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.

[1]  Peterson.  Linear response of the human erythrocyte to mechanical stress. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[2]  L. Addadi,et al.  Force and focal adhesion assembly: a close relationship studied using elastic micropatterned substrates , 2001, Nature Cell Biology.

[3]  Joyce Y. Wong,et al.  Directed Movement of Vascular Smooth Muscle Cells on Gradient-Compliant Hydrogels† , 2003 .

[4]  M. Nakao.  New insights into regulation of erythrocyte shape , 2002, Current opinion in hematology.

[5]  E. Sackmann,et al.  Measurement of erythrocyte membrane elasticity by flicker eigenmode decomposition. , 1995, Biophysical journal.

[6]  E. Evans,et al.  Molecular maps of red cell deformation: hidden elasticity and in situ connectivity. , 1994, Science.

[7]  Masao Doi,et al.  Introduction to Polymer Physics , 1996 .

[8]  G. Oster,et al.  Mechanical aspects of mesenchymal morphogenesis. , 1983, Journal of embryology and experimental morphology.

[9]  C. Lim,et al.  Mechanics of the human red blood cell deformed by optical tweezers , 2003 .

[10]  R. Merkel,et al.  Energy landscapes of receptor–ligand bonds explored with dynamic force spectroscopy , 1999, Nature.

[11]  E. Grood,et al.  The Strain Magnitude and Contact Guidance Determine Orientation Response of Fibroblasts to Cyclic Substrate Strains , 2000, Connective tissue research.

[12]  S. Brenner,et al.  Inhibition of actin polymerization by latrunculin A , 1987, FEBS letters.

[13]  W. Kohn,et al.  Elastic interaction of two atoms adsorbed on a solid surface , 1976 .

[14]  U. Schwarz,et al.  Elastic interactions of active cells with soft materials. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  R. Siems.  Mechanical Interactions of Point Defects , 1968, December 1.

[16]  L. Rayleigh,et al.  XVI. On the instability of a cylinder of viscous liquid under capillary force , 1892 .

[17]  U. Schwarz,et al.  Elastic interactions of cells. , 2002, Physical review letters.

[18]  E. Ling,et al.  Modulation of red cell band 4.1 function by cAMP-dependent kinase and protein kinase C phosphorylation. , 1988, The Journal of biological chemistry.

[19]  B. Geiger,et al.  Encounters in Space , 2001, Science.

[20]  Daniel Choquet,et al.  Extracellular Matrix Rigidity Causes Strengthening of Integrin–Cytoskeleton Linkages , 1997, Cell.

[21]  Benjamin Geiger,et al.  Exploring the Neighborhood Adhesion-Coupled Cell Mechanosensors , 2002, Cell.

[22]  U. Schwarz,et al.  Cell organization in soft media due to active mechanosensing , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[23]  Z. Kam,et al.  Early molecular events in the assembly of matrix adhesions at the leading edge of migrating cells , 2003, Journal of Cell Science.

[24]  E. Sackmann,et al.  Viscoelastic properties of erythrocyte membranes in high-frequency electric fields , 1984, Nature.

[25]  D. Hamann,et al.  Long-Range Elastic Interactions and Staging in Graphite Intercalation Compounds , 1979 .

[26]  J. Hoffman.  Some red blood cell phenomena for the curious. , 2004, Blood cells, molecules & diseases.

[27]  E. Sackmann,et al.  Entropic elasticity of end adsorbed polymer chains: The spectrin network of red blood cells as C*‐gel , 1996 .

[28]  V. Mironov,et al.  Engineering biological structures of prescribed shape using self-assembling multicellular systems. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[29]  S. Safran,et al.  Elastic deformations of grafted layers with surface stress. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[30]  Benjamin Geiger,et al.  Focal Contacts as Mechanosensors Externally Applied Local Mechanical Force Induces Growth of Focal Contacts by an Mdia1-Dependent and Rock-Independent Mechanism , 2001 .

