How deeply does your mutant sleep? Probing arousal to better understand sleep defects in Drosophila.

The fruitfly, Drosophila melanogaster, has become a critical model system for investigating sleep functions. Most studies use duration of inactivity to measure sleep. However, a defining criterion for sleep is decreased behavioral responsiveness to stimuli. Here we introduce the Drosophila ARousal Tracking system (DART), an integrated platform for efficiently tracking and probing arousal levels in animals. This video-based platform delivers positional and locomotion data, behavioral responsiveness to stimuli, sleep intensity measures, and homeostatic regulation effects - all in one combined system. We show how insight into dynamically changing arousal thresholds is crucial for any sleep study in flies. We first find that arousal probing uncovers different sleep intensity profiles among related genetic background strains previously assumed to have equivalent sleep patterns. We then show how sleep duration and sleep intensity can be uncoupled, with distinct manipulations of dopamine function producing opposite effects on sleep duration but similar sleep intensity defects. We conclude by providing a multi-dimensional assessment of combined arousal and locomotion metrics in the mutant and background strains. Our approach opens the door for deeper insights into mechanisms of sleep regulation and provides a new method for investigating the role of different genetic manipulations in controlling sleep and arousal.

How receptor diffusion influences gradient sensing.

Chemotaxis, or directed motion in chemical gradients, is critical for various biological processes. Many eukaryotic cells perform spatial sensing, i.e. they detect gradients by comparing spatial differences in binding occupancy of chemosensory receptors across their membrane. In many theoretical models of spatial sensing, it is assumed, for the sake of simplicity, that the receptors concerned do not move. However, in reality, receptors undergo diverse modes of diffusion, and can traverse considerable distances in the time it takes such cells to turn in an external gradient. This sets a physical limit on the accuracy of spatial sensing, which we explore using a model in which receptors diffuse freely over the membrane. We find that the Fisher information carried in binding and unbinding events decreases monotonically with the diffusion constant of the receptors.

The influence of receptor positioning on chemotactic information.

Chemotaxis, or gradient following, is important in many biological systems, but suffers from noise. How receptors are positioned on the cell or sensing device influences the quality of the inferences they can support about the gradient, suggesting that their configuration might be optimised. We show that for an elliptical sensing device, inhomogeneous receptor placement could be a potential approach for cells to eliminate bias in the posterior distribution of the gradient direction. We use information theory to calculate the mutual information between the gradient and the binding pattern, thus finding the optimal receptor arrangement for gradient sensing.

Induction of epithelial-mesenchymal transition (EMT) in breast cancer cells is calcium signal dependent.

Signals from the tumor microenvironment trigger cancer cells to adopt an invasive phenotype through epithelial-mesenchymal transition (EMT). Relatively little is known regarding key signal transduction pathways that serve as cytosolic bridges between cell surface receptors and nuclear transcription factors to induce EMT. A better understanding of these early EMT events may identify potential targets for the control of metastasis. One rapid intracellular signaling pathway that has not yet been explored during EMT induction is calcium. Here we show that stimuli used to induce EMT produce a transient increase in cytosolic calcium levels in human breast cancer cells. Attenuation of the calcium signal by intracellular calcium chelation significantly reduced epidermal growth factor (EGF)- and hypoxia-induced EMT. Intracellular calcium chelation also inhibited EGF-induced activation of signal transducer and activator of transcription 3 (STAT3), while preserving other signal transduction pathways such as Akt and extracellular signal-regulated kinase 1/2 (ERK1/2) phosphorylation. To identify calcium-permeable channels that may regulate EMT induction in breast cancer cells, we performed a targeted siRNA-based screen. We found that transient receptor potential-melastatin-like 7 (TRPM7) channel expression regulated EGF-induced STAT3 phosphorylation and expression of the EMT marker vimentin. Although intracellular calcium chelation almost completely blocked the induction of many EMT markers, including vimentin, Twist and N-cadherin, the effect of TRPM7 silencing was specific for vimentin protein expression and STAT3 phosphorylation. These results indicate that TRPM7 is a partial regulator of EMT in breast cancer cells, and that other calcium-permeable ion channels are also involved in calcium-dependent EMT induction. In summary, this work establishes an important role for the intracellular calcium signal in the induction of EMT in human breast cancer cells. Manipulation of calcium-signaling pathways controlling EMT induction in cancer cells may therefore be an important therapeutic strategy for preventing metastases.

Generating controlled molecular gradients in 3D gels.

A new method for producing molecular gradients of arbitrary shape in thin three dimensional gels is described. Patterns are produced on the surface of the gel by printing with a micropump that dispenses small droplets of solution at controlled rates. The molecules in the solution rapidly diffuse into the gel and create a smooth concentration profile that is independent of depth. The pattern is relatively stable for long times, and its evolution can be accurately described by finite element modeling of the diffusion equation. As a demonstration of the method, direct measurements of protein gradients are performed by quantitative fluorescence microscopy. A complementary technique for measuring diffusion coefficients is also presented. This rapid, flexible, contactless approach to gradient generation is ideally suited for cell culture experiments to investigate the role of gradients of diffusible substances in processes such as chemotaxis, morphogenesis, and pattern formation, as well as for high-throughput screening of system responses to a wide range of chemical concentrations.

