Multiscale Mechanochemical Interactions Between Cell Membrane and Actin Filaments - Innovative Approaches to Cell Biomechanics - page 90

in the approximated curvature, the curvature, ʺ ʔs is normalized by dividing by the
maximum value of | ʺ ʔs | for each ʔs . Figure 7.2b is an enlarged map of the region
ʔs = 0 to 28 pixels in Fig. 7.2a . The curvature approximation at various spatial inter-
vals, ʔs , as seen in Fig. 7.2a, b , enables us to detect various sizes of concavities and
convexities pattern at the cell periphery. The cycle of color change at a fixed ʔs
along the abscissa represents a characteristic cycle of concavity and convexity
patterns for the spatial interval, ʔs , used for the curvature approximation.

7.4.2 Global Concavity and Convexity Patterns

In this section, we will explore the relationship between the global cell peripheral
activity and the global cell peripheral shape by comparing Fig. 7.2 and Fig. 6.6 in
Chap. 6 . The maps in Fig. 7.2 are the results from the same data as those used to
create the maps in Fig. 6.6 in Chap. 6 .
Based on the map shown in Fig. 6.6 in Chap. 6 , the characteristic scale of the
global protruding region is about 60ﾰ. As represented by the color change along the
abscissa in the boxed area in Fig. 7.2a , the cycle of concavity and convexity patterns
that is estimated with the spatial interval ʔs = 125 pixels is about 60ﾰ. Thus, to
explore the relationship between the pattern of the cell peripheral activity and that
of the cell peripheral shape in the global protruding region, ʺ ʔs for ʔs = 125 pixels is
mapped against space ʸ and time t in Fig. 7.2c , and compared with the map in Fig.
6.6a representing the global protruding region.
The spatiotemporal pattern of the curvature map in Fig. 7.2c shows that regions
with plus curvatures (convex outside) travel along the cell periphery. Similarly,
regions with minus curvatures (concave inside) also travel along the cell periphery.
The travelling speeds of the regions with plus curvatures and those with minus cur-
vatures both fluctuate, in contrast with the pattern shown in the map in Fig. 6.6a
where the travelling speeds of the global protruding region and the global retracting
region are constant. This result suggests that there is no remarkable correlation
between the cell peripheral activity and cell peripheral shape in the global protruding
and retracting regions.

7.4.3 Local Concavity and Convexity Patterns

In this section, we discuss the relationship between the local cell peripheral activity
and the local cell peripheral shape by comparing Fig. 7.2 and Fig. 6.6 in Chap. 6 .
The maps in Fig. 7.2 are the results from the same data as those used to create the
maps in Fig. 6.6 in Chap. 6 .
The local actively protruding domains (APDs) shown in Fig. 6.6b in Chap. 6 , the
characteristic scale that is represented in the map in the igure is approximately 10ﾰ.
As represented by the color change along the abscissa in the boxed area in Fig. 7.2b ,