Drawing to Extend Waddington’s Epigenetic Landscape

We describe a collaboration between an artist, a mathematician, and a biologist, which examines the potential of drawing for understanding biological process. As a case study, it considers C. H. Waddington’s powerful visual representation of the “epigenetic landscape,” whose purpose it is to unify research in genetics, embryology, and evolutionary biology. We explore the strengths, but also the limitations of Waddington’s landscape and attempt to transcend the latter through a collaborative series of exploratory images. Through careful description of this drawing process, we touch on the epistemological consequences it had on all participants, artist and scientist alike

A deep learning approach for staging embryonic tissue isolates with small data

Machine learning approaches are becoming increasingly widespread and are now present in most areas of research. Their recent surge can be explained in part due to our ability to generate and store enormous amounts of data with which to train these models. The requirement for large training sets is also responsible for limiting further potential applications of machine learning, particularly in fields where data tend to be scarce such as developmental biology. However, recent research seems to indicate that machine learning and Big Data can sometimes be decoupled to train models with modest amounts of data. In this work we set out to train a CNN-based classifier to stage zebrafish tail buds at four different stages of development using small information-rich data sets. Our results show that two and three dimensional convolutional neural networks can be trained to stage developing zebrafish tail buds based on both morphological and gene expression confocal microscopy images, achieving in each case up to 100% test accuracy scores. Importantly, we show that high accuracy can be achieved with data set sizes of under 100 images, much smaller than the typical training set size for a convolutional neural net. Furthermore, our classifier shows that it is possible to stage isolated embryonic structures without the need to refer to classic developmental landmarks in the whole embryo, which will be particularly useful to stage 3D culture in vitro systems such as organoids. We hope that this work will provide a proof of principle that will help dispel the myth that large data set sizes are always required to train CNNs, and encourage researchers in fields where data are scarce to also apply ML approaches

A deep learning approach for staging embryonic tissue isolates with small data

Machine learning approaches are becoming increasingly widespread and are now present in most areas of research. Their recent surge can be explained in part due to our ability to generate and store enormous amounts of data with which to train these models. The requirement for large training sets is also responsible for limiting further potential applications of machine learning, particularly in fields where data tend to be scarce such as developmental biology. However, recent research seems to indicate that machine learning and Big Data can sometimes be decoupled to train models with modest amounts of data. In this work we set out to train a CNN-based classifier to stage zebrafish tail buds at four different stages of development using small information-rich data sets. Our results show that two and three dimensional convolutional neural networks can be trained to stage developing zebrafish tail buds based on both morphological and gene expression confocal microscopy images, achieving in each case up to 100% test accuracy scores. Importantly, we show that high accuracy can be achieved with data set sizes of under 100 images, much smaller than the typical training set size for a convolutional neural net. Furthermore, our classifier shows that it is possible to stage isolated embryonic structures without the need to refer to classic developmental landmarks in the whole embryo, which will be particularly useful to stage 3D culture in vitro systems such as organoids. We hope that this work will provide a proof of principle that will help dispel the myth that large data set sizes are always required to train CNNs, and encourage researchers in fields where data are scarce to also apply ML approaches

A damped oscillator imposes temporal order on posterior gap gene expression in Drosophila.

Insects determine their body segments in two different ways. Short-germband insects, such as the flour beetle Tribolium castaneum, use a molecular clock to establish segments sequentially. In contrast, long-germband insects, such as the vinegar fly Drosophila melanogaster, determine all segments simultaneously through a hierarchical cascade of gene regulation. Gap genes constitute the first layer of the Drosophila segmentation gene hierarchy, downstream of maternal gradients such as that of Caudal (Cad). We use data-driven mathematical modelling and phase space analysis to show that shifting gap domains in the posterior half of the Drosophila embryo are an emergent property of a robust damped oscillator mechanism, suggesting that the regulatory dynamics underlying long- and short-germband segmentation are much more similar than previously thought. In Tribolium, Cad has been proposed to modulate the frequency of the segmentation oscillator. Surprisingly, our simulations and experiments show that the shift rate of posterior gap domains is independent of maternal Cad levels in Drosophila. Our results suggest a novel evolutionary scenario for the short- to long-germband transition and help explain why this transition occurred convergently multiple times during the radiation of the holometabolan insects.MINECO BFU2009-10184/BFU2012-33775/SEV-2012-0208 European Commission FP7/KBBE-2011/5/289434 La Caixa Savings Bank (PhD fellowship to BV) KLI Klosterneuburg (PhD Writing-up & Postdoctoral Fellowships to BV) Wissenschaftskolleg zu Berlin (Wiko) (Fellowships to JJ and AC

