ON THE MODIFICATION OF FRACTAL SELF-SPACE DURING CELL DIFFERENTIATION OR TUMOR PROGRESSION

Abstract

A novel parameter called expansion coefficient has been defined to measure both connectivity and collectivity in a population of cells conquering the available space and self-organizing into tissue patterns of the higher order. Connectivity (i.e. interconnectedness) denotes that there are complex dynamic relationships, not just structural, static ones, in a population of cells enabling the emergence of global features in the system that would never appear in single cells existing out of the system. Collectivity denotes that all interconnected cells interact in a common mode.Evolution of this coefficient during differentiation or tumor progression was investigated by the box-counting method. The population of control or retinoid-treated primary cancer cells cultured in the monolayer (i.e. quasi-2D) system possessed fractal dimension and self-similarity. However, the expansion coefficient was close to zero, indicating that connectivity was low, and no collective state emerged. A significant change of the coefficient occurred when primary cells formed aggregates, quasi-3D systems with increased connectivity, and during treatment of the aggregates with retinoid resulting in a collective state (i.e. in differentiation of cells). Those statistical features were lost during tumor progression. All populations of the secondary cancer cells possessed integer dimension and the expansion coefficient was equal to zero.