Regulation of axial patterning of the retina and its topographic mapping in the brain

Topographic maps are a fundamental organizational feature of axonal connections in the brain. A prominent model for studying axial polarity and topographic map development is the vertebrate retina and its projection to the optic tectum (or superior colliculus). Linked processes are controlled by molecules that are graded along the axes of the retina and its target fields. Recent studies indicate that ephrin-As control the temporal-nasal mapping of the retina in the optic tectum/superior colliculus by regulating the topographically-specific interstitial branching of retinal axons along the anterior-posterior tectal axis. This branching is mediated by relative levels of EphA receptor repellent signaling. A major recent advance is the demonstration that EphB receptor forward signaling and ephrin-B reverse signaling mediate axon attraction to control dorsal-ventral retinal mapping along the lateral-medial tectal axis. In addition, several classes of regulatory proteins have been implicated in the control of the axial patterning of the retina, and its ultimate readout of topographic mapping.     

Competitive interactions between retinal ganglion axons for tectal targets explain plasticity of retinotectal projection in the servomechanism model of retinotectal mapping

The mechanism of topographic mapping of retinal ganglion cells to the midbrain was previously elucidated by the servomechanism model, which is based on the fact that cells expressing Eph-receptors respond specifically to surface expressing membrane-bound ephrin-ligands at a critical level. The retina has increased nasal-to-temporal gradient of Eph receptor-density, and the optic tectum/superior colliculus has increased rostral-to-caudal gradient of membrane-bound ephrin-ligand. An axon from the retina has an identification tag of a certain level of Eph-receptor density depending on its retinal position, and adheres to the site on the tectum/superior colliculus expressing ephrin-ligands at a critical ligand-density level. The servomechanism model rigidly defines positions of axon terminals on the midbrain. However, optic nerve regeneration experiments combined with halved retina or tectum show a plastic or flexible mapping (expansion, compression and transposition of tectal projections). To reconcile the discrepancy between the rigid model and the plastic behavior, competition between retinal axon terminals for a target site was introduced to the servomechanism. The servomechanism/competition model succeeded in computer simulations of the plastic mapping of retinal axons on the tectum. Recent experiments of upregulated ligand-density on the tectum during nerve regeneration and the role of axonal competition are discussed.     

Getting into shape: optimal ligand gradients for axonal guidance

During neural development, neurons from downstream, presynaptic regions of the nervous system (such as the retina) send spatially patterned axonal projections to upstream, target regions (the tectum or superior colliculus). A servomechanism model has been proposed to explain the pattern and time-course of axonal growth between these two regions [Honda, H., 1998. Topographic mapping in the retinotectal projection by means of complementary ligand and receptor gradients: a computer simulation study. J. Theor. Biol., 192, 235-246]. Here, we show that a modification of this model incorporating a different criterion for axonal decision-making, called the local optimum rule, is guaranteed to converge to a topographic map under a wide range of conditions encountered during neural development. A theoretical investigation of these conditions leads to new hypotheses regarding map formation.     

Computational modeling of retinotopic map development to define contributions of EphA-ephrinA gradients, axon-axon interactions, and patterned activity

