Abstract: When investigating the development and function of multicellular biological systems it is not enough to only consider the behaviour of individual cells in isolation. For example when studying tissue development, how individual cells interact, both mechanically and biochemically, influences the resulting tissues form and function. Cell based modelling allows you to represent and track the interaction of individual cells in a developing tissue. Existing models including lattice based models (cellular automata and cellular Potts) and off-lattice based models (cell centre and vertex based representations) have given us insight into how tissues maintain homeostasis and how mutations spread. However, when tissues develop they interact biochemically and biomechanically with the environment and in order to capture these interactions, and the effect they have on development, the environment must be considered. We present a framework which allows multiple individual based models to be coupled together, in order to model both the tissue and the surrounding environment. The framework can use different modeling paradigms for each component, and subcellular behaviour (for example the cell cycle) can be considered. In this talk we present two examples of such a coupling, from the fields of developmental biology and vascular remodelling.

Abstract: Continuum partial differential equation models of the movement and growth of large numbers of cells generally involve constitutive assumptions about macro-scale cell population behaviour. It is difficult to know whether these assumptions accurately represent the mechanical and chemical processes that occur at the level of discrete cells. By deriving continuum models from individual-based models (IBMs) we can obtain PDE approximations to IBMs and conditions for their validity. We have developed a hybrid discrete-continuum model of nutrient-dependent growth of a line of discrete cells on a substrate in a nutrient bath. The cells are represented by linear springs connected in series, with resting lengths that evolve according to the local nutrient concentration. In turn, the continuous nutrient field changes as the cells grow due to the change in nutrient uptake with changes in cell density and the length of the cell line. Following Fozard et al. [Math. Med. and Biol., 27(1):39--74, 2010], we have derived a PDE continuum model from the discrete model ODEs for the motion of the cell vertices and cell growth by taking the large cell number limit. We have identified the conditions under which the continuum model accurately approximates the IBM by comparing numerical simulations of the two models. In addition to making the discrete and continuum frameworks more suitable for modelling cell growth by incorporating nutrient transport, our work provides conditions on the cell density to determine whether the IBM or continuum model should be used. This is an important step towards developing a hybrid model of tissue growth that uses both the IBM and its continuum limit in different regions.

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Abstract: Cell lineage tracing is a powerful tool for understanding how proliferation and differentiation of individual cells contribute to population behaviour. In the developing enteric nervous system (ENS), enteric neural crest (ENC) cells move and undergo massive population expansion by cell division within mesenchymal tissue that is itself growing. We use an agent-based model to simulate ENC colonisation and obtain agent lineage tracing data, which we analyse using econometric data analysis tools. Biological trials with clonally labelled ENS cells were also performed. In all realisations a small proportion of identical initial agents accounts for a substantial proportion of the total agent population. We term these individuals superstars. Their existence is consistent across individual realisations and is robust to changes in model parameters. However which individual agents will become a superstar is unpredictable. This inequality of outcome is amplified at elevated proliferation rate. Biological trials revealed identical and heretofore unexpected clonal behaviour. The experiments and model suggest that stochastic competition for resources is an important concept when understanding biological processes that feature high levels of cell proliferation. The results have implications for cell fate processes in the ENS and in other situations with invasive proliferative cells, such as invasive cancer.

Abstract: There are over 40 million people currently infected worldwide, and efforts to develop a vaccine would be improved greatly by a better understanding of how HIV survives and evolves. Recent studies discovered the ability of HIV target cells to present viral particles on the surface and trigger immune recognition and suppression by ÒkillerÓ cells of immune system. The effect of ÒkillersÓ remains to be poorly understood, however it plays a key role in control of HIV infection. While traditional vaccine approaches became unsuccessful, the vaccines against early expressed conservative viral parts are promising and would make possible managing the ability of the virus to mutate and avoid immune recognition. To discover the mechanism of ÒkillerÓ cells I developed an agent-based stochastic model of HIV dynamics at the cellular level. While the classic ODE approach is unable to simulate similar dynamics that I observed in the experimental data, the agent-based stochastic model is easily comprehensible and exposes similar kinetics. The complexity of the method increases greatly with the number of agents in the model and may be effectively resolved by using parallel computations on Graphics Processing Units (GPUs). I found that the simulated dynamics almost completely resembles the experimental data and provides answer on the addressed question. Also, the model may be applied in further developments on the design of experiments to distinguish mechanisms more precisely.

