Latching dynamics in Potts neural networks

One purpose of Computational Neuroscience is to try to understand by using models how at least some parts in the brain work or how cognitive phenomena occur and are organized in terms of neuronal activity. The Hopfield model of a neural network, rooted in Statistical Physics, put forward by J. Hopfield in the 1980s, was one of the first attempts to explain how associative memory could work. It was successful in guiding experiments, e.g., in the hippocampus and primate inferotemporal cortex. However, some higher level cognitive functions that the brain accomplishes require, to be approached quantitaively, by more advanced models beyond simple cued retrieval..

Fractals in the Nervous System: conceptual Implications for Theoretical Neuroscience

This essay is presented with two principal objectives in mind: first, to document the prevalence of fractals at all levels of the nervous system, giving credence to the notion of their functional relevance; and second, to draw attention to the as yet still unresolved issues of the detailed relationships among power law scaling, self-similarity, and self-organized criticality. As regards criticality, I will document that it has become a pivotal reference point in Neurodynamics. Furthermore, I will emphasize the not yet fully appreciated significance of allometric control processes. For dynamic fractals, I will assemble reasons for attributing to them the capacity to adapt task execution to contextual changes across a range of scales. The final Section consists of general reflections on the implications of the reviewed data, and identifies what appear to be issues of fundamental importance for future research in the rapidly evolving topic of this review

Realistic modeling of mesoscopic ephaptic coupling in the human brain

Altres ajuts: The National Institutes of Health (R01HD069776, R01NS073601, R21MH099196, R21 NS082870, R21 NS085491, R21HD07616)Several decades of research suggest that weak electric fields may influence neural processing, including those induced by neuronal activity and proposed as a substrate for a potential new cellular communication system, i.e., ephaptic transmission. Here we aim to model mesoscopic ephaptic activity in the human brain and explore its trajectory during aging by characterizing the electric field generated by cortical dipoles using realistic finite element modeling. Extrapolating from electrophysiological measurements, we first observe that modeled endogenous field magnitudes are comparable to those in measurements of weak but functionally relevant self-generated fields and to those produced by noninvasive transcranial brain stimulation, and therefore possibly able to modulate neuronal activity. Then, to evaluate the role of these fields in the human cortex in large MRI databases, we adapt an interaction approximation that considers the relative orientation of neuron and field to estimate the membrane potential perturbation in pyramidal cells. We use this approximation to define a simplified metric (EMOD1) that weights dipole coupling as a function of distance and relative orientation between emitter and receiver and evaluate it in a sample of 401 realistic human brain models from healthy subjects aged 16-83. Results reveal that ephaptic coupling, in the simplified mesoscopic modeling approach used here, significantly decreases with age, with higher involvement of sensorimotor regions and medial brain structures. This study suggests that by providing the means for fast and direct interaction between neurons, ephaptic modulation may contribute to the complexity of human function for cognition and behavior, and its modification across the lifespan and in response to pathology

Mesoscopic description of hippocampal replay and metastability in spiking neural networks with short-term plasticity

Bottom-up models of functionally relevant patterns of neural activity provide an explicit link between neuronal dynamics and computation. A prime example of functional activity pattern is hippocampal replay, which is critical for memory consolidation. The switchings between replay events and a low-activity state in neural recordings suggests metastable neural circuit dynamics. As metastability has been attributed to noise and/or slow fatigue mechanisms, we propose a concise mesoscopic model which accounts for both. Crucially, our model is bottom-up: it is analytically derived from the dynamics of finite-size networks of Linear-Nonlinear Poisson neurons with short-term synaptic depression. As such, noise is explicitly linked to spike noise and network size, and fatigue is explicitly linked to synaptic dynamics. To derive the mesosocpic model, we first consider a homogeneous spiking neural network and follow the temporal coarse-graining approach of Gillespie ("chemical Langevin equation"), which can be naturally interpreted as a stochastic neural mass model. The Langevin equation is computationally inexpensive to simulate and enables a thorough study of metastable dynamics in classical setups (population spikes and Up-Down states dynamics) by means of phase-plane analysis. This stochastic neural mass model is the basic component of our mesoscopic model for replay. We show that our model faithfully captures the stochastic nature of individual replayed trajectories. Moreover, compared to the deterministic Romani-Tsodyks model of place cell dynamics, it exhibits a higher level of variability in terms of content, direction and timing of replay events, compatible with biological evidence and could be functionally desirable. This variability is the product of a new dynamical regime where metastability emerges from a complex interplay between finite-size fluctuations and local fatigue.Comment: 43 pages, 8 figure

