Ph.D Thesis

Ph.D StudentFriedlander Tamar
SubjectProtein Distributions and Their Role in Cell Population
DepartmentDepartment of Physics
Supervisors PROF. Erez Braun
PROF. Naama Brenner
Full Thesis textFull thesis text - English Version


This thesis addresses two problems of great theoretical interest in biology. Variation in physiological properties that cannot be attributed to either genetic or environmental factors is a well-known phenomenon that raises many theoretical questions. In the first part of the thesis we study protein distributions in dividing unicellular populations, as an example to a physiological trait that is heritable and affects the cell function. We begin with a single variable population description utilizing the framework of the population balance equation (PBE) and focus on its steady state solution.

We address the steady state by asymptotic analysis and show that the steady state distribution tail is determined by a combination of protein production and cell division and is insensitive to other model details. Under general conditions this

tail is exponential with a dependence on parameters consistent with experiment. We discuss the conditions for this effect to be dominant over other sources of variation and the relation to experiments. This description however disregards the relation between the protein content and cell fitness, reflected by its reproduction rate.

We proceed by extending the model to relate the protein content to cell metabolism. We study the relation between the distribution dynamics and protein functionality and conclude that dynamics can reflect differences in protein functionality, even if steady state distributions are similar.

The second part of this thesis addresses adaptive response found in various biological signaling systems, such as bacterial

chemotaxis, synaptic and hormonal receptors and ion channels. We study a prototypic model that unifies various biological systems, showing how they share a common principle despite differences in morphology and context. The essential ingredient in the model is a combination of rapid input-dependent transitions and slow input-independent, state-dependent transitions. We analyze this model with respect to the input-output relation it implements, suggesting the relation to concepts from control theory and signal processing. We show that the slow availability variable encodes an averaging over past activity, and feeds back multiplicatively on the system output, regardless of the details of kinetics. The kinetics of recovery from unavailability determines the effective memory kernel inside the feedback branch, giving rise to a variety of system-specific forms of response: precise or input-dependent, exponential or power-law, as special cases of the same model. We then discuss the dynamic range of these systems by extending the concept of availability from binary to graded.