What, if anything, are topological maps for?

Self-organization of modular activity in immature cortical networks

During development, cortical activity is organized into distributed modular patterns that are a precursor of the mature columnar functional architecture. Theoretically, such structured neural activity can emerge dynamically from local synaptic interactions through a recurrent network with effective local excitation with lateral inhibition (LE/LI) connectivity. Utilizing simultaneous widefield calcium imaging and optogenetics in juvenile ferret cortex prior to eye opening, we directly test several critical predictions of an LE/LI mechanism. We show that cortical networks transform uniform stimulations into diverse modular patterns exhibiting a characteristic spatial wavelength. Moreover, patterned optogenetic stimulation matching this wavelength selectively biases evoked activity patterns, while stimulation with varying wavelengths transforms activity towards this characteristic wavelength, revealing a dynamic compromise between input drive and the network's intrinsic tendency to organize activity. Furthermore, the structure of early spontaneous cortical activity - which is reflected in the developing representations of visual orientation - strongly overlaps that of uniform opto-evoked activity, suggesting a common underlying mechanism as a basis for the formation of orderly columnar maps underlying sensory representations in the brain.

Self-organization of modular activity in immature cortical networks

During development, cortical activity is organized into distributed modular patterns that are a precursor of the mature columnar functional architecture. Theoretically, such structured neural activity can emerge dynamically from local synaptic interactions through a recurrent network with effective local excitation with lateral inhibition (LE/LI) connectivity. Utilizing simultaneous widefield calcium imaging and optogenetics in juvenile ferret cortex prior to eye opening, we directly test several critical predictions of an LE/LI mechanism. We show that cortical networks transform uniform stimulations into diverse modular patterns exhibiting a characteristic spatial wavelength. Moreover, patterned optogenetic stimulation matching this wavelength selectively biases evoked activity patterns, while stimulation with varying wavelengths transforms activity towards this characteristic wavelength, revealing a dynamic compromise between input drive and the network's intrinsic tendency to organize activity. Furthermore, the structure of early spontaneous cortical activity - which is reflected in the developing representations of visual orientation - strongly overlaps that of uniform opto-evoked activity, suggesting a common underlying mechanism as a basis for the formation of orderly columnar maps underlying sensory representations in the brain.

A Guide for the Multiplexed: The Development of Visual Feature Maps in the Brain

Neural maps are found ubiquitously in the brain, where they encode a wide range of behaviourally relevant features into neural space. Developmental studies have shown that animals devote a great deal of resources to establish consistently patterned organization in neural circuits throughout the nervous system, but what purposes maps serve beneath their often intricate appearance and composition is a topic of active debate and exploration. In this article, we review the general mechanisms of map formation, with a focus on the visual system, and then survey notable organizational properties of neural maps: the multiplexing of feature representations through a nested architecture, the interspersing of fine-scale heterogeneity within a globally smooth organization, and the complex integration at the microcircuit level that enables a high dimensionality of information encoding. Finally, we discuss the roles of maps in cortical functions, including input segregation, feature extraction and routing of circuit outputs for higher order processing, as well as the evolutionary basis for the properties we observe in neural maps.

Pooling strategies in V1 can account for the functional and structural diversity across species

Neurons in the primary visual cortex are selective to orientation with various degrees of selectivity to the spatial phase, from high selectivity in simple cells to low selectivity in complex cells. Various computational models have suggested a possible link between the presence of phase invariant cells and the existence of orientation maps in higher mammals’ V1. These models, however, do not explain the emergence of complex cells in animals that do not show orientation maps. In this study, we build a theoretical model based on a convolutional network called Sparse Deep Predictive Coding (SDPC) and show that a single computational mechanism, pooling, allows the SDPC model to account for the emergence in V1 of complex cells with or without that of orientation maps, as observed in distinct species of mammals. In particular, we observed that pooling in the feature space is directly related to the orientation map formation while pooling in the retinotopic space is responsible for the emergence of a complex cells population. Introducing different forms of pooling in a predictive model of early visual processing as implemented in SDPC can therefore be viewed as a theoretical framework that explains the diversity of structural and functional phenomena observed in V1.

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.

