Alexander A. Spector

Finite-element analysis of the adhesion-cytoskeleton-nucleus mechanotransduction pathway during endothelial cell rounding: axisymmetric model.

Endothelial cells possess a mechanical network connecting adhesions on the basal surface, the cytoskeleton, and the nucleus. Transmission of force at adhesions via this pathway can deform the nucleus, ultimately resulting in an alteration of gene expression and other cellular changes (mechanotransduction). Previously, we measured cell adhesion area and apparent nuclear stretch during endothelial cell rounding. Here, we reconstruct the stress map of the nucleus from the observed strains using finite-element modeling. To simulate the disruption of adhesions, we prescribe displacement boundary conditions at the basal surface of the axisymmetric model cell. We consider different scenarios of the cytoskeletal arrangement, and represent the cytoskeleton as either discrete fibers or as an effective homogeneous layer When the nucleus is in the initial (spread) state, cytoskeletal tension holds the nucleus in an elongated, ellipsoidal configuration. Loss of cytoskeletal tension during cell rounding is represented by reactive forces acting on the nucleus in the model. In our simulations of cell rounding, we found that, for both representations of the cytoskeleton, the loss of cytoskeletal tension contributed more to the observed nuclear deformation than passive properties. Since the simulations make no assumption about the heterogeneity of the nucleus, the stress components both within and on the surface of the nucleus were calculated. The nuclear stress map showed that the nucleus experiences stress on the order of magnitude that can be significant for the function of DNA molecules and chromatin fibers. This study of endothelial cell mechanobiology suggests the possibility that mechanotransduction could result, in part, from nuclear deformation, and may be relevant to angiogenesis, wound healing, and endothelial barrier dysfunction.

Effect of outer hair cell piezoelectricity on high-frequency receptor potentials

The low-pass voltage response of outer hair cells predicted by conventional equivalent circuit analysis would preclude the active force production at high frequencies. We have found that the band pass characteristics can be improved by introducing the piezoelectric properties of the cell wall. In contrast to the conventional analysis, the receptor potential does not tend to zero and at any frequency is greater than a limiting value. In addition, the phase shift between the transduction current and receptor potential tends to zero. The piezoelectric properties cause an additional, strain-dependent, displacement current in the cell wall. The wall strain is estimated on the basis of a model of the cell deformation in the organ of Corti. The limiting value of the receptor potential depends on the ratio of a parameter determined by the piezoelectric coefficients and the strain to the membrane capacitance. In short cells, we have found that for the low-frequency value of about 2-3 mV and the strain level of 0.1% the receptor potential can reach 0.4 mV throughout the whole frequency range. In long cells, we have found that the effect of the piezoelectric properties is much weaker. These results are consistent with major features of the cochlear amplifier.

Characterization of the Nuclear Deformation Caused by Changes in Endothelial Cell Shape

We investigated the mechanotransduction pathway in endothelial cells between their nucleus and adhesions to the extracellular matrix. First, we measured nuclear deformations in response to alterations of cell shape as cells detach from a flat surface. We found that the nuclear deformation appeared to be in direct and immediate response to alterations of the cell adhesion area. The nucleus was then treated as a neo-Hookean compressible material, and we estimated the stress associated with the cytoskeleton and acting on the nucleus during cell rounding. With the obtained stress field, we estimated the magnitude of the forces deforming the nucleus. Considering the initial and final components of this adhesion-cytoskeleton-nucleus force transmission pathway, we found our estimate for the internal forces acting on the nucleus to be on the same order of magnitude as previously measured traction forces, suggesting a direct mechanical link between adhesions and the nucleus.

Micropipette aspiration on the outer hair cell lateral wall.

The mechanical properties of the lateral wall of the guinea pig cochlear outer hair cell were studied using the micropipette aspiration technique. A fire-polished micropipette with an inner diameter of approximately 4 microm was brought into contact with the lateral wall and negative pressure was applied. The resulting deformation of the lateral wall was recorded on videotape and subjected to morphometric analysis. The relation between the length of the aspirated portion of the cell and aspiration pressure is characterized by the stiffness parameter, K(s) = 1.07 +/- 0.24 (SD) dyn/cm (n = 14). Values of K(s) do not correlate with the original cell length, which ranges from 29 to 74 microm. Theoretical analysis based on elastic shell theory applied to the experimental data yields an estimate of the effective elastic shear modulus, mu = 15.4 +/- 3.3 dyn/cm. These data were obtained at subcritical aspiration pressures, typically less than 10 cm H2O. After reaching a critical (vesiculation) pressure, the cytoplasmic membrane appeared to separate from the underlying structures, a vesicle with a length of 10-20 microm was formed, and the cytoplasmic membrane resealed. This vesiculation process was repeated until a cell-specific limit was reached and no more vesicles were formed. Over 20 vesicles were formed from the longest cells in the experiment.

