Proton Mobility in b₂ Ion Formation and Fragmentation Reactions of Histidine-Containing Peptides

Characteristic Fragmentation Behavior of Linear and Cyclic O-Linked Glycopeptides and Their Peptide Skeletons in MALDI-TOF/TOF MS

Understanding characteristic post-source decay (PSD) fragmentation patterns in tandem mass spectrometry (MS/MS) is important for the identification of target molecules. In this study, we explored the characteristic PSD patterns associated with O-linked glycopeptides and their cyclization using the MALDI-TOF/TOF MS analysis of linear and cyclic antifreeze glycoproteins. We performed a comparative analysis of the proton and sodium adduct ions of the peptide backbones of antifreeze glycoproteins, which have a simple repeating sequence, shedding light on the characteristics of the fragmentation of the threonine side chain and that of its cyclized form. Furthermore, the presence or absence of a glycan on the threonine side chain and its substitution with serine caused changes in its fragmentation. These findings are expected to contribute to the prediction of three-dimensional peptide structures and the search for physiologically active O-linked glycopeptides and cyclic (glyco)peptides.

Phosphate Migration versus the Loss of Phosphoric Acid in Protonated Phosphopeptides: A Computational Study

Residue-specific phosphorylation is a protein post-translational modification that regulates cellular functions. Experimental determination of the exact sites of protein phosphorylation provides an understanding of the signaling and processes at work for a given cellular state. Any experimental artifact that involves migration of the phosphate group during measurement is a concern, as the outcome can lead to erroneous conclusions that may confound studies on cellular signal transduction. Herein, we examine computationally the mechanism by which a phosphate group migrates from one serine residue to another serine in monoprotonated pentapeptides [BA-pSer-Gly-Ser-BB + H]+ → [BA-Ser-Gly-pSer-BB + H]+ (where BA and BB are different combinations of the three basic amino acids, histidine, lysine, and arginine). In addition to moving the phosphate group, the overall mechanism involves transferring a proton from the N-terminal amino acid, BA, to the C-terminal amino acid, BB. This is not a synchronous process, and there is a key high-energy intermediate, structure C, that is zwitterionic with both the basic amino acids protonated and the phosphate group attached to both serine residues and carrying a negative charge. The barriers to moving the phosphate group are calculated to be in the range of 219-274 kJ mol-1 at the B3LYP/6-31G(d) level. These barriers are systematically slightly lower and in good agreement with single-point energy calculations at both M06-2X/6-311++G(d,p) and MP2/6-31++G(d,p) levels. The competitive reaction, loss of phosphoric acid from the protonated pentapeptides, has a barrier in the range of 176-202 kJ mol-1 at the B3LYP/6-31G(d) level. Extension of the theory to M06-2X/6-311++G(d,p)//B3LYP/6-31G(d) and MP2/6-31++G(d,p)// B3LYP/6-31G(d) gives higher values for the loss of phosphoric acid, falling in the range of 196-226 kJ mol-1; these are comparable to the barriers against phosphate migration at the same levels of theory. For larger peptides His-pSer-(Gly)n-Ser-His, where n has values from 2 to 5, the barriers against the loss of phosphoric acid are higher than those against the phosphate group migration. This difference is most pronounced and significant when n = 4 and 5 (the differences are approximately 80 kJ mol-1 under the single-point energy calculations at the M06-2X and MP2 levels). Energy differences using two more recent functionals, M08-HX and MN15, on His-pSer-(Gly)n-Ser-His, where n = 1 and 5, are in good agreement with the M06-2X and MP2 calculations. These results provide the mechanistic rationale for phosphate migration versus other competing reactions in the gas phase under tandem mass spectrometry conditions.

Disulfide bonds in the SAPA domain of the pulmonary surfactant protein B precursor

