Yanik Tardy

Contribution of the nucleus to the mechanical properties of endothelial cells

The cell nucleus plays a central role in the response of the endothelium to mechanical forces, possibly by deforming during cellular adaptation. The goal of this work was to precisely quantify the mechanical properties of the nucleus. Individual endothelial cells were subjected to compression between glass microplates. This technique allows measurement of the uniaxial force applied to the cell and the resulting deformation. Measurements were made on round and spread cells to rule out the influence of cell morphology on the nucleus mechanical properties. Tests were also carried out with nuclei isolated from cell cultures by a chemical treatment. The non-linear force-deformation curves indicate that round cells deform at lower forces than spread cells and nuclei. Finite-element models were also built with geometries adapted to actual morphometric measurements of round cells, spread cells and isolated nuclei. The nucleus and the cytoplasm were modeled as separate homogeneous hyperelastic materials. The models simulate the compression and yield the force-deformation curve for a given set of elastic moduli. These parameters are varied to obtain a best fit between the theoretical and experimental data. The elastic modulus of the cytoplasm is found to be on the order of 500N/m(2) for spread and round cells. The elastic modulus of the endothelial nucleus is on the order of 5000N/m(2) for nuclei in the cell and on the order of 8000N/m(2) for isolated nuclei. These results represent an unambiguous measurement of the nucleus mechanical properties and will be important in understanding how cells perceive mechanical forces and respond to them.

Non-invasive estimate of the mechanical properties of peripheral arteries from ultrasonic and photoplethysmographic measurements

The non-linear elastic response of arteries implies that their mechanical properties depend strongly on blood pressure. Thus, dynamic measurements of both the diameter and pressure curves over the whole cardiac cycle are necessary to characterise properly the elastic behaviour of an artery. We propose a novel method of estimating these mechanical properties based on the analysis of the arterial diameter against pressure curves derived from ultrasonic and photoplethysmographic measurements. An ultrasonic echo tracking device has been developed that allows continuous recording of the internal diameter of peripheral arteries. It measures the diameter 300 times per second with a resolution of 2.5 microns. This system is linked to a commercially available light-plethysmograph which continuously records the finger arterial pressure (0.25 kPa accuracy). Because of the finite pulse wave velocity, the separation between the diameter and the pressure measurement sites causes a hysteresis to appear in the recorded diameter-pressure curve. Using a model based on haemodynamic considerations, the delay between the diameter variations and the finger arterial pressure is first eliminated. As the pulse wave velocity depends on the pressure, the delay is determined for each pressure value. The relationship between pressure and diameter is then described by a non-linear mathematical expression with three parameters, which best fits the recorded data. The dynamic local behaviour of the vessel is fully characterised by these parameters. Compliance, distensibility and pulse wave velocity can then be calculated at each pressure level. Thus, the mechanical behaviour of peripheral human arteries can now be characterised non-invasively over the pressure range of the whole cardiac cycle. The results obtained in vivo on human radial and brachial arteries show that a thorough analysis of the compliance-pressure curves and their modifications (curving, shift) is needed in order to compare two different vessels in a meaningful way.

Simultaneous Measurements of Actin Filament Turnover, Filament Fraction, and Monomer Diffusion in Endothelial Cells

The analogous techniques of photoactivation of fluorescence (PAF) and fluorescence recovery after photobleaching (FRAP) have been applied previously to the study of actin dynamics in living cells. Traditionally, separate experiments estimate the mobility of actin monomer or the lifetime of actin filaments. A mathematical description of the dynamics of the actin cytoskeleton, however, predicts that the evolution of fluorescence in PAF and FRAP experiments depends simultaneously on the diffusion coefficient of actin monomer, D, the fraction of actin in filaments, FF, and the lifetime of actin filaments, tau (, Biophys. J. 69:1674-1682). Here we report the application of this mathematical model to the interpretation of PAF and FRAP experiments in subconfluent bovine aortic endothelial cells (BAECs). The following parameters apply for actin in the bulk cytoskeleton of subconfluent BAECs. PAF: D = 3.1 +/- 0.4 x 10(-8) cm2/s, FF = 0.36 +/- 0.04, tau = 7.5 +/- 2.0 min. FRAP: D = 5.8 +/- 1.2 x 10(-8) cm2/s, FF = 0.5 +/- 0.04, tau = 4.8 +/- 0.97 min. Differences in the parameters are attributed to differences in the actin derivatives employed in the two studies and not to inherent differences in the PAF and FRAP techniques. Control experiments confirm the modeling assumption that the evolution of fluorescence is dominated by the diffusion of actin monomer, and the cyclic turnover of actin filaments, but not by filament diffusion. The work establishes the dynamic state of actin in subconfluent endothelial cells and provides an improved framework for future applications of PAF and FRAP.

