Inferring circadian phases and quantifying biological desynchrony across single-cell transcriptomes

This paper introduces scRitmo, a probabilistic framework that accurately infers single-cell circadian phases and quantifies biological desynchrony by distinguishing it from technical noise across diverse tissues, organisms, and experimental conditions.

The Gist

Imagine your body is a massive, bustling city. Inside every single building (cell) in this city, there is a tiny, self-sustaining clock ticking away. These clocks tell the cells when to wake up, when to eat, when to repair themselves, and when to sleep. This is your circadian rhythm.

Usually, all these clocks are synchronized by the sun (light and dark cycles), so the whole city operates in harmony. But sometimes, things get messy. Some clocks run a little fast, some run slow, and some get confused. When the clocks in a tissue stop ticking in unison, the tissue becomes "desynchronized," which can lead to health problems.

For a long time, scientists could only look at the city from a helicopter (bulk tissue analysis). They could see the average time, but they couldn't tell if the individual clocks were all ticking together or if they were all over the place.

Recently, scientists developed single-cell RNA sequencing (scRNA-seq). This is like sending a drone into every single building to take a snapshot of the clock's gears. But there's a catch: these snapshots are blurry, noisy, and often incomplete. It's hard to tell if a clock is actually out of sync or if the drone just took a bad photo.

Enter scRitmo: The "Smart Clock Detective"

The paper introduces a new tool called scRitmo (a play on "Rhythm" in Italian). Think of scRitmo as a super-smart detective that looks at these blurry, noisy snapshots of thousands of cells and figures out two things:

1. What time is it for this specific cell? (The Phase)
2. How sure are we about that time? (The Uncertainty)

Here is how it works, using some everyday analogies:

1. The "Noisy Room" Problem

Imagine trying to guess the time of day by listening to a conversation in a very noisy room. If you only hear a few words, you might guess wrong. In biology, the "words" are genes, and the "noise" is the technical messiness of the lab equipment.

• The Old Way: Previous tools tried to guess the time but didn't tell you how confident they were. They might say, "It's 3 PM," even if the room was incredibly loud.
• The scRitmo Way: scRitmo listens to the conversation and says, "It's likely 3 PM, but because the room is noisy, I'm only 60% sure." If the room is quiet (high-quality data), it says, "It's definitely 3 PM, and I'm 99% sure." This "confidence score" is crucial because it helps scientists ignore the bad guesses.

2. Separating "Real Chaos" from "Bad Photos"

This is the paper's biggest breakthrough. Sometimes, a group of cells looks like they are all out of sync. Is it because they are actually chaotic (Biological Desynchrony), or is it just because the camera was shaky (Technical Noise)?

• The Analogy: Imagine a choir singing.

  • Scenario A: Everyone is singing the same note perfectly. (Synchronized)
  • Scenario B: Everyone is singing different notes. (Desynchronized)
  • Scenario C: Everyone is singing the same note, but the microphone is crackling and distorting the sound. (Technical Noise)

  If you just listen to the recording, Scenario C sounds like Scenario B. You can't tell the difference!
  scRitmo solves this by running a "simulation" in its brain. It asks: "If I had a perfect choir singing in unison, but I recorded it with this specific noisy microphone, what would the recording sound like?"
  It calculates the "noise floor" (the crackle). Then, it subtracts that noise from the real recording. What's left is the true biological chaos. This allows scientists to measure exactly how out-of-sync a tissue really is, stripping away the camera shake.

3. The "Phase Attractor" Trap

The paper also discovered a funny bias. In the "city," some buildings (genes) are very active at specific times (like rush hour), while others are quiet. If you only look at the active buildings, your drone might get tricked into thinking everyone is active at that time, even if they aren't.

• The Fix: scRitmo uses a "broad net." Instead of just looking at the 15 most famous clock genes, it looks at hundreds of other rhythmic genes. This gives it a much wider view of the city, preventing it from getting stuck in one specific time zone.

What Did They Discover?

