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B. Czarnik-Matusewicz and Y.M. Jung
into the interior of the lipid bilayers, the α-helix and α-sheet of the protein reorient 
independently toward the surface normal as the surface pressure increases.
As  the  next  example  shows,  βν-correlation  is  very  well  suited  to  the  analysis 
of the temporal order of events during temperature-induced changes in the local
molecular environment of the protein. the subject of interest was a small designed
protein, utilized in the preparation of a “smart” protein micellar system, and because
of a reversible thermal transition, this protein triggers rapid changes in the properties of the micelle [72]. the structural units of this protein have been classified
according to the β e values. Analysis of the changes of the units has shown that a
thermally induced helix-to-sheet protein folding transition plays the role of a switch
for the micelle compacticity and size. The usefulness of the βν- and kν-correlation 
analyses was also shown through studies of the surface pressure–induced effects on
lipid–antibiotic interactions [141] and the influence of temperature on phase transitions in Langmuir polymer films [139].
The  kν-correlation  analysis  has  allowed  the  spectral  intensity  changes  to  be 
quantitatively characterized and has shown excellent performance in the detection of small differences in the rates of dynamic intensity changes in the early
stages of fibrillation of lysosome [31, 32, 114]. The Ψ(k,ν) map helped explain 
the inverse order of events of lysozyme fibrillation deduced from conventional
2dCoS, in which it has been observed that the product of the reaction formed
before the initial components of the studied system started to react. this phenomenon, termed apparent inverse order of secondary structural changes [31], was initially described in [61, 103, 108], but at that time, the counterintuitive fact that the
appearance of ν-structure occurred before the unfolding of the α-helix seemed to 
be specific to 2d results whenever aggregation preceded conformational changes
within the individual protein molecules. Through application of the kν-correlation 
analysis, Lednev’s group performed a quantitative assessment of the sequence of
events using the effective rate constants k eff for each evolution of the secondary
structure. the effective rate constants were determined from the best match of the
2D  and  kν  correlation  maps  for  the  experimental  and  model-specific  simulated 
data. Based on the k eff values, it was clear that “Apparent Inverse order of Events
is the Intrinsic Property of multistep Chemical Reactions” [31] and is typical of
all chemical reactions that involve the formation of intermediate(s); this effect
may lead to the serious misinterpretation of 2d correlation results. the proposed
method of analysis is not limited to a particular spectroscopic technique and can
be used to elucidate the mechanisms of complex chemical processes. the software used to justify the inverse sequential order effect is available as supporting
material to [31].
8.4.4 Chemometric Procedures
A very useful development in 2d correlation spectroscopy in protein research has
been obtained by the incorporation of multivariate chemometric techniques, especially principal component analysis (PCA). moreover, as shown by the results ob-
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