OHC Bundle Damping Cartagena 2019

OHC Bundle Damping — Cartagena-Rivera 2019

First experimental measurement of the viscous damping parameter of mouse cochlear hair bundles by noncontact FM-AFM. Bundle is treated as a Kelvin–Voigt viscoelastic element (elastic stiffness $k_b$ in parallel with damping $c_b$).

Damping equation (verbatim, Eq. 2)

$$c_b=-\frac{3k_b}{A_b\sin \beta }\frac{1}{\pi f_{\text{far}}^2\frac{d\Phi }{df}}$$

where $c_b$ (Pa·s·m⁻¹) is the global bundle damping parameter, $\Phi$ (rad) is the cantilever response phase, $d\Phi /df$ (rad·Hz⁻¹) is the slope of the phase–frequency curve at $f_{\pi /2}$, and $k_b$, $A_b$, $\beta$, $f_{\text{far}}$ are as in Eq. 1 (see Recipe — Noncontact FM-AFM Hair Bundle Mechanics).

Damping values at P13–P15 (apical turn)

Cell	Genotype	Bundle damping $c_b$	Effect of HTC removal
OHC	$Str{c}^{+/-}/Tect{a}^{-/-}$ (control)	10.76 ± 1.2 kPa·s·m⁻¹	—
OHC	$Str{c}^{-/-}/Tect{a}^{-/-}$ (no HTC)	2.85 ± 0.3 kPa·s·m⁻¹	~74% reduction
IHC	$Str{c}^{+/-}/Tect{a}^{-/-}$	unaffected (n.s.)	—
IHC	$Str{c}^{-/-}/Tect{a}^{-/-}$	unaffected (n.s.)	—

Source: [Cartagena-Rivera 2019, Fig. 5B,C; “Absence of horizontal top connectors reduces OHC stereocilia bundle damping” section]. Sample sizes: OHC $n=40$ (control, 7 animals), $n=46$ (mutant, 7 animals); IHC $n=14$ (control, 5), $n=13$ (mutant, 4).

Developmental damping series (apical OHC)

Postnatal age	$Str{c}^{+/-}/Tect{a}^{-/-}$ $c_b$ (kPa·s·m⁻¹)	$Str{c}^{-/-}/Tect{a}^{-/-}$ $c_b$ (kPa·s·m⁻¹)
P9	2.8 ± 1	4.1 ± 0.7
P15	15.3 ± 4.3	3 ± 0.5

Source: [Cartagena-Rivera 2019, Fig. 6B; “Apical turn OHC bundle stiffness and damping significantly increase during development of horizontal top connectors” section].

In the control ($Str{c}^{+/-}$) the damping rises ~5.5× during HTC maturation; in the null it stays flat. Damping change tracks HTC formation, not stereocilium growth.

Interpretation

• HTCs contribute approximately equally to elastic and viscous components — bundle is intrinsically damped.
• Effective bundle viscosity is the same order of magnitude as the bullfrog sacculus hydrodynamic friction coefficient ([Kozlov et al. 2011 Nature; Kozlov et al. 2012 PNAS]), cross-validating the FM-AFM method.
• IHC bundles are unaffected — stereocilin is OHC-specific.
• The viscous damping is the missing parameter for cochlear-amplification models — without HTCs, both restoring force and dissipation drop by ~60–74%.

Connections

• [source] dulon-2019-htc-bundle-mechanics
• [part-of] stereocilia-mechanics
• [see-also] Hair Bundle Stiffness Decomposition
• [see-also] Recipe — Noncontact FM-AFM Hair Bundle Mechanics
• [applies] h09-hydrogel — therapeutic HTC substitute must restore both stiffness and damping
• [applies] h05-calcium-oscillation — bundle damping sets resonance Q for acoustic-driven model
• [about] Stereocilin