D'Arcy Thompson and the theory of transformations

A work in progress: William Bateson's vibratory theory of repetition of parts

In 1891 Cambridge biologist William Bateson (1861-1926) announced his idea that the symmetrical segmentation in living organisms resulted from energy peaks of some vibratory force acting on tissues during morphogenesis. He also demonstrated topographically how folding a radially symmetric organism could produce another with bilateral symmetry. Bateson attended many lectures at the Cambridge Philosophical Society and viewed mechanical models prepared by eminent physicists that illustrated how vibrations affected materials. In his subsequent research, Bateson utilized analogies and metaphors based upon his observations of nature to build a thought model on the effects of vibrations on living tissue, because he realized that the chemistry and biology of his day lacked technologies to perform actual experiments on the subject. He concluded the production of organic segmentation was both a chemical and mechanical phenomenon. By the time of his death Bateson had incorporated new ideas about embryonic organizer regions to suggest a center from which a rhythmic force emanated and then produced the observed repetitive segmentation as a common feature in living organisms.

An archetype and scaling of developmental tissue dynamics across species

Morphometric studies have revealed the existence of simple geometric relationships among various animal shapes. However, we have little knowledge of the mathematical principles behind the morphogenetic dynamics that form the organ/body shapes of different species. Here, we address this issue by focusing on limb morphogenesis in Gallus gallus domesticus (chicken) and Xenopus laevis (African clawed frog). To compare the deformation dynamics between tissues with different sizes/shapes as well as their developmental rates, we introduce a species-specific rescaled spatial coordinate and a common clock necessary for cross-species synchronization of developmental times. We find that tissue dynamics are well conserved across species under this spacetime coordinate system, at least from the early stages of development through the phase when basic digit patterning is established. For this developmental period, we also reveal that the tissue dynamics of both species are mapped with each other through a time-variant linear transformation in real physical space, from which hypotheses on a species-independent archetype of tissue dynamics and morphogenetic scaling are proposed.

Vertebrate Cell Differentiation, Evolution, and Diseases: The Vertebrate-Specific Developmental Potential Guardians VENTX/NANOG and POU5/OCT4 Enter the Stage

During vertebrate development, embryonic cells pass through a continuum of transitory pluripotent states that precede multi-lineage commitment and morphogenesis. Such states are referred to as “refractory/naïve” and “competent/formative” pluripotency. The molecular mechanisms maintaining refractory pluripotency or driving the transition to competent pluripotency, as well as the cues regulating multi-lineage commitment, are evolutionarily conserved. Vertebrate-specific “Developmental Potential Guardians” (vsDPGs; i.e., VENTX/NANOG, POU5/OCT4), together with MEK1 (MAP2K1), coordinate the pluripotency continuum, competence for multi-lineage commitment and morphogenesis in vivo. During neurulation, vsDPGs empower ectodermal cells of the neuro-epithelial border (NEB) with multipotency and ectomesenchyme potential through an “endogenous reprogramming” process, giving rise to the neural crest cells (NCCs). Furthermore, vsDPGs are expressed in undifferentiated-bipotent neuro-mesodermal progenitor cells (NMPs), which participate in posterior axis elongation and growth. Finally, vsDPGs are involved in carcinogenesis, whereby they confer selective advantage to cancer stem cells (CSCs) and therapeutic resistance. Intriguingly, the heterogenous distribution of vsDPGs in these cell types impact on cellular potential and features. Here, we summarize the findings about the role of vsDPGs during vertebrate development and their selective advantage in evolution. Our aim to present a holistic view regarding vsDPGs as facilitators of both cell plasticity/adaptability and morphological innovation/variation. Moreover, vsDPGs may also be at the heart of carcinogenesis by allowing malignant cells to escape from physiological constraints and surveillance mechanisms.

Flagellar kinematics reveals the role of environment in shaping sperm motility

Swimming spermatozoa from diverse organisms often have very similar morphologies, yet different motilities as a result of differences in the flagellar waveforms used for propulsion. The origin of these differences has remained largely unknown. Using high-speed video microscopy and mathematical analysis of flagellar shape dynamics, we quantitatively compare sperm flagellar waveforms from marine invertebrates to humans by means of a novel phylokinematic tree. This new approach revealed that genetically dissimilar sperm can exhibit strikingly similar flagellar waveforms and identifies two dominant flagellar waveforms among the deuterostomes studied here, corresponding to internal and external fertilizers. The phylokinematic tree shows marked discordance from the phylogenetic tree, indicating that physical properties of the fluid environment, more than genetic relatedness, act as an important selective pressure in shaping the evolution of sperm motility. More broadly, this work provides a physical axis to complement morphological and genetic studies to understand evolutionary relationships.

