GPU Assisted Simulation Study of Ion–Ion Reactions within Quadrupole Ion Traps
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In this study, a gas-phase ion–ion reaction model was developed, and it was integrated into an ion trajectory simulation program. GPU parallel computation techniques were also applied to accelerate the simulation process. With this simulation tool, the dependence of ion–ion reaction rate within 3D quadrupole ion traps on both ion trap operation parameters and the characteristics of reaction pair were investigated. It was found that the m/z values and charge states of ions have significant influences on the reaction rate. Moreover, higher ion–ion reaction rate was achieved under higher trapping voltages and higher buffer gas pressures. Furthermore, secondary reaction and/or neutralization of ETD fragment ions were observed from simulation. The reaction and/or neutralization rate depends on the charge state and m/z of each fragment ion.
Key wordsIon trap Ion–ion reaction Electron transfer dissociation Secondary reaction
Gas-phase ion–ion reaction is an important phenomenon observed in mass spectrometry experiments, in which different types of charge transfers would happen, such as proton transfer, electron transfer, anion attachment, anion transfer, and many others . Due to the advent of electrospray ionization , study of ion–ion reaction is not restricted to singly charged ions, but also involves multiply charged ions. The dissociation reactions of multiply charged biomolecules, such as ETD (electron transfer dissociation) [3, 4] and NETD (negative ETD) [5, 6], have been widely applied in the structure analyses of biomolecules, especially for proteins with post-translational modifications [7, 8, 9, 10].
Ion–ion reactions, especially ETD, have been realized and implemented in ion trap mass spectrometers and hybrid instruments. The first instrument used for ion–ion reaction study was a Y-tube/quadrupole mass filter in which ions reacted under near atmospheric pressure region and charge reduction was observed . After that, a lot of ion–ion reaction experiments were performed in vacuum to have a better control of the reaction condition [12, 13, 14, 15]. Different from ion–electron interactions, which are normally performed in Fourier transform ion cyclotron resonance cells (FT-ICR) [16, 17], ion–ion reactions are typically carried out in quadrupole ion traps and multi-pole cells [18, 19, 20, 21]. With the capability of trapping cations and anions at the same time, both 3D and linear ion traps have been modified to realize ETD functions [22, 23].
Ion–ion reaction rate is a very important factor in the application of ETD or other types of ion–ion reactions. The dependence of proton transfer reaction rate on charge state and types of reactant was explored through experiments . To manipulate ion–ion reaction, a method called “ion parking” can inhibit the reaction rate of a specific ion, in which an AC potential was applied on the endcap of a 3D quadrupole ion trap to reduce the spatial overlap and increase the relative velocity of ions [24, 25, 26]. Furthermore, the use of DC potential to control ion–ion reaction rate in ion traps was also reported [27, 28]. Although ETD has the advantage of providing complementary structure information to collision induced dissociation (CID) [29, 30, 31], ETD still suffers from relatively low product ion intensity and slow reaction rate . To address these issues, experiments were also performed to accelerate the reaction process by optimizing ion trap operation parameters and the selection of reactant partners . Considerable theoretical efforts have also been devoted to study ion–ion reaction kinetics ; however, there is a still lack of a theoretical model and simulation tools to provide us with a deeper understanding of the reaction process.
In this study, a new ion–ion reaction model was developed, which could be used to calculate ion–ion reaction cross sections and to model the formation of Coulombically bond orbital complexes of ions. Then, the theoretical model was integrated into the ion trajectory simulation program developed in our lab earlier [27, 33, 34]. Since the simulation of ion–ion interaction is a time-consuming process, GPU parallel computation techniques were applied to accelerate the simulation process. With the simulation tool developed in this work, the dependence of ion–ion reaction rate on ion trap operation parameters and the characteristics of reaction pair were investigated. Operation parameters, such as buffer gas pressure, ion trapping q value, m/z values of cations and anions, were optimized for maximized ion–ion reaction rate. With the assumption that a charge transfer could initiate an ETD reaction, the product ion loss phenomenon (or secondary ion reaction) was found in ETD experiments. Simulation results show that as high as ~74% of product ions (cations) could further react with anions in extreme cases, which results in decreased product ion intensities.
Ion–Ion Reaction Modeling
To be able to simulate the ion–ion reaction process, a suitable theoretical ion–ion reaction model is required, which predicts the ion–ion reaction probability (or ion reaction cross section, RCS); in other words, under what circumstance an ion will react with another ion (ion velocity and relative position). This theoretical model could then be implemented in an ion trajectory simulation program, and the ion–ion reaction process could be simulated afterwards.
Although many collision models exist for ion–molecule collisions, such as the Langevin collision model, the hard-sphere collision model, and the mixed collision model , no ion–ion reaction model has been proposed and implemented in ion trajectory simulations. Estimated reaction rates could be found in literature , however, without detailed derivations. In this work, a practical ion cloud distribution, Gaussian distributions, was considered, instead of uniform ion distributions typically assumed in previous works . For the first time, an effective potential curve and ion–ion reaction model were derived specifically for ion–ion reactions in this study.
Different from ion–molecule interactions, the Coulomb force between two ions with different polarities would be the dominant force in the ion–ion interactions. Nevertheless, there are similarities between the Langevin collision model and the ion–ion reaction model. In the Langevin collision model, the ion–neutral interaction is modeled as the Coulomb force between a point charge and the charge induced dipole within the neutral molecule, which would be weaker than that between two ions [36, 37, 38]. Following the Langevin collision model, an ion–ion reaction would happen when the ion can overcome the centrifugal barrier between these two ions and be “trapped” by another.
Therefore, the total energy is the summation of the translational energy and the effective potential.
