Anisotropic connectivity and cooperative phenomena as a basis for orientation sensitivity in the visual cortex

A computer simulation model of the neural circuitry underlying orientation sensitivity in cortical neurons is examined. The model consists of a network of 3000 neurons divided into two functionally distinct cell types: excitatory (E-cells) and inhibitory (I-cells). We demonstrate that both orientation sensitivity and shape selectivity can be accounted for by making the following assumptions: 1) thalamic afferents to a sheet of cortical neurons are retionotopically organized; 2) thalamic afferents come from a single neuron, or at most a few neurons, in the lateral geniculate nucleus; 3) cortical activity is cooperative, i.e. largely dependent on intracortical connections, some of which have anisotropies along directions parallel to the pial surface. Anisotropies are specified only by the distribution of cells which are postsynaptic to a particular neuron, without specifying the axonal or dendritic contributions. In this paper, orientation sensitivity arises through cooperative interactions among neurons having anisotropic excitatory, and isotropic inhibitory connections.     

Inhibitory synchrony as a mechanism for attentional gain modulation

Recordings from area V4 of monkeys have revealed that when the focus of attention is on a visual stimulus within the receptive field of a cortical neuron, two distinct changes can occur: The firing rate of the neuron can change and there can be an increase in the coherence between spikes and the local field potential (LFP) in the gamma-frequency range (30-50 Hz). The hypothesis explored here is that these observed effects of attention could be a consequence of changes in the synchrony of local interneuron networks. We performed computer simulations of a Hodgkin-Huxley type neuron driven by a constant depolarizing current, I, representing visual stimulation and a modulatory inhibitory input representing the effects of attention via local interneuron networks. We observed that the neuron's firing rate and the coherence of its output spike train with the synaptic inputs was modulated by the degree of synchrony of the inhibitory inputs. When inhibitory synchrony increased, the coherence of spiking model neurons with the synaptic input increased, but the firing rate either increased or remained the same. The mean number of synchronous inhibitory inputs was a key determinant of the shape of the firing rate versus current (f-I) curves. For a large number of inhibitory inputs (approximately 50), the f-I curve saturated for large I and an increase in input synchrony resulted in a shift of sensitivity-the model neuron responded to weaker inputs I. For a small number (approximately 10), the f-I curves were non-saturating and an increase in input synchrony led to an increase in the gain of the response-the firing rate in response to the same input was multiplied by an approximately constant factor. The firing rate modulation with inhibitory synchrony was highest when the input network oscillated in the gamma frequency range. Thus, the observed changes in firing rate and coherence of neurons in the visual cortex could be controlled by top-down inputs that regulated the coherence in the activity of a local inhibitory network discharging at gamma frequencies.     

The significance of action potential bursting in the brain reward circuit

The brain reward circuit consists of specialized cortical and subcortical structural components that code for various cognitive aspects of goal-directed behavior. These components include the prefrontal cortex (PFC), amygdala (AMY), nucleus accumbens (Nac), subiculum (SUB) of the hippocampal formation, and the dopamine (DA) neurons in the ventral tegmental area (VTA). Both serial and parallel processing in the different components of the circuit code the various aspects of reward-related behavior. Individual neurons within each component have developed specialized intrinsic membrane properties that have led them to be typically defined as either single spiking or high frequency burst-firing neurons. However, a strict definition based on the output mode may not be appropriate. Under the right conditions, neurons can switch between bursting and single-spiking modes, therefore providing a conditional output state. The preferred mode of each individual neuron depends on a combination of different plastic neuronal properties such as, dendritic architecture, neuromodulation, intracellular calcium (Ca(++)) buffering, excitatory and inhibitory synaptic strength, and the spatial distribution and density of voltage and ligand-gated channels. It is likely that, in vivo, most neurons in the circuit, despite variations in intrinsic membrane properties, are conditional output neurons equipped with the versatility of switching between output modes under appropriate conditions. Bursting mode may be used to boost the gain of neural signaling of important or novel events by enhancing transmitter release and enhancing dendritic depolarization, thereby increasing synaptic potentiation. Conversely, single spiking mode may be used to dampen neuronal signaling and may be associated with habituation to unimportant events. Mode switching may provide flexibility to the circuit allowing different sets of neurons to conditionally code for the various aspects of reward-related memory and behavior.     