Ecomorphological diversification of some barbs and carps (Cyprininae, Cyprinidae) in the Lower Mekong Basin of Thailand

Morphological variation is fundamentally related to various aspects of fish ecology, including foraging, locomotion, and habitat utilisation. Twenty-six species of closely related cyprinid fish (n = 502) were analysed for patterns of morphological variations by using geometric morphometric methods. Ecological data of feeding and habitat preferences were determined by the observations in fields and laboratory together with the gathering of bibliographic information. The findings of major variation displayed in all parts of the fish body and correlated with ecological parameters. Variations of head shape especially form and position of mouthpart involved with feeding behaviours, whereas the variations of body depth and length which affected swimming patterns reflected responsiveness of water currents and habitat uses. Adaptation of head shape and body elongation was remarkably related to the feeding regime, swimming manoeuvrability and habitat utilisation of the species. Some convergent variation was observed between the tribes Smiliogastrini and Poropuntiini. Therefore, we propose that the morphological diversity of cyprinine fish is mainly affected by ecological gradients, while phylogenetic effects on morphology are minor.

D’Arcy W. Thompson’s Cartesian transformations: a critical evaluation

The images of D’Arcy Wentworth Thompson’s book “On Growth and Form” got an iconic status and became influential for biometrics and other mathematical approaches to organismic form. In particular, this is true for those of the chapter on the theory of transformation, which even has an impact on art and humanities. Based on his approach, Thompson formulated far-reaching conclusions with a partly anti-Darwinian stance. Here, we use the example of Thompson’s transformation of crab carapaces to test to what degree the transformation of grids, landmarks, and shapes result in congruent images. For comparison, we applied the same series of tests to digitized carapaces of real crabs. Both approaches show similar results. Only the simple transformations show a reasonable form of congruence. In particular, the transformations to majoid spider crabs reveal a complicated transformation of grids with partly crossing lines. By contrast, the carapace of the lithodid species is relatively easily created despite the fact that it is no brachyuran, but evolved a spider crab-like shape convergently from a hermit crab ancestor.

From Gregor Mendel to Eric Davidson: Mathematical Models and Basic Principles in Biology

Mathematical models have been widespread in biology since its emergence as a modern experimental science in the 19th century. Focusing on models in developmental biology and heredity, this article (1) presents the properties and epistemological basis of pertinent mathematical models in biology from Mendel's model of heredity in the 19th century to Eric Davidson's model of developmental gene regulatory networks in the 21st; (2) shows that the models differ not only in their epistemologies but also in regard to explicitly or implicitly taking into account basic biological principles, in particular those of biological specificity (that became, in part, replaced by genetic information) and genetic causality. The article claims that models disregarding these principles did not impact the direction of biological research in a lasting way, although some of them, such as D'Arcy Thompson's models of biological form, were widely read and admired and others, such as Turing's models of development, stimulated research in other fields. Moreover, it suggests that successful models were not purely mathematical descriptions or simulations of biological phenomena but were based on inductive, as well as hypothetico-deductive, methodology. The recent availability of large amounts of sequencing data and new computational methodology tremendously facilitates system approaches and pattern recognition in many fields of research. Although these new technologies have given rise to claims that correlation is replacing experimentation and causal analysis, the article argues that the inductive and hypothetico-deductive experimental methodologies have remained fundamentally important as long as causal-mechanistic explanations of complex systems are pursued.

Evolution, kidney development, and chronic kidney disease

There is a global epidemic of chronic kidney disease (CKD) characterized by a progressive loss of nephrons, ascribed in large part to a rising incidence of hypertension, metabolic syndrome, and type 2 diabetes mellitus. There is a ten-fold variation in nephron number at birth in the general population, and a 50% overall decrease in nephron number in the last decades of life. The vicious cycle of nephron loss stimulating hypertrophy by remaining nephrons and resulting in glomerulosclerosis has been regarded as maladaptive, and only partially responsive to angiotensin inhibition. Advances over the past century in kidney physiology, genetics, and development have elucidated many aspects of nephron formation, structure and function. Parallel advances have been achieved in evolutionary biology, with the emergence of evolutionary medicine, a discipline that promises to provide new insight into the treatment of chronic disease. This review provides a framework for understanding the origins of contemporary developmental nephrology, and recent progress in evolutionary biology. The establishment of evolutionary developmental biology (evo-devo), ecological developmental biology (eco-devo), and developmental origins of health and disease (DOHaD) followed the discovery of the hox gene family, the recognition of the contribution of cumulative environmental stressors to the changing phenotype over the life cycle, and mechanisms of epigenetic regulation. The maturation of evolutionary medicine has contributed to new investigative approaches to cardiovascular disease, cancer, and infectious disease, and promises the same for CKD. By incorporating these principles, developmental nephrology is ideally positioned to answer important questions regarding the fate of nephrons from embryo through senescence.

