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Computer model of the mechanical deformation of a cell by the tip of an AFM cantilever. The model is based on continuum mechanics, and it includes contributions from the elasticity of the cell membrane as well as the interior of the cell.

Multiscale Modeling of Cell Mechanics and Force Spectroscopy


Michael McElfresh, Robert E. Rudd, Rod Balhorn, Tim Ratto

The introduction of new technology to characterize biological systems has been crucial to the current bioscience revolution. One of the current challenges is the development of technology for characterization at the cellular and sub-cellular level. This is needed for the direct study of how genome information is expressed at the microscopic level, for example. Scanning Probe Microscopy has been identified as a promising means to characterize biological systems at scales of nanometers to microns. Atomic Force Microscopy (AFM) and its derivatives such as Recognition Force Microscopy (RFM) are well suited to the characterization of biological systems. AFM uses the detection of tiny cantilevers in contact with the specimen to provide information about the topography and elastic properties of cells; RFM goes a step further, using molecules attached to an AFM cantilever tip to study the binding at various sites on the specimen. It is only now becoming possible to use the techniques on living cells, and a group at Lawrence Livermore National Laboratory is among the pioneers of this technique. [1]
One challenge with using RFM on living cells is the fact that the cell is not rigid, and as the force is applied to a receptor site, it is not just the receptor site that is affected. The whole cell deforms under the applied force, and the measured binding force is a convolution of the local, intrinsic binding force of the receptor site and the gross elastic response of the cell. We have developed a model of the elastic deformation of the cell in order to separate the two effects.
The model is based on a continuum level analysis of the elastic deformation. [2] The major contributions to the strain energy come from the constitutive response of the incompressable interior, the tension of the membrane and the curvature of the membrane. The membrane in this context refers to a complex structure of multiple phospholipid bilayers and membrane proteins including the cytoskeleton. The curvature energy is known as the Canham-Helfrich Hamiltonian in the statistical mechanics community [3]; the form of the other terms in the energy has been studied in the context of solid mechanics of hyperelastic media. The novel features of this formalism are the treatment of the Canham-Helfrich Hamiltonian for finite deformations and the combination of these energies in the model of a single system.
The model has been implemented in finite elements. New experimental techniques have been developed to parameterize the model; they are discussed elsewhere. [1] As a validation the model has been compared with force-displacement curves coming from AFM used in a nanoindentation mode. The model then allows site-specific mechanical properties to be deconvoluted from the gross cell deformation in RFM experiments. Eventually, it may be possible to use concurrent multiscale modeling to provide a model of the atomistic interactions at the receptor site too. [4]

SELECTED PUBLICATIONS


  1. M. McElfresh, E. Baesu, R. Balhorn, M.J. Allen, J. Belak and R.E. Rudd, "Combining Constitutive Materials Modeling with Atomic Force Microscopy to Understand the Mechanical Properties of Living Cells," Proc. Natl. Acad. Sci. 99, 6493-7 (2002).
  2. T. V. Ratto, R. E. Rudd, K. C. Langry, R. L. Balhorn and M. W. McElfresh, "Nonlinearly Additive Forces in Multivalent Ligand Binding to a Single Protein Revealed with Force Spectroscopy," Langmuir 22, 1749 - 1757 (2006).
  3. K. C. Langry, T. V. Ratto, R. E. Rudd and M. W. McElfresh, "The AFM Measured Force Required to Rupture the Dithiolate Linkage of Thioctic Acid to Gold Is Less than the Rupture Force of a Simple Gold-Alkyl Thiolate Bond," Langmuir 21, 12064-12067 (2005).
  4. T. V. Ratto, K. C. Langry, R. E. Rudd, R. L. Balhorn, M. J. Allen, M. W. McElfresh, "Force Spectroscopy of the Double-Tethered Concanavalin-A Mannose Bond," Biophys. J. 86, 2430-2437 (2004).
  5. E. Baesu, R.E. Rudd, M. McElfresh, R. Balhorn, M. Allen and J. Belak, "Continuum Modeling of Cell Membranes," Intl. J. Nonlinear Mech. 39, 369-77 (2003).
  6. P. Canham, J. Theor. Biol. 26, 61 (1970); W. Helfrich, Z. Naturforsch. 28C, 693 (1973).
  7. R.E. Rudd and J.Q. Broughton, "Concurrent Coupling of Length Scales in Solid State Systems," Phys. Stat. Sol. (b) 217, 251 (2000).
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Maintained by Robert E. Rudd -- Last updated on 27 March 2006.
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