A transfer matrix for the input impedance of weakly tapered, dissipative cones as of wind instruments (L).

A formula for the local acoustical admittance in a conical waveguide with viscous and thermal losses given by Nederveen [(1969). Acoustical Aspects of Woodwind Instruments (Frits Knuf, Amsterdam)] is rewritten as an impedance transmission matrix. Based on a self-consistent approximation for the cone, it differs from other one-dimensional transmission matrices used in musical acoustics, which implicitly include the loss model of a cylinder. The resonance frequencies of air columns calculated with this transmission matrix are in better agreement with more comprehensive models. Even for long cones with a slight taper, there is no need to discretize along the axis.

Soluble tubulin is significantly enriched at mitotic centrosomes.

During mitosis, the centrosome expands its capacity to nucleate microtubules. Understanding the mechanisms of centrosomal microtubule nucleation is, however, constrained by a lack of knowledge of the amount of soluble and polymeric tubulin at mitotic centrosomes. Here we combined light microscopy and serial-section electron tomography to measure the amount of dimeric and polymeric tubulin at mitotic centrosomes in early C. elegans embryos. We show that a C. elegans one-cell stage centrosome at metaphase contains >10,000 microtubules with a total polymer concentration of 230 µM. Centrosomes concentrate soluble α/ß tubulin by about 10-fold over the cytoplasm, reaching peak values of 470 µM, giving a combined total monomer and polymer tubulin concentration at centrosomes of up to 660 µM. These findings support in vitro data suggesting that microtubule nucleation in C. elegans centrosomes is driven in part by concentrating soluble tubulin.

Positioning of Particles in Active Droplets.

Chemically active droplets are nonequilibrium systems that combine phase separation with chemical reactions. We here investigate how the activity introduced by the chemical reactions influences solid particles inside such droplets. We find that passive particles are centered in active droplets governed by first-order reactions. In autocatalytic active droplets, only catalytically active particles can be centered. An example of such systems in biology are centrosomes. Our study can account for the observed positioning of centrioles and provides a general mechanism to control the position of particles within chemically active droplets.

C. elegans chromosomes connect to centrosomes by anchoring into the spindle network.

The mitotic spindle ensures the faithful segregation of chromosomes. Here we combine the first large-scale serial electron tomography of whole mitotic spindles in early C. elegans embryos with live-cell imaging to reconstruct all microtubules in 3D and identify their plus- and minus-ends. We classify them as kinetochore (KMTs), spindle (SMTs) or astral microtubules (AMTs) according to their positions, and quantify distinct properties of each class. While our light microscopy and mutant studies show that microtubules are nucleated from the centrosomes, we find only a few KMTs directly connected to the centrosomes. Indeed, by quantitatively analysing several models of microtubule growth, we conclude that minus-ends of KMTs have selectively detached and depolymerized from the centrosome. In toto, our results show that the connection between centrosomes and chromosomes is mediated by an anchoring into the entire spindle network and that any direct connections through KMTs are few and likely very transient.

Finite-element model of the active organ of Corti.

The cochlear amplifier that provides our hearing with its extraordinary sensitivity and selectivity is thought to be the result of an active biomechanical process within the sensory auditory organ, the organ of Corti. Although imaging techniques are developing rapidly, it is not currently possible, in a fully active cochlea, to obtain detailed measurements of the motion of individual elements within a cross section of the organ of Corti. This motion is predicted using a two-dimensional finite-element model. The various solid components are modelled using elastic elements, the outer hair cells (OHCs) as piezoelectric elements and the perilymph and endolymph as viscous and nearly incompressible fluid elements. The model is validated by comparison with existing measurements of the motions within the passive organ of Corti, calculated when it is driven either acoustically, by the fluid pressure or electrically, by excitation of the OHCs. The transverse basilar membrane (BM) motion and the shearing motion between the tectorial membrane and the reticular lamina are calculated for these two excitation modes. The fully active response of the BM to acoustic excitation is predicted using a linear superposition of the calculated responses and an assumed frequency response for the OHC feedback.

Tonotopic morphometry of the lamina reticularis of the guinea pig cochlea with associated microstructures and related mechanical implications.

