A neurotrophic model of the development of the retinogeniculocortical pathway induced by spontaneous retinal waves

Computational benefits of structural plasticity, illustrated in songbirds

The plasticity of nervous systems allows animals to quickly adapt to a changing environment. In particular, the structural plasticity of brain networks is often critical to the development of the central nervous system and the acquisition of complex behaviors. As an example, structural plasticity is central to the development of song-related brain circuits and may be critical for song acquisition in juvenile songbirds. Here, we review current evidences for structural plasticity and their significance from a computational point of view. We start by reviewing evidence for structural plasticity across species and categorizing them along the spatial axes as well as the along the time course during development. We introduce the vocal learning circuitry in zebra finches, as a useful example of structural plasticity, and use this specific case to explore the possible contributions of structural plasticity to computational models. Finally, we discuss current modeling studies incorporating structural plasticity and unexplored questions which are raised by such models.

Structural Plasticity on the SpiNNaker Many-Core Neuromorphic System

The structural organization of cortical areas is not random, with topographic maps commonplace in sensory processing centers. This topographical organization allows optimal wiring between neurons, multimodal sensory integration, and performs input dimensionality reduction. In this work, a model of topographic map formation is implemented on the SpiNNaker neuromorphic platform, running in realtime using point neurons, and making use of both synaptic rewiring and spike-timing dependent plasticity (STDP). In agreement with Bamford et al. (2010), we demonstrate that synaptic rewiring refines an initially rough topographic map over and beyond the ability of STDP, and that input selectivity learnt through STDP is embedded into the network connectivity through rewiring. Moreover, we show the presented model can be used to generate topographic maps between layers of neurons with minimal initial connectivity, and stabilize mappings which would otherwise be unstable through the inclusion of lateral inhibition.

A proto-architecture for innate directionally selective visual maps

Self-organizing artificial neural networks are a popular tool for studying visual system development, in particular the cortical feature maps present in real systems that represent properties such as ocular dominance (OD), orientation-selectivity (OR) and direction selectivity (DS). They are also potentially useful in artificial systems, for example robotics, where the ability to extract and learn features from the environment in an unsupervised way is important. In this computational study we explore a DS map that is already latent in a simple artificial network. This latent selectivity arises purely from the cortical architecture without any explicit coding for DS and prior to any self-organising process facilitated by spontaneous activity or training. We find DS maps with local patchy regions that exhibit features similar to maps derived experimentally and from previous modeling studies. We explore the consequences of changes to the afferent and lateral connectivity to establish the key features of this proto-architecture that support DS.

An adaptive neuromorphic model of ocular dominance map using floating gate 'synapse'

A novel analogue CMOS design of a cortical cell, that computes weighted sum of inputs, is presented. The cell's feedback regime exploits the adaptation dynamics of floating gate pFET 'synapse' to perform competitive learning amongst input weights as time-staggered winner take all. A learning rate parameter regulates adaptation time and a bias enforces resource limitation by restricting the number of input branches and winners in a competition. When learning ends, the cell's response favours one input pattern over others to exhibit feature selectivity. Embedded in a 2-D RC grid, these feature selective cells are capable of performing a symmetry breaking pattern formation, observed in some reaction-diffusion models of cortical feature map formation, e.g. ocular dominance. Close similarity with biological networks in terms of adaptability and long term memory indicates that the cell's design is ideally suited for analogue VLSI implementation of Self-Organizing Feature Map (SOFM) models of cortical feature maps.

Neural 'Bubble' Dynamics Revisited

In this paper, we revisit the work of John G Taylor on neural ‘bubble’ dynamics in two-dimensional neural field models. This builds on original work of Amari in a one-dimensional setting and makes use of the fact that mathematical treatments are much simpler when the firing rate function is chosen to be a Heaviside. In this case, the dynamics of an excited or active region, defining a ‘bubble’, reduce to the dynamics of the boundary. The focus of John’s work was on the properties of radially symmetric ‘bubbles’, including existence and radial stability, with applications to the theory of topographic map formation in self-organising neural networks. As well as reviewing John’s work in this area, we also include some recent results that treat more general classes of perturbations.

