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Abstract
Cells continually sample their mechanical environment using exquisite force sensors such as talin, whose folding status triggers mechanotransduction pathways by recruiting binding partners. Mechanical signals in biology change quickly over time and are often embedded in noise; however, the mechanics of force-sensing proteins have only been tested using simple force protocols, such as constant or ramped forces. Here, using our magnetic tape head tweezers design, we measure the folding dynamics of single talin proteins in response to external mechanical noise and cyclic force perturbations. Our experiments demonstrate that talin filters out external mechanical noise but detects periodic force signals over a finely tuned frequency range. Hence, talin operates as a mechanical band-pass filter, able to read and interpret frequency-dependent mechanical information through its folding dynamics. We describe our observations in the context of stochastic resonance, which we propose as a mechanism by which mechanosensing proteins could respond accurately to force signals in the naturally noisy biological environment.
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2
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Abstract
During the detection of sound, hair bundles perform a crucial step by responding to mechanical deflections and converting them into changes in electrical potential that subsequently lead to the release of neurotransmitter. The sensory hair bundle response is characterized by an essential nonlinearity and an energy-consuming amplification of the incoming sound. The active response has been shown to enhance the hair bundle's sensitivity and frequency selectivity of detection. The biological phenomena shown by the bundle have been extensively studied in vitro, allowing comparisons to behaviors observed in vivo. The experimental observations have been well explained by numerical simulations, which describe the cellular mechanisms operant within the bundle, as well as by more sparse theoretical models, based on dynamical systems theory.
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Affiliation(s)
- Dolores Bozovic
- Department of Physics and Astronomy, University of California, Los Angeles, California 90095-1547.,California NanoSystems Institute, University of California, Los Angeles, California 90095-1547
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3
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Lerud KD, Kim JC, Almonte FV, Carney LH, Large EW. A canonical oscillator model of cochlear dynamics. Hear Res 2019; 380:100-107. [PMID: 31234108 DOI: 10.1016/j.heares.2019.06.001] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 02/18/2019] [Revised: 05/06/2019] [Accepted: 06/12/2019] [Indexed: 11/27/2022]
Abstract
Nonlinear responses to acoustic signals arise through active processes in the cochlea, which has an exquisite sensitivity and wide dynamic range that can be explained by critical nonlinear oscillations of outer hair cells. Here we ask how the interaction of critical nonlinearities with the basilar membrane and other organ of Corti components could determine tuning properties of the mammalian cochlea. We propose a canonical oscillator model that captures the dynamics of the interaction between the basilar membrane and organ of Corti, using a pair of coupled oscillators for each place along the cochlea. We analyze two models in which a linear oscillator, representing basilar membrane dynamics, is coupled to a nonlinear oscillator poised at a Hopf instability. The coupling in the first model is unidirectional, and that of the second is bidirectional. Parameters are determined by fitting 496 auditory-nerve (AN) tuning curves of macaque monkeys. We find that the unidirectionally and bidirectionally coupled models account equally well for threshold tuning. In addition, however, the bidirectionally coupled model exhibits low-amplitude, spontaneous oscillation in the absence of stimulation, predicting that phase locking will occur before a significant increase in firing frequency, in accordance with well known empirical observations. This leads us to a canonical oscillator cochlear model based on the fundamental principles of critical nonlinear oscillation and coupling dynamics. The model is more biologically realistic than widely used linear or nonlinear filter-based models, yet parsimoniously displays key features of nonlinear mechanistic models. It is efficient enough for computational studies of auditory perception and auditory physiology.
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Affiliation(s)
- Karl D Lerud
- Department of Psychological Sciences, University of Connecticut, Storrs, CT, USA
| | - Ji Chul Kim
- Department of Psychological Sciences, University of Connecticut, Storrs, CT, USA
| | - Felix V Almonte
- Center for Complex Systems and Brain Sciences, Florida Atlantic University, Boca Raton, FL, USA
| | - Laurel H Carney
- Biomedical Engineering and Neurobiology & Anatomy, University of Rochester, Rochester, NY, USA
| | - Edward W Large
- Department of Psychological Sciences, University of Connecticut, Storrs, CT, USA.
