Influence of cell fate mechanisms upon retinal mosaic formation: a modelling study

Optimization-Based Pairwise Interaction Point Process (O-PIPP): A Precise and Universal Retinal Mosaic Modeling Approach

Purpose

A retinal mosaic, the spatial organization of a population of homotypic neurons, is thought to sample a specific visual feature into the feedforward visual pathway. The purpose of this study was to propose a universal modeling approach for precisely generating retinal mosaics and overcoming the limitations of previous models, especially in modeling abnormal mosaic patterns under disease conditions.

Methods

Here, we developed the optimization-based pairwise interaction point process (O-PIPP). It incorporates optimization techniques into previous simulation approaches, enabling directional control of the simulation process according to the user-designed optimization target. For the convenience of the community, we implemented the O-PIPP approach into a Python package and a website application.

Results

We showed that the O-PIPP can generate more precise neural spatial patterns of healthy and diseased mosaics compared to previous phenomenological approaches. Notably, through modeling the retinal neural circuitry with O-PIPP-simulated retinitis pigmentosa cone mosaics, we elucidated how the cone mosaic rearrangement impacted the information processing of ganglion cells.

Conclusions

The O-PIPP provides a precise and universal tool to simulate realistic mosaics, which could help to investigate the function of retinal mosaics in vision.

Retinal self-organization: a model of retinal ganglion cells and starburst amacrine cells mosaic formation

Individual retinal cell types exhibit semi-regular spatial patterns called retinal mosaics. Retinal ganglion cells (RGCs) and starburst amacrine cells (SACs) are known to exhibit such layouts. Mechanisms responsible for the formation of mosaics are not well understood but follow three main principles: (i) homotypic cells prevent nearby cells from adopting the same type, (ii) cell tangential migration and (iii) cell death. Alongside experiments in mouse, we use BioDynaMo, an agent-based simulation framework, to build a detailed and mechanistic model of mosaic formation. We investigate the implications of the three theories for RGC's mosaic formation. We report that the cell migration mechanism yields the most regular mosaics. In addition, we propose that low-density RGC type mosaics exhibit on average low regularities, and thus we question the relevance of regular spacing as a criterion for a group of RGCs to form a RGC type. We investigate SAC mosaics formation and interactions between the ganglion cell layer (GCL) and inner nuclear layer (INL) populations. We propose that homotypic interactions between the GCL and INL populations during mosaics creation are required to reproduce the observed SAC mosaics' characteristics. This suggests that the GCL and INL populations of SACs might not be independent during retinal development.

From random to regular: Variation in the patterning of retinal mosaics

The various types of retinal neurons are each positioned at their respective depths within the retina where they are believed to be assembled as orderly mosaics, in which like-type neurons minimize proximity to one another. Two common statistical analyses for assessing the spatial properties of retinal mosaics include the nearest neighbor analysis, from which an index of their "regularity" is commonly calculated, and the density recovery profile derived from autocorrelation analysis, revealing the presence of an exclusion zone indicative of anti-clustering. While each of the spatial statistics derived from these analyses, the regularity index and the effective radius, can be useful in characterizing such properties of orderly retinal mosaics, they are rarely sufficient for conveying the natural variation in the self-spacing behavior of different types of retinal neurons and the extent to which that behavior generates uniform intercellular spacing across the mosaic. We consider the strengths and limitations of these and other spatial statistical analyses for assessing the patterning in retinal mosaics, highlighting a number of misconceptions and their frequent misuse. Rather than being diagnostic criteria for determining simply whether a population is "regular," they should be treated as descriptive statistics that convey variation in the factors that influence neuronal positioning. We subsequently apply multiple spatial statistics to the analysis of eight different mosaics in the mouse retina, demonstrating conspicuous variability in the degree of patterning present, from essentially random to notably regular. This variability in patterning has both a developmental as well as a functional significance, reflecting the rules governing the positioning of different types of neurons as the architecture of the retina is assembled, and the distinct mechanisms by which they regulate dendritic growth to generate their characteristic coverage and connectivity.

Conditional Deletion of AP-2α and AP-2β in the Developing Murine Retina Leads to Altered Amacrine Cell Mosaics and Disrupted Visual Function

Purpose

The combined action of the activating protein-2 (AP-2) transcription factors, AP-2α and AP-2β, is important in early retinal development, specifically in the formation of horizontal cells. However, in previous studies, it was not possible to analyze postnatal development and function of additional retinal subtypes.

Methods

We used a double conditional deletion of AP-2α and AP-2β from the retina to further examine the combinatory role of these genes in retinal cell patterning and function in postnatal adult mice as measured by Voronoi domain area and nearest-neighbor distance spatial analyses and ERGs, respectively.

