Geoffrey J. Goodhill

A new chemotaxis assay shows the extreme sensitivity of axons to molecular gradients

Axonal chemotaxis is believed to be important in wiring up the developing and regenerating nervous system, but little is known about how axons actually respond to molecular gradients. We report a new quantitative assay that allows the long-term response of axons to gradients of known and controllable shape to be examined in a three-dimensional gel. Using this assay, we show that axons may be natures most-sensitive gradient detectors, but this sensitivity exists only within a narrow range of ligand concentrations. This assay should also be applicable to other biological processes that are controlled by molecular gradients, such as cell migration and morphogenesis.

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.

Growth cone chemotaxis

Wiring up the nervous system depends on the precise guidance of axonal growth cones to their targets. A key mechanism underlying this guidance is chemotaxis, whereby growth cones detect and follow molecular gradients. Although recent work has uncovered many of the molecules involved in this process, the mechanisms underlying chemotactic axon guidance are still unclear. Here we compare growth cones with neutrophils and Dictyostelium discoideum, systems for which a clear conceptual framework for chemotaxis has recently emerged. This analogy suggests particular ways in which the three key steps of directional sensing, polarisation and motility might be implemented in chemotaxing growth cones.

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.

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.

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 μm. 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 μm is possible if the start of production of the factor is carefully matched to the time when guidance is required.

A Bayesian model predicts the response of axons to molecular gradients

Axon guidance by molecular gradients plays a crucial role in wiring up the nervous system. However, the mechanisms axons use to detect gradients are largely unknown. We first develop a Bayesian “ideal observer” analysis of gradient detection by axons, based on the hypothesis that a principal constraint on gradient detection is intrinsic receptor binding noise. Second, from this model, we derive an equation predicting how the degree of response of an axon to a gradient should vary with gradient steepness and absolute concentration. Third, we confirm this prediction quantitatively by performing the first systematic experimental analysis of how axonal response varies with both these quantities. These experiments demonstrate a degree of sensitivity much higher than previously reported for any chemotacting system. Together, these results reveal both the quantitative constraints that must be satisfied for effective axonal guidance and the computational principles that may be used by the underlying signal transduction pathways, and allow predictions for the degree of response of axons to gradients in a wide variety of in vivo and in vitro settings.

Application of the elastic net algorithm to the formation of ocular dominance stripes

The elastic net algorithm, an iterative technique for the solution of combinatorial optimisation problems that have a geometric interpretation, was applied to the problem of explaining the development of ocular dominance stripes in the vertebrate visual system. Simulations show that this algorithm produces stripes under certain conditions. Analysis is presented that predicts the moment at which stripes form and an expression is derived for how stripe width depends on the parameters of the system. In contrast to most other models for stripe formation, the elastic net algorithm provides a common explanatory framework for the development of stripes and of retinotopically ordered projections.

A unifying objective function for topographic mappings

Many different algorithms and objective functions for topographic mappings have been proposed. We show that several of these approaches can be seen as particular cases of a more general objective function. Consideration of a very simple mapping problem reveals large differences in the form of the map that each particular case favors. These differences have important consequences for the practical application of topographic mapping methods.

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.