# Realistic networks

Patchy lateral connectivity in macaque primary visual cortex: axons from an injection labelling 320 cells in the superficial layers of V1 are super-imposed upon the optical imaging orientation map for that portion of cortex. The white ring is 1 mm in diameter. While the axons proximal to the injection site display little orientation specificity, patches that form  500 m from the injection are targeted to orientation domains of similar preference to their cell bodies.

## Toward more realistic networks

A natural step is to extend the balanced network to topographical and other more realistic networks. Even if homogeneous and random balanced networks are interesting because they capture properties of the neuronal dynamics, they lack more realistic characteristics that can be found in vivo. Considering generic and simple wiring schemes can lead to analytical frameworks where key coding properties such as correlations can be described and predicted. This is for example the work of [Kriener2009], analysing the distribution of pairwise cross-correlations in several random networks in the Asynchronous Irregular regime. Correlations are crucial because they are thought to be a major element in neuronal interactions and the basis of the temporal code. Therefore an important step is to perform a clear and exhaustive study of topographical networks, and especially on how correlations organize in those networks. As already noted in the balanced random network is one of the simplest kinds of network able to generate an irregular activity. But cortical organization seems to be more organized, and anatomical data do not suggest that the connectivity is random. Without knowing if this connectivity is the result of a learning process or hard-wired, we can simply observe that, for example, in V1 neurons are connected in a patchy manner, according to the underlying orientation maps (see Figure from [Stettler2002]). The exact structure of the canonical microcircuits within layers can be assessed by dual recordings in vitro [Binzegger2004, Thomson2003], but such complex organizations, where connections are made not only as a function of distance, but also as a function of other features (preferred orientation, direction selectivity, ...) introduce more complex correlation patterns, and it is important to know what are the relevant quantities that may control such correlation levels.

## Local connectivity

Neuronal connectivity is still poorly understood, but is definitely not as random as it is usually modeled in previous studies. Whether the connectivity graph is small-world (the definition is ambiguous when considering propagation delays), clustered, or Gaussian is still unclear, but biological evidence shows that neurons in the cortex project mainly to their surrounding [Hellwig2000, Bienenstock1996]. As a first approximation, neurons can be considered as being  onnected with a distance-dependent probability following a Gaussian profile. Even if it is well known that realistic connectivity is less isotropic and homogeneous (see for example in V1 the orientation maps and the patchy horizontal connectivity [Gilbert1983]), the Gaussian profile is a good description of a small cortical area where long-range interactions are ignored. Therefore, every neuron in our model is connected with the rest of the network according to a 2D Gaussian probability function and a fixed number of output synapses, while periodic boundary conditions are used throughout the study to avoid any border effects.

## Conduction delays

Propagation delays are known to lead to a large diversity of states in large-scale neuronal networks [Roxin2005]. While they are often discarded in large-scale models, under the assumption that they could be neglected in a small cortical area, biological studies [Bringuier1999, Gonzalez-Burgos2000] have reported typical values of 0.1-0.5 m/s for conduction delays, and comparable values can be observed in Voltage Sensitive Dye Imaging, where activity waves propagate at a similar speed [Grinvald1994, Benucci2007, Nauhaus2009]. Patch recordings in vitro also confirm that these delays scale linearly according to distances [Larkum2001]. Thus, even for a small patch of cortex of , with a synaptic delay of 0.2ms (due to neurotransmitter release), conduction delays are broadly distributed and should not be neglected. Moreover some artificial oscillations could arise in network where delays are homogeneous [Brunel2000].

## Simulated dynamics

Here is an example of such a 2D network, with spontaneous activity. Local connectivity, linear delays. What you can see is, at the conductance level, some waves randomly popping up and propagating. Those waves are somehow reflected at the voltage level, but harder to see if just recording the spikes. This is why an in-depth understanding of sub-threshold dynamics is crucial: spikes are just the visible tip of the iceberg.

## References

[Kriener2009] B. Kriener, M. Helias, A. Aertsen, and S. Rotter, "Correlations in spiking neuronal networks with distance dependent connections.," Journal of computational neuroscience, vol. 27, iss. 2, pp. 177-200, 2009.
