On the origins of developmental robustness: modeling buffering mechanisms against cell-level noise.

During development, cells are subject to stochastic fluctuations in their positions (i.e. cell-level noise) that can potentially lead to morphological noise (i.e. stochastic differences between morphologies that are expected to be equal, e.g. the right and left sides of bilateral organisms). In this study, we explore new and existing hypotheses on buffering mechanisms against cell-level noise. Many of these hypotheses focus on how the boundaries between territories of gene expression remain regular and well defined, despite cell-level noise and division. We study these hypotheses and how irregular territory boundaries lead to morphological noise. To determine the consistency of the different hypotheses, we use a general computational model of development: EmbryoMaker. EmbryoMaker can implement arbitrary gene networks regulating basic cell behaviors (contraction, adhesion, etc.), signaling and tissue biomechanics. We found that buffering mechanisms based on the orientation of cell divisions cannot lead to regular boundaries but that other buffering mechanisms can (homotypic adhesion, planar contraction, non-dividing boundaries, constant signaling and majority rule hypotheses). We also explore the effects of the shape and size of the territories on morphological noise.

Evo-devo beyond development: Generalizing evo-devo to all levels of the phenotypic evolution.

A foundational idea of evo-devo is that morphological variation is not isotropic, that is, it does not occur in all directions. Instead, some directions of morphological variation are more likely than others from DNA-level variation and these largely depend on development. We argue that this evo-devo perspective should apply not only to morphology but to evolution at all phenotypic levels. At other phenotypic levels there is no development, but there are processes that can be seen, in analogy to development, as constructing the phenotype (e.g., protein folding, learning for behavior, etc.). We argue that to explain the direction of evolution two types of arguments need to be combined: generative arguments about which phenotypic variation arises in each generation and selective arguments about which of it passes to the next generation. We explain how a full consideration of the two types of arguments improves the explanatory power of evolutionary theory. Also see the video abstract here: https://youtu.be/Egbvma_uaKc.

A method to predict the response to directional selection using a Kalman filter.

Predicting evolution remains challenging. The field of quantitative genetics provides predictions for the response to directional selection through the breeder's equation, but these predictions can have errors. The sources of these errors include omission of traits under selection, inaccurate estimates of genetic variance, and nonlinearities in the relationship between genetic and phenotypic variation. Previous research showed that the expected value of these prediction errors is often not zero, so predictions are systematically biased. Here, we propose that this bias, rather than being a nuisance, can be used to improve the predictions. We use this to develop a method to predict evolution, which is built on three key innovations. First, the method predicts change as the breeder's equation plus a bias term. Second, the method combines information from the breeder's equation and from the record of past changes in the mean to predict change using a Kalman filter. Third, the parameters of the filter are fitted in each generation using a learning algorithm on the record of past changes. We compare the method to the breeder's equation in two artificial selection experiments, one using the wing of the fruit fly and another using simulations that include a complex mapping of genotypes to phenotypes. The proposed method outperforms the breeder's equation, particularly when traits under selection are omitted from the analysis, when data are noisy, and when additive genetic variance is estimated inaccurately or not estimated at all. The proposed method is easy to apply, requiring only the trait means over past generations.

Mechano-chemical feedback mediated competition for BMP signalling leads to pattern formation.

Developmental patterning is thought to be regulated by conserved signalling pathways. Initial patterns are often broad before refining to only those cells that commit to a particular fate. However, the mechanisms by which pattern refinement takes place remain to be addressed. Using the posterior crossvein (PCV) of the Drosophila pupal wing as a model, into which bone morphogenetic protein (BMP) ligand is extracellularly transported to instruct vein patterning, we investigate how pattern refinement is regulated. We found that BMP signalling induces apical enrichment of Myosin II in developing crossvein cells to regulate apical constriction. Live imaging of cellular behaviour indicates that changes in cell shape are dynamic and transient, only being maintained in those cells that retain vein fate competence after refinement. Disrupting cell shape changes throughout the PCV inhibits pattern refinement. In contrast, disrupting cell shape in only a subset of vein cells can result in a loss of BMP signalling. We propose that mechano-chemical feedback leads to competition for the developmental signal which plays a critical role in pattern refinement.

Evolution of the G Matrix under Nonlinear Genotype-Phenotype Maps.

