Algorithm & Methodology

The Cell-Cell Communication Inference Problem

Cell-cell communication (CCC) involves the transmission of biological signals between cells through ligand-receptor (L-R) interactions. In single-cell transcriptomics, we infer potential CCC events by:

1. Identifying expressed ligands in “sender” cell types
2. Identifying expressed receptors in “receiver” cell types
3. Predicting downstream signaling effects

Why Multi-Sample Analysis?

Traditional cell-level differential expression analysis suffers from several limitations:

1. Pseudobulk Aggregation

For each cell type \(c\) and sample \(s\), we aggregate single-cell expression profiles:

\[\bar{X}_{g,c,s} = \frac{1}{n_{c,s}} \sum_{i \in \text{cells}(c,s)} X_{g,i}\]

where: - \(X_{g,i}\) is the expression of gene \(g\) in cell \(i\) - \(n_{c,s}\) is the number of cells of type \(c\) in sample \(s\)

Benefits: - Reduces technical noise through averaging - Enables proper statistical inference at sample level - Respects experimental design structure

2. Differential Expression Analysis

MultiNicheNet employs the muscat framework for differential state analysis. For each gene \(g\) in cell type \(c\):

\[\log_2(\text{CPM}_{g,c,s} + 1) = \beta_0 + \beta_1 \cdot \text{condition}_s + \epsilon_{g,c,s}\]

Statistical Testing: - Uses negative binomial generalized linear models (edgeR) - Accounts for library size differences - Supports complex designs with covariates

Empirical P-value Correction: MultiNicheNet implements an empirical null distribution approach to control for multiple testing across many cell types:

\[p_{\text{empirical}} = \frac{\#\{|t_{\text{null}}| \geq |t_{\text{observed}}|\}}{N_{\text{null}}}\]

3. NicheNet Ligand Activity Inference

MultiNicheNet integrates the NicheNet ligand-target prior knowledge model to infer ligand activities based on downstream gene expression changes.

Ligand-Target Matrix: The ligand-target matrix \(\mathbf{W}\) contains regulatory potential scores:

\[W_{l,t} = P(\text{gene } t \text{ regulated by ligand } l)\]

Activity Score Calculation: For a set of differentially expressed target genes \(G_{\text{DE}}\):

\[\text{Activity}_l = \text{AUROC}(W_{l,\cdot}, G_{\text{DE}})\]

This measures how well ligand \(l\)’s predicted targets are enriched in the observed DE genes.

4. Multi-Criteria Prioritization

The key innovation of MultiNicheNet is integrating multiple biological criteria into a unified prioritization score.

Prioritization Components:

Unified Score:

\[S_{\text{priority}} = \prod_{i} S_i^{w_i}\]

where \(w_i\) are scenario-specific weights.

Expression Fraction Calculation

For a ligand-receptor pair in sender cell type \(s\) and receiver cell type \(r\):

\[F_{L,s} = \frac{\#\{\text{samples where } \bar{X}_{L,s} > \theta\}}{N_{\text{samples}}}\]

where \(\theta\) is the expression threshold.

Cell-Type Specificity Score

Specificity is calculated using the Gini coefficient or entropy-based measures:

\[\text{Specificity}_g = 1 - H(p_{g,1}, p_{g,2}, ..., p_{g,C}) / \log(C)\]

where \(p_{g,c}\) is the proportion of gene \(g\) expression in cell type \(c\).

Prioritization Score Aggregation

The final prioritization score uses quantile normalization followed by geometric mean:

\[S_{\text{final}} = \left(\prod_{i=1}^{K} Q_i^{w_i}\right)^{1/\sum w_i}\]

where \(Q_i\) is the quantile-normalized score for criterion \(i\).

Computational Complexity

Parallelization

MultiNicheNet supports parallel processing for: - Ligand activity inference across receivers - Permutation-based empirical p-values - Multiple contrast calculations