Title: Application Eigen’s replicator quasispecies model to dynamics growth cancer cells with sequential mutation
Abstract:
Formation of pre-cancer and cancer cells represent branching stochastic process contained many cells Mathematical models consider mutation matrix, fineness landscape matrix and death rates. Each element of mutation matrix present probability of appears new cells in the sequence of mutation cancer and pre-cancer cells. Differentiated description for each species cancer cells describes with help of the open Eigen’s quasispecies system [1-2]. It makes possible to investigate all dynamics sequence cancer and pre-cancer cells and gives value additional information on development illness if there exist information on sequential mutation and proliferation of cancer cells. This approach applies to problem pancreatic cancer [3]. Development illness goes very slowly during long time in special sake (stroma) and present sequential process contained 64 cells and appears only at final stage. Another feature of this illness is coexistence (symbiotic) effect for cancer cells and normal cells inside stroma [4-6] and excess of nutrition for cells. The result of mathematical model well agreement with experimental data