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4
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Cohen O, Safran SA. Physics of Spontaneous Calcium Oscillations in Cardiac Cells and Their Entrainment. PHYSICAL REVIEW LETTERS 2019; 122:198101. [PMID: 31144920 DOI: 10.1103/physrevlett.122.198101] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/17/2018] [Revised: 02/20/2019] [Indexed: 06/09/2023]
Abstract
Mechanical contraction in muscle cells requires Ca to allow myosin binding to actin. Beating cardiomyocytes contain internal Ca stores whose cytoplasmic concentration oscillates. Our theory explains observed single channel dynamics as well as cellular oscillations in spontaneously beating cardiomyocytes. The Ca dependence of channel activity responsible for Ca release includes positive feedback with a delayed response. We use this to predict a dynamical equation for global calcium oscillations with only a few physically relevant parameters. The theory accounts for the observed entrainment of beating to an oscillatory electric or mechanical field.
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Affiliation(s)
- Ohad Cohen
- Department of Chemical and Biological Physics, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Samuel A Safran
- Department of Chemical and Biological Physics, Weizmann Institute of Science, Rehovot 76100, Israel
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Ji S, Bozovic D, Bruinsma R. Amphibian sacculus and the forced Kuramoto model with intrinsic noise and frequency dispersion. Phys Rev E 2018; 97:042411. [PMID: 29758728 DOI: 10.1103/physreve.97.042411] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/22/2017] [Indexed: 06/08/2023]
Abstract
The amphibian sacculus (AS) is an end organ that specializes in the detection of low-frequency auditory and vestibular signals. In this paper, we propose a model for the AS in the form of an array of phase oscillators with long-range coupling, subject to a steady load that suppresses spontaneous oscillations. The array is exposed to significant levels of frequency dispersion and intrinsic noise. We show that such an array can be a sensitive and robust subthreshold detector of low-frequency stimuli, though without significant frequency selectivity. The effects of intrinsic noise and frequency dispersion are contrasted. Intermediate levels of intrinsic noise greatly enhance the sensitivity through stochastic resonance. Frequency dispersion, on the other hand, only degrades detection sensitivity. However, frequency dispersion can play a useful role in terms of the suppression of spontaneous activity. As a model for the AS, the array parameters are such that the system is poised near a saddle-node bifurcation on an invariant circle. However, by a change of array parameters, the same system also can be poised near an emergent Andronov-Hopf bifurcation and thereby function as a frequency-selective detector.
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Affiliation(s)
- Seung Ji
- Department of Physical Science, Los Angeles Mission College, Sylmar, California, USA
| | - Dolores Bozovic
- Department of Physics & Astronomy, University of California, Los Angeles, California, USA and California NanoSystems Institute, University of California, Los Angeles, California, USA
| | - Robijn Bruinsma
- Department of Physics, University of California, Los Angeles, California, USA and Department of Chemistry and Biochemistry, University of California, Los Angeles, California, USA
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Levy M, Molzon A, Lee JH, Kim JW, Cheon J, Bozovic D. High-order synchronization of hair cell bundles. Sci Rep 2016; 6:39116. [PMID: 27974743 PMCID: PMC5156917 DOI: 10.1038/srep39116] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/04/2016] [Accepted: 11/17/2016] [Indexed: 11/09/2022] Open
Abstract
Auditory and vestibular hair cell bundles exhibit active mechanical oscillations at natural frequencies that are typically lower than the detection range of the corresponding end organs. We explore how these noisy nonlinear oscillators mode-lock to frequencies higher than their internal clocks. A nanomagnetic technique is used to stimulate the bundles without an imposed mechanical load. The evoked response shows regimes of high-order mode-locking. Exploring a broad range of stimulus frequencies and intensities, we observe regions of high-order synchronization, analogous to Arnold Tongues in dynamical systems literature. Significant areas of overlap occur between synchronization regimes, with the bundle intermittently flickering between different winding numbers. We demonstrate how an ensemble of these noisy spontaneous oscillators could be entrained to efficiently detect signals significantly above the characteristic frequencies of the individual cells.
