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This work considers an expansion of a dense monolayer of cells: a collective multicellular phenomenon, where cells divide, grow, and maintain contacts with their neighbors. During migration, cells display complex behavior, adjusting both their division rate and their growth after division to the local mechanical environment. Experimental observations show that cells near the edge of the expanding monolayer are larger and move faster than cells deep inside the colony. To explain these observations and describe cell migration patterns, we formulate a spatio-temporal theoretical model for multicellular dynamics in terms of the cell area distribution; the model includes cell growth after division and effective pressure. Numerical simulations of the model predict both the speed of invasion and the width of the outer proliferative rim; these predictions are in a good agreement with experimental observations. Theoretical analysis yields the equation for density of cells and reveals a novel type of propagating front with compact support. The velocity of front propagation (monolayer expansion) is derived analytically and its dependence on all the relevant parameters is determined. [ABSTRACT FROM AUTHOR]

In this work, we analyze an ensemble of dividing and growing living cells that maintain contact with each other. The dynamics of the cell area distribution in a confined system is theoretically investigated in both uniform and nonuniform settings. The effective pressure is introduced to model the experimentally observed phenomenon in which the average cell size dramatically decreases over time. For a nonuniform system, the cell shift due to the gradient of the effective pressure is considered and its effect on the average cell area profiles is examined. [ABSTRACT FROM AUTHOR]

The phenotypic axis of invasion and proliferation in malignant glioma cells is a well-documented phenomenon. Invasive glioma cells exhibit a decreased proliferation rate and a resistance to apoptosis, and invasive tumor cells dispersed in brain subsequently revert to proliferation and contribute to secondary tumor formation. One miRNA can affect dozens of mRNAs, and some miRNAs are potent oncogenes. Multiple miRNAs are implicated in glioma malignancy, and several of which have been identified to regulate tumor cell motility and division. Using rat 9 L gliosarcoma and human U87 glioblastoma cell lines, we investigated miRNAs associated with the switch between glioma cell invasion and proliferation. Using micro-dissection of 9 L glioma tumor xenografts in rat brain, we identified disparate expression of miR-9 between cells within the periphery of the primary tumor, and those comprising tumor islets within the invasive zone. Modifying miR-9 expression in in vitro assays, we report that miR-9 controls the axis of glioma cell invasion/proliferation, and that its contribution to invasion or proliferation is biphasic and dependent upon local tumor cell density. In addition, immunohistochemistry revealed elevated hypoxia inducible factor 1 alpha (HIF-1α) in the invasive zone as compared to the primary tumor periphery. We also found that hypoxia promotes miR-9 expression in glioma cells. Based upon these findings, we propose a hypothesis for the contribution of miR-9 to the dynamics glioma invasion and satellite tumor formation in brain adjacent to tumor. [ABSTRACT FROM AUTHOR]

We present a stochastic model which describes fronts of cells invading a wound. In the model cells can move, proliferate, and experience cell-cell adhesion. We find several qualitatively different regimes of front motion and analyze the transitions between them. Above a critical value of adhesion and for small proliferation large isolated clusters are formed ahead of the front. This is mapped onto the well-known ferromagnetic phase transition in the Ising model. For large adhesion, and larger proliferation the clusters become connected (at some fixed time). For adhesion below the critical value the results are similar to our previous work which neglected adhesion. The results are compared with experiments, and possible directions of future work are proposed. [ABSTRACT FROM AUTHOR]

We present a discrete stochastic model which represents many of the salient features of the biological process of wound healing. The model describes fronts of cells invading a wound. We have numerical results in one and two dimensions. In one dimension we can give analytic results for the front speed as a power series expansion in a parameter, p, that gives the relative size of proliferation and diffusion processes for the invading cells. In two dimensions the model becomes the Eden model for p ≈ 1. In both one and two dimensions for small p, front propagation for this model should approach that of the Fisher-Kolmogorov equation. However, as in other cases, this discrete model approaches Fisher-Kolmogorov behavior slowly. [ABSTRACT FROM AUTHOR]