Schedule for: 17w5164 - Mathematics for Developmental Biology

A buffet dinner is served daily between 5:30pm and 7:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

This was the year that we celebrated the centennial of the seminal work by D'Arcy Thompson, “On Growth and Form”. D'Arcy Thompson and his work has often been criticised for ignoring genetics, or at least considering genetics hardly more than a distraction. Here I will argue that what he instead wanted to offer us are different perspectives on the development of plants and animals. It is through broadening our perspectives that D'Arcy Thompson is able to keep inspiring us in our current work, 100 years after his book, and its illustrations, started to influence scientists and artists alike.

The reaction-diffusion model presented by Alan Turing has recently been supported by experimental data and accepted by most biologists. However, scientists have recognized shortcomings when the model is used as the working hypothesis in biological experiments, particularly in studies in which the underlying molecular network is not fully understood. Temporal models mainly utilize the diffusion of the ligand molecules as the basis of nonlocal interaction. However, recent studies have shown that the nonlocal signals are often transfered by other cellular behavior. Therefore, the mathemtaical model need to be flexible. To address some such problems, I would like to proposes a new simpler version of the Turing model.

This simpler model is not represented by partial differential equations, but rather by the shape of an activation-inhibition kernel. Therefore, it is named the kernel-based Turing model (KT model). Simulation of the KT model with kernels of various shapes showed that it can generate all standard variations of the stable 2D patterns (spot, stripes and network), as well as some complex patterns that are difficult to generate with conventional mathematical models. The KT model can be used even when the detailed mechanism is poorly known, as the interaction kernel can often be detected by a simple experiment and the KT model simulation can be performed based on that experimental data. These properties of the KT model complement the shortcomings of conventional models and will contribute to the understanding of biological pattern formation.

L-systems were introduced in 1968 as a formalism for reasoning about plant development. Soon afterwards, they became a tool for computational modeling of plants at the architectural level. In my talk, I will review the key conceptual contributions of the original formalism, the objectives of subsequent extensions, the resulting range of applications, and the current research problems spawned by L-systems.

Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

Meet in the Corbett Hall Lounge for a guided tour of The Banff Centre campus.

Meet in foyer of TCPL to participate in the BIRS group photo. The photograph will be taken outdoors, so dress appropriately for the weather. Please don't be late, or you might not be in the official group photo!

The mechanisms by which domains of gene activity lead to the generation of tissues with intricate three dimensional shapes are poorly understood. We have been using a combination of genetic, morphological, computational and imaging approaches to address this problem in plants. Our findings suggest that spatiotemporal patterns of gene activity control shape by introducing conflicts at the subcellular, cellular and tissue levels. Resolution and interactions between these different levels of conflicts may underlie the enormous diversity of forms that have evolved in plants and animals.

Rather than being directed by a central control mechanism, embryogenesis can be viewed as an emergent behavior resulting from a complex system in which several sub-processes on very different temporal and spatial scales (ranging from nanometer and nanoseconds to cm and days) are connected into a multi-scale system. In our research we have been focusing on the embryogenesis of basal organisms like the sea anemone Nematostella vectensis . For N. vectensis we have developed methods for analysing spatio-temporal gene expression patterns, methods for spatio-temporal modelling and inferring gene regulatory networks from gene expression data (qPCR data and in–situ hybridizations) and a cell-based mechanical model of early embryogenesis. Currently we are investigating how both levels of organization (gene regulation controlling embryogenesis and cell mechanics) can be coupled.

A growing leaf is a thin sheet of active solid, which expands while obeying the laws of mechanics. The effective rheology of this active solid is nontrivial, allowing the leaf to increase its area by orders of magnitude, keeping its "proper" geometry. The questions of what the characteristics of the leaf growth field are and how it is regulated without any central "headquarter" are still open. I will present measurements of natural leaf growth with high time and space resolution. These show that the growth is a highly fluctuating process in both time and space. We suggest that the entire statistics of the growth field, not just its averages contain information important for the understanding of growth regulation. In another set of experiments we measure the effect of mechanical stress on deformation and growth. The measured effective rheology is viscoelastic with time varying parameters, indicating remodeling of the tissue in response to extended application of mechanical stress.

