A model of cortically induced synchronization in the lateral geniculate nucleus of the cat: a role for low-threshold calcium channels

Firing-rate based network modeling of the dLGN circuit: Effects of cortical feedback on spatiotemporal response properties of relay cells

Visually evoked signals in the retina pass through the dorsal geniculate nucleus (dLGN) on the way to the visual cortex. This is however not a simple feedforward flow of information: there is a significant feedback from cortical cells back to both relay cells and interneurons in the dLGN. Despite four decades of experimental and theoretical studies, the functional role of this feedback is still debated. Here we use a firing-rate model, the extended difference-of-Gaussians (eDOG) model, to explore cortical feedback effects on visual responses of dLGN relay cells. For this model the responses are found by direct evaluation of two- or three-dimensional integrals allowing for fast and comprehensive studies of putative effects of different candidate organizations of the cortical feedback. Our analysis identifies a special mixed configuration of excitatory and inhibitory cortical feedback which seems to best account for available experimental data. This configuration consists of (i) a slow (long-delay) and spatially widespread inhibitory feedback, combined with (ii) a fast (short-delayed) and spatially narrow excitatory feedback, where (iii) the excitatory/inhibitory ON-ON connections are accompanied respectively by inhibitory/excitatory OFF-ON connections, i.e. following a phase-reversed arrangement. The recent development of optogenetic and pharmacogenetic methods has provided new tools for more precise manipulation and investigation of the thalamocortical circuit, in particular for mice. Such data will expectedly allow the eDOG model to be better constrained by data from specific animal model systems than has been possible until now for cat. We have therefore made the Python tool pyLGN which allows for easy adaptation of the eDOG model to new situations.

On route from the retina to primary visual cortex, visually evoked signals have to pass through the dorsal lateral geniculate nucleus (dLGN). However, this is not an exclusive feedforward flow of information as feedback exists from neurons in the cortex back to both relay cells and interneurons in the dLGN. The functional role of this feedback remains mostly unresolved. Here, we use a firing-rate model, the extended difference-of-Gaussians (eDOG) model, to explore cortical feedback effects on visual responses of dLGN relay cells. Our analysis indicates that a particular mix of excitatory and inhibitory cortical feedback agrees best with available experimental observations. In this configuration ON-center relay cells receive both excitatory and (indirect) inhibitory feedback from ON-center cortical cells (ON-ON feedback) where the excitatory feedback is fast and spatially narrow while the inhibitory feedback is slow and spatially widespread. In addition to the ON-ON feedback, the connections are accompanied by OFF-ON connections following a so-called phase-reversed (push-pull) arrangement. To facilitate further applications of the model, we have made the Python tool pyLGN which allows for easy modification and evaluation of the a priori quite general eDOG model to new situations.

Biophysical network modeling of the dLGN circuit: Effects of cortical feedback on spatial response properties of relay cells

Despite half-a-century of research since the seminal work of Hubel and Wiesel, the role of the dorsal lateral geniculate nucleus (dLGN) in shaping the visual signals is not properly understood. Placed on route from retina to primary visual cortex in the early visual pathway, a striking feature of the dLGN circuit is that both the relay cells (RCs) and interneurons (INs) not only receive feedforward input from retinal ganglion cells, but also a prominent feedback from cells in layer 6 of visual cortex. This feedback has been proposed to affect synchronicity and other temporal properties of the RC firing. It has also been seen to affect spatial properties such as the center-surround antagonism of thalamic receptive fields, i.e., the suppression of the response to very large stimuli compared to smaller, more optimal stimuli. Here we explore the spatial effects of cortical feedback on the RC response by means of a a comprehensive network model with biophysically detailed, single-compartment and multicompartment neuron models of RCs, INs and a population of orientation-selective layer 6 simple cells, consisting of pyramidal cells (PY). We have considered two different arrangements of synaptic feedback from the ON and OFF zones in the visual cortex to the dLGN: phase-reversed (‘push-pull’) and phase-matched (‘push-push’), as well as different spatial extents of the corticothalamic projection pattern. Our simulation results support that a phase-reversed arrangement provides a more effective way for cortical feedback to provide the increased center-surround antagonism seen in experiments both for flashing spots and, even more prominently, for patch gratings. This implies that ON-center RCs receive direct excitation from OFF-dominated cortical cells and indirect inhibitory feedback from ON-dominated cortical cells. The increased center-surround antagonism in the model is accompanied by spatial focusing, i.e., the maximum RC response occurs for smaller stimuli when feedback is present.