AbstractThe G matrix is a statistical summary of the genetic basis of a set of traits and a central pillar of quantitative genetics. A persistent controversy is whether G changes slowly or quickly over time. The evolution of G is important because it affects the ability to predict, or reconstruct, evolution by selection. Empirical studies have found mixed results on how fast G evolves. Theoretical work has largely been developed under the assumption that the relationship between genetic variation and phenotypic variation-the genotype-phenotype map (GPM)-is linear. Under this assumption, G is expected to remain constant over long periods of time. However, according to developmental biology, the GPM is typically complex and nonlinear. Here, we use a GPM model based on the development of a multicellular organ to study how G evolves. We find that G can change relatively fast and in qualitative different ways, which we describe in detail. Changes can be particularly large when the population crosses between regions of the GPM that have different properties. This can result in the additive genetic variance in the direction of selection fluctuating over time and even increasing despite the eroding effect of selection.

Cell signaling stabilizes morphogenesis against noise.

Embryonic development involves gene networks, extracellular signaling, cell behaviors (cell division, adhesion, etc.) and mechanical interactions. How should these be coordinated to lead to complex and robust morphologies? To explore this question, we randomly wired genes and cell behaviors into a huge number of networks in EmbryoMaker. EmbryoMaker is a computational model of animal development that simulates how the 3D positions of cells, i.e. morphology, change over time due to such networks. We found that any gene network can lead to complex morphologies if this activates cell behaviors over large regions of the embryo. Importantly, however, for such complex morphologies to be robust to noise, gene networks should include cell signaling that compartmentalizes the embryo into small regions where cell behaviors are regulated differently. If, instead, cell behaviors are equally regulated over large regions, complex but non-robust morphologies arise. We explain how compartmentalization enhances robustness and why it is a general feature of animal development. Our results are consistent with theories proposing that robustness evolved by the co-option of gene networks and extracellular cell signaling in early animal evolution.

Correction: On the evolution and development of morphological complexity: A view from gene regulatory networks.

[This corrects the article DOI: 10.1371/journal.pcbi.1008570.].

On the evolution and development of morphological complexity: A view from gene regulatory networks.

How does morphological complexity evolve? This study suggests that the likelihood of mutations increasing phenotypic complexity becomes smaller when the phenotype itself is complex. In addition, the complexity of the genotype-phenotype map (GPM) also increases with the phenotypic complexity. We show that complex GPMs and the above mutational asymmetry are inevitable consequences of how genes need to be wired in order to build complex and robust phenotypes during development. We randomly wired genes and cell behaviors into networks in EmbryoMaker. EmbryoMaker is a mathematical model of development that can simulate any gene network, all animal cell behaviors (division, adhesion, apoptosis, etc.), cell signaling, cell and tissues biophysics, and the regulation of those behaviors by gene products. Through EmbryoMaker we simulated how each random network regulates development and the resulting morphology (i.e. a specific distribution of cells and gene expression in 3D). This way we obtained a zoo of possible 3D morphologies. Real gene networks are not random, but a random search allows a relatively unbiased exploration of what is needed to develop complex robust morphologies. Compared to the networks leading to simple morphologies, the networks leading to complex morphologies have the following in common: 1) They are rarer; 2) They need to be finely tuned; 3) Mutations in them tend to decrease morphological complexity; 4) They are less robust to noise; and 5) They have more complex GPMs. These results imply that, when complexity evolves, it does so at a progressively decreasing rate over generations. This is because as morphological complexity increases, the likelihood of mutations increasing complexity decreases, morphologies become less robust to noise, and the GPM becomes more complex. We find some properties in common, but also some important differences, with non-developmental GPM models (e.g. RNA, protein and gene networks in single cells).

A set of simple cell processes is sufficient to model spiral cleavage.

During cleavage, different cellular processes cause the zygote to become partitioned into a set of cells with a specific spatial arrangement. These processes include the orientation of cell division according to: an animal-vegetal gradient; the main axis (Hertwig's rule) of the cell; and the contact areas between cells or the perpendicularity between consecutive cell divisions (Sachs' rule). Cell adhesion and cortical rotation have also been proposed to be involved in spiral cleavage. We use a computational model of cell and tissue biomechanics to account for the different existing hypotheses about how the specific spatial arrangement of cells in spiral cleavage arises during development. Cell polarization by an animal-vegetal gradient, a bias to perpendicularity between consecutive cell divisions (Sachs' rule), cortical rotation and cell adhesion, when combined, reproduce the spiral cleavage, whereas other combinations of processes cannot. Specifically, cortical rotation is necessary at the 8-cell stage to direct all micromeres in the same direction. By varying the relative strength of these processes, we reproduce the spatial arrangement of cells in the blastulae of seven different invertebrate species.