[Bibtex]
@article{Kriener2009,
abstract = {Can the topology of a recurrent spiking network be inferred from observed activity dynamics? Which statistical parameters of network connectivity can be extracted from firing rates, correlations and related measurable quantities? To approach these questions, we analyze distance dependent correlations of the activity in small-world networks of neurons with current-based synapses derived from a simple ring topology. We find that in particular the distribution of correlation coefficients of subthreshold activity can tell apart random networks from networks with distance dependent connectivity. Such distributions can be estimated by sampling from random pairs. We also demonstrate the crucial role of the weight distribution, most notably the compliance with Dales principle, for the activity dynamics in recurrent networks of different types.},
author = {Kriener, Birgit and Helias, Moritz and Aertsen, Ad and Rotter, Stefan},
doi = {10.1007/s10827-008-0135-1},
file = {:home/pierre/Mendeley/Kriener et al. - 2009.pdf:pdf},
issn = {1573-6873},
journal = {Journal of computational neuroscience},
keywords = {Action Potentials,Action Potentials: physiology,Algorithms,Animals,Central Nervous System,Central Nervous System: physiology,Computer Simulation,Humans,Nerve Net,Nerve Net: physiology,Neural Networks (Computer),Neural Pathways,Neural Pathways: physiology,Neurons,Neurons: physiology,Synapses,Synapses: physiology,Synaptic Transmission,Synaptic Transmission: physiology},
month = oct,
number = {2},
pages = {177--200},
pmid = {19568923},
title = {{Correlations in spiking neuronal networks with distance dependent connections.}},
url = {http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=2731936\&tool=pmcentrez\&rendertype=abstract},
volume = {27},
year = {2009}
}
[Stettler2002] D. D. Stettler, A. Das, J. Bennett, and C. D. Gilbert, "Lateral connectivity and contextual interactions in macaque primary visual cortex.," Neuron, vol. 36, pp. 739-750, 2002.
[Bibtex]
@article{Stettler2002,
abstract = {Two components of cortical circuits could mediate contour integration in primary visual cortex (V1): intrinsic horizontal connections and feedback from higher cortical areas. To distinguish between these, we combined functional mapping with a new technique for labeling axons, a recombinant adenovirus bearing the gene for green fluorescent protein (GFP), to determine the extent, density, and orientation specificity of V1 intrinsic connections and V2 to V1 feedback. Both connections cover portions of V1 representing regions of visual space up to eight times larger than receptive fields as classically defined, though the intrinsic connections are an order of magnitude denser than the feedback. Whereas the intrinsic connections link similarly oriented domains in V1, V2 to V1 feedback displays no such specificity. These findings suggest that V1 intrinsic horizontal connections provide a more likely substrate for contour integration.},
author = {Stettler, Dan D and Das, Aniruddha and Bennett, Jean and Gilbert, Charles D},
file = {:home/pierre/Mendeley/Stettler et al. - 2002.pdf:pdf},
journal = {Neuron},
keywords = {Adenoviridae; Animals; Axons; Brain Mapping; Domin,Computer-Assisted; Luminescent Proteins; Macaca fa,Confocal; Neural Pathways; Pattern Recognition,Ocular; Feedback; Genetic Vectors; Green Fluoresce,Visual; Visual Cortex; Visual Fields},
month = nov,
pages = {739--750},
pmid = {12441061},
title = {{Lateral connectivity and contextual interactions in macaque primary visual cortex.}},
volume = {36},
year = {2002}
}
[Binzegger2004] T. Binzegger, R. J. Douglas, and K. A. C. Martin, "A quantitative map of the circuit of cat primary visual cortex.," The journal of neuroscience : the official journal of the society for neuroscience, vol. 24, iss. 39, pp. 8441-53, 2004.