The response of cortical neurons to in vivo-like input current: theory and experiment: II. Time-varying and spatially distributed inputs

The response of a population of neurons to time-varying synaptic inputs can show a rich phenomenology, hardly predictable from the dynamical properties of the membrane’s inherent time constants. For example, a network of neurons in a state of spontaneous activity can respond significantly more rapidly than each single neuron taken individually. Under the assumption that the statistics of the synaptic input is the same for a population of similarly behaving neurons (mean field approximation), it is possible to greatly simplify the study of neural circuits, both in the case in which the statistics of the input are stationary (reviewed in La Camera et al. in Biol Cybern, 2008) and in the case in which they are time varying and unevenly distributed over the dendritic tree. Here, we review theoretical and experimental results on the single-neuron properties that are relevant for the dynamical collective behavior of a population of neurons. We focus on the response of integrate-and-fire neurons and real cortical neurons to long-lasting, noisy, in vivo-like stationary inputs and show how the theory can predict the observed rhythmic activity of cultures of neurons. We then show how cortical neurons adapt on multiple time scales in response to input with stationary statistics in vitro. Next, we review how it is possible to study the general response properties of a neural circuit to time-varying inputs by estimating the response of single neurons to noisy sinusoidal currents. Finally, we address the dendrite–soma interactions in cortical neurons leading to gain modulation and spike bursts, and show how these effects can be captured by a two-compartment integrate-and-fire neuron. Most of the experimental results reviewed in this article have been successfully reproduced by simple integrate-and-fire model neurons.     

New attractor states for synchronous activity in synfire chains with excitatory and inhibitory coupling

 In a feedforward network of integrate-and-fire neurons, where the firing of each layer is synchronous (synfire chain), the final firing state of the network converges to two attractor states: either a full activation or complete fading of the tailing layers. In this article, we analyze various modes of pattern propagation in a synfire chain with random connection weights and delta-type postsynaptic currents. We predict analytically that when the input is fully synchronized and the network is noise free, varying the characteristics of the weights distribution would result in modes of behavior that are different from those described in the literature. These are convergence to fixed points, limit cycles, multiple periodic, and possibly chaotic dynamics. We checked our analytic results by computer simulation of the network, and showed that the above results can be generalized when the input is asynchronous and neurons are spontaneously active at low rates. Received: 27 July 2001 / Accepted in revised form: 23 October 2001     

Dynamical features of higher-order correlation events: impact on cortical cells

Cortical neurons receive signals from thousands of other neurons. The statistical properties of the input spike trains substantially shape the output response properties of each neuron. Experimental and theoretical investigations have mostly focused on the second order statistical features of the input spike trains (mean firing rates and pairwise correlations). Little is known of how higher order correlations affect the integration and firing behavior of a cell independently of the second order statistics. To address this issue, we simulated the dynamics of a population of 5000 neurons, controlling both their second order and higher-order correlation properties to reflect physiological data. We then used these ensemble dynamics as the input stage to morphologically reconstructed cortical cells (layer 5 pyramidal, layer 4 spiny stellate cell), and to an integrate and fire neuron. Our results show that changes done solely to the higher-order correlation properties of the network’s dynamics significantly affect the response properties of a target neuron, both in terms of output rate and spike timing. Moreover, the neuronal morphology and voltage dependent mechanisms of the target neuron considerably modulate the quantitative aspects of these effects. Finally, we show how these results affect sparseness of neuronal representations, tuning properties, and feature selectivity of cortical cells. An erratum to this article can be found at     

Spike generating dynamics and the conditions for spike-time precision in cortical neurons

Temporal precision of spiking response in cortical neurons has been a subject of intense debate. Using a canonical model of spike generation, we explore the conditions for precise and reliable spike timing in the presence of Gaussian white noise. In agreement with previous results we find that constant stimuli lead to imprecise timing, while aperiodic stimuli yield precise spike timing. Under constant stimulus the neuron is a noise perturbed oscillator, the spike times follow renewal statistics and are imprecise. Under an aperiodic stimulus sequence, the neuron acts as a threshold element; the firing times are precisely determined by the dynamics of the stimulus. We further study the dependence of spike-time precision on the input stimulus frequency and find a non-linear tuning whose width can be related to the locking modes of the neuron. We conclude that viewing the neuron as a non-linear oscillator is the key for understanding spike-time precision.     