Results

Conditional deletion of both AP-2α and AP-2β from the retina resulted in a variety of abnormalities, including the absence of horizontal cells, defects in the photoreceptor ribbons in which synapses failed to form, along with evidence of aberrant amacrine cell arrangement. Although no significant changes in amacrine cell population numbers were observed in the double mutants, significant irregularities in the mosaic patterning of amacrine cells was observed as demonstrated by both Voronoi domain areas and nearest-neighbor distances analyses. These changes were further accompanied by an alteration in the retinal response to light as recorded by ERGs. In particular, in the double-mutant mice lacking AP-2α and AP-2β, the b-wave amplitude, representative of interneuron signal processing, was significantly reduced compared with control littermates.

Conclusions

Together these findings demonstrate the requirement for both AP-2α and AP-2β in proper amacrine mosaic patterning and a normal functional light response in the retina.

An agent-based model of the Notch signaling pathway elucidates three levels of complexity in the determination of developmental patterning

BACKGROUND

The Notch signaling pathway is involved in cell fate decision and developmental patterning in diverse organisms. A receptor molecule, Notch (N), and a ligand molecule (in this case Delta or Dl) are the central molecules in this pathway. In early Drosophila embryos, these molecules determine neural vs. skin fates in a reproducible rosette pattern.

RESULTS

We have created an agent-based model (ABM) that simulates the molecular components for this signaling pathway as agents acting within a spatial representation of a cell. The model captures the changing levels of these components, their transition from one state to another, and their movement from the nucleus to the cell membrane and back to the nucleus again. The model introduces stochastic variation into the system using a random generator within the Netlogo programming environment. The model uses these representations to understand the biological systems at three levels: individual cell fate, the interactions between cells, and the formation of pattern across the system. Using a set of assessment tools, we show that the current model accurately reproduces the rosette pattern of neurons and skin cells in the system over a wide set of parameters. Oscillations in the level of the N agent eventually stabilize cell fate into this pattern. We found that the dynamic timing and the availability of the N and Dl agents in neighboring cells are central to the formation of a correct and stable pattern. A feedback loop to the production of both components is necessary for a correct and stable pattern.

CONCLUSIONS

The signaling pathways within and between cells in our model interact in real time to create a spatially correct field of neurons and skin cells. This model predicts that cells with high N and low Dl drive the formation of the pattern. This model also be used to elucidate general rules of biological self-patterning and decision-making.

The somal patterning of the AII amacrine cell mosaic in the mouse retina is indistinguishable from random simulations matched for density and constrained by soma size

The orderly spacing of retinal neurons is commonly regarded as a characteristic feature of retinal nerve cell populations. Exemplars of this property include the horizontal cells and the cholinergic amacrine cells, where individual cells minimize the proximity to like-type neighbors, yielding regularity in the patterning of their somata. Recently, two types of retinal bipolar cells in the mouse retina were shown to exhibit an order in their somal patterning no different from density-matched simulations constrained by soma size but being otherwise randomly distributed. The present study has now extended this finding to a type of retinal amacrine cell, the AII amacrine cell. Voronoi domain analysis revealed the patterning in the population of AII amacrine somata to be no different from density-matched and soma-size-constrained random simulations, while analysis of the density recovery profile showed AII amacrine cells to exhibit a minimal intercellular spacing identical to that for those random simulations: AII amacrine somata were positioned side-by-side as often as chance would predict. Regularity indexes and packing factors (PF) were far lower than those achieved by either the horizontal cells or cholinergic amacrine cells, with PFs also being comparable to those derived from the constrained random simulations. These results extend recent findings that call into question the widespread assumption that all types of retinal neurons are assembled as regular somal arrays, and have implications for the way in which AII amacrine cells must distribute their processes to ensure a uniform coverage of the retinal surface.

Neuronal Migration and Lamination in the Vertebrate Retina

In the retina, like in most other brain regions, developing neurons are arranged into distinct layers giving the mature tissue its stratified appearance. This process needs to be highly controlled and orchestrated, as neuronal layering defects lead to impaired retinal function. To achieve successful neuronal layering and lamination in the retina and beyond, three main developmental steps need to be executed: First, the correct type of neuron has to be generated at a precise developmental time. Second, as most retinal neurons are born away from the position at which they later function, newborn neurons have to move to their final layer within the developing tissue, a process also termed neuronal lamination. Third, these neurons need to connect to their correct synaptic partners. Here, we discuss neuronal migration and lamination in the vertebrate retina and summarize our knowledge on these aspects of retinal development. We give an overview of how lamination emerges and discuss the different modes of neuronal translocation that occur during retinogenesis and what we know about the cell biological machineries driving them. In addition, retinal mosaics and their importance for correct retinal function are examined. We close by stating the open questions and future directions in this exciting field.