The disulfide bonds formed in the SAPA domain of a recombinant version of the NH₂-terminal propeptide (SP-B_N) from the precursor of human pulmonary surfactant protein B (SP-B) were identified through sequential digestion of SP-B_N with GluC/trypsin or thermolysin/GluC, followed by mass spectrometry (MS) analysis. MS spectra allowed identification of disulfide bonds between Cys³²-Cys⁴⁹ and Cys⁴⁰-Cys⁵⁵, and we propose a disulfide connectivity pattern of 1-3 and 2-4 within the SAPA domain, with the Cys residues numbered according to their position from the N-terminus of the propeptide sequence. The peaks with m/z ∼ 2136 and ∼ 1780 in the MS spectrum of the GluC/trypsin digest were assigned to peptides ²⁴AWTTSSLACAQGPE³⁷ and ⁴⁵QALQCR⁵⁰ linked by Cys³²-Cys⁴⁹ and ³⁸FWCQSLE⁴⁴ and ⁵¹ALGHCLQE⁵⁸ linked by Cys⁴⁰-Cys⁵⁵ respectively. Tandem mass spectrometry (MS/MS) analysis verified the position of the bonds. The results of the series ions, immonium ions and internal fragment ions were all compatible with the proposed 1-3/2-4 position of the disulfide bonds in the SAPA domain. This X-pattern differs from the kringle-type found in the SAPB domain of the SAPLIP proteins, where the first Cys in the sequence links to the last, the second to the penultimate and the third to the fourth one. Regarding the SAPB domain of the SP-B_N propeptide, the MS analysis of both digests identified the bond Cys¹⁰⁰-Cys¹¹², numbered 7-8, which is coincident with the bond position in the kringle motif. SIGNIFICANCE: The SAPLIP (saposin-like proteins) family encompasses several proteins with homology to saposins (sphingolipids activator proteins). These are proteins with mainly alpha-helical folds, compact packing including well conserved disulfide bonds and ability to interact with phospholipids and membranes. There are two types of saposin-like domains termed as Saposin A (SAPA) and Saposin B (SAPB) domains. While disulfide connectivity has been well established in several SAPB domains, the position of disulfide bonds in SAPA domains is still unknown. The present study approaches a detailed proteomic study to determine disulfide connectivity in the SAPA domain of the precursor of human pulmonary surfactant-associated protein SP-B. This task has been a challenge requiring the combination of different sequential proteolytic treatments followed by MS analysis including MALDI-TOF and tandem mass MS/MS spectrometry. The determination for first time of the position of disulfide bonds in SAPA domains is an important step to understand the structural determinants defining its biological functions.

Influence of N Terminus Amino Acid on Peptide Cleavage in Solution through Diketopiperazine Formation

Diketopiperazine (DKP) formation is an important degradation pathway for peptides and proteins. It can occur during synthesis and storage in either solution or the solid state. The kinetics of peptide cleavage through DKP formation have been analyzed for the model peptides Xaa¹-Pro²-Gly₄-Lys⁷ [Xaa = Gln, Glu, Lys, Ser, Phe, Trp, Tyr, Cha (β-cyclohexylalanine), Aib (α-aminoisobutyric acid), Gly, and Val] at multiple elevated temperatures in ethanol with ion mobility spectrometry-mass spectrometry (IMS-MS). When Xaa is an amino acid with a charged or polar side chain, degradation is relatively fast. When Xaa is an amino acid with a nonpolar alkyl side chain, the peptide is relatively stable. For these peptides, a bulky group on the α carbon speeds up dissociation, but the kinetic effects vary in a complicated manner for bulky groups on the β or γ carbon. Peptides where Xaa has a nonpolar aromatic side chain show moderate dissociation rates. The stability of these peptides is a result of multiple factors. The reaction rate is enhanced by (1) the stabilization of the late transition state through the interaction of an aromatic ring with the nascent DKP ring or lowering the activation energy of nucleophilic attack intermediate state through polar or charged residues and (2) the preference of the cis proline bond favored by the aromatic N-terminus. The number of unseen intermediates and transition state thermodynamic values are derived for each peptide by modeling the kinetics data. Most of the transition states are entropically favored (ΔS^⧧ ∼ -5 to +31 J·mol^-1·K^-1), and all are enthalpically disfavored (ΔH^⧧ ∼ 93 to 109 kJ·mol^-1). The Gibbs free energy of activation is similar for all of the peptides studied here (ΔG^⧧ ∼ 90-99 kJ·mol^-1).

Thermodynamics and Reaction Mechanisms for Decomposition of a Simple Protonated Tripeptide, H+GGA: From H+GGG to H+GAG to H+GGA

