We investigate the migration of glioma cells as a front propagation phenomenon both theoretically (by using both discrete lattice modeling and a continuum approach) and experimentally. For small effective strength of cell-cell adhesion q, the front velocity does not depend on q. When q exceeds a critical threshold, a fingeringlike front propagation is observed due to cluster formation in the invasive zone. We show that the experiments correspond to the transient regime, before the regime of front propagation is established. We performed an additional experiment on cell migration. A detailed comparison with experimental observations showed that the theory correctly predicts the maximal migration distance but underestimates the migration of the main mass of cells.

The effect of chemotaxis on migration of adhesive and proliferative cells on a substrate is analyzed by employing two approaches: by solving a stochastic discrete lattice model for cell dynamics and by deriving and solving a continuum macroscopic equation for cell density. The phenomenon of front propagation is investigated in the framework of the two approaches both for positive and negative chemotaxis. A good agreement between the results of the lattice model and of the continuum model is observed both for front velocities and front profiles. The theoretical model is also able to match recent experimental observations on glioma cell migration.

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.

Researchers have suggested that the fate of a shock-induced wave front at the edge of a “virtual anode” (a region hyperpolarized by the shock) is a key factor determining success or failure during defibrillation of the heart. In this paper, we use a simple one-dimensional computer model to examine propagation speed through a hyperpolarized region. Our goal is to test the hypothesis that rapid propagation through a virtual anode can cause failure of propagation at the edge of the virtual anode. The calculations support this hypothesis and suggest that the time constant of the sodium inactivation gate is an important parameter. These results may be significant in understanding the mechanism of the upper limit of vulnerability.