From retinal waves to activity-dependent retinogeniculate map development

A neural model is described of how spontaneous retinal waves are formed in infant mammals, and how these waves organize activity-dependent development of a topographic map in the lateral geniculate nucleus, with connections from each eye segregated into separate anatomical layers. The model simulates the spontaneous behavior of starburst amacrine cells and retinal ganglion cells during the production of retinal waves during the first few weeks of mammalian postnatal development. It proposes how excitatory and inhibitory mechanisms within individual cells, such as Ca(2+)-activated K(+) channels, and cAMP currents and signaling cascades, can modulate the spatiotemporal dynamics of waves, notably by controlling the after-hyperpolarization currents of starburst amacrine cells. Given the critical role of the geniculate map in the development of visual cortex, these results provide a foundation for analyzing the temporal dynamics whereby the visual cortex itself develops.

Modeling developmental patterns of spontaneous activity

Spontaneous activity is found in many regions of the developing nervous system; such activity is thought to be instructive for guiding developmental processes. In particular, the developing retina generates correlated patterns of activity known as retinal waves. We review the main theoretical models that have been developed to study the mechanisms for generation and propagation of retinal waves. Much of the progress in this field has been due to the close interaction between experimentalists and theorists in analyzing and modeling spontaneous activity. We conclude by describing spontaneous activity models in other systems and suggestions for future modeling work.

Emergence of network structure due to spike-timing-dependent plasticity in recurrent neuronal networks V: self-organization schemes and weight dependence

Spike-timing-dependent plasticity (STDP) determines the evolution of the synaptic weights according to their pre- and post-synaptic activity, which in turn changes the neuronal activity on a (much) slower time scale. This paper examines the effect of STDP in a recurrently connected network stimulated by external pools of input spike trains, where both input and recurrent synapses are plastic. Our previously developed theoretical framework is extended to incorporate weight-dependent STDP and dendritic delays. The weight dynamics is determined by an interplay between the neuronal activation mechanisms, the input spike-time correlations, and the learning parameters. For the case of two external input pools, the resulting learning scheme can exhibit a symmetry breaking of the input connections such that two neuronal groups emerge, each specialized to one input pool only. In addition, we show how the recurrent connections within each neuronal group can be strengthened by STDP at the expense of those between the two groups. This neuronal self-organization can be seen as a basic dynamical ingredient for the emergence of neuronal maps induced by activity-dependent plasticity.

Large developing receptive fields using a distributed and locally reprogrammable address-event receiver

A distributed and locally reprogrammable address-event receiver has been designed, in which incoming address-events are monitored simultaneously by all synapses, allowing for arbitrarily large axonal fan-out without reducing channel capacity. Synapses can change the address of their presynaptic neuron, allowing the distributed implementation of a biologically realistic learning rule, with both synapse formation and elimination (synaptic rewiring). Probabilistic synapse formation leads to topographic map development, made possible by a cross-chip current-mode calculation of Euclidean distance. As well as synaptic plasticity in rewiring, synapses change weights using a competitive Hebbian learning rule (spike-timing-dependent plasticity). The weight plasticity allows receptive fields to be modified based on spatio-temporal correlations in the inputs, and the rewiring plasticity allows these modifications to become embedded in the network topology.

A multi-component model of the developing retinocollicular pathway incorporating axonal and synaptic growth

During development, neurons extend axons to different brain areas and produce stereotypical patterns of connections. The mechanisms underlying this process have been intensively studied in the visual system, where retinal neurons form retinotopic maps in the thalamus and superior colliculus. The mechanisms active in map formation include molecular guidance cues, trophic factor release, spontaneous neural activity, spike-timing dependent plasticity (STDP), synapse creation and retraction, and axon growth, branching and retraction. To investigate how these mechanisms interact, a multi-component model of the developing retinocollicular pathway was produced based on phenomenological approximations of each of these mechanisms. Core assumptions of the model were that the probabilities of axonal branching and synaptic growth are highest where the combined influences of chemoaffinity and trophic factor cues are highest, and that activity-dependent release of trophic factors acts to stabilize synapses. Based on these behaviors, model axons produced morphologically realistic growth patterns and projected to retinotopically correct locations in the colliculus. Findings of the model include that STDP, gradient detection by axonal growth cones and lateral connectivity among collicular neurons were not necessary for refinement, and that the instructive cues for axonal growth appear to be mediated first by molecular guidance and then by neural activity. Although complex, the model appears to be insensitive to variations in how the component developmental mechanisms are implemented. Activity, molecular guidance and the growth and retraction of axons and synapses are common features of neural development, and the findings of this study may have relevance beyond organization in the retinocollicular pathway.

