The Relationship between Cell Shape and Division Plane: Control of Prokaryotic Cell Division by Turing Pattern

Cell division requires the precise placement of the division ring at mid-cell to ensure both daughter cells areviable. However, the mechanisms behind this localization remain poorly characterized. There are a limitednumber of known ways to identify the centre of the cell. One such mechanism is a Turing pattern. One intracellularTuring pattern has been identified, that produced by the Min protein system. In Escherichia coli, the Min proteinsystem plays a role in establishing the division ring position. Membrane-bound Min proteins form an oscillatingspatial pattern where the proteins are concentrated at one pole of the cell and then another, leaving a barezone at the centre of the cell where the FtsZ ring will form.Based on molecular interactions of the Min system, we have formulated a mathematical model that reproducesMin patterning during cell growth and division. This model provides a platform to explore how the Min systemfunctions and what characteristics are likely to be shared with other Turing patterning systems, should they exist.We examine the general characteristics of Turing patterns produced by the Min system. In particular, patterningapproximates a harmonic of the cell shape and selects the dominant harmonic in a predictable manner. This showswhat alternative intracellular Turing patterning systems are likely to appear and how they would behave in relationtion to cell shape. The oscillations of the Min system are shown to be translated into a mid-cell localization signalvia the harmonics generated by non-linear interactions of the system. We show that division plane orientation inthe pleomorphic archeon Haloferax volcanii can be predicted from cell shape by assuming that it is dictated by aTuring mechanism. The H. volcanii cell shapes, which on visual inspect appear to be random, are regulated bythe FtsZ homolog CetZ1.This thesis makes progress towards understanding how the Min system functions to regulate cell division. Moregenerally it develops tools to