Severi varieties and Brill-Noether theory of curves on abelian surfaces

Severi varieties and Brill-Noether theory of curves on K3 surfaces are well understood. Yet, quite little is known for curves on abelian surfaces. Given a general abelian surface $S$ with polarization $L$ of type $(1,n)$, we prove nonemptiness and regularity of the Severi variety parametrizing $\delta$-nodal curves in the linear system $|L|$ for $0\leq \delta\leq n-1=p-2$ (here $p$ is the arithmetic genus of any curve in $|L|$). We also show that a general genus $g$ curve having as nodal model a hyperplane section of some $(1,n)$-polarized abelian surface admits only finitely many such models up to translation; moreover, any such model lies on finitely many $(1,n)$-polarized abelian surfaces. Under certain assumptions, a conjecture of Dedieu and Sernesi is proved concerning the possibility of deforming a genus $g$ curve in $S$ equigenerically to a nodal curve. The rest of the paper deals with the Brill-Noether theory of curves in $|L|$. It turns out that a general curve in $|L|$ is Brill-Noether general. However, as soon as the Brill-Noether number is negative and some other inequalities are satisfied, the locus $|L|^r_d$ of smooth curves in $|L|$ possessing a $g^r_d$ is nonempty and has a component of the expected dimension. As an application, we obtain the existence of a component of the Brill-Noether locus $\mathcal{M}^r_{p,d}$ having the expected codimension in the moduli space of curves $\mathcal{M}_p$. For $r=1$, the results are generalized to nodal curves

The impact of the CACNA1C gene polymorphism on frontolimbic function in bipolar disorder

Genome-wide association studies in bipolar disorder (BD)1 have implicated a single-nucleotide polymorphism (rs1006737, G right arrow A) in the CACNA1C gene, which encodes for the alpha 1c (CAV1.2) subunit of the voltage-gated, L-type calcium channel. Neuroimaging studies of healthy individuals report that this risk allele modulates brain function within limbic (amygdala, anterior cingulate gyrus) and hippocampal regions during tasks of reward processing2, 3 and episodic memory. Moreover, animal studies suggest that the CaV1.2 L-type calcium channels influence emotional behaviour through enhanced neurotransmission via the lateral amygdala pathway. On the basis of this evidence, we tested the hypotheses that the CACNA1C rs1006737 risk allele will modulate neural responses within predefined prefrontal and subcortical regions of interest during emotional face processing and that this effect would be amplified in BD patients

MET and AKT Genetic Influence on Facial Emotion Perception

Background: Facial emotion perception is a major social skill, but its molecular signal pathway remains unclear. The MET/ AKT cascade affects neurodevelopment in general populations and face recognition in patients with autism. This study explores the possible role of MET/AKT cascade in facial emotion perception. Methods: One hundred and eighty two unrelated healthy volunteers (82 men and 100 women) were recruited. Four single nucleotide polymorphisms (SNP) of MET (rs2237717, rs41735, rs42336, and rs1858830) and AKT rs1130233 were genotyped and tested for their effects on facial emotion perception. Facial emotion perception was assessed by the face task of Mayer-Salovey-Caruso Emotional Intelligence Test (MSCEIT). Thorough neurocognitive functions were also assessed. Results: Regarding MET rs2237717, individuals with the CT genotype performed better in facial emotion perception than those with TT (p = 0.016 by ANOVA, 0.018 by general linear regression model [GLM] to control for age, gender, and education duration), and showed no difference with those with CC. Carriers with the most common MET CGA haplotype (frequency = 50.5%) performed better than non-carriers of CGA in facial emotion perception (p = 0.018, df = 1, F = 5.69, p = 0.009 by GLM). In MET rs2237717/AKT rs1130233 interaction, the C carrier/G carrier group showed better facial emotion perception than those with the TT/AA genotype (p = 0.035 by ANOVA, 0.015 by GLM), even when neurocognitive functions were controlled (p = 0.046 by GLM)

A systematic review of associations between functional MRI activity and polygenic risk for schizophrenia and bipolar disorder

Genetic factors account for up to 80% of the liability for schizophrenia (SCZ) and bipolar disorder (BD). Genome-wide association studies have successfully identified several genes associated with increased risk for both disorders. This has allowed researchers to model the aggregate effect of genes associated with disease status and create a polygenic risk score (PGRS) for each individual. The interest in imaging genetics using PGRS has grown in recent years, with several studies now published. We have conducted a systematic review to examine the effects of PGRS of SCZ, BD and cross psychiatric disorders on brain function and connectivity using fMRI data. Results indicate that the effect of genetic load for SCZ and BD on brain function affects task-related recruitment, with frontal areas having a more prominent role, independent of task. Additionally, the results suggest that the polygenic architecture of psychotic disorders is not regionally confined but impacts on the task-dependent recruitment of multiple brain regions. Future imaging genetics studies with large samples, especially population studies, would be uniquely informative in mapping the spatial distribution of the genetic risk to psychiatric disorders on brain processes during various cognitive tasks and may lead to the discovery of biological pathways that could be crucial in mediating the link between genetic factors and alterations in brain networks

Telomere length and bipolar disorder

Variation in telomere length is heritable and is currently considered a promising biomarker of susceptibility for neuropsychiatric disorders, particularly because of its association with memory function and hippocampal morphology. Here, we investigate telomere length in connection to familial risk and disease expression in bipolar disorder (BD). We used quantitative polymerase chain reactions and a telomere-sequence to single-copy-gene-sequence ratio method to determine telomere length in genomic DNA extracted from buccal smears from 63 patients with BD, 74 first-degree relatives (49 relatives had no lifetime psychopathology and 25 had a non-BD mood disorder) and 80 unrelated healthy individuals. Participants also underwent magnetic resonance imaging to determine hippocampal volumes and cognitive assessment to evaluate episodic memory using the verbal paired associates test. Telomere length was shorter in psychiatrically-well relatives (p=0.007) compared to unrelated healthy participants. Telomere length was also shorter in relatives (regardless of psychiatric status; p<0.01) and patients with BD not on lithium (p=0.02) compared to lithium-treated patients with BD. In the entire sample, telomere length was positively associated with left and right hippocampal volume and with delayed recall. This study provides evidence that shortened telomere length is associated with familial risk for BD. Lithium may have neuroprotective properties that require further investigation using prospective designs