Modeling survival–diversity trade-offs and rearrangement cascades in synthetic yeast SCRaMbLE

Technical Summary: Modeling Survival–Diversity Trade-offs and Rearrangement Cascades in Synthetic Yeast SCRaMbLE

Problem Statement
Current experimental investigations of Synthetic Chromosome Rearrangement and Modification by LoxP-mediated Evolution (SCRaMbLE) in the synthetic yeast genome (Sc2.0) primarily rely on sequencing viable endpoint clones. This approach captures only the "survivor-enriched" fraction of the rearrangement landscape, leaving trajectories that result in lethality (specifically, the loss of essential genes) largely unobserved. Furthermore, there is a lack of a quantitative framework that jointly models lox-site relationships, stochastic rearrangement processes, and cellular survival constraints to understand the trade-offs between generating structural diversity and maintaining viability.

Methodology
The authors developed a risk-aware, lox-order stochastic framework to simulate SCRaMbLE trajectories forward in time. Key methodological components include:

• Dynamic State Representation: Each synthetic chromosome is modeled as a dynamic sequence of lox-bounded segments. The system updates segment order, orientation, junctions, active lox copies, and Open Reading Frame (ORF) copy numbers after every event.
• Event Engine: The simulator processes deletion, inversion, and tandem duplication events. Event attempts are sampled from a Bernoulli distribution ($p_{event}$). When an event occurs, an eligible same-chromosome lox pair is selected based on specific sampling schemes, and an event class is chosen based on empirical probabilities derived from prior data.
• Sampling Schemes: Two lox-pair sampling strategies were compared:
  1. Linear-distance sampling: Weighting pairs based on the number of lox-order steps ($d_{ij}$) using a power-law decay ($w \propto [1+d_{ij}]^{-\alpha}$).
  2. Partially Hi-C-informed sampling: Combining the distance component with direct SynII contact matrix data (normalized Hi-C contacts) for SynII, with a distance-based fallback for other chromosomes or pairs lacking contact data.
• Essentiality Gate: A strict viability filter was implemented where a trajectory is classified as "gate-failing" the moment any retained essential ORF reaches zero copies. This allows for the tracking of both surviving (gate-passing) and lethal (gate-failing) trajectories.
• Simulation Grid: The study evaluated 88 scenarios across two sampling families, four distance-decay parameters ($\alpha$), and 11 event probabilities ($p_{event}$). Each scenario involved 10,000 independent trajectories with up to 20 sequential event opportunities.
• Diversity Metrics: Structural diversity was quantified using copy-label-invariant linear-topology signatures to calculate rarefied effective Shannon diversity ($D_1$), distinguishing true structural variation from simulation-specific copy labels.
• State-Replay Analysis: To understand rearrangement cascades, the authors replayed gate-failing trajectories to analyze how preceding non-deletion events (inversions/duplications) altered the accessibility and probability of the terminal deletion event that caused lethality.

Key Results

1. Survival–Diversity Trade-off: There is a continuous, reproducible trade-off between the fraction of trajectories passing the Essentiality Gate and the structural diversity of the surviving endpoints. Increasing $p_{event}$ consistently reduced the gate-passing fraction while increasing structural diversity.

   • The Pareto frontier (non-dominated settings) was defined entirely by linear-distance sampling at $\alpha = 2.0$.
   • At a prespecified gate-passing threshold of 0.70, the most diverse admissible setting occurred at $p_{event} = 0.10$ (passing fraction 0.7285, structural $D_1 = 456.16$).
   • The unrestricted maximum diversity ($D_1 = 1,138.78$) was achieved at $p_{event} = 0.30$, where the passing fraction dropped to 0.3710.

2. Mechanisms of Gate Failure:

   • All gate-failing trajectories terminated with a deletion event, as inversions and duplications preserve or increase copy numbers.
   • However, 44.73% of gate-failing trajectories contained at least one preceding inversion or duplication.
   • Cascade Effects: State-replay analysis revealed that non-deletion events alter the "hazard" of subsequent deletions. Inversions increased the one-step gate-failing deletion hazard in 41.66% of sampled states (often by shortening distance or activating new lethal spans), whereas duplications decreased the hazard in 96.67% of states (primarily through pair-space renormalization and buffering).

3. Spatial Organization and Hi-C:

   • Partial Hi-C information provided a modest improvement in pooled Pearson correlation ($r = 0.4509$) compared to linear-distance sampling ($r = 0.4329$).
   • However, this advantage was not consistent across metrics; linear-distance sampling performed better in Spearman correlation and RMSE.
   • Hotspot ranking performance remained near random for both models, and chromosome-wise holdout correlations were weak, suggesting the Hi-C signal is context-dependent and does not generalize well across chromosomes or to top-10% hotspot prediction.

4. Interval-Level Losses: Gate failures were concentrated in recurrent intervals on SynII containing essential genes such as EXO84, TIM12, CMD1, and ALG1. Genes within the same lox-bounded segment shared identical loss frequencies, indicating that interval structure drives loss patterns more than individual gene identity.

Significance and Claims
The paper claims to provide a reproducible computational basis for:

• Quantifying Trade-offs: Resolving the survival–diversity trade-off via a Pareto frontier, allowing researchers to select induction parameters ($p_{event}$) that balance the generation of structural diversity with the retention of viable clones.
• Unobserved Trajectories: Characterizing the "missing landscape" of lethal rearrangement trajectories, specifically demonstrating that non-deletion events (inversions/duplications) can indirectly trigger lethality by reshaping the accessibility of subsequent deletions.
• Hypothesis Generation: Generating interval-level hypotheses for experimental calibration. The model identifies specific SynII intervals where deletion leads to lethality, providing testable candidates for experimental validation (e.g., via CRISPR-Cas9 deletion).
• Methodological Rigor: Establishing a framework that distinguishes between model-defined event probabilities and experimental induction conditions, emphasizing that the current model focuses on intrachromosomal events and that future work requires wet-lab calibration to map dimensionless probabilities to Cre activity and exposure duration.

The authors maintain a modest stance, noting that the Essentiality Gate captures only one component of viability (essential gene loss) and that the framework does not yet account for dosage sensitivity, translocations, or complex interchromosomal structures observed in experimental populations. The study concludes that while partial Hi-C data offers some predictive gain, the linear-distance model remains robust for defining the core trade-off landscape.