Spiraling ion trajectories in two-dimensional ion cyclotron resonance mass spectroscopy

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Mechanisms of Exchange

The range of pH that we probed was well below the pKa values of the NHδ1 group of the imidazole ring (pKa = 6.0) and of the NH3 + group (pKa = 9.17) so that the protonated forms of nitrogen atoms Nε2 and Nδ1 of the imidazole ring and the amino group NH3 + are dominant in the solution. The three relevant forms of histidine in this pH range are shown in Figure 1.10. Figure 1.10. In the range 1 < pH < 5, histidine is mainly present in three forms (A, B, C). The pKa of the equilibrium between A and B is 1.82, while pKa = 6.0 for the equilibrium between B and C.
The ability to exchange primarily depends upon the ability to trade a proton between an acceptor and donor. Since the imidazolium nitrogen atoms and the amino group of histidine are protonated over this pH range, the propensity of exchange mediated by a positively charged hydronium ions is expected to be small.46 For the exchange, a hydrogen-bonded transition-state complex is formed between the donor (histidine) and the acceptor (H2O or OH-) in two steps: a) redistribution of the proton between the acceptor and donor leading to the elongation of the hydrogen bond and b) breakage of the H-bond and eventual separation from the donor as shown in Figure 1.11. The rapidity of exchange of the protons attached to nitrogen comes from the ability of forming a hydrogen-bonded transition-state complex.

Activation Energy

Additional valuable information which can be extracted from the exchange rate constants is the apparent activation energy defined by the Arrhenius equation (1.11).
The apparent activation energies of the three Hδ1, Hε2 and NH3+ exchange processes were estimated from the temperature dependence of the proton exchange rates over the relevant range of pH values. The extrapolation of the logarithms of kex in the limit 1/T = 0 provides the pre-exponential factor A and the apparent activation energy given in Table 1.5. As expected, the proton exchange rates increase with increasing temperature for all sites (Figure 1.13), and the activation energy can be determined for each NH group at each pH. The apparent activation energies are drawn in Figure 1.14 as a function of pH. We assume that the pH does not depend on the temperature over the limited temperature range considered (we verified this experimentally for the pH 2.55 and 5.10, for a temperature range of 280-312K). The activation energy is roughly constant at low pH and then decreases with increasing pH. These apparent activation energies provide information about the barrier height and thus give insight into the strength of hydrogen bonds. The NHδ1, NHε2 and NH3+ groups are involved in hydrogen bonds with partners (H2O or OH-) with whom they can exchange a proton. The average chemical shifts of all exchanging protons are below 16 ppm. According to Hong et al.51 this implies that the hydrogen bonds can be described by asymmetric energy wells with unequal populations. As discussed before, the elongation of hydrogen bonds plays an important role in exchange processes.46,52 The stronger the hydrogen bond, the more energetically expensive its elongation, thus leading to a higher energy barrier and a slower exchange rate. As indicated in the Figure 1.14, the barrier is lowest for NHδ1, which suggests Table 1.5. Activation energies (Ea) and the pre-exponential factors (A) of NH3 +, NH2, NH1 groups for different pHs.

Pulse Scheme

The power levels were optimized for different samples and experiments, to control the ejection of the desired ions and achieve higher isolation efficiency. The experiments require the application of only two radiofrequency pulses for isolation of the desired ions from a mixture of ions with mass values varying over a wide range. We refer to these two pulses as ‘ejection-isolation pulse’ and ‘detection pulse’. The various pulse schemes applied are shown in the Figure 2.5.
Ejection-isolation pulse: The power level is attenuated so that a slower sweep rate, which is essential for high resolution of high m/z, acts only in the vicinity of the m/z ratio of the ion to be retained. For ions other than the ones which are retained, ejection of the ions is achieved by adjusting the duration and voltage of the pulse such that their cyclotron orbit radii exceed the dimensions of the cell. We attenuated the power level starting from the default voltage value of the spectrometer of 7 dB (Vp-p = 78 V) and a duration of 10 μs. For the second step we lowered the power level to 15 dB (Vp-p = 31 V) and increased the duration to 150 μs. The last step is the most crucial for adjustment as it determines the resolution of the ejection process. It has to be adjusted depending on the m/z of the ion to be isolated. For samples with m/z ≤1000, a pulse attenuation of 25 dB (voltage Vp-p = 10 V) is applied for a duration ranging from 400- 8000 μs and for samples with m/z ≥ 1000, 43 dB (Vp-p = 1 V) power is applied for about 12000-14000 μs. If p is the value of the loop counter at the time of the inversion of the frequency, then the first transition of the voltage and pulse duration is performed at a value of the loop counter p-200 in the frequency list. The second transition is after 100 steps and the third transition is optimized to occur after 200 steps for the case of single ion isolation, when the frequency of the ion to be isolated is in the middle of the pulse (as shown in Figure 2.4). Multiple notches can also be accommodated for multiple ion isolation.

