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.

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.

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.

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).

Why call it developmental bias when it is just development?

The concept of developmental constraints has been central to understand the role of development in morphological evolution. Developmental constraints are classically defined as biases imposed by development on the distribution of morphological variation.This opinion article argues that the concepts of developmental constraints and developmental biases do not accurately represent the role of development in evolution. The concept of developmental constraints was coined to oppose the view that natural selection is all-capable and to highlight the importance of development for understanding evolution. In the modern synthesis, natural selection was seen as the main factor determining the direction of morphological evolution. For that to be the case, morphological variation needs to be isotropic (i.e. equally possible in all directions). The proponents of the developmental constraint concept argued that development makes that some morphological variation is more likely than other (i.e. variation is not isotropic), and that, thus, development constraints evolution by precluding natural selection from being all-capable.This article adds to the idea that development is not compatible with the isotropic expectation by arguing that, in fact, it could not be otherwise: there is no actual reason to expect that development could lead to isotropic morphological variation. It is then argued that, since the isotropic expectation is untenable, the role of development in evolution should not be understood as a departure from such an expectation. The role of development in evolution should be described in an exclusively positive way, as the process determining which directions of morphological variation are possible, instead of negatively, as a process precluding the existence of morphological variation we have no actual reason to expect.This article discusses that this change of perspective is not a mere question of semantics: it leads to a different interpretation of the studies on developmental constraints and to a different research program in evolution and development. This program does not ask whether development constrains evolution. Instead it asks questions such as, for example, how different types of development lead to different types of morphological variation and, together with natural selection, determine the directions in which different lineages evolve.

Is evolution predictable? Quantitative genetics under complex genotype-phenotype maps.

A fundamental aim of post-genomic 21st century biology is to understand the genotype-phenotype map (GPM) or how specific genetic variation relates to specific phenotypic variation. Quantitative genetics approximates such maps using linear models, and has developed methods to predict the response to selection in a population. The other major field of research concerned with the GPM, developmental evolutionary biology, or evo-devo, has found the GPM to be highly nonlinear and complex. Here, we quantify how the predictions of quantitative genetics are affected by a complex, nonlinear map based on the development of a multicellular organ. We compared the predicted change in mean phenotype for a single generation using the multivariate breeder's equation, with the change observed from the model of development. We found that there are frequent disagreements between predicted and observed responses to selection due to the nonlinear nature of the genotype-phenotype map. Our results are a step toward integrating the fields studying the GPM.

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.

Adaptation and Conservation throughout the Drosophila melanogaster Life-Cycle.

Previous studies of the evolution of genes expressed at different life-cycle stages of Drosophila melanogaster have not been able to disentangle adaptive from nonadaptive substitutions when using nonsynonymous sites. Here, we overcome this limitation by combining whole-genome polymorphism data from D. melanogaster and divergence data between D. melanogaster and Drosophila yakuba. For the set of genes expressed at different life-cycle stages of D. melanogaster, as reported in modENCODE, we estimate the ratio of substitutions relative to polymorphism between nonsynonymous and synonymous sites (α) and then α is discomposed into the ratio of adaptive (ωa) and nonadaptive (ωna) substitutions to synonymous substitutions. We find that the genes expressed in mid- and late-embryonic development are the most conserved, whereas those expressed in early development and postembryonic stages are the least conserved. Importantly, we found that low conservation in early development is due to high rates of nonadaptive substitutions (high ωna), whereas in postembryonic stages it is due, instead, to high rates of adaptive substitutions (high ωa). By using estimates of different genomic features (codon bias, average intron length, exon number, recombination rate, among others), we also find that genes expressed in mid- and late-embryonic development show the most complex architecture: they are larger, have more exons, more transcripts, and longer introns. In addition, these genes are broadly expressed among all stages. We suggest that all these genomic features are related to the conservation of mid- and late-embryonic development. Globally, our study supports the hourglass pattern of conservation and adaptation over the life-cycle.

Bracketing phenogenotypic limits of mammalian hybridization.

An increasing number of mammalian species have been shown to have a history of hybridization and introgression based on genetic analyses. Only relatively few fossils, however, preserve genetic material, and morphology must be used to identify the species and determine whether morphologically intermediate fossils could represent hybrids. Because dental and cranial fossils are typically the key body parts studied in mammalian palaeontology, here we bracket the potential for phenotypically extreme hybridizations by examining uniquely preserved cranio-dental material of a captive hybrid between grey and ringed seals. We analysed how distinct these species are genetically and morphologically, how easy it is to identify the hybrids using morphology and whether comparable hybridizations happen in the wild. We show that the genetic distance between these species is more than twice the modern human-Neanderthal distance, but still within that of morphologically similar species pairs known to hybridize. By contrast, morphological and developmental analyses show grey and ringed seals to be highly disparate, and that the hybrid is a predictable intermediate. Genetic analyses of the parent populations reveal introgression in the wild, suggesting that grey-ringed seal hybridization is not limited to captivity. Taken together, we postulate that there is considerable potential for mammalian hybridization between phenotypically disparate taxa.

Quantitative Morphological Variation in the Developing Drosophila Wing.

Quantitative genetic variation in morphology is pervasive in all species and is the basis for the evolution of differences among species. The measurement of morphological form in adults is now beginning to be combined with comparable measurements of form during development. Here we compare the shape of the developing wing to its adult form in a holometabolous insect, Drosophila melanogaster We used protein expression patterns to measure shape in the developing precursors of the final adult wing. Three developmental stages were studied: late larval third instar, post-pupariation and in the adult fly. We studied wild-type animals in addition to mutants of two genes (shf and ds) that have known effects on adult wing shape and size. Despite experimental noise related to the difficulty of comparing developing structures, we found consistent differences in wing shape and size at each developmental stage between genotypes. Quantitative comparisons of variation arising at different developmental stages with the variation in the final structure enable us to determine when variation arises, and to generate hypotheses about the causes of that variation. In addition we provide linear rules allowing us to link wing morphology in the larva, with wing morphology in the pupa. Our approach provides a framework to analyze quantitative morphological variation in the developing fly wing. This framework should help to characterize the natural variation of the larval and pupal wing shape, and to measure the contribution of the processes occurring during these developmental stages to the natural variation in adult wing morphology.

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.

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.

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.

How complexity increases in development: An analysis of the spatial-temporal dynamics of Gene expression in Ciona intestinalis.

The increase in complexity in an embryo over developmental time is perhaps one of the most intuitive processes of animal development. It is also intuitive that the embryo becomes progressively compartmentalized over time and space. In spite of this intuitiveness, there are no systematic attempts to quantify how this occurs. Here, we present a quantitative analysis of the compartmentalization and spatial complexity of Ciona intestinalis over developmental time by analyzing thousands of gene expression spatial patterns from the ANISEED database. We measure compartmentalization in two ways: as the relative volume of expression of genes and as the disparity in gene expression between body parts. We also use a measure of the curvature of each gene expression pattern in 3D space. These measures show a similar increase over time, with the most dramatic change occurring from the 112-cell stage to the early tailbud stage. Combined, these measures point to a global pattern of increase in complexity in the Ciona embryo. Finally, we cluster the different regions of the embryo depending on their gene expression similarity, within and between stages. Results from this clustering analysis, which partially correspond to known fate maps, provide a global quantitative overview about differentiation and compartmentalization between body parts at each developmental stage.

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.

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.