A Biophysical Model for the Staircase Geometry of Stereocilia

Abstract

Cochlear hair cell bundles, made up of 10s to 100s of individual stereocilia, are essential for hearing, and even relatively minor structural changes, due to mutations or injuries, can result in total deafness. Consistent with its specialized role, the staircase geometry (SCG) of hair cell bundles presents one of the most striking, intricate, and precise organizations of actin-based cellular shapes. Composed of rows of actin-filled stereocilia with increasing lengths, the hair cell's staircase-shaped bundle is formed from a progenitor field of smaller, thinner, and uniformly spaced microvilli with relatively invariant lengths. While recent genetic studies have provided a significant increase in information on the multitude of stereocilia protein components, there is currently no model that integrates the basic physical forces and biochemical processes necessary to explain the emergence of the SCG. We propose such a model derived from the biophysical and biochemical characteristics of actin-based protrusions. We demonstrate that polarization of the cell's apical surface, due to the lateral polarization of the entire epithelial layer, plays a key role in promoting SCG formation. Furthermore, our model explains many distinct features of the manifestations of SCG in different species and in the presence of various deafness-associated mutations.

Fig 1. The pushing force resulting from two different promoters of actin polymerization, with different saturation heights, may result in multiple steady-state solutions.

The purple dash-dot and dotted lines are the concentration profiles of the two promoters at the tip. The blue line is the pushing force due to the polymerization rate determined by the promoter concentrations at the tip, and the green line is the restoring force, which is dominated by actin-membrane myosin connectors. The red circles mark the stable steady-state heights, h _st (Eq 2).

Fig 2

(a) Calculated heights and radii using the theoretical model, with the steady-state solutions indicated by the red circles. Here we take a linear spatial gradient in γ _c, and a constant polymerization rate. We get a staircase structure of constant differences in stereocilia heights, but fixed radii (except for the shortest row that are slightly thinner). This result from the model is illustrated in (b). In (c), (d) we compare to the mammalian vestibular stereocilia bundles [26] (Sekerková G et al. (2011) Roles of the espin actin-bundling proteins in the morphogenesis and stabilization of hair cell stereocilia revealed in CBA/CaJ congenic jerker mice. PLoS Genet, 7(3), e1002032-e1002032). The main part of the vestibular bundle has the properties shown in (a,b): stereocilia of equal width (except for thinner first and shortest row), and height increases at a constant gradient between the rows (except for the tallest rows).

Fig 3

(a) Calculated heights and radii using the theoretical model, with the steady-state solutions indicated by the red circles. Here we take a linear spatial gradient in γ _c, and a polymerization rate A(h) that increases with height (as shown in the inset). We get a staircase structure (b) with radii that become smaller for longer stereocilia (c), and a non-linear ratio in the heights of the rows (d). The non-linear growth of the height and the corresponding decrease in radius [2], are due to the increase in the polymerization rate A(h) with the height.

Fig 4

(a) Calculated heights and radii using the theoretical model, with the St.St solutions indicated by the red circles. Here we take a linear spatial gradient in γ _c, and a polymerization rates A(h) that increases sharply with height (as shown in the inset). We get a staircase structure (b) a large jump in height for the first (tallest) row. This row may be either thinner or thicker than the other rows [2], as indicated by the solid green line (a) and dark blue shade in (b) and dashed green line (a) and the light blue shade (b) respectively. This result from the model compares well with the stereocilia bundle of the mammalian inner-hair cell (c) [26] (Sekerková G et al. (2011) Roles of the espin actin-bundling proteins in the morphogenesis and stabilization of hair cell stereocilia revealed in CBA/CaJ congenic jerker mice. PLoS Genet, 7(3), e1002032-e1002032).

Fig 5. We demonstrate the effect of removal of the height-polymerization feedback, i.e. the increasing relation of A(h) on h.

(a) Solid lines show the (normal) condition where A(h) increases with the height (as shown in the inset), and the stereocilia heights increase non-linearly (black circles, similar to Figs 3 and 4). The dashed lines show the result of reducing the polymerization rate to a constant (independent of the height), resulting in lower and thicker stereocilia (red circles). These two different SCGs are illustrated in (b).(c) Experimental results [32] comparing mammalian (mouse) stereocilia for normal inner-hair-cells, and when Eps8 is knocked out [32] (Zampini V et al. (2011) Eps8 Regulates Hair Bundle Length and Functional Maturation of Mammalian Auditory Hair Cells. PLoS Biol 9(4): e1001048. doi:10.1371/journal.pbio.1001048).