Analysis of nonlinear noisy integrate & fire neuron models: blow-up and steady states

Nonlinear Noisy Leaky Integrate and Fire (NNLIF) models for neurons networks can be written as Fokker-Planck-Kolmogorov equations on the probability density of neurons, the main parameters in the model being the connectivity of the network and the noise. We analyse several aspects of the NNLIF model: the number of steady states, a priori estimates, blow-up issues and convergence toward equilibrium in the linear case. In particular, for excitatory networks, blow-up always occurs for initial data concentrated close to the firing potential. These results show how critical is the balance between noise and excitatory/inhibitory interactions to the connectivity parameter.

Podocalyxin is a novel polysialylated neural adhesion protein with multiple roles in neural development and synapse formation

Neural development and plasticity are regulated by neural adhesion proteins, including the polysialylated form of NCAM (PSA-NCAM). Podocalyxin (PC) is a renal PSA-containing protein that has been reported to function as an anti-adhesin in kidney podocytes. Here we show that PC is widely expressed in neurons during neural development. Neural PC interacts with the ERM protein family, and with NHERF1/2 and RhoA/G. Experiments in vitro and phenotypic analyses of podxl-deficient mice indicate that PC is involved in neurite growth, branching and axonal fasciculation, and that PC loss-of-function reduces the number of synapses in the CNS and in the neuromuscular system. We also show that whereas some of the brain PC functions require PSA, others depend on PC per se. Our results show that PC, the second highly sialylated neural adhesion protein, plays multiple roles in neural development.

Podocalyxin is a novel polysialylated neural adhesion protein with multiple roles in neural development and synapse formation

Neural development and plasticity are regulated by neural adhesion proteins, including the polysialylated form of NCAM (PSA-NCAM). Podocalyxin (PC) is a renal PSA-containing protein that has been reported to function as an anti-adhesin in kidney podocytes. Here we show that PC is widely expressed in neurons during neural development. Neural PC interacts with the ERM protein family, and with NHERF1/2 and RhoA/G. Experiments in vitro and phenotypic analyses of podxl-deficient mice indicate that PC is involved in neurite growth, branching and axonal fasciculation, and that PC loss-of-function reduces the number of synapses in the CNS and in the neuromuscular system. We also show that whereas some of the brain PC functions require PSA, others depend on PC per se. Our results show that PC, the second highly sialylated neural adhesion protein, plays multiple roles in neural development.

Observation of a continuous interior crisis in the Hindmarsh-Rose neuron model.

Interior crises are understood as discontinuous changes of the size of a chaotic attractor that occur when an unstable periodic orbit collides with the chaotic attractor. We present here numerical evidence and theoretical reasoning which prove the existence of a chaos-chaos transition in which the change of the attractor size is sudden but continuous. This occurs in the Hindmarsh¿Rose model of a neuron, at the transition point between the bursting and spiking dynamics, which are two different dynamic behaviors that this system is able to present. Moreover, besides the change in attractor size, other significant properties of the system undergoing the transitions do change in a relevant qualitative way. The mechanism for such transition is understood in terms of a simple one-dimensional map whose dynamics undergoes a crossover between two different universal behaviors

Signaling across the synapse: a role for Wnt and Dishevelled in presynaptic assembly and neurotransmitter release

Proper dialogue between presynaptic neurons and their targets is essential for correct synaptic assembly and function. At central synapses, Wnt proteins function as retrograde signals to regulate axon remodeling and the accumulation of presynaptic proteins. Loss of Wnt7a function leads to defects in the localization of presynaptic markers and in the morphology of the presynaptic axons. We show that loss of function of Dishevelled-1 (Dvl1) mimics and enhances the Wnt7a phenotype in the cerebellum. Although active zones appear normal, electrophysiological recordings in cerebellar slices from Wnt7a/Dvl1 double mutant mice reveal a defect in neurotransmitter release at mossy fi ber–granule cell synapses. Deficiency in Dvl1 decreases, whereas exposure to Wnt increases, synaptic vesicle recycling in mossy fi bers. Dvl increases the number of Bassoon clusters, and like other components of the Wnt pathway, it localizes to synaptic sites. These fi ndings demonstrate that Wnts signal across the synapse on Dvl-expressing presynaptic terminals to regulate synaptic assembly and suggest a potential novel function for Wnts in neurotransmitter release.

