Cytoskeletal Mechanics Regulating Amoeboid Cell Locomotion

Abstract

Migrating cells exert traction forces when moving. Amoeboid cell migration is a common type of cell migration that appears in many physiological and pathological processes and is performed by a wide variety of cell types. Understanding the coupling of the biochemistry and mechanics underlying the process of migration has the potential to guide the development of pharmacological treatment or genetic manipulations to treat a wide range of diseases. The measurement of the spatiotemporal evolution of the traction forces that produce the movement is an important aspect for the characterization of the locomotion mechanics. There are several methods to calculate the traction forces exerted by the cells. Currently the most commonly used ones are traction force microscopy methods based on the measurement of the deformation induced by the cells on elastic substrate on which they are moving. Amoeboid cells migrate by implementing a motility cycle based on the sequential repetition of four phases. In this paper we review the role that specific cytoskeletal components play in the regulation of the cell migration mechanics. We investigate the role of specific cytoskeletal components regarding the ability of the cells to perform the motility cycle effectively and the generation of traction forces. The actin nucleation in the leading edge of the cell, carried by the ARP2/3 complex activated through the SCAR/WAVE complex, has shown to be fundamental to the execution of the cyclic movement and to the generation of the traction forces. The protein PIR121, a member of the SCAR/WAVE complex, is essential to the proper regulation of the periodic movement and the protein SCAR, also included in the SCAR/WAVE complex, is necessary for the generation of the traction forces during migration. The protein Myosin II, an important F-actin cross-linker and motor protein, is essential to cytoskeletal contractility and to the generation and proper organization of the traction forces during migration.

Fig. 1

(a) sketch of the configuration of the experiment. Substrate with an upper layer embedded with beads where the cells are moving. (b) DIC image taken with the microscope to identify the cell contours. (c) dilation and erosion application to determine the cell contour from the DIC image. (d) cell contour determination after a second dilation and erosion application. (e) image of the substrate embedded with beads used to calculate the deformation induced by the migrating cells. (f) displacement field for a wild-type cell at an instant of time. The arrows (color red online) represent the direction of the displacements and the contours underneath (color blue online) represent the magnitude of the tractions. This figure is taken from [16].

Fig. 2

Measurement of the Young's modulus with the calculation of the indentation produced by a tungsten carbide ball. This figure is taken from Ref. [57].

Fig. 3

Pole force calculation. The pole force at the front $F_f$ is calculated by integrating the tractions stresses in the front half of the cell, $\xi >0$. The pole force at the back $F_b$ is calculated by integrating the traction stresses in the back half of the cell, $\xi <0$.

Fig. 4

Sketch of the experimental configuration for the measurement of the three-dimensional deformation, where a z-stack of images, $\Delta z$, is acquired with the confocal microscope, and boundary conditions applied for the calculation of the traction forces in the three dimensions. This figure is taken from Ref. [67].

Fig. 5

The central image shows the periodic evolution of the cell length over time, the black color indicates the protrusion phase, the red color indicates the contraction phase, the green colors indicate the retraction phase, and the blue color the relaxation phase. The surrounding images show a sketch of each of the cycle phases and the average stress map for this cell at each of the four phases of the motility cycle. This figure is taken from Ref. [8].

Fig. 6

Average velocity versus motility cycle frequency (determined from the variations of the cell length) shows a linear relationship in WT, mlcE^-, mhcA^-, and scrA^- cells. The blue, red, green, and black circles denote WT, scrA^- , mlcE^-, and mhcA^- cells, respectively. The velocity-frequency slope, λ, for each of the cell lines is represented by the dotted lines, in blue and red for WT and scrA^- cells, respectively, and magenta for both mhcA^- and mlcE^- cells. This figure is a combination of figures from Refs. [8,76].

Fig. 7

(a) conversion of the instantaneous stress map of a cell into a cell-based reference system. x and y are the coordinates in the laboratory reference frame, $\xi$ and $\eta$ are the coordinates in the cell based reference frame. $\phi$ is the angle between the longitudinal axis of the cell and the horizontal axis of the laboratory reference frame, L is the length of the cell, and $x_c$ and $y_c$ are the coordinates of the center of the cell in the laboratory reference frame. The arrow indicates the direction of the velocity, $V$, of the cell at this instant of time. (b) the first column indicates the calculation of the average traction forces in the cell-based reference frame for this cell at this instant of time. The origin is located at the center of the cell and the length of the cell is always between $\xi =-1$ and $\xi =1$. The second and third columns indicate the components of the average traction forces parallel (x-axis component) and perpendicular (y-axis component) to the cell major axis, respectively.

Fig. 8

The upper row shows the traction forces exerted in each of the phases of the motility cycle by WT cells, the second row shows the traction forces exerted in each of the phases of the motility cycle by mlcE^- cells, and the third row shows the traction forces exerted in each of the phases of the motility cycle by mhcA^- cells. This figure is taken from Ref. [8].

Fig. 9

The upper row shows the component of the traction forces exerted in the direction of the major axis of the cell by WT, mlcE^-, and mhcA^- cells. The second row shows the component of the traction forces exerted in the direction perpendicular to the major axis of the cell by WT, mlcE^-, and mhcA^- cells. This figure is taken from Ref. [8].

Fig. 10

The first row shows the traction forces exerted in each of the phases of the cycle by WT cells. The second row shows the traction forces exerted in each of the phases of the cycle by scrA^- mutant cells. This figure is taken from Ref. [76].

Fig. 11

The upper row shows the component of the traction forces exerted in the direction of the major axis of the cell by WT, pirA^-, and scrA^- cells moving over polyacrilamide substrates. The second row shows the component of the traction forces exerted in the perpendicular direction to the major axis of the cell by WT, pirA^-, and scrA^- cells. This figure is taken from Ref. [76].

Fig. 12

(a) horizontal traction forces obtained by using the 3D method, (b) horizontal traction forces obtained by using the 2D method, and (c) difference between the horizontal traction forces calculated by using the 3D and 2D methods. The red color indicates that the traction forces calculated with the 3D method are bigger than the ones calculated with the 2D method, and the blue color indicates the opposite, that the traction forces calculated with the 3D method are lower than the ones calculated with the 2D method.

Fig. 13

Time evolution of the tangential strain energy obtained with the 3D method in blue and time evolution of the total strain energy obtained with the 2D method in red