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Analysis of flexural rigidity of actin filaments propelled by surface adsorbed myosin motors.

Bengtsson E, Persson M, Månsson A - Cytoskeleton (Hoboken) (2013)

Bottom Line: Actin filaments are central components of the cytoskeleton and the contractile machinery of muscle.The filaments are known to exist in a range of conformational states presumably with different flexural rigidity and thereby different persistence lengths.Our results analyze the approaches proposed previously to measure the persistence length from the statistics of the winding paths of actin filaments that are propelled by surface-adsorbed myosin motor fragments in the in vitro motility assay.

View Article: PubMed Central - PubMed

Affiliation: Faculty of Health and Life Sciences, Linnaeus University, Kalmar, Sweden.

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Related in: MedlinePlus

Digitization effects. (A) Illustration of truncation effects when analyzing a given filament path at different frame rates. The circles indicate observed filament positions when sliding at 3 µm·s−1 (filled circles) and 10 µm·s−1 (open circles), and the black, blue and red lines indicate apparent filament paths for 0.1, 0.2, and 0.4 s between analyzed frames, respectively. Each square in the grid corresponds to a pixel. (B) Simulated data. Fit of the CCF based on simulated data at different pixel-sizes to the exponential function (Eq. 1). The simulations of filament paths at low velocity (2.5 µm·s−1) show changes in estimated persistence length value as a complication due to digitization effects related to finite pixel-size. The filaments were assumed to move 0.5 µm between analyzed frames (i.e., frame rate of 5 s-1). (C) Estimated persistence lengths (±95% CI) from the fits in B to simulated data, with the dashed line illustrating the theoretical persistence length (LPtheor). Same color code as in B. (D) Fit of exponential function to CCF for experimental data with different time intervals between analyzed frames. In this experiment blocking actin was omitted, the pixel-size was 0.1652 µm2 and [MgATP] = 0.05 mM to reduce velocity (2.26 ± 0.04 µm·s−1; mean ± 95% CI, number of filaments (nf) 114). Finally, the persistence length was determined to 6.99 ± 0.57 µm (mean ± 95% CI), using 0.8 s between analyzed frames. The number of independent filament paths was 100 at 0.8 s. Note, the same experimental data was used just employing different time intervals between frames. (E) Effect of ratio vfΔt/pixel-size on estimated persistence length. Simulated data. Open circles: LPtheor = 20 µm, filled symbols: LPtheor = 10 µm, included data from B to C (i.e., constant vfΔt, same color code as in B and C), open squares: LPtheor = 5 µm, LPtheor illustrated with dashed lines. (F) Effect of vfΔt on estimated persistence length in relation to underlying theoretical persistence length (LPtheor). Same data as in E.
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fig03: Digitization effects. (A) Illustration of truncation effects when analyzing a given filament path at different frame rates. The circles indicate observed filament positions when sliding at 3 µm·s−1 (filled circles) and 10 µm·s−1 (open circles), and the black, blue and red lines indicate apparent filament paths for 0.1, 0.2, and 0.4 s between analyzed frames, respectively. Each square in the grid corresponds to a pixel. (B) Simulated data. Fit of the CCF based on simulated data at different pixel-sizes to the exponential function (Eq. 1). The simulations of filament paths at low velocity (2.5 µm·s−1) show changes in estimated persistence length value as a complication due to digitization effects related to finite pixel-size. The filaments were assumed to move 0.5 µm between analyzed frames (i.e., frame rate of 5 s-1). (C) Estimated persistence lengths (±95% CI) from the fits in B to simulated data, with the dashed line illustrating the theoretical persistence length (LPtheor). Same color code as in B. (D) Fit of exponential function to CCF for experimental data with different time intervals between analyzed frames. In this experiment blocking actin was omitted, the pixel-size was 0.1652 µm2 and [MgATP] = 0.05 mM to reduce velocity (2.26 ± 0.04 µm·s−1; mean ± 95% CI, number of filaments (nf) 114). Finally, the persistence length was determined to 6.99 ± 0.57 µm (mean ± 95% CI), using 0.8 s between analyzed frames. The number of independent filament paths was 100 at 0.8 s. Note, the same experimental data was used just employing different time intervals between frames. (E) Effect of ratio vfΔt/pixel-size on estimated persistence length. Simulated data. Open circles: LPtheor = 20 µm, filled symbols: LPtheor = 10 µm, included data from B to C (i.e., constant vfΔt, same color code as in B and C), open squares: LPtheor = 5 µm, LPtheor illustrated with dashed lines. (F) Effect of vfΔt on estimated persistence length in relation to underlying theoretical persistence length (LPtheor). Same data as in E.