Topographic map formation and the effects of NMDA receptor blockade in the developing visual system

Studying the emergence of topographic organization in sensory maps has been constrained by spatial limitations of traditional anatomical and physiological techniques early in development in many animal models. Here, we have applied a high-resolution, noninvasive, in vivo calcium imaging approach to study the nascent retinotopic map in the larval Xenopus laevis retinotectal system. We performed longitudinal functional imaging of the three-dimensional organization of emerging retinotopic maps and assessed the effects of N-methyl-D-aspartate (NMDA) receptor blockade on map formation. Our results provide insights into early retinotopic map emergence and the role of NMDA receptors in the refinement of topographic gradients.

The development of functional topography in the developing brain follows a progression from initially coarse to more precisely organized maps. To examine the emergence of topographically organized maps in the retinotectal system, we performed longitudinal visual receptive field mapping by calcium imaging in the optic tectum of GCaMP6-expressing transgenic Xenopus laevis tadpoles. At stage 42, just 1 d after retinal axons arrived in the optic tectum, a clear retinotopic azimuth map was evident. Animals were imaged over the following week at stages 45 and 48, over which time the tectal neuropil nearly doubled in length and exhibited more precise retinotopic organization. By microinjecting GCaMP6s messenger ribonucleic acid (mRNA) into one blastomere of two-cell stage embryos, we acquired bilateral mosaic tadpoles with GCaMP6s expression in postsynaptic tectal neurons on one side of the animal and in retinal ganglion cell axons crossing to the tectum on the opposite side. Longitudinal observation of retinotopic map emergence revealed the presence of orderly representations of azimuth and elevation as early as stage 42, although presynaptic inputs exhibited relatively less topographic organization than the postsynaptic component for the azimuth axis. Retinotopic gradients in the tectum became smoother between stages 42 and 45. Blocking N-methyl-D-aspartate (NMDA) receptor conductance by rearing tadpoles in MK-801 did not prevent the emergence of retinotopic maps, but it produced more discontinuous topographic gradients and altered receptive field characteristics. These results provide evidence that current through NMDA receptors is dispensable for coarse topographic ordering of retinotectal inputs but does contribute to the fine-scale organization of the retinotectal projection.

Is the scalar property of interval timing preserved after hippocampus lesions?

Time perception is fundamental for decision-making, adaptation, and survival. In the peak-interval (PI) paradigm, one of the critical features of time perception is its scale invariance, i.e., the error in time estimation increases linearly with the to-be-timed interval. Brain lesions can profoundly alter time perception, but do they also change its scalar property? In particular, hippocampus (HPC) lesions affect the memory of the reinforced durations. Experiments found that ventral hippocampus (vHPC) lesions shift the perceived durations to longer values while dorsal hippocampus (dHPC) lesions produce opposite effects. Here we used our implementation of the Striatal Beat Frequency (SBFML) model with biophysically realistic Morris-Lecar (ML) model neurons and a topological map of HPC memory to predict analytically and verify numerically the effect of HPC lesions on scalar property. We found that scalar property still holds after both vHPC and dHPC lesions in our SBFML-HPC network simulation. Our numerical results show that PI durations are shifted in the correct direction and match the experimental results. In our simulations, the relative peak shift of the behavioral response curve is controlled by two factors: (1) the lesion size, and (2) the cellular-level memory variance of the temporal durations stored in the HPC. The coefficient of variance (CV) of the behavioral response curve remained constant over the tested durations of PI procedure, which suggests that scalar property is not affected by HPC lesions.

Peeling the Onion of Brain Representations

The brain's function is to enable adaptive behavior in the world. To this end, the brain processes information about the world. The concept of representation links the information processed by the brain back to the world and enables us to understand what the brain does at a functional level. The appeal of making the connection between brain activity and what it represents has been irresistible to neuroscience, despite the fact that representational interpretations pose several challenges: We must define which aspects of brain activity matter, how the code works, and how it supports computations that contribute to adaptive behavior. It has been suggested that we might drop representational language altogether and seek to understand the brain, more simply, as a dynamical system. In this review, we argue that the concept of representation provides a useful link between dynamics and computational function and ask which aspects of brain activity should be analyzed to achieve a representational understanding. We peel the onion of brain representations in search of the layers (the aspects of brain activity) that matter to computation. The article provides an introduction to the motivation and mathematics of representational models, a critical discussion of their assumptions and limitations, and a preview of future directions in this area.

