Previous studies demonstrated that heparin coated on the culture plate inhibited the adhesion and locomotion as well as the invasion, metastasis and network communication of cells of a metastatic carcinomatous line
1-3). Heterogeneity of colonies found in the size and distribution was much more evident than those in the presence of heparin. To investigate physiologic effect of the heparin on the heterogeneity, analyses of pictures of colonies grown on plastic dishes were carried out. The fractal dimension (D) and the power spectrum (power exponent M) were determined. Then the numerical factor, an exponent V of a new power function,
f(
x)=L
x-V (L is constant) was introduced, which was able to demonstrate the change of the complexity of colonies during the development in culture. The comparison of cell colonies with artificial colonies such as random and gradient percolation made by computer programs was also performed. A model experiment using crushed cookie demonstrated that the size distribution of the fractures followed power law with a single V value similar to colonies of random and gradient percolation indicating that there was no particular interaction except friction. Both the colonies of control and heparin had power exponents V; control colonies of fractal dimensions had 1.000 and 1.330, while heparin colonies had 0.660 and 0.500 in the regions of lower and higher frequency, respectively. Power exponent of Fourier spectrum of both the control and heparin colonies had 0.25 with white noise in the regions of higher and lower frequency, respectively. Thus, the power exponent allowed us to evaluate the heterogeneity of the cell colonies, which is perhaps caused by the complex physiologic interaction. From the results, it suggests that the power exponent V causes heterogeneity of cell colonies, and heparin is able to suppress the cellular interaction allowing V values to be smaller than that of control.
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