Protein Structure and Dynamics by NMR in Solution
97
and a similar downfield shift in /3-extended conformations. This method, later
extended to include 13C n , 13C~ and carbonyl 13e' chemical shifts (Wishart and
Sykes 1994), is now known as the chemical shift index method: outside a central
range of shifts (which are interpreted as random-coil) a positive or negative
index is assigned to each residue. Larger stretches of positive or negative numbers correspond to regular secondary structures (helices or sheets) and consensus estimates show a predictive accuracy larger than 90 %.
3.1.4
Chemical Exchange
During the NMR measurements, the protein exhibits internal motions, which
also influence the chemical shift. Let us consider a spin moving back and forth
between two sites A and B: if the motion has a characteristic frequency slower
than the chemical shift difference (.) A - OB), two separate signals are observed.
Otherwise, an averaged signal (more or less broadened) is detected. TypicallH
chemical shift differences are hundreds of Hz and thus only motions in the ms
range and slower are not averaged out. For example, rapidly flipping aromatic
rings such as Phe and Tyr give rise to two or three 'averaged' IH resonances,
whereas four or five resonances are observed when they are sterically hindered.
This is a valuable structural information, because insights on the compactness of
the hydrophobic core of the protein can be obtained (see Wong and Daggett 1998
for example). A weakness of this approach lies in the lack of knowledge of the
chemical shifts, when motion is absent. Consequently, only rough estimates of
flipping rates can generally be derived, but this approach turns out to be
extremely valuable for comparing mutant proteins with wild-type (Gooley and
MacKenzie 1990). Amide protons are labile protons that undergo chemical
exchange with the water protons. This explains why their chemical shifts are so
sensitive to temperature. Unless they are forming a H-bond with a partner,
exchangeable protons in side chains (OH ofSer, Thr, or Tyr, NH/ofLys ... ), which
generally exchange more rapidly with the solvent than HN protons, are extremely
broadened by chemical exchange and can no longer be detected. On the other
hand, their detection provides valuable evidence of a H-bond, but the acceptor
remains unidentified.
3.2
Scalar Coupling Constants
The empirical relation, known as Karplus relationship, between three bond Jcouplings en and the intervening dihedral angle, plays a key role in studying
protein conformation. The values of the coefficients in the equation 3J = A cos 2 8
+ B cos 8 + C, where 8 is the dihedral angle, depend upon the nuclei involved and
their direct neighbors. They have been determined for proteins of known conformation or computed by theoretical methods. The Karplus relationship is degenerate, leading to two (and in some cases four) angles for one experimental coupling. One possibility to resolve this ambiguity consists of measuring several 3J
corresponding to different pairs of spins e H, 13C or 15N) around the same tor-
97
and a similar downfield shift in /3-extended conformations. This method, later
extended to include 13C n , 13C~ and carbonyl 13e' chemical shifts (Wishart and
Sykes 1994), is now known as the chemical shift index method: outside a central
range of shifts (which are interpreted as random-coil) a positive or negative
index is assigned to each residue. Larger stretches of positive or negative numbers correspond to regular secondary structures (helices or sheets) and consensus estimates show a predictive accuracy larger than 90 %.
3.1.4
Chemical Exchange
During the NMR measurements, the protein exhibits internal motions, which
also influence the chemical shift. Let us consider a spin moving back and forth
between two sites A and B: if the motion has a characteristic frequency slower
than the chemical shift difference (.) A - OB), two separate signals are observed.
Otherwise, an averaged signal (more or less broadened) is detected. TypicallH
chemical shift differences are hundreds of Hz and thus only motions in the ms
range and slower are not averaged out. For example, rapidly flipping aromatic
rings such as Phe and Tyr give rise to two or three 'averaged' IH resonances,
whereas four or five resonances are observed when they are sterically hindered.
This is a valuable structural information, because insights on the compactness of
the hydrophobic core of the protein can be obtained (see Wong and Daggett 1998
for example). A weakness of this approach lies in the lack of knowledge of the
chemical shifts, when motion is absent. Consequently, only rough estimates of
flipping rates can generally be derived, but this approach turns out to be
extremely valuable for comparing mutant proteins with wild-type (Gooley and
MacKenzie 1990). Amide protons are labile protons that undergo chemical
exchange with the water protons. This explains why their chemical shifts are so
sensitive to temperature. Unless they are forming a H-bond with a partner,
exchangeable protons in side chains (OH ofSer, Thr, or Tyr, NH/ofLys ... ), which
generally exchange more rapidly with the solvent than HN protons, are extremely
broadened by chemical exchange and can no longer be detected. On the other
hand, their detection provides valuable evidence of a H-bond, but the acceptor
remains unidentified.
3.2
Scalar Coupling Constants
The empirical relation, known as Karplus relationship, between three bond Jcouplings en and the intervening dihedral angle, plays a key role in studying
protein conformation. The values of the coefficients in the equation 3J = A cos 2 8
+ B cos 8 + C, where 8 is the dihedral angle, depend upon the nuclei involved and
their direct neighbors. They have been determined for proteins of known conformation or computed by theoretical methods. The Karplus relationship is degenerate, leading to two (and in some cases four) angles for one experimental coupling. One possibility to resolve this ambiguity consists of measuring several 3J
corresponding to different pairs of spins e H, 13C or 15N) around the same tor-