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Adriana Zanca
(CDEV)
The University of Melbourne
"Multicellular model of collective cell migration with an irregular free boundary"
In many biological systems, including cancer, embryonic development and wound healing, cells migrate in a coordinated fashion. Interactions between individual neighbouring cells at a cellular scale leads to a collective movement at a tissue scale. Cell-based models allow cellular level processes to be explicitly incorporated and can allow us to investigate how tissue heterogeneities influence migration. Here we present our work using a vertex dynamics model to investigate the effect of an irregular free boundary on migration speed, cell density and orientation in a cell monolayer.
Andreas Buttenschoen
(CDEV)
University of British Columbia
"Spatio-Temporal Heterogeneities in a Mechano-Chemical Model of Collective Cell Migration"
Small GTPases, such as Rac and Rho, are well known central regulators of cell morphology and motility, whose dynamics also play a role in coordinating collective cell migration. Experiments have shown GTPase dynamics to be affected by both chemical and mechanical cues, but also to be spatially and temporally heterogeneous. This heterogeneity is found both within a single cell, and between cells in a tissue. For example, sometimes the leader and follower cells display an inverted GTPase configuration. While progress on understanding GTPase dynamics in single cells has been made, a major remaining challenge is to understand the role of GTPase heterogeneity in collective cell migration. Motivated by recent one-dimensional experiments (e.g. micro-channels) we introduce a one-dimensional modelling framework allowing us to integrate cell bio-mechanics, changes in cell size, and detailed intra-cellular signalling circuits (reaction-diffusion equations). Using this framework, we build cell migration models of both loose (mesenchymal) and cohering (epithelial) tissues. We use numerical simulations, and analysis tools, such as local perturbation analysis, to provide insights into the regulatory mechanisms coordinating collective cell migration. We show how feedback from mechanical tension to GTPase activation lead to a variety of dynamics, resembling both normal and pathological behavior.
Camile FD Kunz
(CDEV)
Goethe University - FIAS
"Chemotaxis impact on pattern formation"
During embryo development there is a rapid growth in cell numbers that forms complex structures. Skin pattern formation is an early process during the embryogenesis and happens before the cells fully differentiate. In the present project we consider skin patterning in mouse embryos, where cell aggregates form based on a hierarchical process, involving interactions between the epidermal cell populations. The reaction-diffusion pre-pattern is driven by fibroblast growth factor (FGF20), bone morphogenic protein (BMP) and WNT. Considering mathematical models, there are two main processes involved in the pattern formation: Turing reaction-diffusion systems and chemotaxis. The Turing system models the concentration of two interacting chemicals, and the patterns arises from an instability driven by a difference between their diffusion coefficients. Some previous studies show that this behavior is essential for self-organization in the mouse hair follicle and chicken feather pre-pattern formation. Another key mechanism is chemotaxis, where the cells move in the direction of a chemical attractant, where patterns can also be observed. Experimental data indicates a hierarchical system, where cell chemotaxis is guided by a Turing system. We aim at developing mathematical models to describe the underlying biological processes leading to skin patterning, especially the interaction of chemotaxis with reaction-diffusion (Turing) systems. A mathematical model using partial differential equations is solved numerically, and some results are presented and compared to the experimental data. We study the parameter-dependence of the model and different model structures, and their impact on the pattern forming process. According to the experimental data the Turing system and the chemotaxis seems to be intrinsically related on the mouse skin patterning. Using a numerical approach for the PDE system, we develop a framework to study quantitatively how chemotaxis and Turing systems are related and their impact on the patterning process.
Chiara Villa
(CDEV)
University of St Andrews
"Mechanical pattern formation in biological tissue: Relax and go with the (viscous) flow"
Mechanochemical models of pattern formation in biological tissue have helped us shed light on the role different mechanical cues have in cell aggregation phenomena, by considering the mechanical interaction between cells and the extracellular matrix (ECM). The cells and ECM are modelled as a linearly viscoelastic continuum, usually assumed to be a Kelvin-Voigt material, but this may not be the best model of viscoelasticity to use for biological tissue. We here extend the theory of mechanochemical pattern formation to include a wider variety of models of linear viscoelasticity. Our results clearly indicate that models of linear viscoelasticity presenting viscous flow (linear viscous, Maxwell, 3-parameter viscous model), which are better suited to represent soft tissue, have much higher pattern formation potential than those which do not (linear elastic, Kelvin-Voigt, standard linear solid model).
Cody FitzGerald
(CDEV)
University of Utah
"Red light and the dormancy-germination decision in Arabidopsis seeds"
The Arabidopsis dormancy-germination transition is known to be environmentally-cued by red light and controlled by the competing hormones abscisic acid (ABA) and gibberellin (GA) produced by the seed. Recently, new molecular details emerged concerning the propagation of red light through a complex gene regulatory network involving PhyB, PIF1, and RVE1 and two feedback loops. This network influences the formation of the PIF1-RVE1 complex. The PIF1-RVE1 complex is a transcription factor that regulates the production of ABA and GA and helps shift the balance to high concentration of ABA and low concentration of GA, which corresponds to a dormant seed state. This new gene regulatory network has not been analyzed mathematically. Our analysis shows that this gene regulatory network exhibits switch-like bistability as a function of the red light input and makes a suite of biologically-testable predictions concerning seed dormancy and germination in response to the amplitude and periodicity of an oscillatory red light input.