We present a thorough characterization of fragmentations observed in threshold collision-induced dissociation (TCID) experiments of protonated glycylglycylalanine (H⁺GGA) with Xe using a guided ion beam tandem mass spectrometer. Kinetic energy dependent cross sections for nine ionic products were obtained and analyzed to provide 0 K barriers for the five primary products, [b₂]⁺, [y₁ + 2H]⁺, [b₃]⁺, [y₂ + 2H]⁺, and [a₁]⁺; and four secondary products, [a₂]⁺, [a₃]⁺, high-energy [y₁ + 2H]⁺, and CH₃CHNH₂⁺, after accounting for multiple ion-molecule collisions, the internal energy of reactant ions, unimolecular decay rates, competition between channels, and sequential dissociations. Relaxed potential energy surface scans performed at the B3LYP-GD3BJ/6-311+G(d,p) level of theory are used to identify transition states (TSs) and intermediates of the five primary and three secondary products (with the mechanism of the other secondary product previously established). Geometry optimizations and single point energy calculations of reactants, products, intermediates, and TSs were performed at several levels of theory. These theoretical energies are compared with experimental threshold energies and found to give reasonable agreement, with B3LYP-GD3BJ and M06-2X levels of theory performing slightly better than MP2 and better than B3LYP. The results obtained here are compared with previous results for decomposition of H⁺GGG and H⁺GAG to probe the effect of changing the amino acid sequence. Methylation in H⁺GGA has a significant effect on the competition between the primary sequence products, [b₂]⁺ and [y₁ + 2H]⁺, suppressing the [b₂]⁺ cross section by raising its threshold energy, while enhancing that of [y₁ + 2H]⁺ by lowering its threshold energy.

Size Dependent Fragmentation Chemistry of Short Doubly Protonated Tryptic Peptides

Tandem mass spectrometry of electrospray ionized multiply charged peptide ions is commonly used to identify the sequence of peptide(s) and infer the identity of source protein(s). Doubly protonated peptide ions are consistently the most efficiently sequenced ions following collision-induced dissociation of peptides generated by tryptic digestion. While the broad characteristics of longer (N ≥ 8 residue) doubly protonated peptides have been investigated, there is comparatively little data on shorter systems where charge repulsion should exhibit the greatest influence on the dissociation chemistry. To address this gap and further understand the chemistry underlying collisional-dissociation of doubly charged tryptic peptides, two series of analytes ([G_xR+2H]²⁺ and [A_xR+2H]²⁺, x = 2-5) were investigated experimentally and with theory. We find distinct differences in the preference of bond cleavage sites for these peptides as a function of size and to a lesser extent composition. Density functional calculations at two levels of theory predict that the threshold relative energies required for bond cleavages at the same site for peptides of different size are quite similar (for example, b₂-y_N-2). In isolation, this finding is inconsistent with experiment. However, the predicted extent of entropy change of these reactions is size dependent. Subsequent RRKM rate constant calculations provide a far clearer picture of the kinetics of the competing bond cleavage reactions enabling rationalization of experimental findings. The M06-2X data were substantially more consistent with experiment than were the B3LYP data.

Mass spectral and theoretical investigations of the transient proton-bound dimers on the cleavage processes of the peptide GHK and its analogues

Fragmentation mechanisms of the singly protonated peptides GHK, GHKH and HGHK have been investigated by mass spectrometry and theoretical calculations. Fragmentation behavior of the protonated H-K amide bond in GHK was changed completely when a histidinyl residue was introduced into the C-terminus of GHK. The H-K amide bond breaking was a predominant pathway in the case of GHK and GHKH. For HGHK, the histidinyl residue at the N-terminus hampered significantly breaking of the H-K amide bond resulting in a high potential energy barrier; calculations indicated that this histidinyl effect played a vital role for the H-K amide bond fragmentation. Subsequent analysis of the fragmentation mechanism revealed that recombination processes of the hydrogen bonding for the intermediate products were all exergonic. Formation of a proton-bound dimer (PBD) lowering the energy barriers from a thermodynamic perspective for all the designed fragmentation pathways was demonstrated to be feasible by our systematic calculations. Moreover, the involvement of different PBDs was further confirmed by analyses of the reduced density gradient (RDG) isosurfaces and scatter maps. A dynamically favored pathway was likely via six-membered ring or nine-membered ring structures generated by the diketopiperazine as revealed by atom-in-molecules (AIM) analyses, since the steric interaction energies in the newly formed ring were estimated to be relatively small when compared to the products generated from a lactam and/or an oxazolone pathway. This is the first feasibility investigation from a dynamic viewpoint for formation of different rings involved in the lactam, oxazolone or diketopiperazine pathways in the fragmentation mechanisms proposed.

Quantum chemical mass spectrometry: Ab initio study of b2 -ion formation mechanisms for the singly protonated Gln-His-Ser tripeptide

RATIONALE

Both amide bond protonation triggering peptide fragmentations and the controversial b₂ -ion structures have been subjects of intense research. The involvement of histidine (H), with its imidazole side chain that induces specific dissociation patterns involving inter-side-chain (ISC) interactions, in b₂ -ion formation was investigated, focusing on the QHS model tripeptide.

