Schedule for: 19w5080 - Bridging Cellular and Tissue Dynamics from Normal Development to Cancer: Mathematical, Computational, and Experimental Approaches

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.

A brief introduction to BIRS with important logistical information, technology instruction, and opportunity for participants to ask questions.

The neural crest offer a unique model system to study mechanisms of cell migration since cells are accessible to in vivo imaging and manipulation. Although cranial neural crest cells travel through dense extracellular matrix and mesoderm during vertebrate morphogenesis, very little is known how head tissue dynamics effect neural crest cell migratory behaviors. Here, we examine the relationship between neural crest cell and head mesoderm tissue dynamics using time-lapse imaging, computational modeling, and experimental manipulations in the chick embryo. I will discuss our discovery that head mesoderm dynamics vary dramatically in space and time during neural crest cell migration and share our comparison between model simulations with distinct domain growth profiles in normal and manipulated embryos. Together, our results raise intriguing questions how collective cell migration responds to underlying tissue dynamics during embryonic development and our approach offers a framework to consider this in a broader context of development and disease.

Neural crest cells migrate rapidly over long distances during early embryonic development of vertebrates, and their migration has been much studied as a model for chemotaxis and cancer metastasis. A curious observation is the "group advantage": in a chemokine gradient too shallow to induce a single cell to chemotax, a cluster of cells can demonstrate robust chemotaxis up the gradient. In this talk, I will describe a model that explains this behavior based on cell-cell interaction. Through contact inhibition and co-attraction, the cells modulate each other's Rac1 and RhoA dynamics on their membranes and achieve a common polarity. This affords a group of cells much stronger persistence in their chemotaxis than a single cell against ambient noise.

Collective cell movement is closely related to normal development and cancer metastasis and scientists are studying it from different points of view, on different scales and using different biological systems. We would like to study its mechanism focusing on the mechanical and morphological effects using Cellular Potts Model. Our model is based on the experiments on the trunk ventral cells (TVCs) in Ciona cardiopharyngeal progenitors which include only two migratory cells so that it is the simplest case for collective cell movement. The observation in the experiment tells us that these two cells are polarized as leader and trailer cells with different morphological properties. So, we apply different mechanical properties for these two cells, such as adhesion, surface tension, protruding and retracting forces, to study their effects on cell shape, moving speed, and persistence in direction. We hope to see in what way two cells behave better than one.

Clusters of cells can work together in order to follow a signal gradient, chemotaxing even when single cells do not. This behavior is robust over many cell types and many signals, including gradients of extracellular matrix stiffness (durotaxis) and electrical potential (galvanotaxis). Cells in different regions of collectively migrating neural crest streams show different gene expression profiles, suggesting that cells may specialize to leader and follower roles in collective chemotaxis. We use a simple mathematical model to understand when this specialization would be advantageous. In our model, leader cells sense the gradient with an accuracy that depends on the kinetics of ligand-receptor binding while follower cells attempt to follow the cluster's direction with a finite error. Intuitively, specialization into leaders and followers should be optimal when a few cells have much more information than the rest of the cluster, such as in the presence of a sharp transition from one chemical concentration to another. We do find this - but also find that high levels of specialization can be optimal in the opposite limit of a very shallow gradient. This occurs because in a sufficiently shallow gradient, each leader cell has such little information about the gradient direction that - after a sufficient number of leaders are created - adding leader cells adds more noise to the cluster motion than adding a follower cell. There is also an important tradeoff: clusters have to choose between speed in following a gradient and ability to reorient quickly. We find that clusters with only a few leaders can take orders of magnitude more time to reorient than all-leader clusters.

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!

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.

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.

Glioblastoma is an aggressive form of brain cancer, with patients having an average life expectancy of 14 months using current treatment methods. Several mathematical models for glioma modeling are available in the literature, but they all struggle with the issue of including brain-tissue mechanics. Based on recent measurements of mechanical brain-tissue response, we will develop a new mechanical approach for the deformation of brain tissue as a result of an expanding glioma. As a proof-of-concept, I will discuss the one-dimensional version of the model and analyze deformations that are caused by a growing tumor.

