of wavefronts. Further, those systems cannot support concentric wave trains, which also applies for CDRs, as will be discussed in the next chapter.
For CDRs, the two phosphorylation states of a phospholipid, i.e., PIP2 and PIP3, might constitute a two-state element, which could be responsible for the polarisation of CDRs into an interior and an exterior (Table 2.1). This idea has been proposed by Itoh et al. in form of a qualitative mechanism that is based on the conversion from PIP3 to PIP2 in which the former is localised in patches at the plasma membrane as a response to cell stimulation with growth factors [Itoh and Hasegawa, 2012]. PIP3 is then converted to PIP2 via SHIP2 and SH3YL1, which in turn promotes the polymerization of g-actin into f-actin, forming the characteristic vertical protrusions of CDRs. A similar mechanism is discussed by Hoon et al. [Hoon et al., 2012]. The wave-forming dynamics of the PIP2/PIP3 system has also been studied in the regulation of the actin dynamics in D. discoideum [Gerisch et al., 2012]. Indeed, Khamviwath et al. propose a quantitative model for actin waves inD. discoideum that is closely reminiscent of the qualitative model proposed for CDRs by Itoh, Hoon et al.s [Khamviwath et al., 2013].
Figure 3.10D illustrates a hypothetical scenario in which PIP3, or a related membrane-bound regulator, constitutes the polarity between CDR inside and outside. In this variant actin is assumed only to be present in its monomeric form in CDR interiors.
This is to highlight that within a framework in which PIP3 either functions to facilitate f-actin depolymerization, or to stop actin polymerization, g-actin is not necessarily entirely depleted in CDR interiors. Interestingly, Hasegawa et al. have shown recently that indeed the PIP3-recognizing Arap1 is organized in a secondary ring within CDRs.
Remarkably, Hasegawa et al. do not talk about wavefronts in this respect nor is the term ”wave” mentioned in the entire article. Arap1 functions as a GAP for deactivation of the small GTPase Arf1, which is in turn associated with promotion of actin polymerization [Hasegawa et al., 2012]. Therefore, the secondary ring of Arap1 within CDR wavefronts could be a mark of the negative feedback loop in CDRs, which is responsible for suppression of actin polymerization. We will come back to the discussion of the mechanism of actin depletion in the CDR interior in Section 5.5.
The results presented in this chapter constitute a basic understanding of some of the most important processes involved in the wave machinery of CDRs. In the following chapters, the focus lies on the analysis of the dynamics of CDRs, which will further contribute to this picture. The results from the next chapters will add support to the hypothesis that actin availability is a crucial component in CDR dynamics. However, we will also find evidence confirming the idea of an inherent polarization of CDRs.
Indeed the final picture will be in favour of a scheme as shown in Figure 3.10D in which additionally a limiting factor is constituted by a finite actin reservoir.
bThis idea was proposed by Prof. Nir Gov (Weizmann Insitute of Science, Rehovot, Israel) in a personal communication.
Chapter 4
Wave Dynamics on
Random-Shaped Cells
It is the main thesis of this work that cells form an active medium for the propagation of CDRs. In this section I will present evidence for this stance based on the identification of features of the dynamics of CDR wavefronts that are well known to occur also for waves in two-dimensional active media. In particular, live imaging data sets were systematically scanned for the following events:
• periodic reappearances of CDRs
• annihilation of wavefronts during collisions
• the occurrence of spiral waves.
The wavefront dynamics will be further investigated with respect to the evolution of the velocity as a function of time and local wavefront curvature. Moreover, the behaviour of waves close to the boundaries of cells will be examined.
The data were acquired in long-term experiments, in which cells were imaged under biochemically constant, physiological conditions for several hours. This experimental approach di↵ers from the traditional experimental strategy for investigations on CDRs, which relies on the stimulation of CDR formation by growth factors such as, e.g., PDGF directly before or during imaging [Mellstr¨om et al., 1983, Krueger et al., 2003, Itoh and Hasegawa, 2012, Hoon et al., 2012]. The reason why I chose to refrain from the temporarily punctual addition of growth factors to the cell medium is that this approach involves two issues, which complicate the understanding of the dynamic events resulting from cell stimulation. Let us use the analogy of the stimulation of waves in the FHN system for illustration. The FHN system responds with wave formation to spatiotemporal punctual stimulation of the medium (Section 2.3). However, in experiments on cells this is, due to technical reasons, not easily achievable. In contrast, the stimulation of cells with growth factors means that the whole cell body is exposed to a stimulus.
Accordingly, with growth factor stimulation, no singular point of CDR origin can be 61
62 CHAPTER 4. WAVE DYNAMICS ON RANDOM-SHAPED CELLS determined, which is the first issue. This case will be investigated in Section 4.6. The second issue is based on the fact that cells are known to adapt to sudden changes in their environment such as biochemical disturbance by growth factor stimulation [Itoh and Hasegawa, 2012, Hoon et al., 2012]. In the framework of an active medium description such a disturbance, and the corresponding adaptation of cells, corresponds to a change of the phase space of the system in time, which largely complicates an understanding of the resulting dynamics.
To gain acceptable data yield without the need for external stimuli, I used a cell line (NIH 3T3 X2) that forms CDRs spontaneously at high rates in standard cell medium without the need of punctual growth factor stimulation. Since this approach di↵ers from the standard procedure in the literature, I confirmed that the resulting CDRs have equivalent dynamics as induced CDRs in test experiments (Appendix: 9.1). Di↵erences between spontaneously formed and stimulated CDRs were only found in their initial growth phase, as introduced in the Section 3.1.1. The latter was less pronounced for stimulated CDRs. A possible explanation for this is given by the assumption that growth factor stimulation leads to simultaneous stimulation of the complete dorsal cell surface. This notion will be discussed in detail in Section 4.6. Spontaneous CDR formation, in contrast, is of stochastic nature and only locally leads to wave triggering.
Phase contrast microscopy was used to guarantee that no photo-induced biochemical disturbances occurred, which is - due to phototoxicity - a common issue in fluorescence microscopy. The positions of wavefronts of polymerized actin can equally well be localized based on phase contrast micrographs (Section 8.9.1). Details on the experimental procedures of this chapter are described in Section 8.7.2.
From 41 experimental runs, 600 cells that exhibited CDRs were visually categorized and assigned to subselections, according to the encountered phenomena. This filtering reduced the number of cells that were finally analysed considerably; the respective numbers for each category are explicitly stated in the following presentation of the findings of the phenomena encountered for CDR dynamics. Each of the subsequent sections is dedicated to one specific aspect of CDR dynamics. Whenever possible, we interpret and discuss the data directly in the respective section. The final section (Section 4.7) is a summary and discussion of the data in a holistic sense.