Alexander A. Spector
Mohammed Ameen
Department of Biomedical Engineering
and Center for Computational
Medicine and Biology,
Johns Hopkins University,
720 Rutland Ave.,
Baltimore, MD 21205
Panos G. Charalambides
Department of Mechanical Engineering,
University of Maryland,
Baltimore County,
1000 Hilltop Circle,
Baltimore, MD 21250
Aleksander S. Popel
Department of Biomedical Engineering
and Center for Computational
Medicine and Biology,
Johns Hopkins University,
720 Rutland Ave.,
Baltimore, MD 21205
Nanostructure, Effective
Properties, and Deformation
Pattern of the Cochlear Outer
Hair Cell Cytoskeleton
We consider the mechanical properties of the outer hair cell cytoskeleton. The cytoskel-
eton is represented as a set of microdomains of different sizes and orientations composed
of actin filaments and spectrin crosslinks. An intermediate material between domains is
also introduced. The domain characteristics are randomly generated and the histograms
of the cytoskeleton stiffness moduli are obtained. We solve an inverse problem and esti-
mate the stiffness of the crosslink and connective molecule in the intermediate material.
We discovered a pattern of highly inhomogeneous deformation of the cytoskeleton where
the circumferential strain is primarily determined by the deformation of the intermediate
material. DOI: 10.1115/1.1448521
Introduction
Outer hair cells, receptor/effector cells in the cochlea of the
mammalian ear, play a critical role in the active amplification,
sharp frequency selectivity, and characteristic nonlinearities of the
cochlea 1–3. The outer hair cell exhibits a unique form of mo-
tility, named electromotility 4, changing its length in response to
changes of the cell membrane wall electric potential. The outer
hair cells produce the active force 5,6, affect vibration of the
basilar membrane and other cochlear components 7–9, and pro-
vide energy for the active processes in the cochlea. The outer hair
cell is an elongated cylinder with a pressurized liquid core
bounded by a three-layer composite wall 1. The cell cytoskel-
eton is represented by the intermediate layer between the outer-
most plasma membrane and the innermost subsurface cisternae.
The cytoskeleton, which supports the cell’s cylindrical shape, is
important for normal turgor pressure in the cell. The cytoskeleton
is also critical for the active force production, a mechanism that
includes generation of the active strains in the plasma membrane
and their transmission through the composite cell wall 10.
In first experimental studies with demembranated cells 11, the
molecular structure of the cytoskeleton was analyzed and its lon-
gitudinal stiffness was measured. As a result of such analysis, a
model of the cytoskeleton as a regular two-dimensional network
of coiled helical actin filaments connected by longitudinal spectrin
crosslinks was proposed. The connection of the cytoskeleton to
the plasma membrane was studied, and the geometric parameters
of a system of radial pillars between the two components of the
cell wall were estimated 12. Later, it was discovered 13 that
the outer hair cell cytoskeleton has a more complicated, less regu-
lar, nanostructure. It was shown that the cytoskeleton is composed
of small domains of different sizes 200–1000 nm long and ori-
entations, where each domain is composed of actin filaments and
spectrin crosslinks. The nanostructure of the cytoskeleton is such
that its mechanical properties in the longitudinal along the cell
and circumferential around the cell directions are expected to be
different. Indeed, significant anisotropy was shown by directly
measuring the longitudinal and circumferential stiffness of an iso-
lated cytoskeleton 14. The cytoskeleton determines effective an-
isotropy of the whole outer hair cell wall because other compo-
nents of the wall are practically isotropic. Anisotropy of the whole
wall was estimated and the ratio of the circumferential stiffness
modulus over that for the longitudinal direction was found to be in
the range 3.5–4 15–17. In another study 18, anisotropy of the
outer hair cell wall was also confirmed, but the ratio of the stiff-
ness moduli was close to 1.5. The cytoskeleton in other cells has
been a topic of intensive studies because of its importance for the
cell structural integrity, deformability, and signal transduction.
The behavior and properties of the red blood cell cytoskeleton
19–23 and effective moduli of the endothelial cell cytoskeleton
24 were analyzed on the basis of these cells’ nanostructure.
Modeling of the rearrangement of the endothelial cell cytoskel-
eton in response to external forces stretches or concentration of
the filaments was also developed 25,26.
In the present paper, we consider the multiple-domain nano-
structure of the outer hair cell cytoskeleton and introduce an in-
termediate material connecting adjacent domains Fig. 1. We con-
sider random variation of the major intradomain geometric
parameters together with domain orientation and size. We assume
that these characteristics are distributed within ranges known from
experimental measurements. By using the finite element method
and generating the random parameters of the model, we obtain
histograms of the elements of the 33 symmetric matrix of the
anisotropic stiffness moduli of the cytoskeleton. We find that the
cytoskeleton exhibits a form of anisotropy more general than
orthotropy. By applying our model to experimental values of the
longitudinal and circumferential stiffness of the cytoskeleton, we
estimate the stiffness of the molecules entering our model. We
show that the stiffness of the hypothetical connective molecule in
the intermediate material is close to that of the spectrin crosslink.
Contributed by the Bioengineering Division for publication in the JOURNAL OF
BIOMECHANICAL ENGINEERING. Manuscript received by the Bioengineering Divi-
sion April 2001; revised manuscript received November 2001. Associate Editor: C.
Dong.
180 Õ Vol. 124, APRIL 2002 Copyright © 2002 by ASME Transactions of the ASME