The topographic projection of retinal ganglion cell (RGC) axons to mouse superior colliculus (SC) or chick optic tectum (OT) is formed in three phases: RGC axons overshoot their termination zone (TZ); they exhibit interstitial branching along the axon that is topographically biased for the correct location of their future TZ; and branches arborize preferentially at the TZ and the initial exuberant projection refines through axon and branch elimination to generate a precise retinotopic map. We present a computational model of map development that demonstrates that the countergradients of EphAs and ephrinAs in retina and the OT/SC and bidirectional repellent signaling between RGC axons and OT/SC cells are sufficient to direct an initial topographic bias in RGC axon branching. Our model also suggests that a proposed repellent action of EphAs/ephrinAs present on RGC branches and arbors added to that of EphAs/ephrinAs expressed by OT/SC cells is required to progressively restrict branching and arborization to topographically correct locations and eliminate axon overshoot. Simulations show that this molecular framework alone can develop considerable topographic order and refinement, including axon elimination, a feature not programmed into the model. Generating a refined map with a condensed TZ as in vivo requires an additional parameter that enhances branch formation along an RGC axon near sites that it has a higher branch density, and resembles an assumed role for patterned neural activity. The same computational model generates the phenotypes reported in ephrinA deficient mice and Isl2-EphA3 knockin mice. This modeling suggests that gradients of counter-repellents can establish a substantial degree of topographic order in the OT/SC, and that repellents present on RGC axon branches and arbors make a substantial contribution to map refinement. However, competitive interactions between RGC axons that enhance the probability of continued local branching are required to generate precise retinotopy.     

A neural network study of precollicular saccadic averaging

Saccadic averaging is the phenomenon that two simultaneously presented retinal inputs result in a saccade with an endpoint located on an intermediate position between the two stimuli. Recordings from neurons in the deeper layers of the superior colliculus have revealed neural correlates of saccade averaging, indicating that it takes place at this level or upstream. Recently, we proposed a neural network for internal feedback in saccades. This neural network model is different from other models in that it suggests the possibility that averaging takes place in a stage upstream of the colliculus. The network consists of output units representing the neural map of the deeper layers of the superior colliculus and hidden layers imitating areas in the posterior parietal cortex. The deeper layers of the superior colliculus represent the motor error of a desired saccade, e.g. an eye movement to a visual target. In this article we show that averaging is an emergent property of the proposed network. When two retinal targets with different intensities are simultaneously presented to the network, the activity in the output layer represents a single motor error with a weighted average value. Our goal is to understand the mechanism of weighted averaging in this neural network. It appears that averaging in the model is caused by the linear dependence of the net input, received by the hidden units, on retinal error, independent of its retinal coding format. For nonnormalized retinal error inputs, also the nonlinearity between the net input and the activity of the hidden units plays a role in the averaging process. The averaging properties of the model are in agreement with physiological experiments if the hypothetical retinal error input map is normalized. The neural network predicts that if this normalization is overruled by electrical stimulation, averaging still takes place. However, in this case – as a consequence of the feedback task – the location of the resulting saccade depends on the initial eye position and the total intensity/current applied at the two locations. This could be a way to verify the neural network model. If the assumptions for the model are valid, a physiological implication of this paper is that averaging of saccades takes place upstream of the superior colliculus. Received: 22 June 1997 / Accepted in revised form: 19 February 1998     

Induction of target-directed optic axon outgrowth: effect of retinae transplanted to anophthalmic mice

In previous work using neural transplants (Hankin and Lund, 1987) we demonstrated two basic components of optic axon outgrowth in the mammalian retinotectal system: one category of outgrowth utilizes the subpial margin of the rostral brain stem as a preferential substrate (as do normal retinotectal axons); the other type of outgrowth, from retinae embedded deep within the midbrain parenchyma, is distance-dependent and highly target-oriented, but shows little apparent substrate specificity. One explanation for this directed outgrowth is that it is in response to a diffusible factor emanating from cells in the superior colliculus. In the present study we use congenitally anophthalmic mice as recipients for retinal transplants to test whether prior optic innervation of the superior colliculus plays a role in establishing either component of outgrowth. We show that outgrowth along the subpial pathway from a graft placed on the surface of the brain stem can take place in the absence of prior innervation of the superior colliculus. The target-directed outgrowth exhibited by embedded grafts only occurs if the tectum is also innervated by a second graft placed on the surface of the brain stem. It is proposed that tectal cells produce a factor in response to optic innervation and that this directs the growth patterns of embedded grafts. This suggests that optic innervation is a necessary prerequisite for the superior colliculus to produce the proposed diffusible chemotropic signal. In normal development such a factor could function to improve the efficiency of target-finding by later growing optic axons, but it might serve a quite different role, encouraging branching and trophic maintenance of the optic pathway once it has reached the tectum.     

