Models of evolutionary genetics, cell biology and animal physiology

Members of the research team from the DAMS

doc. Mgr. Richard Kollár, PhD.

Mathematical models in evolutionary genetics, cell biophysics, and animal physiology help to understand the principles of evolution and functionality of biological species on a macroscopic and microscopic scale. In our research, we study telomeric DNA, which is involved in the regulation of cell aging, the population growth in yeast and the regulation of biorhythms under the influence of the external environment. In addition, our research deals with a number of interesting problems on the edge of current mathematical knowledge, which we study thoroughly.

Selected papers

R. Kollár, K. Boďová, J. Nosek, Ľ. Tomáška: Mathematical model of alternative mechanism of telomere length maintenance, Physical Review E 89 (2014), No. 3, 032701.

R. Kollár, K. Šišková: Extension and justification of quasi-steady-state approximation for reversible bimolecular binding, Bulletin of Mathematical Biology 77 (2015), No. 7, 1401-1436.

R. Kollár, S. Novak: Existence of Traveling Waves for the Generalized F–KPP Equation, Bulletin of Mathematical Biology 79 (2017), No. 3, 525-559.

S. Novak, R. Kollár: Spatial Gene Frequency Waves Under Genotype-Dependent Dispersal, Genetics 205 (2017), No. 1 , 367-374.