GeneRhythm uncovers gene expression rhythms that shape the dynamic transcriptional landscape in single-cell omics

Technical Summary of GeneRhythm

Problem Statement
Dynamic gene expression programs drive development and disease, yet current single-cell analytical frameworks predominantly operate in the time domain. These conventional methods capture changes in expression magnitude and trajectory similarity but fail to resolve how those changes are rhythmically organized. Consequently, regulatory programs that differ in periodicity, phase, or multi-scale dynamics often appear indistinguishable if they share similar overall trends. This limitation obscures fundamental dimensions of gene regulation, conflating distinct regulatory mechanisms that possess different rhythmic structures but similar time-domain trajectories.

Methodology
The authors introduce GeneRhythm, a framework that reformulates gene expression in the time–frequency domain to explicitly model rhythmic structure as a primary dimension of gene regulation. The workflow proceeds through the following stages:

1. Trajectory Reconstruction and Interpolation: Single-cell data (scRNA-seq, scATAC-seq, spatial transcriptomics) is processed to infer cellular trajectories (e.g., using Monocle3). Gene expression is aggregated at milestone waypoints and smoothed via cubic spline interpolation to generate continuous time-domain signals.
2. Time–Frequency Transformation: Continuous signals undergo Continuous Wavelet Transform (CWT) using a Mexican hat wavelet. This generates time–frequency maps ($W(a, b)$) that preserve temporal localization and capture oscillatory patterns across multiple scales, defining a "rhythm profile" for each gene.
3. Deep Representation Learning: A multi-branch deep neural network architecture integrates three feature sets:
   • $X_c$: Gene expression across cells.
   • $X_t$: Time-domain dynamic features (trajectory-derived).
   • $X_f$: Frequency-domain rhythm features (wavelet-derived).
     Graph Convolutional Networks (GCNs) incorporate Protein–Protein Interaction (PPI) priors to propagate rhythmic information across regulatory networks. A Variational Autoencoder (VAE) framework learns a unified latent gene embedding that captures expression magnitude, temporal progression, and frequency-resolved structure.
4. Core Functionalities:
   • Rhythmic Clustering: Genes are clustered based on shared rhythmic organization in the latent space, independent of time-domain trajectory shape.
   • Differentially Rhythmic Gene (DRG) Identification: Statistical testing (t-test on frequency profiles) identifies genes with condition-specific rhythmic changes, even when mean expression differences are negligible.
   • Rhythmic In Silico Perturbation: The framework simulates gene or pathway perturbations within the frequency-domain latent space. It quantifies the shift of disease-state representations toward control states to prioritize regulators whose functional impact is encoded in rhythmic structure.
   • Gene Sonification: Frequency-resolved dynamics are translated into structured musical scores (MIDI), mapping wavelet scales to pitch and amplitude to note density, providing an interpretable modality for exploratory analysis.

Key Results

• Rhythmic Clustering: In mouse embryonic blood and neural crest datasets, GeneRhythm identified gene modules coherent in frequency space despite divergent time-domain trajectories. High-frequency clusters were enriched for immune signaling and rapid regulatory programs, while low-frequency clusters aligned with developmental maintenance and housekeeping functions. Benchmarking against scNET, scSTEM, Clust, and WGCNA showed GeneRhythm achieved superior geometric clustering metrics (Calinski–Harabasz, Davies–Bouldin, Dunn, Silhouette) and higher pathway-level biological coherence.
• Differential Rhythm Discovery: Across arsenic exposure, COVID-19, and diabetes datasets, DRG analysis identified disease-specific markers missed by conventional differential expression (DEG) analysis. For instance, in arsenic-exposed cells, the marker Maml2 showed distinct rhythmic reorganization without significant mean expression changes. Similarly, KLRF1 in COVID and THRAP3 in diabetes exhibited structured rhythmic phenotypes invisible to standard DEG methods.
• Multi-Omics and Spatial Applications: In spatial transcriptomics (human dorsolateral prefrontal cortex), rhythmic analysis distinguished "Cross Layers" from "Intra Layers" spatial directions, revealing cortical markers like GLYAT that were undetectable via static expression comparisons. In paired scATAC-seq and scRNA-seq data, the framework identified "primed" genes where chromatin accessibility showed rhythmic differential signals preceding transcriptional changes.
• Perturbation and Clinical Relevance: In silico perturbation in COVID and pancreatic ductal adenocarcinoma (PDAC) datasets identified candidate therapeutic targets (e.g., Azeliragon, Gemcitabine) and pathways that were not prioritized by expression-based methods. In PDAC, genes uniquely identified by frequency-domain perturbation showed significantly stronger prognostic stratification (survival analysis) compared to those identified by conventional non-frequency perturbation.

Significance and Claims
The paper claims that GeneRhythm establishes frequency-domain-defined rhythmic structure as a fundamental, previously unmodeled dimension of gene regulation. By shifting from time-domain to time–frequency representation, the framework:

1. Uncovers Hidden Regulatory Programs: It reveals disease-relevant transcriptional programs and regulatory modules that are invisible to conventional time-domain analyses because they differ in periodicity or phase rather than magnitude.
2. Provides a General Analytical Basis: The approach generalizes across diverse modalities (scRNA-seq, scATAC-seq, spatial transcriptomics) and biological contexts (development, disease), offering a unified basis for analyzing, comparing, and perturbing dynamic regulatory programs.
3. Enables Actionable Insights: Through rhythmic in silico perturbation and sonification, the framework translates complex frequency-domain dynamics into interpretable representations, linking rhythmic sensitivity to drug targets, pathway enrichment, and clinical outcomes.

The authors position GeneRhythm not as a replacement for existing tools but as a complementary lens that resolves regulatory structure systematically missed by trajectory similarity and mean-expression comparisons, thereby reducing ambiguity in aligning dynamic regulatory findings with biological mechanisms.