New model of retinocollicular mapping predicts the mechanisms of axonal competition and explains the role of reverse molecular signaling during development

Adaptation of spontaneous activity in the developing visual cortex

Spontaneous activity drives the establishment of appropriate connectivity in different circuits during brain development. In the mouse primary visual cortex, two distinct patterns of spontaneous activity occur before vision onset: local low-synchronicity events originating in the retina and global high-synchronicity events originating in the cortex. We sought to determine the contribution of these activity patterns to jointly organize network connectivity through different activity-dependent plasticity rules. We postulated that local events shape cortical input selectivity and topography, while global events homeostatically regulate connection strength. However, to generate robust selectivity, we found that global events should adapt their amplitude to the history of preceding cortical activation. We confirmed this prediction by analyzing in vivo spontaneous cortical activity. The predicted adaptation leads to the sparsification of spontaneous activity on a slower timescale during development, demonstrating the remarkable capacity of the developing sensory cortex to acquire sensitivity to visual inputs after eye-opening.

New insights on the modeling of the molecular mechanisms underlying neural maps alignment in the midbrain

We previously identified and modeled a principle of visual map alignment in the midbrain involving the mapping of the retinal projections and concurrent transposition of retinal guidance cues into the superior colliculus providing positional information for the organization of cortical V1 projections onto the retinal map (Savier et al., 2017). This principle relies on mechanisms involving Epha/Efna signaling, correlated neuronal activity and axon competition. Here, using the 3-step map alignment computational model, we predict and validate in vivo the visual mapping defects in a well-characterized mouse model. Our results challenge previous hypotheses and provide an alternative, although complementary, explanation for the phenotype observed. In addition, we propose a new quantification method to assess the degree of alignment and organization between maps, allowing inter-model comparisons. This work generalizes the validity and robustness of the 3-step map alignment algorithm as a predictive tool and confirms the basic mechanisms of visual map organization.

Theoretical Models of Neural Development

Constructing a functioning nervous system requires the precise orchestration of a vast array of mechanical, molecular, and neural-activity-dependent cues. Theoretical models can play a vital role in helping to frame quantitative issues, reveal mathematical commonalities between apparently diverse systems, identify what is and what is not possible in principle, and test the abilities of specific mechanisms to explain the data. This review focuses on the progress that has been made over the last decade in our theoretical understanding of neural development.

Revisiting chemoaffinity theory: Chemotactic implementation of topographic axonal projection

Neural circuits are wired by chemotactic migration of growth cones guided by extracellular guidance cue gradients. How growth cone chemotaxis builds the macroscopic structure of the neural circuit is a fundamental question in neuroscience. I addressed this issue in the case of the ordered axonal projections called topographic maps in the retinotectal system. In the retina and tectum, the erythropoietin-producing hepatocellular (Eph) receptors and their ligands, the ephrins, are expressed in gradients. According to Sperry's chemoaffinity theory, gradients in both the source and target areas enable projecting axons to recognize their proper terminals, but how axons chemotactically decode their destinations is largely unknown. To identify the chemotactic mechanism of topographic mapping, I developed a mathematical model of intracellular signaling in the growth cone that focuses on the growth cone's unique chemotactic property of being attracted or repelled by the same guidance cues in different biological situations. The model presented mechanism by which the retinal growth cone reaches the correct terminal zone in the tectum through alternating chemotactic response between attraction and repulsion around a preferred concentration. The model also provided a unified understanding of the contrasting relationships between receptor expression levels and preferred ligand concentrations in EphA/ephrinA- and EphB/ephrinB-encoded topographic mappings. Thus, this study redefines the chemoaffinity theory in chemotactic terms.

