Growth is a fundamental aspect of development: it results from the tight regulation of a combination of processes including cell differentiation, division and movement. Many of these phenomena have been shown to be controlled by gradients of chemical factors, known as morphogens, which regulate cell behaviour using threshold-specific responses.
The aim of this talk will be to compare deterministic and stochastic models for domain growth. I will outline both PDE and master equation approaches and show that the two can be connected in some limit. Finally, I will apply the methods to a specific instance of periodic patterning and use the results to highlight the differences that arise between deterministic and stochastic models.
A remarkable feature of embryonic development is the reliable and accurate pattern in which cell types arise. This is particularly true in the developing central nervous system where the first step in the assembly of neuronal circuits requires the generation of an extraordinary array of different types of neurons in a precise organization. Different neuronal subtypes are generated from distinct domains of progenitor cells surrounding the lumen of the developing neural tube. Each of these domains is characterized by the combinatorial expression of transcription factors. In ventral regions of the neural tube, this transcriptional code is established by the secreted morphogen Sonic hedgehog (Shh). The ventral neural tube therefore provides an appealing model to address the mechanisms involved in tissue patterning by morphogen gradients during embryonic tissue morphogenesis. Of particular importance is understanding how cells interpret the gradient of Shh signaling. To address this question, we analyzed the dynamic response of progenitor cells to Shh signaling. We have shown that both the duration and the concentration of Shh signal control differential gene expression in neural progenitos. Cells appear to transform the strength of Shh signal into intracellular periods of signal transduction, the duration of which is proportional to the extracellular ligand concentration. This is achieved by the gradual desensitisation of cells to ongoing Shh signal transduction. Hence, these data indicate that cells are not passive recipients of the Shh morphogen gradient but actively participate in fashioning the appropriate response. This raises the question of whether cells continuously adapt their gene expression profile, and consequently their fate, to the extracellular concentration of morphogen or if there is a "memory" effect in which cells retain the identity that corresponds to the highest concentration of morphogen to which they have been exposed. A memory for the highest morphogen concentration has been noted in the case of other morphogens where it has been dubbed the "ratchet effect". Here, we first demonstrate that duration of signalling can control the generation of the whole range of Shh responses in the ventral neural tube. Furthermore, we show that cells continuously sense the extracellular concentration of ligand, consequently adapting their cell fate. Indeed, neural cells appear to lack a "ratchet effect", both in vitro and in vivo. These data highlight the plasticity of the response to Shh and provide a mechanism to explain the robustness and reproducibility of neural tube patterning.
We present a single-cell based model of vertebrate limb development. The fluid-elastic structure of the cells and extracellular matrix are represented within the framework of the immersed boundary method. This cells-based model has been previously applied to biofilm and tumor growth. The model is coupled with reaction diffusion equations for growth factors and morphogens produced in the apical epidermal ridge and in the zone of polarizing activity. Here we present preliminary simulations for limb bud outgrowth.
Together, gastrulation and segmentation lay down the body plan of developing vertebrate embryos. However, despite their importance, many key biological aspects of these processes remain unclear, partly because experimental results involve multiple mechanisms acting simultaneously, and thus are difficult to disentangle. I will present multi-cell simulations using the GGH model (aka the CPM) implemented in the open-source simulation environment CompuCell3D (see www.compucell3d.org) of both processes, focusing on the use of simulations to identify key biological mechanisms. In the chick embryo, gastrulation starts with the elongation of the primitive streak from Koller's Sickle and rapidly develops into two large-scale vortical cell flows. I will discuss the possible roles for cell division, planar-polarity induction, chemoattraction and chemorepulsion.1 Only a combination of chemorepulsion of Hensen's Node cells by Koller's Sickle and planar-polarity alignment reproduces all experimental observations. During somitogenesis, the initially homogeneous presomitic mesoderm created during gastrulation separates into a series of discrete somites. While the clock-and-wavefront model of somitogenesis, in which periodic gene expression, particularly of Notch and Wnt, interacts with an FGF8-based thresholding mechanism explains many aspects of the determination of cell fates, it does not explain how cell determination translates into somite morphology. I will show how a combination of an extension of the models of the somitic clock and the determination front developed by Goldbeter and Pourquie and Lewis, with our own hypotheses for the translation of Wnt and Lfrg levels into N-CAM, N-cadherin, EphA4 and ephrinB2, the regulation of cell division in the tailbud and the translation of adhesion into somite shape, reproduces the dynamics of somitogenesis, including intersomitic separation, boundary shape evolution and sorting of misdifferentiated cells across compartment boundaries.2
1Work conducted by Bakhtier Vasiev, Mark Chaplain and Cornelis J. Weijer at the University of Dundee and Ariel Balter and J. A. G. at Indiana University.
2Work conducted by J. A. G., Ying Zhang, Maciej Swat, Benjamin Zaitlen, Santiago Schnell, Julio Belmonte and Susan Hester at Indiana University.