A complex-valued associative memory for storing patterns as oscillatory states

A neuron model in which the neuron state is described by a complex number is proposed. A network of these neurons, which can be used as an associative memory, operates in two distinct modes: (i) fixed point mode and (ii) oscillatory mode. Mode selection can be done by varying a continuous mode parameter, , between and . At one extreme value of (), the network has conservative dynamics, and at the other (), the dynamics are dissipative and governed by a Lyapunov function. Patterns can be stored and retrieved at any value of by, (i) a one-step outer product rule or (ii) adaptive Hebbian learning. In the fixed point mode patterns are stored as fixed points, whereas in the oscillatory mode they are encoded as phase relations among individual oscillations. By virtue of an instability in the oscillatory mode, the retrieval pattern is stable over a finite interval, the stability interval, and the pattern gradually deteriorates with time beyond this interval. However, at certain values of sparsely distributed over -space the instability disappears. The neurophysiological significance of the instability is briefly discussed. The possibility of physically interpreting dissipativity and conservativity is explored by noting that while conservativity leads to energy savings, dissipativity leads to stability and reliable retrieval. Received: 4 December 1995 / Accepted in revised form: 18 June 1996     

Encoding of spatio-temporal input characteristics by a CA1 pyramidal neuron model

The in vivo activity of CA1 pyramidal neurons alternates between regular spiking and bursting, but how these changes affect information processing remains unclear. Using a detailed CA1 pyramidal neuron model, we investigate how timing and spatial arrangement variations in synaptic inputs to the distal and proximal dendritic layers influence the information content of model responses. We find that the temporal delay between activation of the two layers acts as a switch between excitability modes: short delays induce bursting while long delays decrease firing. For long delays, the average firing frequency of the model response discriminates spatially clustered from diffused inputs to the distal dendritic tree. For short delays, the onset latency and inter-spike-interval succession of model responses can accurately classify input signals as temporally close or distant and spatially clustered or diffused across different stimulation protocols. These findings suggest that a CA1 pyramidal neuron may be capable of encoding and transmitting presynaptic spatiotemporal information about the activity of the entorhinal cortex-hippocampal network to higher brain regions via the selective use of either a temporal or a rate code.     

Emergence of network structure due to spike-timing-dependent plasticity in recurrent neuronal networks. II. Input selectivity—symmetry breaking

Spike-timing-dependent plasticity (STDP) is believed to structure neuronal networks by slowly changing the strengths (or weights) of the synaptic connections between neurons depending upon their spiking activity, which in turn modifies the neuronal firing dynamics. In this paper, we investigate the change in synaptic weights induced by STDP in a recurrently connected network in which the input weights are plastic but the recurrent weights are fixed. The inputs are divided into two pools with identical constant firing rates and equal within-pool spike-time correlations, but with no between-pool correlations. Our analysis uses the Poisson neuron model in order to predict the evolution of the input synaptic weights and focuses on the asymptotic weight distribution that emerges due to STDP. The learning dynamics induces a symmetry breaking for the individual neurons, namely for sufficiently strong within-pool spike-time correlation each neuron specializes to one of the input pools. We show that the presence of fixed excitatory recurrent connections between neurons induces a group symmetry-breaking effect, in which neurons tend to specialize to the same input pool. Consequently STDP generates a functional structure on the input connections of the network.     

