Figures and data in Dynamic curvature regulation accounts for the symmetric and asymmetric beats of Chlamydomonas flagella

11 figures and 2 tables

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Table 1

Parameters for beat generation in wild type axonemes.

https://doi.org/10.7554/eLife.13258.006

		Sliding control	Curvature control	Normal-force control
Coefficient of determination	$R^{2} (%)$	$49 \pm 4$	$95 \pm 1$	$95 \pm 1$
Sliding coefficient	$χ^{'}, χ^{''} (n N \cdot μ m^{- 2})$	$- 12.2 \pm 3.0, - 1.1 \pm 0.1$	$19.8 \pm 3.3, 0$	$13.2 \pm 3.6, 0$
Curvature coefficient	$β^{'}, β^{''} (n N)$	0	$0, - 6.5 \pm 0.4$	0
Normal-force coefficient	$γ^{'}, γ^{′′}$	0	0	$0.12 \pm 0.05, 2.0 \pm 0.2$
Basal impedance	$χ_{b}^{'}, χ_{b}^{''} (n N \cdot μ m^{- 1})$	$42.4 \pm 0.7, 2800 \pm 6900$	$42.2 \pm 12, 2.2 \pm 0.7$	$80 \pm 115, 13000 \pm 34000$
Basal sliding (0th mode)	$Δ_{b, 0} (nm)$	$- 41 \pm 41$	$- 36 \pm 12$	$- 144 \pm 196$
Basal sliding (1st mode)	$\| Δ_{b, 1} \| (nm)$	$23 \pm 19$	$22 \pm 5$	$12 \pm 11$

The values reported are mean and standard deviation calculated from $9$ axonemes. The average static curvature is $C_{0} = - 0.232 \pm 0.009 μ m^{- 1}$ , the length $L = 11.7 \pm 0.4, μ m$ , and the frequency $ω = 427 \pm 19$ rad/s (68 Hz). Note that, for curvature controlled beats, using the value of $β$ and an estimate curvature of $0.1 rad / μ m$ results in a sliding force of $\approx 700 pN / μ m$ . Since the motor density of an active half of the axoneme is $\approx 500 μ m^{- 1}$ the individual motor force is $1 p N$ . For the case of normal force control, the sliding force generated by the motors is of the order of the normal force that they experience, since $| γ | \approx 2$ .

Table 2

Parameters for beat generation in mbo2 mutant axonemes.

https://doi.org/10.7554/eLife.13258.007

		Sliding control	Curvature control	Normal-force control
Coefficient of determination	$R^{2} (%)$	$72 \pm 5$	$95 \pm 1$	$96 \pm 1$
Sliding coefficient	$χ^{'}, χ^{′′} (nN \cdot μ m^{- 2})$	$- 15.0 \pm 1.0, - 0.4 \pm 0.1$	$17.4 \pm 2.5, 0$	$10.5 \pm 4.3, 0$
Curvature coefficient	$β^{'}, β^{′′} (pN)$	0	$0, - 0.66 \pm 0.4$	0
Normal-force coefficient	$γ^{'}, γ^{′′}$	0	0	$1.52 \pm 1.52, 32 \pm 25$
Basal impedance	$χ_{b}^{'}, χ_{b}^{′′} (nN \cdot μ m^{- 1})$	$30.6 \pm 14.1, 1.6 \pm 0.7$	$2.1 \pm 2, 2.3 \pm 1.7$	$2.3 \pm 0.3, 13.6 \pm 6.0$
Basal sliding (0th mode)	$Δ_{b, 0} (nm)$	$- 6 \pm 6$	$- 73 \pm 44$	$- 64 \pm 40$
Basal sliding (1st mode)	$\| Δ_{b, 1} \| (nm)$	$51 \pm 10$	$60 \pm 11$	$77 \pm 28$

Values are averages and standard deviations for $9$ axonemes. The static curvature was $C_{0} = - 0.0276 \pm 0.005 μ m^{- 1}$ , the length $L = 9.2 \pm 0.3 μ m$ , and the frequency $ω = 176 \pm 44$ rad/s, (28 Hz). Note that the values of $γ$ in normal force control are very spread out and compared to the wild type fits. In fact, in one case we obtained $γ \approx 80$ , indicating that motors must amplify the normal force they sense by almost two orders of magnitude. The values for curvature control are very similar to those of wild type fits..