Beyond boundaries--Eph:ephrin signaling in neurogenesis.

Eph:ephrin signaling plays an important role in embryonic development as well as tissue homeostasis in the adult. At the cellular level, this transduction pathway is best known for its role in the control of cell adhesion and repulsion, cell migration and morphogenesis. Yet, a number of publications have also implicated Eph:ephrin signaling in the control of adult and embryonic neurogenesis. As is the case for other biological processes, these studies have reported conflicting and sometimes opposite roles for Eph:ephrin signaling in neurogenesis. Herein, we review these studies and we discuss existing mathematical models of stem cell dynamics and neurogenesis that provide a coherent framework and may help reconcile conflicting results.

Collective decision-making in white-faced capuchin monkeys.

In group-living animals, collective movements are a widespread phenomenon and occur through consensus decision. When one animal proposes a direction for group movement, the others decide to follow or not and hence take part in the decision-making process. This paper examines the temporal spread of individual responses after the departure of a first individual (the initiator) in a semi-free ranging group of white-faced capuchins (Cebus capucinus). We analysed 294 start attempts, 111 succeeding and 183 failing. Using a modelling approach, we have demonstrated that consensus decision-making for group movements is based on two complementary phenomena in this species: firstly, the joining together of group members thanks to a mimetic process; and secondly, a modulation of this phenomenon through the propensity of the initiator to give up (i.e. cancellation rate). This cancellation rate seems to be directly dependent upon the number of followers: the greater this number is, the lower the cancellation rate is seen to be. The coupling between joining and cancellation rates leads to a quorum: when three individuals join the initiator, the group collectively moves. If the initiator abandons the movement, this influences the joining behaviour of the other group members, which in return influences the initiator's behaviour. This study demonstrates the synergy between the initiator's behaviour and the self-organized mechanisms underlying group movements.

From individual to collective displacements in heterogeneous environments.

Animal displacement plays a central role in many ecological questions. It can be interpreted as a combination of components that only depend on the animal (for example a random walk) and external influences given by the heterogeneity of the environment. Here we treat the case where animals switch between random walks in a homogeneous 2D environment and its 1D boundary, combined with a tendency for wall-following behaviour (thigmotactism) that is treated as a Markovian process. In the first part we use mesoscopic techniques to derive from these assumptions a set of partial differential equations (PDE) with specific boundary conditions and parameters that are directly given by the individual displacement parameters. All assumptions and approximations made during this derivation are rigorously validated for the case of exploratory behaviour of the ant Messor sanctus. These PDE predict that the stationary density ratio between the 2D (centre) and 1D (border) environment only depends on the thigmotactic component, not on the size of the centre or border areas. In the second part we test this prediction with the same exploratory behaviour of M. sanctus, in particular when many ants move around simultaneously and may interact directly or indirectly. The prediction holds when there is a low degree of heterogeneity (simple square arena with straight borders), the collective behaviour is "simply" the sum of the individual behaviours. But this prediction breaks down when heterogeneity increases (obstacles inside the arena) due to the emergence of pheromone trails. Our approach may be applied to study the effects of animal displacement in any environment where the animals are confronted with an alternation of 2D space and 1D borders as for example in fragmented landscapes.

Rate coding versus temporal order coding: a theoretical approach.

The belief that neurones transmit information in the form of a firing rate code is almost universal. However, we argue that at least in some situations, the efficiency of a coding strategy based on rate coding is surprisingly poor. A simple mathematical analysis reveals that, due to the stochastic nature of spike generation, even transmitting the simplest signals reliably would require either: (1) excessively long observation periods incompatible with the speed of sensory processing or (2) excessively large numbers of redundant neurones, incompatible with the anatomical constraints imposed by sensory pathways. We argue that such problems may be avoided by using alternative temporal codes which rely on the asynchrony of firing across a population of afferent neurones.

Face processing using one spike per neurone.

The speed with which neurones in the monkey temporal lobe can respond selectively to the presence of a face implies that processing may be possible using only one spike per neurone, a finding that is problematic for conventional rate coding models that need at least two spikes to estimate interspike interval. One way of avoiding this problem uses the fact that integrate-and-fire neurones will tend to fire at different times, with the most strongly activated neurones firing first (Thorpe, 1990, Parallel Processing in Neural Systems). Under such conditions, processing can be performed by using the order in which cells in a particular layer fire as a code. To test this idea, we have explored a range of architectures using SpikeNET (Thorpe and Gautrais, 1997, Neural Information Processing Systems, 9), a simulator designed for modelling large populations of integrate-and-fire neurones. One such network used a simple four-layer feed-forward architecture to detect and localise the presence of human faces in natural images. Performance of the model was tested with a large range of grey-scale images of faces and other objects and was found to be remarkably good by comparison with more classic image processing techniques. The most remarkable feature of these results is that they were obtained using a purely feed-forward neural network in which none of the neurones fired more than one spike (thus ruling out conventional rate coding mechanisms). It thus appears that the combination of asynchronous spike propagation and rank order coding may provide an important key to understanding how the nervous system can achieve such a huge amount of processing in so little time.