Using this new detective tool, the researchers looked at different tissues and found some fascinating things:

• The Liver: Even in a healthy liver, the cells aren't perfectly synchronized. They have a little bit of "wiggle room," which is normal.
• The Skin: Some immune cells in the skin are very chaotic, while others are very disciplined.
• The Fruit Fly Brain: When they put fruit flies in total darkness (no sun to sync them), the clocks in their brains started to drift apart. The "master clocks" (the pacemakers) stayed strong, but the "helper clocks" drifted off, showing that light is essential for keeping the whole network tight.

Why Does This Matter?

Think of chronodisruption (when your body clock is broken) as a city where the traffic lights are all out of sync. Cars crash, deliveries are late, and the city grinds to a halt. This happens in diseases like diabetes, cancer, and aging.

scRitmo gives us the first clear map of where the traffic lights are broken. It tells us if the problem is that the lights are actually broken (biological desynchrony) or if it just looks broken because of a storm (technical noise).

By understanding exactly how desynchronized our cells are, doctors might one day be able to treat diseases by "re-synchronizing" the cellular clocks, rather than just treating the symptoms. It turns a blurry, confusing picture of our biology into a sharp, high-definition map of time.

Technical Summary

1. Problem Statement

Circadian rhythms are cell-autonomous oscillations that coordinate physiology with the solar day. While bulk RNA-seq has mapped tissue-level rhythms, it obscures cell-to-cell heterogeneity. Single-cell RNA sequencing (scRNA-seq) offers the potential to resolve this heterogeneity but faces significant challenges:

• Technical Noise vs. Biological Desynchrony: scRNA-seq data is sparse and noisy (low capture efficiency, transcriptional bursting). It is difficult to distinguish true biological phase dispersion (cells having different intrinsic periods or entrainment sensitivities) from technical artifacts introduced by the sequencing process.
• Lack of Uncertainty Quantification: Existing methods for inferring circadian phase from static snapshots (e.g., Oscope, Cyclum, Tempo) often provide only point estimates without rigorous measures of confidence or uncertainty.
• Gene Set Limitations: Core clock genes are often expressed at low copy numbers. In standard droplet-based scRNA-seq (low sequencing depth), relying solely on these genes leads to biased phase inference (e.g., "phase attractors" where cells cluster artificially).

2. Methodology: scRitmo Framework

The authors introduce scRitmo, an unsupervised, probabilistic framework designed to infer single-cell circadian phases and quantify biological desynchrony.

A. Probabilistic Model

• Distribution: Models gene counts using a Negative Binomial (NB) distribution to account for overdispersion and sparsity inherent in scRNA-seq.
• Expression Model: Assumes periodic gene expression follows a harmonic oscillation. The log-mean expression for gene $g$ in cell $c$ is modeled as:
  $$\log(\mu_{cg}) = \log(s_c) + m_g + A_g \cos(\theta_c - \phi_g)$$
  Where $s_c$ is library size, $m_g$ is basal expression, $A_g$ is amplitude, $\phi_g$ is the peak phase (acrophase), and $\theta_c$ is the latent circadian phase of the cell.
• Inference: Instead of stochastic variational inference (used in similar tools like Tempo), scRitmo maximizes the marginal likelihood by integrating out the latent cell phases. This yields point estimates for gene parameters ($\beta$) and a full posterior distribution $P(\theta_c | x_c)$ for each cell.
• Output: For each cell, it provides:
  1. A point estimate of the phase (Posterior Mode).
  2. A measure of uncertainty (Circular Standard Deviation, $cSTD$, of the posterior).

B. Variance Decomposition (Quantifying Desynchrony)
A key innovation is the separation of observed phase variance ($\sigma_{data}^2$) into biological ($\sigma_{bio}^2$) and technical ($\sigma_{tech}^2$) components:

1. Simulation Calibration: The authors generate synthetic datasets with known ground-truth biological desynchrony ($\sigma_{bio}$) and perfectly synchronized populations ($\sigma_{bio}=0$).
2. Estimation: They calculate the observed dispersion of inferred phases ($\sigma_{data}$) and the technical dispersion ($\sigma_{tech}$) derived from the synchronized simulation.
3. Decomposition: Assuming additive variance, they estimate true biological desynchrony as:
   $$\hat{\sigma}_{bio} = \sqrt{\sigma_{data}^2 - \sigma_{tech}^2}$$
   This allows for the direct estimation of intercellular desynchrony from static transcriptomic data.