Auto-SOM: recursive parameter estimation for guidance of self-organizing feature maps.

An important technique for exploratory data analysis is to form a mapping from the high-dimensional data space to a low-dimensional representation space such that neighborhoods are preserved. A popular method for achieving this is Kohonen's self-organizing map (SOM) algorithm. However, in its original form, this requires the user to choose the values of several parameters heuristically to achieve good performance. Here we present the Auto-SOM, an algorithm that estimates the learning parameters during the training of SOMs automatically. The application of Auto-SOM provides the facility to avoid neighborhood violations up to a user-defined degree in either mapping direction. Auto-SOM consists of a Kalman filter implementation of the SOM coupled with a recursive parameter estimation method. The Kalman filter trains the neurons' weights with estimated learning coefficients so as to minimize the variance of the estimation error. The recursive parameter estimation method estimates the width of the neighborhood function by minimizing the prediction error variance of the Kalman filter. In addition, the "topographic function" is incorporated to measure neighborhood violations and prevent the map's converging to configurations with neighborhood violations. It is demonstrated that neighborhoods can be preserved in both mapping directions as desired for dimension-reducing applications. The development of neighborhood-preserving maps and their convergence behavior is demonstrated by three examples accounting for the basic applications of self-organizing feature maps.

Analysis of the elastic net model applied to the formation of ocular dominance and orientation columns.

The development and structure of orientation (OR) and ocular dominance (OD) maps in the primary visual cortex of cats and monkeys can be modelled using the elastic net algorithm, which attempts to find an 'optimal' cortical representation of the input features. Here we analyse this behaviour in terms of parameters of the feature space. We derive expressions for the OR periodicity, and the first bifurcation point as a function of the annealing parameter using the methods of Durbin et al (Durbin R, Szeliski R and Yuille A 1989 Neural Computation 1 348-58). We also investigate the effect of the relative order of OR and OD development on overall map structure. This analysis suggests that developmental order can be predicted from the final OR and OD periodicities. In conjunction with experimentally measured values for these periodicities, the model predicts that (i) in normal macaques OD develops first, (ii) in normal cats OR develops first and (iii) in strabismic cats OD develops first.

Retinotectal maps: molecules, models and misplaced data.

The mechanisms underlying the formation of topographic maps in the retinotectal system have long been debated. Recently, members of the Eph and ephrin receptor-ligand family have been found to provide a molecular substrate for one type of mechanism, that of chemospecific gradient matching, as proposed by Sperry. However, experiments over several decades have demonstrated that there is more to map formation than gradient matching. This article briefly reviews the old and new findings, argues that these two types of data must be properly integrated in order to understand map formation fully, and suggests some experimental and theoretical ways to begin this process.

Theoretical analysis of gradient detection by growth cones.

Gradients of diffusible and substrate-bound molecules play an important role in guiding axons to appropriate targets in the developing nervous system. Although some of the molecules involved have recently been identified, little is known about the physical mechanisms by which growth cones sense gradients. This article applies the seminal Berg and Purcell (1977) model of gradient sensing to this problem. The model provides estimates for the statistical fluctuations in the measurement of concentration by a small sensing device. By assuming that gradient detection consists of the comparison of concentrations at two spatially or temporally separated points, the model therefore provides an estimate for the steepness of gradient that can be detected as a function of physiological parameters. The model makes the following specific predictions. (a) It is more likely that growth cones use a spatial rather than temporal sensing strategy. (b) Growth cone sensitivity increases with the concentration of ligand, the speed of ligand diffusion, the size of the growth cone, and the time over which it averages the gradient signal. (c) The minimum detectable gradient steepness for growth cones is roughly in the range 1-10%. (d) This value varies depending on whether a bound or freely diffusing ligand is being sensed, and on whether the sensing occurs in three or two dimensions. The model also makes predictions concerning the role of filopodia in gradient detection.

The influence of neural activity and intracortical connectivity on the periodicity of ocular dominance stripes.

Several factors may interact to determine the periodicity of ocular dominance stripes in cat and monkey visual cortex. Previous theoretical work has suggested roles for the width of cortical interactions and the strength of between-eye correlations. Here, a model based on an explicit optimization is presented that allows a thorough characterization of how these and other parameters of the afferent input could affect ocular dominance stripe periodicity. The principle conclusions are that increasing the width of within-eye correlations leads to wider columns, and, surprisingly, that increasing the width of cortical interactions can sometimes lead to narrower columns.

Mathematical guidance for axons.

Axon guidance by gradients plays an important role in wiring up the developing nervous system. Growth cones seem to sense a concentration difference across their spatial extent, and convert this into a signal to move up or down a gradient. In this article, a simple mathematical framework is developed to understand when and where gradient detection can occur as a function of gradient shape. This framework is applied to two examples:the guidance of axons by target-derived diffusible factors in vivo and in collagen gels, and guidance by substrate-bound gradients of optimal shape, as might be relevant in the retinotectal system.Two distinct spatial limits on guidance emerge: I mm for a target-derived diffusible gradient, and I cm for a substrate-bound gradient.