EvoDevo in phase space: the dynamics of gap gene expression

During insect development segments either form sequentially (short-germband) or simultaneously (long-germband) . The gap genes comprise the first zygotic regulatory layer of the segmentation gene hierarchy in flies, which use the long-germband mode. A data-driven mathematical model reveals that two distinct dynamical regimes govern anterior and posterior trunk gap gene patterning in Drosophila melanogaster. Stationary anterior domains rely on multi-stability whilst the observed anterior shifts of posterior domains are an emergent property of a damped oscillator mechanism. Both types of dynamics are recovered by a three-gene sub-network embedded in the gap gene regulatory network, which can also sustain oscillations. Oscillations are not found in the gap gene system but are characteristic of short-germband segmentation, suggesting that both modes are more similar than previously thought. This insight sheds light on how long-germband segmentation could have repeatedly and independently evolved from the ancestral short-germband mode.Durant el desenvolupament dels insectes, els segments es formen seqüencialment (desenvolupament de banda curta) o simultàniament (desenvolupament de banda llarga). Els gens gap constitueixen la primera capa de regulació cigòotica en la jerarquia de la segmentació en mosques, que fan servir un desenvolupament de banda llarga. Amb un model matemàtic posam al descobert que dos règims dinàmics diferents governen la formació de patrons a les parts anteriors i posteriors de la Drosophila melanogaster. Els dominis anteriors són estàtics i depenen de la multi-estabilitat del sistema en aquesta part, mentre que el desplacament anterior dels dominis posteriors es una propietat emergent d’un oscial·ldor amortidor. Una subxarxa de tres gens immersa a la xarxa dels gens gap recupera aquests dos tipus de dinàmiques. Aquesta subxarxa tamb é pot oscil·lar. Al sistema dels gens gap no hi han cap osciacions però sabem que són característiques de la segmentació de banda curta. Això suggereix que els dos tipus de segmentació s’hi assemblen més del que pensavem. Aquest descobriment ens ajudara entendre com pot haver evolucionat la segmentació de banda llarga repetides vegades de la segmentació de banda curta, que es la més ancestral

The unappreciated generative role of cell movements in pattern formation.

The mechanisms underpinning the formation of patterned cellular landscapes has been the subject of extensive study as a fundamental problem of developmental biology. In most cases, attention has been given to situations in which cell movements are negligible, allowing researchers to focus on the cell-extrinsic signalling mechanisms, and intrinsic gene regulatory interactions that lead to pattern emergence at the tissue level. However, in many scenarios during development, cells rapidly change their neighbour relationships in order to drive tissue morphogenesis, while also undergoing patterning. To draw attention to the ubiquity of this problem and propose methodologies that will accommodate morphogenesis into the study of pattern formation, we review the current approaches to studying pattern formation in both static and motile cellular environments. We then consider how the cell movements themselves may contribute to the generation of pattern, rather than hinder it, with both a species specific and evolutionary viewpoint

Zebrafish neuromesodermal progenitors undergo a critical state transition in vivo.

The transition state model of cell differentiation proposes that a transient window of gene expression stochasticity precedes entry into a differentiated state. Here, we assess this theoretical model in zebrafish neuromesodermal progenitors (NMps) in vivo during late somitogenesis stages. We observed an increase in gene expression variability at the 24 somite stage (24ss) before their differentiation into spinal cord and paraxial mesoderm. Analysis of a published 18ss scRNA-seq dataset showed that the NMp population is noisier than its derivatives. By building in silico composite gene expression maps from image data, we assigned an 'NM index' to in silico NMps based on the expression of neural and mesodermal markers and demonstrated that cell population heterogeneity peaked at 24ss. Further examination revealed cells with gene expression profiles incongruent with their prospective fate. Taken together, our work supports the transition state model within an endogenous cell fate decision making event

Classification of transient behaviours in a time-dependent toggle switch model

Background: Waddington’s epigenetic landscape is an intuitive metaphor for the developmental and evolutionary potential of biological regulatory processes. It emphasises time-dependence and transient behaviour. Nowadays, we can derive this landscape by modelling a specific regulatory network as a dynamical system and calculating its so-called potential surface. In this sense, potential surfaces are the mathematical equivalent of the Waddingtonian landscape metaphor. In order to fully capture the time-dependent (non-autonomous) transient behaviour of biological processes, we must be able to characterise potential landscapes and how they change over time. However, currently available mathematical tools focus on the asymptotic (steady-state) behaviour of autonomous dynamical systems, which restricts how biological systems are studied. Results: We present a pragmatic first step towards a methodology for dealing with transient behaviours in non-autonomous systems. We propose a classification scheme for different kinds of such dynamics based on the simulation of a simple genetic toggle-switch model with time-variable parameters. For this low-dimensional system, we can calculate and explicitly visualise numerical approximations to the potential landscape. Focussing on transient dynamics in non-autonomous systems reveals a range of interesting and biologically relevant behaviours that would be missed in steady-state analyses of autonomous systems. Our simulation-based approach allows us to identify four qualitatively different kinds of dynamics: transitions, pursuits, and two kinds of captures. We describe these in detail, and illustrate the usefulness of our classification scheme by providing a number of examples that demonstrate how it can be employed to gain specific mechanistic insights into the dynamics of gene regulation. Conclusions: The practical aim of our proposed classification scheme is to make the analysis of explicitly time-dependent transient behaviour tractable, and to encourage the wider use of non-autonomous models in systems biology. Our method is applicable to a large class of biological processes.This work was supported by a ’la Caixa’ fellowship awarded to BV. AC was supported by the BioPreDyn consortium, funded by European Commission grant FP7-KBBE-2011-5/289434. The laboratory of JJ is funded by the MEC-EMBL agreement for the EMBL/CRG Research Unit in Systems Biology. Additional financial support was provided by SGR Grant 406 from the Catalan funding agency AGAUR, and by grants BFU2009- 10184 and BFU2012-337758 from the Spanish Ministerio de Economia y Competitividad (MINECO