238
B. Czarnik-Matusewicz and Y.M. Jung
spectra has allowed the postulate of significant structural differences between the
first two phases and the last. during the first two transition stages, changes in the
secondary structure of the backbone in the β-domain were mainly detected whereas
in the final transition, the phase changes also take place in the α-domain and side
chain residues dominated by solvent exposure.
8.4.3 Model-based correlation—βν and kν correlation analyses
to overcome some difficulties in the interpretation of temporal or phase relationships between intensity variations within a set of spectra subjected to the generalized 2d approach, dluhy’s group proposed a method in which the experimental
intensities are correlated with a reference set of intensities changing according to a
sinusoidal [137] (βν-correlation) or exponential function [138] (kν-correlation). Additionally, the global correlation phase angle method has been presented by dluhy’s
group as a tool to improve the interpretation of the temporal relationships between
the intensity variations [35].
The βν and kν-correlations fulfill the conditions of heterocorrelation; one set is
the experimental spectra, and the second set is the basis set of sinusoidal reference
functions with systematically varying phase angle ( β) or exponential functions with
rate constants (k) that undergo systematic changes in a user-defined range. In the
proposed method, only the asynchronous correlation spectra are employed; these
spectra are generally more sensitive to differences in the form of the signal variation than the synchronous spectra. the effective phase angle, β e , and the effective
rate constant, k eff , determined from the Ψ(β,ν) and Ψ(k,ν) plots as the points of
maximum correlation intensity have been used to verify the sequence of intensity
changes, as shown in Fig. 8.9 The spectra subjected to the kν-correlation analysis
are superposition of three bands, which order the spectral intensity changes give
numbers in Fig. 8.9a. to correctly determine the order of the intensity changes from
the asynchronous Ψ(ν 1 ,ν 2 ), the synchronous sign around the asynchronous peaks
must be considered. the grey outlines in Fig. 8.9c mark the areas where the sign
was negative. Neglecting this fact results in a false sequence of intensity changes.
The application of the kν-correlation procedure in which the spectra (Fig. 8.9a)
have been correlated with the exponential runs exp(- k t + R) with different k values
(Fig. 8.9b) has allowed the detection of three peaks. the k eff values of these peaks
reflect the a priori known sequence of intensity changes (Fig. 8.9d) because events
at frequencies with a larger k eff value occur earlier than events at frequencies with
smaller k eff value [68].
Because the two correlations are robust and are generally applicable, they have
been used in a wide range of studies. on one hand, the generalized 2dCoS is a
model-free procedure and directly extracts information from the synchronous and
asynchronous spectra. on the other hand, users frequently refer to an assumed model of signal changes, and the 2dCoS pattern of the model is compared with that
obtained from the experimental data [37, 39, 63, 71]. For protein spectra, it could be
B. Czarnik-Matusewicz and Y.M. Jung
spectra has allowed the postulate of significant structural differences between the
first two phases and the last. during the first two transition stages, changes in the
secondary structure of the backbone in the β-domain were mainly detected whereas
in the final transition, the phase changes also take place in the α-domain and side
chain residues dominated by solvent exposure.
8.4.3 Model-based correlation—βν and kν correlation analyses
to overcome some difficulties in the interpretation of temporal or phase relationships between intensity variations within a set of spectra subjected to the generalized 2d approach, dluhy’s group proposed a method in which the experimental
intensities are correlated with a reference set of intensities changing according to a
sinusoidal [137] (βν-correlation) or exponential function [138] (kν-correlation). Additionally, the global correlation phase angle method has been presented by dluhy’s
group as a tool to improve the interpretation of the temporal relationships between
the intensity variations [35].
The βν and kν-correlations fulfill the conditions of heterocorrelation; one set is
the experimental spectra, and the second set is the basis set of sinusoidal reference
functions with systematically varying phase angle ( β) or exponential functions with
rate constants (k) that undergo systematic changes in a user-defined range. In the
proposed method, only the asynchronous correlation spectra are employed; these
spectra are generally more sensitive to differences in the form of the signal variation than the synchronous spectra. the effective phase angle, β e , and the effective
rate constant, k eff , determined from the Ψ(β,ν) and Ψ(k,ν) plots as the points of
maximum correlation intensity have been used to verify the sequence of intensity
changes, as shown in Fig. 8.9 The spectra subjected to the kν-correlation analysis
are superposition of three bands, which order the spectral intensity changes give
numbers in Fig. 8.9a. to correctly determine the order of the intensity changes from
the asynchronous Ψ(ν 1 ,ν 2 ), the synchronous sign around the asynchronous peaks
must be considered. the grey outlines in Fig. 8.9c mark the areas where the sign
was negative. Neglecting this fact results in a false sequence of intensity changes.
The application of the kν-correlation procedure in which the spectra (Fig. 8.9a)
have been correlated with the exponential runs exp(- k t + R) with different k values
(Fig. 8.9b) has allowed the detection of three peaks. the k eff values of these peaks
reflect the a priori known sequence of intensity changes (Fig. 8.9d) because events
at frequencies with a larger k eff value occur earlier than events at frequencies with
smaller k eff value [68].
Because the two correlations are robust and are generally applicable, they have
been used in a wide range of studies. on one hand, the generalized 2dCoS is a
model-free procedure and directly extracts information from the synchronous and
asynchronous spectra. on the other hand, users frequently refer to an assumed model of signal changes, and the 2dCoS pattern of the model is compared with that
obtained from the experimental data [37, 39, 63, 71]. For protein spectra, it could be