Mentions: In experiments, errors are introduced in the estimate of the tangent angle along the filament path due to the finite pixel-sizes. This effect may become severe if the filament slides only a short distance compared to the pixel-size between two subsequent measurements, e.g., with large pixel-size, low velocity, high frame rates, or a combination of these factors. Errors may also be introduced if the sliding distance between subsequent frames is so long that the path curvature is truncated (Fig. 3A) Homsher et al., 1992. In order to elucidate these effects, simulations were performed using different combinations of velocity, pixel-size and time between frames as well as different pre-determined persistence lengths, LPtheor. In Fig. 3B, we present simulated results for the case with low velocity (2.5 µm·s−1) as seen e.g., at low MgATP concentrations or low temperature. We performed the simulations on the assumption of different pixel-sizes (0.02, 0.165, 0.33, and 0.66 µm/pixel) and a frame rate of 5 s−1, corresponding to a sliding distance between analyzed frames of 0.5 µm. Thus, for the largest pixel-size, the simulated data points could end up in the same pixel for two consecutive frames, e.g., if the tangent angle of the filament path was 45% relative to the horizontal axis. Moreover, even for the second largest pixel-size the digitization error may be appreciable. These errors are reflected in the deviation of the cosine correlation function from a single exponential as illustrated in the simulated data in Fig. 3B. These deviations resulted in systematic errors in the persistence length estimated from single exponential fits (Fig. 3C). Thus, for the largest pixel-sizes we found either erroneously low (for the case with 0.33 µm pixel-size) or high (for 0.66 µm pixel-size) persistence length due to this complication. The basis, in the shape of the CCF, for these effects is clear from Fig. 3B. The pixel-size is not necessarily possible to modify in a given experimental set-up. On the other hand, as indicated above, the important parameter is not the pixel-size per se but rather the ratio vfΔt/pixel-size.


Analysis of flexural rigidity of actin filaments propelled by surface adsorbed myosin motors.

Bengtsson E, Persson M, Månsson A - Cytoskeleton (Hoboken) (2013)

