Dendritic integration in a recurrent network

A Perspective on Information Optimality in a Neural Circuit and Other Biological Systems

The nematode worm Caenorhabditis elegans has a relatively simple neural system for analysis of information transmission from sensory organ to muscle fiber. Consequently, this study includes an example of a neural circuit from the nematode worm, and a procedure is shown for measuring its information optimality by use of a logic gate model. This approach is useful where the assumptions are applicable for a neural circuit, and also for choosing between competing mathematical hypotheses that explain the function of a neural circuit. In this latter case, the logic gate model can estimate computational complexity and distinguish which of the mathematical models require fewer computations. In addition, the concept of information optimality is generalized to other biological systems, along with an extended discussion of its role in genetic-based pathways of organisms.

On the neural basis of rule-guided behavior

Human behavior emerges from a complex dynamic interaction between graded and context-sensitive neural processes, the biomechanics of our bodies, and the vicissitudes of our environments. These coupled processes bear little resemblance to the iterated application of simple symbolic rules. Still, there are circumstances under which our behavior appears to be guided by explicit mental rules. A prototypical case is when succinct verbal instructions are communicated and are promptly followed by another. How does the brain support such rule-guided behavior? How are explicit rules represented in the brain? How are rule representations shaped by experience? What neural processes form the foundation of our ability to systematically represent and apply rules from the vast range of possible rules? This article reviews a line of research that has sought a computational cognitive neuroscience account of rule-guided behavior in terms of the functioning of the prefrontal cortex, the basal ganglia, and related brain systems.

Non-additive coupling enables propagation of synchronous spiking activity in purely random networks

Despite the current debate about the computational role of experimentally observed precise spike patterns it is still theoretically unclear under which conditions and how they may emerge in neural circuits. Here, we study spiking neural networks with non-additive dendritic interactions that were recently uncovered in single-neuron experiments. We show that supra-additive dendritic interactions enable the persistent propagation of synchronous activity already in purely random networks without superimposed structures and explain the mechanism underlying it. This study adds a novel perspective on the dynamics of networks with nonlinear interactions in general and presents a new viable mechanism for the occurrence of patterns of precisely timed spikes in recurrent networks.

Quantitative prediction of intermittent high-frequency oscillations in neural networks with supralinear dendritic interactions

The explanation of higher neural processes requires an understanding of the dynamics of complex, spiking neural networks. So far, modeling studies have focused on networks with linear or sublinear dendritic input summation. However, recent single-neuron experiments have demonstrated strongly supralinear dendritic enhancement of synchronous inputs. What are the implications of this amplification for networks of neurons? Here, I show numerically and analytically that such networks can generate intermittent, strong increases of activity with high-frequency oscillations; the models developed predict the shape of these events and the oscillation frequency. As an example, for the hippocampal region CA1, events with 200-Hz oscillations are predicted. I argue that these dynamics provide a plausible explanation for experimentally observed sharp-wave/ripple events. High-frequency oscillations can involve the replay of spike patterns. The models suggest that these patterns may reflect underlying network structures.

Nonlinear local electrovascular coupling. I: A theoretical model

Here we present a detailed biophysical model of how brain electrical and vascular dynamics are generated within a basic cortical unit. The model was obtained from coupling a canonical neuronal mass and an expandable vasculature. In this proposal, we address several aspects related to electroencephalographic and functional magnetic resonance imaging data fusion: (1) the impact of the cerebral architecture (at different physical levels) on the observations; (2) the physiology involved in electrovascular coupling; and (3) energetic considerations to gain a better understanding of how the glucose budget is used during neuronal activity. The model has three components. The first is the canonical neural mass model of three subpopulations of neurons that respond to incoming excitatory synaptic inputs. The generation of the membrane potentials in the somas of these neurons and the electric currents flowing in the neuropil are modeled by this component. The second and third components model the electrovascular coupling and the dynamics of vascular states in an extended balloon approach, respectively. In the first part we describe, in some detail, the biophysical model and establish its face validity using simulations of visually evoked responses under different flickering frequencies and luminous contrasts. In a second part, a recursive optimization algorithm is developed and used to make statistical inferences about this forward/generative model from actual data.

Timing in cognition and EEG brain dynamics: discreteness versus continuity

This article provides an overview of recent developments in solving the timing problem (discreteness vs. continuity) in cognitive neuroscience. Both theoretical and empirical studies have been considered, with an emphasis on the framework of operational architectonics (OA) of brain functioning (Fingelkurts and Fingelkurts in Brain Mind 2:291-29, 2001; Neurosci Biobehav Rev 28:827-836, 2005). This framework explores the temporal structure of information flow and interarea interactions within the network of functional neuronal populations by examining topographic sharp transition processes in the scalp EEG, on the millisecond scale. We conclude, based on the OA framework, that brain functioning is best conceptualized in terms of continuity-discreteness unity which is also the characteristic property of cognition. At the end we emphasize where one might productively proceed for the future research.