METHODS

To identify the effect of histidine on fragmentations issued from ISC interactions, QHS was selected for a comprehensive analysis of the pathways leading to the three possible b₂ -ion structures, using quantum chemical calculations performed at the DFT/B3LYP/6-311+G* level of theory. Electrospray ionization ion trap mass spectrometry allowed the recording of MS² and MS³ tandem mass spectra, whereas the Quantum Chemical Mass Spectrometry for Materials Science (QCMS² ) method was used to predict fragmentation patterns.

RESULTS

Whereas it is very difficult to differentiate among protonated oxazolone, diketopiperazine, or lactam b₂ -ions using MS² and MS³ mass spectra, the calculations indicated that the QH b₂ -ion (detected at m/z 266) is probably a mixture of the lactam and oxazolone structures formed after amide nitrogen protonation, making the formation of diketopiperazine less likely as it requires an additional step for its formation.

CONCLUSIONS

In contrast to glycine-histidine-containing b₂ -ions, known to be issued from the backbone-imidazole cyclization, we found that interactions between the side chains were not obvious to perceive, neither from a thermodynamics nor from a fragmentation perspective, emphasizing the importance of the whole sequence on the dissociation behavior usually demonstrated from simple glycine-containing tripeptides.

Collisional dynamics simulations revealing fragmentation properties of Zn(ii)-bound poly-peptide

Collisional simulations show how peptide fragmentation is modified by the presence of Zn(ii).

Leaving Group Effects in a Series of Electrosprayed CcHhN1 Anthracene Derivatives

We investigate the gas-phase structures and fragmentation pathways of model compounds of anthracene derivatives of the general formula C_cH_hN₁ utilizing tandem mass spectrometry and computational methods. We vary the substituent alkyl chain length, composition, and degree of branching. We find substantial experimental and theoretical differences between the linear and branched congeners in terms of fragmentation thresholds, available pathways, and distribution of products. Our calculations predict that the linear substituents initially isomerize to form lower energy branched isomers prior to loss of the alkyl substituents as alkenes. The rate-determining chemistry underlying these related processes is dominated by the ability to stabilize the alkene loss transition structures. This task is more effectively undertaken by branched substituents. Consequently, analyte lability systematically increased with degree of branching (linear < secondary < tertiary). The resulting anthracen-9-ylmethaniminium ion generated from these alkene loss reactions undergoes rate-limiting proton transfer to enable expulsion of either hydrogen cyanide or CNH. The combination of the differences in primary fragmentation thresholds and degree of radical-based fragmentation processes provide a potential means of distinguishing compounds that contain branched alkyl chain substituents from those with linear ones.

Weak Acid-Base Interactions of Histidine and Cysteine Affect the Charge States, Tertiary Structure, and Zn(II)-Binding of Heptapeptides

Zinc fingers are proteins that are characterized by the coordination of zinc ions by an amino acid sequence that commonly contains two histidines and two cysteines (2His-2Cys motif). Investigations of oligopeptides that contain the 2His-2Cys motif, e.g., acetyl-His₁-Cys₂-Gly₃-Pro₄-Tyr₅-His₆-Cys₇, have discovered they exhibit pH-dependent Zn(II) chelation and have redox activities with Cu(I/II), forming a variety of metal complexes. To further understand how these 2His-2Cys oligopeptides bind these metal ions, we have undertaken a series of ion mobility-mass spectrometry and B3LYP/LanL2DZ computational studies of structurally related heptapeptides. Starting with the sequence above, we have modified the potential His, Cys, or C-terminus binding sites and report how these changes in primary structure affect the oligopeptides positive and negative charge states, conformational structure, collision-induced breakdown energies, and how effectively Zn(II) binds to these sequences. The results show evidence that the weak acid-base properties of Cys-His are intrinsically linked and can result in an intramolecular salt-bridged network that affects the oligopeptide properties.

