On p-adic lattices and Grassmannians

It is well-known that the coset spaces G(k((z)))/G(k[[z]]), for a reductive group G over a field k, carry the geometric structure of an inductive limit of projective k-schemes. This k-ind-scheme is known as the affine Grassmannian for G. From the point of view of number theory it would be interesting to obtain an analogous geometric interpretation of quotients of the form G(W(k)[1/p])/G(W(k)), where p is a rational prime, W denotes the ring scheme of p-typical Witt vectors, k is a perfect field of characteristic p and G is a reductive group scheme over W(k). The present paper is an attempt to describe which constructions carry over from the function field case to the p-adic case, more precisely to the situation of the p-adic affine Grassmannian for the special linear group G=SL_n. We start with a description of the R-valued points of the p-adic affine Grassmannian for SL_n in terms of lattices over W(R), where R is a perfect k-algebra. In order to obtain a link with geometry we further construct projective k-subvarieties of the multigraded Hilbert scheme which map equivariantly to the p-adic affine Grassmannian. The images of these morphisms play the role of Schubert varieties in the p-adic setting. Further, for any reduced k-algebra R these morphisms induce bijective maps between the sets of R-valued points of the respective open orbits in the multigraded Hilbert scheme and the corresponding Schubert cells of the p-adic affine Grassmannian for SL_n.Comment: 36 pages. This is a thorough revision, in the form accepted by Math. Zeitschrift, of the previously published preprint "On p-adic loop groups and Grassmannians

Granzyme B; the chalk-mark of a cytotoxic lymphocyte

During cytotoxic lymphocyte (CL) mediated killing of target cells, granzyme B is released from the CL into the immune synapse. Recent studies have found that ELISPOT-detection of granzyme B correlated well with conventional assays for CL mediated killing. In this way, the released granzyme B can be used to mark the spot where a target cell was murdered. We discuss the benefits and potential limitations of using this assay to measure CL mediated killing of target cells

Behavioral Adaptations of Nursing Brangus Cows to Virtual Fencing: Insights from a Training Deployment Phase

Virtual fencing systems have emerged as a promising technology for managing the distribution of livestock in extensive grazing environments. This study provides comprehensive documentation of the learning process involving two conditional behavioral mechanisms and the documentation of efficient, effective, and safe animal training for virtual fence applications on nursing Brangus cows. Two hypotheses were examined: (1) animals would learn to avoid restricted zones by increasing their use of containment zones within a virtual fence polygon, and (2) animals would progressively receive fewer audio-electric cues over time and increasingly rely on auditory cues for behavioral modification. Data from GPS coordinates, behavioral metrics derived from the collar data, and cueing events were analyzed to evaluate these hypotheses. The results supported hypothesis 1, revealing that virtual fence activation significantly increased the time spent in containment zones and reduced time in restricted zones compared to when the virtual fence was deactivated. Concurrently, behavioral metrics mirrored these findings, with cows adjusting their daily travel distances, exploration area, and cumulative activity counts in response to the allocation of areas with different virtual fence configurations. Hypothesis 2 was also supported by the results, with a decrease in cueing events over time and increased reliance with animals on audio cueing to avert receiving the mild electric pulse. These outcomes underscore the rapid learning capabilities of groups of nursing cows in responding to virtual fence boundaries

Regulation of the Cardiac Na+/K+ ATPase by Phospholemman

Hansraj Dhayan, Rajender Kumar, Andreas Kukol, ‘Regulation of the Cardiac Na+/K+ ATPase by Phospholemman’, in Sajal Chakraborti, Naranjan Dhalla, eds., Regulation of Membrane Na+-K+ ATPase, (Switzerland: Springer, 2016), ISBN 978-3-319-24748-9, eISBN 978-3-319-24750-2.Peer reviewe

Coevolved mutations reveal distinct architectures for two core proteins in the bacterial flagellar motor

Switching of bacterial flagellar rotation is caused by large domain movements of the FliG protein triggered by binding of the signal protein CheY to FliM. FliG and FliM form adjacent multi-subunit arrays within the basal body C-ring. The movements alter the interaction of the FliG C-terminal (FliGC) "torque" helix with the stator complexes. Atomic models based on the Salmonella entrovar C-ring electron microscopy reconstruction have implications for switching, but lack consensus on the relative locations of the FliG armadillo (ARM) domains (amino-terminal (FliGN), middle (FliGM) and FliGC) as well as changes during chemotaxis. The generality of the Salmonella model is challenged by the variation in motor morphology and response between species. We studied coevolved residue mutations to determine the unifying elements of switch architecture. Residue interactions, measured by their coevolution, were formalized as a network, guided by structural data. Our measurements reveal a common design with dedicated switch and motor modules. The FliM middle domain (FliMM) has extensive connectivity most simply explained by conserved intra and inter-subunit contacts. In contrast, FliG has patchy, complex architecture. Conserved structural motifs form interacting nodes in the coevolution network that wire FliMM to the FliGC C-terminal, four-helix motor module (C3-6). FliG C3-6 coevolution is organized around the torque helix, differently from other ARM domains. The nodes form separated, surface-proximal patches that are targeted by deleterious mutations as in other allosteric systems. The dominant node is formed by the EHPQ motif at the FliMMFliGM contact interface and adjacent helix residues at a central location within FliGM. The node interacts with nodes in the N-terminal FliGc α-helix triad (ARM-C) and FliGN. ARM-C, separated from C3-6 by the MFVF motif, has poor intra-network connectivity consistent with its variable orientation revealed by structural data. ARM-C could be the convertor element that provides mechanistic and species diversity.JK was supported by Medical Research Council grant U117581331. SK was supported by seed funds from Lahore University of Managment Sciences (LUMS) and the Molecular Biology Consortium