Traction Force Distribution in Relation to the Cell's Spread Area . 118

Analysing the bead movies as previously described in Chapter 5, the distribution of the traction forces was studied at each given time point. This enabled us to investigate the distribution of the traction forces and their location in comparison to the spread cell. Four examples of the cell outline of a fully spread platelet on the corresponding traction force map can be found in Fig. 7.2. As can be seen, the forces exerted by the cell were always found either on or close to the periphery of the platelet. None of the platelets contracted around its centre.

At the same time, the contraction was not uniformly distributed around the cell outline but instead exhibited a small number of spatially separated maxima. These maxima varied in number but generally showed two to three, sometimes also four, hot spots. Between the maxima, the traction forces were reduced dramatically to a force level close to 0. In rarer cases, like the platelet shown in Fig. 7.1, the single spots could also nearly span the entire periphery but a completely closed pattern

Contractile Behaviour on Substrata of Dierent Stiness 7.2

Figure 7.2.: Four examples of the traction force distribution pattern compared to the spreading area of the platelet. The cell's outline is shown as the white curve in each image. Scale bar:

5µm. Some of the traction force maps are part of Ref. [37].

was never observed.

7.2.2 Temporal Evolution of the Contraction

Next, let us take a look at the evolution of the total force over time. Before go-ing more into detail of the actual force levels exerted by the platelets on their surrounding, let us take a look at the general temporal behaviour of the cells.

In Fig. 7.3A, three examples of different contractile behaviours are shown. All cells here were recorded on substrates of stiffness 54 kPa. In general, we distin-guished between three different behaviours. The first group of platelets, seen in cyan, contracted towards a force plateau. The second group relaxed again after an initial contraction period as shown in green. The last group exhibited a rather dy-namic contractile behaviour in that they started to oscillate after an initial increase in force (magenta). These behaviours were found on substrates of all stiffnesses and thus not linked to the elasticity of the surrounding material. Furthermore, combinations of the different behaviours did occur. Note that due to the finite recording time, it was not possible to exclude that some cells showing either a force plateau or oscillations would not relax later. On the contrary, one can safely assume that all cells relaxed again after a sufficiently long time interval when

Chapter 7 RESULTS

all internal energy storage was used up. Interestingly, the contractile behaviour was not reflected in the dynamics of the spread area, also depicted in Figure 7.3 A. Another example of an oscillating platelet is also shown in Fig. 7.3 B, here recorded on 19 kPa. Independent on the contractile behaviour, the platelet spread towards a final area and stabilised. This does not mean that no changes in the membrane were observed but that, given the resolution of our set-up, no quantifi-able area fluctuations were seen. Additionally, as can be already estimated from these examples, the area stabilised faster than the total force. The area reached its maximal area within the first 3 to 5 minutes while the force lacked behind some minutes. However, the initial contraction was concluded within the first 10 min after adhesion.

Determining whether a platelet was contracting in an oscillating fashion proved to be not as straight forward as one would expect. First, the total force curves were inspected if a continuous increasing and decreasing behaviour after initial contraction could be observed. If such a behaviour was visible, the underlying bead movies were inspected closely. If a clear in-and-out movement of the beads were seen, indicating a continuous contraction and relaxation of the platelets, the cells were deemed oscillatory. In total, 39 % of all studied platelets under static conditions were thus classified as oscillating. Here, we only distinguished between oscillating and non-oscillating cells. Dividing the cells into all three categories, the percentages were 32 %, 18 % and 49 % for oscillating, relaxing and plateauing platelets, respectively. The missing percentage was due to rounding. Note that for this division, double-counting of single platelets was possible if a combination of two behaviours was observed.

One could argue that a Fourier analysis would give a clearer criterion on the question whether a cell was oscillating or not. Indeed, this was also tested. Here, the initial contraction was disregarded for the analysis as we were only interested in the behaviour afterwards. The force data at the later time points was then anal-ysed as described in Section 6.2.2. Note that we studied the oscillatory frequency of the relative force to ensure that the magnitude of the mean force in this interval did not influence the result. As an example, 10 nN variation on a cell that con-tracted up to 40 nN was then deemed to be oscillating while 10 nN variation on a 200 nN contracting platelet most likely was not considered as such. All platelets underwent this analysis and the result can be seen in Fig. 7.3D, where the colour of each marker denotes the classification made previously by eye as described be-fore. We clearly see that non-oscillating cells tended to have lower amplitudes in

Contractile Behaviour on Substrata of Dierent Stiness 7.2

Figure 7.3.: A Three examples of the general temporal contraction behaviour over time. All three cells were recorded on a substrate of 54 kPa. In cyan, a platelet is shown that reaches a force plateau. In green, a cell relaxes again after initial contraction. In magenta, a more dynamic platelet is displayed that starts to oscillate after the rst contraction. For all three cells, their area development is added in the dashed lines. Here, every third cell image was taken for analysis. B Another example for the spread area with error vs total force development, this platelet recorded on a 19 kPa substrate. As can be observed, the platelets spread faster towards its nal area than the force completes the initial contraction period. Also, no synchronisation between the oscillations in area and the force was detected given the resolution and contrast. C The averaged total force curves according to the substrate stiness. The bold lines denote the averaged force until the time point at which half of the included cells do no longer contribute to the mean. The transparent areas in the same colour show the corresponding standard error. The stiness varies from 19 kPa in deep blue to 83 kPa in red. D The dominant frequency of all data determined by Fourier analysis. Only the part after the initial contraction was considered. Furthermore, the Fourier analysis was made over the relative changes in force by dividing the analysable force by their mean value. To exclude too low or high frequencies, a Butterworth band-pass lter was applied to only allow frequencies between 10 mHz and 35 mHz. Panels A, C and D are taken from Ref. [37].

Fourier space as well as reached higher frequencies, a clear distinction from the oscillating cells was, however, not possible. Both groups overlapped in a band of amplitudes around 7·10⁻³. While this analysis points towards the correct clas-sification of the eye subdivision, an unique assignment to one behaviour using a Fourier analysis approach was not possible. On the other hand, this analysis

Chapter 7 RESULTS

allowed us to determine the average oscillatory frequency of the platelets which amounted to 13.5 mHz.