Dynamic-module redundancy confers robustness to the gene regulatory network involved in hair patterning of Arabidopsis epidermis

Redundancy among dynamic modules is emerging as a potentially generic trait in gene regulatory networks. Moreover, module redundancy could play an important role in network robustness to perturbations. We explored the effect of dynamic-module redundancy in the networks associated to hair patterning in Arabidopsis root and leaf epidermis. Recent studies have put forward several dynamic modules belonging to these networks. We defined these modules in a discrete dynamical framework that was previously reported. Then, we addressed whether these modules are sufficient or necessary for recovering epidermal cell types and patterning. After defining two quantitative estimates of the system's robustness, we also compared the robustness of each separate module with that of a network coupling all the leaf or root modules. We found that, considering certain assumptions, all the dynamic modules proposed so far are sufficient on their own for pattern formation, but reinforce each other during epidermal development. Furthermore, we found that networks of coupled modules are more robust to perturbations than single modules. These results suggest that dynamic-module redundancy might be an important trait in gene regulatory networks and point at central questions regarding network evolution, module coupling, pattern robustness and the evolution of development.     

Epidermal patterning in Arabidopsis: models make a difference

The leaf and root epidermis in Arabidopsis provide ideal systems in which to explore the mechanisms that underlie the patterned assignment of cell fates during development. Extensive experimental studies have uncovered a complex interlocked feedback network that operates within the epidermis to coordinate the choice between hair and nonhair fates. A number of recent studies using mathematical models have begun to study this network, highlighting new mechanisms that have subsequently been confirmed in model-directed experiments. These studies illustrate the potential of integrated modeling and experimentation to shed new light on developmental processes. Moreover, these models enable systems-level comparative analyses that may help understand the origin and role of properties, such as robustness and redundancy in developmental systems and, concomitantly, the evolution of development itself.     

Clonal analysis of epidermal patterning during maize leaf development

In plants, specialized epidermal cells are arranged in semiordered patterns. In grasses such as maize, stomata and other specialized cell types differentiate in linear patterns within the leaf epidermis. A variety of mechanisms have been proposed to direct patterns of epidermal cell differentiation. One class of models proposes that patterns of cellular differentiation depend on the lineage relationships among epidermal cells. Another class of models proposes that epidermal patterning depends on positional information rather than lineage relationships. In the dicot epidermis, cell lineage is an important factor in the patterning of stomata, but not trichomes. In this study, the role of cell lineage in the linear patterning of stomata and bulliform cells in the maize leaf epidermis is investigated. Clones of epidermal cells in juvenile leaves were marked by excision of dSpm from gl15-m and in adult leaves by excision of Ds2 from bz2-m. These clones were analyzed in relation to patterns of stomata and bulliform cells, testing specific predictions of clonal origin hypotheses for the patterning of these cell types. We found that the great majority of clones analyzed failed to satisfy these predictions. Our results clearly show that lineage does not account for the linear patterning of stomata and bulliform cells, implying that positional information must direct the differentiation patterns of these cell types in maize.     

A computational model of the effect of gene misexpression on the development of cortical areas

Brain function depends on the specialisation of brain areas. In the murine cerebral cortex, the development of these areas depends on the coordinated expression of several genes in precise spatial patterns in the telencephalon during embryogenesis. Manipulating the expression of these genes during development alters the positions and sizes of cortical areas in the adult. Qualitative data also show that these genes regulate each other’s expression during development so that they form a regulatory network with many feedback loops. However, it is currently unknown which regulatory interactions are critical to generating the correct expression patterns to lead to normal cortical development. Here, we formalise the relationships inferred from genetic manipulations into computational models. We simulate many different networks potentially consistent with the experimental data and show that a surprising diversity of networks produce similar results. This demonstrates that existing data cannot uniquely specify the network. We conclude by suggesting experiments necessary to constrain the model and help identify and understand the true structure of this regulatory network.     

The Role of Human Transportation Networks in Mediating the Genetic Structure of Seasonal Influenza in the United States

Recent studies have demonstrated the importance of accounting for human mobility networks when modeling epidemics in order to accurately predict spatial dynamics. However, little is known about the impact these movement networks have on the genetic structure of pathogen populations and whether these effects are scale-dependent. We investigated how human movement along the aviation and commuter networks contributed to intra-seasonal genetic structure of influenza A epidemics in the continental United States using spatially-referenced hemagglutinin nucleotide sequences collected from 2003–2013 for both the H3N2 and H1N1 subtypes. Comparative analysis of these transportation networks revealed that the commuter network is highly spatially-organized and more heavily traveled than the aviation network, which instead is characterized by high connectivity between all state pairs. We found that genetic distance between sequences often correlated with distance based on interstate commuter network connectivity for the H1N1 subtype, and that this correlation was not as prevalent when geographic distance or aviation network connectivity distance was assessed against genetic distance. However, these patterns were not as apparent for the H3N2 subtype at the scale of the continental United States. Finally, although sequences were spatially referenced at the level of the US state of collection, a community analysis based on county to county commuter connections revealed that commuting communities did not consistently align with state geographic boundaries, emphasizing the need for the greater availability of more specific sequence location data. Our results highlight the importance of utilizing host movement data in characterizing the underlying genetic structure of pathogen populations and demonstrate a need for a greater understanding of the differential effects of host movement networks on pathogen transmission at various spatial scales.     

