Chemomechanical regulation of myosin Ic cross-bridges: Deducing the elastic properties of an ensemble from single-molecule mechanisms

Volterra-series approach to stochastic nonlinear dynamics: Linear response of the Van der Pol oscillator driven by white noise

The Van der Pol equation is a paradigmatic model of relaxation oscillations. This remarkable nonlinear phenomenon of self-sustained oscillatory motion underlies important rhythmic processes in nature and electrical engineering. Relaxation oscillations in a real system are usually coupled to environmental noise, which further enriches their dynamics, but makes theoretical analysis of such systems and determination of the equation parameter values a difficult task. In a companion paper we have proposed an analytic approach to a similar problem for another classical nonlinear model-the bistable Duffing oscillator. Here we extend our techniques to the case of the Van der Pol equation driven by white noise. We analyze the statistics of solutions and propose a method to estimate parameter values from the oscillator's time series. We use experimental data of active oscillations in a biophysical system to demonstrate how our method applies to real observations and can be generalized for more complex models.

Force-Dependent Unbinding Rate of Molecular Motors from Stationary Optical Trap Data

Molecular motors walk along filaments until they detach stochastically with a force-dependent unbinding rate. Here, we show how this unbinding rate can be obtained from the analysis of experimental data of molecular motors moving in stationary optical traps. Two complementary methods are presented, based on the analysis of the distribution for the unbinding forces and of the motor's force traces. In the first method, analytically derived force distributions for slip bonds, slip-ideal bonds, and catch bonds are used to fit the cumulative distributions of the unbinding forces. The second method is based on the statistical analysis of the observed force traces. We validate both methods with stochastic simulations and apply them to experimental data for kinesin-1.

Beyond Cell-Cell Adhesion: Sensational Cadherins for Hearing and Balance

Cadherins form a large family of proteins often involved in calcium-dependent cellular adhesion. Although classical members of the family can provide a physical bond between cells, a subset of special cadherins use their extracellular domains to interlink apical specializations of single epithelial sensory cells. Two of these cadherins, cadherin-23 (CDH23) and protocadherin-15 (PCDH15), form extracellular "tip link" filaments that connect apical bundles of stereocilia on hair cells essential for inner-ear mechanotransduction. As these bundles deflect in response to mechanical stimuli from sound or head movements, tip links gate hair-cell mechanosensitive channels to initiate sensory perception. Here, we review the unusual and diverse structural properties of these tip-link cadherins and the functional significance of their deafness-related missense mutations. Based on the structural features of CDH23 and PCDH15, we discuss the elasticity of tip links and models that bridge the gap between the nanomechanics of cadherins and the micromechanics of hair-cell bundles during inner-ear mechanotransduction.

Thermal Excitation of the Mechanotransduction Apparatus of Hair Cells

Although a hair bundle is normally deflected by mechanical stimuli, we found that irradiation of a hair cell from the bullfrog's sacculus with ultraviolet light causes rapid motion of the hair bundle toward its tall edge. This movement is associated with opening of mechanotransduction channels and disappears when tip links are disrupted. We localized the absorptive element responsible for the motion to the region directly below the hair bundle and measured an action spectrum similar to the absorption spectra of mitochondrial constituents. Temperature measurements revealed heating around the site of absorption; direct heating of the hair bundle confirmed that the response to light is mediated through heat. Although mechanical offsets of the hair bundle revealed that heat softens gating springs, it also acts directly to open transduction channels. This study identifies an unconventional method of hair-cell stimulation and clarifies the previously unexplained sensitivity of auditory organs to thermal stimulation.