Calcium-Binding Protein Protocols Calcium-Binding Protein Protocols

286 Werner et al.
Our research has shown that calcium plays an essential role in stabilizing the
cbEGF domain linkage (7).
In this chapter, we introduce the interpretation of 15 N relaxation data with a
brief overview of the theory. Relaxation of a 15 N nucleus in the presence of a
proton is dominated by the 1 H– 15 N dipolar coupling and by chemical shift anisotropy
(CSA). Ignoring cross-correlation between 1 H– 15 N dipolar and CSA relaxation,
the longitudinal (T 1) and transverse (T 2) relaxation time constants as well
as the [ 1 H]– 15 N heteronuclear NOE are given by the following equations (13):
1/T1 = d 2 /4 [J(ωH – ωN)+3J(ωN)+6J(ωH + ωN)] + c2 J(ωN) 1/T2 = d
(1)
2 /8 [J(0) + J(ωH – ωN)+3J(ωN)+6J(ωH)+6J(ωH + ωN)] + c2 /6 [4J(0) + 3J(ωN)] +Rex (2)
NOE = 1+d 2 /4T1(γH/γN)[6J(ωH + ωN)– J(ωH + ωN)] (3)
in which d = (µ ohγ N γ H) / (8π2)〈r –3
NH 〉 and c = (ω N∆σ) / (√3); µ o is the permeability
of free space; h is Planck’s constant; γ H and γ N are the gyromagnetic ratios
of the 1 H and 15 N spins; respectively; r NH is the N–H bond length; ω H and ω N
are the Larmor frequencies of the 1 H and 15 N spins, respectively; and ∆σ is the
chemical shift anisotropy of the 15 N nucleus, assuming axial symmetry and
colinearity of the symmetry axis and the N–H bond vector.
Motions on a µs to ms time-scale that can contribute to the transverse relaxation
time constant, T 2, are modeled as an exchange term, R ex, in Eq. 2. The
quadratic dependence of exchange line broadening with either B 1, the field in
the rotating frame (14–16), or with B 0, the static magnetic field, has been used
to measure R ex (17–19). Alternatively, exchange can be determined from the
ratio of transverse and longitudinal cross-relaxation rate constants resulting
from 1 H– 15 N dipole and 15 N CSA relaxation interference (20). In this study,
R ex was obtained from measurements of relaxation time-constants at multiple
fields. Provided that the spectral density at the proton frequency is small compared
to the spectral density at zero frequency, it can been shown that 1/T 2 – 1/(2T 1)
is a linear function of the square of the spectrometer field strength (19).
1/T2 – 1/(2T1) = d2 / 2J(0) + [2/9γ2 N ∆σ2 J(0) + A] B2 (4)
0
with y-intercept d 2 /2J(0) and a slope that depends on the value of the chemical
shift anisotropy and exchange contributions, Rex = AB2. The advantage of this
0
method is that it is independent of the estimation of overall rotational diffusion
properties. The precision of the Rex terms is primarily limited by the precision
of the determination of the relaxation rate constants and the range of available
spectrometer fields. In studies of calcium-binding proteins, it is important to
ensure full saturation of the binding sites as most of the effects of calcium
exchange on resonance linewidth are then removed.