The functional role of the dorsal lateral geniculate nucleus (dLGN), placed on route from retina to primary visual cortex in the early visual pathway, is still poorly understood. A striking feature of the dLGN circuit is that dLGN cells not only receive feedforward input from the retina, but also a prominent feedback from cells in the visual cortex. It has been seen in experiments that cortical feedback modifies the spatial properties of dLGN cells in response to visual stimuli. In particular, it has been shown to increase the center-surround antagonism for flashing-spot and patch-grating visual stimuli, i.e., the suppression of responses to very large stimuli compared to smaller stimuli. Here we investigate the putative mechanisms behind this feature by means of a comprehensive network model of biophysically detailed neuron models for RCs and INs in the dLGN and orientation-selective cortical cells providing the feedback. Our results support that the experimentally observed feedback effects may be due to a phase-reversed (‘push-pull’) arrangement of the cortical feedback where ON-symmetry RCs receive (indirect) inhibitory feedback from ON-dominated cortical cell and excitation from OFF-dominated cortical cells, and vice versa for OFF-symmetry RCs.

Extended difference-of-Gaussians model incorporating cortical feedback for relay cells in the lateral geniculate nucleus of cat

A striking feature of the organization of the early visual pathway is the significant feedback from primary visual cortex to cells in the dorsal lateral geniculate nucleus (LGN). Despite numerous experimental and modeling studies, the functional role for this feedback remains elusive. We present a new firing-rate-based model for LGN relay cells in cat, explicitly accounting for thalamocortical loop effects. The established DOG model, here assumed to account for the spatial aspects of the feedforward processing of visual stimuli, is extended to incorporate the influence of thalamocortical loops including a full set of orientation-selective cortical cell populations. Assuming a phase-reversed push-pull arrangement of ON and OFF cortical feedback as seen experimentally, this extended DOG (eDOG) model exhibits linear firing properties despite non-linear firing characteristics of the corticothalamic cells. The spatiotemporal receptive field of the eDOG model has a simple algebraic structure in Fourier space, while the real-space receptive field, as well as responses to visual stimuli, are found by evaluation of an integral. As an example application we use the eDOG model to study effects of cortical feedback on responses to flashing circular spots and patch-grating stimuli and find that the eDOG model can qualitatively account for experimental findings.

A minimal mechanistic model for temporal signal processing in the lateral geniculate nucleus

The receptive fields of cells in the lateral geniculate nucleus (LGN) are shaped by their diverse set of impinging inputs: feedforward synaptic inputs stemming from retina, and feedback inputs stemming from the visual cortex and the thalamic reticular nucleus. To probe the possible roles of these feedforward and feedback inputs in shaping the temporal receptive-field structure of LGN relay cells, we here present and investigate a minimal mechanistic firing-rate model tailored to elucidate their disparate features. The model for LGN relay ON cells includes feedforward excitation and inhibition (via interneurons) from retinal ON cells and excitatory and inhibitory (via thalamic reticular nucleus cells and interneurons) feedback from cortical ON and OFF cells. From a general firing-rate model formulated in terms of Volterra integral equations, we derive a single delay differential equation with absolute delay governing the dynamics of the system. A freely available and easy-to-use GUI-based MATLAB version of this minimal mechanistic LGN circuit model is provided. We particularly investigate the LGN relay-cell impulse response and find through thorough explorations of the model's parameter space that both purely feedforward models and feedback models with feedforward excitation only, can account quantitatively for previously reported experimental results. We find, however, that the purely feedforward model predicts two impulse response measures, the time to first peak and the biphasic index (measuring the relative weight of the rebound phase) to be anticorrelated. In contrast, the models with feedback predict different correlations between these two measures. This suggests an experimental test assessing the relative importance of feedforward and feedback connections in shaping the impulse response of LGN relay cells.

