TORUS-LIKE SOLUTIONS FOR THE LANDAU-DE GENNES MODEL. PART I: THE LYUKSYUTOV REGIME

We study global minimizers of a continuum Landau-De Gennes energy functional for nematic liquid crystals, in three-dimensional domains. Assuming smooth and uniaxial (e.g. homeotropic) boundary conditions and a corresponding physically relevant norm constraint (Lyuksyutov constraint), we prove full regularity up to the boundary for the (constrained) minimizers. As a consequence, in a relevant range of parameters (which we call Lyuksyutov regime), we show that unconstrained minimizers do not exhibit isotropic melting. In the case of a nematic droplet, the radial hedgehog is even shown to be an unstable equilibrium. Finally, we describe a class of boundary data including radial anchoring for which constrained or unconstrained minimizers are smooth configurations whose biaxiality level sets carry nontrivial topology. Results of this paper will be largely employed and refined in the next of our series. In particular in [16], where we prove that biaxiality level sets are generically finite unions of tori for smooth equilibrium configurations minimizing the energy in a restricted axially symmetric class

Unravelling the effects of methylphenidate on the dopaminergic and noradrenergic functional circuits

Functional magnetic resonance imaging (fMRI) can be combined with drugs to investigate the system-level functional responses in the brain to such challenges. However, most psychoactive agents act on multiple neurotransmitters, limiting the ability of fMRI to identify functional effects related to actions on discrete pharmacological targets. We recently introduced a multimodal approach, REACT (Receptor-Enriched Analysis of functional Connectivity by Targets), which offers the opportunity to disentangle effects of drugs on different neurotransmitters and clarify the biological mechanisms driving clinical efficacy and side effects of a compound. Here, we focus on methylphenidate (MPH), which binds to the dopamine transporter (DAT) and the norepinephrine transporter (NET), to unravel its effects on dopaminergic and noradrenergic functional circuits in the healthy brain at rest. We then explored the relationship between these target-enriched resting state functional connectivity (FC) maps and inter-individual variability in behavioural responses to a reinforcement-learning task encompassing a novelty manipulation to disentangle the molecular systems underlying specific cognitive/behavioural effects. Our main analysis showed a significant MPH-induced FC increase in sensorimotor areas in the functional circuit associated with DAT. In our exploratory analysis, we found that MPH-induced regional variations in the DAT and NET-enriched FC maps were significantly correlated with some of the inter-individual differences on key behavioural responses associated with the reinforcement-learning task. Our findings show that main MPH-related FC changes at rest can be understood through the distribution of DAT in the brain. Furthermore, they suggest that when compounds have mixed pharmacological profiles, REACT may be able to capture regional functional effects that are underpinned by the same cognitive mechanism but are related to engagement of distinct molecular targets

The effects of acute Methylene Blue administration on cerebral blood flow and metabolism in humans and rats

Methylene Blue (MB) is a brain-penetrating drug with putative neuroprotective, antioxidant and metabolic enhancing effects. In vitro studies suggest that MB enhances mitochondrial complexes activity. However, no study has directly assessed the metabolic effects of MB in the human brain. We used in vivo neuroimaging to measure the effect of MB on cerebral blood flow (CBF) and brain metabolism in humans and in rats. Two doses of MB (0.5 and 1 mg/kg in humans; 2 and 4 mg/kg in rats; iv) induced reductions in global cerebral blood flow (CBF) in humans (F(1.74, 12.17)5.82, p = 0.02) and rats (F(1,5)26.04, p = 0.0038). Human cerebral metabolic rate of oxygen (CMRO2) was also significantly reduced (F(1.26, 8.84)8.01, p = 0.016), as was the rat cerebral metabolic rate of glucose (CMRglu) (t = 2.6(16) p = 0.018). This was contrary to our hypothesis that MB will increase CBF and energy metrics. Nevertheless, our results were reproducible across species and dose dependent. One possible explanation is that the concentrations used, although clinically relevant, reflect MB’s hormetic effects, i.e., higher concentrations produce inhibitory rather than augmentation effects on metabolism. Additionally, here we used healthy volunteers and healthy rats with normal cerebral metabolism where MB’s ability to enhance cerebral metabolism might be limited

An automatic analysis framework for FDOPA PET neuroimaging

In this study we evaluate the performance of a fully automated analytical framework for FDOPA PET neuroimaging data, and its sensitivity to demographic and experimental variables and processing parameters. An instance of XNAT imaging platform was used to store the King's College London institutional brain FDOPA PET imaging archive, alongside individual demographics and clinical information. By re-engineering the historical Matlab-based scripts for FDOPA PET analysis, a fully automated analysis pipeline for imaging processing and data quantification was implemented in Python and integrated in XNAT. The final data repository includes 892 FDOPA PET scans organized from 23 different studies. We found good reproducibility of the data analysis by the automated pipeline (in the striatum for the Kicer: for the controls ICC = 0.71, for the psychotic patients ICC = 0.88). From the demographic and experimental variables assessed, gender was found to most influence striatal dopamine synthesis capacity (F = 10.7, p < 0.001), with women showing greater dopamine synthesis capacity than men. Our automated analysis pipeline represents a valid resourse for standardised and robust quantification of dopamine synthesis capacity using FDOPA PET data. Combining information from different neuroimaging studies has allowed us to test it comprehensively and to validate its replicability and reproducibility performances on a large sample size

Mutations in the Neuronal Vesicular SNARE VAMP2 Affect Synaptic Membrane Fusion and Impair Human Neurodevelopment

VAMP2 encodes the vesicular SNARE protein VAMP2 (also called synaptobrevin-2). Together with its partners syntaxin-1A and synaptosomal-associated protein 25 (SNAP25), VAMP2 mediates fusion of synaptic vesicles to release neurotransmitters. VAMP2 is essential for vesicular exocytosis and activity-dependent neurotransmitter release. Here, we report five heterozygous de novo mutations in VAMP2 in unrelated individuals presenting with a neurodevelopmental disorder characterized by axial hypotonia (which had been present since birth), intellectual disability, and autistic features. In total, we identified two single-amino-acid deletions and three non-synonymous variants affecting conserved residues within the C terminus of the VAMP2 SNARE motif. Affected individuals carrying de novo non-synonymous variants involving the C-terminal region presented a more severe phenotype with additional neurological features, including central visual impairment, hyperkinetic movement disorder, and epilepsy or electroencephalography abnormalities. Reconstituted fusion involving a lipid-mixing assay indicated impairment in vesicle fusion as one of the possible associated disease mechanisms. The genetic synaptopathy caused by VAMP2 de novo mutations highlights the key roles of this gene in human brain development and function

Variational methods in the Landau-de Gennes theory of nematic liquid crystals

We study the so-called "biaxial torus solutions" in the Landau-de Gennes (LdG) model for nematic liquid crystals. These are smooth minimizers, so far only known through numerical experiments, of a widely-studied LdG energy functional w.r.t. a radial Dirichlet boundary datum, in conditions of "low temperature", with a very rich structure and a peculiar S^1-equivariant profile. We analytically prove that minimizing the energy in the class of S^1-equivariant Q-tensors of constant pointwise norm (which is, surprisingly, physically reasonable) agreeing the assigned boundary condition on the boundary gives back either biaxial torus solutions or the analogue of a special kind of singular solution, also expected from simulations. We then investigate the behavior of minimizers w.r.t. deformations of the boundary datum and, exploiting the very precise classification we got of the possible singularities, we also establish counterparts of some well-known theorems in harmonic maps. Joint work with Vincent Millot (Paris Diderot) and Adriano Pisante (Sapienza)