is a good approximation of k off . There is a tenfold difference
between extrapolated value of k off (from Eq. 2 or 3) and that
determined in the displacement experiment. The displacement
measurements always report on the overall k off , i.e., including all
potential steps in the (un)binding pathway as well as concentrationindependent forward rate constants. For example, Scheme 2 would
result in an apparent k off ¼ k À1 k À2 /(k À1 + k À2 + k 2 ). In the case of
p53TAD and MDM2, there is no kinetic evidence for a slow
conformational change. The crystal structure of MDM2 suggests
that a helix must be displaced to allow binding of p53TAD. However, the observed kinetics fit perfectly to a two-state scenario
[21]. Thus, any conformational changes of the helix must be on a
faster timescale than is accessible by stopped-flow methodology.
Conclusions: Single exponential binding kinetics where k obs increases
linearly with protein concentration is consistent with a one-step binding mechanism (two state). However, it does not rule out more complex mechanisms involving, e.g., fast conformational changes. k off
should be determined in a separate displacement experiment if it is
low in comparison with the smallest k obs directly measured.
3.6.2 Case Study 2: N TAIL
and XD Domain,
a Two-Step Binding
Measles virus expresses the nucleoprotein N TAIL , which interacts
with a domain from a viral phosphoprotein called XD. Upon binding, the disordered N TAIL folds into an α-helix, a mechanism
observed for several IDP interactions. The binding kinetics were
found to occur on a faster timescale where stopped flow could not
be used, and the authors instead employed temperature jump to
perturb the binding equilibrium [15]. Using temperature jump is
not nearly as efficient as mixing two solutions. The K d for the
binding equilibrium may not be particularly sensitive to temperature and in addition the protein complex continues to get more and
ä
Fig. 2 (continued) from the crystal structure (burial of a Trp). (c) A displacement experiment using a
dansylated p53TAD peptide was used to determine k off ¼ 0.63 s
À1
. (d) Upper panel, k obs values increases
linearly as a function of [p53TAD]. Since the concentration of MDM2 is 1 μM, the data points at low [p53TAD]
are not determined under pseudo-first-order conditions. In such cases, Eq. 3 may be fitted to data (solid line).
In the present case, a fit to a linear function (Eq. 2, pseudo-first-order conditions, dashed line) gives a similar
result, but in either case k off is not accurately determined. Lower panel, kinetic amplitudes associated with the
k obs values showed saturation as expected. The amplitudes were fitted to a binding isotherm (solid line), which
yielded a K d ¼ 0.44 Æ 0.08 μM, which is different from the much more accurate K d calculated from k off /k on
(0.63/8.5 ¼ 0.074 μM). The large discrepancy is due to the fact that the total [MDM2] in the experiment is
1 μM. Due to the high affinity, the titration becomes practically stoichiometric and the free [p53TAD peptide] is
not equal to the plotted total concentration. Note the slight decrease in the amplitude at the highest
concentrations resulting from an underestimation of the amplitude in the curve fitting when data is not
corrected for the dead time of the instrument
120
Elin Karlsson and Per Jemth
between extrapolated value of k off (from Eq. 2 or 3) and that
determined in the displacement experiment. The displacement
measurements always report on the overall k off , i.e., including all
potential steps in the (un)binding pathway as well as concentrationindependent forward rate constants. For example, Scheme 2 would
result in an apparent k off ¼ k À1 k À2 /(k À1 + k À2 + k 2 ). In the case of
p53TAD and MDM2, there is no kinetic evidence for a slow
conformational change. The crystal structure of MDM2 suggests
that a helix must be displaced to allow binding of p53TAD. However, the observed kinetics fit perfectly to a two-state scenario
[21]. Thus, any conformational changes of the helix must be on a
faster timescale than is accessible by stopped-flow methodology.
Conclusions: Single exponential binding kinetics where k obs increases
linearly with protein concentration is consistent with a one-step binding mechanism (two state). However, it does not rule out more complex mechanisms involving, e.g., fast conformational changes. k off
should be determined in a separate displacement experiment if it is
low in comparison with the smallest k obs directly measured.
3.6.2 Case Study 2: N TAIL
and XD Domain,
a Two-Step Binding
Measles virus expresses the nucleoprotein N TAIL , which interacts
with a domain from a viral phosphoprotein called XD. Upon binding, the disordered N TAIL folds into an α-helix, a mechanism
observed for several IDP interactions. The binding kinetics were
found to occur on a faster timescale where stopped flow could not
be used, and the authors instead employed temperature jump to
perturb the binding equilibrium [15]. Using temperature jump is
not nearly as efficient as mixing two solutions. The K d for the
binding equilibrium may not be particularly sensitive to temperature and in addition the protein complex continues to get more and
ä
Fig. 2 (continued) from the crystal structure (burial of a Trp). (c) A displacement experiment using a
dansylated p53TAD peptide was used to determine k off ¼ 0.63 s
À1
. (d) Upper panel, k obs values increases
linearly as a function of [p53TAD]. Since the concentration of MDM2 is 1 μM, the data points at low [p53TAD]
are not determined under pseudo-first-order conditions. In such cases, Eq. 3 may be fitted to data (solid line).
In the present case, a fit to a linear function (Eq. 2, pseudo-first-order conditions, dashed line) gives a similar
result, but in either case k off is not accurately determined. Lower panel, kinetic amplitudes associated with the
k obs values showed saturation as expected. The amplitudes were fitted to a binding isotherm (solid line), which
yielded a K d ¼ 0.44 Æ 0.08 μM, which is different from the much more accurate K d calculated from k off /k on
(0.63/8.5 ¼ 0.074 μM). The large discrepancy is due to the fact that the total [MDM2] in the experiment is
1 μM. Due to the high affinity, the titration becomes practically stoichiometric and the free [p53TAD peptide] is
not equal to the plotted total concentration. Note the slight decrease in the amplitude at the highest
concentrations resulting from an underestimation of the amplitude in the curve fitting when data is not
corrected for the dead time of the instrument
120
Elin Karlsson and Per Jemth