Leaf shapes are very variable but restricted to some stereotyped families. Among one family of lobed leaves, this shape can be related to its folded growth within the bud. In general, this open the question of how much the final shape can be constrained by steric constrains during its development. Similarly, since most of the leaves do not first expand flat and straight, but commonly folded or rolled in different ways, there needs to be some regulations to reach the usually rather flat and straight state. This growth, from the primordial to the final leaf, presents several striking motions. On some examples we propose that these motions precisely help the regulation.

Leaves of eudicots show tremendous morphological diversity. Remarkably different leaf morphologies may occur between closely-related species, as within-species variants, or even in the same plant. Diverse leaf shapes also emerge in molecular-level studies of reference plants including Arabidopsis thaliana, Cardamine hirsuta and tomato, where small genetic or hormonal changes yield significantly different forms. This lability of shapes, juxtaposed with similar molecular mechanisms underlying leaf development in reference plants, suggests that the striking diversity of eudicot leaves results from variations of a common generative program. Notably, this mechanism acts jointly on leaf shape and vasculature, patterning both marginal protrusions and corresponding veins in the blade.

Inspired by this perspective, we propose a geometric model of leaf development and diversity. It simulates development as a feedback between two processes: the dynamic patterning of growth centers at the leaf margin, and control of growth directions by veins associated with these points. Our models show that the spatial separation of the processes patterning and directing growth facilitates the generation of a wide range of leaf forms, from simple to lobed and compound. Additionally, transitions between different forms can be controlled in a continuous manner. These transitions reproduce frequently observed, and often drastic, changes in leaf form within the same plant or between closely related species. Our results highlight the flexible and self-organizing nature of leaf development, and provide a path towards an integrated understanding of their development and diversity.

A buffet dinner is served daily between 5:30pm and 7:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

Tentative topics: (i) A survey of open problems in mathematics of development; (ii) Geometry of morphogenesis. Moderators: (i) Eric Mjolsness, (ii) Shigeru Kondo

The cytoskeleton drives many essential processes in the cell, such as division, the specification of the division axis, movements, polarization and changes in cell shape. These fundamental processes are naturally essential in the development of any organism, and are on their own already complicated to model or understand. What is the correct level of description of intracellular state if one wants to model the development of multiple cells? It is possible to capture the dynamics of the cytoskeleton in some simplified way? Alternatively, should we carry the full complexity of these cellular processes in a multicellular model? Is this desirable?

Despite the significance of cellular morphology as a functional phenotype, it remains challenging to quantitatively relate morphological phenotype to the behavior of subcellular molecules. Molecular studies have identified many components controlling cell morphogenesis, but it is unclear how this information is translated into the physical world. In plant cells, growth requires synthesis of cytoplasmic components as well as expansion of the cell wall. The cell wall is a stiff yet flexible polymeric network that encapsulates cells and counterbalances stress created by turgor pressure inside the cell, thereby controlling cell shape. It is now well established that the cytoskeleton plays a key role in the biogenesis and morphogenesis of the cell wall. While the microtubules guide cellulose synthase complex movement (Paredez et al. 2006), the actin network is responsible for global distribution of cellulose synthase complexes (Gutierrez et al. 2009; Sampathkumar et al. 2013). It is also suggested that mechanical stresses orient the microtubules along their principal direction (Hamant et al. 2008; Sampathkumar, Krupinski, et al. 2014; Sampathkumar, Yan, et al. 2014). Nevertheless, to fully understand how plant cells are shaped and how external mechanical stresses influence this process, a quantitative approach to evaluate the mechano-response in single cells needs to be established. Here we present a technique (Chang et al. 2014) to confine single plant protoplasts into molds of defined shapes. The principle is to confine a plant protoplast expressing fluorescent cytoskeletal reporters into micro-wells of different shapes with sizes of 10 to 30 μm. The protoplasts are then monitored with a confocal microscope to evaluate changes in cytoskeletal organization and dynamics during the process of symmetry breaking. These experiments are the basis of assessing quantitatively how different shapes control cytoskeleton organization behavior by regulating the distribution of physical stresses.