Thalamo-cortical processing of near-threshold somatosensory stimuli in humans

Somatosensory stimuli elicit complex cortical responses that are discernible as somatosensory evoked potentials (SEPs) in scalp electroencephalographic recordings. Whereas earlier SEP components, occurring up to 100 ms after stimulus delivery, have been labeled 'preconscious', later responses have been associated with stimulus awareness. To date, how far these processes are primarily cortical or comprise additional subcortical operations remains open. Therefore, we recorded thalamic and scalp SEPs evoked by perceived as well as unperceived median nerve stimulation in neurosurgical patients with electrodes implanted into the ventral intermediate nucleus of the thalamus for deep brain stimulation. At stimulation intensities below perceptual threshold, only thalamic SEP components appeared consistently during the first 75 ms after stimulus delivery. Stimulation that was perceived by the patients elicited cortical as well as thalamic SEPs that lasted longer than 75 ms. These results indicate that the thalamus remains active after the primary propagation of a sensory signal to the cortex, and suggest that the transition from elementary to higher-order somatosensory processing is based on thalamo-cortical interactions.

Towards reproducible descriptions of neuronal network models

Progress in science depends on the effective exchange of ideas among scientists. New ideas can be assessed and criticized in a meaningful manner only if they are formulated precisely. This applies to simulation studies as well as to experiments and theories. But after more than 50 years of neuronal network simulations, we still lack a clear and common understanding of the role of computational models in neuroscience as well as established practices for describing network models in publications. This hinders the critical evaluation of network models as well as their re-use.

We analyze here 14 research papers proposing neuronal network models of different complexity and find widely varying approaches to model descriptions, with regard to both the means of description and the ordering and placement of material. We further observe great variation in the graphical representation of networks and the notation used in equations. Based on our observations, we propose a good model description practice, composed of guidelines for the organization of publications, a checklist for model descriptions, templates for tables presenting model structure, and guidelines for diagrams of networks. The main purpose of this good practice is to trigger a debate about the communication of neuronal network models in a manner comprehensible to humans, as opposed to machine-readable model description languages.

We believe that the good model description practice proposed here, together with a number of other recent initiatives on data-, model-, and software-sharing, may lead to a deeper and more fruitful exchange of ideas among computational neuroscientists in years to come. We further hope that work on standardized ways of describing—and thinking about—complex neuronal networks will lead the scientific community to a clearer understanding of high-level concepts in network dynamics, and will thus lead to deeper insights into the function of the brain.

Scientists make precise, testable statements about their observations and models of nature. Other scientists can then evaluate these statements and attempt to reproduce or extend them. Results that cannot be reproduced will be duly criticized to arrive at better interpretations of experimental results or better models. Over time, this discourse develops our joint scientific knowledge. A crucial condition for this process is that scientists can describe their own models in a manner that is precise and comprehensible to others. We analyze in this paper how well models of neuronal networks are described in the scientific literature and conclude that the wide variety of manners in which network models are described makes it difficult to communicate models successfully. We propose a good model description practice to improve the communication of neuronal network models.

Evaluating information transfer between auditory cortical neurons

Transfer entropy, presented as a new tool for investigating neural assemblies, quantifies the fraction of information in a neuron found in the past history of another neuron. The asymmetry of the measure allows feedback evaluations. In particular, this tool has potential applications in investigating windows of temporal integration and stimulus-induced modulation of firing rate. Transfer entropy is also able to eliminate some effects of common history in spike trains and obtains results that are different from cross-correlation. The basic transfer entropy properties are illustrated with simulations. The information transfer through a network of 16 simultaneous multiunit recordings in cat's auditory cortex was examined for a large number of acoustic stimulus types. Application of the transfer entropy to a large database of multiple single-unit activity in cat's primary auditory cortex revealed that most windows of temporal integration found during spontaneous activity range between 2 and 15 ms. The normalized transfer entropy shows similarities and differences with the strength of cross-correlation; these form the basis for revisiting the neural assembly concept.