Effects of Neural Morphology and Input Distribution on Synaptic Processing by Global and Focal NMDA-Spikes

Cortical neurons can respond to glutamatergic stimulation with regenerative N-Methyl-D-aspartic acid (NMDA)-spikes. NMDA-spikes were initially thought to depend on clustered synaptic activation. Recent work had shown however a new variety of a global NMDA-spike, which can be generated by randomly distributed inputs. Very little is known about the factors that influence the generation of these global NMDA-spikes, as well the potentially distinct rules of synaptic integration and the computational significance conferred by the two types of NMDA-spikes. Here I show that the input resistance (R_IN) plays a major role in influencing spike initiation; while the classical, focal NMDA-spike depended upon the local (dendritic) R_IN, the threshold of global NMDA-spike generation was set by the somatic R_IN. As cellular morphology can exert a large influence on R_IN, morphologically distinct neuron types can have dissimilar rules for NMDA-spikes generation. For example, cortical neurons in superficial layers were found to be generally prone to global NMDA-spike generation. In contrast, electric properties of cortical layer 5b cells clearly favor focal NMDA-spikes. These differences can translate into diverse synaptic integration rules for the different classes of cortical cells; simulated superficial layers neurons were found to exhibit strong synaptic interactions between different dendritic branches, giving rise to a single integrative compartment mediated by the global NMDA-spike. In these cells, efficiency of postsynaptic activation was relatively little dependent on synaptic distribution. By contrast, layer 5b neurons were capable of true multi-unit computation involving independent integrative compartments formed by clustered synaptic input which could trigger focal NMDA-spikes. In a sharp contrast to superficial layers neurons, randomly distributed synaptic inputs were not very effective in driving firing the layer 5b cells, indicating a possibility for different computation performed by these important cortical neurons.     

Mammalian Target of Rapamycin Complex 1 (mTORC1) and 2 (mTORC2) Control the Dendritic Arbor Morphology of Hippocampal Neurons

Dendrites are the main site of information input into neurons. Their development is a multistep process controlled by mammalian target of rapamycin (mTOR) among other proteins. mTOR is a serine/threonine protein kinase that forms two functionally distinct complexes in mammalian cells: mTORC1 and mTORC2. However, the one that contributes to mammalian neuron development remains unknown. This work used short hairpin RNA against Raptor and Rictor, unique components of mTORC1 and mTORC2, respectively, to dissect mTORC involvement in this process. We provide evidence that both mTOR complexes are crucial for the proper dendritic arbor morphology of hippocampal neurons. These two complexes are required for dendritic development both under basal conditions and upon the induction of mTOR-dependent dendritic growth. We also identified Akt as a downstream effector of mTORC2 needed for proper dendritic arbor morphology, the action of which required mTORC1 and p70S6K1.     

A cooperative switch determines the sign of synaptic plasticity in distal dendrites of neocortical pyramidal neurons

Pyramidal neurons in the cerebral cortex span multiple cortical layers. How the excitable properties of pyramidal neuron dendrites allow these neurons to both integrate activity and store associations between different layers is not well understood, but is thought to rely in part on dendritic backpropagation of action potentials. Here we demonstrate that the sign of synaptic plasticity in neocortical pyramidal neurons is regulated by the spread of the backpropagating action potential to the synapse. This creates a progressive gradient between LTP and LTD as the distance of the synaptic contacts from the soma increases. At distal synapses, cooperative synaptic input or dendritic depolarization can switch plasticity between LTD and LTP by boosting backpropagation of action potentials. This activity-dependent switch provides a mechanism for associative learning across different neocortical layers that process distinct types of information.     

Firing-rate models for neurons with a broad repertoire of spiking behaviors

Capturing the response behavior of spiking neuron models with rate-based models facilitates the investigation of neuronal networks using powerful methods for rate-based network dynamics. To this end, we investigate the responses of two widely used neuron model types, the Izhikevich and augmented multi-adapative threshold (AMAT) models, to a range of spiking inputs ranging from step responses to natural spike data. We find (i) that linear-nonlinear firing rate models fitted to test data can be used to describe the firing-rate responses of AMAT and Izhikevich spiking neuron models in many cases; (ii) that firing-rate responses are generally too complex to be captured by first-order low-pass filters but require bandpass filters instead; (iii) that linear-nonlinear models capture the response of AMAT models better than of Izhikevich models; (iv) that the wide range of response types evoked by current-injection experiments collapses to few response types when neurons are driven by stationary or sinusoidally modulated Poisson input; and (v) that AMAT and Izhikevich models show different responses to spike input despite identical responses to current injections. Together, these findings suggest that rate-based models of network dynamics may capture a wider range of neuronal response properties by incorporating second-order bandpass filters fitted to responses of spiking model neurons. These models may contribute to bringing rate-based network modeling closer to the reality of biological neuronal networks.     

