Abstract
Cells maintain protein gradients for establishing cell polarity, positioning the cell division machinery, etc. Organelle size control, for example, the hair cell flagella length regulation is essential for hearing, maintaining two flagella at same length in Chlamydomonas cells is essential for swimming. How the cell achieves length control is the central question of this thesis. First, I examine a model of regulating multiple flagella lengths based on a protein gradient along the length of the flagellum which is established by directed transport of regulatory proteins. Next, I develop a model of how such protein gradients might form in cells via active processes like transport via motor proteins and show that resulting gradients are scale invariant. This is a particularly important feature of a cell gradient as it allows cells to control lengths that are relative to the cell size. Finally, I make estimates regarding the energy consumption needed to maintain these gradients and show that to maintain active gradients driven by motor transport the cell needs to spend less energy than using a diffusion-degradation mechanism.