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Affiliation(s)
- Michael Levy
- Department of Physics and Astronomy, California NanoSystems Institute, University of California, Los Angeles, California 90095, United States
| | - Adrian Molzon
- Department of Physics and Astronomy, California NanoSystems Institute, University of California, Los Angeles, California 90095, United States
| | - Jae-Hyun Lee
- Center for Nanomedicine, Institute for Basic Science (IBS), Seoul 03722, Republic of Korea.,Yonsei-IBS Institute, Yonsei University, Seoul 03722, Republic of Korea.,Department of Chemistry, Yonsei University, Seoul 03722, Republic of Korea
| | - Ji-Wook Kim
- Center for Nanomedicine, Institute for Basic Science (IBS), Seoul 03722, Republic of Korea.,Yonsei-IBS Institute, Yonsei University, Seoul 03722, Republic of Korea.,Department of Chemistry, Yonsei University, Seoul 03722, Republic of Korea
| | - Jinwoo Cheon
- Center for Nanomedicine, Institute for Basic Science (IBS), Seoul 03722, Republic of Korea.,Yonsei-IBS Institute, Yonsei University, Seoul 03722, Republic of Korea.,Department of Chemistry, Yonsei University, Seoul 03722, Republic of Korea
| | - Dolores Bozovic
- Department of Physics and Astronomy, California NanoSystems Institute, University of California, Los Angeles, California 90095, United States
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Roongthumskul Y, Bozovic D. Mechanical amplification exhibited by quiescent saccular hair bundles. Biophys J 2015; 108:53-61. [PMID: 25564852 PMCID: PMC4286608 DOI: 10.1016/j.bpj.2014.11.009] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/28/2014] [Revised: 11/04/2014] [Accepted: 11/06/2014] [Indexed: 12/02/2022] Open
Abstract
Spontaneous oscillations exhibited by free-standing hair bundles from the Bullfrog sacculus suggest the existence of an active process that might underlie the exquisite sensitivity of the sacculus to mechanical stimulation. However, this spontaneous activity is suppressed by coupling to an overlying membrane, which applies a large mechanical load on the bundle. How a quiescent hair bundle utilizes its active process is still unknown. We studied the dynamics of motion of individual hair bundles under different offsets in the bundle position, and observed the occurrence of spikes in hair-bundle motion, associated with the generation of active work. These mechanical spikes can be evoked by a sinusoidal stimulus, leading to an amplified movement of the bundle with respect to the passive response. Amplitude gain reached as high as 100-fold at small stimulus amplitudes. Amplification of motion decreased with increasing amplitude of stimulation, ceasing at ∼6–12 pN stimuli. Results from numerical simulations suggest that the adaptation process, mediated by myosin 1c, is not required for the production of mechanical spikes.
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Affiliation(s)
- Yuttana Roongthumskul
- Department of Physics and Astronomy, University of California, Los Angeles, Los Angeles, California
| | - Dolores Bozovic
- Department of Physics and Astronomy, University of California, Los Angeles, Los Angeles, California; California NanoSystems Institute, University of California, Los Angeles, Los Angeles, California.