Abstract: Spreading cell fronts are essential for embryonic development, tissue repair and cancer. Mathematical models used to describe the motion of cell fronts, such as Fisher’s equation and other partial differential equations, always invoke a mean-field assumption which implies that there is no spatial structure, such as cell clustering, present in the system. We test this ubiquitous assumption using a combination of in vitro cell migration assays, spatial statistics tools and discrete random walk simulations. In particular, we examine the conditions under which spatial structure can form in a spreading cell population. Our results highlight the importance of carefully examining these kinds of modelling assumptions that can be easily overlooked when applying partial differential equation models to describe the collective migration of a population of cells.

Abstract: Cell spreading process involves cell motility and cell proliferation, and is essential to developmental biology, wound healing and immune responses. Such process is inherently stochastic and should be modelled as such. Unfortunately, there is a lack of a general and principled technique to infer the parameters of these models and quantify the uncertainty associated with these estimates based on experimental data. In this talk we present a novel application of approximation Bayesian computation (ABC) that is able to achieve this goal in a coherent framework. We compare the parameter estimates based on two different implementations of the stochastic models. The first implementation uses the exact continuous time Gillespie (CTG) algorithm while the second is the discrete time approximate (DTA) algorithm. Our results indicate that the DTA algorithm provides very similar result to, but more computationally efficient than the CTG algorithm. The key parameter finding is that the posterior distribution of the time duration between motility events is highly correlated to the experimental time and the initial number of cells. That is, the more crowded cells or the longer experiment, the faster of cell motility rate. This trend also appears in the models with cell spreading driven by combined motility and proliferation. In similar studies, parameter estimates are typically based upon the size of the leading edge, since other sources of data from the experiments can be costly to collect. Our ABC analysis suggests that is possible to infer the time duration precisely from the leading edge but unfortunately brings very little information about the cell proliferation rate. This highlight the need to obtain more detailed information from the experimental observations of cell spreading, such as the cell density profile along a diameter, in order to quantify model parameters accurately.

Abstract: The mouse spermatogenic cycle describes the periodic development of male germ cells in the testicular tissue. Understanding the spermatogenic cycle has important clinical relevance, because disruption of the process leads to infertility or subfertility, and being able to regulate the process would provide new avenues to male contraceptives. However, the lengthy process prevents visualizing the cycle through dynamic imaging. Moreover, the precise action of germ cells that leads to the emergence of testicular tissue patterns remains uncharacterized. We develop an agent-based model to simulate the mouse spermatogenic cycle on a cross-section of the seminiferous tubule over a time scale of hours to years, taking consideration of multiple cellular behaviors including feedback regulation, mitotic and meiotic division, differentiation, apoptosis, and movement. The computer model is able to elaborate the temporal-spatial dynamics of germ cells in a time-lapse movie format, allowing us to trace individual cells as they change state and location. More importantly, the model provides the mechanistic understanding of the fundamentals of male fertility, namely, how testicular morphology and sperm production are achieved. By manipulating cellular behaviors either individually or collectively in silico, the model predicts the causal events to the altered arrangement of germ cells upon genetic and environmental perturbations. This in silico platform can serve as an interactive tool to perform long-term simulations and identify optimal approaches for infertility treatment and contraceptive development. Such approach may also be applicable to human spermatogenesis and, hence, may lay the foundation for increasing the effectiveness of male fertility regulation.