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"The beauty of a living thing is not the atoms that go into it, but the way those atoms are put together."
- Carl Sagan
Quick Analysis Plan
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Reciprocal-space kinetic decomposition recovers state-specific structure factors (PCC=1.0 noiseless; PCC>0.85 at SNR 1.0; ~1.5Γ SNR gain in experimental phytochrome data), but its core limitations are fixed concentration profiles, violation at ultra-early delays from coherent motions, and lack of independent ground-truth validation; practical alternatives include relaxed reflection-coverage filtering (PCC 0.98 vs 0.92) and joint fitting of kinetic profiles during decomposition. Source code: github.com/Westenhoff-Lab/fourier-kin-dec
Long Analysis Plan
Method Performance & Core Limitations
What works: On simulated PYP intermediates (pR0, pR1, pR2, pB0), noiseless reconstruction achieves PCC=1.0 for all four states with R=0. Adding Gaussian noise at SNR 1.0 preserves real-space PCC>0.85 for all recovered states; at extreme SNR 0.1, maps remain interpretable though weak density is obscured . In experimental bacterial phytochrome TR-SX (17 timepoints, femtoβmicrosecond), decomposition into four states raises mean ΞF/Ο ~1.5Γ and reflections >3Ο from ~37% to >55% .
Key limitations (reported): (1) Concentration profiles are fixed inputs, not fitted β decomposition validates implementation, not kinetic model correctness; (2) coherent atomic motions at sub-picosecond delays violate the population-state approximation; (3) no independent ground truth for experimental phytochrome states; (4) requiring reflections present at all 17 timepoints discards ~40% of data .
Reflection Coverage: Filtering Sensitivity
A practical mitigation: relaxing the all-timepoint requirement to β₯12/17 retains 131,257 of 141,174 reflections with map PCC=0.98 vs raw, compared to 84,478 reflections at PCC=0.92 with the strict all-17 filter .
Analysis Plan (Python)
Ingest & validate: Load MTZ/structure factors via gemmi or CCP4 tools; verify dark-state phase/sign conventions and Ursby-Bourgeois weighting before decomposition.
Simulate ground truth: Generate PYP-like mixed data with phenix.fmodel; inject known Gaussian noise to test recovery across SNR grid (0.1, 0.5, 1.0, 2.0).
Run decomposition: Apply least-squares matrix inversion (Eq. 5) with known profiles; cross-check with real-space PCC and Fourier residual diagnostics.
Model-correctness test: Repeat with deliberately wrong concentration profiles β if state DED maps converge, the profile choice is underdetermined; if they diverge, profiles are identifiable.
Fit-vs-fixed comparison: Implement joint least-squares fitting of concentration profiles (nonlinear least squares over the kinetic matrix) as an alternative; compare map PCC and ΞF/Ο against fixed-profile results.
Sample-delivery coupling: For experimental design, use fixed-target or segmented-droplet approaches to reduce protein consumption (97% savings reported for segmented droplets) .
Simulating mixed PYP structure factors, applying reciprocal-space kinetic decomposition under varying SNR, and benchmarking recovery quality against fixed versus jointly-fitted kinetic profiles.
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Hypothesis Graveyard
Decomposition success proves the kinetic model is correct β falsified because the method uses profiles as fixed inputs and only validates map reconstruction, not model identification.
Single protein system generalizes broadly β the demonstration is restricted to one phytochrome dataset; generalization to other TR-SX systems is untested.