Random spatial patterning of cone bipolar cell mosaics in the mouse retina

Retinal bipolar cells spread their dendritic arbors to tile the retinal surface, extending them to the tips of the dendritic fields of their homotypic neighbors, minimizing dendritic overlap. Such uniform nonredundant dendritic coverage of these populations would suggest a degree of spatial order in the properties of their somal distributions, yet few studies have examined the patterning in retinal bipolar cell mosaics. The present study examined the organization of two types of cone bipolar cells in the mouse retina, the Type 2 cells and the Type 4 cells, and compared their spatial statistical properties with those of the horizontal cells and the cholinergic amacrine cells, as well as to random simulations of cells matched in density and constrained by soma size. The Delauney tessellation of each field was computed, from which nearest neighbor distances and Voronoi domain areas were extracted, permitting a calculation of their respective regularity indexes (RIs). The spatial autocorrelation of the field was also computed, from which the effective radius and packing factor (PF) were determined. Both cone bipolar cell types were found to be less regular and less efficiently packed than either the horizontal cells or cholinergic amacrine cells. Furthermore, while the latter two cell types had RIs and PFs in excess of those for their matched random simulations, the two types of cone bipolar cells had spatial statistical properties comparable to random distributions. An analysis of single labeled cone bipolar cells revealed dendritic arbors frequently skewed to one side of the soma, as would be expected from a randomly distributed population of cells with dendrites that tile. Taken together, these results suggest that, unlike the horizontal cells or cholinergic amacrine cells which minimize proximity to one another, cone bipolar cell types are constrained only by their physical size.

Modular genetic regulatory networks increase organization during pattern formation

Studies have shown that genetic regulatory networks (GRNs) consist of modules that are densely connected subnetworks that function quasi-autonomously. Modules may be recognized motifs that comprise of two or three genes with particular regulatory functions and connectivity or be purely structural and identified through connection density. It is unclear what evolutionary and developmental advantages modular structure and in particular motifs provide that have led to this enrichment. This study seeks to understand how modules within developmental GRNs influence the complexity of multicellular patterns that emerge from the dynamics of the regulatory networks. We apply an algorithmic complexity to measure the organization of the patterns. A computational study was performed by creating Boolean intracellular networks within a simulated epithelial field of embryonic cells, where each cell contains the same network and communicates with adjacent cells using contact-mediated signaling. Intracellular networks with random connectivity were compared to those with modular connectivity and with motifs. Results show that modularity effects network dynamics and pattern organization significantly. In particular: (1) modular connectivity alone increases complexity in network dynamics and patterns; (2) bistable switch motifs simplify both the pattern and network dynamics; (3) all other motifs with feedback loops increase multicellular pattern complexity while simplifying the network dynamics; (4) negative feedback loops affect the dynamics complexity more significantly than positive feedback loops.

Design principles and developmental mechanisms underlying retinal mosaics

Most structures within the central nervous system (CNS) are composed of different types of neuron that vary in both number and morphology, but relatively little is known about the interplay between these two features, i.e. about the population dynamics of a given cell type. How such arrays of neurons are distributed within a structure, and how they differentiate their dendrites relative to each other, are issues that have recently drawn attention in the invertebrate nervous system, where the genetic and molecular underpinnings of these organizing principles are being revealed in exquisite detail. The retina is one of the few locations where these principles have been extensively studied in the vertebrate CNS, indeed, where the design principles of 'mosaic regularity' and 'uniformity of coverage' were first explicitly defined, quantified, and related to each other. Recent studies have revealed a number of genes that influence the formation of these histotypical features in the retina, including homologues of those invertebrate genes, although close inspection reveals that they do not always mediate comparable developmental processes nor elucidate fundamental design principles. The present review considers just how pervasive these features of 'mosaic regularity' and 'uniform dendritic coverage' are within the mammalian retina, discussing the means by which such features can be assessed in the mature and developing nervous system and examining the limitations associated with those assessments. We then address the extent to which these two design principles co-exist within different populations of neurons, and how they are achieved during development. Finally, we consider the neural phenotypes obtained in mutant nervous systems, to address whether a prospective gene of interest underlies those very design principles.

Functional architecture of the retina: development and disease

Structure and function are highly correlated in the vertebrate retina, a sensory tissue that is organized into cell layers with microcircuits working in parallel and together to encode visual information. All vertebrate retinas share a fundamental plan, comprising five major neuronal cell classes with cell body distributions and connectivity arranged in stereotypic patterns. Conserved features in retinal design have enabled detailed analysis and comparisons of structure, connectivity and function across species. Each species, however, can adopt structural and/or functional retinal specializations, implementing variations to the basic design in order to satisfy unique requirements in visual function. Recent advances in molecular tools, imaging and electrophysiological approaches have greatly facilitated identification of the cellular and molecular mechanisms that establish the fundamental organization of the retina and the specializations of its microcircuits during development. Here, we review advances in our understanding of how these mechanisms act to shape structure and function at the single cell level, to coordinate the assembly of cell populations, and to define their specific circuitry. We also highlight how structure is rearranged and function is disrupted in disease, and discuss current approaches to re-establish the intricate functional architecture of the retina.

