The elastic properties of the substrate are thus characterized http://www.selleckchem.com/products/Perifosine.html by a Young’s modulus Em, which measures effective substrate rigidity, and its Poisson ratio ��, which quantifies the Poisson effect. The Poisson effect states that upon imposing an uniaxial stress ��zz on a rod of this material along its long axis (say the z axis), the rod will not only expand in the z direction with strain uzz = ��zz/Em, but will additionally contract in the normal directions with principal strain uxx = uyy = ?��uzz. In most experiments, incompressible substrates with a Poisson ratio close to 0.5 are used with a stiffness in the kiloPascal (kPa) range. We now ask for the strain field uij(x,y) right at the surface of the substrate that is induced by the force dipole density ��ij of a striated fiber (see Eq. 1).

Using the superposition principle for force dipoles valid for linear elastic materials and a Green’s function of elasticity, we find that the parallel strain component u11(x,y) can be written as a product of a lateral propagation factor, ��, that characterizes the propagation of strain in lateral (y) direction and a harmonic modulation in the (x) direction along the striated fiber (see the Supporting Material for the detailed derivation) u11(x,y)=��(|y|/a,��)2��1Ema2cos(2��x/a). (2) The strain field u11 is periodic in x direction with period a reflecting the periodicity of the striated fiber. The factor �� characterizes the propagation of strain in lateral direction away from the centerline of the fiber. The Poisson-effect significantly affects strain propagation and �� depends also on the Poisson ratio �� of the substrate.

Fig. 3 displays the lateral propagation factor �� for different values of the Poisson ratio ��. For an incompressible Brefeldin_A substrate with �� = 0, �� is positive for all lateral distances |y| > 0 and the parallel strain field consists of alternating stripes of compression and expansion that run parallel to the y axis (not shown). For a compressible substrate with �� > 0, however, �� becomes negative for lateral distances beyond a certain distance d and the parallel strain field is characterized by a checkerboard pattern as shown in Fig. 2 C. Note that in the limit |y| >> a, the factor �� describes an exponential decay �� ~ exp(?2��|y|/a). In this limit, the strain field u11 agrees with the strain field generated by a string of point force dipoles, which has been studied in Bischofs and Schwarz (25). Figure 3 Lateral propagation of substrate strain induced by a single striated fiber is characterized by a factor ��(d/a, ��) (see Eq. 2). This factor also characterizes the dependence of the elastic interaction energy between two parallel striated …