We approach the understanding of metazoan morphogenesis through the quantitative analysis and biomechanical modelling of cell dynamics from multiscale in vivo imaging data. The automated reconstruction of the cell lineage tree, annotated with nucleus and membrane segmentation, provides measurements for cell behaviour: displacement, division, shape and contact changes. This quantitative data is used to derive statistical models for key parameters and calculate descriptors for tissue deformation. Confronting numerical simulations derived from multi-agent based biomechanical models with empirical measurements extracted from the reconstructed digital specimens is the basis for testing biological hypotheses. Further correlating cell behaviour, tissue biomechanics and biochemical activities by comparing the patterns revealed by cell fate, kinematic descriptors or gene expression, is a step toward the integration of multi-level dynamics.

For years, I have been torn by a constant pressure to add more “detail” to our cellular models of plant development while also being driven to capture the essence of a phenomenon. I hope to illustrate this conundrum by a case-study on plant development and nutrient uptake. Through modelling and mathematical analysis and combined with experimental verifications, I will show how 1) very fast temporal cellular responses are critical for maintaining steady-state tissue-level behaviour, even in the absence of external variation; and 2) how sub-cellular spatial compartments, such as the cell wall, enable tissue-scale patterns to arise that are fundamentally distinct from what is possible without these sub-cellular features. We were only able to achieve these insights by capturing certain “details” within multilevel cellular models, only later realising their true significance. Nevertheless, the mechanisms, relying on detailed spatial and temporal structures in a multi-level setting, yielded parsimonious explanations.

Stem cells in the plant shoot are maintained via a gene regulatory feedback network, and perturbations to these genes lead to changes in the size and shape of the stem cell niche. Growth itself is highly dependent on cell wall properties where heterogeneous and anisotropic mechanical properties need to be regulated to generate correct size and shape of the tissue. We use a Computational Morphodynamics approach, combining live imaging and mathematical models of cell wall mechanics and gene networks, to understand how growth and differentiation is coordinated in the plant shoot. I will discuss how mechanical patterning can overlap with gene expression patterns, and how cell size and tissue size are regulated and influence the maintenance of the stem cell niche.

The shape and function of plant cells are thought to be closely related. The puzzle-shaped epidermal cells that appear in the epidermis of many plants are a striking example of a complex cell shape, however their functional benefit has remained elusive. We propose that these intricate forms provide an effective strategy to reduce mechanical stress in the cell wall. When tissue-level growth is isotropic, we hypothesize that lobes emerge at the cellular level to prevent formation of large isodiametric cells that would bulge under the stress produced by turgor pressure. Data from various plant organs and species support the relationship between lobes and growth isotropy, which we test directly with mutants where growth direction is perturbed. Using simulation models we show that a mechanism actively regulating cellular stress plausibly reproduces the development of epidermal cell shape. Together, our results suggest that mechanical stress is a key driver of cell-shape morphogenesis.

How do organs and organisms grow to elongated forms? I will show how the coupling between biochemical polarity and tissue mechanics enables elongated growth forms, by considering three model systems: fission yeast, fruit fly, and Arabidopsis.

We are interested in how cell size and organ size are developmentally determined in Arabidopsis flowers, particularly the sepals. I will discuss two collaborative projects in which modeling both helped us direct our experiments and interpret our experimental results. In examining the robust control of organ size, there was a eureka moment when we realized that our initially separate modeling and biological projects were converging on the same idea: variable cellular growth undergoes spatiotemporal averaging to create reproducibly sized and shaped organs. In this case, the modeling directed us to analyze the cellular variability and explained why reducing cellular variability increased organ shape variability. Second, in examining cell size control, model development coincided with biological experiments and the two informed each other to reveal that fluctuations of a transcription factor determine whether a cell becomes a giant or a small cell.

We present mathematical approaches to study genome wide DNA rearrangements. DNA recombination occurs at both evolutionary and developmental scales, and is often studied through model organisms such as ciliate species Oxytricha and Stylonychia. These species undergo massive genome rearrangements during their development of a somatic macronucleus from a zygotic micronucleus. We investigate the genome-wide scrambled gene architectures that describe all precursor-product relationships in Oxytricha trifallax, the first completely sequenced scrambled genome. The situations are represented by words, graphs and chord diagrams to identify the common features. Furthermore, gene segments that recombine during such rearrangement processes may be organized on the chromosome in a variety of ways. They can overlap, interleave or one may be a subsegment of another. We use colored directed graphs to represent contigs containing rearranged segments where edges represent recombined segment organization. We find that iterating patterns of alternating odd-even segments up to four times can describe over 98% of the scrambled precursor loci. Recurrence of these highly structured patterns within scrambled genes presumably reflects frequent evolutionary events that gave rise to thousands of scrambled genes in the germline genome.

