Effects of extracellular Ca2+ concentration on hair-bundle stiffness and gating-spring integrity in hair cells

When a hair cell is stimulated by positive deflection of its hair bundle, increased tension in gating springs opens transduction channels, permitting cations to enter stereocilia and depolarize the cell. Ca2+ is thought to be required in mechanoelectrical transduction, for exposure of hair bundles to Ca2+ chelators eliminates responsiveness by disrupting tip links, filamentous interstereociliary connections that probably are the gating springs. Ca2+ also participates in adaptation to stimuli by controlling the activity of a molecular motor that sets gating-spring tension. Using a flexible glass fiber to measure hair-bundle stiffness, we investigated the effect of Ca2+ concentration on stiffness before and after the disruption of gating springs. The stiffness of intact hair bundles depended nonmonotonically on the extracellular Ca2+ concentration; the maximal stiffness of ≈1200 μN⋅m−1 occurred when bundles were bathed in solutions containing 250 μM Ca2+, approximately the concentration found in frog endolymph. For cells exposed to solutions with sufficient chelator capacity to reduce the Ca2+ concentration below ≈100 nM, hair-bundle stiffness fell to ≈200 μN⋅m−1 and no longer exhibited Ca2+-dependent changes. Because cells so treated lost mechanoelectrical transduction, we attribute the reduction in bundle stiffness to tip-link disruption. The results indicate that gating springs are not linearly elastic; instead, they stiffen with increased strain, which rises with adaptation-motor activity at the physiological extracellular Ca2+ concentration.

Torsional directed walks, entropic elasticity, and DNA twist stiffness

DNA and other biopolymers differ from classical polymers because of their torsional stiffness. This property changes the statistical character of their conformations under tension from a classical random walk to a problem we call the “torsional directed walk.” Motivated by a recent experiment on single lambda-DNA molecules [Strick, T. R., Allemand, J.-F., Bensimon, D., Bensimon, A. & Croquette, V. (1996) Science 271, 1835–1837], we formulate the torsional directed walk problem and solve it analytically in the appropriate force regime. Our technique affords a direct physical determination of the microscopic twist stiffness C and twist-stretch coupling D relevant for DNA functionality. The theory quantitatively fits existing experimental data for relative extension as a function of overtwist over a wide range of applied force; fitting to the experimental data yields the numerical values C = 120 nm and D = 50 nm. Future experiments will refine these values. We also predict that the phenomenon of reduction of effective twist stiffness by bend fluctuations should be testable in future single-molecule experiments, and we give its analytic form.

Geometric constraints explain much of the species richness pattern in African birds

The world contains boundaries (e.g., continental edge for terrestrial taxa) that impose geometric constraints on the distribution of species ranges. Thus, contrary to traditional thinking, the expected species richness pattern in absence of ecological or physiographical factors is unlikely to be uniform. Species richness has been shown to peak in the middle of a bounded one-dimensional domain, even in the absence of ecological or physiographical factors. Because species ranges are not linear, an extension of the approach to two dimensions is necessary. Here we present a two-dimensional null model accounting for effects of geometric constraints. We use the model to examine the effects of continental edge on the distribution of terrestrial animals in Africa and compare the predictions with the observed pattern of species richness in birds endemic to the continent. Latitudinal, longitudinal, and two-dimensional patterns of species richness are predicted well from the modeled null effects alone. As expected, null effects are of high significance for wide ranging species only. Our results highlight the conceptual significance of an until recently neglected constraint from continental shape alone and support a more cautious analysis of species richness patterns at this scale.

Geometric incompatibility in a fault system.

Interdependence between geometry of a fault system, its kinematics, and seismicity is investigated. Quantitative measure is introduced for inconsistency between a fixed configuration of faults and the slip rates on each fault. This measure, named geometric incompatibility (G), depicts summarily the instability near the fault junctions: their divergence or convergence ("unlocking" or "locking up") and accumulation of stress and deformations. Accordingly, the changes in G are connected with dynamics of seismicity. Apart from geometric incompatibility, we consider deviation K from well-known Saint Venant condition of kinematic compatibility. This deviation depicts summarily unaccounted stress and strain accumulation in the region and/or internal inconsistencies in a reconstruction of block- and fault system (its geometry and movements). The estimates of G and K provide a useful tool for bringing together the data on different types of movement in a fault system. An analog of Stokes formula is found that allows determination of the total values of G and K in a region from the data on its boundary. The phenomenon of geometric incompatibility implies that nucleation of strong earthquakes is to large extent controlled by processes near fault junctions. The junctions that have been locked up may act as transient asperities, and unlocked junctions may act as transient weakest links. Tentative estimates of K and G are made for each end of the Big Bend of the San Andreas fault system in Southern California. Recent strong earthquakes Landers (1992, M = 7.3) and Northridge (1994, M = 6.7) both reduced K but had opposite impact on G: Landers unlocked the area, whereas Northridge locked it up again.