Biomedical Engineering Reference
In-Depth Information
because they will prefer one phase to another (partitioning into one phase). The protein
partitioning is influenced by a few factors: pH, type of buffers, ionic strength, temperature,
and the phase-forming solution.
Since ion in the protein solution redistributes until equilibrium is established, an elec-
trostatic potential exists at the interface. The chemical potential of protein at a constant
temperature and pressure is therefore also a function of ions in the solution
Z
Z
RT
Z
Z
p
p
0
0
=
−
+
RT
lnT
x
−
lnT
+
Z F
i
(5.76)
γ
γ
p
p
p p
γ
γ
γ
γ
F
is Faraday's constant,
z
is net surface charge, and
φ
is electric potential. Subscript p
denotes protein and r denotes a reference ion in the solution. At equilibrium, the partition
of protein from top to the bottom is
A
A
Z
Z
a
a
x
x
γ
γ
p
p
lnT
K
=
lnT
B
A
=
lnT
−
lnT
γ
(5.77)
p
B
B
p
γ
γ
And partition coefficient of reference ion is
x
x
Z F
RT
,
B
lnT
K
=
lnT
γ
= −
γ
∆
(5.78)
p r
,
,
A
χ
Partition of Protein in Hydrogel Membrane
In ATPS, pressure is equal in two phases; however, in the hydrogel membrane (commonly
used as coating in drug delivery systems), a higher pressure is expected because of the
rigidity of the polymer structure, and therefore, the reference state of chemical potential in
the membrane is at a higher pressure compared to aqueous phase
B
B
B
=
(
T P
,
+
)
+
RT
lnT
a
(5.79)
π
p
pure p
p
A
A
A
=
(
T P
,
+
)
+
RT
lnT
a
(5.80)
π
p
pure p
p
∂
∂
v
For a pure incompressible liquid
=
, so
P
T
B
B
B
=
(
T P
,
)
+
v
+
RT
lnT
a
π
p
pure p
p
p
and
(5.81)
B
A
=
purep
pure p
