Modeling the emergence of whisker direction maps in rat barrel cortex

Biological action at a distance: Correlated pattern formation in adjacent tessellation domains without communication

Tessellations emerge in many natural systems, and the constituent domains often contain regular patterns, raising the intriguing possibility that pattern formation within adjacent domains might be correlated by the geometry, without the direct exchange of information between parts comprising either domain. We confirm this paradoxical effect, by simulating pattern formation via reaction-diffusion in domains whose boundary shapes tessellate, and showing that correlations between adjacent patterns are strong compared to controls that self-organize in domains with equivalent sizes but unrelated shapes. The effect holds in systems with linear and non-linear diffusive terms, and for boundary shapes derived from regular and irregular tessellations. Based on the prediction that correlations between adjacent patterns should be bimodally distributed, we develop methods for testing whether a given set of domain boundaries constrained pattern formation within those domains. We then confirm such a prediction by analysing the development of ‘subbarrel’ patterns, which are thought to emerge via reaction-diffusion, and whose enclosing borders form a Voronoi tessellation on the surface of the rodent somatosensory cortex. In more general terms, this result demonstrates how causal links can be established between the dynamical processes through which biological patterns emerge and the constraints that shape them.

Patterns can form in biological systems as a net effect of dynamical interactions that are excitatory over short distances and inhibitory over larger distances. Patterns that form in this way are known to reflect the shape of the boundary conditions that contain them. But observing that a particular pattern is contained by a boundary is not enough to determine whether or not that boundary was a constraint on pattern formation. Here we develop a novel test for the influence of boundary shape on pattern formation, based on comparing patterns contained by boundaries whose shapes tessellate and thus are geometrically related. Applying this test to patterns of cell density measured in the developing neocortex confirms that cortical column boundaries constrain pattern formation during the first postnatal weeks. In more general terms, our analysis reveals that strong relationships between patterns that form in adjacent biological domains are to be expected based purely on geometrical effects, even if no information is exchanged between those domains during the process of pattern formation. Our analysis provides a means for testing current theories about the fundamental role that constraints play in organising biological systems.

A model of lateral interactions as the origin of multiwhisker receptive fields in rat barrel cortex

While cells within barrel cortex respond primarily to deflections of their principal whisker (PW), they also exhibit responses to non-principal, or adjacent, whiskers (AWs), albeit responses with diminished amplitudes and longer latencies. The origin of multiwhisker receptive fields of barrel cells remains a point of controversy within the experimental literature, with three contending possibilities: (i) barrel cells inherit their AW responses from the AW responses of thalamocortical (TC) cells within their aligned barreloid; (ii) the axons of TC cells within a barreloid ramify to innervate multiple barrels, rather than only terminating within their aligned barrel; (iii) lateral intracortical transmission between barrels conveys AW responsivity to barrel cells. In this work, we develop a detailed, biologically plausible model of multiple barrels in order to examine possibility (iii); in order to isolate the dynamics that possibility (iii) entails, we incorporate lateral connections between barrels while assuming that TC cells respond only to their PW and that TC cell axons are confined to their home barrel. We show that our model is capable of capturing a broad swath of experimental observations on multiwhisker receptive field dynamics within barrels, and we compare and contrast the dynamics of this model with model dynamics from prior work in which employ a similar general modeling strategy to examine possibility (i).