On the existence and function of galanin receptor heteromers in the central nervous system

Galanin receptor (GalR) subtypes 1-3 linked to central galanin neurons may form heteromers with each other and other types of G protein-coupled receptors in the central nervous system (CNS). These heteromers may be one molecular mechanism for galanin peptides and their N-terminal fragments (gal 1-15) to modulate the function of different types of glia-neuronal networks in the CNS, especially the emotional and the cardiovascular networks. GalR-5-HT1A heteromers likely exist with antagonistic GalR-5-HT1A receptor-receptor interactions in the ascending midbrain raphe 5-HT neuron systems and their target regions. They represent a novel target for antidepressant drugs. Evidence is given for the existence of GalR1-5-HT1A heteromers in cellular models with trans-inhibition of the protomer signaling. A GalR1-GalR2 heteromer is proposed to be a galanin N-terminal fragment preferring receptor (1-15) in the CNS. Furthermore, a GalR1-GalR2-5-HT1A heterotrimer is postulated to explain why only galanin (1-15) but not galanin (1-29) can antagonistically modulate the 5-HT1A receptors in the dorsal hippocampus rich in gal fragment binding sites. The results underline a putative role of different types of GalR-5-HT1A heteroreceptor complexes in depression. GalR antagonists may also have therapeutic actions in depression by blocking the antagonistic GalR-NPYY1 receptor interactions in putative GalR-NPYY1 receptor heteromers in the CNS resulting in increases in NPYY1 transmission and antidepressant effects. In contrast the galanin fragment receptor (a postulated GalR1-GalR2 heteromer) appears to be linked to the NPYY2 receptor enhancing the affinity of the NPYY2 binding sites in a putative GalR1-GalR2-NPYY2 heterotrimer. Finally, putative GalR-α2-adrenoreceptor heteromers with antagonistic receptor-receptor interactions may be a widespread mechanism in the CNS for integration of galanin and noradrenaline signals also of likely relevance for depression

Drug abuse, brain calcification and glutamate-induced neurodegeneration

Positive and negative reinforcing systems are part of the mechanism of drug dependence. Drugs with abuse potential may change the manner of response to negative emotional stimuli, activate positive emotional reactions and possess primary reinforcing properties. Catecholaminergic and peptidergic processes are of importance in these mechanisms. Current research needs to understand the types of adaptations that underlie the particularly long-lived aspects of addiction. Presently, glutamate is candidate to play a role in the enduring effects of drugs of abuse. For example, it participates in the chronic pathological changes of corticostriatal terminals produced by methamphetamine. At the synaptic level, a link between over-activation of glutamate receptors, [C(a2+)](i) increase and neuronal damage has been clearly established leading to neurodegeneration. Thus, neurodegeneration can start after an acute over-stimulation whose immediate effects depend on a diversity of calcium-activated mechanisms. If sufficient, the initial insult results in calcification and activation of a chronic on-going process with a progressive loss of neurons. At present, long-term effects of drug dependence underlie an excitotoxicity process linked to a polysynaptic pathway that dynamically regulates synaptic glutamate. Retaliatory mechanisms include energy capability of the neurons, inhibitory systems and cytoplasmic calcium precipitation as part of the neuron-glia interactions. This paper presents an integrated view of these molecular and cellular mechanisms to help understand their relationship and interdependence in a chronic pathological process that suggest new targets for therapeutic intervention.

Estudi de les alteracions en la capacitat neuroprotectora dels astròcits reactius en l'envelliment

