Discipline: Mathematics and Statistics
Subcategory: Mathematics and Statistics
Zakiyyah Brown - North Carolina Agricultural and Technical State University
Co-Author(s): Jaime Henderson, North Carolina Agricultural and Technical State University, Greensboro, NC
The purpose of this research is to use the Galton-Watson branching process (GWBP) to investigate cell proliferation and two other biological processes. The GWBP is a stochastic process derived from Francis Galton’s statistical investigation of the extinction or propagation of family names in a patrilineal society. In the proliferation process, after completing its life cycle each cell approximately doubles in size and then divides into two progeny cells of approximately equal sizes. After division, cells either remain quiescent, expire, or proliferate further. The population of proliferating cells evolves according to a GBBP. Hence the GWBP model is utilized to derive the sufficient condition under which the survival and extinction probabilities can be computed with the help of MATLAB programming. MATLAB was also used to simulate and plot these three possible outcomes of a cell’s life based on the number of cell divisions and probabilities of cell death, quiescence, and proliferation. Lastly, the same GWBP model is applied to two other biological processes of the evolution of early life cycle for a polymeric chain of nucleotide and gene amplification and deamplification. Our research indicates that the expected value of offspring distribution proves to be an important factor in determining the survival/distinction of each of the three populations investigated.
Funder Acknowledgement(s): My sincerest gratitude goes to my faculty advisor Dr. Guoqing Tang and my graduate advisor Mr. Brett Hunter for their continuous guidance and support. This work was supported in part by the National Science Foundation under Grant HRD-1036299.
Faculty Advisor: Guoqing Tang,