Bio Applied Gene Regulatory Networks

Gene Regulatory Network Inference

When to Use

• Inferring which transcription factors (TFs) regulate which target genes from bulk or single-cell expression data.
• Comparing correlation, mutual-information (ARACNE), and random-forest (GENIE3/GRNBoost2) GRN inference methods.
• Detecting network motifs (feed-forward loops, autoregulation) in an inferred or curated regulatory network.
• Validating predicted TF-target edges against curated databases (TRRUST, DoRothEA, ChEA3).
• Deciding between a fast correlation screen and a slower, more accurate GENIE3/SCENIC run.

Version Compatibility

scikit-learn >= 1.3, scipy >= 1.11, NetworkX >= 3.2, pandas >= 2.0, Python >= 3.10. For production-scale GRN inference use arboreto (GRNBoost2/GENIE3, Python) or Bioconductor GENIE3/SCENIC (R) — this skill's genie3() is a from-scratch reference implementation for understanding the algorithm, not a substitute for those.

Prerequisites

• pip install scikit-learn scipy pandas networkx matplotlib
• Expression matrix already normalized/log-transformed (see bio-differential-expression-deseq2-basics or bio-single-cell-preprocessing).
• A defined list of candidate TFs (e.g. from AnimalTFDB or a curated TF panel) — GRN inference only makes sense TF-vs-target, not all-vs-all.

GRN vs PPI Networks

Method Comparison

Choosing a method: start with correlation for a quick screen. Move to GENIE3/GRNBoost2 (via arboreto) when you need directionality and non-linear signal. Use SCENIC+ for single-cell multiome data with matched ATAC.

Correlation-Based Inference

Goal: get a fast first-pass list of candidate TF-target edges. Approach: Pearson correlation between each TF and each target, thresholded on |r| and p-value.

import numpy as np
import pandas as pd
from scipy.stats import pearsonr

def infer_grn_correlation(tf_expr, target_expr, tf_names, target_names,
                           r_thresh=0.25, p_thresh=0.01):
    """Infer TF-target edges from Pearson correlation.

    tf_expr, target_expr: (n_samples, n_tfs)/(n_samples, n_targets) arrays.
    Returns a DataFrame of edges with |r| > r_thresh and p < p_thresh.
    """
    edges = []
    for i, tf in enumerate(tf_names):
        for j, tgt in enumerate(target_names):
            r, p = pearsonr(tf_expr[:, i], target_expr[:, j])
            if abs(r) > r_thresh and p < p_thresh:
                edges.append({"TF": tf, "Target": tgt, "r": r, "p": p})
    return pd.DataFrame(edges)

Mutual Information / ARACNE

Goal: capture non-linear TF-target relationships and prune indirect edges. Approach: compute mutual information (MI) per TF-target pair, then apply the Data Processing Inequality (DPI): for a triangle A-B-C, drop the weakest edge.

import numpy as np
from sklearn.feature_selection import mutual_info_regression

def compute_mi_matrix(tf_expr, target_expr, random_state=42):
    """Mutual information between each TF (columns of tf_expr) and every target."""
    n_tfs = tf_expr.shape[1]
    mi = np.zeros((n_tfs, target_expr.shape[1]))
    for i in range(n_tfs):
        mi[i] = mutual_info_regression(
            tf_expr[:, i:i + 1], target_expr,
            discrete_features=False, random_state=random_state,
        )
    return mi

def aracne_dpi_prune(mi_tf_tf, tolerance=0.0):
    """Data Processing Inequality pruning over a square TF-TF MI matrix.

    For every triangle (i, j, k), drop the smallest edge if it is
    smaller than both others by more than `tolerance` (indirect edge).
    Returns a boolean keep-mask matching mi_tf_tf's shape.
    """
    n = mi_tf_tf.shape[0]
    keep = np.ones_like(mi_tf_tf, dtype=bool)
    for i in range(n):
        for j in range(n):
            if i == j:
                continue
            for k in range(n):
                if k in (i, j):
                    continue
                triangle = sorted([mi_tf_tf[i, j], mi_tf_tf[i, k], mi_tf_tf[j, k]])
                weakest = triangle[0]
                if weakest == mi_tf_tf[i, j] and weakest < triangle[1] - tolerance:
                    keep[i, j] = False
    return keep

GENIE3: Random Forest Importance

Goal: rank TF-target edges by how well each TF predicts each target, capturing combinatorial and non-linear regulation. Approach: for every target gene, fit a random forest on all TFs as predictors; the feature importances are the TF -> target edge weights.

import numpy as np
from sklearn.ensemble import RandomForestRegressor

def genie3(expr_matrix, tf_indices, target_indices, n_estimators=100, random_state=42):
    """Simplified GENIE3: rank TF importance for each target via random forest.

