A cooperation and competition based simple cell receptive field model and study of feed-forward linear and nonlinear contributions to orientation selectivity

We present a model for development of orientation selectivity in layer IV simple cells. Receptive field (RF) development in the model, is determined by diffusive cooperation and resource limited competition guided axonal growth and retraction in geniculocortical pathway. The simulated cortical RFs resemble experimental RFs. The receptive field model is incorporated in a three-layer visual pathway model consisting of retina, LGN and cortex. We have studied the effect of activity dependent synaptic scaling on orientation tuning of cortical cells. The mean value of hwhh (half width at half the height of maximum response) in simulated cortical cells is 58° when we consider only the linear excitatory contribution from LGN. We observe a mean improvement of 22.8° in tuning response due to the non-linear spiking mechanisms that include effects of threshold voltage and synaptic scaling factor.     

Correction of Distortion in Flattened Representations of the Cortical Surface Allows Prediction of V1-V3 Functional Organization from Anatomy

Several domains of neuroscience offer map-like models that link location on the cortical surface to properties of sensory representation. Within cortical visual areas V1, V2, and V3, algebraic transformations can relate position in the visual field to the retinotopic representation on the flattened cortical sheet. A limit to the practical application of this structure-function model is that the cortex, while topologically a two-dimensional surface, is curved. Flattening of the curved surface to a plane unavoidably introduces local geometric distortions that are not accounted for in idealized models. Here, we show that this limitation is overcome by correcting the geometric distortion induced by cortical flattening. We use a mass-spring-damper simulation to create a registration between functional MRI retinotopic mapping data of visual areas V1, V2, and V3 and an algebraic model of retinotopy. This registration is then applied to the flattened cortical surface anatomy to create an anatomical template that is linked to the algebraic retinotopic model. This registered cortical template can be used to accurately predict the location and retinotopic organization of these early visual areas from cortical anatomy alone. Moreover, we show that prediction accuracy remains when extrapolating beyond the range of data used to inform the model, indicating that the registration reflects the retinotopic organization of visual cortex. We provide code for the mass-spring-damper technique, which has general utility for the registration of cortical structure and function beyond the visual cortex.     

A computational model for the primate neocortex based on its functional architecture

Experimental evidence has shown that the primate neocortex consists in the main of a set of cortical regions which form a perception hierarchy, an action hierarchy and connections between them. By using a computer science analysis, we develop a computational architecture for the brain in which each cortical region is represented by a computational module with processing and storage abilities. Modules are interconnected according to the connectivity of the corresponding cortical regions. We develop computational principles for designing such a hierarchical and parallel computing system. We demonstrate this approach by proposing a causal functioning model of the brain. We report on results obtained with an implementation of this model. We conclude with a brief discussion of some consequences and predictions of our work.     

A semianalytical model to study the effect of cortical tension on cell rolling

Cell rolling on the vascular endothelium plays an important role in trafficking of leukocytes, stem cells, and cancer cells. We describe a semianalytical model of cell rolling that focuses on the microvillus as the unit of cell-substrate interaction and integrates microvillus mechanics, receptor clustering, force-dependent receptor-ligand kinetics, and cortical tension that enables incorporation of cell body deformation. Using parameters obtained from independent experiments, the model showed excellent agreement with experimental studies of neutrophil rolling on P-selectin and predicted different regimes of cell rolling, including spreading of the cells on the substrate under high shear. The cortical tension affected the cell-surface contact area and influenced the rolling velocity, and modulated the dependence of rolling velocity on microvillus stiffness. Moreover, at the same shear stress, microvilli of cells with higher cortical tension carried a greater load compared to those with lower cortical tension. We also used the model to obtain a scaling dependence of the contact radius and cell rolling velocity under different conditions of shear stress, cortical tension, and ligand density. This model advances theoretical understanding of cell rolling by incorporating cortical tension and microvillus extension into a versatile, semianalytical framework.     

