2009_Book_FoodChemistry

392 5 Aroma Compounds
To calculate the average number of aroma
molecules bound to a biopolymer, the specific
binding capacity, r, has to be introduced:
(BA)
r =
(5.40)
(B)+(BA)
The concentration of the complex BA from Equation
5.39 is substituted in Equation 5.40:
r =
K · c f(B)
=
Kc f
(5.41)
(B)+K(B)c f 1 + Kc f
When a biopolymer binds not only one molecular
species (as A in the above case) but has a number
(n) of binding groups (or sites) equal in binding
ability and independent of each other, then r
has to be multiplied by n, and Equation 5.41 acquires
the form:
r = n · Kc f
1 + Kc f
(5.42)
r
= K · n − K · r = K ′ − K · r
c f
(5.43)
where K ′ = overall binding constant.
The evaluation of data then follows Equation
5.43 presented in graphic form, i. e.
a diagram of r/C f = f (r). Three extreme or
limiting cases should be observed:
a) A straight line (Fig. 5.37, a) indicates that
only one binding region on a polymer, with
n binding sites (all equivalent and independent
from each other) is involved. The values n
and K ′ are obtained from the intersection of
the straight line with the abscissa and the ordinate,
respectively.
b) A straight line parallel to the abscissa
(Fig. 5.37, b) is obtained when the single
binding constant, K, is low and the value
of n is very high. In this special case,
Equation 5.48 has the form:
r = K ′ · c f (5.44)
c) A curve (Fig. 5.37, c) which in approximation
is the merging of two straight lines, as shown
separately (Fig. 5.37, d). This indicates two
binding constants, K 1 ′ ,andK′ 2 , and their respective
binding groups, n 1 and n 2 , which are
equivalent and independent of each other.
By plotting r versus c f ,valuesofK ′ are obtained
from the slope of the curve. An example for
a model system with two binding regions (case c)
is given by aroma binding to starch. It should be
remembered that starch binds the volatiles only
after gelatinization by trapping the volatiles in
its helical structure, and that starch is made up of
two constituents, amylose and amylopectin. The
binding parameters are listed for some aroma
compounds in Table 5.37. Numerous observations
indicate that K 1 ′ and binding region n 1 are
related to the inner space of the helix, while K 2
′
and the n 2 region are related to the outer surface
of the helix. K 1 ′ is larger than K′ 2 ,whichshows
that, within the helix, the aroma compounds are
bound more efficiently to glucose residues of the
helix. The fraction 1/n is a measure of the size of
the binding region. It decreases, as expected, with
Table 5.37. Binding of aroma compounds by potato
starch
Compounds Binding constant
K 1 ′ n 1 K 2 ′ n 2
Fig. 5.37. Binding of aroma compounds by biopolymers.
Graphical determination of binding parameters
according to Solms, 1975
1-Hexanol 5.45 · 10 1 0.10 – –
1-Octanol 2.19 · 10 2 0.05 2.15 · 10 1 0.11
1-Decanol 1.25 · 10 2 0.04 1.29 · 10 1 0.11
Capric acid 3.30 · 10 2 0.07 4.35 · 10 1 0.19
Menthone 1.84 · 10 2 0.012 8.97 0.045
Menthol 1.43 · 10 2 0.007 – –
β-Pinene 1.30 · 10 1 0.027 1.81 0.089