טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentSchreier Hallel Ilan
SubjectPopulation Models of Epigenetic Adaptation Processes in
Asexual Populations
DepartmentDepartment of Applied Mathematics
Supervisor Professor Naama Brenner


Abstract

In the current work we formulate and analyze a dynamic population model for an asexual population. The model we present has complex dynamics which are in accordance with various features of adaptation processes in which epigenetics mechanism play a crucial role.  

In the model we suggest, reproduction is described in a coarse-grained manner by a Poisson process characterized by a rate of division. In addition, our model incorporates a stability parameter assigned to each cell reflecting the degree to which the cell phenotype is inherited. Following the event of a cell division, the phenotype can be stably inherited to the next generation or not. For the first scenario a mean field approximation is employed. We derive the equation of motion, and a solution for the trivial cases s=0 and s=1, as well as the intermediate case 0<s<1 .

The main scope of our work is dedicated to the second case, in which stability is a dynamic variable. For this scenario, the dynamics is characterized by an initial stage in which the population is distributed according to the background population, followed by a series of takeovers of lineages with sufficient combinations of division rate and stability. This scenario repeats itself for a large variety of background distributions.

The dynamical stability parameter adds another degree of freedom to the system which allows a large spectrum of sub-populations which can dominate the population, and thus results in a large variety of trajectories towards adaptation. In contrast to many population models, dominant lineages can be replaced by other linages with smaller division rate. Moreover, in many cases a few dominant lineages co-exist for considerable durations of time. Another interesting feature of the model is the creation of correlation between the division rate and the stability of the population as a whole.