Modelling protein localisation and positional information in subcellular systems
Author(s)
Tostevin, Filipe John
Type
Thesis
Abstract
Cells and their component structures are highly organised. The correct function of
many biological systems relies upon not only temporal control of protein levels but
also spatial control of protein localisation within cells. Mathematical modelling allows
us to quantitatively test potential mechanisms for protein localisation and spatial
organisation. Here we present models of three examples of spatial organisation within
individual cells.
In the bacterium E. coli, the site of cell division is partly determined by the Min
proteins. The Min proteins oscillate between the cell poles and suppress formation of
the division ring here, thereby restricting division to midcell. We present a stochastic
model of the Min protein dynamics, and use this model to investigate partitioning of
the Min proteins between the daughter cells during cell division.
The Min proteins determine the correct position for cell division by forming a timeaveraged
concentration gradient which is minimal at midcell. Concentration gradients
are involved in a range of subcellular processes, and are particularly important for
obtaining positional information. By analysing the low copy number spatiotemporal
uctuations in protein concentrations for a single polar gradient and two oppositelydirected
gradients, we estimate the positional precision that can be achieved in vivo.
We nd that time-averaging is vital for high precision.
The embryo of the nematode C. elegans has become a model system for the study
of cell polarity. At the one-cell stage, the PAR proteins form anterior and posterior
domains in a dynamic process driven by contraction of cortical actomyosin. We
present a continuum model for this system, including a highly simpli ed model of the
actomyosin dynamics. Our model suggests that the known PAR protein interactions
5
are insu cient to explain the experimentally observed cytoplasmic polarity. We discuss
a number of modi cations to the model which reproduce the correct cytoplasmic
distributions.
many biological systems relies upon not only temporal control of protein levels but
also spatial control of protein localisation within cells. Mathematical modelling allows
us to quantitatively test potential mechanisms for protein localisation and spatial
organisation. Here we present models of three examples of spatial organisation within
individual cells.
In the bacterium E. coli, the site of cell division is partly determined by the Min
proteins. The Min proteins oscillate between the cell poles and suppress formation of
the division ring here, thereby restricting division to midcell. We present a stochastic
model of the Min protein dynamics, and use this model to investigate partitioning of
the Min proteins between the daughter cells during cell division.
The Min proteins determine the correct position for cell division by forming a timeaveraged
concentration gradient which is minimal at midcell. Concentration gradients
are involved in a range of subcellular processes, and are particularly important for
obtaining positional information. By analysing the low copy number spatiotemporal
uctuations in protein concentrations for a single polar gradient and two oppositelydirected
gradients, we estimate the positional precision that can be achieved in vivo.
We nd that time-averaging is vital for high precision.
The embryo of the nematode C. elegans has become a model system for the study
of cell polarity. At the one-cell stage, the PAR proteins form anterior and posterior
domains in a dynamic process driven by contraction of cortical actomyosin. We
present a continuum model for this system, including a highly simpli ed model of the
actomyosin dynamics. Our model suggests that the known PAR protein interactions
5
are insu cient to explain the experimentally observed cytoplasmic polarity. We discuss
a number of modi cations to the model which reproduce the correct cytoplasmic
distributions.
Date Issued
2008-04
Date Awarded
2008-09
Copyright Statement
Attribution NoDerivatives 4.0 International Licence (CC BY-ND)
Advisor
Howard, Martin
Sponsor
EPSRC.
Creator
Tostevin, Filipe John
Publisher Department
Mathematics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)