Development of spatial coarse-to-fine processing in the visual pathway

The sequential analysis of information in a coarse-to-fine manner is a fundamental mode of processing in the visual pathway. Spatial frequency (SF) tuning, arguably the most fundamental feature of spatial vision, provides particular intuition within the coarse-to-fine framework: low spatial frequencies convey global information about an image (e.g., general orientation), while high spatial frequencies carry more detailed information (e.g., edges). In this paper, we study the development of cortical spatial frequency tuning. As feedforward input from the lateral geniculate nucleus (LGN) has been shown to have significant influence on cortical coarse-to-fine processing, we present a firing-rate based thalamocortical model which includes both feedforward and feedback components. We analyze the relationship between various model parameters (including cortical feedback strength) and responses. We confirm the importance of the antagonistic relationship between the center and surround responses in thalamic relay cell receptive fields (RFs), and further characterize how specific structural LGN RF parameters affect cortical coarse-to-fine processing. Our results also indicate that the effect of cortical feedback on spatial frequency tuning is age-dependent: in particular, cortical feedback more strongly affects coarse-to-fine processing in kittens than in adults. We use our results to propose an experimentally testable hypothesis for the function of the extensive feedback in the corticothalamic circuit.     

Towards a Mathematical Theory of Cortical Micro-circuits

The theoretical setting of hierarchical Bayesian inference is gaining acceptance as a framework for understanding cortical computation. In this paper, we describe how Bayesian belief propagation in a spatio-temporal hierarchical model, called Hierarchical Temporal Memory (HTM), can lead to a mathematical model for cortical circuits. An HTM node is abstracted using a coincidence detector and a mixture of Markov chains. Bayesian belief propagation equations for such an HTM node define a set of functional constraints for a neuronal implementation. Anatomical data provide a contrasting set of organizational constraints. The combination of these two constraints suggests a theoretically derived interpretation for many anatomical and physiological features and predicts several others. We describe the pattern recognition capabilities of HTM networks and demonstrate the application of the derived circuits for modeling the subjective contour effect. We also discuss how the theory and the circuit can be extended to explain cortical features that are not explained by the current model and describe testable predictions that can be derived from the model.     

Pathological cell-cell interactions elicited by a neuropathogenic form of mutant Huntingtin contribute to cortical pathogenesis in HD mice

Expanded polyglutamine (polyQ) proteins in Huntington's disease (HD) as well as other polyQ disorders are known to elicit a variety of intracellular toxicities, but it remains unclear whether polyQ proteins can elicit pathological cell-cell interactions which are critical to disease pathogenesis. To test this possibility, we have created conditional HD mice expressing a neuropathogenic form of mutant huntingtin (mhtt-exon1) in discrete neuronal populations. We show that mhtt aggregation is a cell-autonomous process. However, progressive motor deficits and cortical neuropathology are only observed when mhtt expression is in multiple neuronal types, including cortical interneurons, but not when mhtt expression is restricted to cortical pyramidal neurons. We further demonstrate an early deficit in cortical inhibition, suggesting that pathological interactions between interneurons and pyramidal neurons may contribute to the cortical manifestation of HD. Our study provides genetic evidence that pathological cell-cell interactions elicited by neuropathogenic forms of mhtt can critically contribute to cortical pathogenesis in a HD mouse model.     

Move it or lose it: axis specification in Xenopus

A long-standing question in developmental biology is how amphibians establish a dorsoventral axis. The prevailing view has been that cortical rotation is used to move a dorsalizing activity from the bottom of the egg towards the future dorsal side. We review recent evidence that kinesin-dependent movement of particles containing components of the Wnt intracellular pathway contributes to the formation of the dorsal organizer, and suggest that cortical rotation functions to align and orient microtubules, thereby establishing the direction of particle transport. We propose a new model in which active particle transport and cortical rotation cooperate to generate a robust movement of dorsal determinants towards the future dorsal side of the embryo.     

