114 INSTRUMENTAL METHODS
COSY pulse sequence. The fi rst 90 ° pulse at the^1 H frequency produces trans-
versey magnetization. This evolves with t 1 and depends on the frequency of
the proton ’ s chemical shift. Protons attached to carbon nuclei will have two
magnetization components precessing at different frequencies. These compo-
nents are refocused halfway throught 1 by inverting the carbon magnetization
with a 180 ° pulse. The proton magnetization at the end of t 1 is a function of t 1.
This magnetization is transferred to the carbon magnetization by a second
proton 90 ° pulse placing the y magnetization into the z direction and permit-
ting polarization transfer. The period Δ 1 allows the two magnetization compo-
nents to come into phase before the second proton 90 ° pulse is applied. This
delay is timed to coincide with 1/2 J (CH), one - half^1 J (CH), the coupling con-
stant between^13 C and^1 H nuclei. The 90 ° pulse applied at the carbon frequency
at the same time as the second proton pulse creates transverse carbon mag-
netization and produces the output FID. The refocusing delay Δ 2 is usually the
same asΔ 1. The experiment is repeated for many values of t 1 , and the stack of
FIDs obtained (which contain both carbon and proton chemical shift informa-
tion) are transformed and plotted. Usually the carbon spectrum appears on
thex axis of the 2D plot with the proton spectrum plotted vertically. Contours
appear at the intersection of carbon and proton resonances corresponding to
the carbon and proton atoms bonded to each other.
Only protons that are two (^2 J) to three (^3 J) bonds apart will exhibit coupling
(and therefore cross peaks) in a 2D experiment. Protons that are more than
three chemical bonds apart give no cross signal because the^4 J coupling con-
stants are close to 0. Taking the example of amino acid residues in a protein,
important cross signals arise between the proton associated with the main -
chain amide group (H N ) and the proton(s) attached to the α carbon atom (H α ).
These cross signals allow derivation of the phi torsion angle ( φ ) of the protein
backbone from the^3 J coupling constant between them (see Figure 2.8 ). Con-
tinuing with the protein example, the H α proton transfers magnetization to the
beta protons, H β , H β protons transfers to the H α and gamma protons, H γ , if any
are present, then the gamma proton(s) transfer to the H β and H δ protons, and
the process continues.
The TOCSY 2D NMR experiment correlates all protons of a spin system,
not just those directly connected via three chemical bonds. For the protein
example, the alpha proton, H α , and all the other protons are able to transfer
magnetization to the beta, gamma, delta, and epsilon protons if they are con-
nected by a continuous chain — that is, the continuous chain of protons in the
side chains of the individual amino acids making up the protein. The COSY
and TOCSY experiments are used to build so - called spin systems — that is, a
list of resonances of the chemical shift of the peptide main chain proton, the
alpha proton(s), and all other protons from each aa side chain. Which chemical
shifts correspond to which nuclei in the spin system is determined by the con-
ventional correlation spectroscopy connectivities and the fact that different
types of protons have characteristic chemical shifts. To connect the different
spin systems in a sequential order, the nuclear Overhauser effect spectroscopy