Neural development is a process that involves a wide range of behaviors. As a result of these behaviors, neurons are able to extend axons to different brain areas and produce stereotypical patterns of innervation. One of the most commonly studied of these projections is in the visual system, where retinal axons project to multiple brain regions and produce retinotopic maps. This study examines the relative roles and interactions of different neural mechanisms in guiding axon growth and generating retinotopic order. We did this by producing a computational model of retinotopic development that represented many of the neural mechanisms thought to be involved, including axon and synapse growth, molecular guidance and synapse plasticity. Our results suggest that synaptic plasticity is realized by variation in the number of synapses between neurons, not through alteration of individual synaptic weights; that lateral connectivity between collicular neurons is not required for organization; and that axon arbor development does not require the gradient tracking abilities of growth cones. The mechanisms underlying neuronal development in the visual system are also observed in many other brain areas, so the findings here should apply more generally.

Theoretical models of spontaneous activity generation and propagation in the developing retina

Spontaneous neural activity is present in many parts of the developing nervous system, including visual, auditory and motor areas. In the developing retina, nearby neurons are spontaneously active and produce propagating patterns of activity, known as retinal waves. Such activity is thought to instruct the refinement of retinal axons. In this article we review several computational models used to help evaluate the mechanisms that might be responsible for the generation of retinal waves. We then discuss the models relative to the molecular mechanisms underlying wave activity, including gap junctions, neurotransmitters and second messenger systems. We examine how well the models represent these mechanisms and propose areas for future modelling research. The retinal wave models are also discussed in relation to models of spontaneous activity in other areas of the developing nervous system.

Emergence of network structure due to spike-timing-dependent plasticity in recurrent neuronal networks. II. Input selectivity--symmetry breaking

Spike-timing-dependent plasticity (STDP) is believed to structure neuronal networks by slowly changing the strengths (or weights) of the synaptic connections between neurons depending upon their spiking activity, which in turn modifies the neuronal firing dynamics. In this paper, we investigate the change in synaptic weights induced by STDP in a recurrently connected network in which the input weights are plastic but the recurrent weights are fixed. The inputs are divided into two pools with identical constant firing rates and equal within-pool spike-time correlations, but with no between-pool correlations. Our analysis uses the Poisson neuron model in order to predict the evolution of the input synaptic weights and focuses on the asymptotic weight distribution that emerges due to STDP. The learning dynamics induces a symmetry breaking for the individual neurons, namely for sufficiently strong within-pool spike-time correlation each neuron specializes to one of the input pools. We show that the presence of fixed excitatory recurrent connections between neurons induces a group symmetry-breaking effect, in which neurons tend to specialize to the same input pool. Consequently STDP generates a functional structure on the input connections of the network.

How does non-random spontaneous activity contribute to brain development?

Highly non-random forms of spontaneous activity are proposed to play an instrumental role in the early development of the visual system. However, both the fundamental properties of spontaneous activity required to drive map formation, as well as the exact role of this information remain largely unknown. Here, a realistic computational model of spontaneous retinal waves is employed to demonstrate that both the amplitude and frequency of waves may play determining roles in retinocollicular map formation. Furthermore, results obtained with different learning rules show that spike precision in the order of milliseconds may be instrumental to neural development: a rule based on precise spike interactions (spike-timing-dependent plasticity) reduced the density of aberrant projections to the SC to a markedly greater extent than a rule based on interactions at much broader time-scale (correlation-based plasticity). Taken together, these results argue for an important role of spontaneous yet highly non-random activity, along with temporally precise learning rules, in the formation of neural circuits.

Getting to Know Your Neighbors: Unsupervised Learning of Topography from Real-World, Event-Based Input

