NMDA-based pattern discrimination in a modeled cortical neuron

Compartmental simulations of an anatomically characterized cortical pyramidal cell were carried out to study the integrative behavior of a complex dendritic tree. Previous theoretical (Feldman and Ballard 1982; Durbin and Rumelhart 1989; Mel 1990; Mel and Koch 1990; Poggio and Girosi 1990) and compartmental modeling (Koch et al. 1983; Shepherd et al. 1985; Koch and Poggio 1987; Rall and Segev 1987; Shepherd and Brayton 1987; Shepherd et al. 1989; Brown et al. 1991) work had suggested that multiplicative interactions among groups of neighboring synapses could greatly enhance the processing power of a neuron relative to a unit with only a single global firing threshold. This issue was investigated here, with a particular focus on the role of voltage-dependent N-methyl-D-asparate (NMDA) channels in the generation of cell responses. First, it was found that when a large proportion of the excitatory synaptic input to dendritic spines is carried by NMDA channels, the pyramidal cell responds preferentially to spatially clustered, rather than random, distributions of activated synapses. Second, based on this mechanism, the NMDA-rich neuron is shown to be capable of solving a nonlinear pattern discrimination task. We propose that manipulation of the spatial ordering of afferent synaptic connections onto the dendritic arbor is a possible biological strategy for pattern information storage during learning

A perspective on cortical layering and layer-spanning neuronal elements

This review article addresses the function of the layers of the cerebral cortex. We develop the perspective that cortical layering needs to be understood in terms of its functional anatomy, i.e., the terminations of synaptic inputs on distinct cellular compartments and their effect on cortical activity. The cortex is a hierarchical structure in which feed forward and feedback pathways have a layer-specific termination pattern. We take the view that the influence of synaptic inputs arriving at different cortical layers can only be understood in terms of their complex interaction with cellular biophysics and the subsequent computation that occurs at the cellular level. We use high-resolution fMRI, which can resolve activity across layers, as a case study for implementing this approach by describing how cognitive events arising from the laminar distribution of inputs can be interpreted by taking into account the properties of neurons that span different layers. This perspective is based on recent advances in measuring subcellular activity in distinct feed-forward and feedback axons and in dendrites as they span across layers

VC Dimension of an Integrate-and-Fire Neuron Model

We find the VC dimension of a leaky integrate-and-fire neuron model. The VC dimension quantifies the ability of a function class to partition an input pattern space, and can be considered a measure of computational capacity. In this case, the function class is the class of integrate-and-fire models generated by varying the integration time constant τ and the threshold ϴ, the input space they partition is the space of continuous-time signals, and the binary partition is specified by whether or not the model reaches threshold and spikes at some specified time. We show that the VC dimension diverges only logarithmically with the input signal bandwidth N , where the signal bandwidth is determined by the noise inherent in the process of spike generation. For reasonable estimates of the signal bandwidth, the VC dimension turns out to be quite small (¡10). We also extend this approach to ar- bitrary passive dendritic trees. The main contributions of this work are (1) it offers a novel treatment of the computational capacity of this class of dynamic system; and (2) it provides a framework for analyzing the computational capabilities of the dynamical systems defined by networks of spiking neurons

Spike-timing control by dendritic plateau potentials in the presence of synaptic barrages

Apical and tuft dendrites of pyramidal neurons support regenerative electrical potentials, giving rise to long-lasting (approximately hundreds of milliseconds) and strong (~50 mV from rest) depolarizations. Such plateau events rely on clustered glutamatergic input, can be mediated by calcium or by NMDA currents, and often generate somatic depolarizations that last for the time course of the dendritic plateau event. We address the computational significance of such single-neuron processing via reduced but biophysically realistic modeling. We introduce a model based on two discrete integration zones, a somatic and a dendritic one, that communicate from the dendritic to the somatic compartment via a long plateau-conductance. We show principled differences in the way dendritic vs. somatic inhibition controls spike timing, and demonstrate how this could implement a mechanism of spike time control in the face of barrages of synaptic inputs

Traveling waves in the Baer and Rinzel model of spine studded dendritic tissue

The Baer and Rinzel model of dendritic spines uniformly distributed along a dendritic cable is shown to admit a variety of regular traveling wave solutions including solitary pulses, multiple pulses and periodic waves. We investigate numerically the speed of these waves and their propagation failure as functions of the system parameters by numerical continuation. Multiple pulse waves are shown to occur close to the primary pulse, except in certain exceptional regions of parameter space, which we identify. The propagation failure of solitary and multiple pulse waves is shown to be associated with the destruction of a saddle-node bifurcation of periodic orbits. The system also supports many types of irregular wave trains. These include waves which may be regarded as connections to periodics and bursting patterns in which pulses can cluster together in well-defined packets. The behavior and properties of both these irregular spike-trains is explained within a kinematic framework that is based on the times of wave pulses. The dispersion curve for periodic waves is important for such a description and is obtained in a straightforward manner using the numerical scheme developed for the study of the speed of a periodic wave. Stability of periodic waves within the kinematic theory is given in terms of the derivative of the dispersion curve and provides a weak form of stability that may be applied to solutions of the traveling wave equations. The kinematic theory correctly predicts the conditions for period doubling bifurcations and the generation of bursting states. Moreover, it also accurately describes the shape and speed of the traveling front that connects waves with two different periods