I am interested in morphogenetic processes from genes to biological shapes. Especially, after genes established cells, processes that associated cells produce physico-mechanical forces in cell aggregates, which perform morphogenesis of tissues. For the purpose I am using a cell-based vertex dynamics for tissues. I will introduce researches of formation of a cell aggregate including a cavity, cell intercalation in tissues and helical looping of embryonic hearts.

The modeling and simulation of morphogenetic phenomena require to take into account the coupling between the processes that take place in a space and the modification of that space due to those processes, leading to a chicken-and-egg problem. To address this issue, we proposed to consider a growing structure as the byproduct of a multitude of interactions between its constitutive elements. An interaction-based model of computation relying on spatial relationships has then been developed leading to an original style of programming implemented in the MGS programming language. Contributions of MGS include a generic programming mechanism that captures most of the unconventional computing models by simply varying the underlying structure of interactions. I will introduce the interaction-based way of programming and review some current works taking roots in the fertile ground of MGS.

A wide variety of modeling problems can be approached by dividing the problem into a spatial arrangement of discrete components which communicate with one another. Modeling multicellular development fits this framework well; a tissue is composed of discrete cells which communicate by methods such as hormonal signaling or mechanosensing. One of the chief challenges in modeling development is that the number and arrangement of components changes, as cells grow and divide. By choosing the right underlying structural representation, however, the task of the modeler can be made easier. Representing a growing tissue with the mathematical formalism of the cell complex lets the modeler consider interactions locally and assign properties to entities of the right dimension. I describe a framework for developmental plant modeling based on cell complexes, and demonstrate models of development in one, two, and three dimensions.

During embryonic development, the behavior of individual cells must be coordinated to create the large scale patterns and tissue movements that shape the whole embryo. Apart from chemical signaling, it has recently become clear that mechanical cell-cell communication is equally important in the coordination of such collective cell behavior. To get a better understanding of mechanical cell-cell communication, we are developing computational models of cells and the extracellular matrix (ECM) - the hard or jelly materials (e.g. collagens, fibronectin) that form the micro-environment of many cells. The models are detailed enough for explaining the response of individual cells to the mechanical properties of the ECM, and sufficiently coarse-grained so as to allow for efficient computational upscaling to the tissue level and beyond. Our model is based on a novel, hybrid Cellular Potts and finite element computational framework. It describes the contractile forces that cells exert on the ECM, the resulting strain fields in the ECM, and the cellular response to local strains. The model simulations reproduce the behavior of individual endothelial cells on compliant matrices, and show that local cell-ECM interactions suffice for explaining interactions of endothelial cell pairs and collective cell behavior, including the formation of cellular networks and sprouting from spheroids [1]. If an external strain is exerted on the ECM, the cells rapidly align with the strain fields, even in response to very subtle strain cues [2]. These initial models relied on phenomenological descriptions of the interactions between cellular protrusions and the ECM. Recently, detailed measurements and new mathematical models of the kinetics of individual focal adhesions (the macromolecular assemblies responsible for mechanical cell-ECM interactions) have become available. In our ongoing work we have include kinetic descriptions of focal adhesions in our models. We will sketch how this approach will allow us to mechanistically predict changes in cell shape and in collective cell behavior from changes in focal adhesion kinetics. Altogether, our models suggest simple mechanisms by which local, mechanical cell-ECM interactions can assist in integrating morphological information in embryos across organizational levels.
[1] R. F. M. van Oers, E. G. Rens, D. J. LaValley, C. A. Reinhart-King, and R. M. H. Merks, “Mechanical Cell-Matrix Feedback Explains Pairwise and Collective Endothelial Cell Behavior In Vitro,” PLoS Comput. Biol., vol. 10, no. 8, p. e1003774, Aug. 2014.
[2] E. G. Rens and R. M. H. Merks, “Cell Contractility Facilitates Alignment of Cells and Tissues to Static Uniaxial Stretch,” Biophysical Journal, vol. 112, no. 4, pp. 755–766, Feb. 2017.

