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GIW 2016: International Conference on Genome Informatics MGT-SM: A Method for Constructing Cellular Signal Transduction Networks Min Li, Ruiqing Zheng, Yaohang Li, Fang-Xiang Wu, and Jianxin Wang School of Information Science and Engineering,

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MGT-SM: A Method for Constructing Cellular Signal Transduction Networks

GIW 2016: International Conference on Genome Informatics

Min Li, Ruiqing Zheng, Yaohang Li, Fang-Xiang Wu, and Jianxin Wang

School of Information Science and Engineering, Central South University Homepage: http://bioinformatics.csu.edu.cn/

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Outline

■ Background ■ Traditional Granger ■ Method ■ Result & Conclusion

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Background

■ signal transduction network refers to a directed network which composes of molecules and genes involved in signal transduction pathways

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Gene expression data is meaningful data for constructing the network ■ Bayesian Network ■ Mutual Information ■ Ensemble method ■ Regression

Regression-Granger causality is an effective method

Background

v1 v2 vn-1 vn v1 v2 vn-1 vn

Granger Test

v1 v2 v3 vn vn-2 vn-1

Gene Expression Directed Network

v3 v3 vn-2 vn-2

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Traditional Granger

■ Pairwise ■ Multivariate General form ■Step 1. linear regression for coefficient matrix pairwise 𝑧#= ∑

𝛽'𝑧#(' + ∑ 𝛾+𝑦#('

+ 𝑓# , 𝑢 = 𝑟 + 1, … 𝑈

with null hypothesis

Multivariate 𝑦',# = ∑

∑ 𝑠

+,#(8𝑦+,#(8

9:+:;

+ 𝑓',# 𝑢 = 𝑟 + 1, … 𝑈, 𝑗 = 1, …, 𝑜

■Step 2. F-test for p-value 𝐺 =

?@@A,B(?@@A /- ?@@A/(E(;-)

F~ freedom (q, m-nq)

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Problem

l Indirect caused by pairwise granger l For real gene expression data，there is sometimes m ≪ nq (n is gene number, m=T-q), traditional granger is not applicable

Traditional Granger

v1 v2 v3 v1 v2 v3

(a)Bivariate Granger (b)Multivariate Granger direct edge indirect edge

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We propose an extended Granger test combining SVD and Monte Carlo Simulation

Step 1 calculate coefficient matrix

n Build 𝑍 = 𝑆𝑌 + 𝐹

𝑌 = 𝑦/,/ ⋯ 𝑦/,#(/ ⋮ ⋱ ⋮ 𝑦;,/ ⋯ 𝑦;,#(/ 𝑍 = 𝑦/,R ⋯ 𝑦/,# ⋮ ⋱ ⋮ 𝑦S,R ⋯ 𝑦;,# n Apply SVD for coefficient matrix R 𝑌 = U ∗ S ∗ 𝑊X 𝑆 Y = 𝑍 ∗ 𝑊 ∗ 𝑇(/∗ 𝑉X

Method

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Step 2 p-value for pairwise <i, j>

Monte Carlo Simulation instead of F-test

Monte Carlo Simulation

In Input：time-series expression data matrix and gene index i Ou Output: the p-value ST STEP 1. Calculate 𝑆𝑇𝑇' based on estimation of R ST STEP 2. Upset the order of the expression of gene j from regression and calculate 𝑆𝑇𝑇',+ ST STEP 3 Repeat step 2 for k times, get the distribution of RSS',+ ST STEP 4 Rank RSS' in RSS',+ in ascending order and calculate the p-value as follows

𝑞 = 𝑠𝑏𝑜𝑙 𝑝𝑔 RSS' /(𝑙 + 1)

Method

MG MGT

SM ALGORI RITHM In Input：time-series gene expression data matrix Output：the directed edge with a significant level ST STEP 1. Normalize time-series gene expression data ST STEP 2. Use lmc test to analyze expression’s stationarity, if the expression is nonstationary, use the first order difference. ST STEP 3. Employ SVD to calculate the coefficient matrix ST STEP 4. For gene i, use Monte Carlo to calculate the p-value of edge(i,j) ST STEP 5. Repeat step 4 for all genes, and save the significant edge in a file.

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Results & Conclusion

Genes Samples Time points Real edges

Simulation

5 10 10 7

Yeast Synthetic Network

5 4 17 7 MDA-MB-468 20 4 8 48

The Datasets of the experiment

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n Recall and AUROC for Evaluation n Comparion of Method: CGC2SPR, PGC, DBN(Dynamic Bayesian Network)

Recall = 𝑈𝑄 𝑈𝑄 + 𝐺𝑂

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8. Result

■ SIMULATION DATA 10 samples: all the TOP 7 edges of MGT-SM is real edges

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8. Result

■ Recall and ROC in Yeast Synthetic Network

0.0 0.5 1.0 0.0 0.5 1.0 0.0 0.5 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.5 1.0 0.0 0.5 1.0 0.0 0.5 1.0 0.0 0.5 1.0

(b) Switch Off 2 (a) Switch Off 1