Eigenvalue sensitivity-based analysis for evaluation of biological network stability versus disturbances

Abstract

Network modeling is an effective tool for understanding the properties of complex systems. Networks are widely used to help us gain insight into biological systems. In this way, the cell, gene, and protein are denoted as nodes, and the connection elements are regarded as links or edges. In this paper, a novel stochastic strategy is developed for identifying the most influential edges on the stability of biological networks. Regarding the principles of networks and control-theory basics like Jacobian and eigenvalue sensitivity-based analysis, a new criterion is proposed, called "random sensitivity index matrix" (RSIM). RSIM evaluates the eigenvalue sensitivity of all edges in a network in the presents of stochastic disturbances based on the Monte Carlo algorithm. Through the values of RSIM elements, the sensitive edges are identifiable. In addition, the contribution of each edge in network instability has been compared through different percentages of disturbances. Different percentages of disturbances did not change the results. The performance of the proposed method was verified by simulation results for Lac (lactose) operon and MAPK (Mitogen-activated protein kinases) as two sample biological networks.

Keywords: Biological networks; Control-theory basics; Monte Carlo algorithm; Sensitivity analysis; Stability evaluation.