Physics of cell elasticity,shape and adhesion

We review recent theoretical work that analyzes experimental measurements of the shape, fluctuations and adhesion properties of biological cells. Particular emphasis is placed on the role of the cytoskeleton and cell elasticity and we contrast the shape and adhesion of elastic cells with fluid-filled vesicles. In red blood cells (RBC), the cytoskeleton consists of a two-dimensional network of spectrin proteins. Our analysis of the wavevector and frequency dependence of the fluctuation spectrum of RBC indicates that the spectrin network acts as a confining potential that reduces the fluctuations of the lipid bilayer membrane. However, since the cytoskeleton is only sparsely connected to the bilayer, one cannot regard the composite cytoskeleton–membrane as a polymerized object with a shear modulus. The sensitivity of RBC fluctuations and shapes to ATP concentration may reflect topological defects induced in the cytoskeleton network by ATP. The shapes of cells that adhere to a substrate are strongly determined by the cytoskeletal elasticity that can be varied experimentally by drugs that depolymerize the cytoskeleton. This leads to a tension-driven retraction of the cell body and a pearling instability of the resulting ray-like protrusions. Recent experiments have shown that adhering cells exert polarized forces on substrates. The interactions of such “force dipoles” in either bulk gels or on surfaces can be used to predict the nature of self-assembly of cell aggregates and may be important in the formation of artificial tissues. Finally, we note that cell adhesion strongly depends on the forces exerted on the adhesion sites by the tension of the cytoskeleton. The size and shape of the adhesion regions are strongly modified as the tension is varied and we present an elastic model that relates this tension to deformations that induce the recruitment of new molecules to the adhesion region. In all these examples, cell shape and adhesion differ from vesicle shape and adhesion due to the presence of the elastic cytoskeleton and to the fact that active processes (ATP, molecular motors) within the cell modify cytoskeletal elasticity and tension.     

Simulation of surface tension in 2D and 3D with smoothed particle hydrodynamics method

The methods for simulating surface tension with smoothed particle hydrodynamics (SPH) method in two dimensions and three dimensions are developed. In 2D surface tension model, the SPH particle on the boundary in 2D is detected dynamically according to the algorithm developed by Dilts [G.A. Dilts, Moving least-squares particle hydrodynamics II: conservation and boundaries, International Journal for Numerical Methods in Engineering 48 (2000) 1503–1524]. The boundary curve in 2D is reconstructed locally with Lagrangian interpolation polynomial. In 3D surface tension model, the SPH particle on the boundary in 3D is detected dynamically according to the algorithm developed by Haque and Dilts [A. Haque, G.A. Dilts, Three-dimensional boundary detection for particle methods, Journal of Computational Physics 226 (2007) 1710–1730]. The boundary surface in 3D is reconstructed locally with moving least squares (MLS) method. By transforming the coordinate system, it is guaranteed that the interface function is one-valued in the local coordinate system. The normal vector and curvature of the boundary surface are calculated according to the reconstructed boundary surface and then surface tension force can be calculated. Surface tension force acts only on the boundary particle. Density correction is applied to the boundary particle in order to remove the boundary inconsistency. The surface tension models in 2D and 3D have been applied to benchmark tests for surface tension. The ability of the current method applying to the simulation of surface tension in 2D and 3D is proved.     

物理学在肿瘤细胞的极性及迁移研究中的应用

肿瘤细胞和所处微环境的物理性质, 以及它们之间的相互物理作用对于肿瘤的产生、发展与转移都有极大的影响, 这使得从物理学角度探索肿瘤研究成为了必然趋势. 肿瘤转移是癌症致死的最大因素, 而肿瘤细胞迁移中的极化是肿瘤转移的重要一步. 本文总结了物理学实验和模型在揭示细胞迁移和极化机理方面的贡献. 实验上应用最新的微流控芯片技术与表面微模型化技术等手段, 研究空间维度、黏附行为、机械力等物理信号对于细胞极性的建立与保持以及细胞迁移行为的影响后, 发现物理信号与生化反应之间的相互耦合对于细胞迁移有着至关重要的作用; 理论上基于扩散反应方程, 已经建立了一系列表征细胞极化的模型. 今后的研究将结合物理实验建立肿瘤细胞迁移中的极化模型, 进而发展针对肿瘤细胞感知物理信号的新的治疗肿瘤转移方法.     

