CDRs share features of waves in active media. Evidence for this hypothesis was presented throughout this whole work. However, so far only limited comparability was possible between experimental and theoretical data such as those presented in the theory chapter of this thesis (sections 2.3.1-2.3.5). In contrast, with the introduction of disc-shaped cells as a model system for systematic investigation of actin waves a direct comparison between experiment and theory came into reach. This was demonstrated in this chapter based on the juxtaposition of experimental data and numerical results from a noisy FHN system. It could be shown that the theoretical framework of a one-dimensional noisy FHN system captures almost all dynamic features exhibited by CDRs on disc-shaped cells. Indeed, there are only slight details in which the patterns obtained from simulations di↵er from their experimental counterparts that we will discuss shortly.
This result underlines that CDRs not only share features of active media, but can in fact be very comprehensively described within this framework. It further adds large support to the hypothesis from Chapter 4, i.e., that the complicated dynamics CDRs exhibited on random-shaped cells is due to their interaction with irregular boundaries
6.3. DISCUSSION 129 and, possibly, also limited availability of a species involved in the wave machinery. The governing processes underlying CDR propagation, however, can e↵ectively be reduced to a simple feedback scheme such as that of the FHN system, as demonstrated here.
The results of this chapter further clearly outline the significance that stochastic processes have in the formation of the spatiotemporal patterns. The consideration of a driving noise allowed to tune the FHN system towards a very close match between experimental and numerical results. Depending on the noise amplitude the periods between successive wave formations were either dominated by the system’s recovery time or the probability of the noise to exceed the threshold for wave formation. This observation o↵ers an explanation for the distribution of periods of experimental data shown in Figure 5.8 of the previous chapter. From this perspective the apparent bimodal character of the distribution has one sharp peak (5 minTP7 min), which results from the recovery time, and one broad peak, which is a signature of noise-dominated periods.
Besides the noise only the existence of the typical characteristics of an active medium, such as its recovery time and the collision behaviour of its waves, were needed for the understanding of the processes underlying spatiotemporal pattern formation. However, as the FHN model is an abstract model and was not designed for actin waves, there is no direct interpretation that could be deduced for the actin machinery in CDRs.
Nevertheless, we also encountered the limitations of the formulation of the FHN system that was studied here. For example the approach that was followed to tune the noise amplitude to mimic the fragmentation of patterns of experimental data led to results that were inconsistent with the experimental observations. We can therefore safely discard the idea of high noise being the major reason for pattern fragmentation.
Also no examples of wave crossings or unilateral wave annihilation could be found in the numerical outputs but exclusively mutual wave annihilation. It is important to note, however, that collision annihilation is a typical albeit not dogmatic characteristic of active media. As shown by Argentina et al the FHN system does indeed support the crossing of wave pulses under certain conditions [Argentina et al., 2000].
Certainly also a formulation or extension of the FHN model could be found that is able to reproduce the observed patterns even more accurately including the simultaneous support of fragmented and line patterns with conserved numbers of waves. However, such an extension should be built on biologically and physically founded considerations.
In this chapter the role of the noise was mainly that of a trigger of wave formation.
It has been shown that noise can in fact also be the reason for wave propagation in active media that are in a sub-excitable regime via stochastic resonance [K´ad´ar et al., 1998]. If this phenomenon has significance for CDRs remains an open question at this stage.
Chapter 7
Conclusions
The phenomenon of ring-shaped actin structures on the dorsal side of adherent euk-aryotic cells, termed CDRs, has been puzzling the biological community for several decades [Mellstr¨om et al., 1983, Dowrick et al., 1993, Krueger et al., 2003, Payne et al., 2014]. The research on this subject has lead to their sound proteomic characterization and revealed that CDRs are central to, e.g., cell motility and endocytosis, which high-lights their biological as well as their medical significance [Buccione et al., 2004, Hoon et al., 2012, Itoh and Hasegawa, 2012, Mercer and Helenius, 2009]. However, the mech-anism that orchestrates the protein interplay towards formation of these structures remained elusive.
The central hypothesis underlying this work is that CDRs can be understood as waves in an active medium, which is constituted by the cellular actin machinery. This idea was first proposed by Zeng et al. and is also implied by the work of Peleg et al. [Zeng et al., 2011, Peleg et al., 2011]. However, a detailed experimental survey of this hypothesis is missing. It was the motivation underlying this work to contribute the experimental data that are needed to link the biological knowledge on CDRs to theoretical concepts. This provides the basis for validation of existing models and shows directives for future modelling approaches.
My data gave much support for the idea that CDRs are waves in an excitable system and provided several novel and fundamental insights into the nature of the corresponding wave machinery. The implications for the fields of biology and biological physics will be outlined in the following. This includes results that are specific to CDRs. However, throughout this work also a new methodological framework for systematic studies on protein waves was introduced that has implications for virtually all areas in which protein waves are involved.