Spanning forests and the q-state Potts model in the limit q \to 0

We study the q-state Potts model with nearest-neighbor coupling v=e^{\beta J}-1 in the limit q,v \to 0 with the ratio w = v/q held fixed. Combinatorially, this limit gives rise to the generating polynomial of spanning forests; physically, it provides information about the Potts-model phase diagram in the neighborhood of (q,v) = (0,0). We have studied this model on the square and triangular lattices, using a transfer-matrix approach at both real and complex values of w. For both lattices, we have computed the symbolic transfer matrices for cylindrical strips of widths 2 \le L \le 10, as well as the limiting curves of partition-function zeros in the complex w-plane. For real w, we find two distinct phases separated by a transition point w=w_0, where w_0 = -1/4 (resp. w_0 = -0.1753 \pm 0.0002) for the square (resp. triangular) lattice. For w > w_0 we find a non-critical disordered phase, while for w < w_0 our results are compatible with a massless Berker-Kadanoff phase with conformal charge c = -2 and leading thermal scaling dimension x_{T,1} = 2 (marginal operator). At w = w_0 we find a "first-order critical point": the first derivative of the free energy is discontinuous at w_0, while the correlation length diverges as w \downarrow w_0 (and is infinite at w = w_0). The critical behavior at w = w_0 seems to be the same for both lattices and it differs from that of the Berker-Kadanoff phase: our results suggest that the conformal charge is c = -1, the leading thermal scaling dimension is x_{T,1} = 0, and the critical exponents are \nu = 1/d = 1/2 and \alpha = 1.Comment: 131 pages (LaTeX2e). Includes tex file, three sty files, and 65 Postscript figures. Also included are Mathematica files forests_sq_2-9P.m and forests_tri_2-9P.m. Final journal versio

A Loss-of-Function HCN4 Mutation Associated With Familial Benign Myoclonic Epilepsy in Infancy Causes Increased Neuronal Excitability

HCN channels are highly expressed and functionally relevant in neurons and increasing evidence demonstrates their involvement in the etiology of human epilepsies. Among HCN isoforms, HCN4 is important in cardiac tissue, where it underlies pacemaker activity. Despite being expressed also in deep structures of the brain, mutations of this channel functionally shown to be associated with epilepsy have not been reported yet. Using Next Generation Sequencing for the screening of patients with idiopathic epilepsy, we identified the p.Arg550Cys (c.1648C>T) heterozygous mutation on HCN4 in two brothers affected by benign myoclonic epilepsy of infancy. Functional characterization in heterologous expression system and in neurons showed that the mutation determines a loss of function of HCN4 contribution to activity and an increase of neuronal discharge, potentially predisposing to epilepsy. Expressed in cardiomyocytes, mutant channels activate at slightly more negative voltages than wild-type (WT), in accordance with borderline bradycardia. While HCN4 variants have been frequently associated with cardiac arrhythmias, these data represent the first experimental evidence that functional alteration of HCN4 can also be involved in human epilepsy through a loss-of-function effect and associated increased neuronal excitability. Since HCN4 appears to be highly expressed in deep brain structures only early during development, our data provide a potential explanation for a link between dysfunctional HCN4 and infantile epilepsy. These findings suggest that it may be useful to include HCN4 screening to extend the knowledge of the genetic causes of infantile epilepsies, potentially paving the way for the identification of innovative therapeutic strategies

