Ax2t2 2RDrr

If the material is homogeneous and isotropic on length scales significantly smaller than the tracer, incompressible, and connected to the tracers by uniform no-slip boundary conditions over their entire surfaces, the two MSDs will be equal (Ax2(t)> 2 (Ax2(t)> . If these boundary and homogeneity conditions are not satisfied, the two MSDs will be unequal. In this case, applying the two-point MSD in the GSER will still yield the bulk rheology of the material (on the long length scale R), while...

Probing with Spherically Tipped Glass Microindenters

To address some of the limitations of microsphere indentation and AFM, a new approach was recently developed that uses a flexible glass microneedle with a spherical tip to probe the gel. The method is identical to AFM in principle, measuring the indentation of the gel in response to calibrated forces exerted at a spherical tip. However, the position of the probe and the indentation of the material are measured through an optical microscope with a calibrated focusing mechanism in conjunction...

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The proportionality factor k is called the spring constant, which describes the elasticity of the spring. Knowing the spring constant and the relaxation length L, it is straightforward to calculate the exerted force from the measured extension u. In a two-dimensional (2D) network with linear elasticity, the force can be reconstructed from the deformation along the same basic principles, that is the force is proportional to the degree of deformation. Due to the increase in dimensionality (from...

Lithography Without a Clean Room

Although the self-assembly of 3D surface structures using techniques such as electrohydrodynamic instabilities are attractive for numerous reasons, the ability to produce exact length scales, spatial arrangements, and arbitrarily defined shapes of surface structures can be especially advantageous for cell-based investigations Clark et al., 1992 Kaihara et al., 2000 Pirone and Chen, 2004 Whitesides et al., 2001 . Direct assembly methods such as lithographic techniques allow for the fabrication...

Probing with Microspheres Under Gravitational Forces

The microsphere indentation method is performed by measuring the indentation depth of a relatively heavy metal microsphere placed on top of the substrate Lo et al., 2000 . It works with a high degree of reproducibility for both polyacryl-amide and gelatin substrates with Young's moduli of E 2.2-33 kPa. Hydrogel substrates are prepared with embedded fluorescent latex beads 0.1-0.2 mm in diameter. As the method relies strongly on the ability to focus accurately on the substrate surface, using...

Basic Rheology for Biologists

Georges, and Soren Hvidt Department of Bioengineering Institute for Medicine and Engineering University of Pennsylvania Philadelphia, Pennsylvania 19104 Departments of Physiology and Physics Institute for Medicine and Engineering University of Pennsylvania Philadelphia, Pennsylvania 19104 Department of Chemistry Roskilde University Roskilde DK-4000, Denmark Abstract I. Introduction and Rationale II. Rheological Concepts III. Rheological Instrumentation F. Strain or...

Nano Digital Chemical Surfaces for Regulating Transmembrane Receptor Clustering

Extended Nanopatterns and Biofunctionalization Precise control of defined spacing between adhesive ligands on interfaces at a length scale of 10-200 nm remains a major challenge. However, it is this length scale on which protein clustering at FA occurs, thus surface patterning at this length scale is highly relevant to cell physiology. Most recently, nanopattern features have been found in adhesive fibers of collagen Jiang et al., 2004 Pompe et al., 2005 , which are major adhesive components...

Contributors

Numbers in parentheses indicate the pages on which the authors' contributions begin. Karen A. Beningo 29 , Department of Biology, Wayne State University, Detroit, Michigan 48202 Timo Betz 495 , Lehrstuhl fur die Physik Weicher Materie, Fakultat fur Physik und Geowissenschaften, Universitat Leipzig, Linnestr. 5, Leipzig D-04103, Germany Nicolas Biais 473 , Department of Biological Sciences, Columbia University, New York, New York 10027 Andrew D. Bicek 237 , Department of Biomedical Engineering,...