Impact of global structure on diffusive exploration of organelle networks

Aidan I Brown,Laura M Westrate,Elena F Koslover

doi:10.1038/s41598-020-61598-8

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.

Highlights

The structure of these living networks is heavily regulated and likely functionally important[32,35]
We have investigated the characteristics that control diffusive search time on planar networks connecting homogeneously distributed nodes over a compact domain
We employ an exact calculation of mean first-passage time on a spatial network (Eqs.(1)–(4)) based on network connectivity and edge lengths

Summary

Introduction

The structure of these living networks is heavily regulated and likely functionally important[32,35]. We analytically calculate the diffusive mean first-passage time (MFPT)[17] between an initial and a target node, given the connectivity and physical length of the network edges. Equation (2) generalizes earlier work[8] to networks with distinct, non-exponential distributions for diffusion time along each edge. It differs from first-passage time calculations which assume all node-node transitions correspond to identical time steps[13,47] or with infinitesimal time spent on edges[23], and from the numerical integration previously used to evaluate diffusion on systems of containers connected with tubes[48].

Methods

Results

Conclusion