Forces between clustered stereocilia minimize friction in the ear on a subnanometre scale

{{Summary
 * title=Forces between clustered stereocilia minimize friction in the ear on a subnanometre scale
 * authors=Andrei S. Kozlov, Johannes Baumgart, Thomas Risler, Corstiaen P. C. Versteegh, A. J. Hudspeth
 * url=http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3150833/pdf/nihms313088.pdf
 * tags=hearing, acoustics, biophysics
 * summary=As hair bundles move, viscous friction between stereocilia and the surrounding liquid poses a physical challenge to the ear’s high sensitivity and sharp frequency selectivity. This letter proposes that some of that energy is used for frequency-selective sound amplification, through fluid–structure interaction between the liquid within the hair bundle and the stereocilia.

A dynamic model is proposed to simulate hair bundles in a viscous environment, to see what large and small scale insights could be gained. Finite-element analysis, a submodel of hydrodynamic forces, stochastic simulation, and models of interferometric measurement all aimed to simulate both a hair bundle in natural conditions and what might be observed in an experiment involving it.

Forces between stereocilia are estimated, and the results suggest that the closeness of stereocilia reduces drag between them, supporting a sliding but not a squeezing mode. Tip links may couple mechanotransduction to this low-friction sliding mode, with motion between neighboring stereocilia of less than 1nm when the hair bundle moves the larger distance [O(10nm)]needed to stimulate its channels.

Goals and Methods
On the one hand, the length scale of viscous fluids inside the ear exceeds the distance between any two stereocilia. On the other, we know stereocilia slide past one another easily, and that the ear has sharp frequency selectivity.

The goal of this paper was to identify some counterintuitive properties of a hair-bundle in viscous medium and probe the molecular-level interactions of cilia with one another and with the fluid.

A model was designed around a bullfrog hair bundle in a viscous methylcellulose solution. It was constructed to make it easy to change the properties of the stereocilia, with a fixed set of properties of the solution. An initial model focused on three parameters: pivotal stiffness, drag, and inetrial mass. This model allowed calculation of the coherence of motion of the entire bundle.

Finally, an experiment was devised to test the theory that the magnitude of relative bundle motion depends on a balance between hydrodynamic and elastic forces, with a small relative motion varying from the highly coherent Brownian motion of the bundle.

Results and Analysis
Top connectors were added with high stiffness (20mN/m), strongly increasing coherence and reducing drag. These were then replaced with tip links oriented obliquely on the stereocilia, with a stiffness of 1mN/m. This increased drag significantly. Including both connectors and tip links led to a model closer to observation: a drag coefficient that is not much dependent on frequency, and an overall bundle stiffness similar to that observed.

In the physical experiment, combination frequencies were observed in a hair bundle when it was stimulated at two different frequencies at once; something that disappeared once tip links were disrupted enzymatically. Similarly, another hair bundle in a viscous solution similar to the model was shown to gain significant drag when its top connectors were removed.
 * relevance=This work provides a detailed model of how hair bundles in the mammalian ear interact with the surrounding fluid, and can stimulate mechanotransduction with motion of less than 1 nm.  This model provides a quantitative understanding of how mechanotransduction can work, and describes ways that the structure of hair bundles can minimize viscous friction, resolving a potential confusion.

This suggests further models along these lines may be helpful }}
 * journal=Nature
 * pub_date=2011/06/16
 * doi=10.1038/nature10073
 * subject=Biology