76 CHAPTER 4. WAVE DYNAMICS ON RANDOM-SHAPED CELLS I correlated the maximal CDR size with the recovery time based on a kymograph analysis (Figure 4.9). For this CDRs were grouped based on their maximal radii into bins of 10, 20, 30, and 40µm. From the data within each of these bins the median, the 25th-, and 75th percentile were calculated and displayed in form of a box and whisker plot (Figure 4.9E). Maximal CDR radii⇢max and the median values of the recovery time are positively correlated. However, the minimal recovery time between successive CDR events varies only weekly, ranging between 1-2 min. The number of observations N for each size class of CDRs reflects the commonness of reappearing CDR events for the respective groups. For CDRs with ⇢max>30µm pulsating dynamics was relatively rare.
The finding of periodically reappearing CDRs presented above contradicts the prevailing descriptions of CDR as singular events [Buccione et al., 2004, Itoh and Hasegawa, 2012]. The origin of this disagreement lies, without much doubt, in the experimental framework that was chosen in this work, i.e., the use of a cell line that forms CDRs spontaneously versus the traditional approach of using growth factors to stimulate CDR formation. This raises questions regarding the origin of CDR formation in both situations that we will discuss in the following.
From the biological perspective, the formation of CDRs is commonly described as a specific response to binding events between extracellular growth factors and growth factor receptors in the cell membrane [Buccione et al., 2004, Hoon et al., 2012, Itoh and Hasegawa, 2012]. Therefore, it is a standard procedure in studies of CDRs to add a growth factor, usually PDGF, to the cell medium. Closure of the resulting CDRs goes along with internalization of occupied receptors, as CDR closure is an endocytotic process [Dowrick et al., 1993, Orth et al., 2006, Gu et al., 2011]. The resulting void of growth factor receptors in the cell membrane o↵ers an explanation why CDRs are only formed once in such experiments, even though growth factors are still present in the cell medium. The replenishment of the cell membrane with new receptors takes time, which is the reason why only one burst of CDRs is observed at the time point of growth factor addition. Moreover, cells might adapt their biochemical states towards the newly faced environmental conditions.
However, standard cell medium always contains small concentrations of growth factors as these are essential to guarantee survival and proliferation of the cell culture (Section 2.1.5). Several growth factors are known to cause CDR formation. The constituent containing these growth factors is Fetal Bovine Serum (FBS). The amounts of growth factors in cell medium are usually too small to trigger CDR formation in standard fibroblast cell lines such as NIH 3T3 WT. But why, in contrast, do NIH 3T3 X2 cells form CDRs frequently without extra stimulation?
To elucidate the role that growth factors play in the spontaneous formation of CDRs on NIH 3T3 X2 cells I conducted experiments in which these cells were kept under serum-free conditions. Surprisingly, NIH 3T3 X2 cells without serum in their medium still formed CDRs. I calculated the fraction of cells exhibiting CDRs in serum-free conditions and compared this to the fraction of cells with CDRs under normal culture
4.4. OSCILLATORY CDR REAPPEARANCE 77 conditions. A total number of about 500 cells was analysed for each situation. The box and whisker plot in Figure 4.10 shows the results.
Figure 4.10: Formation rates of CDRs under growth factor-free and growth factor-containing conditions. The box and whisker plot shows that NIH 3T3 X2 cells form CDRs spontaneously under serum-free conditions, albeit at much reduced rates when compared to normal culture conditions. 10% FBS corresponds to the standard concentration of serum in the cell medium.
Plot legend: page xiv.
Under serum-free conditions, the number of cells exhibiting CDRs is considerably reduced. The median value of the fraction of cells with CDRs is 0.17 in standard cell medium and 0 under serum-free conditions. This reduction of the median value is statistically significant at↵= 5% as could be confirmed via a two-sided Mann-Whitney U test. Even though the median value is zero, this does not mean that CDR formation was completely abolished, as indicated by the box and whisker in positive direction of cells in serum-free medium in Figure 4.10. This means that there must be another mechanism for the formation of CDRs that is independent of growth factor stimulation, which will be discussed in the following.
