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.

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

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.

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.

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.

Extrasynaptic neurotransmission in the modulation of brain function. Focus on the striatal neuronal glial networks

Extrasynaptic neurotransmission is an important short distance form of volume transmission (VT) and describes the extracellular diffusion of transmitters and modulators after synaptic spillover or extrasynaptic release in the local circuit regions binding to and activating mainly extrasynaptic neuronal and glial receptors in the neuroglial networks of the brain. Receptor-receptor interactions in G protein-coupled receptor (GPCR) heteromers play a major role, on dendritic spines and nerve terminals including glutamate synapses, in the integrative processes of the extrasynaptic signaling. Heteromeric complexes between GPCR and ion-channel receptors play a special role in the integration of the synaptic and extrasynaptic signals. Changes in extracellular concentrations of the classical synaptic neurotransmitters glutamate and GABA found with microdialysis is likely an expression of the activity of the neuron-astrocyte unit of the brain and can be used as an index of VT-mediated actions of these two neurotransmitters in the brain. Thus, the activity of neurons may be functionally linked to the activity of astrocytes, which may release glutamate and GABA to the extracellular space where extrasynaptic glutamate and GABA receptors do exist. Wiring transmission (WT) and VT are fundamental properties of all neurons of the CNS but the balance between WT and VT varies from one nerve cell population to the other. The focus is on the striatal cellular networks, and the WT and VT and their integration via receptor heteromers are described in the GABA projection neurons, the glutamate, dopamine, 5-hydroxytryptamine (5-HT) and histamine striatal afferents, the cholinergic interneurons, and different types of GABA interneurons. In addition, the role in these networks of VT signaling of the energy-dependent modulator adenosine and of endocannabinoids mainly formed in the striatal projection neurons will be underlined to understand the communication in the striatal cellular networks

First-passage and escape problems in the Feller process

The Feller process is an one-dimensional diffusion process with linear drift and state-dependent diffusion coefficient vanishing at the origin. The process is positive definite and it is this property along with its linear character that have made Feller process a convenient candidate for the modeling of a number of phenomena ranging from single-neuron firing to volatility of financial assets. While general properties of the process have long been well known, less known are properties related to level crossing such as the first-passage and the escape problems. In this work we thoroughly address these questions.

Oscillations, phase-of-firing coding, and spike timing-dependent plasticity: an efficient learning scheme

Recent experiments have established that information can be encoded in the spike times of neurons relative to the phase of a background oscillation in the local field potential—a phenomenon referred to as “phase-of-firing coding” (PoFC). These firing phase preferences could result from combining an oscillation in the input current with a stimulus-dependent static component that would produce the variations in preferred phase, but it remains unclear whether these phases are an epiphenomenon or really affect neuronal interactions—only then could they have a functional role. Here we show that PoFC has a major impact on downstream learning and decoding with the now well established spike timing-dependent plasticity (STDP). To be precise, we demonstrate with simulations how a single neuron equipped with STDP robustly detects a pattern of input currents automatically encoded in the phases of a subset of its afferents, and repeating at random intervals. Remarkably, learning is possible even when only a small fraction of the afferents (~10%) exhibits PoFC. The ability of STDP to detect repeating patterns had been noted before in continuous activity, but it turns out that oscillations greatly facilitate learning. A benchmark with more conventional rate-based codes demonstrates the superiority of oscillations and PoFC for both STDP-based learning and the speed of decoding: the oscillation partially formats the input spike times, so that they mainly depend on the current input currents, and can be efficiently learned by STDP and then recognized in just one oscillation cycle. This suggests a major functional role for oscillatory brain activity that has been widely reported experimentally.

Transfer entropy reconstruction and labeling of neuronal connections from simulated calcium imaging

Neuronal dynamics are fundamentally constrained by the underlying structural network architecture, yet much of the details of this synaptic connectivity are still unknown even in neuronal cultures in vitro. Here we extend a previous approach based on information theory, the Generalized Transfer Entropy, to the reconstruction of connectivity of simulated neuronal networks of both excitatory and inhibitory neurons. We show that, due to the model-free nature of the developed measure, both kinds of connections can be reliably inferred if the average firing rate between synchronous burst events exceeds a small minimum frequency. Furthermore, we suggest, based on systematic simulations, that even lower spontaneous inter-burst rates could be raised to meet the requirements of our reconstruction algorithm by applying a weak spatially homogeneous stimulation to the entire network. By combining multiple recordings of the same in silico network before and after pharmacologically blocking inhibitory synaptic transmission, we show then how it becomes possible to infer with high confidence the excitatory or inhibitory nature of each individual neuron.

The existence of FGFR1-5-HT1A receptor heterocomplexes in midbrain 5-HT neurons of the rat: relevance for neuroplasticity

The ascending midbrain 5-HT neurons to the forebrain may be dysregulated in depression and have a reduced trophic support. With in situ proximity ligation assay (PLA) and supported by coimmunoprecipitation and colocation of the FGFR1 and 5-HT1A immunoreactivities in the midbrain raphe cells, evidence for the existence of FGFR1-5-HT1A receptor heterocomplexes in the dorsal and median raphe nuclei of the Sprague Dawley rat as well as in the rat medullary raphe RN33B cells has been obtained. Especially after combined FGF-2 and 8-OH-DPAT treatment, a marked and significant increase in PLA clusters was found in the RN33B cells. Similar results were reached with the FRET technique in HEK293T cells, where TM-V of the 5HT1A receptor was found to be part of the receptor interface. The combined treatment with FGF-2 and the 5-HT1A agonist also synergistically increased FGFR1 and ERK1/2 phosphorylation in the raphe midline area of the midbrain and the RN33B cells as well as their differentiation, as seen from development of the increased number and length of extensions per cell and their increased 5-HT immunoreactivity. These signaling and differentiation events were dependent on the receptor interface since they were blocked by incubation with TM-V but not by TM-II. Together, the results indicate that the 5-HT1A autoreceptors by being part of a FGFR1-5-HT1A receptor heterocomplex in the midbrain raphe 5-HT nerve cells appear to have a trophic role in the central 5-HT neuron systems in addition to playing a key role in reducing the firing of these neurons

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

First-passage and escape problems in the Feller process

The Feller process is an one-dimensional diffusion process with linear drift and state-dependent diffusion coefficient vanishing at the origin. The process is positive definite and it is this property along with its linear character that have made Feller process a convenient candidate for the modeling of a number of phenomena ranging from single-neuron firing to volatility of financial assets. While general properties of the process have long been well known, less known are properties related to level crossing such as the first-passage and the escape problems. In this work we thoroughly address these questions.