Albert Compte

Theory of the electrochemical impedance of anomalous diffusion

This paper addresses the electrochemical impedance of diffusion in a spatially restricted layer. A physically grounded framework is provided for the behavior Z(iω)∝(iω)−β/2 (0<β<2), thus generalising the Warburg impedance (β=1). The analysis starts from the notion of anomalous diffusion, which is characterized by a mean squared displacement of the diffusing particles that has a power law dependence on time . Using a theoretical approach to anomalous diffusion that employs fractional calculus, several models are presented. In the first model, the continuity equation is generalised to a situation in which the number of diffusing particles is not conserved. In the second model the constitutive equation is derived from the stochastic scheme of a continuous time random walk. And in the third, the generalised constitutive equation can be interpreted within a non-local transport theory as establishing a relationship of the flux to the previous history of the concentration through a power-law behaving memory kernel. This third model is also related to diffusion in a fractal geometry. The electrochemical impedance is studied for each of these models, and the representation in terms of transmission lines is established. The main finding is that, while models with quite different non-trivial diffusion mechanisms behave similarly in a semi-infinite situation, the consideration of the effect of the boundaries gives rise to neatly different impedance spectra.

Mechanism for top-down control of working memory capacity

Working memory capacity, the maximum number of items that we can transiently store in working memory, is a good predictor of our general cognitive abilities. Neural activity in both dorsolateral prefrontal cortex and posterior parietal cortex has been associated with memory retention during visuospatial working memory tasks. The parietal cortex is thought to store the memories. However, the role of the dorsolateral prefrontal cortex, a top-down control area, during pure information retention is debated, and the mechanisms regulating capacity are unknown. Here, we propose that a major role of the dorsolateral prefrontal cortex in working memory is to boost parietal memory capacity. Furthermore, we formulate the boosting mechanism computationally in a biophysical cortical microcircuit model and derive a simple, explicit mathematical formula relating memory capacity to prefrontal and parietal model parameters. For physiologically realistic parameter values, lateral inhibition in the parietal cortex limits mnemonic capacity to a maximum of 2–7 items. However, at high loads inhibition can be counteracted by excitatory prefrontal input, thus boosting parietal capacity. Predictions from the model were confirmed in an fMRI study. Our results show that although memories are stored in the parietal cortex, interindividual differences in memory capacity are partly determined by the strength of prefrontal top-down control. The model provides a mechanistic framework for understanding top-down control of working memory and specifies two different contributions of prefrontal and parietal cortex to working memory capacity.

The generalized Cattaneo equation for the description of anomalous transport processes

The Cattaneo equation, which describes a diffusion process with a finite velocity of propagation, is generalized to describe anomalous transport. Three possible generalizations are proposed, each one supported by a different scheme: continuous time random walks, non-local transport theory, and delayed flux-force relation. The properties of these generalizations are studied in both the long-time and the short-time regimes. In the long-time limit, we recover the mean-square displacement which is characteristic for these anomalous processes. As expected, the short-time behaviour is modified in comparison to generalized diffusion equations.

The dynamical stability of reverberatory neural circuits

Abstract. The concept of reverberation proposed by Lorente de Nó and Hebb is key to understanding strongly recurrent cortical networks. In particular, synaptic reverberation is now viewed as a likely mechanism for the active maintenance of working memory in the prefrontal cortex. Theoretically, this has spurred a debate as to how such a potentially explosive mechanism can provide stable working-memory function given the synaptic and cellular mechanisms at play in the cerebral cortex. We present here new evidence for the participation of NMDA receptors in the stabilization of persistent delay activity in a biophysical network model of conductance-based neurons. We show that the stability of working-memory function, and the required NMDA/AMPA ratio at recurrent excitatory synapses, depend on physiological properties of neurons and synaptic interactions, such as the time constants of excitation and inhibition, mutual inhibition between interneurons, differential NMDA receptor participation at excitatory projections to pyramidal neurons and interneurons, or the presence of slow intrinsic ion currents in pyramidal neurons. We review other mechanisms proposed to enhance the dynamical stability of synaptically generated attractor states of a reverberatory circuit. This recent work represents a necessary and significant step towards testing attractor network models by cortical electrophysiology.

Non-equilibrium thermodynamics and anomalous diffusion

The convenience of a new thermodynamic frame for the description of anomalous diffusion is explored. Our research, which makes use of a recent new definition for entropy arising from multifractal analysis, shows that both dynamical and thermodynamical effects may contribute to non-classical diffusion.

Inhibitory Modulation of Cortical Up States

The balance between excitation and inhibition is critical in the physiology of the cerebral cortex. To understand the influence of inhibitory control on the emergent activity of the cortical network, inhibition was progressively blocked in a slice preparation that generates spontaneous rhythmic up states at a similar frequency to those occurring in vivo during slow-wave sleep or anesthesia. Progressive removal of inhibition induced a parametric shortening of up state duration and elongation of the down states, the frequency of oscillations decaying. Concurrently, a gradual increase in the network firing rate during up states occurred. The slope of transitions between up and down states was quantified for different levels of inhibition. The slope of upward transitions reflects the recruitment of the local network and was progressively increased when inhibition was decreased, whereas the speed of activity propagation became faster. Removal of inhibition eventually resulted in epileptiform activity. Whereas gradual reduction of inhibition induced linear changes in up/down states and their propagation, epileptiform activity was the result of a nonlinear transformation. A computational network model showed that strong recurrence plus activity-dependent hyperpolarizing currents were sufficient to account for the observed up state modulations and predicted an increase in activity-dependent hyperpolarization following up states when inhibition was decreased, which was confirmed experimentally.