A neural field model of the somatosensory cortex: formation, maintenance and reorganization of ordered topographic maps

We investigate the formation and maintenance of ordered topographic maps in the primary somatosensory cortex as well as the reorganization of representations after sensory deprivation or cortical lesion. We consider both the critical period (postnatal) where representations are shaped and the post-critical period where representations are maintained and possibly reorganized. We hypothesize that feed-forward thalamocortical connections are an adequate site of plasticity while cortico-cortical connections are believed to drive a competitive mechanism that is critical for learning. We model a small skin patch located on the distal phalangeal surface of a digit as a set of 256 Merkel ending complexes (MEC) that feed a computational model of the primary somatosensory cortex (area 3b). This model is a two-dimensional neural field where spatially localized solutions (a.k.a. bumps) drive cortical plasticity through a Hebbian-like learning rule. Simulations explain the initial formation of ordered representations following repetitive and random stimulations of the skin patch. Skin lesions as well as cortical lesions are also studied and results confirm the possibility to reorganize representations using the same learning rule and depending on the type of the lesion. For severe lesions, the model suggests that cortico-cortical connections may play an important role in complete recovery.     

Dynamics of coupled thalamocortical modules

We develop a model of thalamocortical dynamics using a shared population of thalamic neurons to couple distant cortical regions. Behavior of the model is determined as a function of the connection strengths with shared and unshared populations in the thalamus, either within a relay nucleus or the reticular nucleus. When the coupling is via the reticular nucleus, we locate solutions of the model where distant cortical regions maintain the same activity level, and regions where one region maintains an elevated activity level, suppressing activity in the other. We locate and investigate a region where both types of solutions exist and are stable, yielding a mechanism for spontaneous changes in global activity patterns. Power spectra and coherence are computed, and marked differences in the coherence are found between the two kinds of modes. When, on the other hand, the coupling is via a shared relay nuclei, the features seen with the reticular coupling are absent. These considerations suggest a role for the reticular nucleus in modulating long distance cortical communication.     

Maximizing Sensory Dynamic Range by Tuning the Cortical State to Criticality

Modulation of interactions among neurons can manifest as dramatic changes in the state of population dynamics in cerebral cortex. How such transitions in cortical state impact the information processing performed by cortical circuits is not clear. Here we performed experiments and computational modeling to determine how somatosensory dynamic range depends on cortical state. We used microelectrode arrays to record ongoing and whisker stimulus-evoked population spiking activity in somatosensory cortex of urethane anesthetized rats. We observed a continuum of different cortical states; at one extreme population activity exhibited small scale variability and was weakly correlated, the other extreme had large scale fluctuations and strong correlations. In experiments, shifts along the continuum often occurred naturally, without direct manipulation. In addition, in both the experiment and the model we directly tuned the cortical state by manipulating inhibitory synaptic interactions. Our principal finding was that somatosensory dynamic range was maximized in a specific cortical state, called criticality, near the tipping point midway between the ends of the continuum. The optimal cortical state was uniquely characterized by scale-free ongoing population dynamics and moderate correlations, in line with theoretical predictions about criticality. However, to reproduce our experimental findings, we found that existing theory required modifications which account for activity-dependent depression. In conclusion, our experiments indicate that in vivo sensory dynamic range is maximized near criticality and our model revealed an unanticipated role for activity-dependent depression in this basic principle of cortical function.     

Dependence of V2 illusory contour response on V1 cell properties and topographic organization

An illusory contour is an image that is perceived as a contour in the absence of typical contour characteristics, such as a change in luminance or chromaticity across the stimulus. In cats and primates, cells that respond to illusory contours are sparse in cortical area V1, but are found in greater numbers in cortical area V2. We propose a model capable of illusory contour detection that is based on a realistic topographic organization of V1 cells, which reproduces the responses of individual cell types measured experimentally. The model allows us to explain several experimentally observed properties of V2 cells including variability in orientation tuning and inducer spacing preference. As a practical application, the model can be used to estimate the relationship between the severity of a cortical injury in the primary visual cortex and the deterioration of V2 cell responses to real and illusory contours.     

Cortical and cytoplasmic flow polarity in early embryonic cells of Caenorhabditis elegans