Directed early axonal outgrowth from retinal transplants into host rat brains

Axons from retinae transplanted to the brain stem of neonatal rats exhibit two patterns of outgrowth that can be experimentally uncoupled from each other depending upon the location of the graft. Retinae placed close to the surface of the rostral brain stem (as much as 5 mm from the tectum) emit axons that project toward the superior colliculus along the subpial margin of the rostral brain stem. In contrast, axons from grafts embedded deep within the midbrain parenchyma project through the neuropil directly to the overlying superior colliculus, as long as the retina is within about 1 mm of the tectal surface. The present study shows that, as long as the retina is located outside the superior colliculus, and regardless of whether the axons derive from grafts in subpial or intraparenchymal locations, the earliest projections are oriented towards the superior colliculus. We have also found, however, that axons from retinae transplanted directly onto the superior colliculus can form projections that extend along the subpial margin away from the tectum. There are several major conclusions that may be drawn from these observations. First, the final tectopetal, transplant-derived projection does not result from the reorganization of an initially random outgrowth but is directed from the start toward an appropriate region of termination. Second, it appears that the interaction of retinal axons with a primary target alters the ability of the growth cone to respond to directional cues along the optic tract. Thus, although adding support to the proposal that optic axons attain the superior colliculus through an interaction involving substrates distributed along the optic tract and diffusible factors originating in the target region, it is increasingly clear that such interactions are likely to be complex and hierarchical.     

Visual Stimuli Evoked Action Potentials Trigger Rapidly Propagating Dendritic Calcium Transients in the Frog Optic Tectum Layer 6 Neurons

The superior colliculus in mammals or the optic tectum in amphibians is a major visual information processing center responsible for generation of orientating responses such as saccades in monkeys or prey catching avoidance behavior in frogs. The conserved structure function of the superior colliculus the optic tectum across distant species such as frogs, birds monkeys permits to draw rather general conclusions after studying a single species. We chose the frog optic tectum because we are able to perform whole-cell voltage-clamp recordings fluorescence imaging of tectal neurons while they respond to a visual stimulus. In the optic tectum of amphibians most visual information is processed by pear-shaped neurons possessing long dendritic branches, which receive the majority of synapses originating from the retinal ganglion cells. Since the first step of the retinal input integration is performed on these dendrites, it is important to know whether this integration is enhanced by active dendritic properties. We demonstrate that rapid calcium transients coinciding with the visual stimulus evoked action potentials in the somatic recordings can be readily detected up to the fine branches of these dendrites. These transients were blocked by calcium channel blockers nifedipine CdCl₂ indicating that calcium entered dendrites via voltage-activated L-type calcium channels. The high speed of calcium transient propagation, >300 μm in <10 ms, is consistent with the notion that action potentials, actively propagating along dendrites, open voltage-gated L-type calcium channels causing rapid calcium concentration transients in the dendrites. We conclude that such activation by somatic action potentials of the dendritic voltage gated calcium channels in the close vicinity to the synapses formed by axons of the retinal ganglion cells may facilitate visual information processing in the principal neurons of the frog optic tectum.     

Eye-specific segregation of optic afferents in mammals,fish, and frogs: The role of activity

