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Register a new userKinetic models with non-local sensing determining cell polarization and speed according to independent cues
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Cells move by run and tumble, a kind of dynamics in which the cell alternates runs over straight lines and re-orientations. This erratic motion may be influenced by external factors, like chemicals, nutrients, the extra-cellular matrix, in the sense that the cell measures the external field and elaborates the signal eventually adapting its dynamics. We propose a kinetic transport equation implementing a velocity-jump process in which the transition probability takes into account a double bias, which acts, respectively, on the choice of the direction of motion and of the speed. The double bias depends on two different non-local sensing cues coming from the external environment. We analyze how the size of the cell and the way of sensing the environment with respect to the variation of the external fields affect the cell population dynamics by recovering an appropriate macroscopic limit and directly integrating the kinetic transport equation. A comparison between the solutions of the transport equation and of the proper macroscopic limit is also performed.
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Migrating cells choose their preferential direction of motion in response to different signals and stimuli sensed by spanning their external environment. However, the presence of dense fibrous regions, lack of proper substrate, and cell overcrowding may hamper cells from moving in certain directions or even from sensing beyond regions that practically act like physical barriers. We extend the non-local kinetic model proposed by Loy and Preziosi (2019) to include situations in which the sensing radius is not constant, but depends on position, sensing direction and time as cells behavior might be determined on the basis of information collected before reaching physically limiting configurations. We analyze how the actual possible sensing of the environment influences the dynamics by recovering the appropriate macroscopic limits and by integrating numerically the kinetic transport equation.
The aim of the article is to study the stability of a non-local kinetic model proposed by Loy and Preziosi (2019a). We split the population in two subgroups and perform a linear stability analysis. We show that pattern formation results from modulation of one non-dimensional parameter that depends on the tumbling frequency, the sensing radius, the mean speed in a given direction, the uniform configuration density and the tactic response to the cell density. Numerical simulations show that our linear stability analysis predicts quite precisely the ranges of parameters determining instability and pattern formation. We also extend the stability analysis in the case of different mean speeds in different directions. In this case, for parameter values leading to instability travelling wave patterns develop.
Cell proliferation is typically incorporated into stochastic mathematical models of cell migration by assuming that cell divisions occur after an exponentially distributed waiting time. Experimental observations, however, show that this assumption is often far from the real cell cycle time distribution (CCTD). Recent studies have suggested an alternative approach to modelling cell proliferation based on a multi-stage representation of the CCTD. In order to validate and parametrise these models, it is important to connect them to experimentally measurable quantities. In this paper we investigate the connection between the CCTD and the speed of the collective invasion. We first state a result for a general CCTD, which allows the computation of the invasion speed using the Laplace transform of the CCTD. We use this to deduce the range of speeds for the general case. We then focus on the more realistic case of multi-stage models, using both a stochastic agent-based model and a set of reaction-diffusion equations for the cells average density. By studying the corresponding travelling wave solutions, we obtain an analytical expression for the speed of invasion for a general N-stage model with identical transition rates, in which case the resulting cell cycle times are Erlang distributed. We show that, for a general N-stage model, the Erlang distribution and the exponential distribution lead to the minimum and maximum invasion speed, respectively. This result allows us to determine the range of possible invasion speeds in terms of the average proliferation time for any multi-stage model.
Triple-Negative Basal-Like tumors, representing 15 to 20% of breast cancers, are very aggressive and with poor prognosis. Targeted therapies have been developed extensively in preclinical and clinical studies to open the way for new treatment strategies. The present study has focused on developing 3D cell cultures from SUM1315 and MDA-MB-231, two triple-negative basal-like (TNBL) breast cancer cell lines, using the liquid overlay technique. Extracellular matrix concentration, cell density, proliferation, cell viability, topology and ultrastructure parameters were determined. The results showed that for both cell lines, the best conditioning regimen for compact and homogeneous spheroid formation was to use 1000 cells per well and 2% Geltrex. This conditioning regimen highlighted two 3D cell models: non-proliferative SUM1315 spheroids and proliferative MDA-MB-231 spheroids. In both cell lines, the comparison of 2D vs 3D cell culture viability in the presence of increasing concentrations of chemotherapeutic agents i.e. cisplatin, docetaxel and epirubicin, showed that spheroids were clearly less sensitive than monolayer cell cultures. Moreover, a proliferative or non-proliferative 3D cell line property would enable determination of cytotoxic and/or cytostatic drug activity. 3D cell culture could be an excellent tool in addition to the arsenal of techniques currently used in preclinical studies. http://www.impactjournals.com/oncotarget/ Oncotarget, Advance Publications 2017
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.
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