Statistical Geometrical Theories

A statistical way to model the pseudopod formation was introduced by van Haastert in one of his publications (83). In that work, statistical properties of the microscopic

phenomena were used to describe the process and answer the question if statistics would be sufficient to explain the system.

This theoretical description of the pseudopod extension ofD. d. basically regards the pseudopods as self-organized entities, being formed regularly. The position of a new pseudopod is calculated depending on its kind, being a splitting pseudopod or a de-novo pseudopod. Additionally, the existence and the strength of a chemoattractant gradient is also of great interest for the model. In case of a splitting pseudopod, the direction of the new pseudopod is chosen to be identical to the direction of the previous pseudopod. This direction will be modified by a bias imposed by the chemoattractant gradient. To include noise, the direction is the mean value of a von Mises distribution with varianceσ_φ. The new direction is chosen randomly within the range of the von Mises distribution.

In case of a de-novo pseusopod, the initial direction will be picked randomly between [0^◦,360^◦]. The following steps are exactly the same as for splitting pseu-dopods.

With this model, using the statistical properties of the pseudopodia, it is possible to describe the system and as well allowing to make predictions about knock-out mutants (12, 13).

Experimental Setup and Methods

In this chapter we will focus on the experimental setups and the methods used to preform our experiments. We will start by presenting the protocols used prepare the cells for the experiments. The second part of this chapter will include details on the experimental setups, namely the microfluidic devices and the involved microscopy techniques.

3.1 Cell Culture and Genetics

D. d. exists as several cell strains that need to be treated differently. An important difference between strains is the ability to use different food supplies. The cell lines used in this thesis are all axenic, meaning that they are able to feed on medium (HL5 (Formedium, Norwich, England)) free of other organisms (87). A more recent protocol ofD. d. cell culture can be found in (31). Cells are stored either as spores or directly as cells at−80^◦C for extended time periods. To use the cells for experiments,

37

frozen stock is thawed at room temperature and afterwards they are cultured in HL5 medium on Petri dishes. The doubling time of the cells is between 8 to 9 hours at the optimal growing temperature of 21−23^◦C. The cell culture has to be subcultured every 2-3 days, when the cells have become confluent on in the Petri dish. The passage number is increased by one each time for a new subculture and the cells will be discarded after passage 15, due to the increasing probability for a genetic change of the culture.

To perform experiments, we use cells harvested in their exponential growth phase, which are due to the pulsing with cAMP in their highly chemotactic phase. The preparation of the cells starts one day before the experiment. The preparation process starts with pipetting 10⁶ cells into a flask with 25 ml HL5 medium. This flask is cultivated on a shaking table at 22^◦C with 150 rotation per minute. On the day of the experiment, 7 hours prior to the start of the experiment, the cells are centrifuged and the medium is removed. The cells are washed with phosphate buffer and afterwards centrifuged again. The remaining pellet is diluted with 20 ml phosphate buffer and is positioned on the shaking table at 22^◦C, when every 6 minutes a pulse of cAMP (approx. 60µl with concentration 18µMol; Sigma-Aldrich) is dropped into the flask to increase the chemotactical activity of the cells as reported in (18).

We also used mutantD. d. cells. For the curvotaxis project, ACA-Null mutant cells were used, because cells lacking the aggregation stage adenylyl cyclase (ACA) the cells are not able to produce cAMP and hence they are missing the capability to aggregate. Those cells possess the ability to perform chemotaxis but only towards external cAMP as they cannot porduce it. This missing functionality enables us to investigate the effect of the complex geometry without the strong influence of chemotaxis.

To investigate the signaling cascade and its influence on the cell geometry, we use myosin-II-null and PTEN-null knockout cells. The knockout of myosin-II strongly interferes with the cell cortex, which is visible for instance through the fact that myosin-II-null cells are not able to divide without being attached to a surface (21).

Hence after the pulsing, there are many multinucleated cells. Those will divide as soon as they are adherent on a substrate. The PTEN-null knockout is as described in section 2.3.1 interfering with the symmetry breaking of the chemotactic cells mainly. As one of the enzymes for the process is knocked out, the fine-tuned process is disrupted. It leads to cells that have less control of the size and positioning of pseudopodia and show decreased chemotactic efficiency.

To investigate the role of the protein Ras during chemotaxis, we need to image its dynamics. We accomplish this goal via genetic labeling. A common way is to use a marker protein that only interacts with the GTP form. Also important is the fact that the fluorescent label is not tagged directly to the protein itself because otherwise it may change its dynamics.

We used different labels designed by the group of van Haastert (85) and Gerisch/ Müller-Taubenberger (32). To maintain cell lines with comparable properties e.g. the amount of fluorophores, we had to electroporate fresh wildtype cells every three to four weeks with the expression plasmid. After several days of recovery these genetically modified cells could be used similarly as standard wildtype cells.