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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.


Related in: MedlinePlus

Synchronized frequency versus the average frequency of the bundles.(A-B) Numerical calculations of the synchronized frequency (fsync) of three bundles versus the average of their characteristic frequencies (fave). Each data point represents a group of bundles, with a specific distribution of frequencies. The color coding represents different sets of parameter values, which include negative stiffness (μ) of the bundle, friction coefficient (λ), and coupling strength, while all other parameters in the model are fixed (see Table A in S1 File). (A) Elastic coupling (Blue: λ = 2.8 μN*s/m, K = 1000 μN/m, Red: λ = 0.28 μN*s/m, K = 100 μN/m, Green: λ = 0.28 μN*s/m, K = 1000 μN/m, Magenta: λ = 28 μN*s/m, K = 10000μN/m). (B) Viscous coupling (Blue: λ = 2.8 μN*s/m, ξ = 40 μN*s/m, Red: λ = 0.28 μN*s/m, ξ = 4 μN*s/m, Green: λ = 0.28 μN*s/m, ξ = 40 μN*s/m, Magenta: λ = 28 μN*s/m, ξ = 400μN*s/m). The simulations indicate that the synchronized frequencies are clustered near the average frequency values. However, precise values of the synchronized frequency depend on the characteristics of the bundles. (C) Experimental data. The error bars indicate the standard deviation for the three synchronized bundle frequencies.
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pone.0141764.g006: Synchronized frequency versus the average frequency of the bundles.(A-B) Numerical calculations of the synchronized frequency (fsync) of three bundles versus the average of their characteristic frequencies (fave). Each data point represents a group of bundles, with a specific distribution of frequencies. The color coding represents different sets of parameter values, which include negative stiffness (μ) of the bundle, friction coefficient (λ), and coupling strength, while all other parameters in the model are fixed (see Table A in S1 File). (A) Elastic coupling (Blue: λ = 2.8 μN*s/m, K = 1000 μN/m, Red: λ = 0.28 μN*s/m, K = 100 μN/m, Green: λ = 0.28 μN*s/m, K = 1000 μN/m, Magenta: λ = 28 μN*s/m, K = 10000μN/m). (B) Viscous coupling (Blue: λ = 2.8 μN*s/m, ξ = 40 μN*s/m, Red: λ = 0.28 μN*s/m, ξ = 4 μN*s/m, Green: λ = 0.28 μN*s/m, ξ = 40 μN*s/m, Magenta: λ = 28 μN*s/m, ξ = 400μN*s/m). The simulations indicate that the synchronized frequencies are clustered near the average frequency values. However, precise values of the synchronized frequency depend on the characteristics of the bundles. (C) Experimental data. The error bars indicate the standard deviation for the three synchronized bundle frequencies.

Mentions: Fig 6 plots the frequency of the synchronized system as a function of the mean frequency of the individual bundles. Results are presented for elastic (A) and viscous (B) coupling, with different distributions of frequencies of the individual oscillators, and different values chosen for the negative stiffness and friction coefficient of a bundle. Experimental results are shown in part (C). The theoretical results show clustering of the synchronized frequency to the mean frequency of the individual oscillators. The variation around this mean is due to its dependence on the stiffness and friction coefficients of the bundles.


Synchronization of Spontaneous Active Motility of Hair Cell Bundles.

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

Synchronized frequency versus the average frequency of the bundles.(A-B) Numerical calculations of the synchronized frequency (fsync) of three bundles versus the average of their characteristic frequencies (fave). Each data point represents a group of bundles, with a specific distribution of frequencies. The color coding represents different sets of parameter values, which include negative stiffness (μ) of the bundle, friction coefficient (λ), and coupling strength, while all other parameters in the model are fixed (see Table A in S1 File). (A) Elastic coupling (Blue: λ = 2.8 μN*s/m, K = 1000 μN/m, Red: λ = 0.28 μN*s/m, K = 100 μN/m, Green: λ = 0.28 μN*s/m, K = 1000 μN/m, Magenta: λ = 28 μN*s/m, K = 10000μN/m). (B) Viscous coupling (Blue: λ = 2.8 μN*s/m, ξ = 40 μN*s/m, Red: λ = 0.28 μN*s/m, ξ = 4 μN*s/m, Green: λ = 0.28 μN*s/m, ξ = 40 μN*s/m, Magenta: λ = 28 μN*s/m, ξ = 400μN*s/m). The simulations indicate that the synchronized frequencies are clustered near the average frequency values. However, precise values of the synchronized frequency depend on the characteristics of the bundles. (C) Experimental data. The error bars indicate the standard deviation for the three synchronized bundle frequencies.
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC4634766&req=5

pone.0141764.g006: Synchronized frequency versus the average frequency of the bundles.(A-B) Numerical calculations of the synchronized frequency (fsync) of three bundles versus the average of their characteristic frequencies (fave). Each data point represents a group of bundles, with a specific distribution of frequencies. The color coding represents different sets of parameter values, which include negative stiffness (μ) of the bundle, friction coefficient (λ), and coupling strength, while all other parameters in the model are fixed (see Table A in S1 File). (A) Elastic coupling (Blue: λ = 2.8 μN*s/m, K = 1000 μN/m, Red: λ = 0.28 μN*s/m, K = 100 μN/m, Green: λ = 0.28 μN*s/m, K = 1000 μN/m, Magenta: λ = 28 μN*s/m, K = 10000μN/m). (B) Viscous coupling (Blue: λ = 2.8 μN*s/m, ξ = 40 μN*s/m, Red: λ = 0.28 μN*s/m, ξ = 4 μN*s/m, Green: λ = 0.28 μN*s/m, ξ = 40 μN*s/m, Magenta: λ = 28 μN*s/m, ξ = 400μN*s/m). The simulations indicate that the synchronized frequencies are clustered near the average frequency values. However, precise values of the synchronized frequency depend on the characteristics of the bundles. (C) Experimental data. The error bars indicate the standard deviation for the three synchronized bundle frequencies.
Mentions: Fig 6 plots the frequency of the synchronized system as a function of the mean frequency of the individual bundles. Results are presented for elastic (A) and viscous (B) coupling, with different distributions of frequencies of the individual oscillators, and different values chosen for the negative stiffness and friction coefficient of a bundle. Experimental results are shown in part (C). The theoretical results show clustering of the synchronized frequency to the mean frequency of the individual oscillators. The variation around this mean is due to its dependence on the stiffness and friction coefficients of the bundles.

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.


Related in: MedlinePlus