Although hundreds of cytosolic or transmembrane molecules form the primary cilium, few secreted molecules are known to contribute to ciliogenesis. Here, homologous secreted metalloproteases ADAMTS9 and ADAMTS20 are identified as ciliogenesis regulators that act intracellularly. Secreted and furin-processed ADAMTS9 bound heparan sulfate and was internalized by LRP1, LRP2 and clathrin-mediated endocytosis to be gathered in Rab11 vesicles with a unique periciliary localization defined by super-resolution microscopy. CRISPR-Cas9 inactivation of
ADAMTS9
impaired ciliogenesis in RPE-1 cells, which was restored by catalytically active ADAMTS9 or ADAMTS20 acting in
trans
, but not by their proteolytically inactive mutants. Their mutagenesis in mice impaired neural and yolk sac ciliogenesis, leading to morphogenetic anomalies resulting from impaired hedgehog signaling, which is transduced by primary cilia. In addition to their cognate extracellular proteolytic activity, ADAMTS9 and ADAMTS20 thus have an additional proteolytic role intracellularly, revealing an unexpected regulatory dimension in ciliogenesis.
This work provides generalized notions and analysis methods for the hitting time of random walks on graphs. The hitting time, also known as the Kemeny constant or the mean first passage time, of a random walk is widely studied; however, only limited work is available for the multiple random walker scenario. In this work we provide a novel method for calculating the hitting time for a single random walker as well as the first analytic expression for calculating the hitting time for multiple random walkers, which we denote as the group hitting time. We also provide a closed form solution for calculating the hitting time between specified nodes for both the single and multiple random walker cases. Our results allow for the multiple random walks to be different and, moreover, for the random walks to operate on different subgraphs. Finally, using sequential quadratic programming, we show that the combination of transition matrices that generate the minimal group hitting time for various graph topologies is often different.
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