Daniel Tudor
(CDEV)
University of Edinburgh
"Probing immune cell wound recruitment signals using Bayesian inference and random walk models"
The recruitment of immune cells to wounds is a complex spatiotemporal process with the production and diffusion of chemoattractants acting as a beacon for immune cells to respond to damage within the body. Analysing these chemoattractants can be experimentally complex, however, inference of the chemoattractant field is possible by analysing cell trajectories. These trajectories can then be used to infer the main parameters of the underlying chemoattractant.
To undertake this study, we reproduced a previously published modelling framework which utilises biased-persistent random walk to capture immune cell motion and the diffusion equation to capture the chemoattractant dynamics. By applying Bayesian inference, this framework allows us to gain an understanding of the relationship between cell migration parameters and the main chemoattractant parameters such as the diffusion coefficient and production time.
To aid transparency, we implemented an open source version of the modelling framework to allow for future research. We then applied this model to investigate the chemoattractant which is responsible for wound healing within Drosophila, this chemoattract is currently unknown and can be difficult to isolate through experiments. However, by applying the inference model it is possible to isolate the gene responsible for the expression of the chemoattractant. We compared wild type and gene deleted (mutant) datasets and found a significant difference between inferred parameters, which implies that gene deletion is consistent with no production of chemoattractant.
Domenic PJ Germano
(CDEV)
The University of Melbourne
"Towards a realistic 3D deformable model of tissues"
Colorectal Cancer is one of the most prevalent forms of cancer within western society. It is known to develop within the epithelia of the colon, localised to distinct invaginations within the intestinal wall, known as the crypts of Lieberkürn. While much is known about these crypts, the biomechanical process responsible for their structural maintenance remains unknown. One such process believed to be responsible for the crypts structural stability is believed to be a result of the surrounding stromal tissue.
Throughout this talk a 3D, multilayer, cell-centre model of tissue deformation will be presented, where cell movement is governed by the minimisation of a bending potential across the epithelium, and cell-cell adhesion. Using this model, we hope to provide a realistic description of colonic crypt epithelium. Thus far, we have found that the model is capable of describing generalised tissue deformations, and we hope to extend it to describe crypt homeostasis.
Eman Alwani
(CDEV)
The University of Sheffield
"Mathematical Analysis of Feedback Requirements for Planar Polarisation in the Fly Wing"
During animal development, oriented cell behaviours are required to ensure appropriate growth and structure. Planar polarity, which describes polarisation within the plane of a cell sheet, is an important example of such behaviours. During this project, I built a mathematical model aiming to gain a qualitative understanding of the requirements for different feedback interactions to establish planar polarisation in the fly wing.
Erika Tsingos
(CDEV)
Centre for Organismal Studies
"A computational tool to optimise experiments for estimating cell cycle parameters"
Determining how quickly cells traverse the cell cycle is of key interest in growing organ(oid)s, tissues in turnover, and tumours. Estimating cell cycle times requires direct monitoring of a large dynamic cell population [1]. Acquiring and analysing such time-resolved data is challenging, and becomes practicably impossible in complex multicellular tissues. Over the years, several experimental assays have attempted to circumvent these limitations and estimate cell cycle parameters in fixed tissue samples [2-4]. However, there is only fragmentary information on how biological variation, underlying cell heterogeneity, or technical limitations affect the accuracy of these estimates. Here, we develop a computational tool to address these issues with the aim of determining optimal experimental strategies to uncover cell cycle parameters in samples that cannot be monitored directly. We simulate a population of cells traversing a stochastic 4-phase model of the cell cycle. Based on experimental observations and previous theoretical work [1,5], we model the duration of each cell cycle phase with Erlang distributions (a special case of the Gamma distribution), which are parametrised by a shape parameter k and a rate parameter L. These two parameters are used to define the mean phase duration m=k/L and variance B=k/L^2. We implement three different assays used in the literature to estimate cell cycle parameters, then systematically test how biological and technical variability affect the accuracy of the estimate in virtual experiments. Surprisingly, the error of the estimate increases when the duration of the cell cycle is long compared to the duration of the experiment. This implies that the parameter that the assay aims to determine needs to be known beforehand. To overcome this dilemma, we suggest combining different assays to extract maximal information in as few experiments as possible.
Jessica Wellington
(CDEV)
University of Missouri
"A Mathematical Model to Investigate Iron Allocation in Plants"
This presentation discusses the development of a mathematical model to study the mobilization of nutrients in plants – specifically iron. The development of the model involved the combined use of biological principles and the theory of ordinary differential equations. The model merges both biological and mathematical principles to construct a nutrient allocation model that can accurately reproduce experimental data. At each step of the model development process, we will discuss how the principles from both fields worked together to resolve the problems we faced while building a model that produces biologically meaningful results. We demonstrate that the model can be used as a virtual laboratory to study the plant’s response to changes in iron availability in the soil. The quantitative results from the simulations give insights into how to design future lab experiments (predictive biology). The motivation for building the model is the hope that further understanding of the uptake and storage of iron in plants will allow biologists to engineer plants – through precision breeding and gene editing- that can better respond to changes in soil nutrient concentrations.