Multivariate morphometrics, quantitative genetics, and neutral theory: Developing a "modern synthesis" for primate evolutionary morphology

Anthropologists are increasingly turning to explicit model-bound evolutionary approaches for understanding the morphological diversification of humans and other primate lineages. Such evolutionary morphological analyses rely on three interconnected conceptual frameworks; multivariate morphometrics for quantifying similarity and differences among taxa, quantitative genetics for modeling the inheritance and evolution of morphology, and neutral theory for assessing the likelihood that taxon diversification is due to stochastic processes such as genetic drift. Importantly, neutral theory provides a framework for testing more parsimonious explanations for observed morphological differences before considering more complex adaptive scenarios. However, the consistency with which these concepts are applied varies considerably, which mirrors some of the theoretical obstacles faced during the "modern synthesis" of classical population genetics in the early 20th century. Here, each framework is reviewed and some potential stumbling blocks to the full conceptual integration of multivariate morphometrics, quantitative genetics, and neutral theory are considered.

Neural crest and the origin of species-specific pattern

For well over half of the 150 years since the discovery of the neural crest, the special ability of these cells to function as a source of species-specific pattern has been clearly recognized. Initially, this observation arose in association with chimeric transplant experiments among differentially pigmented amphibians, where the neural crest origin for melanocytes had been duly noted. Shortly thereafter, the role of cranial neural crest cells in transmitting species-specific information on size and shape to the pharyngeal arch skeleton as well as in regulating the timing of its differentiation became readily apparent. Since then, what has emerged is a deeper understanding of how the neural crest accomplishes such a presumably difficult mission, and this includes a more complete picture of the molecular and cellular programs whereby neural crest shapes the face of each species. This review covers studies on a broad range of vertebrates and describes neural-crest-mediated mechanisms that endow the craniofacial complex with species-specific pattern. A major focus is on experiments in quail and duck embryos that reveal a hierarchy of cell-autonomous and non-autonomous signaling interactions through which neural crest generates species-specific pattern in the craniofacial integument, skeleton, and musculature. By controlling size and shape throughout the development of these systems, the neural crest underlies the structural and functional integration of the craniofacial complex during evolution.

The old and new faces of morphology: the legacy of D'Arcy Thompson's 'theory of transformations' and 'laws of growth'

In 1917, the publication of On Growth and Form by D'Arcy Wentworth Thompson challenged both mathematicians and naturalists to think about biological shapes and diversity as more than a confusion of chaotic forms generated at random, but rather as geometric shapes that could be described by principles of physics and mathematics. Thompson's work was based on the ideas of Galileo and Goethe on morphology and of Russell on functionalism, but he was first to postulate that physical forces and internal growth parameters regulate biological forms and could be revealed via geometric transformations in morphological space. Such precise mathematical structure suggested a unifying generative process, as reflected in the title of the book. To Thompson it was growth that could explain the generation of any particular biological form, and changes in ontogeny, rather than natural selection, could then explain the diversity of biological shapes. Whereas adaptationism, widely accepted in evolutionary biology, gives primacy to extrinsic factors in producing morphological variation, Thompson's 'laws of growth' provide intrinsic directives and constraints for the generation of individual shapes, helping to explain the 'profusion of forms, colours, and other modifications' observed in the living world.

A tribute to D'Arcy Wentworth Thompson: Elucidation of a developmental principle

We show the vertebrate anterior -posterior axis is made by time space translation (TST). 1/ TST of Hox temporal to spatial collinearity makes the trunk part of the axis. 2/TST continues into the head. 3/ TST is mediated by collinear Hox-Hox interactions. 4/ 'Decision points' involving signalling pathways separate axial domains.