[Bibtex]
@article{Binzegger2004,
abstract = {We developed a quantitative description of the circuits formed in cat area 17 by estimating the "weight" of the projections between different neuronal types. To achieve this, we made three-dimensional reconstructions of 39 single neurons and thalamic afferents labeled with horseradish peroxidase during intracellular recordings in vivo. These neurons served as representatives of the different types and provided the morphometrical data about the laminar distribution of the dendritic trees and synaptic boutons and the number of synapses formed by a given type of neuron. Extensive searches of the literature provided the estimates of numbers of the different neuronal types and their distribution across the cortical layers. Applying the simplification that synapses between different cell types are made in proportion to the boutons and dendrites that those cell types contribute to the neuropil in a given layer, we were able to estimate the probable source and number of synapses made between neurons in the six layers. The predicted synaptic maps were quantitatively close to the estimates derived from the experimental electron microscopic studies for the case of the main sources of excitatory and inhibitory input to the spiny stellate cells, which form a major target of layer 4 afferents. The map of the whole cortical circuit shows that there are very few "strong" but many "weak" excitatory projections, each of which may involve only a few percentage of the total complement of excitatory synapses of a single neuron.},
author = {Binzegger, Tom and Douglas, Rodney J and Martin, Kevan A C},
doi = {10.1523/JNEUROSCI.1400-04.2004},
issn = {1529-2401},
journal = {The Journal of neuroscience : the official journal of the Society for Neuroscience},
keywords = {Afferent Pathways,Afferent Pathways: anatomy \& histology,Animals,Axons,Brain Mapping,Cats,Cats: anatomy \& histology,Cell Count,Dendrites,Imaging, Three-Dimensional,Models, Neurological,Neural Pathways,Neural Pathways: anatomy \& histology,Neural Pathways: cytology,Neural Pathways: ultrastructure,Neurons,Neurons: ultrastructure,Presynaptic Terminals,Pyramidal Cells,Synapses,Thalamic Nuclei,Thalamic Nuclei: cytology,Visual Cortex,Visual Cortex: anatomy \& histology,Visual Cortex: cytology,Visual Cortex: ultrastructure},
month = sep,
number = {39},
pages = {8441--53},
pmid = {15456817},
title = {{A quantitative map of the circuit of cat primary visual cortex.}},
url = {http://www.ncbi.nlm.nih.gov/pubmed/15456817},
volume = {24},
year = {2004}
}
[Thomson2003] A. M. Thomson and P. A. Bannister, "Interlaminar connections in the neocortex.," Cerebral cortex (new york, n.y. : 1991), vol. 13, iss. 1, pp. 5-14, 2003.
[Bibtex]
@article{Thomson2003,
abstract = {This review summarizes the local circuit, interlaminar connections in adult mammalian neocortex. These were first demonstrated with anatomical techniques, which indicate some of the exquisite spatial precision present in the circuitry. Details, such as the class(es) of neurons targeted by some of these projections, have begun to be added in studies that combine paired/triple intracellular recordings with dye-filling of connected neurons. Clear patterns are emerging from these studies, with 'forward' projections from layer 4 to 3 and from 3 to 5 targeting both selected pyramidal cells and interneurons, while 'back' projections from layer 5 to 3 and from 3 to 4 target only interneurons. To place these data in a wider context, the major afferent inputs to and efferent outputs from each of the layers are discussed first.},
author = {Thomson, Alex M and Bannister, A Peter},
issn = {1047-3211},
journal = {Cerebral cortex (New York, N.Y. : 1991)},
keywords = {Afferent Pathways,Afferent Pathways: cytology,Animals,Cats,Dendrites,Efferent Pathways,Efferent Pathways: cytology,Feedback,Humans,Interneurons,Interneurons: classification,Interneurons: cytology,Neocortex,Neocortex: anatomy \& histology,Neocortex: cytology,Nerve Net,Nerve Net: anatomy \& histology,Nerve Net: cytology,Pyramidal Cells,Pyramidal Cells: cytology,Thalamus,Thalamus: cytology,Vision, Ocular,Vision, Ocular: physiology},
month = jan,
number = {1},
pages = {5--14},
pmid = {12466210},
title = {{Interlaminar connections in the neocortex.}},
url = {http://www.ncbi.nlm.nih.gov/pubmed/12466210},
volume = {13},
year = {2003}
}
[Hellwig2000] B. Hellwig, "A quantitative analysis of the local connectivity between pyramidal neurons in layers 2/3 of the rat visual cortex.," Biol cybern, vol. 82, pp. 111-121, 2000.
