TimeCycle

TimeCycle detects rhythmic genes in circadian transcriptomic time-series data using topological data analysis to identify cyclical gene expression patterns.

Key Features:

• Topology-Based Methodology: Reconstructs state space from time-series via time-delay embedding derived from dynamical systems theory.
• Takens' Theorem and Circular Patterns: Uses the expectation that rhythmic dynamics appear as circular patterns in the embedded space per Takens' theorem.
• Persistent Homology: Quantifies the degree of circularity in embeddings using persistence scores computed by persistent homology.
• Statistical Significance via Bootstrapping: Compares persistence scores against a bootstrapped null distribution to identify cycling genes.
• Reference-Free Cycle Detection: Implements a reference-free framework for detecting cycles in transcriptomic time-series.
• Robustness to Sampling Complexity: Explicitly handles custom sampling schemes, varying numbers of replicates, and missing data.
• Validation on Multiple Datasets: Demonstrated on both synthetic and biological circadian transcriptomic datasets.
• Comparative Analysis: Includes comparative evaluations against competing rhythm detection methods.

Scientific Applications:

• Circadian Gene Discovery: Identifies genes exhibiting circadian regulation in transcriptomic time-series.
• Temporal Profiling Across Tissues and Time Points: Facilitates analysis of gene expression dynamics across tissues and sampling times to study circadian regulation.
• Method Comparison and Benchmarking: Supports comparative assessment of rhythm detection approaches on synthetic and biological datasets.

Methodology:

Reconstructs state space with time-delay embedding, computes persistence scores via persistent homology to quantify circularity, and assesses significance by comparing persistence scores to a bootstrapped null distribution.