In many biological processes, whether the formation of embryos or of tumors, cells dynamically organize in a context-dependent and spatiotemporal manner. These cells live and actively migrate in a heterogeneous environment of many cell types with different physical properties. For example, in many types of cancers such as colon, melanoma, prostrate and breast cancers, experiments have shown that the cancer cells are mechanically more deformable than the corresponding non-tumorigenic cells. It is also known that while non-cancerous (epithelial) cells tend to adhere to each other due to the adhesion protein E-cadherin and form a confluent tissue, in cancerous (mesenchymal) cells the expression of this protein is often heavily down-regulated. Motivated by this, we study the organization in a co-culture of two types of self-propelled particles (cells) with different stiffness and adhesion. We observe that the system phase separates into clusters with distinct morphologies and dynamics. We investigate the structure and growth of these segregating clusters with time by studying distribution functions and density structure factors, and characterize differences in the migration of the two cell types by studying their mean square displacements. Our results may elucidate how changes in cell mechano-adhesive properties during tumor progression impact cellular organization and dynamics in tumors.

The robustness of biological performance, whether developmental or physiological, relies heavily on feedback control. The autocatalytic nature of cell proliferation makes such control especially important in tissue homeostasis, and multiple mechanisms of cell cooperation have been described—and seem to be universally necessary—just to balance cell turnover with spatially even, constant cell production, achieve physiologically desirable steady states, respond quickly to perturbations, and resist breaking down in the face of common somatic mutation. It is thus within the context of densely-connected networks of feedback control that cancers arise, yet the implications of this fact are little explored. I will discuss recent progress and current challenges in the quantitative understanding of proliferative dynamics and its control. In addition, I will argue that the fact that cancers, even as they progress, most likely retain pieces of the feedback control machinery that characterizes normal tissues, can help shed light on some of the common peculiarities of cancer, such as slow growth, arrest of benign tumors at fixed sizes, senescence or elimination of oncogene-expressing clones, dormancy, oscillatory responses to therapy, and the prevalence of hierarchical lineage structures (``cancer stem cells'').

Embryonic development requires the precise spatio-temporal activation of specific cell behaviours such as migration and division. Re-activation of these processes in adult cells is a hallmark of cancer. This makes experimental models for studying developmental processes, such as the fruit fly Drosophila melanogaster, highly informative for cancer studies: such research has often provided the first glimpse into the mechanism of action of human cancer-related proteins. In our lab, we use Drosophila to study the basic biology of epithelial-to-mesenchymal transitions (EMTs), as well as the collective migration of heterogenous cell populations, which results from partial-EMTs. We study these processes during normal development of the embryonic midgut, and also during tumour progression in an exciting new model of metastatic colorectal cancer that we recently generated.  The collective migration of the embryonic midgut cells during Drosophila development is a particularly fascinating model for collective migration, as the midgut constitutes a mixed population of epithelial-like, mesenchymal and progenitor cells, yet midgut migration is highly coordinated both within and between these different cell types. Using the midgut as a paradigm, ongoing research in the lab is focused on identifying the mechanisms and mechanics of heterogeneous collective cell migration. Until recently, the study of midgut migration was restricted to simple qualitative analysis in fixed embryos, preventing quantification of cell-to-tissue scale behaviour. We recently pioneered live-imaging of midgut migration, enabled by multi-photon confocal microscopy, and have developed methods to perform 4-D tracking of the different cell populations within the migrating midgut. This has already allowed us to extract quantitative parameters and identify a novel role for E-cadherin mediating adhesion during cell migration. With our studies moving from qualitative descriptions to state-of-the-art deep-tissue imaging, quantitative analysis and generation of complex datasets, there is a pressing need to combine these innovative approaches with biophysical and computational modelling techniques, which we currently need help in developing.

