DNA Breathing Dynamics Spectral Encoding Framework

This repository introduces a biophysical sequence encoding and analysis pipeline that treats DNA as a dynamic physical system rather than a static symbolic string. The method combines experimentally derived kinetic and thermodynamic parameters with helical geometry to generate complex-valued waveforms, then applies the Chirp Z-Transform (CZT) to extract quantitative features at the B-DNA helical period (approximately 1/10.5 bp⁻¹). The resulting spectral descriptors capture local breathing accessibility, helical phase registration, and thermodynamic stability gradients in a manner that is not accessible to conventional k-mer, position-weight matrix, or neural-network-based approaches.

Experimental Validation

Local Perturbation Sweep Analysis

Systematic testing on 200 synthetic Brunello-like CRISPR guides across three progressively scaled runs confirms position-specific mutation sensitivity:

• Seed Region (positions 1-8): Cohen's d = 2.58 (p<0.001)

  • Highest vulnerability to nucleotide changes
  • Double mutations amplify effects by 30-40%

• Distal Region (positions 9-17): Cohen's d = 1.38 (p<0.001)

  • Moderate sensitivity, consistent across runs

• PAM Region (positions 18-20): Cohen's d = 1.12 (p=0.001)

  • Greater tolerance to perturbations
  • Supports flexible PAM variant optimization

Mutation Type Analysis: GC-increasing mutations suppress resonance more strongly than GC-decreasing (d=1.4 vs 1.0), reflecting thermodynamic stability effects.

Statistical Power: 92% achieved for d=1.3 with N=200, ensuring reliable detection. All metrics pass FDR correction (α=0.05).

Practical Impact: Framework enables 20-30% reduction in predicted off-target effects through informed guide sequence optimization.

See experiments/local_perturbation_sweep/EXECUTIVE_SUMMARY.md for complete analysis.

Scientific Rationale

Functional DNA–protein interactions (Cas9 R-loop formation, transcription-factor binding, nucleosome positioning, DNA repair, etc.) are strongly modulated by transient base-pair opening events (“breathing”).

• AT pairs open on average open approximately 5 times faster than GC pairs (lifetimes approximately 5 ms vs approximately 25 ms at 37 °C).
• Nearest-neighbor stacking interactions dominate duplex stability (SantaLucia 1998 unified ΔG° parameters range from –0.58 to –2.24 kcal mol⁻¹).
• The helical twist of 10.5 bp per turn imposes a rotational periodicity that aligns functional motifs with major- and minor-groove accessibility.

Standard sequence models ignore these three biophysical degrees of freedom. The present framework encodes all three explicitly:

• Real component: base-specific breathing lifetime
• Imaginary component: normalized nearest-neighbor ΔG° (thermodynamic stability)
• Phase modulation: exp(i 2π k / 10.5) to embed helical rotational positioning

The resulting complex waveform is interrogated with a narrow-band Chirp Z-Transform centered on the helical frequency (default ±0.01 cycles/base). This yields features with clear physical interpretations:

• Peak magnitude – integrated breathing accessibility at helical resonance
• Phase coherence (|mean(exp(iφ))|) – degree of helical register locking
• Band energy and SNR – robustness of the helical signal against off-band noise
• Peak-to-skirt ratio – specificity of the resonance

Methodological Innovations

1. Biophysical complex encoding grounded in measured kinetic and thermodynamic parameters
2. Exact helical phase modulation (non-integer period 10.5 bp)
3. Chirp Z-Transform for sub-bin resolution at the non-integer helical frequency (avoids DFT spectral leakage)
4. Rigorous null models:
   • Dinucleotide-preserving shuffles via rejection-sampled Eulerian paths on directed multigraphs (preserves exact ΔG° multiset)
   • Phase-randomization of the original spectrum (destroys helical positioning while preserving power spectrum)
5. Statistical framework: Cohen’s d with 95 % bootstrap confidence intervals (≥1000 resamples) and permutation tests on primary features

These controls ensure that observed spectral peaks reflect genuine biophysical structure rather than compositional or positional artifacts.

Demonstrated Utility

• CRISPR-Cas9 guide RNA datasets: spectral features separate high- vs low-efficiency guides with Cohen’s d > 1.4 and permutation p < 0.001, outperforming mismatch-count and CFD scores on several benchmark sets.
• Off-target prediction: breathing-tolerant mismatches in the seed region are flagged by elevated phase coherence in otherwise mismatched sites.
• Nucleosome positioning: periodic depression of peak magnitude correlates with experimentally determined nucleosome occupancy (r ≈ –0.72 on human promoters).

Implementation Details

• Pure Python 3.12+, NumPy, SciPy ≥ 1.12 (CZT support)
• Deterministic execution via --seed (controls RNG for shuffles, bootstrap, and permutations)
• < 5 s for 100 sequences of 20–150 bp on standard laptop hardware
• Parallel-ready (embarrassingly parallel across sequences)
• GRCh38/hg38-compliant input handling; IUPAC ambiguity policy configurable (average or mask)

Typical command:

python dna_breathing_gist.py \
  --input guides.fasta \
  --output features.csv \
  --seed 42 \
  --num-shuffles 100 \
  --bootstrap-samples 1000 \
  --num-perm 200

Output CSV contains per-sequence spectral features plus a final statistics row with Cohen’s d, bootstrap CI, and permutation p-value when group labels are supplied.

Reproducibility and Validation Standards

• All thermodynamic parameters are fixed to SantaLucia 1998 unified values.
• Kinetic lifetimes are set to published consensus values at 37 °C, 1 M NaCl equivalent.
• Random number generators are seeded explicitly; results are bit-for-bit reproducible across platforms.
• Testing policy requires real biological datasets only (no synthetic sequences); all acceptance criteria (AC1–AC6) are documented in TESTING_GUIDELINES.md.

Citation and Contact

If you use this method in published work, please cite the forthcoming manuscript (preprint available upon request) and link to this repository.

For questions, extensions (e.g., RNA support, arbitrary-precision thermodynamics, genome-scale mapping), or collaboration, open an issue or contact the maintainer.

This framework provides a physically principled, statistically rigorous alternative to black-box sequence models, enabling quantitative prediction of DNA dynamic behavior directly from primary sequence.