Novel Models of Visual Topographic Map Alignment in the Superior Colliculus

The establishment of precise neuronal connectivity during development is critical for sensing the external environment and informing appropriate behavioral responses. In the visual system, many connections are organized topographically, which preserves the spatial order of the visual scene. The superior colliculus (SC) is a midbrain nucleus that integrates visual inputs from the retina and primary visual cortex (V1) to regulate goal-directed eye movements. In the SC, topographically organized inputs from the retina and V1 must be aligned to facilitate integration. Previously, we showed that retinal input instructs the alignment of V1 inputs in the SC in a manner dependent on spontaneous neuronal activity; however, the mechanism of activity-dependent instruction remains unclear. To begin to address this gap, we developed two novel computational models of visual map alignment in the SC that incorporate distinct activity-dependent components. First, a Correlational Model assumes that V1 inputs achieve alignment with established retinal inputs through simple correlative firing mechanisms. A second Integrational Model assumes that V1 inputs contribute to the firing of SC neurons during alignment. Both models accurately replicate in vivo findings in wild type, transgenic and combination mutant mouse models, suggesting either activity-dependent mechanism is plausible. In silico experiments reveal distinct behaviors in response to weakening retinal drive, providing insight into the nature of the system governing map alignment depending on the activity-dependent strategy utilized. Overall, we describe novel computational frameworks of visual map alignment that accurately model many aspects of the in vivo process and propose experiments to test them.

Stochastic Interaction between Neural Activity and Molecular Cues in the Formation of Topographic Maps

Topographic maps in visual processing areas maintain the spatial order of the visual world. Molecular cues and neuronal activity both play critical roles in map formation, but their interaction remains unclear. Here, we demonstrate that when molecular- and activity-dependent cues are rendered nearly equal in force, they drive topographic mapping stochastically. The functional and anatomical representation of azimuth in the superior colliculus of heterozygous Islet2-EphA3 knockin (Isl2(EphA3/+)) mice is variable: maps may be single, duplicated, or a combination of the two. This heterogeneity is not due to genetic differences, since map organizations in individual mutant animals often differ between colliculi. Disruption of spontaneous waves of retinal activity resulted in uniform map organization in Isl2(EphA3/+) mice, demonstrating that correlated spontaneous activity is required for map heterogeneity. Computational modeling replicates this heterogeneity, revealing that molecular- and activity-dependent forces interact simultaneously and stochastically during topographic map formation.

Quantitative assessment of computational models for retinotopic map formation

Molecular and activity-based cues acting together are thought to guide retinal axons to their terminal sites in vertebrate optic tectum or superior colliculus (SC) to form an ordered map of connections. The details of mechanisms involved, and the degree to which they might interact, are still not well understood. We have developed a framework within which existing computational models can be assessed in an unbiased and quantitative manner against a set of experimental data curated from the mouse retinocollicular system. Our framework facilitates comparison between models, testing new models against known phenotypes and simulating new phenotypes in existing models. We have used this framework to assess four representative models that combine Eph/ephrin gradients and/or activity-based mechanisms and competition. Two of the models were updated from their original form to fit into our framework. The models were tested against five different phenotypes: wild type, Isl2-EphA3(ki/ki), Isl2-EphA3(ki/+), ephrin-A2,A3,A5 triple knock-out (TKO), and Math5(-/-) (Atoh7). Two models successfully reproduced the extent of the Math5(-/-) anteromedial projection, but only one of those could account for the collapse point in Isl2-EphA3(ki/+). The models needed a weak anteroposterior gradient in the SC to reproduce the residual order in the ephrin-A2,A3,A5 TKO phenotype, suggesting either an incomplete knock-out or the presence of another guidance molecule. Our article demonstrates the importance of testing retinotopic models against as full a range of phenotypes as possible, and we have made available MATLAB software, we wrote to facilitate this process.

Computational and mathematical methods for morphogenetic gradient analysis, boundary formation and axonal targeting

Morphogenesis and axonal targeting are key processes during development that depend on complex interactions at molecular, cellular and tissue level. Mathematical modeling is essential to bridge this multi-scale gap in order to understand how the emergence of large structures is controlled at molecular level by interactions between various signaling pathways. We summarize mathematical modeling and computational methods for time evolution and precision of morphogenetic gradient formation. We discuss tissue patterning and the formation of borders between regions labeled by different morphogens. Finally, we review models and algorithms that reveal the interplay between morphogenetic gradients and patterned activity for axonal pathfinding and the generation of the retinotopic map in the visual system.

Chemoaffinity in topographic mapping revisited--is it more about fiber-fiber than fiber-target interactions?