Spontaneous High-Frequency (10–80 Hz) Oscillations during Up States in the Cerebral Cortex In Vitro

High-frequency oscillations in cortical networks have been linked to a variety of cognitive and perceptual processes. They have also been recorded in small cortical slices in vitro, indicating that neuronal synchronization at these frequencies is generated in the local cortical circuit. However, in vitro experiments have hitherto necessitated exogenous pharmacological or electrical stimulation to generate robust synchronized activity in the β/γ range. Here, we demonstrate that the isolated cortical microcircuitry generates β and γ oscillations spontaneously in the absence of externally applied neuromodulators or synaptic agonists. We show this in a spontaneously active slice preparation that engages in slow oscillatory activity similar to activity during slow-wave sleep. β and γ synchronization appeared during the up states of the slow oscillation. Simultaneous intracellular and extracellular recordings revealed synchronization between the timing of incoming synaptic events and population activity. This rhythm was mechanistically similar to pharmacologically induced γ rhythms, as it also included sparse, irregular firing of neurons within the population oscillation, predominant involvement of inhibitory neurons, and a decrease of oscillation frequency after barbiturate application. Finally, we show in a computer model how a synaptic loop between excitatory and inhibitory neurons can explain the emergence of both the slow (<1 Hz) and the β-range oscillations in the neocortical network. We therefore conclude that oscillations in the β/γ range that share mechanisms with activity reported in vivo or in pharmacologically activated in vitro preparations can be generated during slow oscillatory activity in the local cortical circuit, even without exogenous pharmacological or electrical stimulation.

An Integrated Microcircuit Model of Attentional Processing in the Neocortex

Selective attention is a fundamental cognitive function that uses top-down signals to orient and prioritize information processing in the brain. Single-cell recordings from behaving monkeys have revealed a number of attention-induced effects on sensory neurons, and have given rise to contrasting viewpoints about the neural underpinning of attentive processing. Moreover, there is evidence that attentional signals originate from the prefrontoparietal working memory network, but precisely how a source area of attention interacts with a sensory system remains unclear. To address these questions, we investigated a biophysically based network model of spiking neurons composed of a reciprocally connected loop of two (sensory and working memory) networks. We found that a wide variety of physiological phenomena induced by selective attention arise naturally in such a system. In particular, our work demonstrates a neural circuit that instantiates the “feature-similarity gain modulation principle,” according to which the attentional gain effect on sensory neuronal responses is a graded function of the difference between the attended feature and the preferred feature of the neuron, independent of the stimulus. Furthermore, our model identifies key circuit mechanisms that underlie feature-similarity gain modulation, multiplicative scaling of tuning curve, and biased competition, and provide specific testable predictions. These results offer a synthetic account of the diverse attentional effects, suggesting a canonical neural circuit for feature-based attentional processing in the cortex.

Bistable, Irregular Firing and Population Oscillations in a Modular Attractor Memory Network

Attractor neural networks are thought to underlie working memory functions in the cerebral cortex. Several such models have been proposed that successfully reproduce firing properties of neurons recorded from monkeys performing working memory tasks. However, the regular temporal structure of spike trains in these models is often incompatible with experimental data. Here, we show that the in vivo observations of bistable activity with irregular firing at the single cell level can be achieved in a large-scale network model with a modular structure in terms of several connected hypercolumns. Despite high irregularity of individual spike trains, the model shows population oscillations in the beta and gamma band in ground and active states, respectively. Irregular firing typically emerges in a high-conductance regime of balanced excitation and inhibition. Population oscillations can produce such a regime, but in previous models only a non-coding ground state was oscillatory. Due to the modular structure of our network, the oscillatory and irregular firing was maintained also in the active state without fine-tuning. Our model provides a novel mechanistic view of how irregular firing emerges in cortical populations as they go from beta to gamma oscillations during memory retrieval.

Temperature modulation of slow and fast cortical rhythms.

In the local cortical network, spontaneous emergent activity self-organizes in rhythmic patterns. These rhythms include a slow one (<1 Hz), consisting in alternation of up and down states, and also faster rhythms (10-80 Hz) generated during up states. Varying the temperature in the bath between 26 and 41 degrees C resulted in a strong modulation of the emergent network activity. Up states became shorter for warmer temperatures and longer with cooling, whereas down states were shortest at physiological (36-37 degrees C) temperature. The firing rate during up states was robustly modulated by temperature, increasing with higher temperatures. The sparse firing rate during down states hardly varied with temperature, thus resulting in a progressive merging of up and down states for temperatures around 30 degrees C. Below 30 degrees C and down to 26 degrees C the firing lost rhythmicity, becoming progressively continuous. The slope of the down-to-up transitions, which reflects the speed of recruitment of the local network, was progressively steeper for higher temperatures, whereas wave-propagation speed exhibited only a moderate increase. Fast rhythms were particularly sensitive to temperature. Broadband high-frequency fluctuations in the local field potential were maximal for recordings at 36-38 degrees C. Overall, we found that maintaining cortical slices at physiological temperature is critical for the generated activity to be analogous to that in vivo. We also demonstrate that changes in activity with temperature were not secondary to oxygenation changes. Temperature variation sets the in vitro cortical network at different functional regimes, allowing the exploration of network activity generation and control mechanisms.