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Soto R, Golestanian R. Self-assembly of active colloidal molecules with dynamic function. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:052304. [PMID: 26066174 DOI: 10.1103/physreve.91.052304] [Citation(s) in RCA: 44] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/17/2015] [Indexed: 05/27/2023]
Abstract
Catalytically active colloids maintain nonequilibrium conditions in which they produce and deplete chemicals and hence effectively act as sources and sinks of molecules. While individual colloids that are symmetrically coated do not exhibit any form of dynamical activity, the concentration fields resulting from their chemical activity decay as 1/r and produce gradients that attract or repel other colloids depending on their surface chemistry and ambient variables. This results in a nonequilibrium analog of ionic systems, but with the remarkable novel feature of action-reaction symmetry breaking. We study solutions of such chemically active colloids in dilute conditions when they join up to form molecules via generalized ionic bonds and discuss how we can achieve structures with time-dependent functionality. In particular, we study a molecule that adopts a spontaneous oscillatory pattern of conformations and another that exhibits a run-and-tumble dynamics similar to bacteria. Our study shows that catalytically active colloids could be used for designing self-assembled structures that possess dynamical functionalities that are determined by their prescribed three-dimensional structures, a strategy that follows the design principle of proteins.
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Affiliation(s)
- Rodrigo Soto
- Departamento de Física, Facultad de Ciencias Físicas y Matemáticas Universidad de Chile, Av. Blanco Encalada 2008, Santiago, Chile
| | - Ramin Golestanian
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3NP, United Kingdom
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Bergevin C, Manley GA, Köppl C. Salient features of otoacoustic emissions are common across tetrapod groups and suggest shared properties of generation mechanisms. Proc Natl Acad Sci U S A 2015; 112:3362-7. [PMID: 25737537 PMCID: PMC4371923 DOI: 10.1073/pnas.1418569112] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Otoacoustic emissions (OAEs) are faint sounds generated by healthy inner ears that provide a window into the study of auditory mechanics. All vertebrate classes exhibit OAEs to varying degrees, yet the biophysical origins are still not well understood. Here, we analyzed both spontaneous (SOAE) and stimulus-frequency (SFOAE) otoacoustic emissions from a bird (barn owl, Tyto alba) and a lizard (green anole, Anolis carolinensis). These species possess highly disparate macromorphologies of the inner ear relative to each other and to mammals, thereby allowing for novel insights into the biomechanical mechanisms underlying OAE generation. All ears exhibited robust OAE activity, and our chief observation was that SFOAE phase accumulation between adjacent SOAE peak frequencies clustered about an integral number of cycles. Being highly similar to published results from human ears, we argue that these data indicate a common underlying generator mechanism of OAEs across all vertebrates, despite the absence of morphological features thought essential to mammalian cochlear mechanics. We suggest that otoacoustic emissions originate from phase coherence in a system of coupled oscillators, which is consistent with the notion of "coherent reflection" but does not explicitly require a mammalian-type traveling wave. Furthermore, comparison between SFOAE delays and auditory nerve fiber responses for the barn owl strengthens the notion that most OAE delay can be attributed to tuning.
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Affiliation(s)
- Christopher Bergevin
- Department of Physics & Astronomy and Centre for Vision Research, York University, Toronto, ON, M3J 1P3, Canada; and
| | - Geoffrey A Manley
- Cluster of Excellence "Hearing4all," Research Center Neurosensory Science, and Department of Neuroscience, School of Medicine and Health Sciences, Carl von Ossietzky University, 26129 Oldenburg, Germany
| | - Christine Köppl
- Cluster of Excellence "Hearing4all," Research Center Neurosensory Science, and Department of Neuroscience, School of Medicine and Health Sciences, Carl von Ossietzky University, 26129 Oldenburg, Germany
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Shlomovitz R, Roongthumskul Y, Ji S, Bozovic D, Bruinsma R. Phase-locked spiking of inner ear hair cells and the driven noisy Adler equation. Interface Focus 2014; 4:20140022. [PMID: 25485081 DOI: 10.1098/rsfs.2014.0022] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
The inner ear constitutes a remarkably sensitive mechanical detector. This detection occurs in a noisy and highly viscous environment, as the sensory cells-the hair cells-are immersed in a fluid-filled compartment and operate at room or higher temperatures. We model the active motility of hair cell bundles of the vestibular system with the Adler equation, which describes the phase degree of freedom of bundle motion. We explore both analytically and numerically the response of the system to external signals, in the presence of white noise. The theoretical model predicts that hair bundles poised in the quiescent regime can exhibit sporadic spikes-sudden excursions in the position of the bundle. In this spiking regime, the system exhibits stochastic resonance, with the spiking rate peaking at an optimal level of noise. Upon the application of a very weak signal, the spikes occur at a preferential phase of the stimulus cycle. We compare the theoretical predictions of our model to experimental measurements obtained in vitro from individual hair cells. Finally, we show that an array of uncoupled hair cells could provide a sensitive detector that encodes the frequency of the applied signal.
