Bioelectrorheological model of the cell. 2. Analysis of creep and its experimental verification

The electrorheological model of the cell proposed in Part 1 of this work was used to analyze changes in time of the shape of a cell acted on by a constant-amplitude external alternating electric field, with lossiness of the media taken into account. Shear stress in the cell membrane was determined. This model was then subjected to preliminary experimental verification using Neurospora crassa (slime) spheroplasts subjected to an external alternating electric field of constant frequency (3 MHz) and varying magnitude for different periods of time. Reversible viscoelastic cell deformation and fatigue (stiffening) of the material were observed. A satisfactory fit of the experimental data to Burgers' rheological model was found, and the values of the elastic moduli E1 = 9 X 10(2) N/m2, E2 = 2 X 10(2) N/m2 and viscosities eta 1 = 8 X 10(4) Ns/m2; eta 2 = 7 X 10(3) Ns/m2 were evaluated.     

Bioelectrorheological model of the cell. 3. Viscoelastic shear deformation of the membrane.

An analytical electromechanical model of a spherical cell exposed to an alternating electric field was used to calculate shear stress generated in the cellular membrane. Shape deformation of Neurospora crassa (slime) spheroplasts was measured. Statistical analysis permitted empirical evaluation of creep of the cellular membrane within the range of infinitesimal stress. Final results were discussed in terms of various rheological models.     

Bioelectrorheological model of the cell. 8. Cellular deformation under prolonged and recurrent shear stress.

The influence of a prolonged and recurrent shear stress created by a periodic electric field on the mechanical properties of Neurospora crassa cells was investigated. Conditions were found under which modifications of cellular structures responding to stress become irreversible, and plastic flow of the viscoelastic structural elements is observed. The symmetry of the response of the cell under stress application and relaxation was lost, when compared to the reference conditions. To interpret the results a general rheological model was proposed. As previously described (Paw?owski et al., 1997), the existence of the three hypothetical supramolecular regions of the membrane (F, S and O) was suggested. Rheological parameters for the above regions were calculated. Theoretical functions were satisfactorily fitted to the experimental results.     

Bioelectrorheological model of the cell. 4. Analysis of the extensil deformation of cellular membrane in alternating electric field.

Analysis of the angular distribution of extensil mechanical stress, sigma e, generated in cytoplasmic membranes by an external oscillating electric field, is presented. Theoretical considerations show that sigma e is directly proportional to the local relative increase in membrane area and/or to the local relative decrease in its thickness. The magnitude of this stress depends on the position of the analyzed point of the membrane in relation to field direction. The maximal value, sigma eo, is reached at the cell "poles." The magnitude of sigma eo depends on electric and geometric parameters (in particular on field frequency) of the system studied. The foregoing analysis can be applied to quantitatively describe the destabilizing effects of the electric field on the cellular membrane, leading to its poration, fusion, and destruction.     

Bioelectrorheological model of the cell. 5. Electrodestruction of cellular membrane in alternating electric field.

Recently proposed analysis of the extensil stress developed in a cellular membrane subjected to an alternating electric field (Pawłowski, P., and M. Fikus, 1993. Bioelectrorheological model of the cell. 4. Analysis of the extensil deformation of the membrane in an alternating field. Biophys. J. 65:535-540) was applied in calculations of extensil stress threshold values, sigma eo[d], producing experimentally observed electrodestruction of cells within the frequency range of 7 x 10(1) - 3 x 10(5) Hz. It was shown that the susceptibility (s[d] = 1/sigma eo[d]), of the membrane to this process varies with field frequency and depends on the type of cells. Electrodestruction is facilitated in the 10(5)-Hz field. A rheological hypothesis explaining the experimentally observed dependence of membrane stability on electric field frequency was proposed and successfully tested for two other phenomena: electroporation and electrofusion.     

A theoretical model study of the influence of fluid stresses on a cell adhering to a microchannel wall.

We predict the amplification of mechanical stress, force, and torque on an adherent cell due to flow within a narrow microchannel. We model this system as a semicircular bulge on a microchannel wall, with pressure-driven flow. This two-dimensional model is solved computationally by the boundary element method. Algebraic expressions are developed by using forms suggested by lubrication theory that can be used simply and accurately to predict the fluid stress, force, and torque based upon the fluid viscosity, muoffhannel height, H, cell size, R, and flow rate per unit width, Q2-d. This study shows that even for the smallest cells (gamma = R/H << 1), the stress, force, and torque can be significantly greater than that predicted based on flow in a cell-free system. Increased flow resistance and fluid stress amplification occur with bigger cells (gamma > 0.25), because of constraints by the channel wall. In these cases we find that the shear stress amplification is proportional to Q2-d(1-gamma)-2, and the force and torque are proportional to Q2-d(1-gamma2)-5/2. Finally, we predict the fluid mechanical influence on three-dimensional immersed objects. These algebraic expressions have an accuracy of approximately 10% for flow in channels and thus are useful for the analysis of cells in flow chambers. For cell adhesion in tubes, the approximations are accurate to approximately 25% when gamma > 0.5. These calculations may thus be used to simply predict fluid mechanical interactions with cells in these constrained settings. Furthermore, the modeling approach may be useful in understanding more complex systems that include cell deformability and cell-cell interactions.     