The resonance frequency shift, pattern formation, and dynamical network reorganization via sub-threshold input

We describe a novel mechanism that mediates the rapid and selective pattern formation of neuronal network activity in response to changing correlations of sub-threshold level input. The mechanism is based on the classical resonance and experimentally observed phenomena that the resonance frequency of a neuron shifts as a function of membrane depolarization. As the neurons receive varying sub-threshold input, their natural frequency is shifted in and out of its resonance range. In response, the neuron fires a sequence of action potentials, corresponding to the specific values of signal currents, in a highly organized manner. We show that this mechanism provides for the selective activation and phase locking of the cells in the network, underlying input-correlated spatio-temporal pattern formation, and could be the basis for reliable spike-timing dependent plasticity. We compare the selectivity and efficiency of this pattern formation to a supra-threshold network activation and a non-resonating network/neuron model to demonstrate that the resonance mechanism is the most effective. Finally we show that this process might be the basis of the phase precession phenomenon observed during firing of hippocampal place cells, and that it may underlie the active switching of neuronal networks to locking at various frequencies.     

The Possible Role of Spike Patterns in Cortical Information Processing

When the same visual stimulus is presented across many trials, neurons in the visual cortex receive stimulus-related synaptic inputs that are reproducible across trials (S) and inputs that are not (N). The variability of spike trains recorded in the visual cortex and their apparent lack of spike-to-spike correlations beyond that implied by firing rate fluctuations, has been taken as evidence for a low S/N ratio. A recent re-analysis of in vivo cortical data revealed evidence for spike-to-spike correlations in the form of spike patterns. We examine neural dynamics at a higher S/N in order to determine what possible role spike patterns could play in cortical information processing. In vivo-like spike patterns were obtained in model simulations. Superpositions of multiple sinusoidal driving currents were especially effective in producing stable long-lasting patterns. By applying current pulses that were either short and strong or long and weak, neurons could be made to switch from one pattern to another. Cortical neurons with similar stimulus preferences are located near each other, have similar biophysical properties and receive a large number of common synaptic inputs. Hence, recordings of a single neuron across multiple trials are usually interpreted as the response of an ensemble of these neurons during one trial. In the presence of distinct spike patterns across trials there is ambiguity in what would be the corresponding ensemble, it could consist of the same spike pattern for each neuron or a set of patterns across neurons. We found that the spiking response of a neuron receiving these ensemble inputs was determined by the spike-pattern composition, which, in turn, could be modulated dynamically as a means for cortical information processing.     

Scaling properties of pyramidal neurons in mice neocortex

Dendritic morphology is the structural correlate for receiving and processing inputs to a neuron. An interesting question then is what the design principles and the functional consequences of enlarged or shrinked dendritic trees might be. As yet, only a few studies have examined the effects of neuron size changes. Two theoretical scaling modes have been analyzed, conservative (isoelectrotonic) scaling (preserves the passive and active response properties) and isometric scaling (steps up low pass-filtering of inputs). It has been suggested that both scaling modes were verified in neuroanatomical studies. To overcome obvious limitations of these studies like small size of analyzed samples and restricted validity of utilized scaling measures, we considered the scaling problem of neurons on the basis of large sample data and by employing a more general method of scaling analysis. This method consists in computing the morphoelectrotonic transform (MET) of neurons. The MET maps the neuron from anatomical space into electrotonic space using the logarithm of voltage attenuation as the distance metric. The theory underlying this approach is described and then applied to two samples of morphologically reconstructed pyramidal neurons (cells from neocortex of wildtype and synRas transgenic mice) using the NEURON simulator. In a previous study, we could verify a striking increase of dendritic tree size in synRas pyramidal neurons. Surprisingly, in this study the statistical analysis of the sample MET dendrograms revealed that the electrotonic architecture of these neurons scaled roughly in a MET-conserving mode. In conclusion, our results suggest only a minor impact of the Ras protein on dendritic electroanatomy, with non-significant changes of most regions of the corresponding METs.     

