Variability and Order in Cytoskeletal Dynamics of Motile Amoeboid Cells

The chemotactic motion of eukaryotic cells such as leukocytes or metastatic cancer cells relies on membrane protrusions driven by the polymerization and depolymerization of actin. Here we show that the response of the actin system to a receptor stimulus is subject to a threshold value that varies strongly from cell to cell. Above the threshold, we observe pronounced cell-to-cell variability in the response amplitude. The polymerization time, however, is almost constant over the entire range of response amplitudes, while the depolymerization time increases with increasing amplitude. We show that cell-to-cell variability in the response amplitude correlates with the amount of $\text{Arp}2/3$, a protein that enhances actin polymerization. A time-delayed feedback model for the cortical actin concentration is consistent with all our observations and confirms the role of $\text{Arp}2/3$ in the observed cell-to-cell variability. Taken together, our observations highlight robust regulation of the actin response that enables a reliable timing of cell movement.

Figure 1

Responses to a cAMP stimulation. The signal, normalized as explained in the text, is defined as responsive when the difference between the intensity before cAMP stimulation and the minimum intensity after stimulation is larger than the intensity variations before stimulation (i.e., $\text{mean}-2\times \text{std}$). (a) A schematic diagram showing parameters that characterize the actin response. The polymerization time $T_p$ is defined as the time between the stimulus (red dashed line) and the intensity minimum. The depolymerization time $T_d$ is defined as the time between the extrema (valley to peak) in cytosolic intensity (between gray dashed lines). The amplitude $A$ is defined as the difference in intensity between the peak and valley. (b) Average response amplitude $A$, defined as in (a), at different stimulation strengths. For each concentration, experiments on more than ten cells were carried out. For caged cAMP concentrations larger than $0.1\mu \mathrm{M}$, only signals from responsive cells were averaged. Error bars denote the standard deviation. $A$ is set to zero for 0 and $0.01\mu \mathrm{M}$ caged cAMP as no cells responded (triangle). (c) Dependence of the percentage of responsive cells on the concentration of caged cAMP. For each concentration, experiments on more than ten cells were carried out. (d),(e) Examples of responses to different stimulation strengths in two cells. Different colors show the responses to different cAMP concentrations that were generated by releasing cAMP with different powers of the uncaging laser as indicated in the legend. The red dashed line indicates the time of stimulation.

Figure 2

Characteristics of the actin response to cAMP stimulation. $N=101$ cells. (a) Histogram of $A$ ($\text{mean}\pm \text{std}=0.5\pm 0.15$). (b) Histogram of $T_p$ ($\text{mean}\pm \text{std}=5.7\pm 1.05$). (c) Histogram of $T_d$ ($\text{mean}\pm \text{std}=13.4\pm 3.25$).

Figure 3

Signatures of the response to cAMP stimulation. Each black cross shows the response of one cell to a single stimulus. The parameters are always defined as in Fig. 1. (a) Relation between the polymerization time and response amplitude ($N=102$ cells, Pearson product-moment correlation coefficient $\rho =-0.02$). (b) Relation between the depolymerization time and response amplitude ($N=102$ cells, $\rho =0.42$). (c) Amplitude relation between $\text{Arp}2/3$ and LimE ($N=25$ cells coexpressing $\text{Arp}2/3$-GFP and LimE-mRFP, $\rho =0.46$). (d) Relation between the actin depolymerization time and the amplitude of $\text{Arp}2/3$ ($N=25$ cells coexpressing $\text{Arp}2/3$-GFP and LimE-mRFP, $\rho =0.51$).

Figure 4

Simulations of model Eqs. (1) and (2) with a finite value of $C_{\max }=1.4$ (black line) and in the absence of saturation $C_{\max }\gg 1$ (gray line). They capture the constant $T_p$ as well as the increasing $T_d$ for increasing $A$ in the case of Eq. (2). Parameters are $k_{+}^0=0.2$, $\tau =4$, $k_{-}=0.2$, and $C_{\max }=1.4$. Simulation traces are shown in Ref. [21].