Active control of waves in a cochlear model with subpartitions.

Multiscale asymptotic methods developed previously to study macromechanical wave propagation in cochlear models are generalized here to include active control of a cochlear partition having three subpartitions, the basilar membrane, the reticular lamina, and the tectorial membrane. Activation of outer hair cells by stereocilia displacement and/or by lateral wall stretching result in a frequency-dependent force acting between the reticular lamina and basilar membrane. Wavelength-dependent fluid loads are estimated by using the unsteady Stokes' equations, except in the narrow gap between the tectorial membrane and reticular lamina, where lubrication theory is appropriate. The local wavenumber and subpartition amplitude ratios are determined from the zeroth order equations of motion. A solvability relation for the first order equations of motion determines the subpartition amplitudes. The main findings are as follows: The reticular lamina and tectorial membrane move in unison with essentially no squeezing of the gap; an active force level consistent with measurements on isolated outer hair cells can provide a 35-dB amplification and sharpening of subpartition waveforms by delaying dissipation and allowing a greater structural resonance to occur before the wave is cut off; however, previously postulated activity mechanisms for single partition models cannot achieve sharp enough tuning in subpartitioned models.

Compression, gain, and nonlinear distortion in an active cochlear model with subpartitions

The propagation of inhomogeneous, weakly nonlinear waves is considered in a cochlear model having two degrees of freedom that represent the transverse motions of the tectorial and basilar membranes within the organ of Corti. It is assumed that nonlinearity arises from the saturation of outer hair cell active force generation. I use multiple scale asymptotics and treat nonlinearity as a correction to a linear hydroelastic wave. The resulting theory is used to explain experimentally observed features of the response of the cochlear partition to a pure tone, including: the amplification of the response in a healthy cochlea vs a dead one; the less than linear growth rate of the response to increasing sound pressure level; and the amount of distortion to be expected at high and low frequencies at basal and apical locations, respectively. I also show that the outer hair cell nonlinearity generates retrograde waves.

A transgenic mouse model with an inducible skin blistering disease phenotype

One of the current limitations of gene transfer protocols involving mammalian genomes is the lack of spatial and temporal control over the desired gene manipulation. Starting from a human keratin gene showing a complex regulation as a template, we identified regulatory sequences that confer inducible gene expression in a subpopulation of keratinocytes in stratified epithelia of adult transgenic mice. We used this cassette to produce transgenic mice with an inducible skin blistering phenotype mimicking a form of epidermolytic hyperkeratosis, a keratin gene disorder. Upon induction by topical application of a phorbol ester, the mutant keratin transgene product accumulates in the differentiating layers of epidermis, leading to keratinocyte lysis after application of mechanical trauma. This mouse model will allow for a better understanding of the complex relationship between keratin mutation, keratinocyte cytoarchitecture, and hypersensitivity to trauma. The development of an inducible expression vector showing an exquisite cellular specificity has important implications for manipulating genes in a spatially and temporally controlled fashion in transgenic mice, and for the design of gene therapy strategies using skin as a tissue source for the controlled delivery of foreign substances.

The kinesin walk: a dynamic model with elastically coupled heads.

Recently individual two-headed kinesin molecules have been studied in in vitro motility assays revealing a number of their peculiar transport properties. In this paper we propose a simple and robust model for the kinesin stepping process with elastically coupled Brownian heads that show all of these properties. The analytic and numerical treatment of our model results in a very good fit to the experimental data and practically has no free parameters. Changing the values of the parameters in the restricted range allowed by the related experimental estimates has almost no effect on the shape of the curves and results mainly in a variation of the zero load velocity that can be directly fitted to the measured data. In addition, the model is consistent with the measured pathway of the kinesin ATPase.

Unusual dynamics of extinction in a simple ecological model.

Studies on natural populations and harvesting biological resources have led to the view, commonly held, that (i) populations exhibiting chaotic oscillations run a high risk of extinction; and (ii) a decrease in emigration/exploitation may reduce the risk of extinction. Here we describe a simple ecological model with emigration/depletion that shows behavior in contrast to this. This model displays unusual dynamics of extinction and survival, where populations growing beyond a critical rate can persist within a band of high depletion rates, whereas extinction occurs for lower depletion rates. Though prior to extinction at lower depletion rates the population exhibits chaotic dynamics with large amplitudes of variation and very low minima, at higher depletion rates the population persists at chaos but with reduced variation and increased minima. For still higher values, within the band of persistence, the dynamics show period reversal leading to stability. These results illustrate that chaos does not necessarily lead to population extinction. In addition, the persistence of populations at high depletion rates has important implications in the considerations of strategies for the management of biological resources.