Development of retinal layers

A noticeable characteristic of nervous systems is the arrangement of synapses into distinct layers. Such laminae are fundamental for the spatial organisation of synaptic connections transmitting different kinds of information. A major example of this is the inner plexiform layer (IPL) of the vertebrate retina, which is subdivided into at least ten sublayers. Another noticeable characteristic of these retina layers is that neurons are displayed in the horizontal plane in a non-random array termed as mosaic patterning. Recent studies of vertebrate and invertebrate systems have identified molecules that mediate these interactions. Here, we review the last mechanisms and molecules mediating retinal layering.

Quantification of variability in trichome patterns

While pattern formation is studied in various areas of biology, little is known about the noise leading to variations between individual realizations of the pattern. One prominent example for de novo pattern formation in plants is the patterning of trichomes on Arabidopsis leaves, which involves genetic regulation and cell-to-cell communication. These processes are potentially variable due to, e.g., the abundance of cell components or environmental conditions. To elevate the understanding of regulatory processes underlying the pattern formation it is crucial to quantitatively analyze the variability in naturally occurring patterns. Here, we review recent approaches toward characterization of noise on trichome initiation. We present methods for the quantification of spatial patterns, which are the basis for data-driven mathematical modeling and enable the analysis of noise from different sources. Besides the insight gained on trichome formation, the examination of observed trichome patterns also shows that highly regulated biological processes can be substantially affected by variability.

Modeling Notch signaling: a practical tutorial

Theoretical and computational approaches for understanding different aspects of Notch signaling and Notch dependent patterning are gaining popularity in recent years. These in silico methodologies can provide dynamic insights that are often not intuitive and may help guide experiments aimed at elucidating these processes. This chapter is an introductory tutorial intended to allow someone with basic mathematical and computational knowledge to explore new mathematical models of Notch-mediated processes and perform numerical simulations of these models. In particular, we explain how to define and simulate models of lateral inhibition patterning processes. We provide a Matlab code for simulating various lateral inhibition models in a simple and intuitive manner, and show how to present the results from the computational models. This code can be used as a starting point for exploring more specific models that include additional aspects of the Notch pathway and its regulation.

Regeneration of cone photoreceptors when cell ablation is primarily restricted to a particular cone subtype

We sought to characterize the regenerated cells, if any, when photoreceptor ablation was mostly limited to a particular cone subtype. This allowed us to uniquely assess whether the remaining cells influence specification of regenerating photoreceptors. The ability to replace lost photoreceptors via stem cell therapy holds promise for treating many retinal degenerative diseases. Zebrafish are potent for modelling this because they have robust regenerative capacity emanating from endogenous stem cells, and abundant cone photoreceptors including multiple spectral subtypes similar to human fovea. We ablated the homolog of the human S-cones, the ultraviolet-sensitive (UV) cones, and tested the hypothesis that the photoreceptors regenerating in their place take on identities matching those expected from normal cone mosaic development. We created transgenic fish wherein UV cones can be ablated by addition of a prodrug. Thus photoreceptors developed normally and only the UV cones expressed nitroreductase; the latter converts the prodrug metronidazole to a cell-autonomous neurotoxin. A significant increase in proliferation of progenitor cell populations (p<0.01) was observed when cell ablation was primarily limited to UV cones. In control fish, we found that BrdU primarily incorporated into rod photoreceptors, as expected. However the majority of regenerating photoreceptors became cones when retinal cell ablation was predominantly restricted to UV cones: a 2-fold increase in the relative abundance of cones (p = 0.008) was mirrored by a 35% decrease in rods. By primarily ablating only a single photoreceptor type, we show that the subsequent regeneration is biased towards restoring the cognate photoreceptor type. We discuss the hypothesis that, after cone death, the microenvironment formed by the remaining retinal cells may be influential in determining the identity of regenerating photoreceptors, though other interpretations are plausible. Our novel animal model provides control of ablation that will assist in identifying mechanisms required to replace cone photoreceptors clinically to restore daytime vision.

Effects of growth and mutation on pattern formation in tissues

In many developing tissues, neighboring cells enter different developmental pathways, resulting in a fine-grained pattern of different cell states. The most common mechanism that generates such patterns is lateral inhibition, for example through Delta-Notch coupling. In this work, we simulate growth of tissues consisting of a hexagonal arrangement of cells laterally inhibiting their neighbors. We find that tissue growth by cell division and cell migration tends to produce ordered patterns, whereas lateral growth leads to disordered, patchy patterns. Ordered patterns are very robust to mutations (gene silencing or activation) in single cells. In contrast, mutation in a cell of a disordered tissue can produce a larger and more widespread perturbation of the pattern. In tissues where ordered and disordered patches coexist, the perturbations spread mostly at boundaries between patches. If cell division occurs on time scales faster than the degradation time, disordered patches will appear. Our work suggests that careful experimental characterization of the disorder in tissues could pinpoint where and how the tissue is susceptible to large-scale damage even from single cell mutations.