Replaying evolutionary transitions from the dental fossil record.

The evolutionary relationships of extinct species are ascertained primarily through the analysis of morphological characters. Character inter-dependencies can have a substantial effect on evolutionary interpretations, but the developmental underpinnings of character inter-dependence remain obscure because experiments frequently do not provide detailed resolution of morphological characters. Here we show experimentally and computationally how gradual modification of development differentially affects characters in the mouse dentition. We found that intermediate phenotypes could be produced by gradually adding ectodysplasin A (EDA) protein in culture to tooth explants carrying a null mutation in the tooth-patterning gene Eda. By identifying development-based character inter-dependencies, we show how to predict morphological patterns of teeth among mammalian species. Finally, in vivo inhibition of sonic hedgehog signalling in Eda null teeth enabled us to reproduce characters deep in the rodent ancestry. Taken together, evolutionarily informative transitions can be experimentally reproduced, thereby providing development-based expectations for character-state transitions used in evolutionary studies.

Mechanical constraint from growing jaw facilitates mammalian dental diversity.

Much of the basic information about individual organ development comes from studies using model species. Whereas conservation of gene regulatory networks across higher taxa supports generalizations made from a limited number of species, generality of mechanistic inferences remains to be tested in tissue culture systems. Here, using mammalian tooth explants cultured in isolation, we investigate self-regulation of patterning by comparing developing molars of the mouse, the model species of mammalian research, and the bank vole. A distinct patterning difference between the vole and the mouse molars is the alternate cusp offset present in the vole. Analyses of both species using 3D reconstructions of developing molars and jaws, computational modeling of cusp patterning, and tooth explants cultured with small braces show that correct cusp offset requires constraints on the lateral expansion of the developing tooth. Vole molars cultured without the braces lose their cusp offset, and mouse molars cultured with the braces develop a cusp offset. Our results suggest that cusp offset, which changes frequently in mammalian evolution, is more dependent on the 3D support of the developing jaw than other aspects of tooth shape. This jaw-tooth integration of a specific aspect of the tooth phenotype indicates that organs may outsource specific aspects of their morphology to be regulated by adjacent body parts or organs. Comparative studies of morphologically different species are needed to infer the principles of organogenesis.

Mapping Selection within Drosophila melanogaster Embryo's Anatomy.

We present a survey of selection across Drosophila melanogaster embryonic anatomy. Our approach integrates genomic variation, spatial gene expression patterns, and development with the aim of mapping adaptation over the entire embryo's anatomy. Our adaptation map is based on analyzing spatial gene expression information for 5,969 genes (from text-based annotations of in situ hybridization data directly from the BDGP database, Tomancak et al. 2007) and the polymorphism and divergence in these genes (from the project DGRP, Mackay et al. 2012).The proportion of nonsynonymous substitutions that are adaptive, neutral, or slightly deleterious are estimated for the set of genes expressed in each embryonic anatomical structure using the distribution of fitness effects-alpha method (Eyre-Walker and Keightley 2009). This method is a robust derivative of the McDonald and Kreitman test (McDonald and Kreitman 1991). We also explore whether different anatomical structures differ in the phylogenetic age, codon usage, or expression bias of the genes they express and whether genes expressed in many anatomical structures show more adaptive substitutions than other genes.We found that: 1) most of the digestive system and ectoderm-derived structures are under selective constraint, 2) the germ line and some specific mesoderm-derived structures show high rates of adaptive substitution, and 3) the genes that are expressed in a small number of anatomical structures show higher expression bias, lower phylogenetic ages, and less constraint.

Differential tissue growth and cell adhesion alone drive early tooth morphogenesis: An ex vivo and in silico study.

