A weighted de Rham operator acting on arbitrary tensor fields and their local potentials

We introduce a weighted de Rham operator which acts on arbitrary tensor fields by considering their structure as r-fold forms. We can thereby define associated superpotentials for all tensor fields in all dimensions and, from any of these superpotentials, we deduce in a straightforward and natural manner the existence of 2r potentials for any tensor field, where r is its form-structure number. By specialising this result to symmetric double forms, we are able to obtain a pair of potentials for the Riemann tensor, and a single (2,3)-form potential for the Weyl tensor due to its tracelessness. This latter potential is the n-dimensional version of the double dual of the classical four dimensional (2,1)-form Lanczos potential. We also introduce a new concept of harmonic tensor fields, demonstrate that the new weighted de Rham operator has many other desirable properties and, in particular, it is the natural operator to use in the Laplace-like equation for the Riemann tensor.Comment: 33 pages: corrected typos and minor additions; reference [39] adde

SlgA, the homologue of the human schizophrenia associated PRODH gene, acts in clock neurons to regulate <i>Drosophila </i>aggression

Mutations in the proline dehydrogenase gene PRODH are linked to behavioral alterations in schizophrenia and as part of DiGeorge and velo-cardio-facial syndromes, but the role of PRODH in their etiology remains unclear. Here, we establish a Drosophila model to study the role of PRODH in behavioral disorders. We determine the distribution of the Drosophila PRODH homolog slgA in the brain and show that knockdown and overexpression of human PRODH and slgA in the lateral neurons ventral (LNv) lead to altered aggressive behavior. SlgA acts in an isoform-specific manner and is regulated by casein kinase II (CkII). Our data suggest that these effects are, at least partially, due to effects on mitochondrial function. We thus show that precise regulation of proline metabolism is essential to drive normal behavior and we identify Drosophila aggression as a model behavior relevant for the study of the mechanisms that are impaired in neuropsychiatric disorders

Quasimodo mediates daily and acute light effects on Drosophila clock neuron excitability

We have characterized a light-input pathway regulating Drosophila clock neuron excitability. The molecular clock drives rhythmic electrical excitability of clock neurons, and we show that the recently discovered light-input factor Quasimodo (Qsm) regulates this variation, presumably via an Na+, K+, Cl− cotransporter (NKCC) and the Shaw K+ channel (dKV3.1). Because of light-dependent degradation of the clock protein Timeless (Tim), constant illumination (LL) leads to a breakdown of molecular and behavioral rhythms. Both overexpression (OX) and knockdown (RNAi) of qsm, NKCC, or Shaw led to robust LL rhythmicity. Whole-cell recordings of the large ventral lateral neurons (l-LNv) showed that altering Qsm levels reduced the daily variation in neuronal activity: qsmOX led to a constitutive less active, night-like state, and qsmRNAi led to a more active, day-like state. Qsm also affected daily changes in K+ currents and the GABA reversal potential, suggesting a role in modifying membrane currents and GABA responses in a daily fashion, potentially modulating light arousal and input to the clock. When directly challenged with blue light, wild-type l-LNvs responded with increased firing at night and no net response during the day, whereas altering Qsm, NKKC, or Shaw levels abolished these day/night differences. Finally, coexpression of ShawOX and NKCCRNAi in a qsm mutant background restored LL-induced behavioral arrhythmicity and wild-type neuronal activity patterns, suggesting that the three genes operate in the same pathway. We propose that Qsm affects both daily and acute light effects in l-LNvs probably acting on Shaw and NKCC

Increased interaction between endoplasmic reticulum and mitochondria following sleep deprivation