Kolmogorov complexity of epithelial pattern formation: The role of regulatory network configuration

The tissues of multicellular organisms are made of differentiated cells arranged in organized patterns. This organization emerges during development from the coupling of dynamic intra- and intercellular regulatory networks. This work applies the methods of information theory to understand how regulatory network structure both within and between cells relates to the complexity of spatial patterns that emerge as a consequence of network operation. A computational study was performed in which undifferentiated cells were arranged in a two dimensional lattice, with gene expression in each cell regulated by identical intracellular randomly generated Boolean networks. Cell–cell contact signalling between embryonic cells is modeled as coupling among intracellular networks so that gene expression in one cell can influence the expression of genes in adjacent cells. In this system, the initially identical cells differentiate and form patterns of different cell types. The complexity of network structure, temporal dynamics and spatial organization is quantified through the Kolmogorov-based measures of normalized compression distance and set complexity. Results over sets of random networks that operate in the ordered, critical and chaotic domains demonstrate that: (1) ordered and critical networks tend to create the most information-rich patterns; (2) signalling configurations in which cell-to-cell communication is non-directional mostly produce simple patterns irrespective of the internal network domain; and (3) directional signalling configurations, similar to those that function in planar cell polarity, produce the most complex patterns, but only when the intracellular networks function in non-chaotic domains.     

Scaling and structure of dicotyledonous leaf venation networks

There have been numerous attempts to derive general models for the structure and function of resource delivery networks in biology. Such theories typically predict the quantitative structure of vascular networks across scales. For example, fractal branching models of plant structure predict that the network dimensions within plant stems or leaves should be scale-free. However, very few empirical examples of such networks are available with which to evaluate such hypotheses. Here, we apply recently developed leaf network extraction software to a global leaf dataset. We find that leaf networks are neither entirely scale-free nor governed entirely by a characteristic scale. Indeed, we find many network properties, such as vein length distributions, which are governed by characteristic scales, and other network properties, notably vein diameter distributions, which are typified by power-law behaviour. Our findings suggest that theories of network structure will remain incomplete until they address the multiple constraints on network architecture.     

Spatial distributions of expansion rate, cell division rate and cell size in maize leaves: a synthesis of the effects of soil water status, evaporative demand and temperature

The spatial distributions of leaf expansion rate, cell division rate and cell size was examined under contrasting soil water conditions, evaporative demands and temperatures in a series of experiments carried out in either constant or naturally fluctuating conditions. They were examined in the epidermis and all leaf tissues. (1) Meristem temperature affected relative elongation rate by a constant ratio at all positions in the leaf. If expressed per unit thermal time, the distribution of relative expansion rate was independent of temperature and was similar in all experiments with low evaporative demand and no water deficit. This provides a reference distribution, characteristic of the studied genotype, to which any distribution in stressed plants can be compared. (2) Evaporative demand and soil water deficit affected independently the distribution of relative elongation rate and had near-additive effects. For a given stress, a nearly constant difference was observed, at all positions of the leaf, between the relative elongation rates of stressed plants and those of control plants. This caused a reduction in the length of the zone with tissue elongation. (3) Methods for calculating cell division rate in the epidermis and in all leaf tissues are proposed and discussed. In control plants, the zone with cell division was 30 mm and 60 mm long in the epidermis and in whole tissues, respectively. Both this length and relative division rate were reduced by soil water deficit. The size of epidermal and of mesophyll cells was nearly unaffected in the leaf zone with both cell division and tissue expansion, suggesting that water deficit affects tissue expansion rate and cell division rate to the same extent. Conversely, cell size of epidermis and mesophyll were reduced by water deficit in mature parts of the leaf.     

Pigment cell mechanisms underlying dorsal color‐pattern polymorphism in the japanese four‐lined snake

To provide histological foundation for studying the genetic mechanisms of color‐pattern polymorphisms, we examined light reflectance profiles and cellular architectures of pigment cells that produced striped, nonstriped, and melanistic color patterns in the snake Elaphe quadrivirgata. Both, striped and nonstriped morphs, possessed the same set of epidermal melanophores and three types of dermal pigment cells (yellow xanthophores, iridescent iridophores, and black melanophores), but spatial variations in the densities of epidermal and dermal melanophores produced individual variations in stripe vividness. The densities of epidermal and dermal melanophores were two or three times higher in the dark‐brown‐stripe region than in the yellow background in the striped morph. However, the densities of epidermal and dermal melanophores between the striped and background regions were similar in the nonstriped morph. The melanistic morph had only epidermal and dermal melanophores and neither xanthophores nor iridophores were detected. Ghost stripes in the shed skin of some melanistic morphs suggested that stripe pattern formation and melanism were controlled independently. We proposed complete‐ and incomplete‐dominance heredity models for the stripe‐melanistic variation and striped, pale‐striped, and nonstriped polymorphisms, respectively, according to the differences in pigment‐cell composition and its spatial architecture. J. Morphol. 274:1353–1364, 2013. © 2013 Wiley Periodicals, Inc.     

Function approximation approach to the inference of reduced NGnet models of genetic networks

Background  

The inference of a genetic network is a problem in which mutual interactions among genes are deduced using time-series of gene expression patterns. While a number of models have been proposed to describe genetic regulatory networks, this study focuses on a set of differential equations since it has the ability to model dynamic behavior of gene expression. When we use a set of differential equations to describe genetic networks, the inference problem can be defined as a function approximation problem. On the basis of this problem definition, we propose in this study a new method to infer reduced NGnet models of genetic networks.