The question of how complex animal body patterns arise from seemingly disorganized or formless initial structures is one of the major and unsolved questions in developmental biology. In 1952, a British mathematician Alan Turing proposed a simple mathematical answer to the question. He showed that the reaction and diffusion of chemical substances could make a kind of stationary wave, which functions as the positional information in the embryo. According to the computational studies, the "wave" from autonomously without any pre-pattern, and gives rise to a variety of biological patterns those the simple gradient model can not explain. In spite of its theoretical potential, existence of the Turing pattern in developing embryo has been doubted by most of biologists for many years because of the difficulty in detecting the "wave" in the animal body.
A fundamental problem in neural development is our limited ability to observe and study how the decisions of individual cells lead to stereotypical cell migratory patterns that assemble the vertebrate peripheral nervous system. We combine our expertise in the stem cell-like neural crest and high-resolution optical microscopy to study the mechanisms that regulate the programmed invasion of the neural crest in the chick embryo. In the trunk, neural crest cells navigate in loosely connected streams through expanding tissue microenvironments to assemble the peripheral nervous system. We show that there is a coordination of molecular signals that regulate the attraction and inhibition of neural crest behaviors to sculpt cells into discrete sympathetic ganglia, a major component of the neural circuitry between the spinal cord and organs. Time-lapse analysis of neural crest cell behaviors reveals complex cell interactions that lead to follow-the-leader behavior and differences in local cell proliferation. Our results suggest a model in which cell proliferation at the migratory front drives neural crest expansion into peripheral target sites, the precise invasion of which is regulated by specific receptor-ligand relationships.
Joint work with Frances Lefcort, Jennifer Kasemeier, Bec McLennan and Danny Stark
Many models of axonal elongation are based on the assumption that the rate of lengthening is driven by the production of cellular materials in the soma. These models make specific predictions about transport and concentration gradients of proteins both over time and along the length of the axon. In vivo, it is well accepted that for a particular neuron the length and rate of growth are controlled by the body size and rate of growth of the animal. In terms of modeling axonal elongation this radically changes the relationships between key variables. It raises fundamental questions. For example, during in vivo lengthening is the production of material constant or does it change over time? What is the density profile of material along the nerve during in vivo elongation? Does density change over time or vary along the nerve? To answer these questions we measured the length, mitochondrial density, and estimated the half-life of mitochondria in the axons of the medial segmental nerves of 1st, 2nd, and 3rd instar Drosophila larvae. Our data suggest a complex relationship between axonal length and mass production and that neurons may have an "axonal length sensor."
The neural tube is the embryonic precursor of the central nervous system (CNS), the brain and spinal cord. The CNS tissue starts as a flat "plate" which then rolls up to form the neural tube. During neural tube closure, the neural cells are dividing, undergoing complex patterning to form the appropriate neuronal precursors, changing their shape, and interacting with new neighbors. Failure to close the neural tube results in neural tube defects, like spina bifida and exencephaly, the second most common human birth defect. However, little is known of the genes that control neural tube closure or how these genes work
To gain insight into this complex morphogenetic process, we have used an unbiased approach of forward genetic screening in mice to identify a number of genes that are critically required for neural tube closure. Our goal is to clone the genes which when mutated cause neural tube defects and to determine the mechanisms by which they act to regulate this critical embryonic process. To date we have cloned 12 new genes necessary for neural tube closure. This is leading to novel insights into Hedgehog signaling, regulated proliferation, interactions between head mesenchyme and neural tissue, and neural fold fusion.
Neurulation is a very dynamic process but one in which our knowledge has largely been gained from looking a fixed and stained embryos. In order to understand the cell biological processes involved in neural tube closure, we are employing dynamic imaging of embryos in exo utero culture to study the normal events of neural tube closure. Our next goal is to determine how cell behavior is disrupted in the various neural tube mutants.
Cells sense the environment's mechanical stiffness to control their own shape, migration, and fate. To better understand stiffness sensing, we constructed a stochastic model of the "motor-clutch" force transmission system, where molecular clutches link F-actin to the substrate and mechanically resist myosin-driven F-actin retrograde flow. The model predicts two distinct regimes: (1) "frictional slippage" with fast retrograde flow and low traction forces on stiff substrates, and (2) oscillatory "load-and-fail" dynamics with slower retrograde flow and higher traction forces on soft substrates. We experimentally confirmed these model predictions in embryonic chick forebrain neurons by measuring the nanoscale dynamics of single growth cone filopodia. Furthermore, we experimentally observed a model-predicted switch in F-actin dynamics around an elastic modulus of 1 kPa. Thus, a motor-clutch system inherently senses and responds to the mechanical stiffness of the local environment.
In this talk we will present a number of examples of increasing complexity in which spatial patterning is influenced by growth and possibly mechanics. These range from simple examples in which growth is prescribed and mechanics plays a secondary role to examples in which the growth and patterning is controlled by stresses in the system.