Fluctuations in granular media

Dense slowly evolving or static granular materials exhibit strong force fluctuations even though the spatial disorder of the grains is relatively weak. Typically, forces are carried preferentially along a network of "force chains." These consist of linearly aligned grains with larger-than-average force. A growing body of work has explored the nature of these fluctuations. We first briefly review recent work concerning stress fluctuations. We then focus on a series of experiments in both two- and three-dimension [(2D) and (3D)] to characterize force fluctuations in slowly sheared systems. Both sets of experiments show strong temporal fluctuations in the local stress/force; the length scales of these fluctuations extend up to 10(2) grains. In 2D, we use photoelastic disks that permit visualization of the internal force structure. From this we can make comparisons to recent models and calculations that predict the distributions of forces. Typically, these models indicate that the distributions should fall off exponentially at large force. We find in the experiments that the force distributions change systematically as we change the mean packing fraction, gamma. For gamma's typical of dense packings of nondeformable grains, we see distributions that are consistent with an exponential decrease at large forces. For both lower and higher gamma, the observed force distributions appear to differ from this prediction, with a more Gaussian distribution at larger gamma and perhaps a power law at lower gamma. For high gamma, the distributions differ from this prediction because the grains begin to deform, allowing more grains to carry the applied force, and causing the distributions to have a local maximum at nonzero force. It is less clear why the distributions differ from the models at lower gamma. An exploration in gamma has led to the discovery of an interesting continuous or "critical" transition (the strengthening/softening transition) in which the mean stress is the order parameter, and the mean packing fraction, gamma, must be adjusted to a value gamma(c) to reach the "critical point." We also follow the motion of individual disks and obtain detailed statistical information on the kinematics, including velocities and particle rotations or spin. Distributions for the azimuthal velocity, V(theta), and spin, S, of the particles are nearly rate invariant, which is consistent with conventional wisdom. Near gamma(c), the grain motion becomes intermittent causing the mean velocity of grains to slow down. Also, the length of stress chains grows as gamma-->gamma(c). The 3D experiments show statistical rate invariance for the stress in the sense that when the power spectra and spectral frequencies of the stress time series are appropriately scaled by the shear rate, Omega, all spectra collapse onto a single curve for given particle and sample sizes. The frequency dependence of the spectra can be characterized by two different power laws, P proportional, variant omega(-alpha), in the high and low frequency regimes: alpha approximately 2 at high omega; alpha<2 at low omega. The force distributions computed from the 3D stress time series are at least qualitatively consistent with exponential fall-off at large stresses. (c) 1999 American Institute of Physics.     

Self-propelled particle model for cell-sorting phenomena

A self-propelled particle model is introduced to study cell sorting occurring in some living organisms. This allows us to evaluate the influence of intrinsic cell motility separately from differential adhesion with fluctuations, a mechanism previously shown to be sufficient to explain a variety of cell rearrangement processes. We find that the tendency of cells to actively follow their neighbors greatly reduces segregation time scales. A finite-size analysis of the sorting process reveals clear algebraic growth laws as in physical phase-ordering processes, albeit with unusual scaling exponents.     

Quasistatic and dynamic functional properties of thin superelastic NiTi wires

2D/3D structures made from thin NiTi wires (d < 100μm) are currently considered for engineering applications in textile, medical or robotics fields. The development of such novel applications requires the knowledge of the thermomechanical behaviour of NiTi ultra thin wires in tension, torsion bending and combined loads, which might differ from that of thicker wires due to influence of texture, cold work and higher aspect ratio. To deal with this challenge, a new experimental testing approach presented in this paper has been developed. It includes thermomechanical tensile testing, combined tension-torsion testing and forced tensile vibrational testing realized on self-made testing rigs equipped with Peltier furnaces and in-situ electric measurement systems. The collected experimental datasets provide a basis upon which FEM implementable SMA models describing functional thermomechanical behaviours of 2D/3D NiTi wire structures (quasistatic and dynamic) are presently being constructed     

Structural phase boundary of SrTiO3 under [111] stress

The first electron paramagnetic-resonance (EPR) experiments under tension in an oxide are reported. They show that for SrTiO₃ in the physically accessible region, the cubictetragonal phase boundary is along the [111] tension axis and not temperature near the particular novel multicritical point, which occurs for finite stress. This occurrence is tentatively attributed to the cubic anisotropic fluctuations in this material.     

Anderson transition in 1D systems with spatial disorder

A simple Kronig-Penney model for 1D mesoscopic systems with δ peak potentials is used to study numerically the influence of spatial disorder on conductance fluctuations and distribution at different regimes. The Lévy laws are used to investigate the statistical properties of the eigenstates. It is found that an Anderson transition occurs even in 1D meaning that the disorder can also provide constructive quantum interferences. The critical disorder W_c for this transition is estimated. In these 1D systems, the metallic phase is well characterized by a Gaussian conductance distribution. Indeed, the results relative to conductance distribution are in good agreement with the previous works in 2D and 3D systems for other models. At this transition, the conductance probability distribution has a system size independent shape with large fluctuations in good agreement with previous works.     

