Calculation of rate spectra from noisy time series data

As the resolution of experiments to measure folding kinetics continues to improve, it has become imperative to avoid bias that may come with fitting data to a predetermined mechanistic model. Toward this end, we present a rate spectrum approach to analyze timescales present in kinetic data. Computing rate spectra of noisy time series data via numerical discrete inverse Laplace transform is an ill-conditioned inverse problem, so a regularization procedure must be used to perform the calculation. Here, we show the results of different regularization procedures applied to noisy multiexponential and stretched exponential time series, as well as data from time-resolved folding kinetics experiments. In each case, the rate spectrum method recapitulates the relevant distribution of timescales present in the data, with different priors on the rate amplitudes naturally corresponding to common biases toward simple phenomenological models. These results suggest an attractive alternative to the "Occam's razor" philosophy of simply choosing models with the fewest number of relaxation rates.