[31]  D E Ingber,et al.  Cellular control lies in the balance of forces. , 1998, Current opinion in cell biology.

[32]  M. Dembo,et al.  Cell movement is guided by the rigidity of the substrate. , 2000, Biophysical journal.

[33]  Frank Jülicher,et al.  Membranes with rotating motors. , 2003, Physical review letters.

[34]  Nelson,et al.  Grain-boundary buckling and spin-glass models of disorder in membranes. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[35]  F. Brochard,et al.  Frequency spectrum of the flicker phenomenon in erythrocytes , 1975 .

[36]  D. Discher,et al.  New insights into red cell network structure, elasticity, and spectrin unfolding--a current review. , 2001, Cellular & molecular biology letters.

[37]  M. Dembo,et al.  Stresses at the cell-to-substrate interface during locomotion of fibroblasts. , 1999, Biophysical journal.

[38]  J. Fournier,et al.  Fluctuation spectrum of fluid membranes coupled to an elastic meshwork: jump of the effective surface tension at the mesh size. , 2003, Physical review letters.

[39]  Albert K. Harris,et al.  Fibroblast traction as a mechanism for collagen morphogenesis , 1981, Nature.

[40]  Benjamin Geiger,et al.  Cell mechanosensitivity controls the anisotropy of focal adhesions. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[41]  R. Mukhopadhyay,et al.  Stomatocyte–discocyte–echinocyte sequence of the human red blood cell: Evidence for the bilayer– couple hypothesis from membrane mechanics , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[42]  N. Gov,et al.  Pinning of fluid membranes by periodic harmonic potentials. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[43]  A. Harris,et al.  Silicone rubber substrata: a new wrinkle in the study of cell locomotion. , 1980, Science.

[44]  N. Balaban,et al.  Calculation of forces at focal adhesions from elastic substrate data: the effect of localized force and the need for regularization. , 2002, Biophysical journal.

[45]  Anomalous fluctuations of active polar filaments. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[46]  Y. Wang,et al.  Cell locomotion and focal adhesions are regulated by substrate flexibility. , 1997, Proceedings of the National Academy of Sciences of the United States of America.

[47]  F. C. MacKintosh,et al.  Microscopic Viscoelasticity: Shear Moduli of Soft Materials Determined from Thermal Fluctuations , 1997 .

[48]  R T Tranquillo,et al.  An anisotropic biphasic theory of tissue-equivalent mechanics: the interplay among cell traction, fibrillar network deformation, fibril alignment, and cell contact guidance. , 1997, Journal of biomechanical engineering.

[49]  J. Hoffman,et al.  Questions for red blood cell physiologists to ponder in this millenium. , 2001, Blood cells, molecules & diseases.

[50]  Ben Fabry,et al.  Traction fields, moments, and strain energy that cells exert on their surroundings. , 2002, American journal of physiology. Cell physiology.

[51]  David R Nelson,et al.  Virus shapes and buckling transitions in spherical shells. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[52]  A. Zilman,et al.  Hydrodynamics of confined membranes. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[53]  A. C. Maggs,et al.  Dynamics and rheology of actin solutions , 1996 .

[54]  K. Beningo,et al.  Flexible substrata for the detection of cellular traction forces. , 2002, Trends in cell biology.

[55]  J Toner,et al.  Nonequilibrium fluctuations, traveling waves, and instabilities in active membranes. , 1999, Physical review letters.

[56]  D. Boal,et al.  Mechanics of the cell , 2001 .

[57]  P. Davies,et al.  Quantitative studies of endothelial cell adhesion. Directional remodeling of focal adhesion sites in response to flow forces. , 1994, The Journal of clinical investigation.

[58]  S Levin,et al.  Membrane fluctuations in erythrocytes are linked to MgATP-dependent dynamic assembly of the membrane skeleton. , 1991, Biophysical journal.

[59]  Samuel A. Safran,et al.  Statistical Thermodynamics Of Surfaces, Interfaces, And Membranes , 1994 .

