A Reproducible Two-Stage Protocol for Global Fitting of Time-Resolved Fourier Transform Infrared Difference Spectra

Global analysis of time-resolved spectra fits shared kinetic parameters across all spectral channels, but nonlinear fits can depend on starting values and stopping settings. We describe UFiτ (UFit), a reproducible two-stage protocol for time-resolved Fourier transform infrared (FTIR) difference spectra. Stage 1 fits the M channels with the largest peak-to-peak change to estimate shared lifetimes and stretching exponents; these estimates initialize Stage 2, a variable-projection fit of the full matrix. Using 6940 independently generated matrices with known parameters, we compared this top-M initialization with a direct fit from a fixed generic start, a singular value decomposition (SVD)-assisted prefit, uniform and random channel subsets, and best-of-ten multistart. Starting-value errors differed by up to about twentyfold between methods, yet final recovery was similar in most conditions. In a predeclared close-lifetime test, top-M and SVD initialization recovered all components in 118 and 113 of 200 matrices (p = 0.27); in exploratory comparisons, top-M recovered fewer matrices in two of twelve conditions, and ranking can omit a weak late component. Endpoint agreement depended mainly on stopping settings: with scaled residuals and tighter tolerances, direct, continuation, SVD-assisted and top-M fits of one measured photosystem I recording met a common numerical endpoint screen; uniformly spaced and random-subset prefits ended at a slightly lower objective with a different, undetermined slow component. We provide the protocol, a component-resolution checklist, and benchmark code and results.