Differential networks

Version Compatibility

Reference examples tested with: DiffCorr 0.4.1+, DINGO/iDINGO 1.0.4+, CoDiNA 1.1.2+; Python path uses scipy 1.12+, statsmodels 0.14+, networkx 3.0+.

Before using code patterns, verify installed versions match. If versions differ:

• R: packageVersion('<pkg>') then ?function_name to verify parameters
• Python: pip show <package> then help(module.function) to check signatures

If code throws ImportError, AttributeError, or TypeError, introspect the installed package and adapt the example to match the actual API rather than retrying.

In statsmodels, multipletests() defaults to method 'hs' (Holm-Sidak), NOT Benjamini-Hochberg. Always pass method='fdr_bh' explicitly for differential-correlation FDR.

Differential Networks

"Compare gene co-expression networks between my disease and control groups" -> Test whether gene-gene relationships differ between two conditions, identifying gained, lost, and reversed edges and the genes that rewire.

• R: DiffCorr::comp.2.cc.fdr() (pairwise Fisher z); DiffCoEx (module-level); iDINGO::dingo() (partial-correlation)
• Python: Fisher z-test with scipy.stats + statsmodels FDR

The Single Most Important Modern Insight -- Differential Connectivity Is Not Differential Expression

A gene can have identical mean expression in two conditions yet a completely rewired set of correlation partners -- and that rewiring, not the mean shift, can be the disease signal. The classic demonstration is Hudson, Reverter & Dalrymple 2009 (PLoS Comput Biol 5:e1000382): myostatin received the top Regulatory Impact Factor despite not being differentially expressed, correctly fingering the gene carrying the causal mutation purely from the change in its correlation wiring to differentially-expressed targets. So differential expression (a shift in means) and differential connectivity (a shift in the correlation structure) are orthogonal questions, and the most differentially-connected hub is often not differentially expressed. Three distinct analyses are routinely conflated and must be kept separate: differential expression (mean shift), differential co-expression (pairwise correlation shift, DiffCorr/DiffCoEx), and differential connectivity/rewiring at the conditional-independence level (DINGO).

The dominant practical failure is statistical power. The variance of a difference of two correlations is large, so rewiring detection needs many samples per group -- far more than differential expression. Worse, pairwise differential-correlation testing has a multiple-testing explosion: p genes produce ~p^2/2 edge tests, so without aggressive FDR (or a module-level method that sidesteps per-edge testing) the results are dominated by false positives. Most "rewired hub" findings in small cohorts are underpowered noise.

Differential-Network Method Taxonomy

Method	Citation	Level	Edge type	Note
DiffCorr	Fukushima 2013 Gene	per-edge	marginal	simple Fisher z; p^2/2 tests -> aggressive FDR needed
DiffCoEx	Tesson 2010 BMC Bioinformatics	module	marginal	WGCNA-based; tests modules, sidesteps per-edge multiplicity
DINGO	Ha 2015 Bioinformatics	per-edge	partial	group-specific GGM; bootstrap differential score (direct rewiring)
iDINGO	Class 2018 Bioinformatics	per-edge	partial, multi-omics	chain-graph across data types (e.g. miRNA->mRNA->protein)
CoDiNA	Gysi 2020 PLoS ONE	per-edge	on supplied nets	compares >=2 networks; common/specific/different edge classes

Decision Tree by Scenario

Scenario	Recommended	Why
Two conditions, quick pairwise rewiring	DiffCorr (Fisher z) + strict FDR	simplest; report gained/lost/reversed
Want modules that rewire, not edges	DiffCoEx	module-level testing avoids the p^2/2 explosion
Need direct (not indirect) rewiring	DINGO/iDINGO	partial correlation removes confounded indirect changes
More than two conditions	CoDiNA	n-way comparison with edge classification
Multi-omics rewiring	iDINGO	chain-graph respects the biological hierarchy
Just want mean-expression changes	-> differential-expression/de-results	that is DE, not rewiring
Build the per-condition networks first	-> coexpression-networks	rewiring compares already-built networks

DiffCorr: Pairwise Differential Correlation (R)

Goal: Find gene pairs whose correlation differs significantly between two conditions.

Approach: Fisher z-transform each correlation per condition and test the z-difference with FDR; classify surviving edges as gained, lost, or reversed.

library(DiffCorr)

expr_all <- read.csv('normalized_counts.csv', row.names = 1)        # genes x samples
info <- read.csv('sample_info.csv', row.names = 1)
# Filter to top variable genes first: p^2/2 edge tests make the full matrix intractable.
gene_vars <- apply(expr_all, 1, var)
top <- names(sort(gene_vars, decreasing = TRUE))[1:3000]
d1 <- expr_all[top, info$condition == 'control']
d2 <- expr_all[top, info$condition == 'disease']

# Returns the differential correlations directly (threshold filters exported pairs by lfdr).
# It only writes the file when save = TRUE, so use the returned data.frame. Columns carry
# spaces ('molecule X', 'molecule Y', 'r1', 'r2', 'lfdr (difference)') -- index with [[ ]].
res <- comp.2.cc.fdr(data1 = d1, data2 = d2, threshold = 0.05, save = TRUE,
                     output.file = 'diffcorr.txt')

DINGO: Direct Differential Rewiring (R)

Goal: Detect rewiring at the conditional-independence (direct edge) level rather than marginal correlation.