The active media picture o↵ers an alternative explanation for the spontaneous formation of CDRs on NIH 3T3 X2 cells, which does not depend on growth factors. In the appropriate regime active media such as the FHN system respond to disturbances with the formation of waves. The external stimulation via growth factors is one possible kind of such a disturbance. Additionally, in living cells there are several possible intracellular mechanisms that might correspond to such a disturbance from an abstract point of view, due to, e.g., the omnipresent Brownian noise in biological systems [Tsimring, 2014]. Since the emergence of waves of polymerizing actin is common in living cells, it is a reasonable assumption that cells are situated close to a phase space regime of wave instability. In a similar fashion it could be shown that, e.g.,D.
discoideum indeed organizes its actin machinery in a state that is close to an oscillatory regime [Westendorf et al., 2013].
Apart from the spontaneous formation of CDRs, NIH 3T3 X2 cells exhibit features that point to disturbed actin dynamics, which might facilitate CDR formation as a consequence of growth factor independent dynamics. These are, e.g., their large size
78 CHAPTER 4. WAVE DYNAMICS ON RANDOM-SHAPED CELLS and the often found existence of two or more nuclei in one cell, indicating defective division events. In the latter, actin dynamics plays a crucial role. We may therefore hypothesise that this cell line permanently operates in a state close to wave instability of actin dynamics. The formation of waves under serum-free condition indicates that intracellular noisy events are sufficient to trigger wave formation.
The periodic reappearance of CDRs on NIH 3T3 X2 cells under serum-containing conditions follows naturally from this picture. Situated close to an oscillatory regime, an active medium such as the FHN system, can be driven into a mode of constant firing by the presence of noise [Pikovsky and Kurths, 1997]. The reason for this lies in its integrating properties, which in turn follow from its excitability. When we assume that the binding events between growth factors and growth factor receptors is of stochastic nature, it constitutes an additional source of noise, which is in some cases sufficient to drive the system towards a mode of constant firing.
This framework of an internal and an external source of noise explains why serum is not required for CDR formation, although the rate of CDR formation increases with growth factor concentration and can even reach modes of periodic reappearance. A detailed analysis of the role of noise in active media will be demonstrated in Chapter 6.
The biological implications of the recovery time of the system between succeeding wave pulses will be discussed in Chapter 5 in detail.
The pulsating nature of CDRs was most commonly observed on cells in which wave pulses formed in narrow and confined regions. We have seen in Section 2.3.4 that the FHN system is able to support continuous oscillatory wave formation, albeit with patterns of concentric wave trains, which are not observed for CDRs. However, when confined to a narrow region with Dirichelt boundary condition V(⇢0) = V0 the FHN system forms pulsating structures as shown in Figure 4.11, which resemble small periodically reappearing CDRs. This simulation was carried out on a domain of radial symmetry with radius⇢0= 3 and a constant stimulus of S = 2.5 in the central domain 0⇢2 (all other parameters were chosen as in Section 2.3.4).
Nevertheless, CDRs on cells form sequences in which there is always just one wave at the same time originating from the same spot, regardless of the size of the region from which CDRs originated. It requires the collapse of one wave before the next wave can form, i.e., concentric wave trains do not occur.
We must bear in mind that the FHN model is a minimal system for the description of active media and we thus cannot expect that all phenomena are correctly described.
Vasiev has shown in a study of pattern formation of a modified FHN system that it only requires addition of di↵usivity to the inhibitor species to produce a rich scope of wave dynamics [Vasiev, 2004]. Especially, this system is able to produce opening and closing of wavefronts and pulsating spots termed ”breathing modes” without the necessity of spatial confinement. Breathing modes closely resemble oscillatory reappearing CDRs.
This finding might contribute to the development of a future biological model for CDRs.
The reasons underlying the tendency of increasing recovery times with increasing maximal radii of CDRs remain unclear. Small CDRs usually did not form endocytotic