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Register a new userAnalysis of protrusion dynamics in amoeboid cell motility by means of regularized contour flows
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Amoeboid cell motility is essential for a wide range of biological processes including wound healing, embryonic morphogenesis, and cancer metastasis. It relies on complex dynamical patterns of cell shape changes that pose long-standing challenges to mathematical modeling and raise a need for automated and reproducible approaches to extract quantitative morphological features from image sequences. Here, we introduce a theoretical framework and a computational method for obtaining smooth representations of the spatiotemporal contour dynamics from stacks of segmented microscopy images. Based on a Gaussian process regression we propose a one-parameter family of regularized contour flows that allows us to continuously track reference points (virtual markers) between successive cell contours. We use this approach to define a coordinate system on the moving cell boundary and to represent different local geometric quantities in this frame of reference. In particular, we introduce the local marker dispersion as a measure to identify localized membrane expansions and provide a fully automated way to extract the properties of such expansions, including their area and growth time. The methods are available as an open-source software package called AmoePy, a Python-based toolbox for analyzing amoeboid cell motility (based on time-lapse microscopy data), including a graphical user interface and detailed documentation. Due to the mathematical rigor of our framework, we envision it to be of use for the development of novel cell motility models. We mainly use experimental data of the social amoeba Dictyostelium discoideum to illustrate and validate our approach.
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In this paper we develop mathematical models for collective cell motility. Initially we develop a model using a linear diffusion-advection type equation and fit the parameters to data from cell motility assays. This approach is helpful in classifying the results of cell motility assay experiments. In particular, this model can determine degrees of directed versus undirected collective cell motility. Next we develop a model using a nonlinear diffusion term that is able capture in a unified way directed and undirected collective cell motility. Finally we apply the nonlinear diffusion approach to a problem in tumor cell invasion, noting that neither chemotaxis or haptotaxis are present in the system under consideration in this article.
Studying the development of malignant tumours, it is important to know and predict the proportions of different cell types in tissue samples. Knowing the expected temporal evolution of the proportion of normal tissue cells, compared to stem-like and non-stem like cancer cells, gives an indication about the progression of the disease and indicates the expected response to interventions with drugs. Such processes have been modeled using Markov processes. An essential step for the simulation of such models is then the determination of state transition probabilities. We here consider the experimentally more realistic scenario in which the measurement of cell population sizes is noisy, leading to a particular hidden Markov model. In this context, randomness in measurement is related to noisy measurements, which are used for the estimation of the transition probability matrix. Randomness in sampling, on the other hand, is here related to the error in estimating the state probability from small cell populations. Using aggregated data of fluorescence-activated cell sorting (FACS) measurement, we develop a minimum mean square error estimator (MMSE) and maximum likelihood (ML) estimator and formulate two problems to find the minimum number of required samples and measurements to guarantee the accuracy of predicted population sizes using a transition probability matrix estimated from noisy data. We analyze the properties of two estimators for different noise distributions and prove an optimal solution for Gaussian distributions with the MMSE. Our numerical results show, that for noisy measurements the convergence mechanism of transition probabilities and steady states differ widely from the real values if one uses the standard deterministic approach in which measurements are assumed to be noise free.
Complete understanding of the mechanisms regulating the proliferation and differentiation that takes place during human immune CD8+ T cell responses is still lacking. Human clinical data is usually limited to blood cell counts, yet the initiation of these responses occurs in the draining lymph nodes; antigen-specific effector and memory CD8+ T cells generated in the lymph nodes migrate to those tissues where they are required. We use approximate Bayesian computation with deterministic mathematical models of CD8+ T cell populations (naive, central memory, effector memory and effector) and yellow fever virus vaccine data to infer the dynamics of these CD8+ T cell populations in three spatial compartments: draining lymph nodes, circulation and skin. We have made use of the literature to obtain rates of division and death for human CD8+ T cell population subsets and thymic export rates. Under the decreasing potential hypothesis for differentiation during an immune response, we find that, as the number of T cell clonotypes driven to an immune response increases, there is a reduction in the number of divisions required to differentiate from a naive to an effector CD8+ T cell, supporting the division of labour hypothesis observed in murine studies. We have also considered the reverse differentiation scenario, the increasing potential hypothesis. The decreasing potential model is better supported by the yellow fever virus vaccine data.
Eukaryotic cell motility involves a complex network of interactions between biochemical components and mechanical processes. The cell employs this network to polarize and induce shape changes that give rise to membrane protrusions and retractions, ultimately leading to locomotion of the entire cell body. The combination of a nonlinear reaction-diffusion model of cell polarization, noisy bistable kinetics, and a dynamic phase field for the cell shape permits us to capture the key features of this complex system to investigate several motility scenarios, including amoeboid and fan-shaped forms as well as intermediate states with distinct displacement mechanisms. We compare the numerical simulations of our model to live cell imaging experiments of motile {it Dictyostelium discoideum} cells under different developmental conditions. The dominant parameters of the mathematical model that determine the different motility regimes are identified and discussed.
Amoeboid cell migration is characterized by frequent changes of the direction of motion and resembles a persistent random walk on long time scales. Although it is well known that cell migration is typically driven by the actin cytoskeleton, the cause of this migratory behavior remains poorly understood. We analyze the spontaneous dynamics of actin assembly due to nucleation promoting factors, where actin filaments lead to an inactivation of the nucleators. We show that this system exhibits excitable dynamics and can spontaneously generate waves, which we analyse in detail. By using a phase-field approach, we show that these waves can generate cellular random walks. We explore how the characteristics of these persistent random walks depend on the parameters governing the actin-nucleator dynamics. In particular, we find that the effective diffusion constant and the persistence time depend strongly on the speed of filament assembly and the rate of nucleator inactivation. Our findings point to a deterministic origin of the random walk behavior and suggest that cells could adapt their migration pattern by modifying the pool of available actin.
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