[60]  Kenneth M. Yamada,et al.  Physical state of the extracellular matrix regulates the structure and molecular composition of cell-matrix adhesions. , 2000, Molecular biology of the cell.

[61]  M. Sheetz,et al.  Forces on adhesive contacts affect cell function. , 1998, Current opinion in cell biology.

[62]  E. Sackmann,et al.  Bending undulations and elasticity of the erythrocyte membrane: effects of cell shape and membrane organization , 2004, European Biophysics Journal.

[63]  Rafi Korenstein,et al.  Mechanical Fluctuations of the Membrane–Skeleton Are Dependent on F-Actin ATPase in Human Erythrocytes , 1998, The Journal of cell biology.

[64]  H. Hämmerle,et al.  Orientation of cultured arterial smooth muscle cells growing on cyclically stretched substrates. , 1986, Acta anatomica.

[65]  Moses,et al.  Instability and "pearling" states produced in tubular membranes by competition of curvature and tension. , 1994, Physical review letters.

[66]  Erich Sackmann,et al.  Dynamic reflection interference contrast (RIC-) microscopy : a new method to study surface excitations of cells and to measure membrane bending elastic moduli , 1987 .

[67]  T D Pollard,et al.  Mechanical properties of actin filament networks depend on preparation, polymerization conditions, and storage of actin monomers. , 1998, Biophysical journal.

[68]  A. Zilman,et al.  Cytoskeleton confinement and tension of red blood cell membranes. , 2003, Physical review letters.

[69]  K. Jacobson,et al.  Imaging the traction stresses exerted by locomoting cells with the elastic substratum method. , 1996, Biophysical journal.

[70]  Navin Pokala,et al.  High Rates of Actin Filament Turnover in Budding Yeast and Roles for Actin in Establishment and Maintenance of Cell Polarity Revealed Using the Actin Inhibitor Latrunculin-A , 1997, The Journal of cell biology.

[71]  Nelson,et al.  Defects in flexible membranes with crystalline order. , 1988, Physical review. A, General physics.

[72]  K. Jacobson,et al.  Local measurements of viscoelastic parameters of adherent cell surfaces by magnetic bead microrheometry. , 1998, Biophysical journal.

[73]  Erich Sackmann,et al.  Theoretical and phase contrast microscopic eigenmode analysis of erythrocyte flicker : amplitudes , 1992 .

[74]  E. Evans.  Bending elastic modulus of red blood cell membrane derived from buckling instability in micropipet aspiration tests. , 1983, Biophysical journal.

[75]  S. Timoshenko,et al.  Theory of elasticity , 1975 .

[76]  Joachim P Spatz,et al.  Activation of integrin function by nanopatterned adhesive interfaces. , 2004, Chemphyschem : a European journal of chemical physics and physical chemistry.

[77]  Sriram Ramaswamy,et al.  Hydrodynamic fluctuations and instabilities in ordered suspensions of self-propelled particles. , 2001, Physical review letters.

[78]  N. Mohandas,et al.  Modulation of Erythrocyte Membrane Mechanical Function by β-Spectrin Phosphorylation and Dephosphorylation (*) , 1995, The Journal of Biological Chemistry.

[79]  F. Grinnell,et al.  Fibroblast-collagen-matrix contraction: growth-factor signalling and mechanical loading. , 2000, Trends in cell biology.

[80]  R. Bar-Ziv,et al.  Pearling in cells: a clue to understanding cell shape. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[81]  O. Thoumine,et al.  Time scale dependent viscoelastic and contractile regimes in fibroblasts probed by microplate manipulation. , 1997, Journal of cell science.

[82]  S. Aaronson,et al.  Development of 3T3‐like lines from Balb/c mouse embryo cultures: Transformation susceptibility to SV40 , 1968, Journal of cellular physiology.

[83]  H. Horner,et al.  Elastic interaction and phase transition in coherent metal-hydrogen alloys , 1974 .