Compare gene co-expression and regulatory networks between biological conditions to find rewired relationships using DiffCorr, DiffCoEx, DINGO/iDINGO, and CoDiNA. Covers the differential-connectivity-is-not-differential-expression distinction, the pairwise multiple-testing explosion, marginal vs partial (direct) rewiring, and the underpowered-rewiring failure mode. Use when comparing co-expression networks between disease vs control, treatment, or developmental stages, or finding hub genes that rewire without changing mean expression. For single-condition modules see coexpression-networks; for differential expression of means see differential-expression/de-results.
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Compare gene co-expression and regulatory networks between biological conditions to find rewired relationships using DiffCorr, DiffCoEx, DINGO/iDINGO, and CoDiNA. Covers the differential-connectivity-is-not-differential-expression distinction, the pairwise multiple-testing explosion, marginal vs partial (direct) rewiring, and the underpowered-rewiring failure mode. Use when comparing co-expression networks between disease vs control, treatment, or developmental stages, or finding hub genes that rewire without changing mean expression. For single-condition modules see coexpression-networks; for differential expression of means see differential-expression/de-results.
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 explicitly for differential-correlation FDR.
method='fdr_bh'
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.
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.
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
deffisher_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))
defdifferential_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 inrange(len(genes)):
for j inrange(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.