Cell migration is essential to cell sorting, playing a central role in tissue formation, wound healing, and tumor evolution. In a limit where inner cells are diluted when compared to outer cells, cell sorting can be described directly by the evolution of inner cells in a process of diffusion and fusion. Experiments show that far from finite size boundaries the average mass of inner cell clusters grows as a power law. In active matter systems, the dependency of the diffusion constant with the cluster mass does not follow the expected inverse relation but still preserves a simple relation. The diffusion constant depends on the cluster mass as a power law. In this work, we take into account this dependency within a Mean Cluster Approach (MCA). It results that, out of finite size limits, the average cluster mass evolves as a power law and its exponent depends only on the system dimension and on the exponent in the relation between diffusion constant and cluster mass, independent of the specific segregation mechanism. We confirm this simple prediction using simulations with different segregation hypotheses describing cell-cell interaction: differential adhesion hypothesis (DAH) and different velocities hypothesis (DVH). We performed MCA analysis and simulations below the transition to the ordered phase. However, system behavior above the transition is still not explored. Preliminary analytic and simulation results present a non-trivial positive exponent for the diffusion constant in the ordered phase. These results apply for active matter systems in general and, in particular, the mechanisms found underlying the increase in cell sorting speed and in cell crawling certainly has profound implications in biological evolution as a selection mechanism.

In this talk, I will present a mechanobiochemical model for 3D cell migration which couples the actomyosin dynamics described by a system of reaction-diffusion equations on evolving volumes and a force balance viscoelastic mechanical model for the cell displacements. The novelty is that the pressure and contractile forces are influenced by actin and myosin spatiotemporal dynamics. To analyse the model, we carry out linear stability analysis to determine key bifurcation parameters and find analytical solutions close to bifurcation points. To validate theoretical findings as well as study the longtime behaviour of the model system away from bifurcation points, we employ the evolving finite element method in multi-dimensions. Solutions predicted from linear stability theory are replicated in the early stages of cell movement. Subsequently, both simple and complex cell deformations such as expansions, protrusions, contractions and translations of the cell are observed. This theoretical and computational framework set premises for studying more complex and experimentally-driven reaction kinetics involving, actin, myosin and other molecular species coupled to mechanical properties that play an important role in cell movement and deformation. Cell movement is critical in multicellular organisms due to its role in embryogenesis, wound healing, immune response, cancer metastasis, tumour invasion, and other biomedical processes.

Collective migration is an important phenomenon in many biological processes: from morphogenesis to wound healing and even cancer metastasis. Here we focus on Dictyostelium Discoideumaggregations, a classical toy model for understanding multiscale biological processes in development and disease, in the context of heterogeneous populations. We develop a class of nonlocal transport models for cell movement that incorporate both chemotactic and mechanical cell-cell interactions. In particular, we discuss the effect of two mutually inhibitory cell-cell signaling pathways (cAMP and DIF-1) on the coordinated movement and segregation of different cell types. We then use these models to investigate and classify the biological mechanisms that control the de-differentiation, movement and spatial segregation of cells.

Poster presenters are given 5 minutes each to advertise their posters.

The interface between a tumour and the adjacent stroma is a site of great importance for tumour development. At this site, carcinoma cells are highly proliferative, undergo invasive phenotypic changes, and directly interact with surrounding stromal cells, such as cancer-associated fibroblasts (CAFs) and immune cells, which further exert pro-tumourigenic effects. Here we describe the development of two tissue engineered platforms to probe these interactions: GLAnCE (Gels for Live Analysis of Compartmentalized Environments), an easy-to-use hydrogel-culture platform for investigating CAF-tumour cell interactions in vitro at a tumour-stroma interface, and TRACER a scaffold-based strategy that enables isolation of cells from specific regions within the tumour microenvironment to probe how cell-cell interactions and functions vary across gradients of microenvironmental factors such as oxygen.