[Bibtex]
@article{Hellwig2000,
abstract = {This study provides a detailed quantitative estimate for local synaptic connectivity between neocortical pyramidal neurons. A new way of obtaining such an estimate is presented. In acute slices of the rat visual cortex, four layer 2 and four layer 3 pyramidal neurons were intracellularly injected with biocytin. Axonal and dendritic arborizations were three-dimensionally reconstructed with the aid of a computer-based camera lucida system. In a computer experiment, pairs of pre- and postsynaptic neurons were formed and potential synaptic contacts were calculated. For each pair, the calculations were carried out for a whole range of distances (0 to 500 microm) between the presynaptic and the postsynaptic neuron, in order to estimate cortical connectivity as a function of the spatial separation of neurons. It was also differentiated whether neurons were situated in the same or in different cortical layers. The data thus obtained was used to compute connection probabilities, the average number of contacts between neurons, the frequency of specific numbers of contacts and the total number of contacts a dendritic tree receives from the surrounding cortical volume. Connection probabilities ranged from 50$\backslash$\% to 80$\backslash$\% for directly adjacent neurons and from 0$\backslash$\% to 15$\backslash$\% for neurons 500 microm apart. In many cases, connections were mediated by one contact only. However, close neighbors made on average up to 3 contacts with each other. The question as to whether the method employed in this study yields a realistic estimate of synaptic connectivity is discussed. It is argued that the results can be used as a detailed blueprint for building artificial neural networks with a cortex-like architecture.},
author = {Hellwig, B},
file = {:home/pierre/Mendeley/Hellwig - 2000.pdf:pdf},
journal = {Biol Cybern},
keywords = {Animals; Axons; Cell Count; Cell Size; Computer Si,Computer-Assisted; Lysine; Models,Inbred Lew; Synapses; Visual Cortex,Neurological; Nerve Net; Neural Networks (Computer},
pages = {111--121},
pmid = {10664098},
title = {{A quantitative analysis of the local connectivity between pyramidal neurons in layers 2/3 of the rat visual cortex.}},
volume = {82},
year = {2000}
}
[Bienenstock1996] E. Bienenstock, "On the dimensionality of cortical graphs.," Journal of physiology, paris, vol. 90, iss. 3-4, pp. 251-6, 1996.
[Bibtex]
@article{Bienenstock1996,
abstract = {We propose to use a random-graph model of cortex as a tabula-rasa state, to be contrasted with various types of regular connectivity patterns. Key in our analysis is the notion of graph-theoretic dimensionality, closely linked to that of graph diameter. Our discussion focuses on patterns of synfire type, and on the synfire-superposition model proposed in previous papers.},
author = {Bienenstock, E},
issn = {0928-4257},
journal = {Journal of physiology, Paris},
keywords = {Cerebral Cortex,Cerebral Cortex: physiology,Cybernetics,Mathematics,Neural Networks (Computer),Poisson Distribution,Stochastic Processes,Synaptic Transmission,Synaptic Transmission: physiology},
month = jan,
number = {3-4},
pages = {251--6},
pmid = {9116678},
title = {{On the dimensionality of cortical graphs.}},
url = {http://www.ncbi.nlm.nih.gov/pubmed/9116678},
volume = {90},
year = {1996}
}
[Gilbert1983] C. D. Gilbert and T. N. Wiesel, "Clustered intrinsic connections in cat visual cortex.," The journal of neuroscience : the official journal of the society for neuroscience, vol. 3, iss. 5, pp. 1116-33, 1983.
[Bibtex]
@article{Gilbert1983,
abstract = {The intrinsic connections of the cortex have long been known to run vertically, across the cortical layers. In the present study we have found that individual neurons in the cat primary visual cortex can communicate over suprisingly long distances horizontally (up to 4 mm), in directions parallel to the cortical surface. For all of the cells having widespread projections, the collaterals within their axonal fields were distributed in repeating clusters, with an average periodicity of 1 mm. This pattern of extensive clustered projections has been revealed by combining the techniques of intracellular recording and injection of horseradish peroxidase with three-dimensional computer graphic reconstructions. The clustering pattern was most apparent when the cells were rotated to present a view parallel to the cortical surface. The pattern was observed in more than half of the pyramidal and spiny stellate cells in the cortex and was seen in all cortical layers. In our sample, cells made distant connections within their own layer and/or within another layer. The axon of one cell had clusters covering the same area in two layers, and the clusters in the deeper layer were located under those in the upper layer, suggesting a relationship between the clustering phenomenon and columnar cortical architecture. Some pyramidal cells did not project into the white matter, forming intrinsic connections exclusively. Finally, the axonal fields of all our injected cells were asymmetric, extending for greater distances along one cortical axis than along the orthogonal axis. The axons appeared to cover areas of cortex representing a larger part of the visual field than that covered by the excitatory portion of the cell's own receptive field. These connections may be used to generate larger receptive fields or to produce the inhibitory flanks in other cells' receptive fields.},
author = {Gilbert, C D and Wiesel, T N},
issn = {0270-6474},
journal = {The Journal of neuroscience : the official journal of the Society for Neuroscience},
keywords = {Animals,Axonal Transport,Cats,Horseradish Peroxidase,Pyramidal Tracts,Pyramidal Tracts: anatomy \& histology,Pyramidal Tracts: physiology,Visual Cortex,Visual Cortex: anatomy \& histology,Visual Cortex: cytology,Visual Cortex: physiology},
month = may,
number = {5},
pages = {1116--33},
pmid = {6188819},
title = {{Clustered intrinsic connections in cat visual cortex.}},
url = {http://www.ncbi.nlm.nih.gov/pubmed/6188819},
volume = {3},
year = {1983}
}
[Roxin2005] A. Roxin, N. Brunel, and D. Hansel, "Role of delays in shaping spatiotemporal dynamics of neuronal activity in large networks.," Physical review letters, vol. 94, iss. 23, p. 238103, 2005.
