Multiscale Mechanochemical Interactions Between Cell Membrane and Actin Filaments - Innovative Approaches to Cell Biomechanics - page 100

approximately 3 ʼm peripheral edges of the dendritically branched actin network
〈 V A 〉 3 ʼm . In addition, the global cell peripheral activity reflects the contribution of
the sum of the retrograde low and the net actin elongation on 15-20 ʼm peripheral
edges of the dendritically branched actin network, 〈 V A 〉 15 − 20ʼm (Fig. 7.8a ).

7.6.1 Generation of Hierarchically Correlated

Traveling Waves

In Chap. 6 , we have revealed lateral traveling waves with the spatiotemporal nested
structure. The spatiotemporally nested pattern of the travelling waves of the cell
peripheral activities (Fig. 6.6a, b in Chap. 6 ; Figs. 7.6b and 7.7b ) suggests, as
illustrated in Fig. 7.8a, b , that the organized actin filament elongation in which the
travelling waves of the local net actin elongation, 〈 V A 〉 3ʼm (Fig. 7.8b ), are embedded
in the global travelling wave. The global travelling wave consists of the sum of the
global net actin elongation, 〈 V A 〉 15 − 20ʼm , and retrograde flow (Fig. 7.8a ).
The correlation between the cell peripheral activity and cell peripheral shape,
which is clearly demonstrated in the correlation analysis in Fig. 7.5 , implies that
there exists a mechanochemical feedback that generates the travelling waves of the
local net actin elongation, 〈 V A 〉 3ʼm , as illustrated in the boxed area in Fig. 7.8 . In the
feedback, the spatially non-uniform net actin elongation, ∂ 2 〈 V A 〉 3ʼm /∂ s 2 , mechanically
affects the membrane curvature, ʺ ( s ). Whereas, as illustrated by the T-shaped line
from ʺ ( s ) to V A in the boxed region in Fig. 7.8 , the cell membrane being convex
outside with a higher curvature exerts higher inhibitory effect on the actin elongation,
V A , which is driven by chemical polymerization of actin monomers.
Coordinated cellular protrusion by structurally and kinetically different actin
networks in lamella and lamellipodia has been extensively studied (Vallotton et al.
2005 ), and the protrusion rate and shape maintenance at the cellular scale have been
shown to depend on the regulation of both retrograde flow and actin polymerization.
The multiscale analysis described in this chapter further demonstrates that the actin
filament elongation under the membrane and the membrane curvature affect each
other at the subcellular and molecular scales in the coordination of lamella-type cellular
protrusion. It is also assumed that the membrane curvature affects actin filament
branching under the plasma membrane, which decreases the number of actin
filaments pointing toward the membrane (Risca et al. 2012 ) and results in decreased
efficiency of actin elongation for membrane protrusion. A more detailed molecular
picture of the curvature-dependent inhibitory effect on actin elongation will be
clarified by an advanced analysis. Our possible approach is simultaneous moni-
toring of the cell peripheral activity, the cell peripheral shape, and the spatial
distribution and the dynamics of actin filaments with the methodology shown in this
section in combination with fluorescent speckle microscopy explained in Chaps. 3 ,
4 , and 5 of this topic, and in other literatures (Wilson et al. 2010 ; Yam et al. 2007 ;
Jurado et al. 2005 ).