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# Fast and slow dynamics of the cytoskeleton.

NATURE MATERIALS, no. 8 (2006): 636.0-640

WOS SCOPUS NATURE

Abstract

Material moduli of the cytoskeleton (CSK) influence a wide range of cell functions(1-3). There is substantial evidence from reconstituted F-actin gels that a regime exists in which the moduli scale with frequency with a universal exponent of 3/4. Such behaviour is entropic in origin and is attributable to fluctuations in semi flexible pol...More

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Introduction

- A major constituent of the CSK is F-actin. Reconstituted F-actin gels in vitro show clear evidence of semiflexible-polymer network dynamics[6,7,10,11].
- Where G∗(f ) is the complex modulus, ρ,κ,ζ, and lp are the density, bending stiffness, lateral drag coefficient, and persistence length of actin filaments in the gel, respectively, and i2 = −1; here the authors have suppressed a small newtonian viscosity that contributes little except at very high frequencies.
- In a variety of cell types, as well as in F-actin gels that are pre-stressed and crosslinked by filamin, dynamics of a rather different type have recently been reported[8,9,18,19,20].

Highlights

- A major constituent of the CSK is F-actin
- In a variety of cell types, as well as in F-actin gels that are pre-stressed and crosslinked by filamin, dynamics of a rather different type have recently been reported[8,9,18,19,20]. To fill this gap and to assess the existence of a regime comparable to that suggested by equation (1), here we report rheological properties of the freshly isolated living airway smooth muscle (ASM) cell
- Compared with the CSK of the smooth muscle cell passaged in culture, that of the freshly isolated smooth muscle cell has substantially more organization[21], higher density of contractile filaments, more smooth-muscle-specific actin-binding proteins (h-caldesmon, h-1 calponin, and sm22) and myofilament bundles, but fewer microtubules (K.M., personal communication)
- The observation of G∗ approaching f 3/4 at higher frequencies suggests the emergence of entropic dynamics associated with semiflexible polymers and in this report it is identified for the first time in living cells
- Single ASM cells were freshly isolated from bovine trachea by enzymatic digestion, which was adopted from a previously described method[23]
- The mean of α was 0.05 (95% confidence interval 0.04–0.06) and was different from zero (p < 0.00001); as described below, this implies that at low frequencies the system did not approach a hookean limit
- In constantly oxygenated Krebs solution (120 mM NaCl, 5.9 mM KCl, 1.2 mM NaH2PO4, 25 mM NaHCO3, 11.5 mM dextrose, 1 mM CaCl2, and 1.4 mM MgCl2), 50 mg wet weight of ASM was dissected from the trachea and cut into 2 × 3 mm pieces

Results

- To fill this gap and to assess the existence of a regime comparable to that suggested by equation (1), here the authors report rheological properties of the freshly isolated living airway smooth muscle (ASM) cell.
- The mean of β was 0.75, (95% confidence interval 0.69–0.79) and was different from unity (p < 0.00001); as described below, this implies that at high frequencies the system did not approach a newtonian limit.
- Such high-frequency dynamics have not been noted previously in the living cell in retrospect, a hint of such behaviour is evident in cells passaged in culture[24].
- At lower frequencies semiflexible-polymer dynamics became subdominant, with the complex modulus scaling as f 0.05.
- The exponent β was not influenced by relaxation, but decreased during contraction from 0.75 to 0.64 (95% confidence interval 0.57 to 0.71) (Supplementary Information Fig. S2, top), suggesting that contraction altered the qualitative nature of the high-frequency behaviour, whereas relaxation did not.
- The observation of G∗ approaching f 3/4 at higher frequencies suggests the emergence of entropic dynamics associated with semiflexible polymers and in this report it is identified for the first time in living cells.
- The authors conclude that in the living cell the dynamics of semiflexible polymers and soft glasses coexist, but each dominates nature materials VOL 5 AUGUST 2006 www.nature.com/naturematerials

Conclusion

- All prior measurements in other cell systems show power-law responses with non-universal exponents in the range 0.1–0.3, and it was not clear from those measurements if a distinct highfrequency regime might exist.
- The authors measured the complex modulus as a function of frequency by applying an oscillatory magnetic field and measuring the resultant oscillatory bead motions with light microscopy[24,37] (Fig. 1c).
- This can be converted to familiar material moduli with the use of a length scale derived from a model of cell deformation[40], but to avoid model-dependent assumptions here the authors report all data in primary measurement units of Pa nm−1.

Summary

- A major constituent of the CSK is F-actin. Reconstituted F-actin gels in vitro show clear evidence of semiflexible-polymer network dynamics[6,7,10,11].
- Where G∗(f ) is the complex modulus, ρ,κ,ζ, and lp are the density, bending stiffness, lateral drag coefficient, and persistence length of actin filaments in the gel, respectively, and i2 = −1; here the authors have suppressed a small newtonian viscosity that contributes little except at very high frequencies.
- In a variety of cell types, as well as in F-actin gels that are pre-stressed and crosslinked by filamin, dynamics of a rather different type have recently been reported[8,9,18,19,20].
- To fill this gap and to assess the existence of a regime comparable to that suggested by equation (1), here the authors report rheological properties of the freshly isolated living airway smooth muscle (ASM) cell.
- The mean of β was 0.75, (95% confidence interval 0.69–0.79) and was different from unity (p < 0.00001); as described below, this implies that at high frequencies the system did not approach a newtonian limit.
- Such high-frequency dynamics have not been noted previously in the living cell in retrospect, a hint of such behaviour is evident in cells passaged in culture[24].
- At lower frequencies semiflexible-polymer dynamics became subdominant, with the complex modulus scaling as f 0.05.
- The exponent β was not influenced by relaxation, but decreased during contraction from 0.75 to 0.64 (95% confidence interval 0.57 to 0.71) (Supplementary Information Fig. S2, top), suggesting that contraction altered the qualitative nature of the high-frequency behaviour, whereas relaxation did not.
- The observation of G∗ approaching f 3/4 at higher frequencies suggests the emergence of entropic dynamics associated with semiflexible polymers and in this report it is identified for the first time in living cells.
- The authors conclude that in the living cell the dynamics of semiflexible polymers and soft glasses coexist, but each dominates nature materials VOL 5 AUGUST 2006 www.nature.com/naturematerials
- All prior measurements in other cell systems show power-law responses with non-universal exponents in the range 0.1–0.3, and it was not clear from those measurements if a distinct highfrequency regime might exist.
- The authors measured the complex modulus as a function of frequency by applying an oscillatory magnetic field and measuring the resultant oscillatory bead motions with light microscopy[24,37] (Fig. 1c).
- This can be converted to familiar material moduli with the use of a length scale derived from a model of cell deformation[40], but to avoid model-dependent assumptions here the authors report all data in primary measurement units of Pa nm−1.

Funding

- X.T. is supported by a postdoctoral fellowship from the Spanish Ministerio de Educacion y Ciencia
- This study was financially supported by NIH HL65960, HL33009 and HL31704

Study subjects and analysis

data: 64

Although our technology is limited to frequencies below 1 kHz, our data were sufficient to resolve the exponents α and β and put relatively narrow bounds on their values (see the additional comments on statistical tests in the Supplementary Information). Across the cell population (N = 64), the distributions of α and β were approximately normal (Fig. 4). The mean of α was 0.05 (95% confidence interval 0.04–0.06) and was different from zero (p < 0.00001); as described below, this implies that at low frequencies the system did not approach a hookean limit

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