4.3. E.COSY experiments

The principle of the exclusive correlation spectroscopy, i.e. E.COSY type experiments, was first presented by Griesinger (et al. 1986) and several applications for the measurement of different couplings in proteins have since been demonstrated (Seip et al. 1994; Weisemann et al. 1994; Wang & Bax 1995; Löhr & Rüterjans 1997). The key idea is to measure an unresolved coupling with the aid of a larger coupling that is resolved in a dimension orthogonal to the small coupling. In order to obtain the E.COSY or tilted cross-peak pattern, three magnetically active nuclei are needed, i.e. a three-spin system AMX, in which J_AM is the small coupling about to be measured. In proteins, this type of spin-system contains, for instance, the amide proton (¹H^N), α-proton (¹H^α), and α-carbon (¹³C^α). When ¹H^α couples with its directly bound ¹³C^α during the indirect detection period (t₁) and with ¹H^N during the acquisition, the familiar E.COSY pattern arises (Figure 3).

The E.COSY pattern originates from a superposition of two or more subspectra. In this particular case, two subspectra are superimposed, i.e. magnetization that is absorptive antiphase with respect to the ¹H^α spin at t₁ and t₃, and magnetization that is absorptive in-phase with respect to ¹H^α at t₁ and t₃ (Figure 3). A simple product operator description (Sørensen et al. 1983) of these two magnetization components is as follows:

H^N_xH^α_z sin(ω_Cαt₁) sin(π¹J_Cα_Hαt₁)

H^N_x cos(ω_Cαt₁) cos(π¹J_Cα_Hαt₁)

The resulting spectrum consists of two cross-peaks for each ¹H^N-¹³C^α correlation, corresponding to ¹H^α in the │α> and │β> spin states. These two cross-peaks are separated by ¹J_Cα_Hα in the F₁-dimension, whereas separation in the orthogonal F₂-dimension corresponds to ³J_H^NHα. It is then obvious that the displacement of the │α> and │β> spin states in the F₂-dimension is easily measured if the states are well separated in the F₁-dimension. The E.COSY pattern also provides information on relative signs of the couplings measured in the orthogonal dimensions. A positive tilt, i.e. the direction of the line connecting two E.COSY multiplet components is from the bottom left corner to the upper right corner, results if the couplings in the F₁ and F₂ dimensions have the same sign. A negative tilt, that is, the slope connecting the multiplet components is from the bottom right corner towards the upper left corner, indicates that the couplings in the F₁- and F₂-dimensions have opposite signs (Otting et al. 1996).

It is noteworthy that the E.COSY pattern emerges only if the passive spin is left unperturbed or it is inverted between two evolution periods. If the passive spin has a short longitudinal relaxation time compared with the duration of the experiment, a systematic decrease of the splitting caused by coupling is conceivable due to passive spin flips. This is usually problematic only if the passive spin is a proton, since ¹³C and ¹⁵N T₁ relaxation times increase as protein size increases (Wang & Bax 1995). Pulse imperfections may also cause a collapsed E.COSY pattern. For example, any imperfection in the 180° pulse used for decoupling of a passive spin during another indirect evolution period will lead to a partial collapse of the E.COSY pattern, since the spin-state of the passive spin will not be properly inverted. The E.COSY-based methods are usually most suitable for coupling constant measurements if the coupling to be measured is more than an order of magnitude smaller than the transverse relaxation rate of the observed nucleus (Wang & Bax 1995).