Topics to be selected at the workshop

Lindenmayer systems (L systems) provide a concise mathematical formulation for creating simulations of plants that are descriptively accurate, while also taking into account various molecular-level controls. At present, most plant models are created manually by experts from measured data and scientific knowledge. However, manual creation does not scale to the creation of thousands of models needed to correspond to plants developed by plant breeders. In this talk, we discuss existing and new approaches to the automatic inference of Lindenmayer systems from data, with a focus on inductive inference. This includes exact approaches, approaches using evolutionary algorithms, and other heuristics.

In developmental biology we find modeling problems that stretch the boundaries of traditional computational science: complex local information-processing, regulation of dynamically changing neighborhood relations, reticulated geometric structures of multiple dimensionalities, highly heterogeneous laws of motion, and a rich multiscale structure. It may be advantageous to enlist automation in the form of mathematical AI (artificial intelligence, both symbolic and machine learning) to help manage this essential model complexity. Machine learning (ML) naturally applies to the problem of finding scale changes in mathematical models, as we will show. But a new kind of mathematical AI/ML may be required overall, in order to create such an “intelligent” architecture for multiscale scientific modeling. To that end I suggest desiderata, consider useful new and existing mathematical ingredients, and propose an overall structure for such an architecture.

Within the narrowly defined context of a strictly continuum-mechanical formulation, a body is a differentiable manifold and its material properties are described by one or more functions of its deformations. It is shown that the corresponding differential-geometric object is given precisely by a groupoid, whose variation in time characterizes the various phenomena of material evolution. In this context, one can identify and distinguish between pure remodeling and other evolutive phenomena, which can be further classified according to whether or not material symmetries are preserved.

We discuss a general method for discretizing and simulating numerically thin structures based on the ideas of discrete differential geometry and on variational formulations. The method is successively first applied to elastic rods and viscous jets, and then to active viscous axisymmetric membranes, a model relevant to cytokinesis. We shortly discuss how contact and an enclosed incompressible fluids can be taken into account.

Simulating the mechanics of biological tissues entails a number of challenging requirements, including non-linear, anisotropic and nearly-incompressible materials, organic shapes with flat and thin structures, and large changes in shape such as bending twisting, bulging and stretching. To address these challenges, we are developing an open source dynamics simulator, ArtiSynth, that combines rigid body models with large-deformation finite-element models together with contact and constraints. In this talk, I will describe ArtiSynth’s mathematical framework within the context of the biological problem of simulating the muscle tissue structures found in tongues, tentacles and trunks.

Tentative topic: Problems of oriented and non-homogeneous growth. Moderator: Enrico Coen

Cotyledons (embryonic leaves) in conifer trees form in a single ring, or whorl. The number of cotyledons is quite variable, commonly from 3 to 10, unlike flowering plants, which are classified as to whether they have one or two cotyledons. Our data indicate that cotyledon positioning has a radial component, for the ring position, and a circumferential component, for the between-cotyledon positioning within the ring, and that these have different dependences on polar transport of the growth regulator auxin. We present a two-stage reaction-diffusion mechanism as a framework for understanding these observations and early cotyledon morphogenesis.

The first phyllotaxis pattern formation model was proposed in 1868 by Schwendener, and consists of stacking one disk at a time on the surface of a cylinder. As simple as it is, this model exhibits plenty of geometric and dynamical richness, which are best revealed by systematic computer simulations. It helps explain the predominance of Fibonacci phyllotaxis, where the number of helixes (parastichies) in the two transverse families are successive Fibonacci numbers. It also helped us the mechanisms of formation of a type of pattern never mentioned in the literature, that we called Quasi Symmetric. In these patterns, often characterized by rapid parameter changes, the two parastichies numbers tend to be close to one another. Now go and count parastichies on a strawberry….