From gastrulation to late organogenesis animal development involves many genetic and bio-mechanical interactions between epithelial and mesenchymal tissues. Ectodermal organs, such as hairs, feathers and teeth are well studied examples of organs whose development is based on epithelial-mesenchymal interactions. These develop from a similar primordium through an epithelial folding and its interaction with the mesenchyme. Despite extensive knowledge on the molecular pathways involved, little is known about the role of bio-mechanical processes in the morphogenesis of these organs. We propose a simple computational model for the biomechanics of one such organ, the tooth, and contrast its predictions against cell-tracking experiments, mechanical relaxation experiments and the observed tooth shape changes over developmental time. We found that two biomechanical processes, differential tissue growth and differential cell adhesion, were enough, in the model, for the development of the 3D morphology of the early tooth germ. This was largely determined by the length and direction of growth of the cervical loops, lateral folds of the enamel epithelium. The formation of these cervical loops was found to require accelerated epithelial growth relative to other tissues and their direction of growth depended on specific differential adhesion between the three tooth tissues. These two processes and geometrical constraints in early tooth bud also explained the shape asymmetry between the lateral cervical loops and those forming in the anterior and posterior of the tooth. By performing mechanical perturbations ex vivo and in silico we inferred the distribution and direction of tensile stresses in the mesenchyme that restricted cervical loop lateral growth and forced them to grow downwards. Overall our study suggests detailed quantitative explanations for how bio-mechanical processes lead to specific morphological 3D changes over developmental time.

Adaptive dynamics under development-based genotype-phenotype maps.

It is not known whether natural selection can encounter any given phenotype that can be produced by genetic variation. There has been a long-lasting debate about the processes that limit adaptation and, consequently, about how well adapted phenotypes are. Here we examine how development may affect adaptation, by decomposing the genotype-fitness map-the association between each genotype and its fitness-into two: one mapping genotype to phenotype by means of a computational model of organ development, and one mapping phenotype to fitness. In the map of phenotype and fitness, the fitness of each individual is based on the similarity between realized morphology and optimal morphology. We use three different simulations to map phenotype to fitness, and these differ in the way in which similarity is calculated: similarity is calculated for each trait (in terms of each cell position individually), for a large or a small number of phenotypic landmarks (the 'many-traits' and 'few-traits' phenotype-fitness maps), and by measuring the overall surface roughness of morphology (the 'roughness' phenotype-fitness map). Evolution is simulated by applying the genotype-phenotype map and one phenotype-fitness map to each individual in the population, as well as random mutation and drift. We show that the complexity of the genotype-phenotype map prevents substantial adaptation in some of the phenotype-fitness maps: sustained adaptation is only possible using 'roughness' or 'few-traits' phenotype-fitness maps. The results contribute developmental understanding to the long-standing question of which aspects of phenotype can be effectively optimized by natural selection.

The origin and loss of periodic patterning in the turtle shell.

The origin of the turtle shell over 200 million years ago greatly modified the amniote body plan, and the morphological plasticity of the shell has promoted the adaptive radiation of turtles. The shell, comprising a dorsal carapace and a ventral plastron, is a layered structure formed by basal endochondral axial skeletal elements (ribs, vertebrae) and plates of bone, which are overlain by keratinous ectodermal scutes. Studies of turtle development have mostly focused on the bones of the shell; however, the genetic regulation of the epidermal scutes has not been investigated. Here, we show that scutes develop from an array of patterned placodes and that these placodes are absent from a soft-shelled turtle in which scutes were lost secondarily. Experimentally inhibiting Shh, Bmp or Fgf signaling results in the disruption of the placodal pattern. Finally, a computational model is used to show how two coupled reaction-diffusion systems reproduce both natural and abnormal variation in turtle scutes. Taken together, these placodal signaling centers are likely to represent developmental modules that are responsible for the evolution of scutes in turtles, and the regulation of these centers has allowed for the diversification of the turtle shell.

Computational modeling of development by epithelia, mesenchyme and their interactions: a unified model.

MOTIVATION: The transformation of the embryo during development requires complex gene networks, cell signaling and gene-regulated cell behaviors (division, adhesion, polarization, apoptosis, contraction, extracellular matrix secretion, signal secretion and reception, etc.). There are several models of development implementing these phenomena, but none considers at the same time the very different bio-mechanical properties of epithelia, mesenchyme, extracellular matrix and their interactions. RESULTS: Here, we present a new computational model and accompanying open-source software, EmbryoMaker, that allows the user to simulate custom developmental processes by designing custom gene networks capable of regulating cell signaling and all animal basic cell behaviors. We also include an editor to implement different initial conditions, mutations and experimental manipulations. We show the applicability of the model by simulating several complex examples of animal development. AVAILABILITY AND IMPLEMENTATION: The source code can be downloaded from: http://www.biocenter.helsinki.fi/salazar/software.html. CONTACT: isalazar@mappi.helsinki.fi SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

How complexity increases in development: An analysis of the spatial-temporal dynamics of 1218 genes in Drosophila melanogaster.