Freezing stresses and hydration of isolated cell walls

The hydration of the cell walls of the giant alga Chara australis was measured as a function of temperature using quantitative deuterium nuclear magnetic resonance (NMR) of samples hydrated with D2O. At temperatures 23-5K below freezing, the hydration ratio (the ratio of mass of unfrozen water in microscopic phases in the cell wall to the dry mass) increases slowly with increasing temperature from about 0.2 to 0.4. It then rises rapidly with temperature in the few Kelvin below the freezing temperature. The linewidth of the NMR signal varies approximately linearly with the reciprocal of the hydration ratio, and with the freezing point depression or water potential. These empirical relations may be useful in estimating cell wall water contents in heterogeneous samples.     

HIV-1 Tat targets Tip60 to impair the apoptotic cell response to genotoxic stresses

HIV-1 transactivator Tat uses cellular acetylation signalling by targeting several cellular histone acetyltransferases (HAT) to optimize its various functions. Although Tip60 was the first HAT identified to interact with Tat, the biological significance of this interaction has remained obscure. We had previously shown that Tat represses Tip60 HAT activity. Here, a new mechanism of Tip60 neutralization by Tat is described, where Tip60 is identified as a substrate for the newly reported p300/CBP-associated E4-type ubiquitin-ligase activity, and Tat uses this mechanism to induce the polyubiquitination and degradation of Tip60. Tip60 targeting by Tat results in a dramatic impairment of the Tip60-dependent apoptotic cell response to DNA damage. These data reveal yet unknown strategies developed by HIV-1 to increase cell resistance to genotoxic stresses and show a role of Tat as a modulator of cellular protein ubiquitination.     

Real-time subject-specific monitoring of internal deformations and stresses in the soft tissues of the foot: a new approach in gait analysis

No technology is presently available to provide real-time information on internal deformations and stresses in plantar soft tissues of individuals during evaluation of the gait pattern. Because internal deformations and stresses in the plantar pad are critical factors in foot injuries such as diabetic foot ulceration, this severely limits evaluation of patients. To allow such real-time subject-specific analysis, we developed a hierarchal modeling system which integrates a two-dimensional gross structural model of the foot (high-order model) with local finite element (FE) models of the plantar tissue padding the calcaneus and medial metatarsal heads (low-order models). The high-order whole-foot model provides real-time analytical evaluations of the time-dependent plantar fascia tensile forces during the stance phase. These force evaluations are transferred, together with foot-shoe local reaction forces, also measured in real time (under the calcaneus, medial metatarsals and hallux), to the low-order FE models of the plantar pad, where they serve as boundary conditions for analyses of local deformations and stresses in the plantar pad. After careful verification of our custom-made FE solver and of our foot model system with respect to previous literature and against experimental results from a synthetic foot phantom, we conducted human studies in which plantar tissue loading was evaluated in real time during treadmill gait in healthy individuals (N = 4). We concluded that internal deformations and stresses in the plantar pad during gait cannot be predicted from merely measuring the foot-shoe force reactions. Internal loading of the plantar pad is constituted by a complex interaction between the anatomical structure and mechanical behavior of the foot skeleton and soft tissues, the body characteristics, the gait pattern and footwear. Real-time FE monitoring of internal deformations and stresses in the plantar pad is therefore required to identify elevated deformation/stress exposures toward utilizing it in gait laboratories to protect feet that are susceptible to injury.     

A model for aortic growth based on fluid shear and fiber stresses.

Stress-modulated growth in the aorta is studied using a theoretical model. The model is a thick-walled tube composed of two pseudoelastic, orthotropic layers representing the intima/media and the adventitia. Both layers are assumed to follow a growth law in which the time rates of change of the growth stretch ratios depend linearly on the local smooth muscle fiber stress and on the shear stress due to blood flow on the endothelium. Using finite elasticity theory modified to include volumetric growth, we computed temporal changes in stress, geometry, and opening angle (residual strain) during development and following the onset of sudden hypertension. For appropriate values of the coefficients in the growth law, the model yields results in reasonable agreement with published data for global and local growth of the rat aorta.     