[Bibtex]
@article{Roxin2005,
abstract = {We study the effect of delays on the dynamics of large networks of neurons. We show that delays give rise to a wealth of bifurcations and to a rich phase diagram, which includes oscillatory bumps, traveling waves, lurching waves, standing waves arising via a period-doubling bifurcation, aperiodic regimes, and regimes of multistability. We study the existence and the stability of the various dynamical patterns analytically and numerically in a simplified rate model as a function of the interaction parameters. The results derived in that framework allow us to understand the origin of the diversity of dynamical states observed in large networks of spiking neurons.},
author = {Roxin, Alex and Brunel, Nicolas and Hansel, David},
issn = {0031-9007},
journal = {Physical review letters},
keywords = {Cell Communication,Cell Communication: physiology,Cerebral Cortex,Cerebral Cortex: cytology,Cerebral Cortex: physiology,Models, Neurological,Nerve Net,Nerve Net: cytology,Nerve Net: physiology,Neurons,Neurons: physiology},
month = jun,
number = {23},
pages = {238103},
pmid = {16090506},
title = {{Role of delays in shaping spatiotemporal dynamics of neuronal activity in large networks.}},
url = {http://www.ncbi.nlm.nih.gov/pubmed/16090506},
volume = {94},
year = {2005}
}
[Bringuier1999] V. Bringuier, F. Chavane, L. Glaeser, Y. Fr�gnac, and L. G. F. Y. {Vincent Bringuier Frederic Chavane, "Horizontal propagation of visual activity in the synaptic integration field of area 17 neurons.," Science, vol. 283, iss. January, pp. 695-699, 1999.
[Bibtex]
@article{Bringuier1999,
abstract = {The receptive field of a visual neuron is classically defined as the region of space (or retina) where a visual stimulus evokes a change in its firing activity. At the cortical level, a challenging issue concerns the roles of feedforward, local recurrent, intracortical, and cortico-cortical feedback connectivity in receptive field properties. Intracellular recordings in cat area 17 showed that the visually evoked synaptic integration field extends over a much larger area than that established on the basis of spike activity. Synaptic depolarizing responses to stimuli flashed at increasing distances from the center of the receptive field decreased in strength, whereas their onset latency increased. These findings suggest that subthreshold responses in the unresponsive region surrounding the classical discharge field result from the integration of visual activation waves spread by slowly conducting horizontal axons within primary visual cortex.},
author = {Bringuier, V and Chavane, F and Glaeser, L and Fr�gnac, Y and {Vincent Bringuier, Frederic Chavane, Larry Glaeser}, Fregnac Yves},
file = {:home/pierre/Mendeley/Bringuier et al. - 1999.pdf:pdf},
journal = {Science},
keywords = {Action Potentials,Animals,Axons,Brain Mapping,Non-U.S. Gov't,Patch-Clamp Techniques,Photic Stimulation,Synapses,Visual,Visual Cortex,Visual Fi},
month = jan,
number = {January},
pages = {695--699},
pmid = {9924031},
title = {{Horizontal propagation of visual activity in the synaptic integration field of area 17 neurons.}},
volume = {283},
year = {1999}
}
[Gonzalez-Burgos2000] G. Barrionuevo, D. A. Lewis, and G. Gonzalez-Burgos, "Horizontal Synaptic Connections in Monkey Prefrontal Cortex: An," Cereb cortex, vol. 10, iss. ii, pp. 82-92, 2000.