The neural crest cells are a highly invasive and contribute to many structures in the vertebrate embryo including the face, heart, and trunk peripheral nervous systems. Navigational defects and/or genetic modifications in the adult neural crest lead to highly metastatic melanoma (neuroblastoma) or crest-related birth defects. Neural crest cells have been elegantly traced to follow stereotypical migratory pattern consisting of discrete streams of follow-the-leader chain assemblies (see Kulesa's talk). The mechanisms driving this chain-like pattern are not adequately understood. We are investigating two distinct mechanisms of neural crest cell chain formation: (1) leader cells form a channel in the extracellular matrix and other cells follow the path of least resistance in a follow the leader fashion and (2) filopodia contacts between cells are responsible for providing a guidance mechanism directing cells to line up. Using agent based simulations we have found that the second hypothesis is the more likely explanation for the maintenance of the cell-like migratory pattern. We cannot, however, rule out that the first hypothesis completely and it is possible that a combination of both mechanisms is at work.
Work done in collaboration with Michelle Wynn.
A challenge within the field of morphogenesis is to identify the causal relations between local cellular behaviours and the resulting global tissue movements. To aid this understanding we are developing two new types of technology for studying a classical model system - the vertebrate limb bud. We have built a 3D computer simulation (a finite element model, FEM) of the mouse limb bud, which allows questions of mechanism to be explored. To make these theoretical experiments as accurate as possible, we have also developed new tools for quantifying empirical aspects of the system: (a) the dynamically-changing shape of the bud over time, using optical projection tomography (OPT [1,2]), and (b) a quantification of a double-labelling technique (BrdU plus IddU ) for measuring cell cycle times within their correct spatial context.
It has long been assumed that diffusable signals from the apcial ectodermal ridge act as a mitogen, creating a gradient of proliferation rates within the limb mesenchyme, with highest division rates seen in the distal-most mesenchyme, and that this heterogeneity contributes to the observed shape changes. Through the use of our imaging tools and computational model we show that this is highly unlikely, and that other types of cell behaviour must play essential roles.
Gastrulation has been said to be "the most important event in your life". It is during this time that the three main layers of cells are set up and that the body axis is established, and during which many cells become committed to their fates. However almost all that is known about the mechanisms of gastrulation comes from studying animals with a blastopore (sea urchin, fly, amphibians). Amniotes (mammals and birds) do not have a blastopore and instead gastrulate through a primitive streak. Are the mechanisms of gastrulation the same or fundamentally different?
In amphibians and fish, convergent-extension due to cell intercalation mediated by the non-canonical (planar cell polarity, or PCP) Wnt pathway is generally thought to be the driving force for gastrulation movements. However in amniotes there is considerable current debate about the mechanisms responsible for the formation and elongation of the primitive streak, and mechanisms ranging from positive and negative chemotaxis, oriented cell division and others have been implicated, with some groups explicitly ruling out convergent extension and the PCP. Using a combination of two-photon time-lapse and scanning electron microscopy as well as manipulation of various signalling pathways we will examine cell behaviour during gastrulation. We will show that local cell intercalation is the key driving force for gastrulation and that this is controlled by the PCP pathway, independently from the induction of mesoderm.
But is driving these movements sufficient for gastrulation? In addition, some cells need to move to the inside of the embryo to generate mesoderm and endoderm. In sea urchins, a pioneer groups of cells known as the Primary Mesenchyme is critical in initiating this process, and these cells then induce neigbouring vegetal plate cells to involute into the blastopore. However similar processes have not yet been uncovered in any vertebrate, even those with a blastopore. We will show that the chick embryo does initiate gastrulation by the scattered ingression of cells as individuals ("polyingression") and that these cells do act as pioneers, then inducing other cells to ingress as a population as part of the mesoderm induction process.
Joint work with Octavian Voiculescu, Federica Bertocchini, Isaac Skromne and I-Jun Lau
Growth and movement are an essential component of most biological processes including embryonic development, tumor growth, wound healing, and cell motility. Cell motility itself is also vital in various aspects of development. Growth and movement are inherently mechanical processes that can be described by a modification of the governing equations typically used in continuum solid mechanics. In this talk I present a general three-dimensional model for the displacement and stress fields generated by growth and/or movement of an arbitrarily deformable cell or tissue. The model is illustrated in applications to cell motility, tumor growth, and limb bud development. While the applications are different in scope, their underlying mechanical and mathematical principles are similar, and as a result the model can be applied to a variety of biological systems.
The role of cadherins in the control of cortical actin assembly has been established using the Xenopus blastula as a model system. C-cadherin expressed on the cell surface controls the amount of actin assembly in the cortex, and the amount of C-cadherin in turn is controlled by intercellular signaling through at least two G protein-coupled receptors. As the blastula turns into a gastrula, and then a neurula, new cadherins are expressed in tissue-restricted patterns, and the tissues undergo different types of morphogenetic movement. In this talk, I will discuss the requirement for these tissue-restriced cadherin types for cortical actin assembly, and the role they play in the morphogenetic movements performed by these tissues.