Analyses of RNA–Ligand Interactions by Fluorescence Anisotropy - Biophysical Approaches to Translational Control of Gene Expression - page 182

Fig. 9.6 Binding of HuR to
the fl uorescein-conjugated
TNFa ARE (0.2 nM RNA
substrate). In this experiment
[ P ] 1/2 was calculated to be
2.2 nM and the Hill
coefficient was 1.49. The
solid line indicates the
cooperative fit, and the dotted
line indicates the best fit
possible using a single-site
binding model

where A R and A PxR are the intrinsic anisotropy values of free RNA and the saturated
RNA:protein complex, respectively, [ P ] 1/2 is the concentration of protein at which
the reaction achieves half-maximal binding, and h is the Hill coefficient (Wilson
2005 ). For this scheme, the standard assay requirements of limiting RNA concentra-
tion and constant quantum yield still apply. However, for regression solutions
resolving h = 1, this function simplifies to a single-site binding algorithm, with
[ P ] 1/2 = K d .
The association of the mRNA-stabilizing protein HuR with the TNFa ARE sub-
strate, shown in Fig. 9.6 , illustrates an application of this modified Hill function. The
solution of h > 1 indicates that HuR proteins assemble cooperatively into oligomeric
complexes on this RNA substrate. As indicated on the plot, the one-step binding
model does not resolve these data well, an assertion validated by nonrandom distribu-
tions of residuals for the single-site solution and by pairwise statistical comparisons
of cooperative and single-site fits using the F test (Fialcowitz-White et al. 2007 ) .
When the affinity of an RNA-protein binding event is very high (i.e., K d < 1 nM),
it may not be possible to accurately measure the anisotropy of RNA substrates at
concentrations low enough for the free protein concentration [ P ] to approximate the
total protein added to each binding reaction. In these situations, binding algorithms
that incorporate ligand depletion must be employed, which are normally expressed
in terms of total protein ([ P ] tot ) and RNA substrate ([ R ] tot ) concentrations. Shown
below is the ligand depletion model for reversible one-step binding (Wilson 2005 ) .

AA A A =+ ( − × )

t R PR R

⎡ ⎤

(9.19)

2 2

1[ + KR ] + KP [ ] − (1[ + KR ] + KP [ ] ) − [ R ] [ P ] K

⎢

tot

tot

tot tot tot tot

⎥

2[] KR

⎢ ⎥

⎣ ⎦

tot