Genetic algorithm optimized triply compensated pulses in NMR spectroscopy

Abstract

Sensitivity and resolution in NMR experiments are affected by magnetic field inhomogeneities (of both external and RF), errors in pulse calibration, and offset effects due to finite length of RF pulses. To remedy these problems, built-in compensation mechanisms for these experimental imperfections are often necessary. Here, we propose a new family of phase-modulated constant-amplitude broadband pulses with high compensation for RF inhomogeneity and heteronuclear coupling evolution. These pulses were optimized using a genetic algorithm (GA), which consists in a global optimization method inspired by Nature’s evolutionary processes. The newly designed π and π/2 pulses belong to the ‘Type A’ (or general rotors) symmetric composite pulses. These GA-optimized pulses are relatively short compared to other general rotors and can be used for excitation and inversion, as well as refocusing pulses in spin-echo experiments. The performance of the GA-optimized pulses was assessed in Magic Angle Spinning (MAS) solid-state NMR experiments using a crystalline U – 13C, 15N NAVL peptide as well as U – 13C, 15N microcrystalline ubiquitin. GA optimization of NMR pulse sequences opens a window for improving current experiments and designing new robust pulse sequences.

Enhancing the sensitivity of multidimensional NMR experiments by using triply-compensated π pulses

“…The G5 pulse has a built-in simultaneous compensation for RF inhomogeneity, offset, and heteronuclear J-coupling/dipolar coupling. The G5 pulse was designed using a Genetic Algorithm (GA) and was described in our earlier work 27 . IBriefly, GA defines a pulse as an array of phase values ( i.e.…”

“…Based on the fidelity plot at 99% efficiency ( i.e. , 99% fidelity rectangle) 27 , the RF compensation for the G5 pulse is greater than 10% and the zz - coupling compensation bandwidth in relative coupling strength D/B 1 is greater than 1, where D is the coupling strength in Hz and B 1 is the RF amplitude in Hz. Experimentally, one should calibrate the RF amplitude by evaluating the pulse length of a π/2 pulse.…”

“…In contrast, the G5 is relatively short ( 1 H π pulse of 144 μs) and is applied at the same power level as a hard π/2 pulse, which is sufficiently short to avoid signal losses due to transverse relaxation. Importantly, the G5 pulse was developed via GA optimization 30,31 and is designed to operate on both inversion of longitudinal magnetization and refocusing of transverse magnetization 27 . Although the Gaussian cascade pulse (Q3) is also able to operate on both longitudinal and transverse magnetization, the bandwidth of the G5 pulse is 20% wider while using ~75% of the maximum RF amplitude necessary for the Q3 π pulses 14 .…”

“…Recently, using a genetic algorithm (GA) optimization, we designed a triply-compensated pulse (G5), with simultaneous compensation for off-resonance effects, RF inhomogeneity/miscalibrations, and J -coupling evolution 27 . According to the nomenclature of Levitt 4 , the G5 pulse is a ‘type A composite pulse’, which can be used for both inversion and refocusing.…”

“…The total nutation angle of the G5 pulse is 5π and its duration is five times that of a single π pulse. 27 Compared to G3 and Q3 pulses 13,14 , the G5 pulse has three major advantages: i) it exhibits wider inversion and refocusing bandwidths for 1 H, 13 C, and 15 N nuclei, ii) it has a significantly shorter duration, and iii) it requires substantially lower RF power.…”