Initiation of sodium spikelets in basal dendrites of neocortical pyramidal neurons

Cortical information processing relies critically on the processing of electrical signals in pyramidal neurons. Electrical transients mainly arise when excitatory synaptic inputs impinge upon distal dendritic regions. To study the dendritic aspect of synaptic integration one must record electrical signals in distal dendrites. Since thin dendritic branches, such as oblique and basal dendrites, do not support routine glass electrode measurements, we turned our effort towards voltage-sensitive dye recordings. Using the optical imaging approach we found and reported previously that basal dendrites of neocortical pyramidal neurons show an elaborate repertoire of electrical signals, including backpropagating action potentials and glutamate-evoked plateau potentials. Here we report a novel form of electrical signal, qualitatively and quantitatively different from backpropagating action potentials and dendritic plateau potentials. Strong glutamatergic stimulation of an individual basal dendrite is capable of triggering a fast spike, which precedes the dendritic plateau potential. The amplitude of the fast initial spikelet was actually smaller that the amplitude of the backpropagating action potential in the same dendritic segment. Therefore, the fast initial spike was dubbed "spikelet". Both the basal spikelet and plateau potential propagate decrementally towards the cell body, where they are reflected in the somatic whole-cell recordings. The low incidence of basal spikelets in the somatic intracellular recordings and the impact of basal spikelets on soma-axon action potential initiation are discussed.

fMRI MODELS OF DENDRITIC AND ASTROCYTIC NETWORKS

In order to elucidate the relationships between hierarchical structures within the neocortical neuropil and the information carried by an ensemble of neurons encompassing a single voxel, it is essential to predict through volume conductor modeling LFPs representing average extracellular potentials, which are expressed in terms of interstitial potentials of individual cells in networks of gap-junctionally connected astrocytes and synaptically connected neurons. These relationships have been provided and can then be used to investigate how the underlying neuronal population activity can be inferred from the measurement of the BOLD signal through electrovascular coupling mechanisms across the blood-brain barrier. The importance of both synaptic and extrasynaptic transmission as the basis of electrophysiological indices triggering vascular responses between dendritic and astrocytic networks, and sequential configurations of firing patterns in composite neural networks is emphasized. The purpose of this review is to show how fMRI data may be used to draw conclusions about the information transmitted by individual neurons in populations generating the BOLD signal.

A DISCRETE APPROACH FOR A MODEL OF TEMPORAL LEARNING BY THE CEREBELLUM:IN SILICOCLASSICAL CONDITIONING OF THE EYEBLINK REFLEX

Cerebellar cortex is known to be involved in acquisition and expression of eyeblink conditioned reflex. These phenomena imply temporal intervals of learning. Several cellular and network mechanisms have been proposed to produce the eyeblink. In this paper we briefly review the main theories concerning temporal coding, and we propose an alternative way of producing and storing delays and signal sequences after supervised learning. A network of Leaky Integrate-and-Fire (LIF) neurons is built, taking into account several cerebellar features. This network is then trained to produce simple or multiple eyeblink delays using (i) the classical conditioning paradigm and (ii) known data on cerebellar spike timing dependent plasticity (STDP). The resulting model behaves like an adaptive temporal filter. It improves cell subpopulations effects according to their mean firing rate. This rate based selection allows robust supervised learning of temporal events (i.e., delayed signals) and gives the network ability to react with anticipation on the arousal of a noxious event.

On the mathematical integration of the nervous tissue based on the S-propagator formalism

The integration of physiological functions in living organisms corresponds to the reconstruction of a biological system from its components. This calls for a sound theoretical framework based on the rigorous definition of the elementary physiological function within the context of multiple levels of biological organization. One of the main problems encountered in the neurosciences is that of extending the current theory of automata, as used in the study of artificial neural networks, to real neural networks. The difficulty arises because the theory of automata fails to take into account the various levels of biological organization involved in nervous activity. This article recalls the main elements of G. A. Chauvet's novel n-level field theory, i.e., the properties of non-symmetry and non-locality of functional interactions, and the S-propagator formalism that governs the propagation of a functional interaction across the different levels of the structural organization of a biological system. The neural field equations derived from this theory allow the inclusion of multiple organizational levels of a biological system into the analysis by incorporating specific local models into a global non-local model. The main advantage of the method presented here is the simplification obtained by breaking down the physiological function into its components according to the time scales and space scales of operation. Moreover, the method takes into account the non-locality of the functional interaction, assuming it to be propagated at finite velocity in a continuous and hierarchical space. Finally, this approach allows the systematic study of physiological functions within a single theoretical framework, the complexity of which could be progressively increased by integrating specific local models as new findings become available.