A Network Architecture for Bidirectional Neurovascular Coupling in Rat Whisker Barrel Cortex

Neurovascular coupling is typically considered as a master-slave relationship between the neurons and the cerebral vessels: the neurons demand energy which the vessels supply in the form of glucose and oxygen. In the recent past, both theoretical and experimental studies have suggested that the neurovascular coupling is a bidirectional system, a loop that includes a feedback signal from the vessels influencing neural firing and plasticity. An integrated model of bidirectionally connected neural network and the vascular network is hence required to understand the relationship between the informational and metabolic aspects of neural dynamics. In this study, we present a computational model of the bidirectional neurovascular system in the whisker barrel cortex and study the effect of such coupling on neural activity and plasticity as manifest in the whisker barrel map formation. In this model, a biologically plausible self-organizing network model of rate coded, dynamic neurons is nourished by a network of vessels modeled using the biophysical properties of blood vessels. The neural layer which is designed to simulate the whisker barrel cortex of rat transmits vasodilatory signals to the vessels. The feedback from the vessels is in the form of available oxygen for oxidative metabolism whose end result is the adenosine triphosphate (ATP) necessary to fuel neural firing. The model captures the effect of the feedback from the vascular network on the neuronal map formation in the whisker barrel model under normal and pathological (Hypoxia and Hypoxia-Ischemia) conditions.

Stability analysis of a neural field self-organizing map

We provide theoretical conditions guaranteeing that a self-organizing map efficiently develops representations of the input space. The study relies on a neural field model of spatiotemporal activity in area 3b of the primary somatosensory cortex. We rely on Lyapunov's theory for neural fields to derive theoretical conditions for stability. We verify the theoretical conditions by numerical experiments. The analysis highlights the key role played by the balance between excitation and inhibition of lateral synaptic coupling and the strength of synaptic gains in the formation and maintenance of self-organizing maps.

Neuronal Circuits in Barrel Cortex for Whisker Sensory Perception

The array of whiskers on the snout provides rodents with tactile sensory information relating to the size, shape and texture of objects in their immediate environment. Rodents can use their whiskers to detect stimuli, distinguish textures, locate objects and navigate. Important aspects of whisker sensation are thought to result from neuronal computations in the whisker somatosensory cortex (wS1). Each whisker is individually represented in the somatotopic map of wS1 by an anatomical unit named a 'barrel' (hence also called barrel cortex). This allows precise investigation of sensory processing in the context of a well-defined map. Here, we first review the signaling pathways from the whiskers to wS1, and then discuss current understanding of the various types of excitatory and inhibitory neurons present within wS1. Different classes of cells can be defined according to anatomical, electrophysiological and molecular features. The synaptic connectivity of neurons within local wS1 microcircuits, as well as their long-range interactions and the impact of neuromodulators, are beginning to be understood. Recent technological progress has allowed cell-type-specific connectivity to be related to cell-type-specific activity during whisker-related behaviors. An important goal for future research is to obtain a causal and mechanistic understanding of how selected aspects of tactile sensory information are processed by specific types of neurons in the synaptically connected neuronal networks of wS1 and signaled to downstream brain areas, thus contributing to sensory-guided decision-making.

Supra-barrel Distribution of Directional Tuning for Global Motion in the Mouse Somatosensory Cortex

Rodents explore their environment with an array of whiskers, inducing complex patterns of whisker deflections. Cortical neuronal networks can extract global properties of tactile scenes. In the primary somatosensory cortex, the information relative to the global direction of a spatiotemporal sequence of whisker deflections can be extracted at the single neuron level. To further understand how the cortical network integrates multi-whisker inputs, we imaged and recorded the mouse barrel cortex activity evoked by sequences of multi-whisker deflections generating global motions in different directions. A majority of barrel-related cortical columns show a direction preference for global motions with an overall preference for caudo-ventral directions. Responses to global motions being highly sublinear, the identity of the first deflected whiskers is highly salient but does not seem to determine the global direction preference. Our results further demonstrate that the global direction preference is spatially organized throughout the barrel cortex at a supra-columnar scale.

