First-passage-time statistics of a Brownian particle driven by an arbitrary unidimensional potential with a superimposed exponential time-dependent drift

In one-dimensional systems, the dynamics of a Brownian particle are governed by the force derived from a potential as well as by diffusion properties. In this work, we obtain the first-passage-time statistics of a Brownian particle driven by an arbitrary potential with an exponential temporally decaying superimposed field up to a prescribed threshold. The general system analyzed here describes the sub-threshold signal integration of integrate-and-fire neuron models, of any kind, supplemented by an adaptation-like current, whereas the first-passage-time corresponds to the declaration of a spike. Following our previous studies, we base our analysis on the backward Fokker Planck equation and study the survival probability and the first-passage-time density function in the space of the initial condition. By proposing a series solution we obtain a system of recurrence equations, which given the specific structure of the exponential time-dependent drift, easily admit a simpler Laplace representation. Naturally, the present general derivation agrees with the explicit solution we found previously for the Wiener process in (2012 JPhysA 45 185001). However, to demonstrate the generality of the approach, we further explicitly evaluate the first-passage-time statistics of the underlying Ornstein Uhlenbeck process. To test the validity of the series solution, we extensively compare theoretical expressions with the data obtained from numerical simulations in different regimes. As shown, agreement is precise whenever the series is truncated at an appropriate order. Beyond the fact that both the Wiener and Ornstein Uhlenbeck processes have a direct interpretation in the context of neuronal models, given their ubiquity in different fields, our present results will be of interest in other settings where an additive state-independent temporal relaxation process is being developed as the particle diffuses.Comment: 22 pages (20 pages in the journal version), 3 figures, published in J. Phys.

Neural coding in early stages of visual processing

El procesamiento temprano de la información visual ocurre en la retina, mediante distintos procesos bioquímicos y fisiológicos que tienen lugar entre diferentes clases de neuronas en una organización laminar bien definida. En conjunto, el procesamiento ocurre en cascada y tiene una señal de salida bien determinada: los potenciales de acción que las células ganglionares colectan en el nervio óptico y le envían a la corteza visual primaria. La contribución más importante de esta actividad de disparo es la codificación que ocurre en las llamadas células bipolares, las cuales relevan y procesan la información visual transducida en los fotorreceptores. En este proyecto, estudiaremos en forma detallada las etapas de procesamiento de la información que ocurren para generar la respuesta en las distintas células bipolares encontradas en la retina de los mamíferos. Mediante una adecuada descripción matemática de la fototransducción, la transmisión sináptica, la integración espacial-cromática temporal y la realimentación negativa mediada por las células horizontales, derivaremos las propiedades de respuesta de las células bipolares, tanto en la definición de su campo receptivo como en el procesamiento no lineal que ocurre debido a la adaptación a distintas luminosidades. Por otro lado, en base a la definición de este modelo detallado, exploraremos numéricamente el efecto de nuevos procesos encontrados experimentalmente, las consecuencias computacionales de distintas alternativas sobre las que existen controversias, y el efecto del ruido intrínseco originado en distintos sitios sobre la respuesta del sistema.Early processing of visual information takes place in the retina, via diverse biochemical and physiological processes that relate neural responses of different neuronal classes in a well-defined laminar organization. Overall, this is a feedforward processing and it has a well determined output signal: the action potentials that ganglionar cells send through the optical nerve to the primary visual cortex. The most important contribution of this firing activity is the coding occurying in the so called bipolar cells, which gate and process the visual information transduced in the photoreceptors. In this project, we will study with some detail those information processing stages that mediate the different bipolar cells' responses found in mammalian retina. Based on an adequate mathematical model of the phototransduction, the synaptic transmission, the temporal-spatial-chromatic integration of visual information, and the negative feedback provided by horizontal cells, we will derive the response properties of bipolar cells, not only regarding the definition of their receptive fields but also with respect to the nonlinear processing attributed to adaptation to different mean luminosities. On the other hand, relying on this detailed description, we will numerically explore the effect of new processes recently found in experiments, the computational consequences of different conflicting alternatives, and the effect of intrinsic noise originated at different locations on the system's response

Complex interplay between spectral harmonicity and different types of cross-frequency couplings in nonlinear oscillators and biologically plausible neural network models