Axon guidance: stretching gradients to the limit.

Neuronal growth cones, the sensory-motile structures at the tips of developing axons, navigate to their targets over distances that can be many times greater than their diameter. They may accomplish this impressive task by following spatial gradients of axon guidance molecules in their environment (Bonhoeffer & Gierer, 1984; Tessier-Lavigne & Placzek, 1991; Baier & Bonhoeffer, 1994). We calculate the optimal shape of a gradient and the distance over which it can be detected by a growth cone for two competing mechanistic models of axon guidance. The results are surprisingly simple: Regardless of the mechanism, the maximum distance is about 1 cm. Since gradients and growth cones have coevolved, we suggest that the shape of the gradient in situ will predict the mechanism of gradient detection. In addition, we show that the experimentally determined dissociation constants for receptor-ligand complexes implicated in axon guidance are about optimal with respect to maximizing guidance distance. The relevance of these results to the retinotectal system is discussed.

Diffusion in axon guidance.

Axon guidance by target-derived diffusible factors plays an important role in the development of the nervous system. This paper considers the constraints imposed on this process by the mathematics of diffusion. A point source continuously producing a factor into an infinite three-dimensional volume is considered as a model for both the in vivo and in vitro situation. Basic constraints for effective guidance are assumed to be that the concentration falls between certain maximum and minimum limits, and that the percentage change in concentration across the width of the growth cone exceeds a certain minimum value. The evolution of the shape of the gradient over time is analysed. Using biologically reasonable parameter values, it is shown that the maximum range over which growth cone guidance by a diffusible factor is possible for large times (several days) after the start of the production of the factor is 500-1000 microm. This maximum distance is independent of the diffusion constant of the diffusing molecule, applies to both chemoattractants and chemorepellents, and agrees with experimental data. At earlier times, however, the constraints may be satisfied for distances up to several millimetres. The time it takes for this maximum guidance distance to fall to the asymptotic value depends on the diffusion constant. This time is a few hours for a small molecule but as much as a few days for a large molecule. The model therefore predicts that guidance over distances larger than 1000 microm is possible if the start of production of the factor is carefully matched to the time when guidance is required.

Influences on the global structure of cortical maps.

Cortical maps often contain global spatial structure: however, theoretical accounts for their development have generally concentrated on reproducing only local structure. We show that the elastic net model of cortical map formation can closely approximate the global structure of the ocular dominance column map observed in macaque primary visual cortex. A key component is the assumption of spatially non-uniform and anisotropic correlations in the retina. This work shows how genetic and epigenetic effects could combine to establish characteristic global structure in cortical maps.

Theory meets experiment: correlated neural activity helps determine ocular dominance column periodicity.

The development of ocular dominance columns in primary visual cortex has attracted much interest from both experimentalists and theoreticians. One key parameter of these columns is their periodicity - it is thus important to understand how this is determined. Novel experimental work demonstrates that the periodicity is influenced by the temporal patterning of afferent activity, as predicted by recent theoretical work.

An evaluation of the use of multidimensional scaling for understanding brain connectivity.

A large amount of data is now available about the pattern of connections between brain regions. Computational methods are increasingly relevant for uncovering structure in such datasets. There has been recent interest in the use of non-metric multidimensional scaling (NMDS) for such analysis. NMDS produces a spatial representation of the 'dissimilarities' between a number of entities. Normally, it is applied to data matrices containing a large number of levels of dissimilarity, whereas for brain connectivity data there is a very small number. We address the suitability of NMDS for this case. Systematic numerical studies are presented to evaluate the ability of this method to reconstruct known geometrical configurations from dissimilarity data processing few levels. In this case there is a strong bias for NMDS to produce annular configurations, whether or not such structure exists in the original data. For the case of a connectivity dataset derived from the primate cortical visual system, we demonstrate that great caution is needed in interpreting the resulting configuration. Application of an independent method that we developed also strongly suggests that the visual system NMDS configuration is affected by an annular bias. We question the strength of support that an NMDS analysis of the visual system data provides for the two streams view of visual processing.

Topography and ocular dominance: a model exploring positive correlations.

The map from eye to brain in vertebrates is topographic, i.e., neighbouring points in the eye map to neighbouring points in the brain. In addition, when two eyes innervate the same target structure, the two sets of fibres segregate to form ocular dominance stripes. Experimental evidence from the frog and goldfish suggests that these two phenomena may be subserved by the same mechanisms. We present a computational model that addresses the formation of both topography and ocular dominance. The model is based on a form of competitive learning with subtractive enforcement of a weight normalization rule. Inputs to the model are distributed patterns of activity presented simultaneously in both eyes. An important aspect of this model is that ocular dominance segregation can occur when the two eyes are positively correlated, whereas previous models have tended to assume zero or negative correlations between the eyes. This allows investigation of the dependence of the pattern of stripes on the degree of correlation between the eyes: we find that increasing correlation leads to narrower stripes. Experiments are suggested to test this prediction.