Morphometry of the lamina reticularis of the guinea pig cochlea was performed using scanning electron microscopy. Seventy-four geometrical parameters of the lamina reticularis, the bundles of stereocilia, and individual stereocilia, in all rows of hair cells and within the individual hair cells, were measured at ten equally spaced locations along the longitudinal direction of the cochlea. Variations of the parameters versus the longitudinal coordinate were statistically analyzed and fitted with polynomials (constant, linear, or quadratic). Our data show that a unique set of geometrical parameters of inner and outer hair cells is typical for every frequency-dependent position at the lamina reticularis. Morphology of the outer hair cell structures varies more than respective parameters of the inner hair cells. Mechanical modeling using the obtained geometrical parameters provides a novel glance at the mechanical characteristics with respect to the cochlear tonotopy.

XMAP215 activity sets spindle length by controlling the total mass of spindle microtubules.

Metaphase spindles are microtubule-based structures that use a multitude of proteins to modulate their morphology and function. Today, we understand many details of microtubule assembly, the role of microtubule-associated proteins, and the action of molecular motors. Ultimately, the challenge remains to understand how the collective behaviour of these nanometre-scale processes gives rise to a properly sized spindle on the micrometre scale. By systematically engineering the enzymatic activity of XMAP215, a processive microtubule polymerase, we show that Xenopus laevis spindle length increases linearly with microtubule growth velocity, whereas other parameters of spindle organization, such as microtubule density, lifetime and spindle shape, remain constant. We further show that mass balance can be used to link the global property of spindle size to individual microtubule dynamic parameters. We propose that spindle length is set by a balance of non-uniform nucleation and global microtubule disassembly in a liquid-crystal-like arrangement of microtubules.

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

The detection of sound begins when energy derived from an acoustic stimulus deflects the hair bundles on top of hair cells. As hair bundles move, the viscous friction between stereocilia and the surrounding liquid poses a fundamental physical challenge to the ear's high sensitivity and sharp frequency selectivity. Part of the solution to this problem lies in the active process that uses energy for frequency-selective sound amplification. Here we demonstrate that a complementary part of the solution involves the fluid-structure interaction between the liquid within the hair bundle and the stereocilia. Using force measurement on a dynamically scaled model, finite-element analysis, analytical estimation of hydrodynamic forces, stochastic simulation and high-resolution interferometric measurement of hair bundles, we characterize the origin and magnitude of the forces between individual stereocilia during small hair-bundle deflections. We find that the close apposition of stereocilia effectively immobilizes the liquid between them, which reduces the drag and suppresses the relative squeezing but not the sliding mode of stereociliary motion. The obliquely oriented tip links couple the mechanotransduction channels to this least dissipative coherent mode, whereas the elastic horizontal top connectors that stabilize the structure further reduce the drag. As measured from the distortion products associated with channel gating at physiological stimulation amplitudes of tens of nanometres, the balance of viscous and elastic forces in a hair bundle permits a relative mode of motion between adjacent stereocilia that encompasses only a fraction of a nanometre. A combination of high-resolution experiments and detailed numerical modelling of fluid-structure interactions reveals the physical principles behind the basic structural features of hair bundles and shows quantitatively how these organelles are adapted to the needs of sensitive mechanotransduction.

The creation of geometric three-dimensional models of the inner ear based on micro computer tomography data.

The modeling of the mechanical process of hearing requires an accurate geometrical model of the inner ear (cochlea). The purpose of this study was the creation of a 3-D model of the fluid chambers of Guinea pig cochlea, which could serve as a basis for further mechanical modeling. Micro computer tomography used in this study is a noninvasive method to visualize bony structures. The visualization of the membranous labyrinth was achieved by additional staining of the specimen with OsO(4). The resulting stack of images has been transformed into a cylindrical coordinate system. To suppress noise on tomography images, a nonlinear smoothing method, anisotropic diffusion, were applied. A new approach has been proposed to estimate algorithm parameters automatically. Then, a segmentation using active contours (snakes) was performed. In this study, a new energy linking the contours on adjacent slices has been added to the standard approach. This compensates the inconsistencies between adjacent contours. The images segmented in this way were used as a basis for a 3-D reconstruction of the hearing organ.