Eye-specific patches or stripes normally develop in the visual cortex and superior colliculus of many (but not all) mammals and are also formed, after surgically produced binocular innervation, in the optic tectum of fish and frogs. The segregation of ocular dominance patches or columns has been studied using a variety of anatomical pathway-tracing techniques, by electrophysiological recording of postsynaptic units or field potentials, and by the 2-deoxyglucose method following visual stimulation of only one eye. In the tectum of both fish and frogs and in the cortex and colliculus of mammals, eye-specific patches develop from initially diffuse, overlapping projections. Of the various mechanisms that might cause such segregation, the evidence favors an activity-dependent process that stabilizes synapses from the same eye because of their correlated activity. First, several environmental manipulations affect the segregation of afferents in visual cortex: strabismus and alternate monocular exposure apparently enhance segregation, whereas dark rearing slows the segregation process, and monocular deprivation causes the experienced eye to form larger patches at the expense of those of the deprived eye. Second, blocking activity in both eyes is effective in preventing the segregation both in the tectum of fish and frog and in the visual cortex of cat. With the eyes blocked, alternate stimulation of the optic nerves permits the segregation of ocular dominance, at least onto single cells in the cat visual cortex. These findings are discussed in terms of an activity-dependent stabilization of those synapses having correlated activity (those from neighboring ganglion cells within one eye) but not of those lacking correlated activity (those from left and right eyes). We suggest that the eye-specific patches represent a compromise between total segregation of the projections from the two eyes and the formation of a single continuous retinotopic map across the surface of the cortex or tectum.     

Contributions of theoretical modeling to the understanding of neural map development

Theoretical/computational models have played an important role in developing our understanding of the fundamental mechanisms involved in neural map formation. I review models based on both chemospecific and activity-dependent matching of inputs to targets, with a particular focus on map development in the optic tectum and primary visual cortex.     

Two homeobox genes define the domain of EphA3 expression in the developing chick retina

Graded expression of the Eph receptor EphA3 in the retina and its two ligands, ephrin A2 and ephrin A5 in the optic tectum, the primary target of retinal axons, have been implicated in the formation of the retinotectal projection map. Two homeobox containing genes, SOHo1 and GH6, are expressed in a nasal-high, temporal-low pattern during early retinal development, and thus in opposing gradients to EphA3. Retroviral misexpression of SOHo1 or GH6 completely and specifically repressed EphA3 expression in the neural retina, but not in other parts of the central nervous system, such as the optic tectum. Under these conditions, some temporal ganglion cell axons overshot their expected termination zones in the rostral optic tectum, terminating aberrantly at more posterior locations. However, the majority of ganglion cell axons mapped to the appropriate rostrocaudal locations, although they formed somewhat more diffuse termination zones. These findings indicate that other mechanisms, in addition to differential EphA3 expression in the neural retina, are required for retinal ganglion axons to map to the appropriate rostrocaudal locations in the optic tectum. They further suggest that the control of topographic specificity along the retinal nasal-temporal axis is split into several independent pathways already at a very early time in development.     

Analysis of mouse EphA knockins and knockouts suggests that retinal axons programme target cells to form ordered retinotopic maps

I present a novel analysis of abnormal retinocollicular maps in mice in which the distribution of EphA receptors over the retina has been modified by knockin and/or knockout of these receptor types. My analysis shows that in all these cases, whereas the maps themselves are discontinuous, the graded distribution of EphA over the nasotemporal axis of the retina is recreated within the pattern of axonal terminations across rostrocaudal colliculus. This suggests that the guiding principle behind the formation of ordered maps of nerve connections between vertebrate retina and superior colliculus, or optic tectum, is that axons carrying similar amounts of Eph receptor terminate near to one another on the target structure. I show how the previously proposed marker induction model embodies this principle and predicts these results. I then describe a new version of the model in which the properties of the markers, or labels, are based on those of the Eph receptors and their associated ligands, the ephrins. I present new simulation results, showing the development of maps between two-dimensional structures, exploring the role of counter-gradients of labels across the target and confirming that the model reproduces the retinocollicular maps found in EphA knockin/knockout mice. I predict that abnormal distributions of label within the retina lead to abnormal distributions of label over the target, so that in each of the types of knockin/knockout mice analysed, there will be a different distribution of labels over the target structure. This mechanism could be responsible for the flexibility with which neurons reorganise their connections during development and the degree of precision in the final map. Activity-based mechanisms would play a role only at a later stage of development to remove the overlap between individual retinal projection fields, such as in the development of patterns of ocular dominance stripes.     

