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Nuclei on the Move - Physical Aspects of Interkinetic Nuclear Migration



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Embryonic development is a highly complex procedure, leading from initial, unspecialised cell types - the stem cells - to ever more specialised ones. In part, this process is regulated by genes; but interactions between cells, such as mechanical contacts and the exchange of diffusive signalling molecules, also play pivotal roles for the correct execution of developmental programmes. Therefore, unravelling the rules of cell differentiation requires insights from both biology and physics.

In this dissertation, we focus on the process of interkinetic nuclear migration (IKNM). IKNM takes place in cells of so-called pseudostratified epithelia (PSE) during development. In these tissues, the nuclei of cells move in a cell cycle dependent manner and position themselves in a specific region of the cells for each cell division. The correct nuclear positioning has been shown to be crucial for proper development in PSE. And because organs like the brain and the spinal cord develop from pseudostratified epithelial tissues, IKNM appears to be of paramount importance for the entire embryo.

The work presented here concerns IKNM in the retina, an experimentally accessible outgrowth of the brain, and relies on experimental data obtained from zebrafish. However, the conclusions are likewise relevant for understanding the development of many other PSE tissues.

Based on the experimental data, two previously posed hypotheses on how the majority of nuclear movements might be driven can be tested. The data is consistent with the idea that nuclear movements depend on the build-up of a gradient in nuclear packing density across the retinal tissue. Consequently, we develop the first mathematical model for the distribution of nuclei across the retinal tissue as a function of time. Underlying this model is the notion that individual nuclear trajectories phenomenologically resemble random walks during most of the cell cycle. Therefore, we model the time evolution of the nuclear density using a diffusion equation with an effective diffusion constant to be determined from the data. Furthermore, we specifically account for the fact that nuclear divisions always take place in a defined region of the cells - leading to the aforementioned gradient in nuclear packing density. Finally, we also pay attention to the spherical geometry of the retinal tissue. Although the simplest linear model describes well the data from early in the experiments, it fails to do so for data from later stages in which nuclei approach close-packing. We hypothesise that the reason for this mismatch between model and data might result from the neglect of crowding. Therefore, we present a second, nonlinear model which now takes the volume of nuclei into account by introducing a maximum possible packing density. This enables us to replicate the experimental nuclear distribution across the whole range of experimental time points. We finally employ this second model to make statements about the influence of experimental parameters, specifically incubation temperature, on the dynamics of IKNM. The result also provides some indications for possible microscopic mechanisms underlying the nuclear movements.

Having studied the distribution of nuclei across the retinal tissue, we aim to investigate the significance of our obtained results on the level of individual cells. First, we compare the mobility of nuclei during IKNM with the expected mobility in the cases of Brownian motion and membrane-hindered Brownian motion. We find that IKNM appears to be both membrane-hindered and additionally driven throughout the entire cell cycle. Assuming a stochastic driving force and calculating its typical strength we deduce IKNM to be consistent with cytoskeletal transport. We then devise possible Langevin models for individual nuclear movements which are consistent with the model for the distribution of nuclei derived previously. The numerical simulation of each of these Langevin models enables us to distinguish between them; we identify the model which most likely reflects the biological process in each individual cell. This again leads to predictions about the potential microscopic underpinnings of nuclear movements during IKNM.

The apparent importance of the cell membrane in restricting nuclear mobility prompts us to examine the shape of PSE cells in closer detail. We numerically solve the Helfrich elastic model for lipid bilayers for increasingly large cell aspect ratios. In the case of long, slender cells and high membrane tension, we recover shapes not unlike those previously reported for membrane tethers. In contrast, shorter cells are almost cylindrical. The results of this systematic investigation into cell shapes might explain the different geometries of cells in various types of PSE. Furthermore, they might also be of relevance for more generally understanding peculiar cell shapes, such as those of neurons.





Goldstein, Raymond E


Biophysics, Applied Mathematics, Interkinetic Nuclear Migration, Zebrafish, Retina, Diffusive Process


Doctor of Philosophy (PhD)

Awarding Institution

University of Cambridge
EPSRC; Helen Stone Scholarship at the University of Cambridge (through the Cambridge Commonwealth, European & International Trust); The Cambridge Philosophical Society Research Studentship