On FPL configurations with four sets of nested arches

The problem of counting the number of Fully Packed Loop (FPL) configurations with four sets of a,b,c,d nested arches is addressed. It is shown that it may be expressed as the problem of enumeration of tilings of a domain of the triangular lattice with a conic singularity. After reexpression in terms of non-intersecting lines, the Lindstr\"om-Gessel-Viennot theorem leads to a formula as a sum of determinants. This is made quite explicit when min(a,b,c,d)=1 or 2. We also find a compact determinant formula which generates the numbers of configurations with b=d.Comment: 22 pages, TeX, 16 figures; a new formula for a generating function adde

Partial Recursive Functions and Finality

Abstract. We seek universal categorical conditions ensuring the representability of all partial recursive functions. In the category Pfn of sets and partial functions, the natural numbers provide both an initial algebra and a final coalgebra for the functor 1 + −. We recount how finality yields closure of the partial functions on natural numbers under Kleene’s µ-recursion scheme. Noting that Pfn is not cartesian, we then build on work of Paré and Román, obtaining weak initiality and finality conditions on natural numbers algebras in monoidal categories that ensure the (weak) representability of all partial recursive functions. We further obtain some positive results on strong representability. All these results adapt to Kleisli categories of cartesian categories with natural numbers algebras. However, in general, not all partial recursive functions need be strongly representable.

Actin: its cumbersome pilgrimage through cellular compartments

In this article, we follow the history of one of the most abundant, most intensely studied proteins of the eukaryotic cells: actin. We report on hallmarks of its discovery, its structural and functional characterization and localization over time, and point to present days’ knowledge on its position as a member of a large family. We focus on the rather puzzling number of diverse functions as proposed for actin as a dual compartment protein. Finally, we venture on some speculations as to its origin

Neuronal Profilin Isoforms Are Addressed by Different Signalling Pathways

Profilins are prominent regulators of actin dynamics. While most mammalian cells express only one profilin, two isoforms, PFN1 and PFN2a are present in the CNS. To challenge the hypothesis that the expression of two profilin isoforms is linked to the complex shape of neurons and to the activity-dependent structural plasticity, we analysed how PFN1 and PFN2a respond to changes of neuronal activity. Simultaneous labelling of rodent embryonic neurons with isoform-specific monoclonal antibodies revealed both isoforms in the same synapse. Immunoelectron microscopy on brain sections demonstrated both profilins in synapses of the mature rodent cortex, hippocampus and cerebellum. Both isoforms were significantly more abundant in postsynaptic than in presynaptic structures. Immunofluorescence showed PFN2a associated with gephyrin clusters of the postsynaptic active zone in inhibitory synapses of embryonic neurons. When cultures were stimulated in order to change their activity level, active synapses that were identified by the uptake of synaptotagmin antibodies, displayed significantly higher amounts of both isoforms than non-stimulated controls. Specific inhibition of NMDA receptors by the antagonist APV in cultured rat hippocampal neurons resulted in a decrease of PFN2a but left PFN1 unaffected. Stimulation by the brain derived neurotrophic factor (BDNF), on the other hand, led to a significant increase in both synaptic PFN1 and PFN2a. Analogous results were obtained for neuronal nuclei: both isoforms were localized in the same nucleus, and their levels rose significantly in response to KCl stimulation, whereas BDNF caused here a higher increase in PFN1 than in PFN2a. Our results strongly support the notion of an isoform specific role for profilins as regulators of actin dynamics in different signalling pathways, in excitatory as well as in inhibitory synapses. Furthermore, they suggest a functional role for both profilins in neuronal nuclei

Distinct Molecular Evolutionary Mechanisms Underlie the Functional Diversification of the Wnt and TGFβ Signaling Pathways

The canonical Wnt pathway is one of the oldest and most functionally diverse of animal intercellular signaling pathways. Though much is known about loss-of-function phenotypes for Wnt pathway components in several model organisms, the question of how this pathway achieved its current repertoire of functions has not been addressed. Our phylogenetic analyses of 11 multigene families from five species belonging to distinct phyla, as well as additional analyses employing the 12 Drosophila genomes, suggest frequent gene duplications affecting ligands and receptors as well as co-evolution of new ligand–receptor pairs likely facilitated the expansion of this pathway’s capabilities. Further, several examples of recent gene loss are visible in Drosophila when compared to family members in other phyla. By comparison the TGFβ signaling pathway is characterized by ancient gene duplications of ligands, receptors, and signal transducers with recent duplication events restricted to the vertebrate lineage. Overall, the data suggest that two distinct molecular evolutionary mechanisms can create a functionally diverse developmental signaling pathway. These are the recent dynamic generation of new genes and ligand–receptor interactions as seen in the Wnt pathway and the conservative adaptation of ancient pre-existing genes to new roles as seen in the TGFβ pathway. From a practical perspective, the former mechanism limits the investigator’s ability to transfer knowledge of specific pathway functions across species while the latter facilitates knowledge transfer

Zinc Substitution of Cobalt in Vitamin B12: Zincobyric acid and Zincobalamin as Luminescent Structural B12-Mimics

Replacing the central cobalt ion of vitamin B12 by other metals has been a long‐held aspiration within the B12‐field. Herein, we describe the synthesis from hydrogenobyric acid of zincobyric acid (Znby) and zincobalamin (Znbl), the Zn‐analogues of the natural cobalt‐corrins cobyric acid and vitamin B12, respectively. The solution structures of Znby and Znbl were studied by NMR‐spectroscopy. Single crystals of Znby were produced, providing the first X‐ray crystallographic structure of a zinc corrin. The structures of Znby and of computationally generated Znbl were found to resemble the corresponding CoII‐corrins, making such Zn‐corrins potentially useful for investigations of B12‐dependent processes. The singlet excited state of Znby had a short life‐time, limited by rapid intersystem crossing to the triplet state. Znby allowed the unprecedented observation of a corrin triplet (ET=190 kJ mol−1) and was found to be an excellent photo‐sensitizer for 1O2 (ΦΔ=0.70)

Comparing the degrees of enumerability and the closed Medvedev degrees

We compare the degrees of enumerability and the closed Medvedev degrees and find that many situations occur. There are nonzero closed degrees that do not bound nonzero degrees of enumerability, there are nonzero degrees of enumerability that do not bound nonzero closed degrees, and there are degrees that are nontrivially both degrees of enumerability and closed degrees. We also show that the compact degrees of enumerability exactly correspond to the cototal enumeration degrees