Stochastic modelling and analysis of early mouse development
Doktorsavhandling, 2011

The aim of this thesis is to model and describe dynamical events for biological cells using statistical and mathematical tools. The thesis includes five papers that all relate to stochastic modelling of cells. In order to understand the development and patterning of the early mammalian embryo, stochastic modelling has become a more important tool than ever. It allows for studying the processes that mediate the transition from pluripotency of the embryonic cells to their differentiation. It is still unclear whether the positions of cells determine their future fates. One alternative possibility is that cells are pre-specified at random positions and then sort according to a already set fate. Mouse embryonic cells are thought to be equivalent in their developmental properties until approaching the eight-cell stage. Some biological studies show, in comparison, that patterning can be present already at sperm entry and in the pronuclei migration. We investigate in Paper I the dynamics of the pronuclei migration by analysing their trajectories and find that not only do the pronuclei follow a noise corrupted path towards the centre of the egg but they also have some attraction to each other which affects their dynamics. Continuing in Paper II and III, we use these results to model this behaviour with a coupled stochastic differential equation model. This enables us to simulate distributions that describe the meeting plane between pronuclei which in turn can be related to the orientation of the first cleavage of the egg. Our results show that adding randomness in sperm entry point is different from the randomness added through the environment of the egg. We are also able to show that data sets with normal eggs and eggs treated with an actin growth inhibitor give rise to considerably different model dynamics, suggesting that the treatment is affecting the migration in an invasive way. Altering the pronuclei dynamics can alter the polarity of the egg and may transfer into the later axis-formation process. Invasiveness of experimental procedures is a difficult issue to handle. The alternative to invasive procedures is not appealing since it means that important developmental features may not be discovered because of individual variability and noise, leading to guesswork of the underlying mechanisms. The embryonic cells are easily affected by treatments performed to make the measuring, made by hand, easier or by the light exposure of the microscope. Treatments as such are used for example for producing flourescent proteins in membranes or slowing processes down. Paper IV and Paper V serve to analyse how light induced stress affects yeast cells and we employ a method for analysing the noisy non-stationary time series, which are a result of the yeast experiments, using wavelet decomposition.



wavelet decomposition





time series

stochastic differential equation

Pascal, Chalmers tvärgata 3
Opponent: Prof. Ola Hössjer, Stockholms universitet


Sofia Tapani

Göteborgs universitet

Chalmers, Matematiska vetenskaper, matematisk statistik

Chalmers, Matematiska vetenskaper

Continuous light exposure causes cumulative stress that affects the localization oscillation dynamics of the transcription factor Msn2p.

Biochimica et biophysica acta,; Vol. 1813(2011)p. 358-366

Artikel i vetenskaplig tidskrift

Three dimensional mathematical modelling of pronuclei migration for the mouse

Stereology and Image Analysis. Ecs10: Proceeding of the 10th European Conference of ISS., (V.Capasso et al. Ed.), The MIRIAM Project Series,; Vol. 4(2009)p. 1-6

Paper i proceeding

Hur slumpmässig är en mus? Hittills har den gängse inställningen varit att det är helt styrt av slumpen vilka celler i det tidiga musembryot som ger upphov till fostret och vilka celler som bildar yttre strukturer, t ex moderkakan. För många icke-däggdjur, såsom amfibier, är det så att utvecklingen är väldigt styrd och följer ett förbestämt regelverk. Jämfört med detta så är embryonala däggdjursceller väldigt flexibla och återhämtar sig från rätt så stora störningar. Å andra sidan så verkar det som att musembryot inte endast är en sammansatt boll som består av helt identiska celler. Genom observationer har man sett att cellerna verkar anta specifika framtida egenskaper utifrån vilka positioner de hade i det tidiga embryot. Dessa egenskaper kommer sedan i sin tur att styra cellernas utveckling och till exempel avgöra vilka cell-linjer som kommer att bilda baksidan och vilka som bildar framsidan på musen. Vi beskriver den här slumpmässiga men ändå styrda dynamiken med matematiska modeller. En svårighet är att slumpen ibland döljer huvudmekanismerna som styr utvecklingen. Dessutom är cellerna i embryot väldigt känsliga för yttre påverkan som till exempel ljusstress från mikroskopet. Därför använder vi oss av statistiska metoder för att försöka upplösa okända egenskaper i data. För att studera detta vidare har vi utvecklat och tillämpat olika metoder för att ta bort brus i data från en enklare modellorganism, nämligen jästcellen som också reagerar på ljusinducerad stress.

How random is a mouse? The prevailing opinion has been that it is completely random whether cells in the early mouse embryo become the fetus and/or become extraembryonic structures such as the placenta. In many non-mammalian species the development follows a fixed set of instructions. In comparison, mammalian cell fates are very flexible as the cells easily recover from quite extensive perturbations. On the other hand, the early mammalian embryo is not merely a blob of uniform cells. Cells do show some preferences of adopting certain fates according to their initial positions, which in turn will govern their development, and for instance which cells will form the front or the back of a mouse. We describe these random, but still guided dynamics, with mathematical models. However, a difficulty is that the randomness hides the main guidelines of the dynamics. Also, the cells of the embryos are very sensitive to light exposure, which is necessary during imaging of the processes. We turn to statistical tools to try to tackle these difficulties and to resolve unknown features in the data. To further study how this can be carried out, we develop and apply denoising methods in data from a simpler model organism, namely yeast, which also reacts to light induced stress.



Cell- och molekylärbiologi

Biologiska vetenskaper


Annan matematik


Sannolikhetsteori och statistik



Grundläggande vetenskaper


Livsvetenskaper och teknik



Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie

Pascal, Chalmers tvärgata 3

Opponent: Prof. Ola Hössjer, Stockholms universitet