Cancer invasion may be viewed as collective phenomenon emerging from the interplay of individual biological cells with their environment. Cell-based mathematical models can be used to decipher the rules of interaction. In these models cells are regarded as separate movable units. Here, we introduce an integrative modelling approach based on mesoscopic biological lattice-gas cellular automata (BIO-LGCA) to analyse collective effects in cancer invasion. This approach is rule- and cell-based, computationally efficient, and integrates statistical and biophysical models for different levels of biological knowledge. In particular, we provide BIO-LGCA models to analyse mechanisms of invasion in glioma and breast cancer cell lines. Ref.: Deutsch, A., Dormann, S.: Cellular automaton modeling of biological pattern formation: characterization, applications, and analysis. Birkhauser, Boston, 2018

Pattern formation through reaction-diffusion of proteins is core to establishing functionally distinct domains within cells. In fact, cells are able to be in either a “rest state”, in which such proteins are distributed homogeneously along its interior, or in a “polarised” state, in which clear domains establish. This phenomenon of polarization, allows cells to change shape. Animal cells move accordingly to these domains, while plant cells, encased in a rigid cellulose cell wall, use them for cell shape changes and polar transmission of signals. Molecular studies reveal that even though plants and animals diverged 1.6 billion years ago, they still share the a similar core machinery required for cell shape changes. A fascinating similarity between animal and plant cells with respect to the organization of cytoskeletal elements in the regions of active protrusive growth and cell wall extension (the `leading edges'), is paralleled by a striking conserved molecular mechanism responsible for the creation and organization of these `leading edges'. To unravel and understand the interplay and feedbacks which brings about animate cell motility, we have developed a multiscale model of a motile cells, describing how the reaction-diffusion module can be biophysically coupled to the cells' deformation. We then contrast this to the cell shape changes that occur in the pavement cells (PCs) in the leaves: PCs grow multiple lobes, which fit perfectly into the indentations of the neighboring cells, generating interdigitating, jigsaw-like patterns. Finally, we use both systems to show how polarity formation can also be used as an integrator for sensing external cues, and discuss how alterations of this could cause tissue-level disruption. Hence, we argue that part of cell signaling can be seen as an outcome of feedbacks between intracellular reaction-diffusion patterning, cell shape dynamics and external signals. Lastly, I will show how our modelling framework can also be used for segmentation of imaging data, showing examp les that range from complex epithelia to organoids.

Wild-type zebrafish feature black and yellow stripes across their body and fins, but mutants display a range of altered patterns, including spots and labyrinth curves. All these patterns form due to the interactions of pigment cells, which sort out through movement, birth, competition, and transitions in cellular shape during early development. The diversity of patterns on zebrafish makes it a useful organism for helping elucidate how genes, cell behavior, and visible animal characteristics are related, and the goal of our work is to help link genetic mutations to altered cell behaviors. Using an agent-based approach, we couple deterministic cell migration by ODEs with stochastic rules for updating population size to reproduce a range of fish patterns. Within a single zebrafish mutation, however, there is a lot of variability, and this makes it challenging to first identify the features of a pattern that we are trying to reproduce and then judge model success. Moreover, cells interact in a noisy environment on the fish skin, and model results need to be robust to realistic biological stochasticity. To help address these challenges, here we present a study of pattern variability and model robustness using topological tools to quantify zebrafish pattern features. This is joint work with Melissa McGuirl and Bjorn Sandstede.

Collective behaviors emerge from coordinated cell–cell interactions during the morphogenesis of tissues and tumors. For instance, cells may display density-dependent phase transitions from a fluid-like “unjammed” phase to a solid-like “jammed” phase, while different cell types can “self-sort”. We use comprehensive single cell tracking to elucidate these spatially and temporally heterogeneous behaviors in the context of self-organizing patterns. First, we consider co-cultured mixtures of sheet-forming epithelial cells and dispersed mesenchymal cells, which show a composition-dependent “unjamming” transition. Second, we consider a gelation-like mechanism whereby cells at very subconfluent densities organize into spanning network architectures. Finally, we analyze the disorganization and dissemination of cells cultured in 3D matrix, which exhibit both collective and individual invasion phenotypes with distinct topological and traction signatures. These complex behaviors exhibit striking analogies with non-living systems, suggesting that these physical concepts may be applicable to understand development and disease.