Axonal projections between two populations of neurons, which preserve neighborhood relationships, are called topographic. They are ubiquitous in the brain. The development of the retinotectal projection, mapping the retinal output onto the roof of the midbrain, has been studied for decades as a model system. The rigid precision of normal retinotopic mapping has prompted the chemoaffinity hypothesis, positing axonal targeting to be based on fixed biochemical affinities between fibers and targets. In addition, however, abundant evidence has been gathered mainly in the 1970s and 80s that the mapping can adjust to variegated targets with stunning flexibility demonstrating the extraordinary robustness of the guidance process. The identification of ephrins and Eph-receptors as the underlying molecular cues has mostly been interpreted as supporting the fiber-target chemoaffinity hypothesis, while the evidence on mapping robustness has largely been neglected. By having a fresh look on the old data, we expound that they indicate, in addition to fiber-target chemoaffinity, the existence of a second autonomous guidance influence, which we call fiber-fiber chemoaffinity. Classical in vitro observations suggest both influences be composed of opposing monofunctional guidance activities. Based on the molecular evidence, we propose that those might be ephrin/Eph forward and reverse signaling, not only in fiber-target but also in fiber-fiber interactions. In fact, computational models based on this assumption can reconcile the seemingly conflicting findings on rigid and flexible topographic mapping. Supporting the suggested parsimonious and powerful mechanism, they contribute to an understanding of the evolutionary success of robust topographic mass wiring of axons.

Different roles of axon guidance cues and patterned spontaneous activity in establishing receptive fields in the mouse superior colliculus

Visual neurons in the superior colliculus (SC) respond to both bright (On) and dark (Off) stimuli in their receptive fields. This receptive field property is due to proper convergence of On- and Off-centered retinal ganglion cells to their target cells in the SC. In this study, we have compared the receptive field structure of individual SC neurons in two lines of mutant mice that are deficient in retinotopic mapping: the ephrin-A knockouts that lack important retinocollicular axonal guidance cues and the nAChR-β2 knockouts that have altered activity-dependent refinement of retinocollicular projections. We find that even though the receptive fields are much larger in the ephrin-A knockouts, their On-Off overlap remains unchanged. These neurons also display normal level of selectivity for stimulus direction and orientation. In contrast, the On-Off overlap is disrupted in the β2 knockouts. Together with the previous finding of disrupted direction and orientation selectivity in the β2 knockout mice, our results indicate that molecular guidance cues and activity-dependent processes play different roles in the development of receptive field properties in the SC.

Ephrin signalling in the developing nervous system

Ephrin ligands and their Eph receptors hold our attention since their link to axon guidance almost twenty years ago. Since then, they have been shown to be critical for short distance cell-cell interactions in the nervous system. The interest in their function has not abated, leading to ever-more sophisticated studies generating as many surprising answers about their function as new questions. We discuss recent insights into their functions in the developing nervous system, including neuronal progenitor sorting, stochastic cell migration, guidance of neuronal growth cones, topographic map formation, as well as synaptic plasticity.

Retinal overexpression of Ten-m3 alters ipsilateral retinogeniculate projections in the wallaby (Macropus eugenii)

The dorsal lateral geniculate nucleus (dLGN) contains a retinotopic map where input from the two eyes map in register to provide a substrate for binocular vision. Ten-m3, a transmembrane protein, mediates homophilic interactions and has been implicated in the patterning of ipsilateral visual projections. Ease of access to early developmental stages in a marsupial wallaby has been used to manipulate levels of Ten-m3 during the development of retinogeniculate projections. In situ hybridisation showed a high dorsomedial to low ventrolateral gradient of Ten-m3 in the developing dLGN, matching retinotopically with the previously reported high ventral to low dorsal retinal gradient. Overexpression of Ten-m3 in ventronasal but not dorsonasal retina resulted in an extension of ipsilateral projections beyond the normal binocular zone. These results demonstrate that Ten-m3 influences ipsilateral projections and support a role for it in binocular mapping.

A role for correlated spontaneous activity in the assembly of neural circuits

Before the onset of sensory transduction, developing neural circuits spontaneously generate correlated activity in distinct spatial and temporal patterns. During this period of patterned activity, sensory maps develop and initial coarse connections are refined, which are critical steps in the establishment of adult neural circuits. Over the last decade, there has been substantial evidence that altering the pattern of spontaneous activity disrupts refinement, but the mechanistic understanding of this process remains incomplete. In this review, we discuss recent experimental and theoretical progress toward the process of activity-dependent refinement, focusing on circuits in the visual, auditory, and motor systems. Although many outstanding questions remain, the combination of several novel approaches has brought us closer to a comprehensive understanding of how complex neural circuits are established by patterned spontaneous activity during development.

