Seminar on mathematical modeling in biology and medicine under the guidance of prof. V. Volpert

Speaker: Maxim Kuznetsov, Junior Researcher, P.N. Lebedev Physical Institute of the Russian Academy of Sciences and the Interdisciplinary Scientific Center "Mathematical Modeling in Biomedicine" of the Peoples Friendship University of Russia

Topic: Investigation of solid tumor progression via Darwinian mathematical model

Annotation. One of the key characteristics of malignant cells is the high frequency of mutations in their genome, leading to an increase in the aggressiveness of cancer tumors over time and causing the emergence of tumor resistance to chemotherapeutic drugs. However, in the overwhelming majority of works on mathematical modeling of cancer diseases, a malignant tumor is considered as a monoclonal population of cells, each of which has the same characteristics. This approach does not allow to simulate a tumor progression, which seriously limits its potential. This deficiency has led to the emergence of more complex models in which the population of tumor cells is structured according to a phenotypic parameter that determines the properties of individual cells.

In this work, a new continuous spatially distributed model of a solid tumor progression is presented, in which mutations / epimutations of tumor cells occurring during their division are explicitly taken into account. The model takes into account two reasons for the displacement of tumor cells in space: their own mobility and convective currents arising from cell proliferation in incompressible tissue. A study was made of the progression of a model solid tumor with phenotypic changes that have a reciprocal effect on the rate of proliferation and cell motility, increasing the value of one of the parameters while decreasing the other. The biological substantiation of the problem is related to the fact that cell proliferation and mobility depend on two parallel metabolic pathways, each of which actively uses glucose: the pentose phosphate pathway generates the necessary elements for the synthesis of amino acids, nucleotides and fatty acids; while glycolysis is the main pathway for the production of energy used to move malignant cells. However, there is experimental evidence that inhibition of one of the enzymes associated with one of these two processes slows down the corresponding process and accelerates the other.