The concept of cell states is increasingly used to classify cellular behaviour in development, regeneration, and cancer. This is driven in part by a deluge of data comprising snapshots of cell populations at single-cell resolution. Yet quantitative predictive models of cell states and their transitions remain lacking. Such models could help, for example, to optimise differentiation protocols in vitro. Here, starting with a tractable immunostaining dataset of transcription factor expression we explore systematically if cell state transition rates can be inferred quantitatively and what information is required to do this. We investigate early cell fate decisions in primitive streak-like populations derived from epiblast stem cells (Tsakiridis et al., 2014). A particular challenge of the existing data is that labelling of cell states can be incomplete, i.e., not all of the markers that define a cell state are read out simultaneously in a given experiment. Using a top-down approach, we enumerate all possible cell states from known lineage markers, and build a minimal mathematical model for the transitions between these states in a growing colony. We adopt a Bayesian inference approach to quantify cell state transition rates and their uncertainties.

One of the major challenges in biology concerns the integration of data across length and time scales into a consistent framework: how do macroscopic properties and functionalities arise from the molecular regulatory networks and how do they evolve? Morphogenesis provides an excellent model system to study how simple molecular networks robustly control complex pattern forming processes. In my talk, I will focus on lung and kidney branching morphogenesis and discuss how chemical signaling and mechanical constraints shape the developing organs. Using light-sheet microscopy, we can observe epithelial dynamics during branching at cellular resolution, and I will discuss the physical principles of epithelial organization.

The control and downstream interpretation of gene expression dynamics is crucial in many biological contexts. For example, gene expression oscillations have been proposed to control the timing of cell differentiation during embryonic neurogenesis. However, mathematical analysis of gene expression dynamics may be hindered by sparse data and parameter uncertainty. Here, we combine Bayesian inference and quantitative experimental data on mouse and zebrafish neurogenesis to explore mechanisms controlling aperiodic and oscillatory gene expression dynamics during cell differentiation. We find that quantitatively accurate model predictions are possible despite high parameter uncertainty. We identify examples of stochastic amplification, where oscillations are enhanced by intrinsic noise and we show how such oscillations can be initiated by changes in biophysical parameters. We further consider mechanisms that may enable the down-stream interpretation of dynamic gene expression. Our analysis illustrates how quantitative modelling can help unravel fundamental mechanisms of dynamic gene regulation.

A critical first even in mammalian development is construction of the inner cell mass and trophoectoderm surrounding it. Using imaging and computational modeling, we show that by controlling the pace of cell fate specification, the embryo creates a crucial window of time where regulatory noise promotes accurate organization of these structures. Imaging results further indicate different gene products (Oct4 and Cdx2) exhibit significantly different levels of noise variation. Surprisingly, this asymmetry provides a novel means to balance the positive and negative influence of stochasticity. More generally, these results indicate noise has a positive role in spatially organizing the embryo.

In this talk, I will discuss several examples, drawn from our ongoing studies in worm, fruit fly and ascidian embryos, in which strong coupling between biochemical signaling, force generation and transmission leads to complex emergent spatiotemporal dynamics. At the cellular scale, I will focus on spatiotemporal dynamics of pulsed contractility, and dynamic stabilization of cell polarity in one-cell C. elegans embryos. At the tissue scale, I will highlight two examples in which mechanochemical coupling drives waves of morphogenesis across a sheet of epithelial cells. My goal is to highlight My goal is to highlight a class of problems that could really benefit from development of new mathematical and computational tools.

Retinal vasculature is essential for adequate oxygen supply to the inner layers of the retina, the light sensitive tissue in the eye. In embryonic development, formation of the retinal vasculature via angiogenesis is critically dependent on prior establishment of a mesh of astrocytes, which are a type of brain glial cell. Astrocytes emerge from the optic nerve head and then migrate over the retinal surface as a proliferating cell population in a radially symmetric manner. Astrocytes begin as stem cells, termed astrocyte precursor cells (APCs), then transition to immature perinatal astrocytes (IPAs), which eventually transition to mature astrocytes. We develop a partial differential equation model describing the migration of astrocytes where APCs and IPAs are represented as two subpopulations. Numerical simulations are compared to experimental data to assist in elucidating the mechanisms responsible for the distribution of astrocytes.