Luke Andrejek
(CDEV)
The Ohio State University
"A Robust Mathematical Model of Adaxial-Abaxial Patterning"
Biological development results from intricate and dynamic interactions between members of gene regulatory networks. This is exemplified by the production of flat leaf architecture. Leaves flatten by driving growth along the boundary between their adaxial (top) and abaxial (bottom) domains. These domains are generated by interactions between a complex network of transcription factors and small RNAs. Despite its complexity, flat leaf production is robust to genetic and environmental noise. To help us study this system, we mathematically modeled the determinants and interactions that pattern the adaxial-abaxial boundary. Our model recapitulates observations of adaxial-abaxial patterning and small RNA-target interactions. Positioning of the adaxial-abaxial boundary is highly robust to noise in the model. Furthermore, we identify degradation rates as possible factors contributing to robustness of adaxial-abaxial patterning.
Lutz Brusch
(CDEV)
Technische Universität Dresden
"Morpheus: A user-friendly simulation framework for multi-cellular systems biology"
Computational modeling and simulation become increasingly important to analyze tissue morphogenesis. A number of corresponding software tools have been developed but require scientists to encode their models in an imperative programming language. Morpheus, on the other hand, is an extensible open-source software framework that is entirely based on declarative modeling. It uses the domain-specific language MorpheusML to define multicellular models through a user-friendly GUI and has since proven applicable by a much broader community, including experimentalists and trainees. We here present how MorpheusML and the open-source framework allow for rapid model prototyping and advanced scientific work-flows. MorpheusML provides a bio-mathematical language in which symbolic identifiers in mathematical expressions describe the dynamics of and coupling between the various model components. It represents the spatial and mechanical aspects of interacting cells in terms of the cellular Potts model formalism and follows the software design rule of separation of model from implementation, enabling model sharing, versioning and archiving. A numerical simulation is then composed by parsing the MorpheusML model definition and automatic scheduling of predefined components in the simulator. Moreover, Morpheus supports simulations based on experimental data, e.g. segmented cell configurations, and offers a broad set of analysis tools to extract features right during simulation. A rich c++ API allows to extend MorpheusML and the simulator with user-tailored plugins. Finally, we apply Morpheus and image-based modeling to study the regulatory mechanisms underlying liver tissue architecture and flatworm regeneration.
Mikahl Banwarth-Kuhn
(CDEV)
UC Merced
"Quantifying the Biophysical Impact of Budding Cell Division on the Spatial Organization of Growing Yeast Colonies"
Spatial patterns in microbial colonies are the consequence of cell-division dynamics coupled with cell-cell interactions on a physical media. Agent-based models (ABMs) are a powerful tool for understanding the emergence of large scale structure from individual cell processes. In particular, the yeast, mph{Saccharomyces cerevisiae}, is a model eukaryote which commonly undergoes an asymmetric division process called budding. In this work, we develop and analyze an ABM to study the impact of budding cell division on yeast colony structure. We find that while large-scale properties of the colony (such as shape and size) are preserved, local spatial organization of the colony, with respect to mother-daughter relationships, subcolonies and their connectivities, are greatly impacted. This difference in spatial organization, coupled with differential growth rates from nutrient limitation, create distinct sectoring patterns in the subcolony structure, which offers novel insights into mechanisms driving experimentally observed sectored yeast colony phenotypes. Moreover, our work illustrates the need to include relevant biophysical mechanisms when using ABMs to compare to experimental studies.
Stephen Y Zhang
(CDEV)
Univ. British Columbia
"Inference of stochastic cellular dynamics from time-series data using optimal transport"
Cellular and developmental biology presents a wealth of processes that are inherently stochastic in nature, ranging from development to wound healing and carcinogenesis. Modern technologies such as single-cell transcriptomics and epigenomics have enabled interrogation of biological phenomena with unprecedented precision and throughput. These technologies necessarily destroy the cells being measured. Thus, any instance of a biological process can only be measured once to produce a static snapshot, and the underlying behaviour of cells over time is lost. The development of tools for reconstructing temporal dynamics from such snapshots is therefore a major challenge that is crucial to painting an accurate biological picture.
We propose a method for inferring governing dynamics from a series of temporal snapshots (such as single-cell transcriptomic profiles) sampled from populations of cells that evolve following some biological stochastic process. Our approach is based on optimal transport, a contemporary mathematical theory at the intersection of analysis, probability and geometry that provides a natural means of comparing probability distributions. Equipped with a corresponding convex optimisation framework, we provide an initial demonstration of accurate recovery of dynamics from simulated data. We also discuss how we tackle the biologically important challenge of dealing with high dimensionality and cellular growth, with a view to application to experimental datasets.
This is a joint work with Young-Heon Kim, Hugo Lavenant and Geoffrey Schiebinger.
Hosted by eSMB2020 Follow
Virtual conference of the Society for Mathematical Biology, 2020.