[Bibtex]
@article{Gonzalez-Burgos2000,
abstract = {In monkey dorsolateral prefrontal cortex (PFC), long-distance, horizontally oriented intrinsic axon collaterals interconnect clusters of pyramidal neurons in the supragranular layers. In order to study the electrophysiological responses mediated by these long-distance projections, an in vitro slice preparation of monkey PFC was used to obtain whole-cell patch clamp recordings from layer 3 pyramidal neurons. Using in vivo tracer injections, we found that long-distance projections were well preserved in PFC slices cut in the coronal plane. Postsynaptic currents were evoked by low-intensity electrical extracellular stimulation applied successively to 20–30 discrete sites located up to 2200 µm lateral to the recorded cell. Several criteria were applied to discriminate between mono- and poly- synaptic responses. Long-distance monosynaptic connections were mediated by fibers with relatively slow conduction velocity (0.14 m/s). Excitatory postsynaptic currents (EPSCs) evoked by stimulation of short- or long-distance horizontal connections did not differ in kinetic properties. The majority (77\%) of the 35 layer 3 PFC neurons studied were monosynaptic targets of long-distance connections. EPSCs mediated by long-distance connections had amplitudes that were similar or even larger than short-distance EPSCs, suggesting that excitatory input provided by the former was relatively robust. For most neurons (87.5\%) in which a full complement of monosynaptic EPSCs was evoked by multisite stimulation, the EPSC amplitude as a function of stimulation distance from the recorded cells exhibited statistically significant peaks. The spacing between peaks was similar to the spacing between interconnected clusters of neurons observed in previous anatomical studies. The results show that long-distance excitatory connections constitute a significant intrinsic pathway of synaptic communication in layer 3 of monkey PFC.},
author = {Barrionuevo, German and Lewis, David A and Gonzalez-Burgos, G},
file = {:home/pierre/Mendeley/Barrionuevo, Lewis, Gonzalez-Burgos - 2000.pdf:pdf},
journal = {Cereb Cortex},
keywords = {Animals,Electric Stimulation,Electrophysiology},
month = jan,
number = {ii},
pages = {82--92},
pmid = {10639398},
title = {{Horizontal Synaptic Connections in Monkey Prefrontal Cortex: An}},
volume = {10},
year = {2000}
}
[Grinvald1994] A. Grinvald, E. E. Lieke, R. D. Frostig, and R. Hildesheim, "Cortical point-spread function and long-range lateral interactions revealed by real-time optical imaging of macaque monkey primary visual cortex.," The journal of neuroscience : the official journal of the society for neuroscience, vol. 14, iss. 5 Pt 1, pp. 2545-68, 1994.
[Bibtex]
@article{Grinvald1994,
abstract = {Processing of retinal images is carried out in the myriad dendritic arborizations of cortical neurons. Such processing involves complex dendritic integration of numerous inputs, and the subsequent output is transmitted to multiple targets by extensive axonal arbors. Thus far, details of this intricate processing remained unexaminable. This report describes the usefulness of real-time optical imaging in the study of population activity and the exploration of cortical dendritic processing. In contrast to single-unit recordings, optical signals primarily measure the changes in transmembrane potential of a population of neuronal elements, including the often elusive subthreshold synaptic potentials that impinge on the extensive arborization of cortical cells. By using small visual stimuli with sharp borders and real-time imaging of cortical responses, we found that shortly after its onset, cortical activity spreads from its retinotopic site of initiation, covering an area at least 10 times larger, in upper cortical layers. The activity spreads at velocities from 100 to 250 microns/msec. Near the V1/V2 border the direct activation is anisotropic and we detected also anisotropic spread; the "space constant" for the spread was approximately 2.7 mm parallel to the border and approximately 1.5 mm along the perpendicular axis. In addition, we found cortical interactions between cortical activities evoked by a small "center stimulus" and by large "surround stimuli" positioned outside the classical receptive field. All of the surround stimuli used suppressed the cortical response to the center stimulus. Under some stimulus conditions iso-orientation suppression was more pronounced than orthogonal-orientation suppression. The orientation dependence of the suppression and its dependency on the size of some specific stimuli indicate that at least part of the center surround inhibitory interaction was of cortical origin. This findings reported here raise the possibility that distributed processing over a very large cortical area plays a major role in the processing of visual information by the primary visual cortex of the primate.},
author = {Grinvald, A and Lieke, E E and Frostig, R D and Hildesheim, R},
issn = {0270-6474},
journal = {The Journal of neuroscience : the official journal of the Society for Neuroscience},
keywords = {Animals,Axons,Axons: physiology,Brain Mapping,Coloring Agents,Cortical Spreading Depression,Craniotomy,Discrimination (Psychology),Electric Stimulation,Electroencephalography,Eye Movements,Functional Laterality,Macaca fascicularis,Neurons,Neurons: physiology,Time Factors,Vision, Ocular,Visual Cortex,Visual Cortex: physiology,Visual Perception,Visual Perception: physiology},
month = may,
number = {5 Pt 1},
pages = {2545--68},
pmid = {8182427},
title = {{Cortical point-spread function and long-range lateral interactions revealed by real-time optical imaging of macaque monkey primary visual cortex.}},
url = {http://www.ncbi.nlm.nih.gov/pubmed/8182427},
volume = {14},
year = {1994}
}
[Benucci2007] A. Benucci, R. A. Frazor, and M. Carandini, "Standing waves and traveling waves distinguish two circuits in visual cortex.," Neuron, vol. 55, iss. 1, pp. 103-17, 2007.