En el periodo 2005-2008 hemos publicado tres artículos sobre las alteraciones de los astrocitos reactivos en el cerebro durante el envejecimiento. En el primer estudio, evaluamos la capacidad neuroprotectora de los astrocitos en un modelo experimental in vitro de envejecimiento. Los cambios en el estrés oxidativo, la captación del glutamato y la expresión proteica fueron evaluados en los astrocitos corticales de rata cultivados durante 10 y 90 días in vitro (DIV). Los astrocitos envejecidos tenían una capacidad reducida de mantener la supervivencia neuronal. Estos resultados indican que los astrocitos pueden perder parcialmente su capacidad neuroprotectora durante el envejecimiento. En el segundo estudio el factor neurotrófico derivado de la línea glial (GDNF) fue probado para observar sus efectos neurotróficos contra la atrofia neuronal que causa déficits cognitivos en la vejez. Las ratas envejecidas Fisher 344 con deficiencias en el laberinto de Morris recibieron inyecciones intrahippocampales de un vector lentiviral que codifica GDNF humano en los astrocitos o del mismo vector que codifica la proteína fluorescente verde humana como control. El GDNF secretado por los astrocitos mejoró la función de la neurona como se muestra por aumentos locales en la síntesis de los neurotransmisores acetilcolina, dopamina y serotonina. El aprendizaje espacial y la prueba de memoria demostraron un aumento significativo en las capacidades cognitivas debido a la exposición de GDNF, mientras que las ratas control mantuvieron sus resultados al nivel del azar. Estos resultados confirman el amplio espectro de la acción neurotrófica del GDNF y abre nuevas posibilidades de terapia génica para reducir la neurodegeneración asociada al envejecimiento. En el último estudio, examinamos cambios en la fosforilación de tau, el estrés oxidativo y la captación de glutamato en los cultivos primarios de astrocitos corticales de ratones neonatos de senescencia acelerada (SAMP8) y ratones resistentes a la senescencia (SAMR1). Nuestros resultados indican que las alteraciones en cultivos del astrocitos de los ratones SAMP8 son similares a las detectadas en cerebros enteros de los ratones SAMP8 de 1-5 meses de edad. Por otra parte, nuestros resultados sugieren que esta preparación in vitro es adecuada para estudiar en este modelo murino el envejecimiento temprano y sus procesos moleculares y celulares.

A decision-making Fokker-Planck model in computational neuroscience

Minimal models for the explanation of decision-making in computational neuroscience are based on the analysis of the evolution for the average firing rates of two interacting neuron populations. While these models typically lead to multi-stable scenario for the basic derived dynamical systems, noise is an important feature of the model taking into account finite-size effects and robustness of the decisions. These stochastic dynamical systems can be analyzed by studying carefully their associated Fokker-Planck partial differential equation. In particular, we discuss the existence, positivity and uniqueness for the solution of the stationary equation, as well as for the time evolving problem. Moreover, we prove convergence of the solution to the the stationary state representing the probability distribution of finding the neuron families in each of the decision states characterized by their average firing rates. Finally, we propose a numerical scheme allowing for simulations performed on the Fokker-Planck equation which are in agreement with those obtained recently by a moment method applied to the stochastic differential system. Our approach leads to a more detailed analytical and numerical study of this decision-making model in computational neuroscience.

Estudio de la calidad ambiental de la Bahía de Cárdenas para un futuro manejo integrado de zonas costeras

Estudi de la qualitat ambiental de la Bahía de Cárdenas (Cuba) mitjançant una sèrie d’indicadors físico-químics de l’aigua que reflecteixen l’estat actual de l’ecosistema. Els resultats s’han contrastat amb la legislació cubana per tal de determinar el grau de contaminació de l’aigua. S’han estudiat les fonts contaminants i finalment s’han proposat una sèrie d’actuacions per a la seva millora

Hedgehog signaling governs the development of otic sensory epithelium and its associated innervation in zebrafish

The inner ear is responsible for the perception of motion and sound in vertebrates. Its functional unit, the sensory patch, contains mechanosensory hair cells innervated by sensory neurons from the statoacoustic ganglion (SAG) that project to the corresponding nuclei in the brainstem. How hair cells develop at specific positions, and how otic neurons are sorted to specifically innervate each endorgan and to convey the extracted information to the hindbrain is not completely understood. In this work, we study the generation of macular sensory patches and investigate the role of Hedgehog (Hh) signaling in the production of their neurosensory elements. Using zebrafish transgenic lines to visualize the dynamics of hair cell and neuron production, we show that the development of the anterior and posterior maculae is asynchronic, suggesting they are independently regulated. Tracing experiments demonstrate the SAG is topologically organized in two different neuronal subpopulations, which are spatially segregated and innervate specifically each macula. Functional experiments identify the Hh pathway as crucial in coordinating the production of hair cells in the posterior macula, and the formation of its specific innervation. Finally, gene expression analyses suggest that Hh influences the balance between different SAG neuronal subpopulations. These results lead to a model in which Hh orients functionally the development of inner ear towards an auditory fate in all vertebrate species.

