Chemistry Reference
In-Depth Information
Table 1 Theoretical parameters for the equilibrium surface pressure isotherm
of lysozyme: a
¼
Frumkin intermolecular interaction parameter;
a
¼
coefficient;
o
0
¼
molar area of one segment of the protein
molecule;
o
1
¼
minimal molar area of the protein molecule;
o
max
¼
maximal molar area of the protein molecule; b
¼
adsorption
equilibrium constant;
p
*
¼
critical surface pressure;
e
¼
additional
parameter for the critical regime. The symbol * refers to parameters
obtained from fitting the surface pressure data at low concentrations
0.69 (0.2
*
)
a
2 (2.82
*
)
a
o
0,
m
2
mol
1
(
10
5
)
4.95 (9.95
*
)
o
1,
m
2
mol
1
(
10
6
)
6.72
o
max
,m
2
mol
1
(
10
7
)
2.54 (5.08
*
)
e
0.032
p
*
,mNm
1
14.5
b,m
3
mol
1
2
10
3
The equilibrium surface pressure of lysozyme having been analysed in terms
of the theoretical model, the dynamic surface tension can be considered. The
fitting of each of the experimental dynamic surface tension curves was per-
formed on the basis of the parameters listed in Table 2. As is well known from
the literature,
35,41,42
the adsorption of proteins at fluid interfaces follows three
regimes of surface tension lowering. First, proteins adsorb at the interface, but
the surface tension remains unchanged, or it changes only slightly (the induc-
tion period). As time passes, the adsorption proceeds, the interfacial concen-
tration increases, and the surface tension decreases. At longer times, adsorption
and conformational rearrangements continue; multilayers may develop; and
interfacial aggregation and gelation might occur. Figures 8-10 present the
dynamic surface tension curves for 10
7
,5
10
7
and 7
10
7
M lysozyme as
representative examples, and the respective model parameters are summarized
in Table 2. We can see that the correlation between the experimental curves and
the theory is very good, with the exception of the last part of the curves at very
long adsorption times, where the surface tension passes through a minimum as
described above. Regarding the parameters of the thermodynamic model, they
are practically the same as in the fitting of the equilibrium isotherm with only
one additional parameter - the diffusion coefficient D. In order to match the
experimental data for each protein concentration, and to keep the value of the
diffusion coefficient constant, the parameters
o
0
and
o
max
were varied too. As
discussed already, this is required by the fact that, at low concentrations, the
proteins adsorb in an unfolded state at the interface, and their molar surface
areas are larger in comparison to those at higher concentrations. Nevertheless,
a detailed quantitative interpretation of the dynamic surface tension of lys-
ozyme remains to be provided.
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