Microrheometry underestimates the values of the viscoelastic moduli in measurements on F-actin solutions compared to macrorheometry

We present a systematic comparison of microrheological and macrorheological measurements of the viscoelastic storage and loss moduli, $G^{\prime }\mathrm{}\left(f\right)\mathrm{}$ and $G^{″}\mathrm{}\left(f\right),$ respectively, of solutions of the semiflexible biopolymer F-actin. Using magnetic tweezers microrheometry and rotating disk macrorheometry, we show that microscopic values for $G^{\prime }\mathrm{}\left(f\right)\mathrm{}$ and $G^{″}\mathrm{}\left(f\right)\mathrm{}$ are significantly smaller than macroscopic results over the frequency range $f=0.004\mathrm{}–4$ Hz, whereas the qualitative shape of the spectra is similar. These findings confirm recent theoretical predictions [A. C. Maggs, Phys. Rev. E 57, 2091 (1998)]. The discrepancy affects not only absolute values of $G^{\prime }\mathrm{}\left(f\right)\mathrm{}$ and $G^{″}\mathrm{}\left(f\right):$ although microscopic and macroscopic plateau regime are found in the same frequency range, the two methods yield different values for the entanglement time which determines the high-frequency end of the plateau. By investigating F-actin solutions of different mean filament lengths, we show that microscopic and macroscopic $G^{\prime }\mathrm{}\left(f\right)\mathrm{}$ and $G^{″}\mathrm{}\left(f\right)\mathrm{}$ converge, if the probe particle used in microrheometry becomes large compared to the length of actin filaments.