George Lykotrafitis

Refractive index maps and membrane dynamics of human red blood cells parasitized by Plasmodium falciparum

Parasitization by malaria-inducing Plasmodium falciparum leads to structural, biochemical, and mechanical modifications to the host red blood cells (RBCs). To study these modifications, we investigate two intrinsic indicators: the refractive index and membrane fluctuations in P. falciparum-invaded human RBCs (Pf-RBCs). We report experimental connections between these intrinsic indicators and pathological states. By employing two noninvasive optical techniques, tomographic phase microscopy and diffraction phase microscopy, we extract three-dimensional maps of refractive index and nanoscale cell membrane fluctuations in isolated RBCs. Our systematic experiments cover all intraerythrocytic stages of parasite development under physiological and febrile temperatures. These findings offer potential, and sufficiently general, avenues for identifying, through cell membrane dynamics, pathological states that cause or accompany human diseases.

Cytoskeletal dynamics of human erythrocyte

The human erythrocyte (red blood cell, RBC) demonstrates extraordinary ability to undergo reversible large deformation and fluidity. Such mechanical response cannot be consistently rationalized on the basis of fixed connectivity of the cell cytoskeleton that comprises the spectrin molecular network tethered to phospholipid membrane. Active topological remodeling of spectrin network has been postulated, although detailed models of such dynamic reorganization are presently unavailable. Here we present a coarse-grained cytoskeletal dynamics simulation with breakable protein associations to elucidate the roles of shear stress, specific chemical agents, and thermal fluctuations in cytoskeleton remodeling. We demonstrate a clear solid-to-fluid transition depending on the metabolic energy influx. The solid networks plastic deformation also manifests creep and yield regimes depending on the strain rate. This cytoskeletal dynamics model offers a means to resolve long-standing questions regarding the reference state used in RBC elasticity theory for determining the equilibrium shape and deformation response. In addition, the simulations offer mechanistic insights into the onset of plasticity and void percolation in cytoskeleton. These phenomena may have implication for RBC membrane loss and shape change in the context of hereditary hemolytic disorders such as spherocytosis and elliptocytosis.

Torsional surface waves in a gradient-elastic half-space

Abstract The present work deals with torsional wave propagation in a linear gradient-elastic half-space. More specifically, we prove that torsional surface waves (i.e. waves with amplitudes exponentially decaying with distance from the free surface) do exist in a homogeneous gradient-elastic half-space. This finding is in contrast with the well-known result of the classical theory of linear elasticity that torsional surface waves do not exist in a homogeneous half-space. The weakness of the classical theory, at this point, is only circumvented by modeling the half-space as having material properties variable with depth (E. Meissner, Elastische Oberflachenwellen mit Dispersion in einem inhomogenen Medium, Vierteljahrsschrift der Naturforschenden Gesellschaft in Zurich 66 (1921) 181–195; I. Vardoulakis, Torsional surface waves in inhomogeneous elastic media, Internat. J. Numer. Anal. Methods Geomech. 8 (1984) 287–296; G.A. Maugin, Shear horizontal surface acoustic waves on solids, in: D.F. Parker, G.A. Maugin (Eds.), Recent Developments in Surface Acoustic Waves, Springer Series on Wave Phenomena, vol. 7, Springer, Berlin, 1988, pp. 158–172), as a layered structure (Maugin, 1988; E. Reissner, Freie und erzwungene Torsionsschwingungen des elastischen Halbraumes, Ingenieur-Archiv 8 (1937) 229–245) or by considering couplings with electric and magnetic fields for different types of materials (Maugin, 1988). The theory employed here is the simplest possible version of Mindlin’s (R.D. Mindlin, Micro-structure in linear elasticity, Arch. Rat. Mech. Anal. 16 (1964) 51–78) generalized linear elasticity. A simple wave-propagation analysis based on Hankel transforms and complex-variable theory was done in order to determine the conditions for the existence of the torsional surface motions and to derive dispersion curves and cut-off frequencies. Also, we notice that, up to date, no other generalized linear continuum theory (including the integral-type non-local theory) has successfully been proposed to predict torsional surface waves in a homogeneous half-space.

