Abstract

This work presents an adapted Random Sampling - High Dimensional Model Representation (RS-HDMR) algorithm for synergistically addressing three key problems in network biology: (1) identifying the structure of biological networks from multivariate data, (2) predicting network response under previously unsampled conditions, and (3) inferring experimental perturbations based on the observed network state. RS-HDMR is a multivariate regression method that decomposes network interactions into a hierarchy of non-linear component functions. Sensitivity analysis based on these functions provides a clear physical and statistical interpretation of the underlying network structure. The advantages of RS-HDMR include efficient extraction of nonlinear and cooperative network relationships without resorting to discretization, prediction of network behavior without mechanistic modeling, robustness to data noise, and favorable scalability of the sampling requirement with respect to network size. As a proof-of-principle study, RS-HDMR was applied to experimental data measuring the single-cell response of a protein-protein signaling network to various experimental perturbations. A comparison to network structure identified in the literature and through other inference methods, including Bayesian and mutual-information based algorithms, suggests that RS-HDMR can successfully reveal a network structure with a low false positive rate while still capturing non-linear and cooperative interactions. RS-HDMR identified several higher-order network interactions that correspond to known feedback regulations among multiple network species and that were unidentified by other network inference methods. Furthermore, RS-HDMR has a better ability to predict network response under unsampled conditions in this application than the best statistical inference algorithm presented in the recent DREAM3 signaling-prediction competition. RS-HDMR can discern and predict differences in network state that arise from sources ranging from intrinsic cell-cell variability to altered experimental conditions, such as when drug perturbations are introduced. This ability ultimately allows RS-HDMR to accurately classify the experimental conditions of a given sample based on its observed network state.

Highlights

  • The development of high-throughput and multiplexed biological measurement techniques has led to the growing richness of data sets that describe biological networks [1,2,3,4,5,6]

  • Bayesian networks (BNs) analysis was previously employed to characterize the protein-signaling network from data used in this work [25]

  • BN analysis is similar to Random Sampling - High Dimensional Model Representation (RS-High Dimensional Model Representation (HDMR)) in that it serves as a powerful tool to characterize network interactions from stochastically sampled multivariate data

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Summary

Introduction

The development of high-throughput and multiplexed biological measurement techniques has led to the growing richness of data sets that describe biological networks [1,2,3,4,5,6] These methods include particle-based and multiplex flow cytometric assays [7,8,9], kinase and protease activity assays [10,11], and higher-throughput mass-spectrometry [2,12,13]. Network identification algorithms based on linearized steady-state models and regression analysis [14,15,16,17,18] are effective in conditions of sparse sampling and noisy data They often discount nonlinear interactions which may become significant in complex biological networks. Several nonlinear regression methods have an ability to predict biological network structures and their corresponding responses from multivariate and time-dependent data [26,27,28], in general these methods do not readily support network structure inference while efficiently allowing for the determination of higher-order cooperative statistical relationships

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