Somatosensory maps

Somatosensory areas containing topographic maps of the body surface are a major feature of parietal cortex. In primates, parietal cortex contains four somatosensory areas, each with its own map, with the primary cutaneous map in area 3b. Rodents have at least three parietal somatosensory areas. Maps are not isomorphic to the body surface, but magnify behaviorally important skin regions, which include the hands and face in primates, and the whiskers in rodents. Within each map, intracortical circuits process tactile information, mediate spatial integration, and support active sensation. Maps may also contain fine-scale representations of touch submodalities, or direction of tactile motion. Functional representations are more overlapping than suggested by textbook depictions of map topography. The whisker map in rodent somatosensory cortex is a canonic system for studying cortical microcircuits, sensory coding, and map plasticity. Somatosensory maps are plastic throughout life in response to altered use or injury. This chapter reviews basic principles and recent findings in primate, human, and rodent somatosensory maps.

Organization of sensory feature selectivity in the whisker system

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Neurons in the whisker system are selective to spatial and dynamical properties – features – of sensory stimuli.

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At each stage of the pathway, different neurons encode distinct features, generating a rich population representation.

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Whisker touch is robustly represented; neurons respond to touch-driven fast fluctuations in forces at the whisker base.

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Cortical neurons have more complex and context-dependent selectivity than subcortical, e.g., to collective whisker motion.

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Understanding how these signals are integrated to construct whisker-mediated percepts requires further research.

Our sensory receptors are faced with an onslaught of different environmental inputs. Each sensory event or encounter with an object involves a distinct combination of physical energy sources impinging upon receptors. In the rodent whisker system, each primary afferent neuron located in the trigeminal ganglion innervates and responds to a single whisker and encodes a distinct set of physical stimulus properties – features – corresponding to changes in whisker angle and shape and the consequent forces acting on the whisker follicle. Here we review the nature of the features encoded by successive stages of processing along the whisker pathway. At each stage different neurons respond to distinct features, such that the population as a whole represents diverse properties. Different neuronal types also have distinct feature selectivity. Thus, neurons at the same stage of processing and responding to the same whisker nevertheless play different roles in representing objects contacted by the whisker. This diversity, combined with the precise timing and high reliability of responses, enables populations at each stage to represent a wide range of stimuli. Cortical neurons respond to more complex stimulus properties – such as correlated motion across whiskers – than those at early subcortical stages. Temporal integration along the pathway is comparatively weak: neurons up to barrel cortex (BC) are sensitive mainly to fast (tens of milliseconds) fluctuations in whisker motion. The topographic organization of whisker sensitivity is paralleled by systematic organization of neuronal selectivity to certain other physical features, but selectivity to touch and to dynamic stimulus properties is distributed in “salt-and-pepper” fashion.

Familiarization: A theory of repetition suppression predicts interference between overlapping cortical representations

Repetition suppression refers to a reduction in the cortical response to a novel stimulus that results from repeated presentation of the stimulus. We demonstrate repetition suppression in a well established computational model of cortical plasticity, according to which the relative strengths of lateral inhibitory interactions are modified by Hebbian learning. We present the model as an extension to the traditional account of repetition suppression offered by sharpening theory, which emphasises the contribution of afferent plasticity, by instead attributing the effect primarily to plasticity of intra-cortical circuitry. In support, repetition suppression is shown to emerge in simulations with plasticity enabled only in intra-cortical connections. We show in simulation how an extended 'inhibitory sharpening theory' can explain the disruption of repetition suppression reported in studies that include an intermediate phase of exposure to additional novel stimuli composed of features similar to those of the original stimulus. The model suggests a re-interpretation of repetition suppression as a manifestation of the process by which an initially distributed representation of a novel object becomes a more localist representation. Thus, inhibitory sharpening may constitute a more general process by which representation emerges from cortical re-organisation.

A Global Orientation Map in the Primary Visual Cortex (V1): Could a Self Organizing Model Reveal Its Hidden Bias?

