Target search on networks-within-networks with applications to protein-DNA interactions

TL;DR

This paper introduces a three-layer multiplex network model to analyze complex node target search processes across hierarchical systems, extending traditional network search theories to multilayered real-world scenarios.

Contribution

It develops a general theoretical framework with closed-form solutions for search efficiency in multilayer networks, broadening understanding of hierarchical search dynamics.

Findings

Derived universal relationship between search efficiency and network parameters

Extended network search models to multilayer, hierarchical systems

Applicable to diverse fields like epidemiology and cellular biology

Abstract

We present a novel framework for understanding node target search in systems organized as hierarchical networks-within-networks. Our work generalizes traditional search models on complex networks, where the mean-first passage time is typically inversely proportional to the node degree. However, real-world search processes often span multiple network layers, such as moving from an external environment into a local network, and then navigating several internal states. This multilayered complexity appears in scenarios such as international travel networks, tracking email spammers, and the dynamics of protein-DNA interactions in cells. Our theory addresses these complex systems by modeling them as a three-layer multiplex network: an external source layer, an intermediate spatial layer, and an internal state layer. We derive general closed-form solutions for the steady-state flux through a target node, which serves as a proxy for inverse mean-first passage time. Our results reveal a universal relationship between search efficiency and network-specific parameters. This work extends the current understanding of multiplex networks by focusing on systems with hierarchically connected layers. Our findings have broad implications for fields ranging from epidemiology to cellular biology and provide a more comprehensive understanding of search dynamics in complex, multilayered environments.