The role of molecular motors in the mechanics of active gels and the effects of inertia, hydrodynamic interaction and compressibility in passive microrheology

The mechanical properties of soft biological materials are essential to their physiological function and cannot easily be duplicated by synthetic materials. The study of the mechanical properties of biological materials has lead to the development of new rheological characterization techniques. In the technique called passive microbead rheology, the positional autocorrelation function of a micron-sized bead embedded in a viscoelastic fluid is used to infer the dynamic modulus of the fluid. Single particle microrheology is limited to fluids were the microstructure is much smaller than the size of the probe bead. To overcome this limitation in two-bead microrheology the cross-correlated thermal motion of pairs of tracer particles is used to determine the dynamic modulus. Here we present a time-domain data analysis methodology and generalized Brownian dynamics simulations to examine the effects of inertia, hydrodynamic interaction, compressibility and non-conservative forces in passive microrheology. A type of biological material that has proven specially challenging to characterize are active gels. They are formed by semiflexible polymer filaments driven by motor proteins that convert chemical energy from the hydrolysis of adenosine triphosphate (ATP) to mechanical work and motion. Active gels perform essential functions in living tissue. Here we introduce a single-chain mean-field model to describe the mechanical properties of active gels. We model the semiflexible filaments as bead-spring chains and the molecular motors are accounted for by using a mean-field approach. The level of description of the model includes the end-to-end length and attachment state of the filaments, and the motor-generated forces, as stochastic state variables which evolve according to a proposed differential Chapman-Kolmogorov equation. The model allows accounting for physics that are not available in models that have been postulated on coarser levels of description. Moreover it allows the prediction of observables at time scales that will be too difficult to achieve in multi-chain simulations.