Mesoscopic descriptions of complex networks

[spa] El objetivo de la presente tesis es el estudio de las subestructuras que aparecen a un nivel de resolución mesoscópico en las redes complejas. Dichas subestructuras, que en el campo de las redes complejas son denominadas comunidades, intentan agrupar los nodos de una red de manera que los nodos que forman parte de una misma comunidad estén más conectados entre ellos que con el resto de nodos de la red. La importada del análisis de estas estructuras radica en que nos permiten comprender mejor las redes complejas dándonos información sobre la funcionalidad de las comunidades que las componen. Hemos llevado a cabo el estudio de estas estructuras mesoscópicas utilizando la información topológica de las redes, y en cuanto a los métodos empleados éstos se pueden agrupar en dos grandes familias conocidas habitualmente como clustering jerárquico y clustering modular. Dentro de la primera familia de métodos nos hemos fijado en la existencia de un problema de no unicidad en el clustering jerárquico aglomerativo, y hemos propuesto una solución a dicho problema basada en el uso de una nueva herramienta de clasificación que denominamos multidendrograma. A continuación, hemos aplicado el resultado de una clasificación jerárquica para resolver un problema dentro de las redes complejas financieras. Más concretamente, hemos aprovechado una partición en clusters para resolver de manera más eficiente el problema de optimizar una cartera de valores. Por lo que respecta a la segunda familia de métodos de clustering estudiados, ésta se basa en la optimización de una función objetivo llamada modularidad El inconveniente que presenta la optimización de la modularidad es su elevado coste computacional, la cual cosa nos ha llevado a idear una reducción analítica del tamaño de las redes complejas de manera que se conserva toda la información necesaria en la red original de cara a hallar la estructura de comunidades que optimice la modularidad. A continuación hemos podido utilizar dicha simplificación de los cálculos en el análisis de toda la mesoescala topológica de las redes complejas. Dicho mesoescala la hemos estudiado añadiendo un mismo valor a todos los nodos de una red que mide su resistencia a formar parte de comunidades, La optimización de la modularidad para estas nuevas instancias de la red original obtenidas a partir de unos valores de resistencia acotados analíticamente, nos permite analizar la mesoescala topológica de las redes. Por último, hemos propuesto una generalización de la función de modularidad donde los bloques constituyentes ya no son solamente arcos sino que pueden ser distintos tipos de motifs. Esto nos permite obtener descripciones más generales de grupos de nodos que incluyen como caso particular a las comunidades

Field-control, phase-transitions, and life's emergence

Instances of critical-like characteristics in living systems at each organizational level as well as the spontaneous emergence of computation (Langton), indicate the relevance of self-organized criticality (SOC). But extrapolating complex bio-systems to life's origins, brings up a paradox: how could simple organics--lacking the 'soft matter' response properties of today's bio-molecules--have dissipated energy from primordial reactions in a controlled manner for their 'ordering'? Nevertheless, a causal link of life's macroscopic irreversible dynamics to the microscopic reversible laws of statistical mechanics is indicated via the 'functional-takeover' of a soft magnetic scaffold by organics (c.f. Cairns-Smith's 'crystal-scaffold'). A field-controlled structure offers a mechanism for bootstrapping--bottom-up assembly with top-down control: its super-paramagnetic components obey reversible dynamics, but its dissipation of H-field energy for aggregation breaks time-reversal symmetry. The responsive adjustments of the controlled (host) mineral system to environmental changes would bring about mutual coupling between random organic sets supported by it; here the generation of long-range correlations within organic (guest) networks could include SOC-like mechanisms. And, such cooperative adjustments enable the selection of the functional configuration by altering the inorganic network's capacity to assist a spontaneous process. A non-equilibrium dynamics could now drive the kinetically-oriented system towards a series of phase-transitions with appropriate organic replacements 'taking-over' its functions.Comment: 54 pages, pdf fil

Steep, Spatially Graded Recruitment of Feedback Inhibition by Sparse Dentate Granule Cell Activity

The dentate gyrus of the hippocampus is thought to subserve important physiological functions, such as 'pattern separation'. In chronic temporal lobe epilepsy, the dentate gyrus constitutes a strong inhibitory gate for the propagation of seizure activity into the hippocampus proper. Both examples are thought to depend critically on a steep recruitment of feedback inhibition by active dentate granule cells. Here, I used two complementary experimental approaches to quantitatively investigate the recruitment of feedback inhibition in the dentate gyrus. I showed that the activity of approximately 4% of granule cells suffices to recruit maximal feedback inhibition within the local circuit. Furthermore, the inhibition elicited by a local population of granule cells is distributed non-uniformly over the extent of the granule cell layer. Locally and remotely activated inhibition differ in several key aspects, namely their amplitude, recruitment, latency and kinetic properties. Finally, I show that net feedback inhibition facilitates during repetitive stimulation. Taken together, these data provide the first quantitative functional description of a canonical feedback inhibitory microcircuit motif. They establish that sparse granule cell activity, within the range observed in-vivo, steeply recruits spatially and temporally graded feedback inhibition