## 1 Methods for the Analysis of Protein Fluorescence Spectra
### Accuracy of decomposition algorithms  
In order to test how various factors might affect the accuracy of the solution, a series of decompositions were carried out for simulated spectra [45]. Among varied factors were: number of spectra (N) with various \"quencher concentrations\"; number of points in each spectrum (M); randomly introduced noise, (S, %); distance between positions of maximum of spectral components (\(\Delta\lambda_{\rm max}\), nm); ratio of Stern-Volmer constants, and contribution of a component in the total spectrum. The quality of the solution was evaluated by the deviation of initial positions of component maxima from those obtained as a result of spectra decomposition (\(\Delta\lambda\), nm). It was found that the decomposition methods provide an acceptable level of accuracy (\(\Delta\lambda<1\) nm and \(<1.5\) nm for the two-component and three-component solutions, respectively) in case of S = 0.5 - 1.5%; N = 3 - 10; M = 10 - 20; \(\Delta\lambda_{\rm max}>7\) nm; and contribution of an individual component in a range of 10 - 90% - conditions of a typical experimental set up. In addition to validation of the decomposition algorithms, it is extremely important to know that the spectral components indeed correspond to the fluorescence of individual fluorophores. As already mentioned, the problem of data deconvolution is very typical in biophysical sciences. However, in the majority of cases it is not clear whether the obtained components have any physical meaning. Therefore, very important studies were carried with two proteins i) outer envelope protein 16, OEP16 and ii) Eosinophil Cationic Protein, ECP. Both proteins contain two tryptophan residues located in different parts of the protein molecules. Two single-tryptophan mutants were generated for each protein. Steady-state fluorescence spectra of wild-type and single-tryptophan mutants were recorded and decomposition analysis was applied [51,52]. The spectral components revealed by the decomposition of the fluorescence spectra of the wild-type proteins were strongly correlated with the position of the maximum of the single-tryptophan-containing mutants. The decomposition methods were tested on model compounds and single-tryptophan containing proteins and applied for the deconvolution of the fluorescence spectra of more than 150 proteins [46,53]. The application of the decomposition algorithms was successfully extended for the analysis of fluorescence spectra of Acrylodan and Prodan [47]. Algorithm for the Analysis of Structural Properties of Environment of Tryptophan Residues from Atomic Structures of Proteins  
The methods of spectral analysis allow extraction of the fluorescence properties of individual tryptophan residues, thus creating an opportunity to investigate the spectral-structural relationship. More than 35 years ago the first attempts were made to reveal a correlation between fluorescence parameters and structural characteristics of the tryptophan fluorophore's environment based on the atomic structures of several proteins [54-56]. Since then rapid progress in X-ray crystallography and NMR spectroscopy methods have led to an increase in the number of works where the measured fluorescence properties of individual proteins were analyzed in relation to structural features [57-66]. A number of databases and algorithms were proposed for calculating different structural and physical characteristics of individual residues in proteins [67-73]. Here we present the major aspects of an algorithm for the calculation of structural properties of the environment of tryptophan residues derived from the atomic structures data contained in the Protein Data Bank (PDB) [46,53]. The specially created program identifies and characterizes the environment of tryptophan residues in proteins. All protein atoms and water molecules located at distance of \(\leq\)7.5 A from the indole atoms are considered as belonging to the tryptophan fluorophore environment.