Two generic mechanisms for emergence of direction selectivity coexist in recurrent neural networks

Poster presentation: Twenty Second Annual Computational Neuroscience Meeting: CNS*2013. Paris, France. 13-18 July 2013. In the mammalian visual cortex, the time-averaged response of many neurons is maximal for stimuli moving in a particular direction. Such a direction selective response is not found in LGN, upstream of the visual processing pathway, suggesting that cortical networks play a strong role in the generation of direction selectivity. Here we investigate the mechanisms for the emergence of direction selectivity in the recurrent networks of nonlinear firing rate neurons in layer 4 of V1 receiving the input from LGN. In the model the LGN inputs are characterized by different receptive field positions, and their relative temporal phase shifts are reversed for the stimuli moving in the opposite direction. We propose that two distinct mechanisms result in the neuronal direction selective response in these recurrent networks. The first one is a result of nonlinear feed-forward summation of several time-shifted inputs. The second mechanism is based on the competition between neurons for firing in a winner-take-all regime. Both mechanisms rely on inhibitory interactions in the connectivity matrix of lateral connections, but the second one involves inhibitory loops. Typically, the first mechanism results in lower selectivity values than the second, but the time-course of acquiring direction selective response is faster for the first mechanism. Importantly, the two mechanisms have different input frequency tuning. The first mechanism, based on the nonlinear summation, result in a relatively narrow tuning curve around the preferred frequency of the stimulus in the case of the moving grating. In contrast, the direction selectivity arising from the second mechanism depends only weakly on the input frequency, i.e. has a broader tuning curve. These differences allow us to provide the recipe for identifying in experiment which of the two mechanisms is used by a given direction selective neuron. We then analyze how the statistics of the connections in the random recurrent networks affect the relative contributions from these two mechanisms and determine the distributions of the direction selectivity values. We identify the motifs in the connectivity matrix, which are required for each mechanism and show that the minimal conditions for both mechanisms are met in a very broad set of random recurrent networks with sufficiently strong inhibitory connections. Thus, we propose that these mechanisms coexist in generic recurrent networks with inhibition. Our results may account for the recent experimental observations that direction selectivity is present in dark-reared mice and ferrets [1,2]. It can also explain the emergence of direction selectivity in species lacking a spatially organized direction selectivity map

Optimal Axonal and Dendritic Branching Strategies During the Development of Neural Circuitry

In developing brain, axons and dendrites are capable of connecting to each other with high precision. Imaging of axonal and dendritic dynamics in vivo shows that the majority of axonal and dendritic branches are formed ‘in error’, only to be retracted later. The functional significance of the overproduction of branches is not clear. Here we show that branching of both axons and dendrites can accelerate finding appropriate synaptic targets during the development of neuronal circuitry. We suggest that branching rules implemented by axons and dendrites minimize the number of erroneous branches. We find that optimal branching rules are different for axons and dendrites in agreement with experimentally observed branch dynamics. Thus, our studies suggest that the developing neural system employs a set of sophisticated computational strategies that facilitate the formation of required circuitry in the fastest and most frugal way

Sperry versus Hebb: topographic mapping in Isl2/EphA3 mutant mice

BACKGROUND: In wild-type mice, axons of retinal ganglion cells establish topographically precise projection to the superior colliculus of the midbrain. This means that axons of neighboring retinal ganglion cells project to the proximal locations in the target. The precision of topographic projection is a result of combined effects of molecular labels, such as Eph receptors and ephrins, and correlated neural activity. In the Isl2/EphA3 mutant mice the expression levels of molecular labels are changed. As a result the topographic projection is rewired so that the neighborhood relationships between retinal cell axons are disrupted. RESULTS: Here we study the computational model for retinocollicular connectivity formation that combines the effects of molecular labels and correlated neural activity. We argue that the effects of correlated activity presenting themselves in the form of Hebbian learning rules can facilitate the restoration of the topographic connectivity even when the molecular labels carry conflicting instructions. This occurs because the correlations in electric activity carry information about retinal cells' origin that is independent on molecular labels. We argue therefore that partial restoration of the topographic property of the retinocollicular projection observed in Isl2/EphA3 heterozygous knockin mice may be explained by the effects of correlated neural activity. We address the maps observed in Isl2/EphA3 knockin/EphA4 knockout mice in which the levels of retinal labels are uniformly reduced. These maps can be explained by either the saturation of EphA receptor mapping leading to the relative signaling model or by the reverse signaling conveyed by ephrin-As expressed by retinal axons. CONCLUSION: According to our model, experiments in Isl2/EphA3 knock-in mice test the interactions between effects of molecular labels and correlated activity during the development of neural connectivity. Correlated activity can partially restore topographic order even when molecular labels carry conflicting information

A stochastic model for retinocollicular map development

We present a theoretical model for retinocollicular map development, which can account for intriguing behaviors observed in gain-of-function experiments in knock-in mice by Brown et al., including bifurcation in heterozygous Isl2/EphA3 knock-ins. The model is based on known chemical labels, axonal repulsion/competition, stochasticity and uses Markov chain description. Our model suggests that the map in heterozygotes is single-valued in the temporal region of retina due to reduced gradient of ephrin in the corresponding region of SC. The remaining map is double-valued since the gradient of ephrin is high there. We predict therefore that if gradient of ephrin is reduced by a genetic manipulation, the single-valued region of the map should occupy a larger portion of temporal retina, i.e. the point of transition between single- and doulble-valued maps should move to a more nasal position in Isl2-EphA3 heterozygotes. We also discuss the importance of inhomogeneous EphA gradient and mapping in Isl2/EphB knock-ins.Comment: 19 pages, 11 color figure