Supplementary website for

“Reconstruction of genetic association networks from microarray data:

A partial least squares approach”

Vasyl Pihur, Somnath Datta, Susmita Datta*

*e-mail: susmita.datta_AT_louisville.edu

Abstract

Motivation: Gene association networks provide vast amounts of information about essential processes inside the cell. A complete picture of gene-gene interactions would open new horizons for biologists, ranging from pure appreciation to successful manipulation of biological pathways for therapeutic purposes. Therefore, identification of important biological complexes whose members (genes and their products proteins) interact with each other is of prime importance. Numerous experimental methods exist but, for the most part, they are costly and labor-intensive. Computational techniques, such as the one proposed in this work, provide a quick “budget” solution that can be used as a screening tool before more expensive techniques are attempted. Here, we introduce a novel computational method based on the Partial Least Squares (PLS) regression technique for reconstruction of genetic networks from microarray data.

Results: The proposed PLS based method is shown to be an effective screening procedure for the detection of gene-gene interactions from microarray data. Both simulated and real microarray experiments show that the PLS based approach is superior to its competitors both in terms of performance and applicability.

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Download

R-Code (distributed as is without warrantee; needs the base distribution of R and the R package locfdr from http://www.r-project.org/)

Additional Results for the Simulated Data

Additional Results for the Real Data

Distribution function of the overall scores for two groups

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Effect of the number of PLS components on the performance of the genetic network procedure

# of components

fdr	1	2	3	4	5	6	7	8	9	10	15	20	25	30	35	40	45	50	55	60	65	70	75	80	85	90
0.0001	766	1293	989	754	579	428	333	261	204	156	51	24	17	16	15	15	16	16	16	16	16	16	16	16	16	16
0.01	1321	1861	1509	1232	1001	776	623	506	413	327	130	61	43	39	37	36	37	37	37	37	37	37	37	37	37	37
0.1	1894	2399	2084	1757	1503	1251	1052	877	721	592	267	144	108	98	96	96	97	96	96	96	96	96	96	96	96	96
0.2	2157	2679	2377	2055	1807	1531	1322	1122	937	779	364	211	162	152	148	150	152	151	151	151	151	151	151	151	151	151
0.3	2370	2921	2632	2312	2073	1780	1570	1345	1138	953	455	280	227	213	205	209	209	209	208	207	208	208	208	208	208	208
0.4	2569	3152	2883	2560	2323	2043	1820	1585	1343	1138	559	354	295	279	274	277	278	277	277	277	277	277	277	277	277	277
0.5	2780	3381	3125	2822	2594	2311	2095	1849	1588	1357	672	446	377	359	349	354	354	354	352	352	352	352	352	352	352	352
0.6	3010	3611	3381	3108	2905	2629	2409	2152	1881	1622	816	557	481	457	444	449	450	450	449	449	449	449	449	449	449	449
0.7	3287	3886	3666	3440	3256	2994	2799	2532	2261	1969	1006	701	619	592	571	579	582	582	579	579	579	579	579	579	579	579
0.8	3658	4205	4016	3837	3678	3450	3288	3048	2767	2464	1278	916	817	792	765	776	780	781	777	776	777	777	777	777	777	777
0.9	4219	4673	4556	4418	4255	4101	3968	3777	3551	3193	1767	1303	1174	1144	1096	1112	1119	1119	1113	1112	1114	1113	1113	1113	1113	1113
0.99	5072	5817	5543	5382	5264	5305	4967	4951	4766	4431	3199	2254	2115	2231	2025	2068	2089	2091	2078	2077	2080	2079	2079	2079	2079	2079

The average number of discovered interactions for the simulated data (over 10 datasets). The larger the number of PLS components, the smaller the number of discovered interactions. At about 30 components, convergence for each level of fdr (false discovery rate) is observed.

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Performance of Scores based on estimated PLS coefficients

(see the last but one paragraph of Section 2 in the paper)

1. The locfdr procedure may break down if one uses the estimated PLS coefficients as measures of association/interaction (not recommended). This table shows the number of such breakdowns with 100 simulated data sets.

# of Components	3	4	5	6	7	8	10	15
# of datasets for which locfdr breaks down	77	77	70	50	39	35	24	14

2. The scores proposed in the paper results in better sensitivity/specificity than the corresponding procedure based on

estimated PLS coefficients (as in the last but one paragraph of Section 2 in the paper).

Since the locfdr procedure may break down while using the PLS coefficients, we can either calculated sensitivity/specificity only for those simulated data sets for which the locfdr control works or set the thresholds so that the same number of "interactions" are discovered by the two procedures (note that the locfdr control works with the scores introduced in the paper). In either case, the estimated PLS coefficients lead to worse performance than the scores introduced in the paper.

Here are some examples:

(In these plots, the term "PLS-like Scores" is used to indicate network discovery procedure using the scores introduced in the paper and the term "True PLS scores" is used to indicate the network discovery procedure using the estimated PLS coefficients)

3. The scores proposed in the paper results in better performance than the corresponding procedure based on

estimated PLS coefficients even for the real data set as shown by the following table:

Fdr level	Discovered	PLS-like Scores True Positive	PLS Scores True Positive
0.01	29	4	0
0.1	118	17	1
0.13	160	17	1
0.16	210	19	1
0.2	272	22	15