Quantifying Shape Changes and Tissue Deformation in Leaf Development

The analysis of biological shapes has applications in many areas of biology, and tools exist to quantify organ shape and detect shape differences between species or among variants. However, such measurements do not provide any information about the mechanisms of shape generation. Quantitative data on growth patterns may provide insights into morphogenetic processes, but since growth is a complex process occurring in four dimensions, growth patterns alone cannot intuitively be linked to shape outcomes. Here, we present computational tools to quantify tissue deformation and surface shape changes over the course of leaf development, applied to the first leaf of Arabidopsis (Arabidopsis thaliana). The results show that the overall leaf shape does not change notably during the developmental stages analyzed, yet there is a clear upward radial deformation of the leaf tissue in early time points. This deformation pattern may provide an explanation for how the Arabidopsis leaf maintains a relatively constant shape despite spatial heterogeneities in growth. These findings highlight the importance of quantifying tissue deformation when investigating the control of leaf shape. More generally, experimental mapping of deformation patterns may help us to better understand the link between growth and shape in organ development.

Evolutionary uniformitarianism

I present a new compilation of the distribution of the temporal distribution of new morphologies of marine invertebrates associated with the Ediacaran-Cambrian (578-510 Ma) diversification of Metazoa. Combining this data with previous work on the hierarchical structure of gene regulatory networks, I argue that the distribution of morphologies may be, in part, a record of the time-asymmetric generation of variation. Evolution has been implicitly viewed as a uniformitarian process where the rates may vary but the underlying processes, including the types of variation, are essentially invariant through time. Recent studies demonstrate that this uniformitarian assumption is false, suggesting that the types of variation may vary through time.

Age synthesis and estimation via faces: a survey

Human age, as an important personal trait, can be directly inferred by distinct patterns emerging from the facial appearance. Derived from rapid advances in computer graphics and machine vision, computer-based age synthesis and estimation via faces have become particularly prevalent topics recently because of their explosively emerging real-world applications, such as forensic art, electronic customer relationship management, security control and surveillance monitoring, biometrics, entertainment, and cosmetology. Age synthesis is defined to rerender a face image aesthetically with natural aging and rejuvenating effects on the individual face. Age estimation is defined to label a face image automatically with the exact age (year) or the age group (year range) of the individual face. Because of their particularity and complexity, both problems are attractive yet challenging to computer-based application system designers. Large efforts from both academia and industry have been devoted in the last a few decades. In this paper, we survey the complete state-of-the-art techniques in the face image-based age synthesis and estimation topics. Existing models, popular algorithms, system performances, technical difficulties, popular face aging databases, evaluation protocols, and promising future directions are also provided with systematic discussions.

Scaling and shear transformations capture beak shape variation in Darwin's finches

Evolution by natural selection has resulted in a remarkable diversity of organism morphologies that has long fascinated scientists and served to establish the first relations among species. Despite the essential role of morphology as a phenotype of species, there is not yet a formal, mathematical scheme to quantify morphological phenotype and relate it to both the genotype and the underlying developmental genetics. Herein we demonstrate that the morphological diversity in the beaks of Darwin's Finches is quantitatively accounted for by the mathematical group of affine transformations. Specifically, we show that all beak shapes of Ground Finches (genus Geospiza) are related by scaling transformations (a subgroup of the affine group), and the same relationship holds true for all the beak shapes of Tree, Cocos, and Warbler Finches (three distinct genera). This analysis shows that the beak shapes within each of these groups differ only by their scales, such as length and depth, which are genetically controlled by Bmp4 and Calmodulin. By measuring Bmp4 expression in the beak primordia of the species in the genus Geospiza, we provide a quantitative map between beak morphology and the expression levels of Bmp4. The complete morphological variation within the beaks of Darwin's finches can be explained by extending the scaling transformations to the entire affine group, by including shear transformations. Altogether our results suggest that the mathematical theory of groups can help decode morphological variation, and points to a potentially hierarchical structure of morphological diversity and the underlying developmental processes.

The golden section and American psychology, 1892-1938

The golden section has been said by many to be the most beautiful proportion. Fechner was the first to investigate it experimentally, and several late-nineteenth- and early-twentieth-century American psychologists followed up on his work. Among these were four prominent names: Lightner Witmer (1867-1956), Edward L. Thorndike (1874-1949), Robert S. Woodworth (1869-1962), and Robert M. Ogden (1877-1959). Why did such well-known psychologists bother with the golden section? In attempting to answer this question we discovered that the golden section was surprisingly well known during this period, not only in psychology but also in advertising and design. It would have been entirely congruent with their stature for prominent psychologists to take an interest in it.