Diffusive search and trajectories on spatial networks: a propagator approach

TL;DR

This paper introduces analytical and simulation methods to study diffusive search processes within complex tubular networks, revealing how network structure influences search efficiency and biomolecular interactions.

Contribution

It develops exact propagator-based analytical tools and efficient Monte Carlo algorithms for modeling diffusion in tubular networks, applicable to biological organelle structures.

Findings

Heterogeneity in search times across network regions

Distribution of target sites affects search efficiency

Methodology applicable to synthetic and biological networks

Abstract

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.