Biomedical Engineering Reference
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where
A
R
,
A
PR
, etc. represent the intrinsic anisotropy values of the free RNA or
specific RNA:protein complexes designated by the subscripts. The general expres-
sion relating observed anisotropy to protein concentration then becomes
x
∏
x
AAPK
+
[]
+
+
AP
[]
K
R
PR
1
PxR
i
A
=
i
=
1
(9.15)
t
x
∏
x
1[]
+
PK
+
+
[]
P
K
1
i
i
=
1
which incorporates the expressions describing each equilibrium association con-
stant and sample protein concentration into the total measured anisotropy
A
t
. In
order for this relationship to be useful, [
R
]
tot
must be limiting and should be at least
fivefold less than any
K
d
(= 1/
K
) so that the free protein concentration in solution
([
P
]) approximates the total protein concentration in each reaction ([
P
]
tot
). Explicit
values of
K
may then be calculated by nonlinear regression of
A
t
vs. [
P
], although
this sequential binding function becomes increasingly complicated as the number of
binding events increases and for most purposes is impractical beyond the first two
discrete binding events. In some cases, however, conditions can be imposed on the
system to prevent
x
from becoming larger than 2. One example is to limit the length
of RNA so that only one or two binding events can take place (more on site size
determination below). It may also be possible to generate mutant proteins that can-
not form oligomeric complexes on RNA substrates (Wilson
2005
) .
The simplest RNA-protein binding relationships can be described by reversible
one-step binding. An example of this model is given by the major inducible heat
shock protein, Hsp70, which interacts with members of a discrete family of mRNA-
destabilizing sequences termed AU-rich elements (AREs) (Wilson et al.
2001
)
found in many cytokine and proto-oncogene transcripts. Here,
AAKP
+
[]
A
=
R
PR
(9.16)
t
1[
+
KP
]
In Fig.
9.4
, the upper asymptote of the isotherm represents
A
PR
and the lower
asymptote resolves
A
R
. The concentration of probe used to generate this isotherm
was 0.15 nM, appropriate for a reaction with a
K
d
of 25 nM, but still high enough to
present a favorable signal-to-noise ratio. Although the anisotropy isotherm describ-
ing Hsp70 binding to this RNA substrate is consistent with a 1:1 binding model, a
similar result would also be observed if multiple thermodynamically equivalent
binding events were occurring. To discriminate between these possibilities, we have
found it useful to perform electrophoretic mobility shift assays (EMSAs) in parallel
with binding experiments resolved by fluorescence anisotropy. In the case of Hsp70
binding the TNFa ARE substrate, EMSAs spanning a range of protein concentra-
tions resolved a single RNA-protein binding event, supporting a 1:1 binding equi-
librium (Wilson et al.
2001
). As a general rule, EMSAs are unreliable as a quantitative
tool for measuring binding affinities owing to ribonucleoprotein complex dissocia-
tion during loading and fractionation through the gel; this is particularly trouble-
some for highly dynamic binding equilibria. However, we find that EMSAs remain
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