Influence of cell-to-cell variability on spatial pattern formation

Many spatial patterns in biology arise through differentiation of selected cells within a tissue, which is regulated by a genetic network. This is specified by its structure, parameterisation and the noise on its components and reactions. The latter, in particular, is not well examined because it is rather difficult to trace. The authors use suitable local mathematical measures based on the Voronoi diagram of experimentally determined positions of epidermal plant hairs (trichomes) to examine the variability or noise in pattern formation. Although trichome initiation is a highly regulated process, the authors show that the experimentally observed trichome pattern is substantially disturbed by cell-to-cell variations. Using computer simulations, they find that the rates concerning the availability of the protein complex that triggers trichome formation plays a significant role in noise-induced variations of the pattern. The focus on the effects of cell noise yields further insights into pattern formation of trichomes. The authors expect that similar strategies can contribute to the understanding of other differentiation processes by elucidating the role of naturally occurring fluctuations in the concentration of cellular components or their properties.

Limit-cycle oscillations and stable patterns in repressor lattices

As a model for cell-to-cell communication in biological tissues, we construct repressor lattices by repeating a regulatory three-node motif on a hexagonal structure. Local interactions can be unidirectional, where a node either represses or activates a neighbor that does not communicate backwards. Alternatively, they can be bidirectional where two neighboring nodes communicate with each other. In the unidirectional case, we perform stability analyses for the transitions from stationary to oscillating states in lattices with different regulatory units. In the bidirectional case, we investigate transitions from oscillating states to ordered patterns generated by local switches. Finally, we show how such stable patterns in two-dimensional lattices can be generalized to three-dimensional systems.

Models at the single cell level

Many cellular behaviors cannot be completely captured or appropriately described at the cell population level. Noise induced by stochastic chemical reactions, spatially polarized signaling networks, and heterogeneous cell-cell communication are among the many phenomena that require fine-grained analysis. Accordingly, the mathematical models used to describe such systems must be capable of single cell or subcellular resolution. Here, we review techniques for modeling single cells, including models of stochastic chemical kinetics, spatially heterogeneous intracellular signaling, and spatial stochastic systems. We also briefly discuss applications of each type of model.

Development of the retina and optic pathway

Our understanding of the development of the retina and visual pathways has seen enormous advances during the past 25years. New imaging technologies, coupled with advances in molecular biology, have permitted a fuller appreciation of the histotypical events associated with proliferation, fate determination, migration, differentiation, pathway navigation, target innervation, synaptogenesis and cell death, and in many instances, in understanding the genetic, molecular, cellular and activity-dependent mechanisms underlying those developmental changes. The present review considers those advances associated with the lineal relationships between retinal nerve cells, the production of retinal nerve cell diversity, the migration, patterning and differentiation of different types of retinal nerve cells, the determinants of the decussation pattern at the optic chiasm, the formation of the retinotopic map, and the establishment of ocular domains within the thalamus.

Development of a three dimensional multiscale computational model of the human epidermis

Transforming Growth Factor (TGF-β1) is a member of the TGF-beta superfamily ligand-receptor network. and plays a crucial role in tissue regeneration. The extensive in vitro and in vivo experimental literature describing its actions nevertheless describe an apparent paradox in that during re-epithelialisation it acts as proliferation inhibitor for keratinocytes. The majority of biological models focus on certain aspects of TGF-β1 behaviour and no one model provides a comprehensive story of this regulatory factor's action. Accordingly our aim was to develop a computational model to act as a complementary approach to improve our understanding of TGF-β1. In our previous study, an agent-based model of keratinocyte colony formation in 2D culture was developed. In this study this model was extensively developed into a three dimensional multiscale model of the human epidermis which is comprised of three interacting and integrated layers: (1) an agent-based model which captures the biological rules governing the cells in the human epidermis at the cellular level and includes the rules for injury induced emergent behaviours, (2) a COmplex PAthway SImulator (COPASI) model which simulates the expression and signalling of TGF-β1 at the sub-cellular level and (3) a mechanical layer embodied by a numerical physical solver responsible for resolving the forces exerted between cells at the multi-cellular level. The integrated model was initially validated by using it to grow a piece of virtual epidermis in 3D and comparing the in virtuo simulations of keratinocyte behaviour and of TGF-β1 signalling with the extensive research literature describing this key regulatory protein. This research reinforces the idea that computational modelling can be an effective additional tool to aid our understanding of complex systems. In the accompanying paper the model is used to explore hypotheses of the functions of TGF-β1 at the cellular and subcellular level on different keratinocyte populations during epidermal wound healing.

Multiple genes on chromosome 7 regulate dopaminergic amacrine cell number in the mouse retina

PURPOSE

The size of neuronal populations is modulated by gene variants that influence cell production and survival, in turn influencing neuronal connectivity, function, and disease risk. The size of the dopaminergic amacrine (DA) cell population is a highly heritable trait exhibiting sixfold variation among inbred strains of mice and is used here to identify genes that modulate the number of DA cells.

METHODS

The entire population was counted in retinal wholemounts from 37 genetically defined lines of mice, including six standard inbred strains, 25 recombinant inbred strains (AXB/BXA), reciprocal F1 hybrids, a chromosome (Chr) 7 consomic line, and three additional genetically modified lines.

