Double electron-electron resonance

While dipolar-broadened CW spectra resolve distances between nitroxide spin labels in the 8 – 20 Å range, pulsed EPR is capable of determining distances between two nitroxides up to 80 Å. This experiment is called double electron-electron resonance (DEER); the 4-pulse DEER technique is discussed herein.36

DEER EPR monitors the dipolar coupling between spins in the time domain, which begins with an electron spin-echo (ESE) pulse sequence to manipulate the direction of spin magnetization, shown in Fig. 2.1. A 90° pulse tips the spin magnetization, which was aligned mostly with the z-axis as described in Section 2.2.3, into the xy-plane (Fig. 2.1a), whereafter the

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Figure 2.12 In (a-d), the spin echo experiment is shown graphically. Spin magnetization is tipped into the xy-plane in (a) by a 90° pulse, which dephase after a time “t” in (b). A 180° pulse is applied, which mirror the spins across the y-axis, allowing them to rephase after an equal time “t”. The echo in (d) is then monitored at time “2t” after the start of the experiment. In (e), the four-pulse DEER sequence is shown, which induces transitions in two populations of spins at two frequencies (“observe” and “pump”).

spins dephase due to local field inhomogeneities (Fig. 2.1b). After a specified time interval 𝜏₁, a second 180° pulse mirrors the spin directions (in Fig. 2.1c, this 180° inversion is across the y- axis). The spins come back into phase during a second 𝜏₁ interval. The echo monitors the recovery of spin magnetization in the –x axis (Fig. 2.1d).37

Four-pulse DEER builds on the ESE pulse sequence by introducing a pulse at a second frequency, called the “pump” frequency (𝜔₂), in contrast to the 90° and 180° spin-echo pulses at

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the “observe” frequency (𝜔₁). A 180° pulse at 𝜔₂ at a specified time 𝑡_𝑝 induces a change in the local field of spins at the “observe” frequency (𝜔₁) according to the strength of dipolar

interaction. The spins at 𝜔₁ experience a phase gain related to the dipolar coupling between the nitroxide electrons 𝜙 = 𝜔𝑑𝑑𝑡𝑝, where 𝜔𝑑𝑑 is the dipolar coupling frequency and 𝑡𝑝 is the time

position of the “pump” pulse, which varies from some 𝑡𝑚𝑖𝑛 to 𝑡𝑚𝑎𝑥 relative to the primary ESE.

A final 180° pulse at 𝜔₁ at a time interval 𝜏₂ > 𝑡_𝑝 after the primary ESE inverts the spin precession direction again, which produces a secondary ESE at a time 2𝜏₂. The DEER signal comprises secondary ESE, which is modulated by the dipolar coupling probed by the time position of the “pump” pulse.

Data fitting through a Pake transform36 or via a library of DEER dipolar evolution functions (DEFs) determines the encoded distance distributions. Because biomolecules are not static structures and the distances derived from DEER data are statistical distributions, DEER gives insight into the structure and dynamics of proteins on long distance scales. Fig. 2 demonstrates the relationship between short and long oscillations and corresponding distance distributions; strong dipolar couplings produce DEER DEFs that are sharp (Fig. 2.13a, blue) are closely spaced (Fig. 2.13b, blue) compared to broader DEFs (Fig. 2b, magenta) which are due to nitroxides spaced further apart (Fig. 2.13b, magenta). Determination of complex distance

distributions is a particular strength of DEER EPR, in which the distribution of conformational arrangements can be directly measured (Fig 2.13a and Fig. 2.13b, cyan). Software

(LongDistances, written by Christian Altenbach, or DeerAnalaysis, written by Gunnar Jeschke) is available to facilitate analysis of DEER data.

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Figure 2.13 In (a), simulated DEER DEFs are shown. Fits to these time-domain distributions provide corresponding distance distributions shown in (b).

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