Intrinsic Neuronal Properties Switch the Mode of Information Transmission in Networks

Diverse ion channels and their dynamics endow single neurons with complex biophysical properties. These properties determine the heterogeneity of cell types that make up the brain, as constituents of neural circuits tuned to perform highly specific computations. How do biophysical properties of single neurons impact network function? We study a set of biophysical properties that emerge in cortical neurons during the first week of development, eventually allowing these neurons to adaptively scale the gain of their response to the amplitude of the fluctuations they encounter. During the same time period, these same neurons participate in large-scale waves of spontaneously generated electrical activity. We investigate the potential role of experimentally observed changes in intrinsic neuronal properties in determining the ability of cortical networks to propagate waves of activity. We show that such changes can strongly affect the ability of multi-layered feedforward networks to represent and transmit information on multiple timescales. With properties modeled on those observed at early stages of development, neurons are relatively insensitive to rapid fluctuations and tend to fire synchronously in response to wave-like events of large amplitude. Following developmental changes in voltage-dependent conductances, these same neurons become efficient encoders of fast input fluctuations over few layers, but lose the ability to transmit slower, population-wide input variations across many layers. Depending on the neurons'' intrinsic properties, noise plays different roles in modulating neuronal input-output curves, which can dramatically impact network transmission. The developmental change in intrinsic properties supports a transformation of a networks function from the propagation of network-wide information to one in which computations are scaled to local activity. This work underscores the significance of simple changes in conductance parameters in governing how neurons represent and propagate information, and suggests a role for background synaptic noise in switching the mode of information transmission.     

Multiple origins of the cortical γ rhythm

Gamma rhythms (30-80 Hz) are a near-ubiquitous feature of neuronal population activity in mammalian cortices. Their dynamic properties permit the synchronization of neuronal responses to sensory input within spatially distributed networks, transient formation of local neuronal "cell assemblies," and coherent response patterns essential for intercortical regional communication. Each of these phenomena form part of a working hypothesis for cognitive function in cortex. All forms of physiological gamma rhythm are inhibition based, being characterized by rhythmic trains of inhibitory postsynaptic potentials in populations of principal neurons. It is these repeating periods of relative enhancement and attenuation of the responsivity of major cell groups in cortex that provides a temporal structure shared across many millions of neurons. However, when considering the origins of these repeating trains of inhibitory events considerable divergence is seen depending on cortical region studied and mode of activation of gamma rhythm generating networks. Here, we review the evidence for involvement of multiple subtypes of interneuron and focus on different modes of activation of these cells. We conclude that most massively parallel brain regions have different mechanisms of gamma rhythm generation, that different mechanisms have distinct functional correlates, and that switching between different local modes of gamma generation may be an effective way to direct cortical communication streams. Finally, we suggest that developmental disruption of the endophenotype for certain subsets of gamma-generating interneuron may underlie cognitive deficit in psychiatric illness.     

Emergence of network structure due to spike-timing-dependent plasticity in recurrent neuronal networks. I. Input selectivity–strengthening correlated input pathways

Spike-timing-dependent plasticity (STDP) determines the evolution of the synaptic weights according to their pre- and post-synaptic activity, which in turn changes the neuronal activity. In this paper, we extend previous studies of input selectivity induced by (STDP) for single neurons to the biologically interesting case of a neuronal network with fixed recurrent connections and plastic connections from external pools of input neurons. We use a theoretical framework based on the Poisson neuron model to analytically describe the network dynamics (firing rates and spike-time correlations) and thus the evolution of the synaptic weights. This framework incorporates the time course of the post-synaptic potentials and synaptic delays. Our analysis focuses on the asymptotic states of a network stimulated by two homogeneous pools of “steady” inputs, namely Poisson spike trains which have fixed firing rates and spike-time correlations. The (STDP) model extends rate-based learning in that it can implement, at the same time, both a stabilization of the individual neuron firing rates and a slower weight specialization depending on the input spike-time correlations. When one input pathway has stronger within-pool correlations, the resulting synaptic dynamics induced by (STDP) are shown to be similar to those arising in the case of a purely feed-forward network: the weights from the more correlated inputs are potentiated at the expense of the remaining input connections.