C. Gene Sets

• Clock-Reference: A fixed set of 15 core clock genes derived from bulk time-series data across organs.
• Extended-Set: To overcome low sequencing depth biases, the authors construct cell-type-specific gene sets (70–100 genes) using pseudobulk harmonic regression or knockout-validated criteria (genes rhythmic in WT but arrhythmic in Bmal1/Cry knockouts).

3. Key Results

A. Validation with Simulations and Protein Data

• Simulation: scRitmo accurately recovers ground-truth phases. At low sequencing depths (<10k UMI/cell), using only core clock genes causes phase clustering (attractor bias), which is resolved by using Extended-Set genes or higher depth (>20k UMI/cell).
• Protein Correlation: In unsynchronized 3T3 fibroblasts (FLASH-seq, high depth), scRitmo-inferred phases strongly correlated with endogenous Nr1d1 mRNA and the RevErbα-Venus protein fluorescence ($R^2 = 0.73$ for mRNA, $R^2 = 0.55$ for protein).
• Genome-wide Rhythmicity: Using inferred phases, genome-wide harmonic regression identified >100 rhythmic genes (cell cycle, signaling, ECM) not included in the input set, validating the biological relevance of the inferred phases.

B. Tracking Progressive Desynchrony (SABER-FISH)

• Applied to time-series SABER-FISH data of synchronized 3T3 fibroblasts drifting over 55 hours.
• Result: $\sigma_{tech}$ remained constant, while $\sigma_{bio}$ increased linearly over time.
• Period Estimation: The slope of $\sigma_{bio}$ increase allowed the authors to mathematically derive the distribution of single-cell free-running periods ($\sigma_T \approx 1.78$ hours), a metric traditionally requiring continuous live imaging.

C. Application to Murine Tissues (Liver, Aorta, Skin)

• Cell-Type Specificity: scRitmo revealed distinct phase coherence levels. Fibroblasts, smooth muscle cells, and hepatocytes showed tight coherence ($\sigma_{bio} \approx 1.1–1.6$ h).
• Immune Cells: Lyve1+ macrophages showed high desynchrony ($\sigma_{bio} \approx 4.2$ h) and weaker clock gene expression. Other immune cells (T-cells, dendritic cells) exhibited arrhythmic patterns with high uncertainty.
• Benchmarking: scRitmo outperformed the state-of-the-art tool Tempo in accuracy (lower Median Absolute Error) and computational speed.

D. Drosophila Clock Neurons (LD vs. DD)

• Applied to clock neurons under Light-Dark (LD) and Constant Darkness (DD) conditions.
• Phase Shifts: Under DD, most clusters (e.g., DN1p) showed phase advances, while pacemaker neurons (s-LNv) remained stable.
• Desynchrony: $\sigma_{bio}$ significantly increased in DD compared to LD, confirming that light acts as a synchronizing cue. The increase varied by cluster, suggesting differential sensitivity to photic entrainment.

4. Significance and Contributions

1. Principled Uncertainty Quantification: scRitmo moves beyond point estimates by providing a posterior distribution for every cell, allowing researchers to filter low-confidence data and assess the reliability of phase inference.
2. Decoupling Biology from Noise: The simulation-calibrated variance decomposition is a novel method to quantitatively separate technical noise from true biological desynchrony, addressing a major gap in the field.
3. Static to Dynamic Inference: The framework enables the estimation of dynamic properties (like the distribution of free-running periods) from static snapshot data, reducing the need for resource-intensive live-imaging experiments.
4. Scalability and Robustness: By demonstrating the utility of "Extended-Set" genes, the paper provides a practical solution for analyzing standard, low-depth droplet-based scRNA-seq data, making circadian analysis accessible for diverse tissues and organisms.
5. Biological Insights: The study confirms that population-level damping of rhythms is primarily due to desynchronization of intact oscillators rather than the loss of rhythmicity in individual cells, and highlights tissue-specific differences in clock coherence and entrainment sensitivity.

In summary, scRitmo provides a rigorous, probabilistic toolkit for transforming static single-cell transcriptomes into quantitative maps of circadian time and coherence, enabling new discoveries in chronobiology across scales from single cells to whole organisms.