A remarkable accomplishment of self organizing models is their ability to simulate the development of feature maps in the cortex. Additionally, these models have been trained to tease out the differential causes of multiple feature maps, mapped on to the same output space. Recently, a Laterally Interconnected Synergetically Self Organizing Map (LISSOM) model has been used to simulate the mapping of eccentricity and meridional angle onto orthogonal axes in the primary visual cortex (V1). This model is further probed to simulate the development of the radial bias in V1, using a training set that consists of both radial (rectangular bars of random size and orientation) as well as non-radial stimuli. The radial bias describes the preference of the visual system toward orientations that match the angular position (meridional angle) of that orientation with respect to the point of fixation. Recent fMRI results have shown that there exists a coarse scale orientation map in V1, which resembles the meridional angle map, thereby providing a plausible neural basis for the radial bias. The LISSOM model, trained for the development of the retinotopic map, on probing for orientation preference, exhibits a coarse scale orientation map, consistent with these experimental results, quantified using the circular cross correlation (r_c ). The r_c between the orientation map developed on probing with a thin annular ring containing sinusoidal gratings with a spatial frequency of 0.5 cycles per degree (cpd) and the corresponding meridional map for the same annular ring, has a value of 0.8894. The results also suggest that the radial bias goes beyond the current understanding of a node to node correlation between the two maps.

Cortical Maps

In this article, we review functional organization in sensory cortical regions—how the cortex represents the world. We consider four interrelated aspects of cortical organization: (1) the set of receptive fields of individual cortical sensory neurons, (2) how lateral interaction between cortical neurons reflects the similarity of their receptive fields, (3) the spatial distribution of receptive-field properties across the horizontal extent of the cortical tissue, and (4) how the spatial distributions of different receptive-field properties interact with one another. We show how these data are generally well explained by the theory of input-driven self-organization, with a family of computational models of cortical maps offering a parsimonious account for a wide range of map-related phenomena. We then discuss important challenges to this explanation, with respect to the maps present at birth, maps present under activity blockade, the limits of adult plasticity, and the lack of some maps in rodents. Because there is not at present another credible general theory for cortical map development, we conclude by proposing key experiments to help uncover other mechanisms that might also be operating during map development.

Time-sensitive reorganization of the somatosensory cortex poststroke depends on interaction between Hebbian and homeoplasticity: a simulation study

Together with Hebbian plasticity, homeoplasticity presumably plays a significant, yet unclear, role in recovery postlesion. Here, we undertake a simulation study addressing the role of homeoplasticity and rehabilitation timing poststroke. We first hypothesize that homeoplasticity is essential for recovery and second that rehabilitation training delivered too early, before homeoplasticity has compensated for activity disturbances postlesion, is less effective for recovery than training delivered after a delay. We developed a neural network model of the sensory cortex driven by muscle spindle inputs arising from a six-muscle arm. All synapses underwent Hebbian plasticity, while homeoplasticity adjusted cell excitability to maintain a desired firing distribution. After initial training, the network was lesioned, leading to areas of hyper- and hypoactivity due to the loss of lateral synaptic connections. The network was then retrained through rehabilitative arm movements. We found that network recovery was unsuccessful in the absence of homeoplasticity, as measured by reestablishment of lesion-affected inputs. We also found that a delay preceding rehabilitation led to faster network recovery during the rehabilitation training than no delay. Our simulation results thus suggest that homeoplastic restoration of prelesion activity patterns is essential to functional network recovery via Hebbian plasticity.

Selectivity and sparseness in randomly connected balanced networks

Neurons in sensory cortex show stimulus selectivity and sparse population response, even in cases where no strong functionally specific structure in connectivity can be detected. This raises the question whether selectivity and sparseness can be generated and maintained in randomly connected networks. We consider a recurrent network of excitatory and inhibitory spiking neurons with random connectivity, driven by random projections from an input layer of stimulus selective neurons. In this architecture, the stimulus-to-stimulus and neuron-to-neuron modulation of total synaptic input is weak compared to the mean input. Surprisingly, we show that in the balanced state the network can still support high stimulus selectivity and sparse population response. In the balanced state, strong synapses amplify the variation in synaptic input and recurrent inhibition cancels the mean. Functional specificity in connectivity emerges due to the inhomogeneity caused by the generative statistical rule used to build the network. We further elucidate the mechanism behind and evaluate the effects of model parameters on population sparseness and stimulus selectivity. Network response to mixtures of stimuli is investigated. It is shown that a balanced state with unselective inhibition can be achieved with densely connected input to inhibitory population. Balanced networks exhibit the “paradoxical” effect: an increase in excitatory drive to inhibition leads to decreased inhibitory population firing rate. We compare and contrast selectivity and sparseness generated by the balanced network to randomly connected unbalanced networks. Finally, we discuss our results in light of experiments.