Electromechanical Models of the Outer Hair Cell Composite Membrane

The outer hair cell (OHC) is an extremely specialized cell and its proper functioning is essential for normal mammalian hearing. This article reviews recent developments in theoretical modeling that have increased our knowledge of the operation of this fascinating cell. The earliest models aimed at capturing experimental observations on voltage-induced cellular length changes and capacitance were based on isotropic elasticity and a two-state Boltzmann function. Recent advances in modeling based on the thermodynamics of orthotropic electroelastic materials better capture the cell’s voltage-dependent stiffness, capacitance, interaction with its environment and ability to generate force at high frequencies. While complete models are crucial, simpler continuum models can be derived that retain fidelity over small changes in transmembrane voltage and strains occurring in vivo. By its function in the cochlea, the OHC behaves like a piezoelectric-like actuator, and the main cellular features can be described by piezoelectric models. However, a finer characterization of the cell’s composite wall requires understanding the local mechanical and electrical fields. One of the key questions is the relative contribution of the in-plane and bending modes of electromechanical strains and forces (moments). The latter mode is associated with the flexoelectric effect in curved membranes. New data, including a novel experiment with tethers pulled from the cell membrane, can help in estimating the role of different modes of electromechanical coupling. Despite considerable progress, many problems still confound modelers. Thus, this article will conclude with a discussion of unanswered questions and highlight directions for future research.

Estimation of elastic moduli and bending stiffness of the anisotropic outer hair cell wall

The outer hair cell makes both passive and active contributions to basilar membrane mechanics. The outer hair cell mechanics is strongly coupled to the elastic properties of the cell lateral wall. The lateral wall experiences both in-plane deformations and bending under physiological and experimental conditions. To characterize the outer hair cell wall, the model of an orthotropic cylindrical shell is used. The elastic constants of the wall are estimated by solving a set of three equations based on the analyses of three independent experiments. The first equation is derived from a new interpretation of the micropipet experiment; the other two are obtained from the axial loading and the osmotic challenge experiments. The two Youngs moduli corresponding to the longitudinal and circumferential directions and two Poissons ratios are estimated. The longitudinal, circumferential, and mixed modes of the bending stiffness are also estimated. The sensitivity of the derived constants to the variation of the cell axial stiffness, which has been measured by several independent groups, is examined. The new estimates are also compared with results obtained by using the assumption of the wall isotropy.

Kinetic and mechanical analysis of live tube morphogenesis

Ribbon is a nuclear Broad Tramtrack Bric‐a‐brac (BTB) ‐domain protein required for morphogenesis of the salivary gland and trachea. We recently showed that ribbon mutants exhibit decreased Crumbs and Rab11‐coincident apical vesicles and increased apical Moesin activity and microvillar structure during tube elongation. To learn how these molecular and morphological changes affect the dynamics of tubulogenesis, we optimized an advanced two‐photon microscope to enable high‐resolution live imaging of the salivary gland and trachea. Live imaging revealed that ribbon mutant tissues exhibit slowed and incomplete lumenal morphogenesis, consistent with previously described apical defects. Because Moesin activity correlates with cortical stiffness, we hypothesize that ribbon mutants suffer from increased apical stiffness during morphogenesis. We develop this hypothesis through mechanical analysis, using the advantages of live imaging to construct computational elastic and analytical viscoelastic models of tube elongation, which suggest that ribbon mutant tubes exhibit three‐ to fivefold increased apical stiffness and twofold increased effective apical viscosity. Developmental Dynamics 237:2874–2888, 2008.

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, k 0 and k 1 (with k 0>k 1), and a viscous coefficient. While both stiffness parameters contribute to the time-dependant mechanical behavior of the protrusions, k 0 and k 1 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 k 0 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 k 0 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.

Nonlinear active force generation by cochlear outer hair cell.

We analyze the nonlinear behavior of the longitudinal and circumferential components of the active force generated by the outer hair cell wall in response to changes of its transmembrane potential. We treat the material of the wall as electroelastic, linear orthotropic in terms of strains and as nonlinear in terms of the transmembrane potential. To describe the nonlinear behavior of the active force versus the transmembrane potential, we use two (Boltzmann and simple exponential) types of approximation. We estimate free parameters of these approximations by combining the previously reported passive stiffnesses with the active strains measured in the microchamber experiment. We analyze the sensitivity of the estimated parameters corresponding to changes of the cell axial stiffness, a characteristic independently measured by several groups. We also study the effect of combining the active strains measured in the microchamber experiment with those measured in the whole cell recording experiment. We show agreement between our prediction of the active force and measurements in the whole cochlea and in isolated cells.

A nonlinear electroelastic model of the auditory outer hair cell

Abstract Mechanically linear and electrically nonlinear constitutive relations for the auditory outer hair cell membrane (wall) are proposed. These relationships are derived on the basis of dual thermodynamic potentials. The active forces and active strains generated by the cell, important characteristics of the cell’s behavior under physiological conditions, are associated with the mixed (piezoelectric) terms in the dual thermodynamic potentials. By using experimental information from four independent experiments, where the cell is loaded mechanically or electrically, the free parameters of the model are estimated. In addition, the model is extended to a composite representation of the cell membrane. In that representation, the outer layer is considered active (electroelastic) and the inner layer is considered passive (purely elastic). The layers are connected by elastic springs. The graphs for the elastic energy stored in the passive layer versus the cell wall potential are presented.