A Principle of Complexity, Gompertzian Dynamics, and Chemoprevention
Department of Theoretical Chemistry, University of Poznan, Poznan, Poland
AIMS: This work defines a universal relationship between time and space for any non-linear process with Gompertzian dynamics such as tumor growth. METHODS: Mathematical modelling, fractal analysis, and Relative RT-PCR. RESULTS: We demonstrate that equilibrium of regular states, (i.e., states with dynamics predictable for any time-point, (e.g., sinusoidal glycolytic oscillations)) and chaotic states, (i.e., states with dynamics unpredictable in time, but characterized by certain regularities, (e.g., the existence of strange attractor for any biochemical reaction)) is described by the Gompertzian curve. Chaotic states can be quenched by regular states until the point U of the minimum of energy of intercellular exchange is attained during the evolution of the interacting system in time. The changes in complexity, connectivity, and energy exchange in cellular system imply changes at the molecular level, (e.g., expression of TGH or HNF1b gene). CONCLUSIONS: Both the equilibrium of regular and chaotic states and volume of the available, complementary Euclidean space determine temporal and spatial expansion of tumor. A principle of complexity and the basic laws of Gompertzian growth bound efficacy of cancer chemoprevention.
Paper presented at the International Symposium on Predictive Oncology and Intervention Strategies; Nice, France; February 7 - 10, 2004; in poster session 997 (Chemoprevention).