Digitization effects. (A) Illustration of truncation effects when analyzing a given filament path at different frame rates. The circles indicate observed filament positions when sliding at 3 µm·s−1 (filled circles) and 10 µm·s−1 (open circles), and the black, blue and red lines indicate apparent filament paths for 0.1, 0.2, and 0.4 s between analyzed frames, respectively. Each square in the grid corresponds to a pixel. (B) Simulated data. Fit of the CCF based on simulated data at different pixel-sizes to the exponential function (Eq. 1). The simulations of filament paths at low velocity (2.5 µm·s−1) show changes in estimated persistence length value as a complication due to digitization effects related to finite pixel-size. The filaments were assumed to move 0.5 µm between analyzed frames (i.e., frame rate of 5 s-1). (C) Estimated persistence lengths (±95% CI) from the fits in B to simulated data, with the dashed line illustrating the theoretical persistence length (LPtheor). Same color code as in B. (D) Fit of exponential function to CCF for experimental data with different time intervals between analyzed frames. In this experiment blocking actin was omitted, the pixel-size was 0.1652 µm2 and [MgATP] = 0.05 mM to reduce velocity (2.26 ± 0.04 µm·s−1; mean ± 95% CI, number of filaments (nf) 114). Finally, the persistence length was determined to 6.99 ± 0.57 µm (mean ± 95% CI), using 0.8 s between analyzed frames. The number of independent filament paths was 100 at 0.8 s. Note, the same experimental data was used just employing different time intervals between frames. (E) Effect of ratio vfΔt/pixel-size on estimated persistence length. Simulated data. Open circles: LPtheor = 20 µm, filled symbols: LPtheor = 10 µm, included data from B to C (i.e., constant vfΔt, same color code as in B and C), open squares: LPtheor = 5 µm, LPtheor illustrated with dashed lines. (F) Effect of vfΔt on estimated persistence length in relation to underlying theoretical persistence length (LPtheor). Same data as in E.
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fig03: Digitization effects. (A) Illustration of truncation effects when analyzing a given filament path at different frame rates. The circles indicate observed filament positions when sliding at 3 µm·s−1 (filled circles) and 10 µm·s−1 (open circles), and the black, blue and red lines indicate apparent filament paths for 0.1, 0.2, and 0.4 s between analyzed frames, respectively. Each square in the grid corresponds to a pixel. (B) Simulated data. Fit of the CCF based on simulated data at different pixel-sizes to the exponential function (Eq. 1). The simulations of filament paths at low velocity (2.5 µm·s−1) show changes in estimated persistence length value as a complication due to digitization effects related to finite pixel-size. The filaments were assumed to move 0.5 µm between analyzed frames (i.e., frame rate of 5 s-1). (C) Estimated persistence lengths (±95% CI) from the fits in B to simulated data, with the dashed line illustrating the theoretical persistence length (LPtheor). Same color code as in B. (D) Fit of exponential function to CCF for experimental data with different time intervals between analyzed frames. In this experiment blocking actin was omitted, the pixel-size was 0.1652 µm2 and [MgATP] = 0.05 mM to reduce velocity (2.26 ± 0.04 µm·s−1; mean ± 95% CI, number of filaments (nf) 114). Finally, the persistence length was determined to 6.99 ± 0.57 µm (mean ± 95% CI), using 0.8 s between analyzed frames. The number of independent filament paths was 100 at 0.8 s. Note, the same experimental data was used just employing different time intervals between frames. (E) Effect of ratio vfΔt/pixel-size on estimated persistence length. Simulated data. Open circles: LPtheor = 20 µm, filled symbols: LPtheor = 10 µm, included data from B to C (i.e., constant vfΔt, same color code as in B and C), open squares: LPtheor = 5 µm, LPtheor illustrated with dashed lines. (F) Effect of vfΔt on estimated persistence length in relation to underlying theoretical persistence length (LPtheor). Same data as in E.
Mentions: In experiments, errors are introduced in the estimate of the tangent angle along the filament path due to the finite pixel-sizes. This effect may become severe if the filament slides only a short distance compared to the pixel-size between two subsequent measurements, e.g., with large pixel-size, low velocity, high frame rates, or a combination of these factors. Errors may also be introduced if the sliding distance between subsequent frames is so long that the path curvature is truncated (Fig. 3A) Homsher et al., 1992. In order to elucidate these effects, simulations were performed using different combinations of velocity, pixel-size and time between frames as well as different pre-determined persistence lengths, LPtheor. In Fig. 3B, we present simulated results for the case with low velocity (2.5 µm·s−1) as seen e.g., at low MgATP concentrations or low temperature. We performed the simulations on the assumption of different pixel-sizes (0.02, 0.165, 0.33, and 0.66 µm/pixel) and a frame rate of 5 s−1, corresponding to a sliding distance between analyzed frames of 0.5 µm. Thus, for the largest pixel-size, the simulated data points could end up in the same pixel for two consecutive frames, e.g., if the tangent angle of the filament path was 45% relative to the horizontal axis. Moreover, even for the second largest pixel-size the digitization error may be appreciable. These errors are reflected in the deviation of the cosine correlation function from a single exponential as illustrated in the simulated data in Fig. 3B. These deviations resulted in systematic errors in the persistence length estimated from single exponential fits (Fig. 3C). Thus, for the largest pixel-sizes we found either erroneously low (for the case with 0.33 µm pixel-size) or high (for 0.66 µm pixel-size) persistence length due to this complication. The basis, in the shape of the CCF, for these effects is clear from Fig. 3B. The pixel-size is not necessarily possible to modify in a given experimental set-up. On the other hand, as indicated above, the important parameter is not the pixel-size per se but rather the ratio vfΔt/pixel-size.

Bottom Line: Actin filaments are central components of the cytoskeleton and the contractile machinery of muscle.The filaments are known to exist in a range of conformational states presumably with different flexural rigidity and thereby different persistence lengths.Our results analyze the approaches proposed previously to measure the persistence length from the statistics of the winding paths of actin filaments that are propelled by surface-adsorbed myosin motor fragments in the in vitro motility assay.

View Article: PubMed Central - PubMed

Affiliation: Faculty of Health and Life Sciences, Linnaeus University, Kalmar, Sweden.

Show MeSH
Related in: MedlinePlus