Visual response properties of burst and tonic firing in the mouse dorsal lateral geniculate nucleus

Thalamic relay cells fire action potentials in two modes: burst and tonic. Previous studies in cats have shown that these two modes are associated with significant differences in the visual information carried by spikes in the dorsal lateral geniculate nucleus (dLGN). Here we describe the visual response properties of burst and tonic firing in the mouse dLGN. Extracellular recordings of activity in single geniculate cells were performed under halothane and nitrous oxide anesthesia in vivo. After confirming that the criteria used to isolate burst spikes from these recordings identify firing events with properties described for burst firing in other species and preparations, we show that burst firing in the mouse dLGN occurs during visual stimulation. We then compare burst and tonic firing across a wide range of visual response characteristics. While the two firing modes do not differ with respect to spatial summation or spatial frequency tuning, they show significant differences in the temporal domain. Burst spikes are phase advanced relative to their tonic counterparts. Burst firing is also more rectified, possesses sharper temporal frequency tuning, and prefers lower temporal frequencies than tonic firing. In addition, contrast-response curves are more step-like for burst responses. Finally, we present analyses that describe the stimulus detection abilities and spike timing reliability of burst and tonic firing.

Recordings, behaviour and models related to corticothalamic feedback

In this paper, we review recent work on aspects of corticothalamic interactions in the auditory and in the visual systems. There are gross similarities in the arrangements of these systems, but considerable contrasts in the processing computations and in the effects of corticothalamic feedback.

Fractal features of dark, maintained, and driven neural discharges in the cat visual system

We employ a number of statistical measures to characterize neural discharge activity in cat retinal ganglion cells (RGCs) and in their target lateral geniculate nucleus (LGN) neurons under various stimulus conditions, and we develop a new measure to examine correlations in fractal activity between spike-train pairs. In the absence of stimulation (i.e., in the dark), RGC and LGN discharges exhibit similar properties. The presentation of a constant, uniform luminance to the eye reduces the fractal fluctuations in the RGC maintained discharge but enhances them in the target LGN discharge, so that neural activities in the pair cease to be mirror images of each other. A drifting-grating stimulus yields RGC and LGN driven spike trains similar in character to those observed in the maintained discharge, with two notable distinctions: action potentials are reorganized along the time axis so that they occur only during certain phases of the stimulus waveform, and fractal activity is suppressed. Under both uniform-luminance and drifting-grating stimulus conditions (but not in the dark), the discharges of pairs of LGN cells are highly correlated over long time scales; in contrast discharges of RGCs are nearly uncorrelated with each other. This indicates that action-potential activity at the LGN is subject to a common fractal modulation to which the RGCs are not subjected.

Neural assemblies: technical issues, analysis, and modeling

Neurons often work together to compute and process information, and neural assemblies arise from synaptic interactions and neural circuits. One way to study neural assemblies is to simultaneously record from several or many neurons and study the statistical relations among their spike trains. From this analysis researchers can try to understand the nature of the assemblies, which can also lead to attempts at modeling the underlying mechanisms. In this review we discuss three important parts of this process: (1) technical issues related to simultaneously recording more than one single unit, (2) ways of analyzing the data and (3) recent models offering hypothetical mechanisms of neural assemblies, especially models which incorporate feedback.

