Generic flow profiles induced by a beating cilium

We describe a multipole expansion for the low-Reynolds-number fluid flows generated by a localized source embedded in a plane with a no-slip boundary condition. It contains 3 independent terms that fall quadratically with the distance and 6 terms that fall with the third power. Within this framework we discuss the flows induced by a beating cilium described in different ways: a small particle circling on an elliptical trajectory, a thin rod and a general ciliary beating pattern. We identify the flow modes present based on the symmetry properties of the ciliary beat.

The binding dynamics of tropomyosin on actin

We discuss a theoretical model for the cooperative binding dynamics of tropomyosin to actin filaments. Tropomyosin binds to actin by occupying seven consecutive monomers. The model includes a strong attraction between attached tropomyosin molecules. We start with an empty lattice and show that the binding goes through several stages. The first stage represents fast initial binding and leaves many small vacancies between blocks of bound molecules. In the second stage the vacancies annihilate slowly as tropomyosin molecules detach and reattach. Finally, the system approaches equilibrium. Using a grain-growth model and a diffusion-coagulation model we give analytical approximations for the vacancy density in all regimes.

Dynamics and cooperativity of microtubule decoration by the motor protein kinesin

We describe a theoretical and experimental analysis of the interaction between microtubules and dimeric motor proteins (kinesin, NCD), with special emphasis on the stoichiometry of the interaction, cooperative effects, and their consequences for the interpretation of biochemical and image reconstruction results. Monomeric motors can bind equivalently to microtubules without interference, at a stoichiometry of one motor head per tubulin subunit (alphabeta-heterodimer). By contrast, dimeric motors can interact with stoichiometries ranging between one and two heads per tubulin subunit, depending on binding constants of the first head and the subsequent binding of the second head, and the concentration of dimers in solution. Further, we show that an attractive interaction between the bound motor molecules can explain the higher periodicities observed in decorated microtubules (e.g. 16 nm periodicity), and the non-uniform decoration of a population of microtubules and give an estimate of the strength of this interaction.