Johannes Baumgart

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.

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.

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.

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.

EFFICIENT SOUND POWER COMPUTATION OF OPEN STRUCTURES WITH INFINITE/FINITE ELEMENTS AND BY MEANS OF THE PADÉ-VIA-LANCZOS ALGORITHM

The solution of time-harmonic acoustic problems suffers from a frequency dependency which usually requires to solve the systems for many discrete frequencies independently. Among others, the Pade-via-Lanczos approximation provides an efficient solution. Herein, this method is applied to the external acoustic problem by using a finite and infinite element formulation. The state-space system matrix is first reduced to a condensed transfer matrix which is approximated in a power series, i.e. Pade approximation. The coefficients of this power series are reconstructed by using a Krylov basis, i.e. Lanczos method. Based on this method, the authors provide a formulation for the radiated sound power. The necessary integration over the boundary for the sound power is done in the first vectors of the Lanczos method. Thus the scalar sound power can be approximated in a certain frequency band by means of a transfer matrix, which is several orders of magnitude smaller than the total numbers of degrees of freedom of the overall problem. The error of this additional approximation can be estimated. The method is tested in an example of an open cavity including two loadcases, one representing a cavity with an open window, the other one being a radiating obstacle.

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.

Kinetochore Microtubules indirectly link Chromosomes and Centrosomes in C. elegans Mitosis

The mitotic spindle is a dynamic microtubule-based apparatus that ensures the faithful segregation of chromosomes by connecting chromosomes to spindle poles. How this pivotal connection is established and maintained during mitosis is currently debated. Here we combined large-scale serial electron tomography with live-cell imaging to uncover the spatial and dynamic organization of microtubules in the mitotic spindles in C. elegans. With this we quantified the position of microtubule minus and plus-ends as well as distinguished the different classes of microtubules, such as kinetochore, astral and spindle microtubules with their distinct properties. Although microtubules are nucleated from the centrosomes, we find only a few, if any, kinetochore microtubules directly connected to the spindle poles, suggesting an indirect pole to chromosome connection. We propose a model of kinetochore microtubule assembly and disassembly, in which microtubules undergo minus-end depolymerisation, resulting in a detachment from the centrosome. Our reconstructions and analyses of complete spindles expand our understanding of spindle architecture beyond the light microscopic limit.The mitotic spindle ensures the faithful segregation of chromosomes. To discover the nature of the crucial centrosome-to-chromosome connection during mitosis, we combined the first large-scale serial electron tomography of whole mitotic spindles in early C. elegans embryos with live-cell imaging. Using tomography, we reconstructed the positions of all microtubules in 3D, and identified their plus- and minus-ends. We classified them as kinetochore (KMTs), spindle (SMTs), or astral microtubules (AMTs) according to their positions, and quantified 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 are 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.

Modelling motions within the organ of Corti

Most cochlear models used to describe the basilar membrane vibration along the cochlea are concerned with macromechanics, and often assume that the organ of Corti moves as a single unit, ignoring the individual motion of different components. New experimental technologies provide the opportunity to measure the dynamic behaviour of different components within the organ of Corti, but only for certain types of excitation. It is thus still difficult to directly measure every aspect of cochlear dynamics, particularly for acoustic excitation of the fully active cochlea. The present work studies the dynamic response of a model of the cross-section of the cochlea, at the microscopic level, using the finite element method. The elastic components are modelled with plate elements and the perilymph and endolymph are modelled with inviscid fluid elements. The individual motion of each component within the organ of Corti is calculated with dynamic pressure loading on the basilar membrane and the motions of the experimentally accessible parts are compared with measurements. The reticular lamina moves as a stiff plate, without much bending, and is pivoting around a point close to the region of the inner hair cells, as observed experimentally. The basilar membrane shows a slightly asymmetric mode shape, with maximum displacement occurring between the second-row and the third-row of the outer hair cells. The dynamics responses is also calculated, and compared with experiments, when driven by the outer hair cells. The receptance of the basilar membrane motion and of the deflection of the hair bundles of the outer hair cells is thus obtained, when driven either acoustically or electrically. In this way, the fully active linear response of the basilar membrane to acoustic excitation can be predicted by using a linear superposition of the calculated receptances and a defined gain function for the outer hair cell feedback.

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.