טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentElhanati Yuval
SubjectVariability and Environment-Mediated Interactions
in Populations of Microorganisms
DepartmentDepartment of Physics
Supervisors Professor Erez Braun
Professor Naama Brenner
Full Thesis textFull thesis text - English Version


Abstract

Populations are a major theme in biology research. Understanding how the properties of the single individual are reflected in the entire population is a major challenge in modern biology. One central such property is variability - organisms in a population are highly variable. In this work we aim to study how the natural variability of the individual living cell is carried over to measurable quantities of the entire population. This problem has several significant differences from ensembles of physical or chemical entities, since living cells proliferate and engage in complex interactions through the common environment. Typically, interactions are mediated by molecules and proteins that are products of cell metabolism; they therefore reflect the internal dynamics of the single cell. We construct two population dynamics models that incorporate variability on the cellular level and study the outcomes on the population's level, by integrating single-cell metabolic properties that affect indirect interactions under challenging conditions. First we study a microbial population secreting a protein that can actively extract a growth-limiting resource from the environment. The genes coding for the protein can undergo random epigenetic transitions between active and silenced states, and can be repressed by the product of their reaction. We model interactions between protein producing and non-producing phenotypes by nonlinear dynamical systems and analyze them in terms of asymptotic states and of transient dynamics. Our model shows that phenotypic transitions allow a stable coexistence of the two phenotypes, and enables us to make predictions regarding the conditions required for such coexistence and the timescales of transient dynamics. In the second part of our work, we study inter-population variability and initial conditions dependence in micro-populations - intermediate-sized populations that grow in finite times. Recent technologies of microdroplet-based population growth realize this kind of populations and make them immediately relevant for experiments and biotechnological application. We study the statistical properties, arising from single cells variability, in an ensemble of micro-populations grown to saturation in a finite environment such as a micro-droplet. We develop a discrete stochastic model for this process, describing the possible histories as a random walk in a phenotypic space with an absorbing boundary. Using a mapping to Polya’s Urn, we find that distributions approach a limiting inoculum-dependent form after a large number of divisions. Thus, population size and structure are random variables whose mean, variance and in general their distribution, can reflect initial conditions after many generations of growth.