Gradual appearance of a regulated retinotectal projection pattern in Xenopus laevis

The topographic projection pattern formed by the retinal ganglion cell axons in the tectum of the lower vertebrate appears to require positional cues that guide the optic nerve fibers to their appropriate targets. One approach to understanding these positional cues or "positional information" has been to investigate changes in the pattern of the retinotectal projection after surgical manipulation of the embryonic eyebud. Analysis of these apparent changes in the patterns of positional information in the eye, termed "pattern regulation," may provide clues to both the nature of positional information and the mechanisms by which it is assigned to cells in the eyebud. Here we examine pattern regulation in the Xenopus visual system following the replacement of the temporal half of a right eyebud with the temporal half of a left eyebud. This manipulation requires that the left half-eyebud be inverted along its dorsoventral axis. Electrophysiological maps of these compound eyes in postmetamorphic frogs reveal regulated maps; the cells in the temporal half of the NrTl eye project to the tectum with a dorsoventral polarity appropriate for their position in the host eye and not appropriate for the original positions of the grafted cells in the donor eyebud. Paradoxically, the regulated patterns are not apparent in the projections of the original grafted eyebud cells during early larval development. Using fiber-tracing and electrophysiological mapping techniques, we now show that the regulated patterns appear gradually in the projections made by peripheral retinal cells added during mid-larval development. Because the regulation occurs relatively late in development and probably only in the peripheral retinal cells, simple models of epimorphic or morphallactic regulation do not appear to fit this system. Thus, new or more complex models must be invoked to explain the phenomenon of pattern regulation in the developing visual system of Xenopus.     

Two models for transforming auditory signals from head-centered to eye-centered coordinates

Two models for transforming auditory signals from head-centered to eye-centered coordinates are presented. The vector subtraction model subtracts a rate-coded eye position signal from a topographically weighted auditory target position signal to produce a rate-code of target location with respect to the eye. The rate-code is converted into a place-code through a graded synaptic weighting scheme and inhibition. The dendrite model performs a mapping of head-centered auditory space onto the dendrites of eye-centered units. Individual dendrites serve as logical comparators of target location and eye position. Both models produce a topographic map of auditory space in eye-centered coordinates like that found in the primate superior colliculus. Either type can be converted into a model for transforming visual signals from retinal to head-centered coordinates.     

Visual map development: bidirectional signaling, bifunctional guidance molecules, and competition

Topographic maps are a two-dimensional representation of one neural structure within another and serve as the main strategy to organize sensory information. The retina's projection via axons of retinal ganglion cells to midbrain visual centers, the optic tectum/superior colliculus, is the leading model to elucidate mechanisms of topographic map formation. Each axis of the retina is mapped independently using different mechanisms and sets of axon guidance molecules expressed in gradients to achieve the goal of representing a point in the retina onto a point within the target. An axon's termination along the temporal-nasal mapping axis is determined by opposing gradients of EphAs and ephrin-As that act through their forward and reverse signaling, respectively, within the projecting axons, each of which inhibits interstitial branching, cooperating with a branch-promoting activity, to generate topographic specific branching along the shaft of the parent axons that overshoot their correct termination zone along the anterior-posterior axis of the target. The dorsal-ventral termination position is then determined using a gradient of ephrin-B that can act as a repellent or attractant depending on the ephrin-B concentration relative to EphB levels on the interstitial branches to guide them along the medial-lateral axis of the target to their correct termination zone, where they arborize. In both cases, axon-axon competition results in axon mapping based on relative rather than absolute levels of repellent or attractant activity. The map is subsequently refined through large-scale pruning driven in large part by patterned retinal activity.     