Background: Prolonged cellular activity may overload cell function, leading to high rates of protein synthesis and accumulation of misfolded or unassembled proteins, which cause endoplasmic reticulum (ER) stress and activate the unfolded protein response (UPR) to re-establish normal protein homeostasis. Previous molecular work has demonstrated that sleep deprivation (SD) leads to ER stress in neurons, with a number of ER-specific proteins being upregulated to maintain optimal cellular proteostasis. It is still not clear which cellular processes activated by sleep deprivation lead to ER-stress, but increased cellular metabolism, higher request for protein synthesis, and over production of oxygen radicals have been proposed as potential contributing factors. Here, we investigate the transcriptional and ultrastructural ER and mitochondrial modifications induced by sleep loss.Results: We used gene expression analysis in mouse forebrains to show that SD was associated with significant transcriptional modifications of genes involved in ER stress but also in ER-mitochondria interaction, calcium homeostasis, and mitochondrial respiratory activity. Using electron microscopy, we also showed that SD was associated with a general increase in the density of ER cisternae in pyramidal neurons of the motor cortex. Moreover, ER cisternae established new contact sites with mitochondria, the so-called mitochondria associated membranes (MAMs), important hubs for molecule shuttling, such as calcium and lipids, and for the modulation of ATP production and redox state. Finally, we demonstrated that Drosophila male mutant flies (elav &gt; linker), in which the number of MAMs had been genetically increased, showed a reduction in the amount and consolidation of sleep without alterations in the homeostatic sleep response to SD. Conclusions: We provide evidence that sleep loss induces ER stress characterized by increased crosstalk between ER and mitochondria. MAMs formation associated with SD could represent a key phenomenon for the modulation of multiple cellular processes that ensure appropriate responses to increased cell metabolism. In addition, MAMs establishment may play a role in the regulation of sleep under baseline conditions

Drosophila PINK1 and parkin loss-of-function mutants display a range of non-motor Parkinson’s disease phenotypes.

Parkinson’s disease (PD) is more commonly associated with its motor symptoms and the related degeneration of dopamine (DA) neurons. However, it is becoming increasingly clear that PD patients also display a wide range of non-motor symptoms, including memory deficits and disruptions of their sleep-wake cycles. These have a large impact on their quality of life, and often precede the onset of motor symptoms, but their etiology is poorly understood. The fruit fly Drosophila has already been successfully used to model PD, and has been used extensively to study relevant non-motor behaviours in other contexts, but little attention has yet been paid to modelling non-motor symptoms of PD in this genetically tractable organism. We examined memory performance and circadian rhythms in flies with loss-of-function mutations in two PD genes: PINK1 and parkin. We found learning and memory abnormalities in both mutant genotypes, as well as a weakening of circadian rhythms that is underpinned by electrophysiological changes in clock neurons. Our study paves the way for further work that may help us understand the mechanisms underlying these neglected aspects of PD, thus identifying new targets for treatments to address these non-motor problems specifically and perhaps even to halt disease progression in its prodromal phase

A neural network underlying circadian entrainment and photoperiodic adjustment of sleep and activity in Drosophila

A sensitivity of the circadian clock to light/dark cycles ensures that biological rhythms maintain optimal phase relationships with the external day. In animals, the circadian clock neuron network (CCNN) driving sleep/activity rhythms receives light input from multiple photoreceptors, but how these photoreceptors modulate CCNN components is not well understood. Here we show that the Hofbauer-Buchner eyelets differentially modulate two classes of ventral lateral neurons (LNvs) within the Drosophila CCNN. The eyelets antagonize Cryptochrome (CRY)- and compound-eye-based photoreception in the large LNvs while synergizing CRY-mediated photoreception in the small LNvs. Furthermore, we show that the large LNvs interact with subsets of “evening cells” to adjust the timing of the evening peak of activity in a day length-dependent manner. Our work identifies a peptidergic connection between the large LNvs and a group of evening cells that is critical for the seasonal adjustment of circadian rhythms. SIGNIFICANCE STATEMENT In animals, circadian clocks have evolved to orchestrate the timing of behavior and metabolism. Consistent timing requires the entrainment these clocks to the solar day, a process that is critical for an organism's health. Light cycles are the most important external cue for the entrainment of circadian clocks, and the circadian system uses multiple photoreceptors to link timekeeping to the light/dark cycle. How light information from these photorecptors is integrated into the circadian clock neuron network to support entrainment is not understood. Our results establish that input from the HB eyelets differentially impacts the physiology of neuronal subgroups. This input pathway, together with input from the compound eyes, precisely times the activity of flies under long summer days. Our results provide a mechanistic model of light transduction and integration into the circadian system, identifying new and unexpected network motifs within the circadian clock neuron network