UC San Diego

The mechanical properties of the cell cytoplasm, individual cell constituents and their surrounding medium play a determinant role in many cell functions, including migration, mechanotransduction, disease, etc. Several methods have been developed to measure the shear moduli of microscopic materials, being Passive Particle Tracking Microrheology one of the most prominent. It employs embedded microparticles subjected to Brownian thermal motion. From the statistics of the particles' motion, we extract the shear modulus of the sample. Particle Tracking Microrheology presents practical limitations when applied to complex materials. In this dissertation, we analyze two of these limitations : the Laplace transform of the microrheology data, and the anisotropy of the sample under study. In the first part, we examine the numerical Laplace transform techniques currently used and their limitations. We then provide a new alternative and show that it yields more accurate results than the methods currently in use. In the second part we focus on a type of anisotropy ubiquitously present in nature and technology: directionality. We describe the mechanical properties of a directional nematic fluid, and calculate the dynamics of interacting particles embedded in a directional medium. We use this result to formulate the directional particle tracking microrheology. We conclude that the motion of single particles don't provide enough information to fully characterize the rheology of a directional material. However, we design a protocol to extract the directional rheology of a sample by correlating the motion of pairs of distant particles, naming it Directional Two-Point Particle Tracking Microrheology. We assess the accuracy of the method by simulating the motion of groups of particles embedded in a directional viscoelastic fluid, and applying the method to them. We then apply this technique to a nematic F-actin gel, in the first report of the directional microrheological properties of F-actin. In the final part of this dissertation, we study the rheology of a different anisotropic system : a viscoelastic membrane embedded in a different fluid. By using this model system, we study the viscoelastic properties of the membrane- cortex complex of red blood cells, obtaining results that are consistent with reported data acquired through independent techniques