Modeling tumor cell shedding.

Cell shedding is an important step in the development of tumor invasion and metastasis. It influences growth saturation, latency, and tumor surface roughness. In spite of careful experiments carried out using multicellular tumor spheroids (MTS), the effects of the shedding process are not yet completely understood. Using a simulational model, we study how the nature and intensity of cell shedding may influence tumor morphology and examine the dependence of the total number of shed cells with the relevant parameters, finding the ranges that maximize cell detachment. These ranges correspond to intermediate values of the adhesion, for which we observe the emergence of a rough tumor surface. They are also likely to maximize the probability of generating invasion and metastases. Using numerical values taken from experiments, we find that the shedding-induced reduction in the growth rate is not intense enough to lead to latency, except when cell adhesion is assumed to be very weak. This suggests that the presence of inhibitors is a necessary condition for the observed MTS growth saturation.

Cancer growth: predictions of a realistic model.

Simulations of avascular cancer growth are performed using experimental values of the relevant parameters. This permits a realistic assessment of the influence of these parameters on cancer growth dynamics. In general, an early exponential growth phase is followed by a linear regime (as observed in recent experiments), while the thickness of the viable cell layer remains approximately constant. Contrary to some predictions, a transition to latency is not observed.

Regularization of the displacement moments for asymmetric Lévy flights.

Although the second displacement moments for Lévy flights are not defined in their usual sense, a few years ago it was shown that nonextensive statistical mechanics can be used to define them for symmetric flights. Here it is shown that the displacement moments for long-jump asymmetric Lévy flights can also be regularized by calculating the averages in the form prescribed by nonextensive statistical mechanics. The dependence of the generalized diffusion coefficient on the asymmetry strength is investigated. It is also shown that no extremum q -entropy principle can be associated with the asymmetric Lévy attractors.

Randomly curved runs interrupted by tumbling: a model for bacterial motion.

Small bacteria are strongly buffeted by Brownian forces that make completely straight runs impossible. A model for bacterial motion is formulated in which the effects of fluctuational forces and torques on the run phase are taken into account by using coupled Langevin equations. An integrated description of the motion, including runs and tumbles, is then obtained by the use of convolution and Laplace transforms. The properties of the velocity-velocity correlation function, of the mean displacement, and of the two relevant diffusion coefficients are examined in terms of the bacterial sizes and of the magnitude of the propelling forces. For bacteria smaller than E. coli, the integrated diffusion coefficient crosses over from a jump-dominated to a rotational-diffusion-dominated form.