(TTT)2I3+δ compounds--superconducting fluctuations?

We suggest that the high conductivity observed in non-stoichiometric (TTT)₂I_3+δ samples is a consequence of the suppression of 3D corrections by the incommensurate iodine chains which produce a random potential on the conducting TTT chains. As a result, the TTT chains can act as an array of independent 1D conductors for which it is known that superconducting fluctuations, suppressed in the 3D case, are strong and lead to high conductivity.     

Comparison between lattice Boltzmann method and Navier–Stokes high order schemes for computational aeroacoustics

Computational aeroacoustic (CAA) simulation requires accurate schemes to capture the dynamics of acoustic fluctuations, which are weak compared with aerodynamic ones. In this paper, two kinds of schemes are studied and compared: the classical approach based on high order schemes for Navier–Stokes-like equations and the lattice Boltzmann method. The reference macroscopic equations are the 3D isothermal and compressible Navier–Stokes equations. A Von Neumann analysis of these linearized equations is carried out to obtain exact plane wave solutions. Three physical modes are recovered and the corresponding theoretical dispersion relations are obtained. Then the same analysis is made on the space and time discretization of the Navier–Stokes equations with the classical high order schemes to quantify the influence of both space and time discretization on the exact solutions. Different orders of discretization are considered, with and without a uniform mean flow. Three different lattice Boltzmann models are then presented and studied with the Von Neumann analysis. The theoretical dispersion relations of these models are obtained and the error terms of the model are identified and studied. It is shown that the dispersion error in the lattice Boltzmann models is only due to the space and time discretization and that the continuous discrete velocity Boltzmann equation yield the same exact dispersion as the Navier–Stokes equations. Finally, dispersion and dissipation errors of the different kind of schemes are quantitatively compared. It is found that the lattice Boltzmann method is less dissipative than high order schemes and less dispersive than a second order scheme in space with a 3-step Runge–Kutta scheme in time. The number of floating point operations at a given error level associated with these two kinds of schemes are then compared.     

Two-dimensional gas phases of Ar,Kr, AND Xe on Ag(111)

Observations and calculations are reported for the 2D gas phase of Ar, Kr, and Xe adsorbed on the (111) face of Ag. The measurement of the coverage of 2D gas is sensitive to the gas adsorbed on the coherently diffracting regions of the Ag; appreciable contributions to the measured coverage from gas adsorbed at extrinsic sites can be excluded. The gas density at the condensation of the solid monolayer is remarkably high, of the order of 15% of the 2D solid density. Statistical mechanical calculations, using Monte Carlo simulations, show that the unusually dense 2D gas is stabilized against condensation because substrate-mediated interactions raise the energy of the 2D solid relative to the value which would be calculated using the bare 3D pair potentials. The simulations show that the gas is very nonideal, with large specific heat and large density fluctuations. The only comparable states of a 3D gas occur near the gas-liquid critical point.     

Negative filament tension at high excitability in a model of cardiac tissue

One of the fundamental mechanisms for the onset of turbulence in 3D excitable media is negative filament tension. Thus far, negative tension has always been obtained in media under low excitability. For this reason, its application to normal (nonischemic) cardiac tissue has been questionable, as such cardiac turbulence typically occurs at high excitability. Here, we report expansion of scroll rings (low curvature negative filament tension) in a medium with high excitability by numerical integration of the Luo-Rudy model of cardiac tissue. We discuss the relation between negative tension and the meandering of 2D spiral waves and the possible applications to cardiac modeling.     

Fluctuation approach to the problem of thermodynamics’ applicability to nanoparticles

The root-mean square fluctuations of the temperature and energetic surface tension of metallic and molecular nanoparticles have been estimated. It is revealed that the relative value of mentioned fluctuations is not higher than several percents even for the particles of 0.5 nm in size. We thus conclude that it is possible to apply the thermodynamic approach to nanoparticles with fluctuating properties, and the fluctuations do not lead to nanoparticle instability and decay.     

Dynamic strength of fluid membranes

Rupturing fluid membrane vesicles with a steady ramp of micropipette suction yields a tension distribution that images the kinetic process of membrane failure. When plotted on a log scale of tension loading rate, the distribution peaks (membrane strengths) define a dynamic tension spectrum with distinct regimes that reflect passage of prominent energy barriers along the pathway to rupture. Demonstrated here by tests on giant PC lipid vesicles over loading rates from 0.06–60 mN/m/s, the stochastic process of rupture can be modelled as a causal sequence of two thermally-activated transitions where each transition governs membrane strength on separate scales of loading rate. Under fast ramps of tension, a steep linear regime appears in each spectrum at high strengths which implies that failure requires nucleation of a rare nanoscale defect. The slope and projected intercept yield defect size and spontaneous production rate respectively. However, under slow ramps of loading, the spectrum crosses over to a shallow-curved regime at lower strength, which is consistent with the kinetic impedance to opening an unstable hole in a fluid film. The dependence of rupture tension on rate reveals hole edge energy and frequency scale for thermal fluctuations in size. To cite this article: E. Evans, V. Heinrich, C. R. Physique 4 (2003).     