We have examined the cortex of Caenorhabditis elegans eggs during pseudocleavage (PC), a period of the first cell cycle which is important for the generation of asymmetry at first cleavage (Strome, S. 1989. Int. Rev. Cytol. 114: 81-123). We have found that directed, actin dependent, cytoplasmic, and cortical flow occurs during this period coincident with a rearrangement of the cortical actin cytoskeleton (Strome, S. 1986. J. Cell Biol. 103: 2241-2252). The flow velocity (4-7 microns/min) is similar to previously determined particle movements driven by cortical actin flows in motile cells. We show that directed flows occur in one of the daughters of the first division that itself divides asymmetrically, but not in its sister that divides symmetrically. The cortical and cytoplasmic events of PC can be mimicked in other cells during cytokinesis by displacing the mitotic apparatus with the microtubule polymerization inhibitor nocodazole. In all cases, the polarity of the resulting cortical and cytoplasmic flows correlates with the position of the attenuated mitotic spindle formed. These cortical flows are also accompanied by a change in the distribution of the cortical actin network. The polarity of this redistribution is similarly correlated with the location of the attenuated spindle. These observations suggest a mechanism for generating polarized flows of cytoplasmic and cortical material during embryonic cleavages. We present a model for the events of PC and suggest how the poles of the mitotic spindle mediate the formation of the contractile ring during cytokinesis in C. elegans.     

Multi-scale lines and edges in V1 and beyond: Brightness,object categorization and recognition,and consciousness

In this paper we present an improved model for line and edge detection in cortical area V1. This model is based on responses of simple and complex cells, and it is multi-scale with no free parameters. We illustrate the use of the multi-scale line/edge representation in different processes: visual reconstruction or brightness perception, automatic scale selection and object segregation. A two-level object categorization scenario is tested in which pre-categorization is based on coarse scales only and final categorization on coarse plus fine scales. We also present a multi-scale object and face recognition model. Processing schemes are discussed in the framework of a complete cortical architecture. The fact that brightness perception and object recognition may be based on the same symbolic image representation is an indication that the entire (visual) cortex is involved in consciousness.     

Modeling the establishment of PAR protein polarity in the one-cell C. elegans embryo

At the one-cell stage, the C. elegans embryo becomes polarized along the anterior-posterior axis. The PAR proteins form complementary anterior and posterior domains in a dynamic process driven by cytoskeletal rearrangement. Initially, the PAR proteins are uniformly distributed throughout the embryo. After a cue from fertilization, cortical actomyosin contracts toward the anterior pole. PAR-3/PAR-6/PKC-3 (the anterior PAR proteins) become restricted to the anterior cortex. PAR-1 and PAR-2 (the posterior PAR proteins) become enriched in the posterior cortical region. We present a mathematical model of this polarity establishment process, in which we take a novel approach to combine reaction-diffusion dynamics of the PAR proteins coupled to a simple model of actomyosin contraction. We show that known interactions between the PAR proteins are sufficient to explain many aspects of the observed cortical PAR dynamics in both wild-type and mutant embryos. However, cytoplasmic PAR protein polarity, which is vital for generating daughter cells with distinct molecular components, cannot be properly explained within such a framework. We therefore consider additional mechanisms that can reproduce the proper cytoplasmic polarity. In particular we predict that cytoskeletal asymmetry in the cytoplasm, in addition to the cortical actomyosin asymmetry, is a critical determinant of PAR protein localization.     

Dissociating ocular dominance column development and ocular dominance plasticity: a neurotrophic model

 Recent experimental data indicate that both neurotrophic factors (NTFs) and intracortical inhibitory circuitry are implicated in the development and plasticity of ocular dominance columns. We extend a neurotrophic model of developmental synaptic plasticity, which previously failed to account correctly for the differences between monocular deprivation and binocular deprivation, and show that the inclusion of lateral cortical inhibition is indeed necessary in understanding the effects of visual deprivation in the model. In particular, we argue that monocular deprivation causes a differential shift in the balance between inhibition and excitation in cortical columns, down-regulating NTFs in deprived-eye columns and up-regulating NTFs in undeprived-eye columns; during binocular deprivation, however, no such shift occurs. We thus postulate that the response to visual deprivation is at the level of the cortical circuit, while the mechanisms of afferent segregation are at the molecular or cellular level. Such a dissociation is supported by recent experimental work challenging the assumption that columnar organisation develops in an activity-dependent, competitive fashion. Our extended model also questions recent attempts to distinguish between heterosynaptic and homosynaptic models of synaptic plasticity. Received: 17 April 2001 / Accepted in revised form: 7 November 2001     

Sgt1 acts via an LKB1/AMPK pathway to establish cortical polarity in larval neuroblasts

