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Synchronization of Spontaneous Active Motility of Hair Cell Bundles.

Zhang TY, Ji S, Bozovic D - PLoS ONE (2015)

Bottom Line: Hair bundles are coupled by overlying membranes in vivo; hence, explaining the potential role of innate bundle motility in the generation of otoacoustic emissions requires an understanding of the effects of coupling on the active bundle dynamics.The frequency of synchronized oscillation was found to be near the mean of the innate frequencies of individual bundles.Coupling also led to an improved regularity of entrained oscillations, demonstrated by an increase in the quality factor.

View Article: PubMed Central - PubMed

Affiliation: Department of Physics and Astronomy, University of California Los Angeles, Los Angeles, California, United States of America.

ABSTRACT
Hair cells of the inner ear exhibit an active process, believed to be crucial for achieving the sensitivity of auditory and vestibular detection. One of the manifestations of the active process is the occurrence of spontaneous hair bundle oscillations in vitro. Hair bundles are coupled by overlying membranes in vivo; hence, explaining the potential role of innate bundle motility in the generation of otoacoustic emissions requires an understanding of the effects of coupling on the active bundle dynamics. We used microbeads to connect small groups of hair cell bundles, using in vitro preparations that maintain their innate oscillations. Our experiments demonstrate robust synchronization of spontaneous oscillations, with either 1:1 or multi-mode phase-locking. The frequency of synchronized oscillation was found to be near the mean of the innate frequencies of individual bundles. Coupling also led to an improved regularity of entrained oscillations, demonstrated by an increase in the quality factor.

No MeSH data available.


Multi-mode phase-locking by elastic or viscous coupling.(A) Multi-mode locking due to elastic coupling (Winding Number = 1.98). The red trace shows the bead motion, and the blue trace shows the motion of the hair bundle with the weaker coupling coefficient. The innate frequencies of the three oscillators are Ω1 = 7Hz, Ω2 = 17Hz and Ω3 = 25Hz; the coupling strength is K1 = 1000 μN /m, K2 = 1000 μN /m and K3 = 300 μN /m. (B) Multi-mode locking due to viscous coupling (Winding Number = 2.06). The red trace shows the bead motion, and the blue trace shows the motion of the hair bundle with the weaker coupling coefficient. The innate frequencies of the three oscillators are Ω1 = 7Hz, Ω2 = 17Hz and Ω3 = 25 Hz; the coupling strength is ξ1 = 40 μN*s/m, ξ2 = 40 μN*s/m and ξ3 = 2 μN*s/m. Both forms of coupling lead to multi-mode phase-locking. (C-D) Winding Number vs. frequency of one of the oscillators. Both forms of coupling show the devil’s staircase. (C) K1 = K2 = 1000 μN /m and K3 = 300 μN /m, Ω1 = 7 Hz, Ω3 = 17 Hz. (D) ξ1 = ξ2 = 40 μN*s/m, and ξ3 = 5 μN *s/m, Ω1 = 7 Hz, Ω3 = 17 Hz.
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pone.0141764.g007: Multi-mode phase-locking by elastic or viscous coupling.(A) Multi-mode locking due to elastic coupling (Winding Number = 1.98). The red trace shows the bead motion, and the blue trace shows the motion of the hair bundle with the weaker coupling coefficient. The innate frequencies of the three oscillators are Ω1 = 7Hz, Ω2 = 17Hz and Ω3 = 25Hz; the coupling strength is K1 = 1000 μN /m, K2 = 1000 μN /m and K3 = 300 μN /m. (B) Multi-mode locking due to viscous coupling (Winding Number = 2.06). The red trace shows the bead motion, and the blue trace shows the motion of the hair bundle with the weaker coupling coefficient. The innate frequencies of the three oscillators are Ω1 = 7Hz, Ω2 = 17Hz and Ω3 = 25 Hz; the coupling strength is ξ1 = 40 μN*s/m, ξ2 = 40 μN*s/m and ξ3 = 2 μN*s/m. Both forms of coupling lead to multi-mode phase-locking. (C-D) Winding Number vs. frequency of one of the oscillators. Both forms of coupling show the devil’s staircase. (C) K1 = K2 = 1000 μN /m and K3 = 300 μN /m, Ω1 = 7 Hz, Ω3 = 17 Hz. (D) ξ1 = ξ2 = 40 μN*s/m, and ξ3 = 5 μN *s/m, Ω1 = 7 Hz, Ω3 = 17 Hz.

Mentions: In Fig 7A and 7B, we plot traces of motion for one of the three coupled oscillators and the spherical mass, with the coupling strength of one of the oscillators assumed to be weaker than the other two. Both purely elastic and viscous coupling produce clear multi-mode phase-locking. Variations in the frequency of the oscillator with the weaker coupling coefficient lead to the devil's staircase (Fig 7C and 7D). The experimentally observed multi-mode locking is readily reproduced by the numerical simulation, indicating that the nonlinearity of the system is well described by the model.