Animals develop from a single cell. While much is known about the regulatory programs that control development, it is still an open question how size and shape are determined in a growing animal. In my talk, I will present a novel mechanism for size control and growth termination. During growth, patterns emerge that define different parts of the developing animal. I will discuss how scaled patterning can be achieved on growing domains with a classical threshold-based French Flag read-out mechanism. The branched trees of lungs, kidneys and many glands provide a fascinating example of complex shape formation. I will show how the very different branching patterns in lungs and kidneys can robustly emerge from the same regulatory mechanism - implemented by very different protein families in the different organs. Finally, I will discuss the role of mechanics in epithelial organisation and the origin of Lewis' law.

During development and growth tissues expand while the vascular network is developing. We are studying how tissue growth affects the patterning of the vascular network. I will discuss two models: vasculogenesis in the chicken embryo yolk sac and the growth of the gastrovascular system in the jellyfish Aurelia Aurita. For the chicken yolk sac I will show that a growth-induced gradient of tissue pressure in the chicken yolk sac mesoderm drives early blood flow and I will discuss how these growth-related forces might affect the vascular patterning. For the jellyfish we will challenge the hypothesis that, in analogy with crack propagation, the vessels grow to relax the highest compressive stresses in the endodermal unicellular sheet in which the vessels grow.

We have developed several models of branching morphogenesis in the lung, considering a variety of factors, including transport and mechanics. How reasonable a model appears initially is not necessarily correlated with its explanatory power. In this talk, we will present a variety of models of branching morphogenesis, and compare their implications.

Tree-forms are ubiquitous in nature and recent observation technologies make it increasingly easy to capture their details, as well as the dynamics of their development, in 3 dimensions with unprecedented accuracy. These massive and complex structural data raise new conceptual and computational issues related to their analysis and to the quantification of their variability. Mathematical and computational techniques that usually successfully apply to traditional scalar or vectorial datasets fail to apply to such structural objects: How to define the average form of a set of tree-forms? How to compare and classify tree-forms? Can we solve efficiently optimization problems in tree-form spaces? How to approximate tree-forms? Can their intrinsic exponential computational curse be circumvented? In this talk, I will present a recent work that I have made with my colleague Romain Azais to approach these questions from a new perspective, in which tree-forms show properties similar to that of numbers or real functions: they can be decomposed, approximated, averaged, and transformed in dual spaces where specific computations can be carried out more efficiently. I will discuss how these first results can be applied to the analysis and simulation of tree-forms in developmental biology.

L-systems are widely used for modelling the growth and development of plants. However, until now L-systems did not simulate mechanical collisions between plant parts and entire plants. We show that L-systems can be combined with the position-based collision detection and resolution method, originally devised in computer graphics and subsequently extended to plant modelling. To this end, we extend turtle interpretation by creating a persistent geometric representation of a plant and updating it after each simulated growth step while resolving collisions. We also augment the method to simulate propagation of mechanical collisions between terminal organs represented as surfaces and their supporting branches represented as rods. We illustrate the methods using models of individual plants and fields of plants with all collisions resolved automatically. The presented work is the starting point for faithfully representing different phenotypes in virtual plant breeding trials, and visualizing plants in the field.

The Hippo pathway, which is a central pathway in the control of cell proliferation and apoptosis in Drosophila and mammalian cells, contains a core kinase mechanism that affects control of the cell cycle and growth. Studies involving over- and under-expression of components in the morphogen and Hippo pathways in Drosophila reveal conditions that lead to over- or undergrowth. In this talk we discuss a mathematical model that incorporates the current understanding of the Hippo signal transduction network in Drosophila and which can explain qualitatively both the observations on whole-disc manipulations and the results arising from mutant clones. We find that a number of non-intuitive experimental results can be explained by subtle changes in the balances between inputs to the Hippo pathway. Since signal transduction and growth control pathways are highly conserved across species and directly involved in tumor growth, much of what is learned about Drosophila may have relevance to tumor dynamics in mammalian systems.