RESULTS

Much of this variation was mapped to a broad locus on Chr 7 (Dopaminergic amacrine cell number control, Chr 7 [Dacnc7]). The Dacnc7 locus is flanked by two candidate genes known to modulate the number of other types of retinal neuron-the proapoptotic gene, Bax, and tyrosinase. The Tyr mutation was shown to modulate DA cell number modestly, though in the direction opposite that predicted. In contrast, Bax deficiency increased the population fourfold. Bax expression was significantly greater in the A/J than in the C57BL/6J strain, an effect that may be attributed to an SNP in a p53 consensus binding site known to modulate transcription. Finally, we note a strong candidate situated at the peak of the Dacnc7 locus, Lrrk1, a Parkinson's disease gene exhibiting missense mutations segregating within the AXB/BXA cross.

CONCLUSIONS

Multiple polymorphic genes on Chr 7 modulate the size of the population of DA cells.

An integrated systems biology approach to understanding the rules of keratinocyte colony formation

Closely coupled in vitro and in virtuo models have been used to explore the self-organization of normal human keratinocytes (NHK). Although it can be observed experimentally, we lack the tools to explore many biological rules that govern NHK self-organization. An agent-based computational model was developed, based on rules derived from literature, which predicts the dynamic multicellular morphogenesis of NHK and of a keratinocyte cell line (HaCat cells) under varying extracellular Ca++ concentrations. The model enables in virtuo exploration of the relative importance of biological rules and was used to test hypotheses in virtuo which were subsequently examined in vitro. Results indicated that cell-cell and cell-substrate adhesions were critically important to NHK self-organization. In contrast, cell cycle length and the number of divisions that transit-amplifying cells could undergo proved non-critical to the final organization. Two further hypotheses, to explain the growth behaviour of HaCat cells, were explored in virtuo-an inability to differentiate and a differing sensitivity to extracellular calcium. In vitro experimentation provided some support for both hypotheses. For NHKs, the prediction was made that the position of stem cells would influence the pattern of cell migration post-wounding. This was then confirmed experimentally using a scratch wound model.

Regular mosaic pattern development: a study of the interplay between lateral inhibition, apoptosis and differential adhesion

Background

A significant body of literature is devoted to modeling developmental mechanisms that create patterns within groups of initially equivalent embryonic cells. Although it is clear that these mechanisms do not function in isolation, the timing of and interactions between these mechanisms during embryogenesis is not well known. In this work, a computational approach was taken to understand how lateral inhibition, differential adhesion and programmed cell death can interact to create a mosaic pattern of biologically realistic primary and secondary cells, such as that formed by sensory (primary) and supporting (secondary) cells of the developing chick inner ear epithelium.

Results

Four different models that interlaced cellular patterning mechanisms in a variety of ways were examined and their output compared to the mosaic of sensory and supporting cells that develops in the chick inner ear sensory epithelium. The results show that: 1) no single patterning mechanism can create a 2-dimensional mosaic pattern of the regularity seen in the chick inner ear; 2) cell death was essential to generate the most regular mosaics, even through extensive cell death has not been reported for the developing basilar papilla; 3) a model that includes an iterative loop of lateral inhibition, programmed cell death and cell rearrangements driven by differential adhesion created mosaics of primary and secondary cells that are more regular than the basilar papilla; 4) this same model was much more robust to changes in homo- and heterotypic cell-cell adhesive differences than models that considered either fewer patterning mechanisms or single rather than iterative use of each mechanism.

Conclusion

Patterning the embryo requires collaboration between multiple mechanisms that operate iteratively. Interlacing these mechanisms into feedback loops not only refines the output patterns, but also increases the robustness of patterning to varying initial cell states.

Spatial clustering analysis in neuroanatomy: applications of different approaches to motor nerve fiber distribution

Spatial organization of the nerve fibers in the peripheral nerves may be important for the studies of axonal regeneration, the degenerative nerve diseases and the construction of interfaces with peripheral nerves, such as nerve prostheses. Functional topography of motor axons related to the gastrocnemius muscle was revealed in the ventral spinal roots by retrograde tracing. Gastrocnemius muscles of adult rats were injected with the tracer Fluoro-Gold. After 3 days of survival the animals were sacrificed and their ventral roots were harvested, sectioned, and imaged on a fluorescence microscope. Maps of the traced fibers were automatically analyzed using a novel approach, local spatial clustering statistics, that tested for occurrences of clusters of motor fibers and visualized them. Thresholds indicating the presence of clustering at various scales of observation were computed based on series of Monte Carlo simulations of random spatial point patterns. Clusters were visualized by kernel interpolation. The approach was tested on simulated data and subsequently applied to the motor fiber maps in the ventral roots. Results revealed clustering of the motor fibers innervating the gastrocnemius muscle at the level of the L6 ventral spinal root. The analysis was validated using Voronoi tessellation and nearest neighbor analysis.