Assessment of Strain Field in Endothelial Cells Subjected to Uniaxial Deformation of Their Substrate

A stretch chamber has been developed in order to visualize the deformation of cells subjected to controlled uniaxial stretch of their substrate. A rectangular, custom-made, transparent silicone channel is used as a deformable substrate. Bovine aortic endothelial cells are plated at the bottom of the channel whose lateral deformation is controlled by two piezoelectric translators. The system is mounted on the stage of a confocal microscope where three-dimensional (3D) images of the cells can be acquired simultaneously in the three RGB channels. The first channel provides images of 216 nm fluorescent beads embedded in the cytoskeleton (used as internal markers). The second is used to image the shape of the nucleus revealed by live cell nucleic acid staining. The third one provides a transmitted light image of the cell outline. 3D images of the cell are taken before deformation, after uniaxial deformation of the substrate (up to 25%) and after relaxation. Results indicate that: (a) the cell closely follows the deformation imposed by the substrate with no measurable residual strain after relaxation, and (b) there is a clear mechanical coupling between the extracellular matrix and the nucleus, which deforms significantly under the applied substrate stretch. Suggesting that the nucleus can directly sense the mechanical environment of the cell, the latter result has potentially important implications for signal transduction.

Nonlinear separation of forward and backward running waves in elastic conduits

A new method for the separation of forward and backward running waves in elastic conduits, with possible extension to the arterial system, has been developed. The mathematical model is based on the one-dimensional flow equations which allow the treatment of non-periodic or transient pressure and flow pulses. The method is fully nonlinear, i.e. no linearizing assumptions are made. The method includes the effects of convective acceleration and pressure-dependent vessel compliance. A first approximation for the fluid friction at the wall is also included. The application of the method requires the knowledge of the elastic properties, the instantaneous pressure and flow, as well as the instantaneous spatial derivatives of pressure and flow. Analysis of simulated data shows good results and suggests that the proposed method, unlike previous quasi-nonlinear and frequency domain methods, can be applied to strongly nonlinear and/or nonperiodic flows. The method predicts that if a linear analysis is applied to a nonlinear system errors arise.

Dynamic non-invasive measurements of arterial diameter and wall thickness

Aim Non-invasive measurements of arterial diameter and wall thickness are critical in characterizing the onset and development of vascular disease. A precise dynamic method was proposed and tested for this purpose. Design A non-invasive method of measuring the variations in diameter and thickness of human arteries throughout the cardiac cycle was developed, using a high-precision ultrasonic echo-tracking system. An adaptive filtering technique was used to suppress artefacts caused by the layered tissue structure of the vessel wall. Results Based on decorrelation of microstructure noise, this technique improved the detectability of the wall interfaces, which allowed a determination of thickness and diameter. The accuracy and reproducibility of the method were tested by measurements of plastic films with known thicknesses. The discrepancies between standard micrometer and pulse-echo measurement were consistently less than 5 μm for film thicknesses ranging from 220 to 800 μm. The difference between two successive measurements was less than 2 μm. The identity of the measured vascular interfaces was checked in two ways. First, experiments on fixed bovine carotid arteries showed that the identified echogenic interfaces corresponded to the actual anatomical structure, as obtained by acoustic microscopy. Second, the radial artery thickness and diameter were extrapolated to obtain the change in wall volume over one cardiac cycle. The volume was found to be nearly constant, indicating incompressibility. Conclusion This method will make it possible to obtain new information on atherogenesis and other vascular diseases.

Measuring actin dynamics in endothelial cells

Cytoplasmic actin distributes between monomeric and filamentous phases in cells. As cells crawl, actin polymerizes near the plasma membrane of expanding peripheral cytoplasm and depolymerizes elsewhere. Thus, the finite actin filament lifetime, the diffusivity of actin monomer, and the distribution of actin between the polymer and monomer phases are key parameters in cell motility. The dynamics of cellular actin can be determined by following the evolution of fluorescence in the techniques of photoactivated fluorescence (PAF) or fluorescence recovery after photobleaching (FRAP) of microinjected actin derivatives. A mathematical model is discussed that measures monomer diffusion coefficients, filament turnover rates, and the fraction of actin polymerized from measurements of the evolution of fluorescence from a photoactivated band [Tardy et al. (1995) Biophys. J., 69:1674–1682; McGrath et al. (1998) Biophys. J., in press]. Applying this model to subconfluent endothelial cells shows that ∼40% of the actin is polymer and that these filaments turn over on average every 6 minutes. This report dicusses how PAF and FRAP can be combined with more traditional biochemistry to probe actin cytoskeleton remodeling in endothelial cells. Microsc. Res. Tech. 43:385–394