It can be seen from Equation 4 that the ion–ion reaction rate is in proportion to ion number density and the square of ion charges. The ion number density and the relative spatial distribution of anions and cations are affected by the mass-to-charge ratios of ions and ion trap operation parameters. Detailed derivation of the relationship between reaction constant and ion trap operation parameters can be found in the Supplementary Information.
In this study, reactions of multiply charged cations and singly charged anions in ideal 3D ion traps with pure quadrupole electric fields and dimensions of r 0 = 5 mm and z 0 = 3.536 mm (center to electrodes) were investigated. The ion trajectory simulation program developed in our lab was used . The ion motion differential equation, which takes Coulomb forces into consideration, was solved using the fourth Runge-Kutta integration method. Helium was used as the buffer gas and the hard-sphere collision model was applied to model the ion–neutral collisions. Since the cations studied in this work have high masses, the hard-sphere collision model is more realistic than the Langevin collision model . The calculation of energy transfer of ion and neutral molecules is based on the assumption of elastic collision. The simulation step is 10 ns to minimize numerical integration error. At the beginning of the simulation, ions are placed in the center of the ion trap, and the velocities of ions are in Gaussian distribution with a given standard deviation. After the size of ion cloud becomes stable, the simulation of ion–ion reaction begins to run.
Ion–ion reaction model was integrated in the ion trajectory simulation program as follows: for each ion, pick up the nearest oppositely charged ion at every time step; if the distance is smaller than the given value (2*10–7 m), judge whether they could form an orbital complex by the total energy; if two ions could form an orbital complex, reaction happens and anion transfers an electron to cation; as a result, the anion becomes a neutral and the charges of cation minus one (details in Supplementary Information).
In this simulation, both the calculations of Coulomb forces and ion–ion reactions are time-consuming processes. Multi-core CPU in a single computer can hardly be burdened with such a large amount of calculation. To accelerate the simulation process, a GPU card (NVIDIA tesla k40c with 2880 compute unified device architecture (CUDA) cores) was used to run these two parts of simulations. Details about integrating GPU technique in ion trajectory simulation can be found in our earlier work .
Results and Discussions
In ETD experiments, it is important to optimize instrument operation parameters to maximize fragment ion intensity, which is highly related with ion–ion reaction rates. Different ions and operation conditions have significant impacts on reaction rates, so it is critical to know the influence of different parameters on ion–ion reactions. Generally speaking, ion–ion reaction rate is highly related with factors, which would affect ion cloud distribution and the Coulomb interaction force between ions. In this study, the simulation conditions were set as follows (otherwise specified): 30,000 anions (azobenzene, 182.2 Da) and 10,000 cations (angiotensin I, 1299 Da) were placed in the 3D ion trap, with helium as the buffer gas and pressure 1 mTorr; rf signal: 1 MHz, 300 V 0-p.
m/z Values of Cations
Charge States of Cations
Ion Trapping Voltage
Buffer Gas Pressures
Secondary Reactions in ETD Experiments
Simulation Versus Experiment
Results from simulations were compared with those from experiments. In general, many phenomena in experiments could be well observed in simulations (as discussed earlier), and actual reaction rates are on the same order. For instance, the simulated reaction rate of angiotensin I (3+) was about 41 s–1 (1 mTorr, cation 104, anion 3*104), as shown in Figure 6a. In experiments, very similar a reaction rate (45 s–1) was found for vasoactive intestinal peptide (1 − 12, m/z 475 Da, z = 3+) at similar working conditions. However, there are very limited data that could be compared with experiments, since the experiment results available were obtained in a commercial linear ion trap at 1 mTorr . Most of the results in this work were obtained in an ideal 3D ion trap at 5 or 7 mTorr. Since higher pressure would improve the ion reaction speed (Figure 6a), this optimized pressure condition was used in simulations (an ion trap and most electron multipliers will not work well at higher pressures practically [45, 48]). The ion reaction rate would be ~4 times higher at 5 mTorr than that at 1 mTorr for the presence of 104 cation and 3*104 anions as shown in Figure 6a. In fact, the simulated ion reaction rate of angiotensin I (3+) at 5 mTorr (Figure 4a, cation 104, anion 1–5*104) is about three to four times of the measured ion reaction rates at 1 mTorr (Figure 4a inset extracted from reference , cation 104, anion 1–5*104).
The ETD reaction time in Figure 7 is much shorter than in conventional experiments, which is because simulation was performed at 7 mTorr. The ion reaction rate at 7 mTorr was about five to six times larger than that at 1 mTorr (Figure 6a). Therefore, the reaction duration in simulation would be five to six times shorter than that in conventional experiments, which are typically performed at 1 mTorr. For instance, maximized fragment ion intensities were obtained at ~5 ms at 7 mTorr in simulation, which is expected to be 25–30 ms in experiments at 1 mTorr. Actually, a 15–20 ms optimized reaction duration was found by monitoring product ion intensities in experiments .
A theoretical model and a simulation program accelerated by GPU parallel computing techniques were developed to study ion–ion reactions in quadrupole ion traps for the first time. It was found that the ion–ion reaction rate is related to the ion cloud density and ion charge states. A higher reaction rate can be achieved under higher trapping voltages (q < 0.87), higher pressures, higher charge states, and for a reaction pair with closer m/z values. Simulation shows that ETD product ions would undergo further reactions and/or neutralizations, which cause the decrease of product ion intensities. The ratio of product ion loss depends on their m/z and number of charges, and as high as 74% of the product ions could be lost in specific conditions. Theoretical and simulation results could be applied as a guideline for the optimization of ETD reactions.
The authors acknowledge support for his work by MOST China (2011YQ0900502 and 2012YQ040140-07), NNSF of China (21205005 and 21475010), and 1000 Plan China.
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