The choice of a constitutive formulation for modeling limb flexion-induced deformations and stresses in the human femoropopliteal arteries of different ages

Open and endovascular treatments for peripheral arterial disease are notorious for high failure rates. Severe mechanical deformations experienced by the femoropopliteal artery (FPA) during limb flexion and interactions between the artery and repair materials play important roles and may contribute to poor clinical outcomes. Computational modeling can help optimize FPA repair, but these simulations heavily depend on the choice of constitutive model describing the arterial behavior. In this study finite element model of the FPA in the standing (straight) and gardening (acutely bent) postures was built using computed tomography data, longitudinal pre-stretch and biaxially determined mechanical properties. Springs and dashpots were used to represent surrounding tissue forces associated with limb flexion-induced deformations. These forces were then used with age-specific longitudinal pre-stretch and mechanical properties to obtain deformed FPA configurations for seven age groups. Four commonly used invariant-based constitutive models were compared to determine the accuracy of capturing deformations and stresses in each age group. The four-fiber FPA model most accurately portrayed arterial behavior in all ages, but in subjects younger than 40 years, the performance of all constitutive formulations was similar. In older subjects, Demiray (Delfino) and classic two-fiber Holzapfel–Gasser–Ogden formulations were better than the Neo-Hookean model for predicting deformations due to limb flexion, but both significantly overestimated principal stresses compared to the FPA or Neo-Hookean models.     

A musculoskeletal model of the equine forelimb for determining surface stresses and strains in the humerus-part II. Experimental testing and model validation

The first objective of this study was to experimentally determine surface bone strain magnitudes and directions at the donor site for bone grafts, the site predisposed to stress fracture, the medial and cranial aspects of the transverse cross section corresponding to the stress fracture site, and the middle of the diaphysis of the humerus of a simplified in vitro laboratory preparation. The second objective was to determine whether computing strains solely in the direction of the longitudinal axis of the humerus in the mathematical model was inherently limited by comparing the strains measured along the longitudinal axis of the bone to the principal strain magnitudes and directions. The final objective was to determine whether the mathematical model formulated in Part I [Pollock et al., 2008, ASME J. Biomech. Eng., 130, p. 041006] is valid for determining the bone surface strains at the various locations on the humerus where experimentally measured longitudinal strains are comparable to principal strains. Triple rosette strain gauges were applied at four locations circumferentially on each of two cross sections of interest using a simplified in vitro laboratory preparation. The muscles included the biceps brachii muscle in addition to loaded shoulder muscles that were predicted active by the mathematical model. Strains from the middle grid of each rosette, aligned along the longitudinal axis of the humerus, were compared with calculated principal strain magnitudes and directions. The results indicated that calculating strains solely in the direction of the longitudinal axis is appropriate at six of eight locations. At the cranial and medial aspects of the middle of the diaphysis, the average minimum principal strain was not comparable to the average experimental longitudinal strain. Further analysis at the remaining six locations indicated that the mathematical model formulated in Part I predicts strains within +/-2 standard deviations of experimental strains at four of these locations and predicts negligible strains at the remaining two locations, which is consistent with experimental strains. Experimentally determined longitudinal strains at the middle of the diaphysis of the humerus indicate that tensile strains occur at the cranial aspect and compressive strains occur at the caudal aspect while the horse is standing, which is useful for fracture fixation.     

Cytomechanics of cell deformations and migration: from models to experiments

A cytomechanical model bas been proposed to analyse cell-cell interactions and cell migration through chemotaxis. We consider as the leading assumption that the cell cortical tension is locally modified by the protrusive activity of neighbour cells and binding of chemoattractant molecules to membrane receptors respectively. The model derives from the one initially proposed by Alt and Tranquillo (1995), which successfully describes experimentally observed cyclic autonomous cell shape changes. It is based on force balance equations coupling intracellular hydrostatic pressure and cell cortex contraction. Considering the protrusive dynamics of L929 fibroblats observed by videomicroscopy, we simulated the influence of neighbouring protrusions on a cell spontaneous pulsating behaviour. We further investigated the role of an extracellular gradient as another kind of external stimulus. The model illustrates how binding of chemoattractant molecules can induce a cell morphological instability that, above an intracellular stress threshold, will break the cell-substratum attachment. As a result, realistic cell chemotaxis can be simulated.     