Biological neural systems must grow their own connections and maintain topological relations between elements that are related to the sensory input surface. Artificial systems have traditionally prewired such maps, but the sensor arrangement is not always known and can be expensive to specify before run time. Here we present a method for learning and updating topographic maps in systems comprising modular, event-based elements. Using an unsupervised neural spike-timing-based learning rule combined with Hebbian learning, our algorithm uses the spatiotemporal coherence of the external world to train its network. It improves on existing algorithms by not assuming a known topography of the target map and includes a novel method for automatically detecting edge elements. We show how, for stimuli that are small relative to the sensor resolution, the temporal learning window parameters can be determined without using any user-specified constants. For stimuli that are larger relative to the sensor resolution, we provide a parameter extraction method that generally outperforms the small-stimulus method but requires one user-specified constant. The algorithm was tested on real data from a 64 × 64-pixel section of an event-based temporal contrast silicon retina and a 360-tile tactile luminous floor. It learned 95.8% of the correct neighborhood relations for the silicon retina within about 400 seconds of real-world input from a driving scene and 98.1% correct for the sensory floor after about 160 minutes of human pedestrian traffic. Residual errors occurred in regions receiving little or ambiguous input, and the learned topological representations were able to update automatically in response to simulated damage. Our algorithm has applications in the design of modular autonomous systems in which the interfaces between components are learned during operation rather than at design time.

Modeling brain dynamics using computational neurogenetic approach

The paper introduces a novel computational approach to brain dynamics modeling that integrates dynamic gene-protein regulatory networks with a neural network model. Interaction of genes and proteins in neurons affects the dynamics of the whole neural network. Through tuning the gene-protein interaction network and the initial gene/protein expression values, different states of the neural network dynamics can be achieved. A generic computational neurogenetic model is introduced that implements this approach. It is illustrated by means of a simple neurogenetic model of a spiking neural network of the generation of local field potential. Our approach allows for investigation of how deleted or mutated genes can alter the dynamics of a model neural network. We conclude with the proposal how to extend this approach to model cognitive neurodynamics.

Retinal wave behavior through activity-dependent refractory periods

In the developing mammalian visual system, spontaneous retinal ganglion cell (RGC) activity contributes to and drives several aspects of visual system organization. This spontaneous activity takes the form of spreading patches of synchronized bursting that slowly advance across portions of the retina. These patches are non-repeating and tile the retina in minutes. Several transmitter systems are known to be involved, but the basic mechanism underlying wave production is still not well-understood. We present a model for retinal waves that focuses on acetylcholine mediated waves but whose principles are adaptable to other developmental stages. Its assumptions are that a) spontaneous depolarizations of amacrine cells drive wave activity; b) amacrine cells are locally connected, and c) cells receiving more input during their depolarization are subsequently less responsive and have longer periods between spontaneous depolarizations. The resulting model produces waves with non-repeating borders and randomly distributed initiation points. The wave generation mechanism appears to be chaotic and does not require neural noise to produce this wave behavior. Variations in parameter settings allow the model to produce waves that are similar in size, frequency, and velocity to those observed in several species. Our results suggest that retinal wave behavior results from activity-dependent refractory periods and that the average velocity of retinal waves depends on the duration a cell is excitatory: longer periods of excitation result in slower waves. In contrast to previous studies, we find that a single layer of cells is sufficient for wave generation. The principles described here are very general and may be adaptable to the description of spontaneous wave activity in other areas of the nervous system.

Neurons from the immature retina extend axons that make connections in the visual centers of the brain. Chemical markers provide guidance for these axons, but patterned neural activity is necessary to refine their connections. Much of this activity occurs in a distinctive pattern of waves before the retina is responsive to light, but it is not known how these waves are generated. In this study, we describe a simple mechanism that can explain the production of retinal waves. We use the knowledge that immature retinal cells are spontaneously active and show that waves will result if cells that receive more input when they are spontaneously active have longer intervals between activity. The resulting model reproduces experimentally observed waves in a variety of species, including ferret, chick, mouse, rabbit, and turtle, both at the level of individual cells and of the entire retina. The behavior appears intrinsically chaotic and the model is not tied to the properties of any particular biochemical pathway. We suggest that this mechanism could underlie not only the spontaneous patterns of activity that are generated in the retina but other areas of the developing brain as well.

A burst-based "Hebbian" learning rule at retinogeniculate synapses links retinal waves to activity-dependent refinement

Patterned spontaneous activity in the developing retina is necessary to drive synaptic refinement in the lateral geniculate nucleus (LGN). Using perforated patch recordings from neurons in LGN slices during the period of eye segregation, we examine how such burst-based activity can instruct this refinement. Retinogeniculate synapses have a novel learning rule that depends on the latencies between pre- and postsynaptic bursts on the order of one second: coincident bursts produce long-lasting synaptic enhancement, whereas non-overlapping bursts produce mild synaptic weakening. It is consistent with “Hebbian” development thought to exist at this synapse, and we demonstrate computationally that such a rule can robustly use retinal waves to drive eye segregation and retinotopic refinement. Thus, by measuring plasticity induced by natural activity patterns, synaptic learning rules can be linked directly to their larger role in instructing the patterning of neural connectivity.