Cellular pattern formation during retinal regeneration: a role for homotypic control of cell fate acquisition

A dominant mechanism of cellular patterning in the growing fish retina is control of cell fate acquisition by negative feedback signals arising from differentiated cells. We tested the ability of a computational model of this pattern formation mechanism to simulate cellular patterns in regenerated goldfish retina. The model successfully simulated quantitative features of in vivo regenerated patterns, indicating that regenerating retina has access to and utilizes patterning mechanisms that are operational during normal growth. The atypical patterns of regenerated retina could arise in part from regenerative progenitors that, compared to normal growth progenitors, are less responsive to the feedback patterning signals.

Notch activity is downregulated just prior to retinal ganglion cell differentiation

The Notch signaling pathway is important at several stages of retinal development including the differentiation of retinal ganglion cells and Muller glia. The downstream effectors of Notch signaling, Hes1 and Hes5, have been shown to be critical in the retina as well. While Notch activity directly regulates Hes1 and Hes5 elsewhere in the nervous system, it has been unclear whether Hes1 and/or Hes5 are directly regulated by Notch activity in the developing retina. Here, we report that both Hes1 and Hes5 are directly regulated by Notch activity during retinal development. Using fluorescence-based Hes1 and Hes5 reporter constructs, we can monitor Notch activity in progenitor cells in the intact retina, and we find that Notch activity is downregulated just prior to retinal ganglion cell differentiation.

Homotypic constraints dominate positioning of on- and off-center beta retinal ganglion cells

Beta retinal ganglion cells (RGCs) of the cat are classified as either on-center or off-center, according to their response to light. The cell bodies of these on- and off-center RGCs are spatially distributed into regular patterns, known as retinal mosaics. In this paper, we investigate the nature of spatial dependencies between the positioning of on- and off-center RGCs by analysing maps of RGCs and simulating these patterns. We introduce principled approaches to parameter estimation, along with likelihood-based techniques to evaluate different hypotheses. Spatial constraints between cells within-type and between-type are assumed to be controlled by two univariate interaction functions and one bivariate interaction function. By making different assumptions on the shape of the bivariate interaction function, we can compare the hypothesis of statistical independence against the alternative hypothesis of functional independence, where interactions between type are limited to preventing somal overlap. Our findings suggest that the mosaics of on- and off-center beta RGCs are likely to be generated assuming functional independence between the two types. By contrast, allowing a more general form of bivariate interaction function did not improve the likelihood of generating the observed maps. On- and off-center beta RGCs are therefore likely to be positioned subject only to homotypic constraints and the physical constraint that no two somas of opposite type can occupy the same position.

Control of cellular pattern formation in the vertebrate inner retina by homotypic regulation of cell-fate decisions

The vertebrate retina is composed of cellular arrays that are nonrandom across two-dimensional space. The determinants of these nonrandom two-dimensional cellular patterns in the inner nuclear layer of the retina were investigated using empirical and computational modeling techniques. In normal and experimental models of goldfish retinal growth, the patterns of tyrosine hydroxylase- and serotonin-positive cells indicated that neither cell death nor lateral migration of differentiated cells were dominant mechanisms of cellular pattern formation. A computational model of cellular pattern formation that used a signaling mechanism arising from differentiated cells that inhibited homotypic cell-fate decisions generated accurate simulations of the empirically observed patterns in normal retina. This model also predicted the principal atypical cellular pattern characteristic, a transient cell-type-specific hyperplasia, which was empirically observed in the growing retina subsequent to selective ablation of differentiated retinal cells, either tyrosine hydroxylase positive or serotonin positive. The results support the hypothesis that inhibitory spatiotemporal regulation of homotypic cell-fate decisions is a dominant mechanistic determinant of nonrandom cellular patterns in the vertebrate retina.

Developmental improvement in the regularity and packing of mouse horizontal cells: implications for mechanisms underlying mosaic pattern formation

The present investigation has sought to determine whether the population of retinal horizontal cells undergoes an increase in the precision of its mosaic patterning during postnatal development, and if so, whether this increase is compatible with three different mechanistic accounts of retinal mosaic formation. Horizontal cells were labeled with antibodies to neurofilaments or calbindin at different developmental stages, and then visualized in retinal wholemounts. Multiple fields were sampled from each retina to determine horizontal cell density, while the X-Y coordinates of each cell in a field were determined. An estimate of total horizontal cell number was calculated for each retina, while the Voronoi domain regularity index and the packing factor were computed for each field. Two strains of mice showing a two-fold difference in the size of their horizontal cell population in maturity were sampled, C57BL/6J and A/J. Horizontal cell number in C57BL/6J was approximately twice that observed in A/J at all postnatal stages, with neither strain showing an effect of age on horizontal cell number. In both strains, however, the Voronoi domain regularity index and the packing factor were significantly lower at P-1 relative to later developmental stages. These results show that accounts of mosaic formation proposing the selective death of irregularly positioned cells, or the periodic occurrence of fate-determining events, are insufficient to establish the final patterning achieved by horizontal cells. Rather, they support the hypothesis that tangential dispersion enhances mosaic patterning during postnatal development.