Synchronization of Spontaneous Active Motility of Hair Cell Bundles.

Zhang TY, Ji S, Bozovic D - PLoS ONE (2015)

Multi-mode phase-locking by elastic or viscous coupling.(A) Multi-mode locking due to elastic coupling (Winding Number = 1.98). The red trace shows the bead motion, and the blue trace shows the motion of the hair bundle with the weaker coupling coefficient. The innate frequencies of the three oscillators are Ω1 = 7Hz, Ω2 = 17Hz and Ω3 = 25Hz; the coupling strength is K1 = 1000 μN /m, K2 = 1000 μN /m and K3 = 300 μN /m. (B) Multi-mode locking due to viscous coupling (Winding Number = 2.06). The red trace shows the bead motion, and the blue trace shows the motion of the hair bundle with the weaker coupling coefficient. The innate frequencies of the three oscillators are Ω1 = 7Hz, Ω2 = 17Hz and Ω3 = 25 Hz; the coupling strength is ξ1 = 40 μN*s/m, ξ2 = 40 μN*s/m and ξ3 = 2 μN*s/m. Both forms of coupling lead to multi-mode phase-locking. (C-D) Winding Number vs. frequency of one of the oscillators. Both forms of coupling show the devil’s staircase. (C) K1 = K2 = 1000 μN /m and K3 = 300 μN /m, Ω1 = 7 Hz, Ω3 = 17 Hz. (D) ξ1 = ξ2 = 40 μN*s/m, and ξ3 = 5 μN *s/m, Ω1 = 7 Hz, Ω3 = 17 Hz.
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pone.0141764.g007: Multi-mode phase-locking by elastic or viscous coupling.(A) Multi-mode locking due to elastic coupling (Winding Number = 1.98). The red trace shows the bead motion, and the blue trace shows the motion of the hair bundle with the weaker coupling coefficient. The innate frequencies of the three oscillators are Ω1 = 7Hz, Ω2 = 17Hz and Ω3 = 25Hz; the coupling strength is K1 = 1000 μN /m, K2 = 1000 μN /m and K3 = 300 μN /m. (B) Multi-mode locking due to viscous coupling (Winding Number = 2.06). The red trace shows the bead motion, and the blue trace shows the motion of the hair bundle with the weaker coupling coefficient. The innate frequencies of the three oscillators are Ω1 = 7Hz, Ω2 = 17Hz and Ω3 = 25 Hz; the coupling strength is ξ1 = 40 μN*s/m, ξ2 = 40 μN*s/m and ξ3 = 2 μN*s/m. Both forms of coupling lead to multi-mode phase-locking. (C-D) Winding Number vs. frequency of one of the oscillators. Both forms of coupling show the devil’s staircase. (C) K1 = K2 = 1000 μN /m and K3 = 300 μN /m, Ω1 = 7 Hz, Ω3 = 17 Hz. (D) ξ1 = ξ2 = 40 μN*s/m, and ξ3 = 5 μN *s/m, Ω1 = 7 Hz, Ω3 = 17 Hz.
Mentions: In Fig 7A and 7B, we plot traces of motion for one of the three coupled oscillators and the spherical mass, with the coupling strength of one of the oscillators assumed to be weaker than the other two. Both purely elastic and viscous coupling produce clear multi-mode phase-locking. Variations in the frequency of the oscillator with the weaker coupling coefficient lead to the devil's staircase (Fig 7C and 7D). The experimentally observed multi-mode locking is readily reproduced by the numerical simulation, indicating that the nonlinearity of the system is well described by the model.

Bottom Line: Hair bundles are coupled by overlying membranes in vivo; hence, explaining the potential role of innate bundle motility in the generation of otoacoustic emissions requires an understanding of the effects of coupling on the active bundle dynamics.The frequency of synchronized oscillation was found to be near the mean of the innate frequencies of individual bundles.Coupling also led to an improved regularity of entrained oscillations, demonstrated by an increase in the quality factor.

View Article: PubMed Central - PubMed

Affiliation: Department of Physics and Astronomy, University of California Los Angeles, Los Angeles, California, United States of America.

ABSTRACT
Hair cells of the inner ear exhibit an active process, believed to be crucial for achieving the sensitivity of auditory and vestibular detection. One of the manifestations of the active process is the occurrence of spontaneous hair bundle oscillations in vitro. Hair bundles are coupled by overlying membranes in vivo; hence, explaining the potential role of innate bundle motility in the generation of otoacoustic emissions requires an understanding of the effects of coupling on the active bundle dynamics. We used microbeads to connect small groups of hair cell bundles, using in vitro preparations that maintain their innate oscillations. Our experiments demonstrate robust synchronization of spontaneous oscillations, with either 1:1 or multi-mode phase-locking. The frequency of synchronized oscillation was found to be near the mean of the innate frequencies of individual bundles. Coupling also led to an improved regularity of entrained oscillations, demonstrated by an increase in the quality factor.

No MeSH data available.