Statistical physics of neural systems with non-additive dendritic coupling

How neurons process their inputs crucially determines the dynamics of biological and artificial neural networks. In such neural and neural-like systems, synaptic input is typically considered to be merely transmitted linearly or sublinearly by the dendritic compartments. Yet, single-neuron experiments report pronounced supralinear dendritic summation of sufficiently synchronous and spatially close-by inputs. Here, we provide a statistical physics approach to study the impact of such non-additive dendritic processing on single neuron responses and the performance of associative memory tasks in artificial neural networks. First, we compute the effect of random input to a neuron incorporating nonlinear dendrites. This approach is independent of the details of the neuronal dynamics. Second, we use those results to study the impact of dendritic nonlinearities on the network dynamics in a paradigmatic model for associative memory, both numerically and analytically. We find that dendritic nonlinearities maintain network convergence and increase the robustness of memory performance against noise. Interestingly, an intermediate number of dendritic branches is optimal for memory functionality

Solitary waves in a model of dendritic cable with active spines

We consider a continuum model of dendritic spines with active membrane dynamics uniformly distributed along a passive dendritic cable. Byconsidering a systematic reduction of the Hodgkin-Huxleydy namics that is valid on all but very short time-scales we derive 2 dimensional and 1 dimensional systems for excitable tissue, both of which may be used to model the active processes in spine-heads. In the first case the coupling of the spine head dynamics to a passive dendritic cable via a direct electrical connection yields a model that may be regarded as a simplification of the Baer and Rinzel cable theory of excitable spinynerv e tissue [3]. This model is computationally simple with few free parameters. Importantly, as in the full model, numerical simulation illustrates the possibilityof a traveling wave. We present a systematic numerical investigation of the speed and stability of the wave as a function of physiologically important parameters. A further reduction of this model suggests that active spine-head dynamics mayb e modeled byan all or none type process which we take to be of the integrate-and-fire (IF) type. The model is analytically tractable allowing the explicit construction of the shape of traveling waves as well as the calculation of wave speed as a function of system parameters. In general a slow and fast wave are found to co-exist. The behavior of the fast wave is found to closely reproduce the behavior of the wave seen in simulations of the more detailed model. Importantly a linear stability theory is presented showing that it is the faster of the two solutions that is stable. Beyond a critical value the speed of the stable wave is found to decrease as a function of spine density. Moreover, the speed of this wave is found to decrease as a function of the strength of the electrical resistor coupling the spine-head and the cable, such that beyond some critical value there is propagation failure. Finally we discuss the importance of a model of passive electrical cable coupled to a system of integrate-and-fire units for physiological studies of branching dendritic tissue with active spines

Dendritic NMDA receptors in parvalbumin neurons enable strong and stable neuronal assemblies

Parvalbumin-expressing (PV+) GABAergic interneurons mediate feedforward and feedback inhibition and have a key role in gamma oscillations and information processing. The importance of fast synaptic recruitment, action potential initiation and repolarization, and rapid synchronous GABA release by PV+ cells is well established. In contrast, the functional significance of PV+ cell NMDA receptors (NMDARs), which generate relatively slow postsynaptic currents, is unclear. Underlining their importance, several studies implicate PV+ cell NMDAR disruption in impaired network function and circuit pathologies. Here, we show that dendritic NMDARs underlie supralinear integration of feedback excitation from local pyramidal neurons onto mouse CA1 PV+ cells. Furthermore, by incorporating NMDARs at feedback connections onto PV+ cells in spiking networks, we show that these receptors enable cooperative recruitment of PV+ interneurons, strengthening and stabilising principal cell assemblies. Failure of this phenomenon provides a parsimonious explanation for cognitive and sensory gating deficits in pathologies with impaired PV+ NMDAR signalling

The Microcircuit Concept Applied to Cortical Evolution: from Three-Layer to Six-Layer Cortex

Understanding the principles of organization of the cerebral cortex requires insight into its evolutionary history. This has traditionally been the province of anatomists, but evidence regarding the microcircuit organization of different cortical areas is providing new approaches to this problem. Here we use the microcircuit concept to focus first on the principles of microcircuit organization of three-layer cortex in the olfactory cortex, hippocampus, and turtle general cortex, and compare it with six-layer neocortex. From this perspective it is possible to identify basic circuit elements for recurrent excitation and lateral inhibition that are common across all the cortical regions. Special properties of the apical dendrites of pyramidal cells are reviewed that reflect the specific adaptations that characterize the functional operations in the different regions. These principles of microcircuit function provide a new approach to understanding the expanded functional capabilities elaborated by the evolution of the neocortex