  Several organelles in eukaryotic cells, including mitochondria and the
endoplasmic reticulum, form interconnected tubule networks extending throughout
the cell. These tubular networks host many biochemical pathways that rely on
proteins diffusively searching through the network to encounter binding
partners or localized target regions. In this work we develop both exact
analytical methods to compute mean first passage times and efficient kinetic
Monte Carlo algorithms to simulate trajectories of particles diffusing in a
tubular network. Our approach leverages exact propagator functions for the
distribution of transition times between network nodes and allows large
simulation time steps determined by the network structure. The methodology is
applied to both synthetic planar networks and organelle network structures,
demonstrating key general features such as the heterogeneity of search times in
different network regions and the functional advantage of broadly distributing
target sites throughout the network. The proposed algorithms pave the way for
future exploration of the interrelationship between tubular network structure
and biomolecular reaction kinetics.
