SPARK

Stability-optimised Program Architecture Reconstruction frameworK

SPARK is a graph-based transcriptomic framework for identifying stable, coordinated pathway modules from pathway activity landscapes using multimodality filtering, network-based organisation, Leiden community detection, and stability optimisation.

The framework reconstructs higher-order transcriptomic programs from GSVA-derived pathway activity matrices and is designed for robust pathway-level systems biology analyses in cancer and complex biological systems.

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Workflow Overview

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Overview

SPARK combines:

• Gaussian mixture model (GMM)-based multimodal pathway filtering
• Bayesian Information Criterion (ΔBIC)-driven pathway selection
• Signed pathway co-activity network construction
• WGCNA-inspired soft-thresholding
• Leiden graph community detection
• Bootstrap stability optimisation
• Principal component-derived module eigengenes

to identify stable transcriptomic pathway modules representing coordinated biological programs.

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Features

• Multimodal pathway filtering using Gaussian mixture models
• ΔBIC-based identification of biologically informative pathways
• Graph-based pathway organisation
• Resolution-wise Leiden community detection
• Stability-aware module optimisation
• Bootstrap-adjusted Rand Index (ARI) evaluation
• Principal component-based module summarisation
• Publication-ready module-level outputs and diagnostics

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Repository Structure

SPARK_repository/
│
├── README.md
├── LICENSE
├── .gitignore
│
├── scripts/
│   ├── 01_gmm_multimodal_filtering.R
│   ├── 02_graph_module_discovery.R
│   └── run_spark_pipeline.R
│
├── example_data/
│   └── GSVA_scores.csv
│
├── example_output/
│   ├── gmm_filtering/
│   └── module_discovery/
│
├── docs/
│   ├── workflow_schematic.png
│   ├── mathematical_overview.pdf
│   ├── methodology.md
│   └── parameter_descriptions.md
│
└── environment/
    ├── required_packages.R
    └── sessionInfo.txt

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Installation

Clone Repository

git clone https://github.com/rdk004/SPARK.git
cd SPARK

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Install Dependencies

Open R and run:

source("environment/required_packages.R")

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Input Data

SPARK requires a GSVA pathway activity matrix where:

• rows represent pathways
• columns represent samples
• values represent GSVA enrichment scores

Place the matrix inside:

example_data/GSVA_scores.csv

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Running SPARK

Run the complete pipeline using:

source("scripts/run_spark_pipeline.R")

The workflow sequentially performs:

1. Multimodal pathway filtering
2. Correlation network construction
3. Leiden-based module discovery
4. Stability optimisation
5. Module eigengene generation

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Workflow Components

1. Multimodal Pathway Filtering

Pathways are evaluated using Gaussian mixture models (GMMs).

Model selection is performed using the Bayesian Information Criterion (BIC):

$$\Delta BIC = BIC_{best} - BIC_{G=1}$$

Pathways with:

$$\Delta BIC > 10$$

are retained for downstream graph analysis.

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2. Graph-based Module Discovery

A signed pathway co-activity network is constructed using pathway-pathway correlations across samples.

Soft-thresholding is performed using WGCNA-inspired adjacency transformation:

$$A_{ij} = \left(\frac{1 + cor(i,j)}{2}\right)^\beta$$

Leiden community detection is then performed across multiple resolutions.

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3. Stability Optimisation

For each resolution:

• bootstrap pathway resampling is performed
• bootstrap sample resampling is performed
• Adjusted Rand Index (ARI) stability is computed

Resolution selection is based on a composite score integrating:

• module coherence (MAPC)
• graph stability

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4. Module Eigengene Generation

For each identified module:

• principal component analysis (PCA) is performed
• PC1 is used as the module eigengene
• pathway PC1 loadings are exported

These eigengenes represent coordinated transcriptomic pathway programs.

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Outputs

GMM Filtering Outputs

Located in:

example_output/gmm_filtering/

Includes:

• ΔBIC statistics
• retained pathway lists
• filtered GSVA matrices
• multimodality diagnostic plots

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Module Discovery Outputs

Located in:

example_output/module_discovery/

Includes:

• module assignments
• module eigengene matrices
• PC1 loading matrices
• resolution optimisation metrics
• module correlation heatmaps

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Documentation

Additional methodological details are available in:

docs/

Including:

• workflow schematic
• mathematical overview
• parameter descriptions
• methodological summaries

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Reproducibility

The repository includes:

• dependency installation scripts
• session information
• example input data
• example output files

for reproducible execution.

Environment information is provided in:

environment/sessionInfo.txt

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Citation

If you use SPARK in your work, please cite the associated manuscript.

Rishabh Kulkarni SPARK: Stability-optimised Program Architecture Reconstruction Framework (Manuscript in preparation)

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Contact

Rishabh Kulkarni Indian Institute of Science Education and Research (IISER) Pune rdkulkarni04@gmail.com

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License

This project is released under the MIT License.