One of the most apparent phenomena in development is that it starts with something apparently simple and leads to something clearly complex with a specific and functional structure. At the level of gene expression it seems also clear that the embryo becomes progressively compartmentalized over time and space. However, there have not been any systematic attempts to quantify how this occurs. Here, we present a quantitative analysis of the compartmentalization and spatial complexity of gene expression in Drosophila melanogaster over developmental time by analyzing thousands of gene expression spatial patterns from FlyExpress database. We use three different mathematical measures of compartmentalization of gene expression in space. All these measures show a similar non-linear increase in compartmentalization over time, with the most dramatic change occurring from the maternal to the early gastrula stage. Transcription factors and growth factors showed an earlier compartmentalization. Finally, we partitioned the embryo space in 257 equally sized regions and clustered them depending on their expression similarity, within and between stages. This provides a global overview about the effective degree of differentiation and compartmentalization between body parts at each developmental stage and when and where in the embryo there are more changes, due to signaling or movement.

A computational model of teeth and the developmental origins of morphological variation.

The relationship between the genotype and the phenotype, or the genotype-phenotype map, is generally approached with the tools of multivariate quantitative genetics and morphometrics. Whereas studies of development and mathematical models of development may offer new insights into the genotype-phenotype map, the challenge is to make them useful at the level of microevolution. Here we report a computational model of mammalian tooth development that combines parameters of genetic and cellular interactions to produce a three-dimensional tooth from a simple tooth primordia. We systematically tinkered with each of the model parameters to generate phenotypic variation and used geometric morphometric analyses to identify, or developmentally ordinate, parameters best explaining population-level variation of real teeth. To model the full range of developmentally possible morphologies, we used a population sample of ringed seals (Phoca hispida ladogensis). Seal dentitions show a high degree of variation, typically linked to the lack of exact occlusion. Our model suggests that despite the complexity of development and teeth, there may be a simple basis for dental variation. Changes in single parameters regulating signalling during cusp development may explain shape variation among individuals, whereas a parameter regulating epithelial growth may explain serial, tooth-to-tooth variation along the jaw. Our study provides a step towards integrating the genotype, development and the phenotype.

Making quantitative morphological variation from basic developmental processes: Where are we? The case of the Drosophila wing.

One of the aims of evolutionary developmental biology is to discover the developmental origins of morphological variation. The discipline has mainly focused on qualitative morphological differences (e.g., presence or absence of a structure) between species. Studies addressing subtle, quantitative variation are less common. The Drosophila wing is a model for the study of development and evolution, making it suitable to investigate the developmental mechanisms underlying the subtle quantitative morphological variation observed in nature. Previous reviews have focused on the processes involved in wing differentiation, patterning and growth. Here, we investigate what is known about how the wing achieves its final shape, and what variation in development is capable of generating the variation in wing shape observed in nature. Three major developmental stages need to be considered: larval development, pupariation, and pupal development. The major cellular processes involved in the determination of tissue size and shape are cell proliferation, cell death, oriented cell division and oriented cell intercalation. We review how variation in temporal and spatial distribution of growth and transcription factors affects these cellular mechanisms, which in turn affects wing shape. We then discuss which aspects of the wing morphological variation are predictable on the basis of these mechanisms. Developmental Dynamics 244:1058-1073, 2015. © 2015 Wiley Periodicals, Inc.

Morphological evolution and embryonic developmental diversity in metazoa.

Most studies of pattern formation and morphogenesis in metazoans focus on a small number of model species, despite the fact that information about a wide range of species and developmental stages has accumulated in recent years. By contrast, this article attempts to use this broad knowledge base to arrive at a classification of developmental types through which metazoan body plans are generated. This classification scheme pays particular attention to the diverse ways by which cell signalling and morphogenetic movements depend on each other, and leads to several testable hypotheses regarding morphological variation within and between species, as well as metazoan evolution.