Negative tension induced by lipid uptake

Membrane fusion is an important process in cell biology. While the molecular mechanisms of fusion are actively studied at a very local scale, the consequences of fusion at a larger scale on the shape and stability of the membrane are still not explored. In this Letter, the evolution of the membrane tension during the fusion of positive small unilamellar vesicles with a negative giant unilamellar vesicle has been experimentally investigated and compared to an existing theoretical model. The tension has been deduced using videomicroscopy from the measurement of the fluctuation spectrum and of the time correlation function of the fluctuations. We show that fusion induces a strong decrease in the effective tension of the membrane which eventually reaches negative values. Under these conditions, we show that localized instabilities appear on the vesicle. The membrane finally collapses, forming dense lipid structures.     

Self-Dual Strings in Six Dimensions: Anomalies,the <Emphasis Type="Italic">ADE</Emphasis>-Classification,and the World-Sheet <Emphasis Type="Italic">WZW</Emphasis>-Model

We consider the (2,0) supersymmetric theory of tensor multiplets and self-dual strings in six space-time dimensions. Space-time diffeomorphisms that leave the string world-sheet invariant appear as gauge transformations on the normal bundle of the world-sheet. The naive invariance of the model under such transformations is however explicitly broken by anomalies: The electromagnetic coupling of the string to the two-form gauge field of the tensor multiplet suffers from a classical anomaly, and there is also a one-loop quantum anomaly from the chiral fermions on the string world-sheet. Both of these contributions are proportional to the Euler class of the normal bundle of the string world-sheet, and consistency of the model requires that they cancel. This imposes strong constraints on possible models, which are found to obey an ADE-classification. We then consider the decoupled world-sheet theory that describes low-energy fluctuations (compared to the scale set by the string tension) around a configuration with a static, straight string. The anomaly structure determines this to be a supersymmetric version of the level one Wess-Zumino-Witten model based on the group      

Reply to comment on “Polymerization,bending, tension: What happens at the leading edge of motile cells?” by Falko Ziebert and Igor S. Aranson

We are grateful to Falko Ziebert and Igor Aranson, who continue with their comment on our publication [5] a discussion on modelling concepts. Ziebert and Aranson present in their contribution to this volume [14] a model concept for cell motility and morphodynamics focusing on gel flow and its determinants. This type of models is particularly useful for describing slow dynamics on the length scale of the whole cell and modelling of cell shape [1,8,11,13,14]. Our approach is set apart from the gel models by taking into account a weakly cross-linked F-actin network region close to the location of polymerization in the lamellipodia of motile cells (semi-flexible region) in addition to the gel in the bulk. This addition explains a variety of non-linear dynamic regimes in cellular and reconstituted systems, and the force-velocity relation of fish keratocytes. Ziebert and Aranson point out in their comment that 1) a more detailed modelling of gel processes may be required to capture large cell deformations, 2) the dynamics of adhesion strength and distribution may be relevant for understanding the relation between cell shape, the dynamic regime of motion and cell velocity, 3) coarse grained models may allow for unifying both concepts, and 4) fluctuations are important in morphodynamics.     

Fluctuations, dynamics, and the stretch-coil transition of single actin filaments in extensional flows

Semiflexible polymers subject to hydrodynamic forcing play an important role in cytoskeletal motions in the cell, particularly when filaments guide molecular motors whose motions create flows. Near hyperbolic stagnation points, filaments experience a competition between bending elasticity and tension and are predicted to display suppressed thermal fluctuations in the extensional regime and a buckling instability under compression. Using a microfluidic cross-flow geometry, we verify these predictions in detail, including a fluctuation-rounded stretch-coil transition of actin filaments.     

Description of the fluctuating colloid-polymer interface

To describe the full spectrum of surface fluctuations of the interface between phase-separated colloid-polymer mixtures from low scattering vector q (classical capillary wave theory) to high q (bulklike fluctuations), one must take account of the interface's bending rigidity. We find that the bending rigidity is negative and that on approach to the critical point it vanishes proportionally to the interfacial tension. Both features are in agreement with Monte Carlo simulations.