Non-invasive determination of arterial diameter and distensibility by echo-tracking techniques in hypertension

Methodology: A new non-invasive ultrasonic device was developed to characterize the biomechanical properties of medium and large peripheral arteries. Simultaneous recordings of internal diameter and blood pressure over the whole cardiac cycle are used to establish compliance-pressure curves. Since blood pressure, which is an inherent co-determinant of arterial compliance, is taken into account, the comparison of arteries from patients with markedly different blood pressures has become possible. In a first study, the effects of three different antihypertensive drugs (20 mg lisinopril, 100 mg atenolol, 20 mg nitrendipine administered once a day) on arterial compliance and distensibility were investigated in young healthy volunteers. Results: After 8 days of treatment, lisinopril induced a significant increase in arterial compliance. Subsequently, we compared the mechanical behaviour of arteries from newly diagnosed hypertensive patients (radial artery) or the carotid artery from spontaneously hypertensive rats (SHR) with that of corresponding arteries in normotensive counterparts. No decrease in arterial distensibility was found in the hypertensive groups over the measured blood pressure range. This result is not totally consistent with previous in vitro or in situ localized studies. Methodological differences, the absence of blood flow and/or denervation may partly explain these contradictory results. Finally, we tested the effects of hydralazine (5 mg/day) and captopril (25 mg/day), administered for 6 weeks in drinking water, on the behaviour of the carotid arteries of 16-week-old SHR. The two drugs effectively reduced blood pressure while shifting the distensibility-pressure curves upward in comparison to the placebo-treated animals, suggesting an improvement in arterial compliance. Conclusions: While hypertension does not itself appear to alter the elastic behaviour of large peripheral arteries, antihypertensive treatment may increase the compliance of these blood vessels.

Modeling actin filament reorganization in endothelial cells subjected to cyclic stretch

Hemodynamic forces affect endothelial cell morphology and function. In particular, circumferential cyclic stretch of blood vessels, due to pressure changes during the cardiac cycle, is known to affect the endothelial cell shape, mediating the alignment of the cells in the direction perpendicular to stretch. This change in cell shape proceeds a drastic reorganization at the internal level. The cellular scaffolding, mainly composed of actin filaments, reorganize in the direction which later becomes the cell’s long axis. How this external mechanical stimulus is ’sensed’ and transduced into the cell is still unknown. Here, we develop a mathematical model depicting the dynamics of actin filaments, and the influence of the cyclic stretch of the substratum based on the experimental evidence that external stimuli may be transduced inside the cell via transmembrane proteins which are coupled with actin filaments on the cytoplasmic side. Based on this view, we investigate two approaches describing the formulation of the transduction mechanisms involving the coupling between filaments and the membrane proteins. As a result, we find that the mechanical stimulus could cause the experimentally observed reorganization of the entire cytoskeleton simply by altering the dynamics of the filaments connected with the integral membrane proteins, as described in our model. Comparison of our results with previous studies of cytoskeletal dynamics reveals that the cytoskeleton, which, in the absence of the effect of stretch would maintain its isotropic distribution, slowly aligns with the precise direction set by the external stimulus. It is found that even a feeble stimulus, coupled with a strong internal dynamics, is sufficient to align actin filaments perpendicular to the direction of stretch.

Non-invasive method for the assessment of non-linear elastic properties and stress of forearm arteries in vivo

Aim To propose a method for obtaining non-invasive highly accurate measurements of arterial diameter, thickness and pressure at a single location on a peripheral arm artery, and use this data to estimate the status of the arterial wall. Methods Diameter and thickness were measured with an A-mode ultrasonic echo-tracking device, with a precision of close to 1μm. Pressure was measured with a photoplethysmograph at the finger level. A simple hemodynamic model was used to estimate, from the measured pressure pulse, the pressure waveform at the diameter-measuring site. Results The collected data made it possible to assess (1) the elastic response of the artery, through the compliance and distensibility, (2) the loading conditions, through the average stress-diameter curve and (3) the elastic properties of the wall material, through the incremental modulus of elasticity. Conclusion This information can be used to assess the overall status of the arterial wall.