One-dimensional discrete aggregation-fragmentation model

Phase diagram of generalized totally asymmetric simple exclusion process on an open chain: Liggett-like boundary conditions

The totally asymmetric simple exclusion process with generalized update is a version of the discrete time totally asymmetric exclusion process with an additional interparticle interaction that controls the degree of particle clustering. Though the model was shown to be integrable on the ring and on the infinite lattice, on the open chain it was studied mainly numerically, while no analytic results existed even for its phase diagram. In this paper, we introduce boundary conditions associated with the infinite translation invariant stationary states of the model, which allow us to obtain the exact phase diagram analytically. We discuss the phase diagram in detail and confirm the analytic predictions by extensive numerical simulations.

Multivalent interactions facilitate motor-dependent protein accumulation at growing microtubule plus-ends

Growing microtubule ends organize end-tracking proteins into comets of mixed composition. Here using a reconstituted fission yeast system consisting of end-binding protein Mal3, kinesin Tea2 and cargo Tip1, we found that these proteins can be driven into liquid-phase droplets both in solution and at microtubule ends under crowding conditions. In the absence of crowding agents, cryo-electron tomography revealed that motor-dependent comets consist of disordered networks where multivalent interactions may facilitate non-stoichiometric accumulation of cargo Tip1. We found that two disordered protein regions in Mal3 are required for the formation of droplets and motor-dependent accumulation of Tip1, while autonomous Mal3 comet formation requires only one of them. Using theoretical modelling, we explore possible mechanisms by which motor activity and multivalent interactions may lead to the observed enrichment of Tip1 at microtubule ends. We conclude that microtubule ends may act as platforms where multivalent interactions condense microtubule-associated proteins into large multi-protein complexes.