Cross-frequency coupling (CFC) refers to the nonlinear interaction between oscillations in different frequency bands, and it is a rather ubiquitous phenomenon that has been observed in a variety of physical and biophysical systems. In particular, the coupling between the phase of slow oscillations and the amplitude of fast oscillations, referred as phase-Amplitude coupling (PAC), has been intensively explored in the brain activity recorded from animals and humans. However, the interpretation of these CFC patterns remains challenging since harmonic spectral correlations characterizing nonsinusoidal oscillatory dynamics can act as a confounding factor. Specialized signal processing techniques are proposed to address the complex interplay between spectral harmonicity and different types of CFC, not restricted only to PAC. For this, we provide an in-depth characterization of the time locked index (TLI) as a tool aimed to efficiently quantify the harmonic content of noisy time series. It is shown that the proposed TLI measure is more robust and outperforms traditional phase coherence metrics (e.g., phase locking value, pairwise phase consistency) in several aspects. We found that a nonlinear oscillator under the effect of additive noise can produce spurious CFC with low spectral harmonic content. On the other hand, two coupled oscillatory dynamics with independent fundamental frequencies can produce true CFC with high spectral harmonic content via a rectification mechanism or other post-interaction nonlinear processing mechanisms. These results reveal a complex interplay between CFC and harmonicity emerging in the dynamics of biologically plausible neural network models and more generic nonlinear and parametric oscillators. We show that, contrary to what is usually assumed in the literature, the high harmonic content observed in nonsinusoidal oscillatory dynamics is neither a sufficient nor necessary condition to interpret the associated CFC patterns as epiphenomenal. There is mounting evidence suggesting that the combination of multimodal recordings, specialized signal processing techniques, and theoretical modeling is becoming a required step to completely understand CFC patterns observed in oscillatory rich dynamics of physical and biophysical systems.Fil: Dellavale Clara, Hector Damian. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina. Universidad Nacional de Cuyo; ArgentinaFil: Velarde, Osvaldo Matias. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina. Universidad Nacional de Cuyo; ArgentinaFil: Mato, German. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina. Universidad Nacional de Cuyo; ArgentinaFil: Urdapilleta, Eugenio. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina. Universidad Nacional de Cuyo; Argentin

Characterization of cross frequency couplings produced by harmonic and non-harmonic frequency bands during seizure activity from intracerebral recordings in patients candidate to epilepsy surgery

Cross frequency coupling (CFC) phenomenon has been proposed to be functionally involved in neuronal communication, memory formation and learning. Besides, experimental findings have shown that phase-amplitude (PAC) and phase-phase (PPC) couplings are important variants of CFC linked to physiological and pathological brain states. In particular, PAC and PPC have been observed in local field potentials (LFP) recorded during epileptic seizures. PPC represents the phase coherence across frequency bands and/or recording sites, which in general increases between nearby areas of the neural tissue recruited to the ictal event. In PAC, the amplitude of a high frequency band is modulated by the phase of another band with a lower frequency content. Recent works have shown that nested oscillations, associated to the scale free neural activity, and sharp waveforms both produce PAC, however, they reflect two distinct neural mechanisms that are anatomically segregated in the human brain.In this work, we study the CFC dynamics during the seizure activity in patients with focal epilepsy who were candidates for surgery treatment. The analysis was performed on LFP obtained from 5 patients undergoing intracerebral electroencephalography (stereo EEG) and 2 patients undergoing subdural electrocorticography (ECoG). To quantify the CFC dynamics during the seizure activity we use non-parametric methods: the Phase Locking Value (PLV) and the Modulation Index based on the Kullback-Leibler distance (KLMI). In addition, we have developed specialized tools to characterize the nature of the observed CFC patterns. Specifically, the Time Locked Index (TLI) and Harmonic Index (HI) were implemented to quantify the presence of harmonics associated to the emergence of CFC. Moreover, the correlation of LFP and CFC for a given recording site across seizures was evaluated in order to quantify the seizure stereotypy.We have found that the ictal activity gives rise to different types of CFC, which were highly stereotyped during the seizure dynamics. Importantly, two essentially different PAC patterns produced by non-sinusoidal waveforms were identified. In the first one, the PAC was elicited by highly cyclostationary (pseudo-periodic) LFP signals, which were characterized by well-defined harmonic spectral components present in their Fourier spectrum. In the second one, the PAC was produced by sharp waveforms constituted by non-harmonic high frequency components. The proposed tools allowed us to better characterize the CFC patterns emerging during the seizure dynamics, which could pave the way to unveil the underlying neural mechanisms that initiate and propagate the ictal activity.Fil: Dellavale Clara, Hector Damian. Comisión Nacional de Energía Atómica. Unidad Ejecutora Instituto de Nanociencia y Nanotecnología. - Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Unidad Ejecutora Instituto de Nanociencia y Nanotecnología; ArgentinaFil: Urdapilleta, Eugenio. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica. Gerencia de Área de Investigaciones y Aplicaciones No Nucleares. Gerencia de Física (CAB); ArgentinaFil: Cámpora, Nuria Elide. Universidad Nacional Arturo Jauretche. Unidad Ejecutora de Estudios en Neurociencias y Sistemas Complejos. Provincia de Buenos Aires. Ministerio de Salud. Hospital Alta Complejidad en Red El Cruce Dr. Néstor Carlos Kirchner Samic. Unidad Ejecutora de Estudios en Neurociencias y Sistemas Complejos. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Unidad Ejecutora de Estudios en Neurociencias y Sistemas Complejos; ArgentinaFil: Velarde, Osvaldo Matias. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica. Gerencia de Área de Investigaciones y Aplicaciones No Nucleares. Gerencia de Física (CAB); ArgentinaFil: Kochen, Sara Silvia. Universidad Nacional Arturo Jauretche. Unidad Ejecutora de Estudios en Neurociencias y Sistemas Complejos. Provincia de Buenos Aires. Ministerio de Salud. Hospital Alta Complejidad en Red El Cruce Dr. Néstor Carlos Kirchner Samic. Unidad Ejecutora de Estudios en Neurociencias y Sistemas Complejos. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Unidad Ejecutora de Estudios en Neurociencias y Sistemas Complejos; ArgentinaFil: Mato, German. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica. Gerencia de Área de Investigaciones y Aplicaciones No Nucleares. Gerencia de Física (CAB); ArgentinaNeuroscience 2018San DiegoEstados UnidosSociety for Neuroscienc

