Bio Gene Regulatory Networks 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

Decision Tree by Scenario

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.