The awareness of thirst: proposed neural correlates

The neural and endocrine bases of the generation of thirst are reviewed. Based on this review, a hierarchical system of neural structures that regulate water conservation and acquisition is proposed. The system includes primary sensory-receptive areas; secondary sensory structures (circumventricular organs), which detect levels of hormones, including angiotensin II and vasopressin, which are involved in generating thirst; preoptic and hypothalamic structures; and an area within the ventrolateral quadrant of the periaqueductal gray matter. Hodological and other data are used to determine the hierarchical organization of the system. Based on studies of the effects of lesions to various structures within the hierarchy of the system, it is proposed that the awareness of thirst in rodents is either entirely or predominantly due to neuronal activities in a subsection of the ventrolateral periaqueductal gray matter. It is also hypothesized that the awareness of thirst in primates is due to neuronal activities in both the ventrolateral periaqueductal gray and in a region within the medial prefrontal and anterior cingulate cortex.

Oscillations and long-lasting correlations in a model of the lateral geniculate nucleus and visual cortex

We have previously developed a model of the corticogeniculate system to explore cortically induced synchronization of lateral geniculate nucleus (LGN) neurons. Our model was based on the experiments of Sillito et al. Recently Brody discovered that the LGN events found by Sillito et al. correlate over a much longer period of time than expected from the stimulus-driven responses and proposed a cortically induced slow covariation in LGN cell membrane potentials to account for this phenomenon. We have examined the data from our model, and we found, to our surprise, that the model shows the same long-term correlation. The model's behavior was the result of a previously unsuspected oscillatory effect, not a slow covariation. The oscillations were in the same frequency range as the well-known spindle oscillations of the thalamocortical system. In the model, the strength of feedback inhibition from the cortex and the presence of low-threshold calcium channels in LGN cells were important. We also found that by making the oscillations more pronounced, we could get a better fit to the experimental data.

A feedback model of attention and context dependence in visual cortical networks

We have modeled biologically realistic neural networks that may be involved in contextual modulation of stimulus responses, as reported in the neurophysiological experiments of Motter (1994a, 1994b) (Journal of Neuroscience, 14:2179-2189 and 2190-2199). The networks of our model are structured hierarchically with feedforward, feedback, and lateral connections, totaling several thousand cells and about 300,000 synapses. The contextual modulation, arising from attention cues, is explicitly modeled as a feedback signal coming from the highest-order cortical network. The feedback signal arises from mutually inhibitory neurons with different stimulus preferences. Although our model is probably the simplest one consistent with available anatomical and physiological evidence and ignores the complexities that may exist in high-level cortical networks such as the prefrontal cortex, it reproduces the experimental results quite well and offers some guidance for future experiments. We also report the unexpected observation of 40 Hz oscillations in the model.

Slow covariations in neuronal resting potentials can lead to artefactually fast cross-correlations in their spike trains

Slow covariations in neuronal resting potentials can lead to artefactually fast cross-correlations in their spike trains. J. Neurophysiol. 80: 3345-3351, 1998. A model of two lateral geniculate nucleus (LGN) cells, which interact only through slow (tens of seconds) covariations in their resting membrane potentials, is used here to investigate the effect of such covariations on cross-correlograms taken during stimulus-driven conditions. Despite the slow timescale of the interactions, the model generates cross-correlograms with peak widths in the range of 25-200 ms. These bear a striking resemblance to those reported in studies of LGN cells by Sillito et al., which were taken at the time as evidence of a fast spike timing synchronization interaction; the model highlights the possibility that those correlogram peaks may have been caused by a mechanism other than spike synchronization. Slow resting potential covariations are suggested instead as the dominant generating mechanism. How can a slow interaction generate covariogram peaks with a width 100-1,000 times thinner than its timescale? Broad peaks caused by slow interactions are modulated by the cells' poststimulus time histograms (PSTHs). When the PSTHs have thin peaks (e.g., tens of milliseconds), the cross-correlogram peaks generated by slow interactions will also be thin; such peaks are easily misinterpretable as being caused by fast interactions. Although this point is explored here in the context of LGN recordings, it is a general point and applies elsewhere. When cross-correlogram peak widths are of the same order of magnitude as PSTH peak widths, experiments designed to reveal short-timescale interactions must be interpreted with the issue of possible contributions from slower interactions in mind.