Neuronal death induced by endogenous extracellular ATP in retinal cholinergic neuron density control

The precise assembly of neuronal circuits requires that the correct number of pre- and postsynaptic neurons form synaptic connections. Neuronal cell number is thus tightly controlled by cell death during development. Investigating the regulation of cell number in the retina we found an ATP gated mechanism of neuronal death control. By degrading endogenous extracellular ATP or blocking the P2X(7) ATP receptors we found that endogenous extracellular ATP triggers the death of retinal cholinergic neurons during normal development. ATP-induced death eliminates cholinergic cells too close to one another, thereby controlling the total number, the local density and the regular spacing of these neurons.

Cellular patterns in the inner retina of adult zebrafish: quantitative analyses and a computational model of their formation

The mechanisms that control cellular pattern formation in the growing vertebrate central nervous system are poorly understood. In an effort to reveal mechanistic rules of cellular pattern formation in the central nervous system, quantitative spatial analysis and computational modeling techniques were applied to cellular patterns in the inner retina of the adult zebrafish. All the analyzed cell types were arrayed in nonrandom patterns tending toward regularity; specifically, they were locally anticlustered. Over relatively large spatial scales, only one cell type exhibited consistent evidence for pattern regularity, suggesting that cellular pattern formation in the inner retina is dominated by local anticlustering mechanisms. Cross-correlation analyses revealed independence between the patterns of different cell types, suggesting that cellular pattern formation may involve multiple, independent, homotypic anticlustering mechanisms. A computational model of cellular pattern formation in the growing zebrafish retina was developed, which featured an inhibitory, homotypic signaling mechanism, arising from differentiated cells, that controlled the spatial profile of cell fate decisions. By adjusting the spatial profile of this decaying-exponential signal, the model provided good estimates of all the cellular patterns that were observed in vivo, as objectively judged by quantitative spatial pattern analyses. The results support the hypothesis that cellular pattern formation in the inner retina of zebrafish is dominated by a set of anticlustering mechanisms that may control events at, or near, the spatiotemporal point of cell fate decision.

Dopaminergic amacrine cells in the inner nuclear layer and ganglion cell layer comprise a single functional retinal mosaic

Many types of retinal neuron are distributed in an orderly manner across the surface of the retina. Indeed, the existence of such regularity amongst a population of neurons, termed a retinal mosaic, may be a defining feature of functionally independent types of retinal neuron. We have examined the spatial distribution of dopaminergic amacrine cells in the ferret retina both in the inner nuclear layer (INL) and in the ganglion cell layer (GCL) to determine whether the cells in each layer form an independent retinal mosaic as evidence of whether they should be considered as two separate types. Ferret retinas contain approximately 1,900 dopaminergic amacrine cells, of which 27% are located in the GCL, and the rest in the INL. Based on analysis of their Voronoi domains as well as autocorrelation analysis and tests for complete spatial randomness, we found that the distribution of INL cells was statistically regular, while that of the GCL cells was not. However, by using cross-correlation analysis, these two groups of cells were found to be spatially dependent: an exclusion zone was detected in the cross-correlogram of roughly the same size as that found in the autocorrelograms of both INL and GCL cells. Such a pattern would be expected if dopaminergic amacrine cells in the INL and GCL were members of a single regular population differing only in their somatic depth. By using computer simulations, we tested this hypothesis directly, confirming that a random assignment of 27% from the total population produces cross-correlograms that are indistinguishable from those of the biological mosaics. We conclude, therefore, that the cells in the two layers form a single functional population; those in the GCL appear to be misplaced. Somatic positioning with respect to depth within the retina is not, by itself, a reliable guide for functional classification.

Determinants of the exclusion zone in dopaminergic amacrine cell mosaics

A fundamental organizing feature of the retina is the presence of regularly spaced distributions of neurons, yet we have little knowledge of how this patterning emerges during development. Among these retinal mosaics, the spatial organization of the dopaminergic amacrine cells is unique: using nearest-neighbor and Vornoi domain analysis, we found that the dopaminergic amacrine cells were neither randomly distributed, nor did they achieve the regularity documented for other retinal cell types. Autocorrelation analysis revealed the presence of an exclusion zone surrounding individual dopaminergic amacrine cells and modeling studies confirmed this organization, as the mosaic could be simulated by a minimal distance spacing rule defined by a broad set of parameters. Experimental studies determined the relative contributions of tangential dispersion, fate determination, and cell death in the establishment of this exclusion zone. Clonal boundary analysis and simulations of proximity-driven movement discount tangential dispersion, while data from bcl-2 overexpressing mice rule out feedback-inhibitory fate-deterministic accounts. Cell death, by contrast, appears to eliminate dopaminergic amacrine cells that are within close proximity, thereby establishing the exclusion zone surrounding individual cells and in turn creating their mosaic regularity.