Modulation of trophoblast stem cell and giant cell phenotypes: analyses using the Rcho-1 cell model

Trophoblast giant cells are located at the maternal-embryonic interface and have fundamental roles in the invasive and endocrine phenotypes of the rodent placenta. In this report, we describe the experimental modulation of trophoblast stem cell and trophoblast giant cell phenotypes using the Rcho-1 trophoblast cell model. Rcho-1 trophoblast cells can be manipulated to proliferate or differentiate into trophoblast giant cells. Differentiated Rcho-1 trophoblast cells are invasive and possess an endocrine phenotype, including the production of members of the prolactin (PRL) family. Dimethyl sulfoxide (DMSO), a known differentiation-inducing agent, was found to possess profound effects on the in vitro development of trophoblast cells. Exposure to DMSO, at non-toxic concentrations, inhibited trophoblast giant cell differentiation in a dose-dependent manner. These concentrations of DMSO did not significantly affect trophoblast cell proliferation or survival. Trophoblast cells exposed to DMSO exhibited an altered morphology; they were clustered in tightly packed colonies. Trophoblast giant cell formation was disrupted, as was the expression of members of the PRL gene family. The effects of DMSO were reversible. Removal of DMSO resulted in the formation of trophoblast giant cells and expression of the PRL gene family. The phenotype of the DMSO-treated cells was further determined by examining the expression of a battery of genes characteristic of trophoblast stem cells and differentiated trophoblast cell lineages. DMSO treatment had a striking stimulatory effect on eomesodermin expression and a reciprocal inhibitory effect on Hand1 expression. In summary, DMSO reversibly inhibits trophoblast differentiation and induces a quiescent state, which mimics some but not all aspects of the trophoblast stem cell phenotype.     

Energetics of inclusion-induced bilayer deformations.

The material properties of lipid bilayers can affect membrane protein function whenever conformational changes in the membrane-spanning proteins perturb the structure of the surrounding bilayer. This coupling between the protein and the bilayer arises from hydrophobic interactions between the protein and the bilayer. We analyze the free energy cost associated with a hydrophobic mismatch, i.e., a difference between the length of the protein's hydrophobic exterior surface and the average thickness of the bilayer's hydrophobic core, using a (liquid-crystal) elastic model of bilayer deformations. The free energy of the deformation is described as the sum of three contributions: compression-expansion, splay-distortion, and surface tension. When evaluating the interdependence among the energy components, one modulus renormalizes the other: e.g., a change in the compression-expansion modulus affects not only the compression-expansion energy but also the splay-distortion energy. The surface tension contribution always is negligible in thin solvent-free bilayers. When evaluating the energy per unit distance (away from the inclusion), the splay-distortion component dominates close to the bilayer/inclusion boundary, whereas the compression-expansion component is more prominent further away from the boundary. Despite this complexity, the bilayer deformation energy in many cases can be described by a linear spring formalism. The results show that, for a protein embedded in a membrane with an initial hydrophobic mismatch of only 1 A, an increase in hydrophobic mismatch to 1.3 A can increase the Boltzmann factor (the equilibrium distribution for protein conformation) 10-fold due to the elastic properties of the bilayer.     

Effect of aging on mechanical stresses,deformations, and hemodynamics in human femoropopliteal artery due to limb flexion

Femoropopliteal artery (FPA) reconstructions are notorious for poor clinical outcomes. Mechanical and flow conditions that occur in the FPA with limb flexion are thought to play a significant role, but are poorly characterized. FPA deformations due to acute limb flexion were quantified using a human cadaver model and used to build a finite element model that simulated surrounding tissue forces associated with limb flexion-induced deformations. Strains and intramural principal mechanical stresses were determined for seven age groups. Computational fluid dynamics analysis was performed to assess hemodynamic variables. FPA shape, stresses, and hemodynamics significantly changed with age. Younger arteries assumed straighter positions in the flexed limb with less pronounced bends and more uniform stress distribution along the length of the artery. Even in the flexed limb posture, FPAs younger than 50 years of age experienced tension, while older FPAs experienced compression. Aging resulted in localization of principal mechanical stresses to the adductor hiatus and popliteal artery below the knee that are typically prone to developing vascular pathology. Maximum principal stresses in these areas increased threefold to fivefold with age with largest increase observed at the adductor hiatus. Atheroprotective wall shear stress reduced after 35 years of age, and atheroprone and oscillatory shear stresses increased after the age of 50. These data can help better understand FPA pathophysiology and can inform the design of targeted materials and devices for peripheral arterial disease treatments.     

Mathematical model study of megakaryocytopoiesis. 1. The simulation model, cell steady-state distribution and the number of divisions in a proliferating population

A method of simulation has been proposed for studying megakaryocytopoiesis. A model has been developed which takes into account the age structure of cell population, the stochasticity of their maturation, and the principles of megakaryocytopoiesis regulation (known from the experiments). The mean number of divisions in a proliferating pool has been determined, as well as the duration of development of the cells with a positive acetylcholine esterase reaction.