# Impact of global structure on diffusive exploration of organelle networks

## TL;DR

This study analyzes how the overall structure of organelle networks influences diffusive search efficiency, revealing that global properties like total edge length and loops significantly impact search times, with implications for cellular function and network design.

## Contribution

The paper demonstrates that global structural properties of planar networks largely determine diffusive search times, connecting network topology with physical models and biological regulation.

## Key findings

- Search time depends on total edge length and number of loops.
- Increasing loops reduces search times significantly.
- Global network properties can be used to optimize search efficiency.

## Abstract

We investigate diffusive search on planar networks, motivated by tubular organelle networks in cell biology that contain molecules searching for reaction partners and binding sites. Exact calculation of the diffusive mean first-passage time on a spatial network is used to characterize the typical search time as a function of network connectivity. We find that global structural properties --- the total edge length and number of loops --- are sufficient to largely determine network exploration times for a variety of both synthetic planar networks and organelle morphologies extracted from living cells. For synthetic networks on a lattice, we predict the search time dependence on these global structural parameters by connecting with percolation theory, providing a bridge from irregular real-world networks to a simpler physical model. The dependence of search time on global network structural properties suggests that network architecture can be designed for efficient search without controlling the precise arrangement of connections. Specifically, increasing the number of loops substantially decreases search times, pointing to a potential physical mechanism for regulating reaction rates within organelle network structures.