    expr_matrix: (n_samples, n_genes) full expression matrix.
    tf_indices, target_indices: column indices into expr_matrix for TFs/targets.
    Returns an (n_tfs, n_targets) importance matrix (TF rows, target columns).
    """
    X = expr_matrix[:, tf_indices]
    importance = np.zeros((len(tf_indices), len(target_indices)))
    for j, tgt_idx in enumerate(target_indices):
        y = expr_matrix[:, tgt_idx]
        rf = RandomForestRegressor(
            n_estimators=n_estimators, random_state=random_state,
            n_jobs=-1, max_features="sqrt",
        )
        rf.fit(X, y)
        importance[:, j] = rf.feature_importances_
    return importance

For genome-scale data use arboreto.algo.grnboost2(expression_data=df, tf_names=tfs) (gradient boosting, much faster than this reference loop).

Network Motifs: Feed-Forward Loops

Goal: find A -> B -> C, A -> C triads (the most common GRN motif) in a directed edge list. Approach: build a networkx.DiGraph from thresholded edges and enumerate triangles that satisfy the FFL pattern.

import networkx as nx

def find_feed_forward_loops(G, tf_names):
    """Enumerate feed-forward loops A->B->C, A->C where A,B are TFs.

    G: networkx.DiGraph of TF/target edges.
    Returns a list of (A, B, C) triples.
    """
    ffls = []
    for a in tf_names:
        if a not in G:
            continue
        for b in G.successors(a):
            if b not in tf_names or b not in G:
                continue
            for c in G.successors(b):
                if c not in tf_names and G.has_edge(a, c):
                    ffls.append((a, b, c))
    return ffls

Evaluation Against a Reference Network

def evaluate_grn(predicted_binary, true_binary):
    """Precision/recall/F1 of a predicted binary TF-target adjacency vs. ground truth."""
    tp = (predicted_binary & true_binary).sum()
    fp = (predicted_binary & ~true_binary).sum()
    fn = (~predicted_binary & true_binary).sum()
    precision = tp / (tp + fp) if (tp + fp) > 0 else 0
    recall = tp / (tp + fn) if (tp + fn) > 0 else 0
    f1 = 2 * precision * recall / (precision + recall) if (precision + recall) > 0 else 0
    return {"precision": precision, "recall": recall, "f1": f1}

Use TRRUST (8,444 curated human TF-target pairs, grnpedia.org/trrust), DoRothEA, or ChEA3 as the true_binary reference. Published BEELINE benchmark numbers (Pratapa et al. 2020, Nat Methods): GENIE3 AUPRC ~0.15, GRNBoost2 ~0.16, ARACNE ~0.09, Pearson ~0.07 — all methods perform modestly; use them to rank candidates, not as ground truth.

Key Concepts

• Regulon: the set of genes regulated by one TF.
• Feed-forward loop (FFL): A->B->C and A->C — most common 3-node motif; coherent FFLs filter noise/delay response, incoherent FFLs produce pulses/adaptation.
• VIPER: infers TF activity (not just mRNA expression) from a regulon's target expression pattern — more informative than raw TF expression, especially when the TF itself is post-translationally regulated.

Pitfalls

• Correlation != regulation: two genes co-expressed due to a shared upstream regulator will appear as a direct edge.
• Symmetric methods (correlation, MI) cannot infer direction: need orthogonal evidence (ChIP-seq, perturbation, known TF/target roles) to resolve A->B vs B->A.
• High false-positive rate: GRN inference on bulk RNA-seq is noisy; always validate top edges against TRRUST/DoRothEA/ChIP-seq before acting on them.
• Sample size: reliable inference needs n >> number of TFs; partial correlation and Graphical Lasso fail outright when n < p.
• Batch effects: check for batch confounding before interpreting co-expression as regulation — batch is a classic shared upstream "regulator."
• Multiple testing: apply FDR correction when testing thousands of TF-target pairs (correlation/MI approaches).
• GENIE3 has no sign: importance scores don't say activation vs. repression — check correlation sign or use signed resources (CollecTRI) if direction of effect matters.

See Also

• bio-applied-ppi-networks — undirected protein-protein interaction networks (STRING/BioGRID), centrality, community detection.
• bio-applied-network-modules — Louvain/Leiden module detection and WGCNA co-expression modules, complementary to directed GRN edges.
• bio-applied-regulatory-analysis — promoter-level analysis (PWM/PFM, TFBS scanning) to corroborate inferred TF-target edges.
• arboreto — production GRNBoost2/GENIE3 implementation for genome-scale inference.