Onset of negative interspike interval correlations in adapting neurons

Negative serial correlations in single spike trains are an effective method to reduce the variability of spike counts. One of the factors contributing to the development of negative correlations between successive interspike intervals is the presence of adaptation currents. In this work, based on a hidden Markov model and a proper statistical description of conditional responses, we obtain analytically these correlations in an adequate dynamical neuron model resembling adaptation. We derive the serial correlation coefficients for arbitrary lags, under a small adaptation scenario. In this case, the behavior of correlations is universal and depends on the first-order statistical description of an exponentially driven time-inhomogeneous stochastic process.Comment: 12 pages (10 pages in the journal version), 6 figures, published in Phys. Rev. E; http://link.aps.org/doi/10.1103/PhysRevE.84.04190

Noise-induced interspike interval correlations and spike train regularization in spike-triggered adapting neurons

Spike generation in neurons produces a temporal point process, whose statistics is governed by intrinsic phenomena and the external incoming inputs to be coded. In particular, spike-evoked adaptation currents support a slow temporal process that conditions spiking probability at the present time according to past activity. In this work, we study the statistics of interspike interval correlations arising in such non-renewal spike trains, for a neuron model that reproduces different spike modes in a small adaptation scenario. We found that correlations are stronger as the neuron fires at a particular firing rate, which is defined by the adaptation process. When set in a subthreshold regime, the neuron may sustain this particular firing rate, and thus induce correlations, by noise. Given that, in this regime, interspike intervals are negatively correlated at any lag, this effect surprisingly implies a reduction in the variability of the spike count statistics at a finite noise intensity

Transition to synchronization in heterogeneous inhibitory neural networks with structured synapses

Inhibitory neurons form an extensive network involved in the development of different rhythms in the cerebral cortex. A transition from an incoherent state, where all inhibitory neurons fire unrelated to each other, to a synchronized or locked state, where all or most neurons define a tight firing pattern, is maybe the most salient process to analyze when considering neuronal rhythms. In this work, we analyzed whether different patterns of effective synaptic connectivity may support a first-order-like transition in this path to synchronization. Such an "explosive"phenomenon may be relevant in neural processes, as normal cognitive processing in different tasks and some neurological disorders manifest an increased power in many neuronal rhythms, supported by an extended concerted spiking activity and an abrupt change to this state. Furthermore, we built an adaptive mechanism that supports the generation of this kind of network, which rapidly creates the underlying structure based on the ongoing firing statistics.Fil: Urdapilleta, Eugenio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Área de Investigación y Aplicaciones No Nucleares. Gerencia de Física (Centro Atómico Bariloche); Argentina. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro. Archivo Histórico del Centro Atómico Bariloche e Instituto Balseiro | Universidad Nacional de Cuyo. Instituto Balseiro. Archivo Histórico del Centro Atómico Bariloche e Instituto Balseiro; Argentin