Bio Gene Regulatory Networks Differential Networks

Version Compatibility

Reference examples tested with: matplotlib 3.8+, numpy 1.26+, pandas 2.2+, scipy 1.12+, statsmodels 0.14+

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

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

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

Differential Networks

"Compare gene co-expression networks between my disease and control groups" → Test whether gene-gene correlations differ significantly between two conditions using Fisher's z-transform, identifying gained, lost, and reversed regulatory relationships.

• R: DiffCorr::comp.2.cc.fdr() for differential correlation analysis
• Python: custom Fisher z-test with scipy.stats and statsmodels for FDR correction

Compare co-expression and regulatory networks between biological conditions to identify rewired gene-gene relationships.

DiffCorr Workflow

DiffCorr uses Fisher's z-transform to test whether the correlation between two genes differs significantly between two conditions.

Required Libraries

library(DiffCorr)
library(igraph)

Input Preparation

# Separate expression matrices by condition (genes as columns, samples as rows)
expr_all <- read.csv('normalized_counts.csv', row.names = 1)
sample_info <- read.csv('sample_info.csv', row.names = 1)

expr_condition1 <- t(expr_all[, sample_info$condition == 'control'])
expr_condition2 <- t(expr_all[, sample_info$condition == 'disease'])

# Filter to variable genes (top 2000-5000 most variable)
gene_vars <- apply(expr_all, 1, var)
top_genes <- names(sort(gene_vars, decreasing = TRUE))[1:3000]
expr_condition1 <- expr_condition1[, top_genes]
expr_condition2 <- expr_condition2[, top_genes]

Run DiffCorr Analysis

# Compute correlation matrices
cor1 <- cor(expr_condition1, method = 'pearson')
cor2 <- cor(expr_condition2, method = 'pearson')

n1 <- nrow(expr_condition1)
n2 <- nrow(expr_condition2)

# Fisher z-transform test for differential correlation
# Compares correlation coefficients between two groups
result <- comp.2.cc.fdr(
    output.file = 'diffcorr_results.txt',
    data1 = expr_condition1,
    data2 = expr_condition2,
    threshold = 0.05  # FDR threshold
)

Parse and Classify Results

diffcorr <- read.delim('diffcorr_results.txt')

# Classify differential correlations
classify_edge <- function(cor1, cor2, threshold = 0.3) {
    if (abs(cor1) < threshold & abs(cor2) >= threshold) return('gained')
    if (abs(cor1) >= threshold & abs(cor2) < threshold) return('lost')
    if (cor1 > threshold & cor2 < -threshold) return('reversed')
    if (cor1 < -threshold & cor2 > threshold) return('reversed')
    return('unchanged')
}

diffcorr$edge_type <- mapply(classify_edge, diffcorr$cor1, diffcorr$cor2)
table(diffcorr$edge_type)

# Focus on significant rewired edges
significant <- diffcorr[diffcorr$p.adj < 0.05, ]
rewired <- significant[significant$edge_type != 'unchanged', ]
print(paste('Significant rewired edges:', nrow(rewired)))

Identify Rewired Hub Genes

# Genes involved in most differential correlations
gene_rewiring <- c(rewired$gene1, rewired$gene2)
rewiring_counts <- sort(table(gene_rewiring), decreasing = TRUE)
top_rewired_genes <- head(rewiring_counts, 20)
print(top_rewired_genes)

# These genes have the most condition-specific regulatory changes

DGCA (Alternative)

DGCA (Differential Gene Correlation Analysis) was archived from CRAN in May 2024. It is still available via GitHub.

# Install from GitHub (archived from CRAN 2024-05)
devtools::install_github('andymckenzie/DGCA')
library(DGCA)

# Run differential correlation analysis
dgca_results <- ddcorAll(
    inputMat = expr_all,
    design = sample_info$condition,
    compare = c('control', 'disease'),
    adjust = 'BH',         # multiple testing correction
    nPerm = 0,             # 0 for analytical p-values (faster)
    corrType = 'pearson'
)

# Filter significant results
sig_dgca <- dgca_results[dgca_results$pValDiff_adj < 0.05, ]

# Classify by correlation change category
# DGCA provides: +/+, +/-, -/+, -/-, +/0, 0/+, -/0, 0/-, 0/0
table(sig_dgca$Classes)

Python NetworkX Approach

Goal: Identify gene pairs whose co-expression relationship changes significantly between two conditions using a Python-native workflow.