The coordinated movement of groups of cells, termed collective cell migration, is fundamental to many developmental, repair, and disease processes. Collectively migrating cells are self-propelled, but they coordinate their movements through neighbor-neighbor interactions. Within individual cells, cell propulsion is driven by protrusive and contractile actin cytoskeletal dynamics, as well as by their coupling to the substrate. A major question in the field of collective cell migration has been how polarity signals are transmitted from one cell to another across symmetrical cadherin junctions. During my talk, I will first introduce cadherin fingers, asymmetric junctional structures between collectively migrating cadherin fingers, and discuss how they are involved in collective cell guidance. I will then talk about our current approaches to study RhoGTPase signaling using FRET-based biosensors and how RhoGTPase signaling dynamics are coordinated between neighboring, collectively migrating cells.

Cutting-edge cancer treatments like immunotherapy and engineered microbes are examples of current and upcoming cell-based therapeutics. The success, failure, and side effects of these therapies critically depend upon multicellular cancer systems biology: the dynamical chemical and mechanical interactions between the engineered cells, tumor cells, and the microenvironment. Computational models can act as "virtual laboratories" for multicellular systems. The ideal laboratory would include cell and tissue biomechanics, biotransport of multiple chemical substrates including signaling factors, and many interacting cells. In this talk, we will introduce PhysiCell (\url{http://dx.doi.org/10.1371/journal.pcbi.1005991}), an open source agent-based platform for 3D multicellular systems biology. With this platform, desktop workstations can routinely simulate systems of ten or more cell-secreted chemical signals and tissue substrates, along with $10^5$ to $10^6$ individual cells that grow, divide, die, secrete chemical signals, move, exchange mechanical forces, and remodel their tissue microenvironment. After introducing PhysiCell, we will describe some recent projects that help expand its use. One project demonstrates how customized Jupyter notebook GUIs for PhysiCell models can be automatically generated and ported to nanoHUB (\url{https://nanohub.org}) where they can be run by anyone using just a Web browser. This makes it possible to 1) provide easy-to-run simulators to accompany models discussed in publications, and 2) let students submit demo simulators as part of class assignments and also be part of their academic portfolio. Another project describes two extreme-scale model explorations using the EMEWS framework on Cray supercomputers at Argonne National Lab. In our most recent collaboration, we explored a six-parameter therapeutic design space for cancer immunotherapy. This combined high-performance/high-throughput computing and active learning to optimize the immunotherapeutic design, characterize the topology (shape) of the design space, and automatically rank the importance of design parameters. We will close by pointing to some of the free online simulators and briefly discuss the future outlook for using high-throughput multicellular simulations to efficiently explore high-dimensional design spaces and accelerate discovery. Joint work with: Gary An, Nicholson Collier, Jonathan Ozik, and Paul Macklin.

