Biomedical Engineering Reference
In-Depth Information
A frequent approach is to measure the anisotropy of limiting concentrations of
fluorescent substrate (in this case, RNA) across a titration of its putative binding
partner. To extract equilibrium binding constants from these binding isotherms, the
use of anisotropy rather than the polarization parameter presents a significant advan-
tage. Under conditions of constant fluorescence quantum yield, the total measured
anisotropy of a sample (
A
t
) is an additive function of the intrinsic anisotropy (
A
i
) and
fractional concentration (
f
i
) of each fluorescing species.
=
∑
A
A f
(9.11)
t
ii
i
This conceptual framework is the basis for analytical models of RNA-protein
binding equilibria discussed below. Considerations and options for cases where
quantum yield is not constant throughout the binding isotherm are also described.
9.3.2
Derivation and Analysis of Binding Models
Consider a sequential association reaction model by which proteins successively
bind an RNA substrate conforming to the general scheme
K
K
K
PR PRP PRP P PR
+←⎯→ +←⎯→
+
+←⎯→
x
1
2
2
x
where
R
is the fluorescently tagged RNA molecule,
P
is the protein partner, and
values of
K
x
represent the equilibrium association constants describing each binding
event (
K
= 1/
K
d
) (Wilson
2005
) . For this reaction,
[ ] [ []
[
PR
=
R
P K
1
2
PR
] [ []
=
R P KK
2
1
2
↓
x
∏
[
PR
] [ []
=
R P
x
K
(9.12)
x
i
i
=
1
By conservation of mass,
[] [][ ] [ ]
R
=
R
+
PR
+
+
P R
(9.13)
x
tot
where [
R
]
tot
is the total concentration of the fluorescent RNA substrate in the bind-
ing reaction. Employing the additivity of anisotropy, we get
1
A
=
([]
A
R
+
A
[ ]
PR
+
+
A
[ )
P R
(9.14)
t
R
PR
PxR
x
[]
R
tot
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