Modeling electrically active viscoelastic membranes

Generalized Boussinesq-Scriven surface fluid model with curvature dissipation for liquid surfaces and membranes

Curvature dissipation is relevant in synthetic and biological processes, from fluctuations in semi-flexible polymer solutions, to buckling of liquid columns, tomembrane cell wall functioning. We present a micromechanical model of curvature dissipation relevant to fluid membranes and liquid surfaces based on a parallel surface parameterization and a stress constitutive equation appropriate for anisotropic fluids and fluid membranes.The derived model, aimed at high curvature and high rate of change of curvature in liquid surfaces and membranes, introduces additional viscous modes not included in the widely used 2D Boussinesq-Scriven rheological constitutive equation for surface fluids.The kinematic tensors that emerge from theparallel surface parameterization are the interfacial rate of deformation and the surface co-rotational Zaremba-Jaumann derivative of the curvature, which are used to classify all possibledissipative planar and non-planar modes. The curvature dissipation function that accounts for bending, torsion and twist rates is derived and analyzed under several constraints, including the important inextensional bending mode.A representative application of the curvature dissipation model to the periodic oscillation in nano-wrinkled outer hair cells show how and why curvature dissipation decreases with frequency, and why the 100kHz frequency range is selected. These results contribute to characterize curvature dissipation in membranes and liquid surfaces.

Chloride Anions Regulate Kinetics but Not Voltage-Sensor Qmax of the Solute Carrier SLC26a5

In general, SLC26 solute carriers serve to transport a variety of anions across biological membranes. However, prestin (SLC26a5) has evolved, now serving as a motor protein in outer hair cells (OHCs) of the mammalian inner ear and is required for cochlear amplification, a mechanical feedback mechanism to boost auditory performance. The mechanical activity of the OHC imparted by prestin is driven by voltage and controlled by anions, chiefly intracellular chloride. Current opinion is that chloride anions control the Boltzmann characteristics of the voltage sensor responsible for prestin activity, including Qmax, the total sensor charge moved within the membrane, and Vh, a measure of prestin's operating voltage range. Here, we show that standard narrow-band, high-frequency admittance measures of nonlinear capacitance (NLC), an alternate representation of the sensor's charge-voltage (Q-V) relationship, is inadequate for assessment of Qmax, an estimate of the sum of unitary charges contributed by all voltage sensors within the membrane. Prestin's slow transition rates and chloride-binding kinetics adversely influence these estimates, contributing to the prevalent concept that intracellular chloride level controls the quantity of sensor charge moved. By monitoring charge movement across frequency, using measures of multifrequency admittance, expanded displacement current integration, and OHC electromotility, we find that chloride influences prestin kinetics, thereby controlling charge magnitude at any particular frequency of interrogation. Importantly, however, this chloride dependence vanishes as frequency decreases, with Qmax asymptoting at a level irrespective of the chloride level. These data indicate that prestin activity is significantly low-pass in the frequency domain, with important implications for cochlear amplification. We also note that the occurrence of voltage-dependent charge movements in other SLC26 family members may be hidden by inadequate interrogation timescales, and that revelation of such activity could highlight an evolutionary means for kinetic modifications within the family to address hearing requirements in mammals.

Piezoelectric Effects of Materials on Bio-Interfaces

Electrical stimulation of cells and tissues is an important approach of interaction with living matter, which has been traditionally exploited in the clinical practice for a wide range of pathological conditions, in particular, related to excitable tissues. Standard methods of stimulation are, however, often invasive, being based on electrodes and wires used to carry current to the intended site. The possibility to achieve an indirect electrical stimulation, by means of piezoelectric materials, is therefore of outstanding interest for all the biomedical research, and it emerged in the latest decade as a most promising tool in many bioapplications. In this paper, we summarize the most recent achievements obtained by our group and by others in the exploitation of piezoelectric nanoparticles and nanocomposites for cell stimulation, describing the important implications that these studies present in nanomedicine and tissue engineering. A particular attention will be also dedicated to the physical modeling, which can be extremely useful in the description of the complex mechanisms involved in the mechanical/electrical transduction, yet also to gain new insights at the base of the observed phenomena.

Modified protein expression in the tectorial membrane of the cochlea reveals roles for the striated sheet matrix

The tectorial membrane (TM) of the mammalian cochlea is a complex extracellular matrix which, in response to acoustic stimulation, displaces the hair bundles of outer hair cells (OHCs), thereby initiating sensory transduction and amplification. Here, using TM segments from the basal, high-frequency region of the cochleae of genetically modified mice (including models of human hereditary deafness) with missing or modified TM proteins, we demonstrate that frequency-dependent stiffening is associated with the striated sheet matrix (SSM). Frequency-dependent stiffening largely disappeared in all three TM mutations studied where the SSM was absent either entirely or at least from the stiffest part of the TM overlying the OHCs. In all three TM mutations, dissipation of energy is decreased at low (<8 kHz) and increased at high (>8 kHz) stimulus frequencies. The SSM is composed of polypeptides carrying fixed charges, and electrostatic interaction between them may account for frequency-dependent stiffness changes in the material properties of the TM. Through comparison with previous in vivo measurements, it is proposed that implementation of frequency-dependent stiffening of the TM in the OHC attachment region facilitates interaction among tones, backward transmission of energy, and amplification in the cochlea.

Effects of plasma membrane cholesterol level and cytoskeleton F-actin on cell protrusion mechanics

Protrusions are deformations that form at the surface of living cells during biological activities such as cell migration. Using combined optical tweezers and fluorescent microscopy, we quantified the mechanical properties of protrusions in adherent human embryonic kidney cells in response to application of an external force at the cell surface. The mechanical properties of protrusions were analyzed by obtaining the associated force-length plots during protrusion formation, and force relaxation at constant length. Protrusion mechanics were interpretable by a standard linear solid (Kelvin) model, consisting of two stiffness parameters, k0 and k1 (with k0>k1), and a viscous coefficient. While both stiffness parameters contribute to the time-dependant mechanical behavior of the protrusions, k0 and k1 in particular dominated the early and late stages of the protrusion formation and elongation process, respectively. Lowering the membrane cholesterol content by 25% increased the k0 stiffness by 74%, and shortened the protrusion length by almost half. Enhancement of membrane cholesterol content by nearly two-fold increased the protrusion length by 30%, and decreased the k0 stiffness by nearly two-and-half-fold as compared with control cells. Cytoskeleton integrity was found to make a major contribution to protrusion mechanics as evidenced by the effects of F-actin disruption on the resulting mechanical parameters. Viscoelastic behavior of protrusions was further characterized by hysteresis and force relaxation after formation. The results of this study elucidate the coordination of plasma membrane composition and cytoskeleton during protrusion formation.