Macroscopic information-based taste representations in insular cortex are shaped by stimulus concentration

Taste processing is an essential ability in all animals signaling potential harm or benefit of ingestive behavior. However, current evidence for cortical taste representations remains contradictory. To address this issue, high-resolution functional MRI (fMRI) and multivariate pattern analysis were used to characterize taste-related informational content in human insular cortex, which contains primary gustatory cortex. Human participants judged pleasantness and intensity of low- and high-concentration tastes (salty, sweet, sour, and bitter) in two fMRI experiments on two different days to test for task- and concentration-invariant taste representations. We observed patterns of fMRI activity within insular cortex narrowly tuned to specific tastants consistently across tasks in all participants. Fewer patterns responded to more than one taste category. Importantly, changes in taste concentration altered the spatial layout of putative taste-specific patterns with distinct, almost nonoverlapping patterns for each taste category at different concentration levels. Together, our results point at macroscopic representations in human insular cortex as a complex function of taste category and concentration rather than representations based solely on taste identity.

Limit cycle dynamics can guide the evolution of gene regulatory networks towards point attractors

Developmental dynamics in Boolean models of gene networks self-organize, either into point attractors (stable repeating patterns of gene expression) or limit cycles (stable repeating sequences of patterns), depending on the network interactions specified by a genome of evolvable bits. Genome specifications for dynamics that can map specific gene expression patterns in early development onto specific point attractor patterns in later development are essentially impossible to discover by chance mutation alone, even for small networks. We show that selection for approximate mappings, dynamically maintained in the states comprising limit cycles, can accelerate evolution by at least an order of magnitude. These results suggest that self-organizing dynamics that occur within lifetimes can, in principle, guide natural selection across lifetimes.

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.

Topographic Independent Component Analysis reveals random scrambling of orientation in visual space

Neurons at primary visual cortex (V1) in humans and other species are edge filters organized in orientation maps. In these maps, neurons with similar orientation preference are clustered together in iso-orientation domains. These maps have two fundamental properties: (1) retinotopy, i.e. correspondence between displacements at the image space and displacements at the cortical surface, and (2) a trade-off between good coverage of the visual field with all orientations and continuity of iso-orientation domains in the cortical space. There is an active debate on the origin of these locally continuous maps. While most of the existing descriptions take purely geometric/mechanistic approaches which disregard the network function, a clear exception to this trend in the literature is the original approach of Hyvärinen and Hoyer based on infomax and Topographic Independent Component Analysis (TICA). Although TICA successfully addresses a number of other properties of V1 simple and complex cells, in this work we question the validity of the orientation maps obtained from TICA. We argue that the maps predicted by TICA can be analyzed in the retinal space, and when doing so, it is apparent that they lack the required continuity and retinotopy. Here we show that in the orientation maps reported in the TICA literature it is easy to find examples of violation of the continuity between similarly tuned mechanisms in the retinal space, which suggest a random scrambling incompatible with the maps in primates. The new experiments in the retinal space presented here confirm this guess: TICA basis vectors actually follow a random salt-and-pepper organization back in the image space. Therefore, the interesting clusters found in the TICA topology cannot be interpreted as the actual cortical orientation maps found in cats, primates or humans. In conclusion, Topographic ICA does not reproduce cortical orientation maps.

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.

Functional implications of orientation maps in primary visual cortex

Stimulus orientation in the primary visual cortex of primates and carnivores is mapped as iso-orientation domains radiating from pinwheel centres, where orientation preferences of neighbouring cells change circularly. Whether this orientation map has a function is currently debated, because many mammals, such as rodents, do not have such maps. Here we show that two fundamental properties of visual cortical responses, contrast saturation and cross-orientation suppression, are stronger within cat iso-orientation domains than at pinwheel centres. These differences develop when excitation (not normalization) from neighbouring oriented neurons is applied to different cortical orientation domains and then balanced by inhibition from un-oriented neurons. The functions of the pinwheel mosaic emerge from these local intra-cortical computations: Narrower tuning, greater cross-orientation suppression and higher contrast gain of iso-orientation cells facilitate extraction of object contours from images, whereas broader tuning, greater linearity and less suppression of pinwheel cells generate selectivity for surface patterns and textures.

Stimulus orientation in the primary visual cortex of primates and carnivores is mapped into a geometrical mosaic but the functional implications of these maps remain debated. Here the authors reveal an association between the structure of cortical orientation maps in cats, and the functions of local cortical circuits in processing patterns and contours.

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.