The Cochlear Tuning Curve

The tuning curve of the cochlea measures how large an input is required to elicit a given output level as a function of the frequency. It is a fundamental object of auditory theory, for it summarizes how to infer what a sound was on the basis of the cochlear output. A simple model is presented showing that only two elements are sufficient for establishing the cochlear tuning curve: a broadly tuned traveling wave, moving unidirectionally from high to low frequencies, and a set of mechanosensors poised at the threshold of an oscillatory (Hopf) instability. These two components suffice to generate the various frequency-response regimes which are needed for a cochlear tuning curve with a high slope

Essential nonlinearities in hearing

Our hearing organ, the cochlea, evidently poises itself at a Hopf bifurcation to maximize tuning and amplification. We show that in this condition several effects are expected to be generic: compression of the dynamic range, infinitely shrap tuning at zero input, and generation of combination tones. These effects are "essentially" nonlinear in that they become more marked the smaller the forcing: there is no audible sound soft enough not to evoke them. All the well-documented nonlinear aspects of hearing therefore appear to be consequences of the same underlying mechanism.Comment: 4 pages, 3 figure

Self-tuning to the Hopf bifurcation in fluctuating systems

The problem of self-tuning a system to the Hopf bifurcation in the presence of noise and periodic external forcing is discussed. We find that the response of the system has a non-monotonic dependence on the noise-strength, and displays an amplified response which is more pronounced for weaker signals. The observed effect is to be distinguished from stochastic resonance. For the feedback we have studied, the unforced self-tuned Hopf oscillator in the presence of fluctuations exhibits sharp peaks in its spectrum. The implications of our general results are briefly discussed in the context of sound detection by the inner ear.Comment: 37 pages, 7 figures (8 figure files

Genetic Background of Prop1df Mutants Provides Remarkable Protection Against Hypothyroidism-Induced Hearing Impairment

Hypothyroidism is a cause of genetic and environmentally induced deafness. The sensitivity of cochlear development and function to thyroid hormone (TH) mandates understanding TH action in this sensory organ. Prop1df and Pou1f1dw mutant mice carry mutations in different pituitary transcription factors, each resulting in pituitary thyrotropin deficiency. Despite the same lack of detectable serum TH, these mutants have very different hearing abilities: Prop1df mutants are mildly affected, while Pou1f1dw mutants are completely deaf. Genetic studies show that this difference is attributable to the genetic backgrounds. Using embryo transfer, we discovered that factors intrinsic to the fetus are the major contributor to this difference, not maternal effects. We analyzed Prop1df mutants to identify processes in cochlear development that are disrupted in other hypothyroid animal models but protected in Prop1df mutants by the genetic background. The development of outer hair cell (OHC) function is delayed, but Prestin and KCNQ4 immunostaining appear normal in mature Prop1df mutants. The endocochlear potential and KCNJ10 immunostaining in the stria vascularis are indistinguishable from wild type, and no differences in neurofilament or synaptophysin staining are evident in Prop1df mutants. The synaptic vesicle protein otoferlin normally shifts expression from OHC to IHC as temporary afferent fibers beneath the OHC regress postnatally. Prop1df mutants exhibit persistent, abnormal expression of otoferlin in apical OHC, suggesting delayed maturation of synaptic function. Thus, the genetic background of Prop1df mutants is remarkably protective for most functions affected in other hypothyroid mice. The Prop1df mutant is an attractive model for identifying the genes that protect against deafness

Are biological systems poised at criticality?

Many of life's most fascinating phenomena emerge from interactions among many elements--many amino acids determine the structure of a single protein, many genes determine the fate of a cell, many neurons are involved in shaping our thoughts and memories. Physicists have long hoped that these collective behaviors could be described using the ideas and methods of statistical mechanics. In the past few years, new, larger scale experiments have made it possible to construct statistical mechanics models of biological systems directly from real data. We review the surprising successes of this "inverse" approach, using examples form families of proteins, networks of neurons, and flocks of birds. Remarkably, in all these cases the models that emerge from the data are poised at a very special point in their parameter space--a critical point. This suggests there may be some deeper theoretical principle behind the behavior of these diverse systems.Comment: 21 page

Evidence of a Hopf Bifurcation in Frog Hair Cells

The membrane potential of hair cells in the low-frequency hearing organ of the bullfrog, the amphibian papilla, sinusoidally oscillates at small amplitude in the absence of acoustical input. We stimulate the cell with a series of periodic currents close to this natural frequency and observe that its current-to-voltage transfer function is compressively nonlinear, having a large gain for small stimuli and a smaller gain for larger currents. Along with the spontaneous oscillation, this implies that the cell is poised close to a dynamical instability such as a Hopf bifurcation, because distant from the instability the transfer function becomes linear. The cell’s frequency selectivity is enhanced for small stimuli. Simulations show that the cell’s membrane capacitance is effectively reduced due to a current gain provided by this dynamical instability. We propose that the Hopf resonance is widely used by transducer cells on the sensory periphery to achieve small-signal amplification.This work was supported by National Institutes of Health Grant DC00241 to Dr. A. J. Hudspeth. During the conduct of this research M.O. was an Associate of Howard Hughes Medical Institute.Peer reviewe

Hopf bifurcations and hair cells

22 pages, 8 figures.-- Pre-print archive.The Hopf bifurcation is the dynamical instability which occurs in a feedback amplifier as the positive feedback is increased to the point where the system starts to oscillate spontaneously. The howl heard in a public address system when the presenter moves so the microphone gets too close to the loudspeaker is an example of increased positive feedback leading to oscillatory behaviour through a Hopf bifurcation. Hair cells are the sensory cells responsible for hearing and balance; they contain mechanosensitive transducer channels that convert mechanical vibration into an oscillation of their membrane potential. In many hair cells the membrane potential sinusoidally oscillates at small amplitude without input; their input-output transfer function has a large gain for small input and a reduced gain for larger inputs. These and other features are easily explained if hair cells are poised at a Hopf bifurcation. An amplifier poised at the Hopf bifurcation will have a compressively-nonlinear transfer function and also infinitely sharp tuning for vanishingly small input. The cube-root shape of its transfer function provides for an extraordinarily large gain for a small input signal at the natural frequency and a reduced gain for larger inputs. Moreover, any biosensor for detecting periodic signals of any sort would enjoy these great advantages by employing this commonly occurring instability.Peer reviewe

Stochastic Modelling of Coherent Phenomena in Strongly Inhomogeneous Media.

A procedure of numerical simulation for coherent phenomena in multiply scattering media is developed on the basis of the juxtaposition of a Monte Carlo stochastic method with an iterative approach to the solution of the Bethe- Salpeter equation. The time correlation function and the interference component of coherent backscattering are calculated for scalar and electromagnetic fields. The results of simulation are in good agreement with experimental results, as well as with theoretical results obtained by generalizing the Milne solution

Coherent multiple scattering effects and Monte Carlo method

Based on the comparison of the iteration procedure of solving the Bethe-Salpeter equation and the Monte Carlo method, we developed a method for simulating coherent multiple-scattering effects within the framework of a unified stochastic approach. The time correlation function and the interference component were calculated for the coherent backscattering from a multiply scattering medium