Alteration of the retinotectal projection map by the graft of mesencephalic floor plate or sonic hedgehog

The floor plate plays crucial roles in the specification and differentiation of neurons along the dorsal-ventral (DV) axis of the neural tube. The transplantation of the mesecephalic floor plate (mfp) into the dorsal mesencephalon in chick embryos alters the fate of the mesencephalon adjacent to the transplant from the tectum to the tegmentum, a ventral tissue of the mesencephalon. In this study, to test whether the mfp is involved in the specification of the DV polarity of the tectum and affects the projection patterns of retinal fibers to the tectum along the DV axis, we transplanted quail mfp into the dorsal mesencephalon of chick embryos, and analyzed projection patterns of dorsal and ventral retinal fibers to the tectum. In the embryos with the mfp graft, dorsal retinal fibers grew into the dorsal part of the tectum which is the original target for ventral but not dorsal retinal fibers and formed tight focuses there. In contrast, ventral retinal fibers did not terminate at any part of the tectum. Transplantation of Sonic hedgehog (Shh)-secreting quail fibroblasts into the dorsal mesencephalon also induced the ectopic tegmentum and altered the retinotectal projection along the DV axis, as the mfp graft did. These results suggest that some factors from the mesencephalic floor plate or the tegmentum, or Shh itself, play a crucial role in the establishment of the DV polarity of the tectum and the retinotectal projection map along the DV axis.     

On the Importance of Countergradients for the Development of Retinotopy: Insights from a Generalised Gierer Model

During the development of the topographic map from vertebrate retina to superior colliculus (SC), EphA receptors are expressed in a gradient along the nasotemporal retinal axis. Their ligands, ephrin-As, are expressed in a gradient along the rostrocaudal axis of the SC. Countergradients of ephrin-As in the retina and EphAs in the SC are also expressed. Disruption of any of these gradients leads to mapping errors. Gierer''s (1981) model, which uses well-matched pairs of gradients and countergradients to establish the mapping, can account for the formation of wild type maps, but not the double maps found in EphA knock-in experiments. I show that these maps can be explained by models, such as Gierer''s (1983), which have gradients and no countergradients, together with a powerful compensatory mechanism that helps to distribute connections evenly over the target region. However, this type of model cannot explain mapping errors found when the countergradients are knocked out partially. I examine the relative importance of countergradients as against compensatory mechanisms by generalising Gierer''s (1983) model so that the strength of compensation is adjustable. Either matching gradients and countergradients alone or poorly matching gradients and countergradients together with a strong compensatory mechanism are sufficient to establish an ordered mapping. With a weaker compensatory mechanism, gradients without countergradients lead to a poorer map, but the addition of countergradients improves the mapping. This model produces the double maps in simulated EphA knock-in experiments and a map consistent with the Math5 knock-out phenotype. Simulations of a set of phenotypes from the literature substantiate the finding that countergradients and compensation can be traded off against each other to give similar maps. I conclude that a successful model of retinotopy should contain countergradients and some form of compensation mechanism, but not in the strong form put forward by Gierer.     

Growth preferences of adult rat retinal ganglion cell axons in retinotectal cocultures

We examined whether regenerating axons from adult rat ganglion cells are able to recognize their appropriate target region in vitro. Explants from adult rat retina were cocultured with embryonic sagittal midbrain slices in Matrigel®. The midbrain sections contained the superior colliculus, the main target for retinal ganglion cell axons in rats, and the inferior colliculus. We observed a statistically significant preference of both temporal and nasal retinal axons to grow toward their appropriate target region (anterior and posterior superior colliculus, respectively). No preferential growth of retinal ganglion cell axons was detected in controls, for which retinal explants were cultured on their own. When retinal ganglion cell axons were given a choice between superior colliculus and inferior colliculus, axons from nasal retina preferentially grew toward the posterior superior colliculus and avoided the inferior colliculus. In contrast, temporal axons in the same assay did not show preference for either of the colliculi. These findings suggest that regenerating axons from adult rat retina are able to recognize target-specific guidance cues released from embryonic midbrain targets in vitro. © 1998 John Wiley & Sons, Inc. J Neurobiol 35: 379–387, 1998