The brain is comprised of an immense number of connections between neurons, and clever strategies are required to achieve the correct wiring during development. One common strategy uses neural activity itself as feedback to instruct individual connections (synapses) through synaptic learning rules that delineate which patterns of activity strengthen the synapse and which weaken it. Throughout life, such activity-dependent synaptic changes are likely driven by experience and are thought to underlie learning and memory, but during early stages of development, they are often driven by activity spontaneously generated within the brain. Here, we study connections in the visual pathway between the retina and lateral geniculate nucleus (LGN), which—to develop correctly—require spontaneous “retinal waves” before the eye is responsive to light. By replaying the retinal wave activity as it appears at single LGN synapses, we observe a novel learning rule that describes a relatively simple computation for the developing synapse in the context of retinal wave activity. We then demonstrate how this learning rule is matched to properties of the retinal waves in order to robustly drive the synaptic refinement that occurs in the visual system.

A novel learning rule describes a simple computation by which retinal wave activity robustly drives the synaptic refinement that occurs in the visual system.

Spontaneous symmetry breaking in self-organizing neural fields

We extend the theory of self-organizing neural fields in order to analyze the joint emergence of topography and feature selectivity in primary visual cortex through spontaneous symmetry breaking. We first show how a binocular one-dimensional topographic map can undergo a pattern forming instability that breaks the underlying symmetry between left and right eyes. This leads to the spatial segregation of eye specific activity bumps consistent with the emergence of ocular dominance columns. We then show how a 2-dimensional isotropic topographic map can undergo a pattern forming instability that breaks the underlying rotation symmetry. This leads to the formation of elongated activity bumps consistent with the emergence of orientation preference columns. A particularly interesting property of the latter symmetry breaking mechanism is that the linear equations describing the growth of the orientation columns exhibits a rotational shift-twist symmetry, in which there is a coupling between orientation and topography. Such coupling has been found in experimentally generated orientation preference maps.

Normal eye-specific patterning of retinal inputs to murine subcortical visual nuclei in the absence of brain-derived neurotrophic factor

Brain-derived neurotrophic factor (BDNF) is a preferred ligand for a member of the tropomyosin-related receptor family, trkB. Activation of trkB is implicated in various activity-independent as well as activity-dependent growth processes in many developing and mature neural systems. In the subcortical visual system, where electrical activity has been implicated in normal development, both differential survival, as well as remodeling of axonal arbors, have been suggested to contribute to eye-specific segregation of retinal ganglion cell inputs. Here, we tested whether BDNF is required for eye-specific segregation of visual inputs to the lateral geniculate nucleus and the superior colliculus, and two other major subcortical target fields in mice. We report that eye-specific patterning is normal in two mutants that lack BDNF expression during the segregation period: a germ-line knockout for BDNF, and a conditional mutant in which BDNF expression is absent or greatly reduced in the central nervous system. We conclude that the availability of BDNF is not necessary for eye-specific segregation in subcortical visual nuclei.

Developmental robotics: manifesto and application

We argue that all embodied organisms, whether robots or animals, face the same challenge: of adapting to bodies, brains and environments that undergo constant and inevitable change. After highlighting the evidence for the universal role of a class of molecular factors called neurotrophic factors in the response of animals to this challenge, we suggest that implementing models of neurotrophic interactions on robots may confer on them the adaptability and robustness exhibited by animals. We briefly review a mathematical model of neurotrophic interactions and then discuss its application in a robotic context. Finally, we examine the potential, or otherwise, of our approach to developmental robotics.

Visual maps in the adult primate cerebral cortex: some implications for brain development and evolution

In this paper, the topology of cortical visuotopic maps in adult primates is reviewed, with emphasis on recent studies. The observed visuotopic organisation can be summarised with reference to two basic rules. First, adjacent radial columns in the cortex represent partially overlapping regions of the visual field, irrespective of whether these columns are part of the same or different cortical areas. This primary rule is seldom, if ever, violated. Second, adjacent regions of the visual field tend to be represented in adjacent radial columns of a same area. This rule is not as rigid as the first, as many cortical areas form discontinuous, second-order representations of the visual field. A developmental model based on these physiological observations, and on comparative studies of cortical organisation, is then proposed, in order to explain how a combination of molecular specification steps and activity-driven processes can generate the variety of visuotopic organisations observed in adult cortex.