Approach: Compute per-condition Pearson correlation matrices, test each gene pair for differential correlation using Fisher's z-transform, apply BH FDR correction, then classify edges as gained, lost, or reversed based on correlation magnitude thresholds.

import pandas as pd
import numpy as np
from scipy import stats
import networkx as nx

def build_correlation_network(expr_matrix, threshold=0.6):
    '''Build network from correlation matrix, keeping edges above threshold.'''
    cor_matrix = expr_matrix.corr(method='pearson')
    genes = cor_matrix.columns.tolist()
    G = nx.Graph()
    G.add_nodes_from(genes)

    for i in range(len(genes)):
        for j in range(i + 1, len(genes)):
            r = cor_matrix.iloc[i, j]
            if abs(r) >= threshold:
                G.add_edge(genes[i], genes[j], weight=r)
    return G


def fisher_z_test(r1, n1, r2, n2):
    '''Fisher z-transform test for difference between two correlations.'''
    z1 = np.arctanh(np.clip(r1, -0.9999, 0.9999))
    z2 = np.arctanh(np.clip(r2, -0.9999, 0.9999))
    se = np.sqrt(1 / (n1 - 3) + 1 / (n2 - 3))
    z_stat = (z1 - z2) / se
    p_value = 2 * stats.norm.sf(abs(z_stat))
    return z_stat, p_value


def differential_network_analysis(expr_cond1, expr_cond2, fdr_threshold=0.05):
    '''Compare correlation networks between two conditions.'''
    genes = expr_cond1.columns.tolist()
    n1, n2 = len(expr_cond1), len(expr_cond2)
    cor1 = expr_cond1.corr()
    cor2 = expr_cond2.corr()

    results = []
    for i in range(len(genes)):
        for j in range(i + 1, len(genes)):
            r1, r2 = cor1.iloc[i, j], cor2.iloc[i, j]
            z_stat, p_val = fisher_z_test(r1, n1, r2, n2)
            results.append({
                'gene1': genes[i], 'gene2': genes[j],
                'cor_cond1': r1, 'cor_cond2': r2,
                'z_stat': z_stat, 'p_value': p_val
            })

    df = pd.DataFrame(results)

    # FDR correction
    from statsmodels.stats.multitest import multipletests
    _, df['p_adj'], _, _ = multipletests(df['p_value'], method='fdr_bh')

    # Classify edges
    def classify(row, threshold=0.3):
        r1, r2 = row['cor_cond1'], row['cor_cond2']
        if abs(r1) < threshold and abs(r2) >= threshold:
            return 'gained'
        if abs(r1) >= threshold and abs(r2) < threshold:
            return 'lost'
        if r1 > threshold and r2 < -threshold:
            return 'reversed'
        if r1 < -threshold and r2 > threshold:
            return 'reversed'
        return 'unchanged'

    df['edge_type'] = df.apply(classify, axis=1)
    return df


# Usage
expr_all = pd.read_csv('normalized_counts.csv', index_col=0).T
sample_info = pd.read_csv('sample_info.csv', index_col=0)

expr_ctrl = expr_all.loc[sample_info[sample_info['condition'] == 'control'].index]
expr_disease = expr_all.loc[sample_info[sample_info['condition'] == 'disease'].index]

# Filter to top variable genes
gene_vars = expr_all.var()
top_genes = gene_vars.nlargest(3000).index.tolist()
expr_ctrl, expr_disease = expr_ctrl[top_genes], expr_disease[top_genes]

diff_results = differential_network_analysis(expr_ctrl, expr_disease)
significant = diff_results[diff_results['p_adj'] < 0.05]
print(significant['edge_type'].value_counts())

Visualize Differential Network

Goal: Render the rewired gene-gene connections as a color-coded network graph distinguishing gained, lost, and reversed edges.

Approach: Build a NetworkX graph from significant rewired edges, assign edge colors by change type, and draw with a spring layout.

import matplotlib.pyplot as plt

rewired = significant[significant['edge_type'] != 'unchanged']

G_diff = nx.Graph()
color_map = {'gained': '#2ca02c', 'lost': '#d62728', 'reversed': '#9467bd'}

for _, row in rewired.iterrows():
    G_diff.add_edge(row['gene1'], row['gene2'],
                    color=color_map[row['edge_type']], weight=abs(row['z_stat']))

edge_colors = [G_diff[u][v]['color'] for u, v in G_diff.edges()]

fig, ax = plt.subplots(figsize=(12, 12))
pos = nx.spring_layout(G_diff, k=2, seed=42)
nx.draw_networkx(G_diff, pos, edge_color=edge_colors, node_size=50,
                 font_size=6, width=0.5, alpha=0.7, ax=ax)

# Legend
import matplotlib.patches as mpatches
legend_handles = [mpatches.Patch(color=c, label=l) for l, c in color_map.items()]
ax.legend(handles=legend_handles, loc='upper left')
ax.set_title('Differential co-expression network')
plt.savefig('differential_network.pdf', bbox_inches='tight')

Statistical Considerations

Related Skills

• coexpression-networks - Build WGCNA networks for individual conditions
• scenic-regulons - TF regulon inference from scRNA-seq
• differential-expression/deseq2-basics - DE analysis to complement network rewiring
• temporal-genomics/temporal-grn - Time-delayed regulatory inference from temporal data

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