Abstract
A new algorithm for the Maximum Entropy Method (MEM) is proposed for recovering the lifetime distribution in time-resolved fluorescence decays. The procedure is based on seeking the distribution that maximizes the Skilling entropy function subjected to the chi-squared constraint χ 2 ~ 1 through iterative linear approximations, LU decomposition of the Hessian matrix of the lagrangian problem and the Golden Section Search for backtracking. The accuracy of this algorithm has been investigated through comparisons with simulated fluorescence decays both of narrow and broad lifetime distributions. The proposed approach is capable to analyse datasets of up to 4,096 points with a discretization ranging from 100 to 1,000 lifetimes. A good agreement with non linear fitting estimates has been observed when the method has been applied to multi-exponential decays. Remarkable results have been also obtained for the broad lifetime distributions where the position is recovered with high accuracy and the distribution width is estimated within 3 %. These results indicate that the procedure proposed generates MEM lifetime distributions that can be used to quantify the real heterogeneity of lifetimes in a sample.
Highlights
Fluorescence spectroscopy is a classical method for studying the structural and dynamical aspects of biological systems such as proteins, membranes and living cells [1,2,3]
The tryptophan residues in the exited state are usually involved in a energy transfer process to intra-molecular acceptors that depends on the relative distance and affects the fluorescence lifetime [4, 8]
To test the performances of our algorithm with broad lifetime distributions, we considered Gaussian distributions centred at τ = 5,000 ps with different standards deviation τ = 500 ps, 1,000 ps, 1,500 ps (i.e. 10, 20 % and the 30 % of τ ), that are assumed as a measure of their width
Summary
Fluorescence spectroscopy is a classical method for studying the structural and dynamical aspects of biological systems such as proteins, membranes and living cells [1,2,3]. J Fluoresc (2013) 23:203–211 proteins that characterise their folding process from an extended random polypeptide chain In complex situations, such as those encountered even in small proteins, the rate of energy transfer and the intramolecular distances can be described by a continuum distribution due to heterogeneity of the structure that turns out to a continuum lifetime distribution for the fluorescence decay [9,10,11,12]. The accuracy of the algorithm is investigated through comparisons with numerical simulations of fluorescence decay data It results that the MEM algorithm proposed can analyse datasets with up to 4,096 data points, that is a typical value of an experimental set up based on a time-correlated single photon counting technique, by considering distributions with a number of lifetimes that ranges from 100 to 1,000
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