A wide variety of multiscale models address complex biological dynamics, ranging from the organization of the cytoskeleton inside a cell to the organization of cells into tissues in development. However, as these models and their simulations become more complicated, their reproduction (confirmation of a scientific result using independent methods) for the purpose of scientific validation and the reuse of their components become more problematic. An increasing number of software frameworks aim to simplify the simulation of such models (Cytoscape, Physicell, VCell, CompuCell3D, \dots) and these frameworks often make replication (confirmation of a scientific result using the same means) more practical. However, reproducibility remains very difficult because the specification of a model in one framework cannot be executed in another framework. This difficulty occurs because the model specification does not preserve the underlying biological hypotheses and concepts. As a result, a researcher trying to reproduce a result in computational biology first needs to try to extract the underlying biological model, then translate it into a new mathematical and computational instantiation. The effort required at each step is large and error-prone and publications often lack enough information to allow unambiguous disassembly into the biological concepts need for reassembly and reproduction. The Systems Biology Markup Language (SBML) community has made significant progress in defining standards for specifying biochemical network dynamics models based on the underlying biological concepts while also describing their specific mathematical implementation. This approach couples biological descriptors with mathematical implementation in a way that allows the two to be separated. SBML’s preservation of the underlying conceptual model in the mathematical model and its simulation in turn supports understanding, reproducibility, portability, knowledge extraction, reuse and extension. However, ODE based networks are much simpler than the spatially-defined models of virtual tissues. We consider some of the difficulties in building reproducible virtual tissue models and discuss possible approaches to enhance reproducibility of virtual tissues, including: 1) Standards for the conceptual description of cell and tissue-level objects and processes. 2) Standards for the parametrization of key biological processes (e.g., mean velocity and velocity and angular persistence times for cell motility). 3) Standards for the static specification of spatial structure in tissues for simulation initialization and outputs (like MultiCellDS or VCell’s efforts to specify spatial configuration of cells and components). 4) Approaches to allow the componentization of submodels and their interconnection (model APIs, e.g., to combine an SBML based cell cycle model with a spatial cell model of division). 5) Approaches to allow the interconnection and interoperability of software components (software APIs, e.g., to allow the use of a Physicell diffusion equation solver with a CompuCell3D cell dynamics solver). 6) Standards for the visualization of simulations. 7) Standards for the specification of input, output and tolerance data sets for the validation of models. 8) Standards for the specifications of virtual populations, parameter exploration, sensitivity analysis and optimization. Clearly, we cannot pursue all of these goals at once, but we can perhaps begin to identify communities of the willing to begin work on some and prioritize the development of others.

Scratch assays are standard in-vitro experimental methods for studying cell migration. In these experiments, a scratch is made on a cell monolayer and imaging of the recolonisation of the scratched region is performed to quantify cell migration rates. This experimental technique is commonly used in the pharmaceutical industry to identify new compounds that may promote cell migration in wound healing; and to evaluate the efficacy of potential drugs that inhibit cancer invasion. Two mathematical frameworks will be presented that analyse the dynamics of these experiments. First, a new migration quantification method will be presented that fits experimental data more closely than existing quantification methods, as well as providing a more accurate statistical classification of the migration rate between different assays. Moreover, it is also able to analyse experimental data of lower quality. The method’s robustness is validated using in-vitro and in-silico data. Then, an age-structured population model will be presented that aims to explain the two phases of proliferation in scratch assays previously observed experimentally. The cell population is modelled by a McKendrick-von Foerster partial differential equation. The conditions under which the model captures this two-phase behaviour are presented.

Cellular migration is a tightly regulated process that involves actin cytoskeleton, adaptor proteins, and integrin receptors. Forces are transmitted extracellularly through complexes of these molecules called adhesions. We recently developed a biophysical model of nascent adhesions (NA), as co-localized clusters of integrins and adaptor proteins, to understand their dynamics and mechanosensitive properties. The model was then analyzed to characterize the dependence of NA area on biophysical parameters that regulate the number of integrins and adaptor proteins within NA through a mechanosensitive co-aggregation mechanism. Our results revealed that NA formation is triggered beyond a threshold of adaptor protein, integrin, or extracellular ligand densities (listed in a decreasing order of relative influence), that an increase in co-aggregation or reductions in integrin mobility inside NA potentiate their formation, and that stress (rather than adhesion load) is the permissive mechanical parameter which allows for NA-assembly/disassembly via a bistable-switch possessing a hysteresis. These results were then confirmed by performing stochastic simulations of the model. In this talk, I will give an overview of the model and the predictions made in connection with experimental findings.