Emergence in the central nervous system

"Emergence" is an idea that has received much attention in consciousness literature, but it is difficult to find characterizations of that concept which are both specific and useful. I will precisely define and characterize a type of epistemic ("weak") emergence and show that it is a property of some neural circuits throughout the CNS, on micro-, meso- and macroscopic levels. I will argue that possession of this property can result in profoundly altered neural dynamics on multiple levels in cortex and other systems. I will first describe emergent neural entities (ENEs) abstractly. I will then show how ENEs function specifically and concretely, and demonstrate some implications of this type of emergence for the CNS.

Building a mechanistic model of the development and function of the primary visual cortex

Researchers have used a very wide range of different experimental and theoretical approaches to help understand mammalian visual systems. These approaches tend to have quite different assumptions, strengths, and weaknesses. Computational models of the visual cortex, in particular, have typically implemented either a proposed circuit for part of the visual cortex of the adult, assuming a very specific wiring pattern based on findings from adults, or else attempted to explain the long-term development of a visual cortex region from an initially undifferentiated starting point. Previous models of adult V1 have been able to account for many of the measured properties of V1 neurons, while not explaining how these properties arise or why neurons have those properties in particular. Previous developmental models have been able to reproduce the overall organization of specific feature maps in V1, such as orientation maps, but are generally formulated at an abstract level that does not allow testing with real images or analysis of detailed neural properties relevant for visual function. In this review of results from a large set of new, integrative models developed from shared principles and a set of shared software components, I show how these models now represent a single, consistent explanation for a wide body of experimental evidence, and form a compact hypothesis for much of the development and behavior of neurons in the visual cortex. The models are the first developmental models with wiring consistent with V1, the first to have realistic behavior with respect to visual contrast, and the first to include all of the demonstrated visual feature dimensions. The goal is to have a comprehensive explanation for why V1 is wired as it is in the adult, and how that circuitry leads to the observed behavior of the neurons during visual tasks.

Neural computation via neural geometry: a place code for inter-whisker timing in the barrel cortex?

The place theory proposed by Jeffress (1948) is still the dominant model of how the brain represents the movement of sensory stimuli between sensory receptors. According to the place theory, delays in signalling between neurons, dependent on the distances between them, compensate for time differences in the stimulation of sensory receptors. Hence the location of neurons, activated by the coincident arrival of multiple signals, reports the stimulus movement velocity. Despite its generality, most evidence for the place theory has been provided by studies of the auditory system of auditory specialists like the barn owl, but in the study of mammalian auditory systems the evidence is inconclusive. We ask to what extent the somatosensory systems of tactile specialists like rats and mice use distance dependent delays between neurons to compute the motion of tactile stimuli between the facial whiskers (or ‘vibrissae’). We present a model in which synaptic inputs evoked by whisker deflections arrive at neurons in layer 2/3 (L2/3) somatosensory ‘barrel’ cortex at different times. The timing of synaptic inputs to each neuron depends on its location relative to sources of input in layer 4 (L4) that represent stimulation of each whisker. Constrained by the geometry and timing of projections from L4 to L2/3, the model can account for a range of experimentally measured responses to two-whisker stimuli. Consistent with that data, responses of model neurons located between the barrels to paired stimulation of two whiskers are greater than the sum of the responses to either whisker input alone. The model predicts that for neurons located closer to either barrel these supralinear responses are tuned for longer inter-whisker stimulation intervals, yielding a topographic map for the inter-whisker deflection interval across the surface of L2/3. This map constitutes a neural place code for the relative timing of sensory stimuli.

