Analysis of chemomechanical behavior of stress fibers by continuum mechanics-based FRAP

Abstract

Fluorescence recovery after photobleaching (FRAP) is a common technique to analyze the turnover of molecules in living cells. Numerous physicochemical models have been developed to quantitatively evaluate the rate of turnover driven by chemical reaction and diffusion that occurs in a few seconds to minutes. On the other hand, they have limitations in interpreting long-term FRAP responses where intracellular active movement inevitably provides target molecular architectures with additional effects other than chemical reaction and diffusion, namely directed transport and structural deformation. To overcome the limitations, we develop a continuum mechanics-based model that allows for decoupling FRAP response into the intrinsic turnover rate and subcellular mechanical characteristics such as displacement vector and strain tensor. Our approach was validated using fluorescently labeled β-actin in an actomyosin-mediated contractile apparatus called stress fibers, revealing spatially distinct patterns of the multi-physicochemical events, in which the turnover rate, which represents effective off-rate of β-actin, was significantly higher at the center of the cell. We also found that the turnover rate is negatively correlated with the rate of displacement or velocity along stress fibers but, interestingly, not with the absolute magnitude of strain. Moreover, stress fibers are subjected to centripetal flow that is facilitated by the circulation of actin molecules. Taken together, this novel framework for long-term FRAP analysis allows for unveiling the contribution of overlooked microscopic mechanics to molecular turnover in living cells.

Figure 1

Schematic of the continuum mechanics-based FRAP model to analyze the chemomechanical properties within the region labeled by photobleaching. SF represents a part of a single stress fiber. See the text for details of the variables and coordinates. To see this figure in color, go online.

Figure 2

Determination of actin molecular turnover and mechanical properties (displacement and strain) of stress fibers in A7r5 cells. (A) The region of interest (ROI), automatically detected as shown in yellow, is labeled by photobleaching ($t=0$ s). (B, C) The ROI, shown in cyan ($t=0$ s) and magenta ($t=600$ s), is often spatially transported in a long-term observation (see Video S1). Arrows represent the tracked displacement vectors. (D) Time course of the fluorescence intensity within the ROI. The regression curve based on Eq. 3 determines the molecular turnover rate. (E) Time course of the norm of representative displacement vector. (F) Time course of the coordinate-independent volumetric strain. To see this figure in color, go online.

Figure 3

Multiple bleached regions on stress fibers in a single cell with the displacement and deformation distribution. Arrows and overlaid rectangular regions represent the displacement vectors and volumetric strain, respectively. (A) Pre-bleach image. (B–D) Displacement vectors at t = 0 s (B), t = 600 s (C), and t = 1000 s (D). Color bar represents the angle of the displacement vectors (see Video S2). Insets of the indicated regions are magnified 3×. (E–G) Volumetric strains at t = 0 s (E), t = 600 s (F), and t = 1000 s (G). Color bar represents the value of the volumetric strain (see Video S3). To see this figure in color, go online.

Figure 4

Long-term strain analysis of stress fibers. The displacement vectors and strain tensors are transformed to either parallel with or perpendicular to stress fibers. The subscripts $\parallel$ and $\perp$ represent parallel with and perpendicular to stress fibers, respectively. (A) The orientation index defined in Eq. 11 at $t=1000$ s. (B) Time course of the displacement vectors parallel with (green) and perpendicular to (magenta) stress fibers. (C) Time course of the parallel components of the Green’s (green) and Almansi’s (magenta) strain tensors. (D) Time course of the error defined as $\left|\left(E_{\parallel }-e_{\parallel }\right)/E_{\parallel }\right|$. (E) Time course of strain parallel with stress fibers. (F) The values of strain parallel with stress fibers in the reference frame are overlaid in the cell image (see Video S4). To see this figure in color, go online.

Figure 5

The chemical turnover and mechanical strain are high at the cell center and periphery, respectively. (A) Schematic of stripe pattern of photobleaching in a cell. (B–D) Actin turnover rate (B), $v_{\parallel }=u_{\parallel }/t$ of the displacement rate (C), and strain (D) along stress fibers are shown by mean $\pm$ SD analyzed at each stripe ($n=14,34,33,32\text{and }16$ from independent experiments of $N=3$ cells for S1, S2, S3, S4, and S5, respectively); different numbers of photobleached regions (namely stress fibers) are included in each of the stripes, and consequently $n$ values could differ among the experiments. Asterisks represent a statistically significant difference among the stripes: ^∗$p<0.05$; ^∗∗$p<0.01$; ^∗∗∗$p<0.01$. To see this figure in color, go online.

Figure 6

Correlation analysis represents the relationship between the molecular turnover and mechanical behaviors. The actin molecular turnover is negatively correlated with the magnitude of velocity parallel with stress fibers ($R\left(k,\left|v_{\parallel }\right|\right)=-0.34$; $p=0.93\times {10}^{-4}$; $n=129$ from independent $N=3$ cells) (A) but not with the magnitude of strain parallel with stress fibers ($R\left(k,\left|{\epsilon }_{\parallel }\right|\right)=0.04$; $p=0.65;$$n=129$ from independent $N=3$ cells) (B). Lines represent the regression fitting for variables of S1 and S5 (blue), S2 and S4 (green), and S3 (red), where the definition of S1–S5 is shown in Fig. 5A. To see this figure in color, go online.

Figure 7

Continuum mechanics-based FRAP onto mClover2-actin in stress fibers of A7r5 cells treated with 10-nM Latrunculin A. (A) Pre-bleach image. (B) The displacement vectors. Color bar represents the angle of the displacement vectors. Insets of the indicated regions are magnified 3×. (C) The values of strain parallel with stress fibers in the reference frame are overlaid in the cell image. (D) The actin molecular turnover results in no correlation with the magnitude of velocity parallel with stress fibers ($R\left(k,\left|v_{\parallel }\right|\right)=-0.17$; $p=0.059$; $n$ = 119 from independent $N$ = 3 cells). (E) The actin molecular turnover is not correlated with the magnitude of strain parallel with stress fibers ($R\left(k,\left|{\epsilon }_{\parallel }\right|\right)=0.19$; $p=0.45$; $n$ = 119 from independent $N$ = 3 cells). Lines represent the regression fitting for variables of S1 and S5 (blue), S2 and S4 (green), and S3 (red), where the definition of S1–S5 is shown in Fig. 5A. (F) Model of chemomechanical behavior of stress fibers in cells. To see this figure in color, go online.