Drosophila neuroblasts are a model system for studying stem cell self-renewal and the establishment of cortical polarity. Larval neuroblasts generate a large apical self-renewing neuroblast, and a small basal cell that differentiates. We performed a genetic screen to identify regulators of neuroblast self-renewal, and identified a mutation in sgt1 (suppressor-of-G2-allele-of-skp1) that had fewer neuroblasts. We found that sgt1 neuroblasts have two polarity phenotypes: failure to establish apical cortical polarity at prophase, and lack of cortical Scribble localization throughout the cell cycle. Apical cortical polarity was partially restored at metaphase by a microtubule-induced cortical polarity pathway. Double mutants lacking Sgt1 and Pins (a microtubule-induced polarity pathway component) resulted in neuroblasts without detectable cortical polarity and formation of "neuroblast tumors." Mutants in hsp83 (encoding the predicted Sgt1-binding protein Hsp90), LKB1, or AMPKα all show similar prophase apical cortical polarity defects (but no Scribble phenotype), and activated AMPKα rescued the sgt1 mutant phenotype. We propose that an Sgt1/Hsp90-LKB1-AMPK pathway acts redundantly with a microtubule-induced polarity pathway to generate neuroblast cortical polarity, and the absence of neuroblast cortical polarity can produce neuroblast tumors.     

Plasticity-Driven Self-Organization under Topological Constraints Accounts for Non-random Features of Cortical Synaptic Wiring

Understanding the structure and dynamics of cortical connectivity is vital to understanding cortical function. Experimental data strongly suggest that local recurrent connectivity in the cortex is significantly non-random, exhibiting, for example, above-chance bidirectionality and an overrepresentation of certain triangular motifs. Additional evidence suggests a significant distance dependency to connectivity over a local scale of a few hundred microns, and particular patterns of synaptic turnover dynamics, including a heavy-tailed distribution of synaptic efficacies, a power law distribution of synaptic lifetimes, and a tendency for stronger synapses to be more stable over time. Understanding how many of these non-random features simultaneously arise would provide valuable insights into the development and function of the cortex. While previous work has modeled some of the individual features of local cortical wiring, there is no model that begins to comprehensively account for all of them. We present a spiking network model of a rodent Layer 5 cortical slice which, via the interactions of a few simple biologically motivated intrinsic, synaptic, and structural plasticity mechanisms, qualitatively reproduces these non-random effects when combined with simple topological constraints. Our model suggests that mechanisms of self-organization arising from a small number of plasticity rules provide a parsimonious explanation for numerous experimentally observed non-random features of recurrent cortical wiring. Interestingly, similar mechanisms have been shown to endow recurrent networks with powerful learning abilities, suggesting that these mechanism are central to understanding both structure and function of cortical synaptic wiring.     

Generalized spin models for coupled cortical feature maps obtained by coarse graining correlation based synaptic learning rules

We derive generalized spin models for the development of feedforward cortical architecture from a Hebbian synaptic learning rule in a two layer neural network with nonlinear weight constraints. Our model takes into account the effects of lateral interactions in visual cortex combining local excitation and long range effective inhibition. Our approach allows the principled derivation of developmental rules for low-dimensional feature maps, starting from high-dimensional synaptic learning rules. We incorporate the effects of smooth nonlinear constraints on net synaptic weight projected from units in the thalamic layer (the fan-out) and on the net synaptic weight received by units in the cortical layer (the fan-in). These constraints naturally couple together multiple feature maps such as orientation preference and retinotopic organization. We give a detailed illustration of the method applied to the development of the orientation preference map as a special case, in addition to deriving a model for joint pattern formation in cortical maps of orientation preference, retinotopic location, and receptive field width. We show that the combination of Hebbian learning and center-surround cortical interaction naturally leads to an orientation map development model that is closely related to the XY magnetic lattice model from statistical physics. The results presented here provide justification for phenomenological models studied in Cowan and Friedman (Advances in neural information processing systems 3, 1991), Thomas and Cowan (Phys Rev Lett 92(18):e188101, 2004) and provide a developmental model realizing the synaptic weight constraints previously assumed in Thomas and Cowan (Math Med Biol 23(2):119–138, 2006).