Similarities and differences between ICR and NMR

As the inspiration for performing 2D FT-ICR comes from 2D NMR, developing simple models to explain the ion behaviour in analogy to the classical models of NMR and exploring their similarities and differences becomes pertinent.
On the one hand, 2D ICR allows one to correlate pairs of frequencies that are characteristic of precursor and fragment ions before and after a modification of their mass-to-charge ratio by fragmentation, protonation, loss of neutral fragments, etc. These modifications can be induced by collisions with neutral molecules or by irradiation with infrared or electron beams. On the other hand, in applications to NMR, 2D EXSY allows one to correlate pairs of chemical shifts that are characteristic of the environments of nuclei before and after a chemical reaction or cross-relaxation processes. The magnetic field leads to circular motion of spins and ions manifested and measured as Larmor precession of magnetic moment for NMR and cyclotron rotation of ion for ICR, where the sense of rotation is determined by the magnetogyric ratio and charge of ion respectively which are observed by applying linearly polarised radio frequency (rf) pulses.
In its most basic form, two-dimensional exchange spectroscopy (2D EXSY) which provided the inspiration for two-dimensional ICR, uses a sequence comprising three pulses:  – t1 – ’ – m – ’’ – t2. The pulse scheme is shown in Figure 3.1. For ICR, the pulse sequence is like: P1 – t1 – P2– m – P3 – t2 In NMR, the three radio-frequency (rf) pulses are characterized by the ‘nutation angles’ ’ and ’’ that are determined by the product of their durations p, p’ andp’’ and their rf amplitudes, t1 represents the evolution time, t2 represents the detection period and m represents the mixing time. On the other hand, in ICR the three radio-frequency (rf) pulses are characterized by the energy they confer to the ions (acceleration or deceleration) that is likewise determined by the product of their durations 1, T2 and 3 and their amplitudes. In NMR, the frequency range is usually in the order of parts per million (ppm), so that the three rf pulses can have the same monochromatic carrier frequency to cover the bandwidth, chosen in the vicinity of the Larmor frequency of the nuclei under investigation. In contrast, in ICR to cover a broad range of spectral widths, ranging from a few kHz to many MHz, needs to be covered and frequency swept chirp pulses are used. In their most common forms, 2D EXSY and 2D NOESY use three equal nutation angles = ’ = ’’ = /2. Similarly, in the initial 2D ICR experiments, three pulses with the same amplitude were considered.
If 2D EXSY experiments are performed using three pulses with identical flip angles  = ’ = ’’ = /2, the fate of the magnetization can be readily described. The first pulse converts the longitudinal magnetization Mzk into a transverse component Mxk, the second pulse ’ has the opposite effect and generates a t1-dependent longitudinal component Mzk(t1), which, after  ’’. a partial conversion of Mz k(t1) into Mz l(t1) through exchange or cross-relaxation, is again converted by the third pulse  ’’ from Mz l into Mx l that induces a signal in the second interval t2. Unlike many other 2D NMR experiments that involve a transfer of coherence, and therefore require a quantum-mechanical treatment, most applications of 2D EXSY and 2D NOESY can be discussed purely in classical terms. Thus 2D EXSY NMR and 2D ICR share a reassuring common ground.

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2D FT-ICR pulse scheme

The 2D FT-ICR allows one to map correlations between precursor and fragment ions without ion isolation and without any a-priori information about the sample, thus making it a sample-independent technique.
The conventional 2D spectrum can be represented by a contour plot of intensities as a function of two frequencies (ω1 and ω2) which are obtained by the Fourier transformation of the data recorded as a function of two time variables (t1 and t2). The position of each peak is specified by two co-ordinates. By convention, the spectrum is arranged so that ω1, which represents the evolution in the indirect dimension, is plotted along the vertical axis, while the evolution in the direct dimension ω2 is along the horizontal axis. The general scheme for obtaining such a spectrum for FT-ICR MS is given in Figure 3.2(A). The preparation time consists of encoding period (t1), sandwiched between excitation (T1) and encoding (T2) pulses. In an ICR cell, we wish to monitor the conversion of a precursor ion Ik into a fragment ion Il.

Table of contents :

Acknowledgements i Abstract and keywords
Part I Chapter 1 Fast proton exchange in histidine: measurement of rate constants through indirect detection by NMR spectroscopy 1.1 Introduction 
1.2 Experimental Section
1.2.1 Instrumental details
1.2.2 Sample preparation
1.2.3 Pulse Sequence
1.3 Methodology
1.4 Results and Discussions
1.4.1 Mechanism of Exchange
1.4.2 Activation Energy
1.5 Conclusions
Glossary Part-I
Part II
Chapter 2 High-resolution ion isolation in Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometry by modulating the RF phase during the frequency
2.1 Introduction
2.2 Theory
2.3 Experimental Section
2.3.1 Pulse Scheme
2.3.2 Sample preparation
2.4 Results and Discussions
2.5 Conclusions and Perspectives
Chapter 3 Spiraling ion trajectories in two-dimensional ion cyclotron resonance mass spectroscopy
3.1 Introduction
3.1.1 History of 2D FT-ICR
3.1.2 Similarities and differences between ICR and NMR
3.2 2D FT-ICR pulse scheme
3.3 Equations of motion
3.3.1 Excitation pulse period
3.3.2 Encoding period 90 3.3.3 Encoding pulse period
3.3.4 Fragmentation period
3.4 Trajectory Mapping 92
3.4.1 Case I: kt1 = 2nπ and kT = 2π
3.4.2 Case II: kt1 < 2nπ and kT = 2π
3.4.3 Case III: kt1 = 2nπ and kT < 2π
3.4.4 Case IV: kt1 < 2nπ and kT < 2π
3.5 Harmonics in 2D spectra
3.6 Conclusions and Perspectives


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