To perceive how stimuli move over sensor surfaces like the retina or the fingertips, neurons in the brain must report the relative timing of signals arriving at different locations on the sensor surface. The rat whisker system is ideal for exploring how the brain performs this computation, because the layout of a small number of sensors (whiskers) maps directly onto the layout of corresponding columns of neurons in the sensory cortex. Previous studies have found that neurons located between adjacent cortical columns are most likely to respond when the corresponding adjacent whiskers are stimulated in rapid succession. These results suggest a link between the location of the neuron and the relative timing of sensory signals reported by its activity. We hypothesized that, if the time taken for whisker signals to arrive at a neuron is related to its distance from each cortical column, then neurons closer to a particular column will report stimuli moving towards that particular whisker. In a model approximating the geometry of cortical connections, responses of artificial neurons matched those of real neurons on a wide range of details. These results suggest an important role for neural geometry in neural computation.

Late emergence of the vibrissa direction selectivity map in the rat barrel cortex

In the neocortex, neuronal selectivities for multiple sensorimotor modalities are often distributed in topographical maps thought to emerge during a restricted period in early postnatal development. Rodent barrel cortex contains a somatotopic map for vibrissa identity, but the existence of maps representing other tactile features has not been clearly demonstrated. We addressed the issue of the existence in the rat cortex of an intrabarrel map for vibrissa movement direction using in vivo two-photon imaging. We discovered that the emergence of a direction map in rat barrel cortex occurs long after all known critical periods in the somatosensory system. This map is remarkably specific, taking a pinwheel-like form centered near the barrel center and aligned to the barrel cortex somatotopy. We suggest that this map may arise from intracortical mechanisms and demonstrate by simulation that the combination of spike-timing-dependent plasticity at synapses between layer 4 and layer 2/3 and realistic pad stimulation is sufficient to produce such a map. Its late emergence long after other classical maps suggests that experience-dependent map formation and refinement continue throughout adult life.

The pattern of retinoic acid receptor expression and subcellular, anatomic and functional area translocation during the postnatal development of the rat cerebral cortex and white matter

Retinoic acid (RA), which is an important modulator of brain development, neural cell proliferation, neurite outgrowth, and synaptic plasticity, is regulated via changes in RA receptors. The pattern of RA receptor changes in the rat cerebral cortex and white matter during postnatal development has not been extensively studied. Therefore, we studied the mRNA expression patterns of 6 RA receptors in the postnatal rat cerebral cortex and white matter at 1, 3, 7, 10, 14, 21, 28, and 35days. We found that RARβ, RXRα and RXRβ mRNA levels gradually increased during postnatal development. RARα presented a nearly unimodal trend, but RARγ and RXRγ were generally bimodal. RARα, RARγ, and RXRγ mRNA levels peaked at postnatal day 21 (P21). The pattern of RARα expression was consistent with that of its mRNA levels. RARα and RXRγ mRNA levels were the highest among those of all RA receptors during postnatal development. Interestingly, RARα expression was mainly located in the cytoplasm in the postnatal development apart from P3d. We further showed that RARα is expressed mainly in layers 2 and 3, partly in layers 1 and 4, and in a limited manner in layers 5 and 6 in the parietal cortex. Most RARα expression occurs in layers 2, 3, and 4 in the temporal lobe cortex. We realized that the M1 S2 region of RARα is highly expressed and that the position of RARα changes dynamically to meet the needs of different regions during development. These results support the idea that the RA receptor plays an important role in the cerebrum during postnatal development and implementation of these functions may be mainly dependent on the non-transcriptional or post- transcriptional regulation.