Coupling an aVLSI neuromorphic vision chip to a neurotrophic model of synaptic plasticity: the development of topography

We couple a previously studied, biologically inspired neurotrophic model of activity-dependent competitive synaptic plasticity and neuronal development to a neuromorphic retina chip. Using this system, we examine the development and refinement of a topographic mapping between an array of afferent neurons (the retinal ganglion cells) and an array of target neurons. We find that the plasticity model can indeed drive topographic refinement in the presence of afferent activity patterns generated by a real-world device. We examine the resilience of the developing system to the presence of high levels of noise by adjusting the spontaneous firing rate of the silicon neurons.

Correlation model for joint development of refined retinotopic map and ocular dominance columns

We describe a modification to a standard correlation model for the development of the geniculocortical projection that relays visual input to the visual cortex. The modification is to include threshold-activation of cortical cells as opposed to linear activation and it is shown that this can account for topographic map refinement (TMR). This contrasts with other models that require cortical cells to compete for activation or for neurotrophic support. Simulations are conducted for the joint development of ocular dominance columns and TMR in normal animals and parameter variations are used to both confirm robustness and to simulate some experimental conditions.

Retinal waves: implications for synaptic learning rules during development

Neural activity is often required for the final stages of synaptic refinement during brain development. It is thought that learning rules acting at the individual synapse level, which specify how pre- and postsynaptic activity lead to changes in synaptic efficacy, underlie such activity-dependent development. How such rules might function in vivo can be addressed in the retinogeniculate system because the input activity from the retina and its importance in development are both known. In fact, detailed studies of retinal waves have revealed their complex spatiotemporal properties, providing insights into the mechanisms that use such activity to guide development. First of all, the information useful for development is contained in the retinal waves and can be quantified, placing constraints on synaptic learning rules that use this information. Furthermore, knowing the distribution of activity over the entire set of inputs makes it possible to address a necessary component of developmental refinement: rules governing competition between synaptic inputs. In this way, the detailed knowledge of retinal input and lateral geniculate nucleus development provides a unique opportunity to relate the rules of synaptic plasticity directly to their role in development.

Multiplicative synaptic normalization and a nonlinear Hebb rule underlie a neurotrophic model of competitive synaptic plasticity

Synaptic normalization is used to enforce competitive dynamics in many models of developmental synaptic plasticity. In linear and semilinear Hebbian models, multiplicative synaptic normalization fails to segregate afferents whose activity patterns are positively correlated. To achieve this, the biologically problematic device of subtractive synaptic normalization must be used instead. Our own model of competition for neurotrophic support, which can segregate positively correlated afferents, was developed in part in an attempt to overcome these problems by removing the need for synaptic normalization altogether. However, we now show that the dynamics of our model decompose into two decoupled subspaces, with competitive dynamics being implemented in one of them through a nonlinear Hebb rule and multiplicative synaptic normalization. This normalization is "emergent" rather than imposed. We argue that these observations permit biologically plausible forms of synaptic normalization to be viewed as abstract and general descriptions of the underlying biology in certain scaleless models of synaptic plasticity.

The information content of spontaneous retinal waves

Spontaneous neural activity that is present in the mammalian retina before the onset of vision is required for the refinement of retinotopy in the lateral geniculate nucleus and superior colliculus. This paper explores the information content of this retinal activity, with the goal of determining constraints on the nature of the developmental mechanisms that use it. Through information-theoretic analysis of multielectrode and calcium-imaging experiments, we show that the spontaneous retinal activity present early in development provides information about the relative positions of retinal ganglion cells and can, in principle, be used at retinogeniculate and retinocollicular synapses to refine retinotopy. Remarkably, we find that most retinotopic information provided by retinal waves exists on relatively coarse time scales, suggesting that developmental mechanisms must be sensitive to timing differences from 100 msec up to 2 sec to make optimal use of it. In fact, a simple Hebbian-type learning rule with a correlation window on the order of seconds is able to extract the bulk of the available information. These findings are consistent with bursts of action potentials (rather than single spikes) being the unit of information used during development and suggest new experimental approaches for studying developmental plasticity of the retinogeniculate and retinocollicular synapses. More generally, these results demonstrate how the properties of neuronal systems can be inferred from the statistics of their input.