Neuronal differentiation and synapse formation in the space-time with temporal fractal dimension.
An improvement of the Waliszewski and Konarski approach ([2002] Synapse 43:252-258) to determine the temporal fractal dimension b(t) and scaling factor a(t) for the process of neuronal differentiation and synapse formation in the fractal space-time is presented. In particular the analytical formulae describing the time-dependence of b(t)(t) and a(t)(t), which satisfy the appropriate boundary conditions for t-->0 and t-->infinity, are derived. They have been used to determine the temporal fractal dimension and scaling factor from the two-parametric Gompertz function fitted to experimental data obtained by Jones-Villeneuve et al. ([1982] J Cell Biol 94:253-262) for embryonal carcinoma P19 cells treated by retinoic acid. The results of the calculations differ from those obtained previously by making use of the three- and four-parametric Gompertz function as well as other S-shape functions (Chapman, Hill, Logistic, Sigmoid) evaluated by the fitting of the experimental curve. The temporal fractal dimension can be used as a numerical measure of the neuronal complexity emerging in the process of differentiation, which can be related to the morphofunctional cell organization. A hypothesis is formulated that neuronal differentiation and synapse formation have a lot in common with the process of tumorigenesis. They are qualitatively described by the same Gompertz function of growth and take place in the fractal space-time whose mean temporal fractal dimension is lost during progression.
Molski
Marcin
M
Department of Theoretical Chemistry, Faculty of Chemistry, A. Mickiewicz University of Poznań, Poznań, Poland. marcin@rovib.amu.edu.pl
Konarski
Jerzy
J
D000465:Algorithms; D000818:Animals; D001921:Brain / Q000196:embryology / Q000502:physiology; D002454:Cell Differentiation / Q000187:drug effects / Q000502:physiology*; D045744:Cell Line, Tumor; D049109:Cell Proliferation / Q000187:drug effects; D002471:Cell Transformation, Neoplastic / Q000187:drug effects; D054278:Embryonal Carcinoma Stem Cells; D017709:Fractals; D051379:Mice; D008954:Models, Biological; D009361:Neoplasm Invasiveness; D014411:Neoplastic Stem Cells / Q000187:drug effects / Q000502:physiology*; D009414:Nerve Growth Factors / Q000494:pharmacology; D009434:Neural Pathways / Q000187:drug effects / Q000196:embryology / Q000502:physiology; D009474:Neurons / Q000187:drug effects / Q000502:physiology*; D013234:Stem Cells / Q000187:drug effects / Q000502:physiology*; D013569:Synapses / Q000187:drug effects / Q000502:physiology*; D013997:Time Factors; D014212:Tretinoin / Q000494:pharmacology
D009414:Nerve Growth Factors; D014212:Tretinoin