## 3 Correlation between Spectral and Structural Properties of Tryptophan Residues
### Model of discrete classes of tryptophan residues in proteins  
Canonical discriminant analysis was applied to establish correlation between spectral and structural classes of tryptophan residues. The resulting model suggests the existence of discrete spectral-structural classes of emitting tryptophan fluorophores in proteins, which assumes that various processes might occur in the excited state of the tryptophan fluorophores belonging to five different classes, and as a result different spectral responses can be observed [53, 76]:  
**Class A** (\(\lambda_{m}=308\) nm, structured spectra) - these fluorophores do not form hydrogen-bound complexes in the excited state (no exciplexes) with the solvent or neighboring protein groups; they are deeply buried into the protein matrix and are located in non-polar (mainly carbon atoms), non-flexible protein environments. The tryptophan residues of class A are separated from other classes mainly by parameters polarity and flexibility of microenvironment.  
**Class S** (\(\lambda_{m}=316\) nm, structured spectra) includes buried tryptophan residues that can form the exciplexes with 1:1 stoichiometry. The major difference between fluorophores of classes A and S is that the latter one has higher relative polarity and flexibility of the microenvironment.  
**Class I** (\(\lambda_{m}=330-332\) nm, \(\Delta\lambda=48-50\) nm) represents the buried fluorophores that can form the exciplexes with 2:1 stoichiometry. The fluorophores of this class have much lower packing density, which could lead to a greater mobility of the environment in contrast to Trps of class S.  
**Class II** (\(\lambda_{m}=340-342\) nm, \(\Delta\lambda=53-55\) nm) the main feature of the fluorophores of this class is their contact with the structured water molecules. The discrimination between classes I and II are mostly defined by the parameters of packing density, total solvent accessibility, and \"dynamic accessibility\".  
**Class III** (\(\lambda_{m}=350-353\) nm, \(\Delta\lambda=59-61\) nm) contains fully exposed fluorophores surrounded by the highly mobile free water molecules, the time of dipole relaxation is in the femto-, pico- second range. This makes their spectra almost coinciding with those of free tryptophan residues in water.  
Examples of Application of Spectral and Structural Algorithms for the Study of Protein Structure, Conformation and Dynamics  
Classification of spectral and structural parameters of tryptophan residues in proteins within five discrete classes (presented above) are already accepted and widely used [78-86]. Here we would like to provide several examples of the application of our algorithms in the study of protein structure and dynamics.  
Spectral and structural analysis was applied to investigate conformational changes of 20S proteasome of rat natural killer cells induced by mono and divalent cations [87]. It was found that the emission of Trp13 (one of 19 tryptophan residues in protein) from \(\alpha\)6 subunit located near the cluster of highly conserved proteasome residues is mostly sensitive to the activation of the enzyme. It was concluded that the expression of maximal chymotrypsin-like activity of 20S proteasome is associated with the conformational changes that occur in this cluster, and that leads to the proteasome open conformation, allowing substrate access into the proteolytic chamber.  
Analysis of fluorescence spectra of isoforms of recombinant rat nucleoside diphosphate kinase (NDPK), which catalyze the transfer of \(\gamma\)-phosphate from nucleoside triphosphates to nucleosidediphosphates, revealed an unusual fluorescence (extremely high quantum yield) in NDPK alpha. This fluorescence was associated with tyrosinase formation in the active center of the alpha enzyme crucial for the activity of the protein [88]. Spectral and structural analysis were used to probe interactions of peptides and proteins with the lipid bilayer of membrane [51-52,89-90].