[Bibtex]
@article{Benucci2007,
abstract = {The visual cortex represents stimuli through the activity of neuronal populations. We measured the evolution of this activity in space and time by imaging voltage-sensitive dyes in cat area V1. Contrast-reversing stimuli elicit responses that oscillate at twice the stimulus frequency, indicating that signals originate mostly in complex cells. These responses stand clear of the noise, whose amplitude decreases as 1/frequency, and yield high-resolution maps of orientation preference and retinotopy. We first show how these maps are combined to yield the responses to focal, oriented stimuli. We then study the evolution of the oscillating activity in space and time. In the orientation domain, it is a standing wave. In the spatial domain, it is a traveling wave propagating at 0.2-0.5 m/s. These different dynamics indicate a fundamental distinction in the circuits underlying selectivity for position and orientation, two key stimulus attributes.},
author = {Benucci, Andrea and Frazor, Robert A and Carandini, Matteo},
doi = {10.1016/j.neuron.2007.06.017},
file = {:home/pierre/Mendeley/Benucci, Frazor, Carandini - 2007.pdf:pdf},
issn = {0896-6273},
journal = {Neuron},
keywords = {Algorithms,Animals,Cats,Dendrites,Dendrites: physiology,Fluorescent Dyes,Fourier Analysis,Image Processing, Computer-Assisted,Nerve Net,Nerve Net: physiology,Neurons,Neurons: physiology,Photic Stimulation,Retina,Retina: physiology,Space Perception,Space Perception: physiology,Visual Cortex,Visual Cortex: physiology},
month = jul,
number = {1},
pages = {103--17},
pmid = {17610820},
title = {{Standing waves and traveling waves distinguish two circuits in visual cortex.}},
url = {http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=2171365\&tool=pmcentrez\&rendertype=abstract},
volume = {55},
year = {2007}
}
[Nauhaus2009] I. Nauhaus, L. Busse, M. Carandini, and D. L. Ringach, "Stimulus contrast modulates functional connectivity in visual cortex.," Nature neuroscience, vol. 12, iss. 1, pp. 70-6, 2009.
[Bibtex]
@article{Nauhaus2009,
abstract = {Neurons in visual cortex are linked by an extensive network of lateral connections. To study the effect of these connections on neural responses, we recorded spikes and local field potentials (LFPs) from multi-electrode arrays that were implanted in monkey and cat primary visual cortex. Spikes at each location generated outward traveling LFP waves. When the visual stimulus was absent or had low contrast, these LFP waves had large amplitudes and traveled over long distances. Their effect was strong: LFP traces at any site could be predicted by the superposition of waves that were evoked by spiking in a approximately 1.5-mm radius. As stimulus contrast increased, both the magnitude and the distance traveled by the waves progressively decreased. We conclude that the relative weight of feedforward and lateral inputs in visual cortex is not fixed, but rather depends on stimulus contrast. Lateral connections dominate at low contrast, when spatial integration of signals is perhaps most beneficial.},
author = {Nauhaus, Ian and Busse, Laura and Carandini, Matteo and Ringach, Dario L},
doi = {10.1038/nn.2232},
file = {:home/pierre/Mendeley/Nauhaus et al. - 2009.pdf:pdf},
issn = {1546-1726},
journal = {Nature neuroscience},
keywords = {Action Potentials,Animals,Cats,Contrast Sensitivity,Contrast Sensitivity: physiology,Macaca fascicularis,Neurons,Neurons: physiology,Photic Stimulation,Photic Stimulation: methods,Visual Cortex,Visual Cortex: cytology,Visual Cortex: physiology,Visual Pathways,Visual Pathways: physiology},
month = jan,
number = {1},
pages = {70--6},
pmid = {19029885},
title = {{Stimulus contrast modulates functional connectivity in visual cortex.}},
url = {http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=2610236\&tool=pmcentrez\&rendertype=abstract},
volume = {12},
year = {2009}
}
[Larkum2001] M. E. Larkum, J. J. Zhu, and B. Sakmann, "Dendritic mechanisms underlying the coupling of the dendritic with the axonal action potential initiation zone of adult rat layer 5 pyramidal neurons.," J physiol, vol. 533, pp. 447-466, 2001.