HCN-related channelopathies

HCN channels are the molecular subunits of native funny (f-) channels of cardiac pacemaker cells and neurons. Although funny channels were first functionally described in cardiac cells in the late 1970s, cloning of HCN channels, of which four subunits are known today (HCN1-4), had to wait some 20 years to be accomplished, which delayed the investigation of HCN-related channelopathies. In cardiac pacemaker cells, the main function of f-channels is to contribute substantially to the generation of spontaneous activity of pacemaker cells and control of heart rate. Given this role in cardiac rhythm, it is natural to expect that defective f-channels (or their molecular correlates HCN4 channels) might be responsible for inheritable forms of cardiac arrhythmogenic diseases. Indeed, the recent search for HCN4-related inheritable arrhythmias has resulted in the finding of four different mutations of the hHcn4 gene, which have been reported to be associated with bradycardia and/or more complex arrhythmic conditions. In neurons, HCN channels display a variety of functions including the regulation of excitability, dendritic integration, plasticity, motor learning, generation of repetitive firing, and others. Defective HCN channels may therefore in principle also contribute to pathological conditions in the nervous system. While full evidence for neuronal HCN channelopathies is not yet available, several indications point to a link between temporal lobe and absence epilepsies and altered distribution of HCN1/HCN2 isoforms. Here we briefly review the current knowledge of HCN-related channelopathies in the heart and the brain

Alpha-synuclein nitration and autophagy response are induced in peripheral blood cells from patients with Parkinson disease

Several lines of evidence implicate a central role for alpha-synuclein (aSN) in the pathogenesis of Parkinson's disease (PD). Besides rare genetic mutations, post-translational mechanisms, such as oxidative stress-related nitration, may alter the protein properties in terms of propensity to aggregate or be degraded. Our group previously described increased reactive oxygen species (ROS) production within easily accessible peripheral blood mononuclear cells (PBMCs) in PD patients compared to healthy elderly subjects. In the present work, we demonstrated a significant induction of nitrotyrosine (NT)-modifications of aSN within PBMCs derived from individuals with idiopathic PD compared to controls, while aSN protein appeared similarly expressed in the two populations. The amount of NT-modified aSN within PBMCs was positively correlated with intracellular ROS concentration and inversely related to daily dosage of levodopa, making its measurement potentially relevant for disease-intervention studies. Neither aSN expression nor its NT-modifications showed any correlation to specific REP1 genotypes, polymorphic variants within aSN gene promoter whose association to PD susceptibility may occur through the modulation of aSN protein expression. Moreover, although NT-modified aSN has been linked to enhanced propensity to aggregate, we failed to detect an increased presence of insoluble aSN aggregates in PBMCs from PD subjects relative to controls, despite a lack of changes in the ubiquitin-proteasome expression or activity. Nonetheless, a significant activation of the autophagy response was identified within PBMCs from PD individuals, which could represent a protective mechanism against abnormal protein accumulation and may explain the lack of aSN aggregation. We discuss the relevance of these findings with respect to PD pathogenesis and biomarker development

Adult-Onset Epilepsy in Presymptomatic Alzheimer&apos;s Disease : a Retrospective Study

Background: The prevalence of epilepsy with onset in adulthood increases with age, mainly due to the accumulation of brain damage. However, a significant proportion of patients experience seizures of unknown cause. Alzheimer's disease (AD) is associated with an increased risk of seizures. Seizure activity is interpreted as a secondary event related to hyperexcitability caused by amyloid-\uce\ub2 aggregation. Objective: Since neurodegenerative processes begin several years before clinical symptoms, epilepsy could be more frequent in the presymptomatic stages of dementia. Methods: We retrospectively reviewed the prevalence of epilepsy of unknown origin with adult onset before cognitive decline in a large cohort of AD patients (EPS-AD) recruited based on clinical and neuropsychological data. Data of patients with epilepsy followed by AD were compared with two control groups: patients with AD without seizures (no EPS-AD) and a large reference population (RP). Results: In AD patients, the prevalence of epilepsy of unknown origin, with onset in the adulthood before cognitive decline is 17.1 times higher compared with the RP (95% CI: 10.3-28.3). In EPS-AD, seizures begin on average 4.6 years (median 2.0) before the onset of cognitive symptoms and cognitive decline starts 3.6 years earlier compared with noEPS-AD. Conclusions: Neurodegenerative processes of dementia could play a key role in the pathogenesis of epilepsy in a subgroup of individuals intended to develop cognitive decline. Adult-onset epilepsy of undefined cause could thus represent a risk factor for the ongoing neurodegenerative damage, even preceding by years the onset of clinical symptoms of dementia