Turing’s famous theory for explaining embryonic pattern formation, laid out in his seminal study ``The chemical basis of morphogenesis'', remains a cornerstone of theoretical biology and has inspired enormous interest, both from theoretical and experimental communities. Despite a number of ups and downs along the way, technical advances coupled to the increased collaboration between experimentalists and theoreticians has led to a number of convincing cases in which Turing’s idea may play a key role. In this talk I will recount some key milestones in the history of this theory and describe how it is clarifying our understanding of development in a number of processes, using our exploration of feather bud morphogenesis as a principal case study. Yet Turing’s paper opens with the disclaimer that ``This model will be a simplification and an idealization, and consequently a falsification.'' I will therefore also describe how recent results are pointing the way towards exciting new extensions and directions for Turing’s theory, particularly as links emerge between chemical-based and mechanical/cell motility based mechanisms for generating tissue pattern formation.

Progression from a ductal carcinoma in situ (DCIS) to an invasive tumor is a major step initiating a devastating and often lethal metastatic cascade. We will discuss biological events leading to the formation of small invasive cohorts streaming from the DCIS. Using mathematical models on micro- and macro-scales integrated with information extracted from patients’ histology samples, we investigated how changes in the local microenvironmental niche near the DCIS edge enable initiation and progression of ductal microinvasions. Of particular interest are the biomechanical interactions between the cells and the ECM fiber structure, and microenvironmental features that define tumor niche prone to microinvasions.

Two dominant models of mitotic spindle assembly are search-and-capture (SAC) and acentrosomal microtubule assembly (AMA). SAC predicts that kinetochores are captured randomly by dynamically unstable centrosomal microtubules (MTs), while AMA posits that kinetochore-associated MT bundles get integrated with centrosomal asters at random times. Both models predict a slow spindle assembly plagued by errors. Recent data shows that randomness in kinetochore capture is very low, that spindle assembles in relatively precise stages, and that small and dynamic MT ‘clouds’ near the kinetochores are critical in assisting centrosomal MTs in the spindle assembly. We used 3D tracking of centrosomes and kinetochores in mitotic animal cells to inform a computational model, according to which: 1) initially, when the centrosomes are proximal, the centrosomal MTs rapidly and indiscriminately ‘skewer’ the kinetochore MT clouds, effectively establishing lateral MT-kinetochore connections. When the pole-pole distance reaches a threshold, the polarity sorting of the kinetochore MTs and integration of the kinetochore and centrosomal MTs lead to establishing a vast majority of amphitelic attachments within a narrow time window.

To form patterns in vivo or in vitro, cells must carefully coordinate their behavior. Here I will present mathematical modeling approaches for modeling cell-ECM cross-talk. The models predict how the ECM can regulate the shape of individual cells, and how it can coordinate collective cell behavior as it occurs, e.g., during the formation of blood vessels or the alignment of cells in muscles and tendons. After discussing these initial models, I will show how detailed measurements and new mathematical models of the mechanosensitive kinetics of focal adhesions have helped us to model cell-ECM interactions in more biophysical detail. I will sketch how this approach allows us to mechanistically predict changes in cell shape and in collective cell behavior from changes in focal adhesion kinetics, e.g., due to genetic knockouts or pharmacological treatment. I will end by showing our recent steps to include anisotropy of the cytoskeleton into our models. Altogether, our models help explain how local, cell-ECM interactions assist in global coordination of cell behavior during multicellular patterning.

Accumulating experimental and clinical evidence suggests that the immune response to cancer is not exclusively anti-tumor. In fact, several pro-tumor effects of the immune system have been identified, such as production of growth factors, establishment of angiogenesis, inhibition of immune response, initiation of cell movement and metastasis, and establishment of metastatic niches. Based on experimental data, we develop a mathematical model for the immune-mediated theory of metastasis, which includes anti- and pro-tumor effects of the immune system. The immune-mediated theory of metastasis can explain dormancy of metastasis and metastatic blow-up after resection of the primary tumor. It can explain increased metastasis at sites of injury, and the relatively poor performance of Immunotherapies, due to pro-tumor effects of the immune system. Our results suggest that further work is warranted to fully elucidate and control the pro-tumor effects of the immune system in metastatic cancer. (with Adam Rhodes).

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.