[Bibtex]
@article{Larkum2001,
abstract = {1. Double, triple and quadruple whole-cell voltage recordings were made simultaneously from different parts of the apical dendritic arbor and the soma of adult layer 5 (L5) pyramidal neurons. We investigated the membrane mechanisms that support the conduction of dendritic action potentials (APs) between the dendritic and axonal AP initiation zones and their influence on the subsequent AP pattern. 2. The duration of the current injection to the distal dendritic initiation zone controlled the degree of coupling with the axonal initiation zone and the AP pattern. 3. Two components of the distally evoked regenerative potential were pharmacologically distinguished: a rapidly rising peak potential that was TTX sensitive and a slowly rising plateau-like potential that was Cd(2+) and Ni(2+) sensitive and present only with longer-duration current injection. 4. The amplitude of the faster forward-propagating Na(+)-dependent component and the amplitude of the back-propagating AP fell into two classes (more distinctly in the forward-propagating case). Current injection into the dendrite altered propagation in both directions. 5. Somatic current injections that elicited single Na(+) APs evoked bursts of Na(+) APs when current was injected simultaneously into the proximal apical dendrite. The mechanism did not depend on dendritic Na(+)-Ca(2+) APs. 6. A three-compartment model of a L5 pyramidal neuron is proposed. It comprises the distal dendritic and axonal AP initiation zones and the proximal apical dendrite. Each compartment contributes to the initiation and to the pattern of AP discharge in a distinct manner. Input to the three main dendritic arbors (tuft dendrites, apical oblique dendrites and basal dendrites) has a dominant influence on only one of these compartments. Thus, the AP pattern of L5 pyramids reflects the laminar distribution of synaptic activity in a cortical column.},
author = {Larkum, M E and Zhu, J J and Sakmann, B},
journal = {J Physiol},
keywords = {Action Potentials; Animals; Axons; Cadmium; Calciu,Wistar; Sodium; Somatosensory Cortex; Tetrodotoxin},
pages = {447--466},
pmid = {11389204},
title = {{Dendritic mechanisms underlying the coupling of the dendritic with the axonal action potential initiation zone of adult rat layer 5 pyramidal neurons.}},
volume = {533},
year = {2001}
}
[Brunel2000] N. Brunel, "Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons.," J comput neurosci, vol. 8, pp. 183-208, 2000.
[Bibtex]
@article{Brunel2000,
abstract = {The dynamics of networks of sparsely connected excitatory and inhibitory integrate-and-fire neurons are studied analytically. The analysis reveals a rich repertoire of states, including synchronous states in which neurons fire regularly; asynchronous states with stationary global activity and very irregular individual cell activity; and states in which the global activity oscillates but individual cells fire irregularly, typically at rates lower than the global oscillation frequency. The network can switch between these states, provided the external frequency, or the balance between excitation and inhibition, is varied. Two types of network oscillations are observed. In the fast oscillatory state, the network frequency is almost fully controlled by the synaptic time scale. In the slow oscillatory state, the network frequency depends mostly on the membrane time constant. Finite size effects in the asynchronous state are also discussed.},
author = {Brunel, N},
file = {:home/pierre/Mendeley/Brunel - 2000.pdf:pdf},
journal = {J Comput Neurosci},
keywords = {Action Potentials; Biological Clocks; Brain; Corti,Neurological; Nerve Net; Neural Inhibition; Neural},
pages = {183--208},
pmid = {10809012},
title = {{Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons.}},
volume = {8},
year = {2000}
}