Is cancer a pure growth curve or does it follow a kinetics of dynamical structural transformation?

BACKGROUND: Unperturbed tumor growth kinetics is one of the more studied cancer topics; however, it is poorly understood. Mathematical modeling is a useful tool to elucidate new mechanisms involved in tumor growth kinetics, which can be relevant to understand cancer genesis and select the most suitable treatment. METHODS: The classical Kolmogorov-Johnson-Mehl-Avrami as well as the modified Kolmogorov-Johnson-Mehl-Avrami models to describe unperturbed fibrosarcoma Sa-37 tumor growth are used and compared with the Gompertz modified and Logistic models. Viable tumor cells (1×105) are inoculated to 28 BALB/c male mice. RESULTS: Modified Gompertz, Logistic, Kolmogorov-Johnson-Mehl-Avrami classical and modified Kolmogorov-Johnson-Mehl-Avrami models fit well to the experimental data and agree with one another. A jump in the time behaviors of the instantaneous slopes of classical and modified Kolmogorov-Johnson-Mehl-Avrami models and high values of these instantaneous slopes at very early stages of tumor growth kinetics are observed. CONCLUSIONS: The modified Kolmogorov-Johnson-Mehl-Avrami equation can be used to describe unperturbed fibrosarcoma Sa-37 tumor growth. It reveals that diffusion-controlled nucleation/growth and impingement mechanisms are involved in tumor growth kinetics. On the other hand, tumor development kinetics reveals dynamical structural transformations rather than a pure growth curve. Tumor fractal property prevails during entire TGK.

Epileptogenic drugs in a model nervous system: electrophysiological effects and incorporation into a phospholipid layer.

Mechanisms of epileptiform activity in a model nervous system (buccal ganglia of Helix pomatia) are presented. The ganglia contain the identified giant neurons B1 through B4. For epileptiform activity, pentylenetetrazol (1 mmol/L to 40 mmol/L) or etomidate (12.5 micromol/L to 500 micromol/L) were applied. Membrane pressure was measured using a Wilhelmy film balance. In electrophysiological experiments, both drugs induced several effects in all studied neurons: membrane resistance increased, down-stroke of action potentials declined, and all types of chemical synaptic potentials decreased (the latter concerns pentylenetetrazol only). The threshold was 1 mmol/L of pentylenetetrazol and 12.5 micromol/L of etomidate. Epileptiform potentials developed in neurons that had expressed the membrane mechanisms underlying pacemaker potentials. The threshold of this development was again 1 mmol/L of pentylenetetrazol and 12.5 micromol/L of etomidate. Epileptiform depolarizations appeared with 40 mmol/L of pentylenetetrazol and 500 micromol/L of etomidate. In biochemical experiments, both drugs incorporated into an artificial phospholipids membrane and increased pressure in the membrane. The threshold of pressure increase was 1 mmol/L of pentylenetetrazol and 12.5 micromol/L of etomidate. Pressure increased dose-dependently and was 69% and 63% above starting pressure of 10 mN/m with epileptogenic concentrations of pentylenetetrazol (40 mmol/L) and of etomidate (500 micromol/L), respectively. It is postulated that amphiphilic substances incorporate into cell membranes and increase intramembranous pressure, and that this disturbs several membrane processes mechanically and leads to epileptic depolarizations in pacemaker neurons.