Impairment of mossy fiber long-term potentiation and associative learning in pituitary adenylate cyclase activating polypeptide type I receptor-deficient Mice

The pituitary adenylate cyclase activating polypeptide (PACAP) type I receptor (PAC1) is a G-protein-coupled receptor binding the strongly conserved neuropeptide PACAP with 1000-fold higher affinity than the related peptide vasoactive intestinal peptide. PAC1-mediated signaling has been implicated in neuronal differentiation and synaptic plasticity. To gain further insight into the biological significance of PAC1-mediated signaling in vivo, we generated two different mutant mouse strains, harboring either a complete or a forebrain-specific inactivation of PAC1. Mutants from both strains show a deficit in contextual fear conditioning, a hippocampus-dependent associative learning paradigm. In sharp contrast, amygdala-dependent cued fear conditioning remains intact. Interestingly, no deficits in other hippocampus-dependent tasks modeling declarative learning such as the Morris water maze or the social transmission of food preference are observed. At the cellular level, the deficit in hippocampus-dependent associative learning is accompanied by an impairment of mossy fiber long-term potentiation (LTP). Because the hippocampal expression of PAC1 is restricted to mossy fiber terminals, we conclude that presynaptic PAC1-mediated signaling at the mossy fiber synapse is involved in both LTP and hippocampus-dependent associative learning.

Bradykinin, but not muscarinic, inhibition of M-current in rat sympathetic ganglion neurons involves phospholipase C-β4

Rat superior cervical ganglion (SCG) neurons express low-threshold noninactivating M-type potassium channels (I-K(M)), which can be inhibited by activation of M-1 muscarinic receptors (M-1 mAChR) and bradykinin (BK) B-2 receptors. Inhibition by the M1 mAChR agonist oxotremorine methiodide (Oxo-M) is mediated, at least in part, by the pertussis toxin-insensitive G-protein G alpha (q) (Caulfield et al., 1994; Haley et al., 1998a), whereas BK inhibition involves G alpha (q) and/or G alpha (11) (Jones et al., 1995). G alpha (q) and G alpha (11) can stimulate phospholipase C-beta (PLC-beta), raising the possibility that PLC is involved in I-K(M) inhibition by Oxo-M and BK. RT-PCR and antibody staining confirmed the presence of PLC-beta1, - beta2, - beta3, and - beta4 in rat SCG. We have tested the role of two PLC isoforms (PLC-beta1 and PLC-beta4) using antisense-expression constructs. Antisense constructs, consisting of the cytomegalovirus promoter driving antisense cRNA corresponding to the 3'-untranslated regions of PLC-beta1 and PLC-beta4, were injected into the nucleus of dissociated SCG neurons. Injected cells showed reduced antibody staining for the relevant PLC-beta isoform when compared to uninjected cells 48 hr later. BK inhibition of I-K(M) was significantly reduced 48 hr after injection of the PLC-beta4, but not the PLC-beta1, antisense-encoding plasmid. Neither PLC-beta antisense altered M-1 mAChR inhibition by Oxo-M. These data support the conclusion of Cruzblanca et al. (1998) that BK, but not M-1 mAChR, inhibition of I-K(M) involves PLC and extends this finding by indicating that PLC-beta4 is involved.

Quality coding by neural populations in the early olfactory pathway: analysis using information theory

In this article, we analyze the ability of the early olfactory system to detect and discriminate different odors by means of information theory measurements applied to olfactory bulb activity images. We have studied the role that the diversity and number of receptor neuron types play in encoding chemical information. Our results show that the olfactory receptors of the biological system are low correlated and present good coverage of the input space. The coding capacity of ensembles of olfactory receptors with the same receptive range is maximized when the receptors cover half of the odor input space - a configuration that corresponds to receptors that are not particularly selective. However, the ensemble's performance slightly increases when mixing uncorrelated receptors of different receptive ranges. Our results confirm that the low correlation between sensors could be more significant than the sensor selectivity for general purpose chemo-sensory systems, whether these are biological or biomimetic.