has been found that two genes, glp-1 and lin-12, are required for many of these decisions. glp-1 is required for induction of mitotic proliferation in the germline by the somatic distal tip cell and for induction of the anterior pharynx early in embryogenesis. lin-12 is required for the interactions between cells of equivalent developmental potential, which allow them to take on different fates. Comparison of these two genes on a molecular level indicates that they are similar in sequence and organization, suggesting that the mechanisms of these two different sets of cell-cell interactions are similar

Note on W3 Realizations of the Bosonic String

In order to investigate to what extent string theories are different vacua of a general string theory (the ``universal string"), we discuss realizations of the bosonic string as particular background of certain types of $W$-strings. Our discussions include linearized $W_3^{lin}$, non-critical $W_3$, linearized $W_3^{(2)lin}$ and critical $W_3^{(2)}$ realizations of the bosonic string.Comment: 9 pages, Late