Dendritic and axonal targeting patterns of a genetically-specified class of retinal ganglion cells that participate in image-forming circuits

Background

There are numerous functional types of retinal ganglion cells (RGCs), each participating in circuits that encode a specific aspect of the visual scene. This functional specificity is derived from distinct RGC morphologies and selective synapse formation with other retinal cell types; yet, how these properties are established during development remains unclear. Islet2 (Isl2) is a LIM-homeodomain transcription factor expressed in the developing retina, including approximately 40% of all RGCs, and has previously been implicated in the subtype specification of spinal motor neurons. Based on this, we hypothesized that Isl2⁺ RGCs represent a related subset that share a common function.

Results

We morphologically and molecularly characterized Isl2⁺ RGCs using a transgenic mouse line that expresses GFP in the cell bodies, dendrites and axons of Isl2⁺ cells (Isl2-GFP). Isl2-GFP RGCs have distinct morphologies and dendritic stratification patterns within the inner plexiform layer and project to selective visual nuclei. Targeted filling of individual cells reveals that the majority of Isl2-GFP RGCs have dendrites that are monostratified in layer S3 of the IPL, suggesting they are not ON-OFF direction-selective ganglion cells. Molecular analysis shows that most alpha-RGCs, indicated by expression of SMI-32, are also Isl2-GFP RGCs. Isl2-GFP RGCs project to most retino-recipient nuclei during early development, but specifically innervate the dorsal lateral geniculate nucleus and superior colliculus (SC) at eye opening. Finally, we show that the segregation of Isl2⁺ and Isl2^- RGC axons in the SC leads to the segregation of functional RGC types.

Conclusions

Taken together, these data suggest that Isl2⁺ RGCs comprise a distinct class and support a role for Isl2 as an important component of a transcription factor code specifying functional visual circuits. Furthermore, this study describes a novel genetically-labeled mouse line that will be a valuable resource in future investigations of the molecular mechanisms of visual circuit formation.

Molecular guidance of retinotopic map development in the midbrain

Topographic maps are utilized in many sensory and motor systems to efficiently transfer information between brain regions. The retina's projection to the superior colliculus has served as a model for the identification of molecular cues and mechanistic strategies by which topographic maps are formed. Evidence from both in vitro and in vivo studies points to graded cell surface cues playing a central role, but support for axon-axon competition and selective degeneration have also been advanced recently. In combination with mathematical models, these studies suggest that topographic maps are established using a complex combination of strategies to ensure precise connectivity.

Retinocollicular mapping explained?

We review and comment on the recent model of Grimbert and Cang of the development of topographically ordered maps from the retina to the superior colliculus. This model posits a phase in which arbors are created in zones permitted by Eph and ephrin signaling, followed by a phase in which activity-dependent synaptic plasticity refines the map. We show that it is not possible to generate the arborization probability functions used in the simulations of Grimbert and Cang using gradients of Ephs and ephrins and the interaction mechanism that Grimbert and Cang propose in their results. Furthermore, the arborization probabilities we do generate are far less sharp than we imagine truly “permissive” ones would be. It remains to be seen if maps can be generated from the nonpermissive arborization probabilities generated from gradients.

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.

Developmental mechanisms of topographic map formation and alignment

Brain connections are organized into topographic maps that are precisely aligned both within and across modalities. This alignment facilitates coherent integration of different categories of sensory inputs and allows for proper sensorimotor transformations. Topographic maps are established and aligned by multistep processes during development, including interactions of molecular guidance cues expressed in gradients; spontaneous activity-dependent axonal and dendritic remodeling; and sensory-evoked plasticity driven by experience. By focusing on the superior colliculus, a major site of topographic map alignment for different sensory modalities, this review summarizes current understanding of topographic map development in the mammalian visual system and highlights recent advances in map alignment studies. A major goal looking forward is to reveal the molecular and synaptic mechanisms underlying map alignment and to understand the physiological and behavioral consequences when these mechanisms are disrupted at various scales.