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Affiliation(s)
- Roie Shlomovitz
- Department of Physics and Astronomy , University of Washington , Seattle, WA , USA
| | - Yuttana Roongthumskul
- Department of Physics and Astronomy , University of California , Los Angeles, CA , USA
| | - Seung Ji
- Department of Physics and Astronomy , University of California , Los Angeles, CA , USA
| | - Dolores Bozovic
- Department of Physics and Astronomy , University of California , Los Angeles, CA , USA ; California NanoSystems Institute , University of California , Los Angeles, CA , USA
| | - Robijn Bruinsma
- Department of Physics and Astronomy , University of California , Los Angeles, CA , USA ; Departments of Chemistry and Biochemistry , University of California , Los Angeles, CA , USA
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Reichenbach T, Hudspeth AJ. The physics of hearing: fluid mechanics and the active process of the inner ear. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2014; 77:076601. [PMID: 25006839 DOI: 10.1088/0034-4885/77/7/076601] [Citation(s) in RCA: 72] [Impact Index Per Article: 7.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/25/2023]
Abstract
Most sounds of interest consist of complex, time-dependent admixtures of tones of diverse frequencies and variable amplitudes. To detect and process these signals, the ear employs a highly nonlinear, adaptive, real-time spectral analyzer: the cochlea. Sound excites vibration of the eardrum and the three miniscule bones of the middle ear, the last of which acts as a piston to initiate oscillatory pressure changes within the liquid-filled chambers of the cochlea. The basilar membrane, an elastic band spiraling along the cochlea between two of these chambers, responds to these pressures by conducting a largely independent traveling wave for each frequency component of the input. Because the basilar membrane is graded in mass and stiffness along its length, however, each traveling wave grows in magnitude and decreases in wavelength until it peaks at a specific, frequency-dependent position: low frequencies propagate to the cochlear apex, whereas high frequencies culminate at the base. The oscillations of the basilar membrane deflect hair bundles, the mechanically sensitive organelles of the ear's sensory receptors, the hair cells. As mechanically sensitive ion channels open and close, each hair cell responds with an electrical signal that is chemically transmitted to an afferent nerve fiber and thence into the brain. In addition to transducing mechanical inputs, hair cells amplify them by two means. Channel gating endows a hair bundle with negative stiffness, an instability that interacts with the motor protein myosin-1c to produce a mechanical amplifier and oscillator. Acting through the piezoelectric membrane protein prestin, electrical responses also cause outer hair cells to elongate and shorten, thus pumping energy into the basilar membrane's movements. The two forms of motility constitute an active process that amplifies mechanical inputs, sharpens frequency discrimination, and confers a compressive nonlinearity on responsiveness. These features arise because the active process operates near a Hopf bifurcation, the generic properties of which explain several key features of hearing. Moreover, when the gain of the active process rises sufficiently in ultraquiet circumstances, the system traverses the bifurcation and even a normal ear actually emits sound. The remarkable properties of hearing thus stem from the propagation of traveling waves on a nonlinear and excitable medium.
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