Self-Healing Pulse-Like Shear Ruptures in the Laboratory

Models predict that dynamic shear ruptures during earthquake faulting occur as either sliding cracks, where a large section of the interface slides behind a fast-moving rupture front, or self-healing slip pulses, where the fault relocks shortly behind the rupture front. We report experimental visualizations of crack-like, pulse-like, and mixed rupture modes propagating along frictionally held, “incoherent” interfaces separating identical solids, and we describe the conditions under which those modes develop. A combination of simultaneously performed measurements via dynamic photoelasticity and laser interferometry reveals the rupture mode type, the exact point of rupture initiation, the sliding velocity history, and the rupture propagation speed.

Sickle cell trait human erythrocytes are significantly stiffer than normal.

Atomic force microscopy (AFM) allows for high-resolution topography studies of biological cells and measurement of their mechanical properties in physiological conditions. In this work, AFM was employed to measure the stiffness of abnormal human red blood cells from human subjects with the genotype for sickle cell trait. The determined Youngs modulus was compared with that obtained from measurements of erythrocytes from healthy subjects. The results showed that Youngs modulus of pathological erythrocytes was approximately three times higher than in normal cells. Observed differences indicate the effect of the polymerization of sickle hemoglobin as well as possible changes in the organization of the cell cytoskeleton associated with the sickle cell trait.

Frictional sliding modes along an interface between identical elastic plates subject to shear impact loading

Frictional sliding along an interface between two identical isotropic elastic plates under impact shear loading is investigated experimentally and numerically. The plates are held together by a compressive stress and one plate is subject to edge impact near the interface. The experiments exhibit both a crack-like and a pulse-like mode of sliding. Plane stress finite element calculations modeling the experimental configuration are carried out, with the interface characterized by a rate and state dependent frictional law. A variety of sliding modes are obtained in the calculations depending on the impact velocity, the initial compressive stress and the values of interface variables. For low values of the initial compressive stress and impact velocity, sliding occurs in a crack-like mode. For higher values of the initial compressive stress and/or impact velocity, sliding takes place in a pulse-like mode. One pulse-like mode involves well-separated pulses with the pulse amplitude increasing with propagation distance. Another pulse-like mode involves a pulse train of essentially constant amplitude. The propagation speed of the leading pulse (or of the tip of the crack-like sliding region) is near the longitudinal wave speed and never less than √2 times the shear wave speed. Supersonic trailing pulses are seen both experimentally and computationally. The trends in the calculations are compared with those seen in the experiments.

Microelasticity of red blood cells in sickle cell disease

Translation of cellular mechanics findings is crucial in many diseases, including Alzheimer’s disease, Parkinson’s disease, type II diabetes, malaria, sickle cell disease, and cancer. Atomic force microscopy (AFM) is appropriate for measuring mechanical properties of living and fixed cells due to its high force sensitivity and its ability to measure local and overall properties of individual cells under physiological conditions. A systemic force–displacement curve analysis is reported on the quantification of material stiffness via AFM using two theoretical models derived from the Hertz model. This analysis was applied to red blood cells from patients with sickle cell disease to determine the Young’s modulus of these cells in the oxygenated and deoxygenated state. Sickle cell disease pathophysiology is a consequence of the polymerization of sickle hemoglobin in red blood cells upon partial deoxygenation and the impaired flow of these cells in the microcirculation. A model is presented for a four-sided pyramidal indenter that is subsequently shown to have a better fit to the obtained data than that using a model of a parabolic indenter. It is concluded that deoxygenation and therapeutic treatment have a significant impact on the stiffness. This analysis presents a new approach to addressing medical disorders.