The development of plant organ primordia into mature organs – leaves, flowers, or entire branching structures - astonishes by the magnitude of change in scale and shape. Correspondingly, the construction of mesoscopic models bridging microscopic into macroscopic forms has remained a largely open problem. Previous work suggests that the interplay between the vascular system and the margin of developing leaves plays a crucial role in the development of lobed and dissected leaves. In this process, the emerging vascular branching structure acts as a skeleton defining local directions of growth. Extending this concept, I will present a method for modeling the development of organ primordia into branching forms as an interplay between the vascular skeleton and the epidermis. The mathematical background for this technique draws upon the notion of skinning, devised in computer graphics to animate digital characters by manipulating their skeletons. In the application to mesoscopic modeling, skinning requires the dynamic addition of new skeletal elements, controlled by the morphogenetic processes in the epidermis, and a dynamic remeshing of the epidermis.

Immune cells, specifically T cells, patrol the body in search of pathogens, which they detect using receptors. Recent discoveries have allowed the development of T cells with "engineered" receptors, used in therapies to help a patient's own T cells to combat disease. These therapies are complicated by the unusual nature of T cell receptors: They attach to other surfaces (rather than to diffusible ligands), and they are subject to tremendous sequence diversity (to fight against a wide range of pathogens). Work by us and others suggest that T cell receptors overcome these challenges by being force-sensitive and having dynamic spatial organization. In other words, they use force, space and time to transduce their signals. The spatial patterns have several mathematically interesting features: They must form dynamically on seconds-timescales (and revert to homogeneity with similar speed); they are driven by forces rather than passive diffusion; and they often involve small numbers of molecules, necessitating stochastic description. We develop mathematical models of the interface between the T cell and its target cells to understand how these forces influence T cell function. Our results suggest how changing spatial organization and molecular properties might modify T cell function, and hint at new ways T cells might be engineered to improve function.

In multicellular organisms, ranging from cellular amoebae to the human body, it is essential for cells to communicate with each other. One common mechanism to initiate communication between cells that are not in close contact is for cells to secrete diffusible signaling molecules into the extracellular space between the spatially segregated units to initiate some collective response. We formulate and analyze a class of coupled cell-bulk ODE-PDE models in a two-dimensional domain. For this coupled system, the method of matched asymptotic expansions is used to construct steady-state solutions and to formulate a spectral problem that characterizes the linear stability properties of the steady-state solutions, with the aim of predicting whether temporal oscillations can be triggered by the cell-bulk coupling. Different ranges of diffusion coefficient are considered and conditions for which the release of this signaling molecule leads to the triggering of some collective synchronous oscillatory behavior among the localized cells are characterized.

Tentative topics: (i) Relations between mathematical models of development. Moderator: Stan Maree (tentative). (ii) Models and reality. Moderator: Adrienne Roeder (tentative).

I will present two programs that facilitate computational exploration of reaction-diffusion patterns. The first program operates on a flat 2D grid and employs a graphical processing unit to simulate such patterns at interactive rates. The second program allows for simulation of reaction-diffusion processes on arbitrary triangulated surfaces. Parameter values and initial distributions of morphogens can be interactively “painted” on the domain to simulate non-homogeneous environments and different starting conditions. Experimentation with the models is facilitated by the use of a software versioning system, adapted to organize computational experiments and the models.

Interactive simulations put the "human in the loop", i.e. they make it possible for the human modeller or analyst to change parameters and immediately see the effects, to explore the model's dynamics in novel directions, to quickly gain an intuition about the most beneficial questions to ask next. Due to the field's importance and the need communicated to us by experts in the field, we are committed to realising according interactive simulations in the domain of developmental biology.

In this joint presentation, we first summarise the challenges developmental biologists laid out for us in terms of data integration, model building, simulation and optimisation. Second, we present our efforts addressing them. In particular, we elaborate on various computational approaches that we have integrated to meet the specified requirements -- from visual programming over importing and editing annotated volumetric data to efficient, GPU-based simulation and effective methods of visualisation and interaction. For honing these aspects, we have devised a virtual cell model that runs at realtime speeds and realises some of the basic morphogenetic interactions, including morphogen-based signalling, adhesion, proliferation, and growth. We present an according prototype that serves as a basis to gain feedback from developmental biologists and experts in developmental models.

5-day workshop participants are welcome to use BIRS facilities (BIRS Coffee Lounge, TCPL and Reading Room) until 3 pm on Friday, although participants are still required to checkout of the guest rooms by 12 noon.