Approach: Estimate a group-specific Gaussian graphical model and bootstrap an edge-wise differential score.

library(iDINGO)
# dingo(dat, x, ...): dat = samples x genes; x = the binary group covariate (length n).
fit <- dingo(dat = expr_mat, x = group, B = 100, cores = 8)   # B = bootstrap reps
# fit$diff.score / fit$p.val give edge-wise differential connectivity (direct edges).

Python: Fisher z Differential Network

Goal: Compare correlation networks between two conditions in a Python-native workflow.

Approach: Compute per-condition correlation matrices, test each pair with Fisher's z, apply BH FDR (explicitly), and classify edges.

import numpy as np, pandas as pd
from scipy import stats
from statsmodels.stats.multitest import multipletests

def fisher_z(r1, n1, r2, n2):
    z1, z2 = np.arctanh(np.clip([r1, r2], -0.9999, 0.9999))
    se = np.sqrt(1 / (n1 - 3) + 1 / (n2 - 3))
    z = (z1 - z2) / se
    return z, 2 * stats.norm.sf(abs(z))

def differential_network(e1, e2, fdr=0.05):
    genes = e1.columns.tolist()
    n1, n2 = len(e1), len(e2)
    c1, c2 = e1.corr().values, e2.corr().values
    rows = []
    for i in range(len(genes)):
        for j in range(i + 1, len(genes)):
            z, p = fisher_z(c1[i, j], n1, c2[i, j], n2)
            rows.append((genes[i], genes[j], c1[i, j], c2[i, j], z, p))
    df = pd.DataFrame(rows, columns=['g1', 'g2', 'r1', 'r2', 'z', 'p'])
    # statsmodels default is Holm-Sidak ('hs'); BH must be requested explicitly.
    df['padj'] = multipletests(df['p'], method='fdr_bh')[1]
    return df

Per-Method Failure Modes

Underpowered rewiring claims

Trigger: declaring rewired hubs from a small cohort. Mechanism: the variance of a correlation difference is large; rewiring needs more samples than DE. Symptom: few or no edges survive FDR, or unstable results across resampling. Fix: require adequate n per group; treat low-power results as exploratory.

Pairwise multiple-testing explosion

Trigger: testing all gene pairs with weak/no FDR. Mechanism: p genes -> ~p^2/2 tests. Symptom: thousands of "significant" edges, irreproducible. Fix: pre-filter to variable genes, apply strict FDR, or use a module-level method (DiffCoEx).

Conflating DE with rewiring

Trigger: interpreting differentially-connected genes as differentially expressed (or vice versa). Mechanism: they are orthogonal. Symptom: a rewired hub dismissed because it is not DE. Fix: report DE and differential connectivity separately; a non-DE gene can be the key rewired hub.

Marginal rewiring read as direct

Trigger: interpreting a DiffCorr gained edge as a direct regulatory change. Mechanism: marginal correlation mixes direct and indirect edges; a changed edge may reflect a shifted common driver. Symptom: mechanistic claims from marginal rewiring. Fix: use DINGO (partial correlation) when directness matters.

Holm-Sidak instead of BH

Trigger: multipletests(p) without method=. Mechanism: statsmodels defaults to 'hs', more conservative than intended. Symptom: unexpectedly few hits. Fix: pass method='fdr_bh'.

Quantitative Thresholds

Threshold	Source	Rationale
>= 15-20 samples per group	correlation-stability convention	rewiring is lower-powered than DE; small n gives noise
Pre-filter to top ~2000-5000 variable genes	practical	bounds the p^2/2 test count
BH FDR < 0.05	standard	controls the false-discovery rate across many edge tests
effect-size filter abs(delta r) > 0.3	convention	avoid reporting trivially different correlations
DINGO bootstrap B = 100	iDINGO default-scale	stabilizes the differential score

Common Errors

Error / symptom	Cause	Solution
millions of edge tests / out of memory	full gene matrix	pre-filter to variable genes
far fewer hits than expected	statsmodels Holm-Sidak default	use method='fdr_bh'
rewired hub "should be DE" objection	conflating connectivity with expression	report them as separate, orthogonal results
DGCA not installable from CRAN	archived May 2024	install from GitHub (andymckenzie/DGCA)
reversed edges look like noise	no effect-size filter	require abs(delta r) above a threshold

References

• Hudson NJ, Reverter A, Dalrymple BP. 2009. A differential wiring analysis... correctly identifies the gene containing the causal mutation. PLoS Comput Biol 5(5):e1000382.
• de la Fuente A. 2010. From 'differential expression' to 'differential networking'. Trends Genet 26(7):326-333.
• Fukushima A. 2013. DiffCorr: analyze and visualize differential correlations in biological networks. Gene 518(1):209-214.
• Tesson BM, Breitling R, Jansen RC. 2010. DiffCoEx: differentially coexpressed gene modules. BMC Bioinformatics 11:497.
• Ha MJ, Baladandayuthapani V, Do KA. 2015. DINGO: differential network analysis in genomics. Bioinformatics 31(21):3413-3420.
• Class CA, Ha MJ, Baladandayuthapani V, Do KA. 2018. iDINGO: integrative differential network analysis in genomics. Bioinformatics 34(7):1243-1245.
• Gysi DM, et al. 2020. Co-expression differential network analysis (CoDiNA). PLoS ONE 15(10):e0240523.

Related Skills

• coexpression-networks - build the per-condition co-expression networks being compared
• scenic-regulons - TF regulon activity differences as a complementary rewiring readout
• grn-inference - VIPER differential protein activity between conditions
• differential-expression/de-results - differential expression of means (the orthogonal question)
• temporal-genomics/temporal-grn - time-resolved network change across stages