Two-Component Coarse-Grained Molecular-Dynamics Model for the Human Erythrocyte Membrane

We present a two-component coarse-grained molecular-dynamics model for simulating the erythrocyte membrane. The proposed model possesses the key feature of combing the lipid bilayer and the erythrocyte cytoskeleton, thus showing both the fluidic behavior of the lipid bilayer and the elastic properties of the erythrocyte cytoskeleton. In this model, three types of coarse-grained particles are introduced to represent clusters of lipid molecules, actin junctions, and band-3 complexes, respectively. The proposed model facilitates simulations that span large length scales (approximately micrometers) and timescales (approximately milliseconds). By tuning the interaction potential parameters, we were able to control the diffusivity and bending rigidity of the membrane model. We studied the membrane under shearing and found that at a low shear strain rate, the developed shear stress was due mainly to the spectrin network, whereas the viscosity of the lipid bilayer contributed to the resulting shear stress at higher strain rates. In addition, we investigated the effects of a reduced spectrin network connectivity on the shear modulus of the membrane.

A Method Based on the Radon Transform for Three-Dimensional Elastodynamic Problems of Moving Loads

An integral transform procedure is developed to obtain fundamental elastodynamic three-dimensional (3D) solutions for loads moving steadily over the surface of a half-space. These solutions are exact, and results are presented over the entire speed range (i.e., for subsonic, transonic and supersonic source speeds). Especially, the results obtained here for the tangential loads (one of these loads is along the direction of motion and the other is orthogonal to the direction of motion) are quite new in the literature. The solution technique is based on the use of the Radon transform and elements of distribution theory. It also fully exploits as auxiliary solutions the ones for the corresponding plane-strain and anti-plane shear problems (the latter problems are 2D and uncoupled from each other). In particular, it should be noticed that the plane-strain problem here is completely analogous to the original 3D problem, not only with respect to the field equations but also with respect to the boundary conditions. This makes the present technique more advantageous than other techniques, which require first the determination of a fictitious auxiliary plane-strain problem through the solution of an integral equation. Our approach becomes particularly simple when there is no angular dependence in the boundary conditions (i.e., when axially symmetric problems regarding their boundary conditions are considered). On the contrary, no such constraint needs to be fulfilled as regards the material response (and, therefore, the governing equations of the problem) and/or also possible loss of axisymmetry due to the generation of shock (Mach-type) waves in the medium. Therefore, the solution technique can easily deal with general 3D problems having a largely arbitrary radial dependence in the boundary conditions and involving: (i) material anisotropy in static and dynamic situations, and (ii) asymmetry caused by changes in the nature of governing PDEs due to the existence of different velocity regimes (super-Rayleigh, transonic, supersonic) in dynamic situations.

Erythrocyte Membrane Model with Explicit Description of the Lipid Bilayer and the Spectrin Network

The membrane of the red blood cell (RBC) consists of spectrin tetramers connected at actin junctional complexes, forming a two-dimensional (2D) sixfold triangular network anchored to the lipid bilayer. Better understanding of the erythrocyte mechanics in hereditary blood disorders such as spherocytosis, elliptocytosis, and especially, sickle cell disease requires the development of a detailed membrane model. In this study, we introduce a mesoscale implicit-solvent coarse-grained molecular dynamics (CGMD) model of the erythrocyte membrane that explicitly describes the phospholipid bilayer and the cytoskeleton, by extending a previously developed two-component RBC membrane model. We show that the proposed model represents RBC membrane with the appropriate bending stiffness and shear modulus. The timescale and self-consistency of the model are established by comparing our results with experimentally measured viscosity and thermal fluctuations of the RBC membrane. Furthermore, we measure the pressure exerted by the cytoskeleton on the lipid bilayer. We find that defects at the anchoring points of the cytoskeleton to the lipid bilayer (as in spherocytes) cause a reduction in the pressure compared with an intact membrane, whereas defects in the dimer-dimer association of a spectrin filament (as in elliptocytes) cause an even larger decrease in the pressure. We conjecture that this finding may explain why the experimentally measured diffusion coefficients of band-3 proteins are higher in elliptocytes than in spherocytes, and higher than in normal RBCs. Finally, we study the effects that possible attractive forces between the spectrin filaments and the lipid bilayer have on the pressure applied on the lipid bilayer by the filaments. We discover that the attractive forces cause an increase in the pressure as they diminish the effect of membrane protein defects. As this finding contradicts with experimental results, we conclude that the attractive forces are moderate and do not impose a complete attachment of the filaments to the lipid bilayer.