Statistical Methods for Network Analysis of Biological Data

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1 The Protein Interaction Workshop, 8 12 June 2015, IMS Statistical Methods for Network Analysis of Biological Data Minghua Deng, dengmh@pku.edu.cn School of Mathematical Sciences Center for Quantitative Biology Peking University, Beijing June 2015, NUS

2 Outline Part I: Correlation inference for genomic survey data Part II: Network based eqtl analysis

3 Part I: Correlation Inference for Genomic Survey Data Joint work with Huaying Fang, Chengcheng Huang, Hongyu Zhao Fang et al. Bioinformatics. June 4, 2015

4 Metagenomics Microbes play important role in environment and human life. Metagenomics is the direct sequencing of microbe community. HMP (Human Microbiome Project) aims to investigate the fundamental roles of the microbes in human health and disease. But only relative abundances of different microbes make sense for metagenomics data.

5 Genomic Survey Data Such a data is called as genomic survey data It s called as compositional data in statistics. Suppose the data is for p species, where Y=(y 1,,y p ) is the latent absolute abundance.

6 Correlation for Compositional Data It has been known since Karl Pearson that direct correlation for compositional data can produce unreliable results. Aitchison (1982) proposed a family of log ratio transformation Aitchison, J. (1982). The statistical analysis of compositional data. J. Roy. Stat. Soc. B Met., 44(2),

7 Correlation for Compositional Data A natural way is to study the correlation among the latent variable ys For technical reason, we can focus on the correlation among log transform of ys. The objective is to estimate this from observed data.

8 Correlation for Compositional Data Covariance estimation is very challenging because of small sample size (n<p). But now the problem is more challenging because estimate from is underdetermined. Number of parameters

9 SparCC Frideman and Alm (2012) proposed a algorithm SparCC based on the following addition assumption to solve estimation equation, An iterative algorithm was proposed. Note that the iterative procedure can result in correlations whose magnitude is greater than 1. Friedman, J. and Alm, E. J. (2012). Inferring correlation networks from genomic survey data. PLoS Comput. Biol., 8(9), e

10 Our Method Let F be a p x p matrix with where 1p is a p dimensional vector with all entries 1. We have where is the sample variance of lnx.

11 Our Method We propose a novel method CCLasso based on least square with lasso type penalty, with the sparsity assumption CCLasso minimize following objective function where Tuning parameter can be selected through cross validation.

12 Algorithm The above minimization can be solved by Alternating Direction Augmented Lagrangian Method (ADAM) In most cases, the algorithm can convergent to a positive definite matrix.

13 Random model Simulation

14 Simulation Neighbor model Random select p points, and select its 10 neighbors with strength 0.5.

15 Simulation Hub model Random select 3 points as hubs and other p 3 points as common points. Hubs are connecting to common with probability 0.7, common points are connecting with probability 0.2. Strength is set to 0.2. The diagonal is selected so that the matrix is positive definite, and then normalized to 1.

16 AR(4) model Simulation

17 Simulation Block Model First divide nodes into 5 blocks equally. Then is equal to 0.2 with probability 0.2 if node iand j are in different block; 0.4 with probability 0.6 if nodes iand j are in the same block. The diagonal is selected so that the matrix is positive definite, and then normalized to 1.

18 Measure the Performance Distance between the real matrix and estimated one AUC of ROC curve

22 Notes Expected number of edges in neighbor and AR(4) model is proportional to p, while p 2 for others. Random model roughly satisfies the assumption of SparCC, so SparCC is better than our method Our method outperforms SparCC in all other models.

23 Real Data Real data are download from HMP, including microbes in 18 body sites. Species are characterized by OUT As no benchmark is available, the following two measurements are used Consistent Accuracy: Frobenius norm of the difference between two estimated covariance matrix from part and all samples. Consistent reproducibility: Fraction of same edges between two estimated covariance matrix from part and all samples.

25 Result on Permutated Data Binning sets: [0,0.001], [0.001, 0.1], [0.1, 03]

26 Future Work Theoretical works Identifiability Edge select consistency How to deal 0s in compositional data? How to explore non-linear relation among the latent variables?

27 Part II: Network based eqtl Analysis Joint work with Lin Wang, Wei Zheng, Hongyu Zhao Lin Wang et al. Plos Genetics, 9(3): e , 2013

28 eqtl DNA mrna Genotype Data (SNP polymorphism) Gene Expression Data Expression QTL (eqtl): Treat gene expression intensity as a continuous trait. Goal: Identify genetic loci where DNA significantly affects gene expression.

29 Cis eqtl and Trans eqtl Copied from Harm Jan Westra s PPT

30 eqtl Mapping 1D 2D

31 2D trait Conditional Bivariate Model (Ho, et al, 2011; Chen, et al. 2011; Daye, et al. 2012)

32 Methods Finding interacting loci (epistasis) associated with 2D traits Lin Wang et al. Plos Genetics, 9(3): e , 2013

33 Filtering Process Computational burden ~800*400*4000*2000=2.56*10 12 Potential of Association Where n ij is the number of individuals having the genotype iand j. In yeast data, it can achieve about 16 fold reduction of computation time.

34 Application Yeast dataset (Kruglyak group, 2008, Plos Bio) The experiments were performed under two conditions: glucose and ethanol. 4,482 genes measured in 109 segregants derived from a cross between BY and RM. Genotypes at 2,956 loci. (We combined neighboring loci having fewer than 5 discordant calls among the 109 samples, leading to 820 merged markers.)

35 Result Cutoff for p value from LR test is (FDR<0.2) FDR is estimated from permutation test 225 and 224 Epistasis 2D modules (2 genes+2 Markers) were detected in glucose and ethanol condition

36 GO Enrichment There is an enrichment of pairs having the same functional annotations according to GO slim. (31 out of 225 with a p value of 0.05 and 58 out of 224 with a p value of ) Most pairs have different functional annotations suggesting either unknown functions for these genes or interactions between different biology processes.

37 An Example The two genes (GOT1 and ERV14) are functional in ER to Golgi vesicle mediated transport. The two loci are located at two genes Yip1 and Mst28 which also functions in ER to Golgi vesiclemediated transport. Literature suggests the regulatory relationships between the two loci and the two genes.

Clustering in the Epistasis Map We applied the hierarchical clustering to this interaction map and found densely interacting locus clusters

38 Clustering in the Epistasis Map We applied the hierarchical clustering to this interaction map and found densely interacting locus clusters which contains a group of loci mapping to oxidative phosphorylation pathway. Their 2D traits also contain lots of genes in this pathway. p

39 Environment Modulates Regulatory Modules

40 Environment Modulates Regulatory Modules Glucose response pathway modulates ribosome related modules We observed that ribosome biogenesis related regulation was only identified under the glucose condition Previous study found that ribosome biogenesis genes induced in response to high, but not low glucose signals

41 Environment Modulates Regulatory Modules Glucose modulates ribosome related modules through glucose response pathway

42 Extensions Finding the locus associated with the network among a group of genes A simple way is to test each pairs individually. Or we can test

43 Summary We developed penalized likelihood model to infer the correlation for genomic survey data. We developed an conditional bivariate model to find higher level association in eqtl analysis.

44 Thanks for your attention! Questions?

Package trigger. R topics documented: August 16, Type Package

Package trigger. R topics documented: August 16, Type Package Type Package Package trigger August 16, 2018 Title Transcriptional Regulatory Inference from Genetics of Gene ExpRession Version 1.26.0 Author Lin S. Chen , Dipen P. Sangurdekar