Spectroscopic Evidence for Lactam Formation in Terminal Ornithine b2+ and b3+ Fragment Ions

Infrared multiple photon dissociation action spectroscopy was performed on the AlaOrn b₂⁺ and AlaAlaOrn b₃⁺ fragment ions from ornithine-containing tetrapeptides. Infrared spectra were obtained in the fingerprint region (1000-2000 cm^-1) using the infrared free electron lasers at the Centre Laser Infrarouge d'Orsay (CLIO) facility in Orsay, France, and the free electron lasers for infrared experiments (FELIX) facility in Nijmegen, the Netherlands. A novel terminal ornithine lactam AO⁺ b₂⁺ structure was synthesized for experimental comparison and spectroscopy confirms that the b₂⁺ fragment ion from AOAA forms a lactam structure. Comparison of experimental spectra with scaled harmonic frequencies at the B3LYP/6-31+G(d,p) level of theory shows that AO⁺ b₂⁺ forms a terminal lactam protonated either on the lactam carbonyl oxygen or the N-terminal nitrogen atom. Several low-lying conformers of these isomers are likely populated following IRMPD dissociation. Similarly, a comparison of the experimental IRMPD spectrum with calculated spectra shows that AAO⁺ b₃⁺-ions also adopt a lactam structure, again with multiple different protonation sites, during fragmentation. This study provides spectroscopic confirmation for the lactam cyclization proposed for the "ornithine effect" and represents an alternative b_n⁺ structure to the oxazolone and diketopiperazine/macrocycle structures most often formed.

Chemical dynamics simulations of CID of peptide ions: comparisons between TIK(H+)2 and TLK(H+)2 fragmentation dynamics, and with thermal simulations

Gas phase unimolecular fragmentation of the two model doubly protonated tripeptides threonine-isoleucine-lysine (TIK) and threonine-leucine-lysine (TLK) is studied using chemical dynamics simulations. Attention is focused on different aspects of collision induced dissociation (CID): fragmentation pathways, energy transfer, theoretical mass spectra, fragmentation mechanisms, and the possibility of distinguishing isoleucine (I) and leucine (L). Furthermore, discussion is given regarding the differences between single collision CID activation, which results from a localized impact between the ions and a colliding molecule N₂, and previous thermal activation simulation results; Z. Homayoon, S. Pratihar, E. Dratz, R. Snider, R. Spezia, G. L. Barnes, V. Macaluso, A. Martin-Somer and W. L. Hase, J. Phys. Chem. A, 2016, 120, 8211-8227. Upon thermal activation unimolecular fragmentation is statistical and in accord with RRKM unimolecular rate theory. Simulations show that in collisional activation some non-statistical fragmentation occurs, including shattering, which is not present when the ions dissociate statistically. Products formed by non-statistical shattering mechanisms may be related to characteristic mass spectrometry peaks which distinguish the two isomers I and L.

Cationized Carbohydrate Gas-Phase Fragmentation Chemistry

We investigate the fragmentation chemistry of cationized carbohydrates using a combination of tandem mass spectrometry, regioselective labeling, and computational methods. Our model system is D-lactose. Barriers to the fundamental glyosidic bond cleavage reactions, neutral loss pathways, and structurally informative cross-ring cleavages are investigated. The most energetically favorable conformations of cationized D-lactose were found to be similar. In agreement with the literature, larger group I cations result in structures with increased cation coordination number which require greater collision energy to dissociate. In contrast with earlier proposals, the B _n -Y _m fragmentation pathways of both protonated and sodium-cationized analytes proceed via protonation of the glycosidic oxygen with concerted glycosidic bond cleavage. Additionally, for the sodiated congeners our calculations support sodiated 1,6-anhydrogalactose B _n ion structures, unlike the preceding literature. This affects the subsequent propensity of formation and prediction of B _n /Y _m branching ratio. The nature of the anomeric center (α/β) affects the relative energies of these processes, but not the overall ranking. Low-energy cross-ring cleavages are observed for the metal-cationized analytes with a retro-aldol mechanism producing the ^0,2 A ₂ ion from the sodiated forms. Theory and experiment support the importance of consecutive fragmentation processes, particularly for the protonated congeners at higher collision energies. Graphical Abstract ᅟ.

Stereochemical Sequence Ion Selectivity: Proline versus Pipecolic-acid-containing Protonated Peptides

Substitution of proline by pipecolic acid, the six-membered ring congener of proline, results in vastly different tandem mass spectra. The well-known proline effect is eliminated and amide bond cleavage C-terminal to pipecolic acid dominates instead. Why do these two ostensibly similar residues produce dramatically differing spectra? Recent evidence indicates that the proton affinities of these residues are similar, so are unlikely to explain the result [Raulfs et al., J. Am. Soc. Mass Spectrom. 25, 1705-1715 (2014)]. An additional hypothesis based on increased flexibility was also advocated. Here, we provide a computational investigation of the "pipecolic acid effect," to test this and other hypotheses to determine if theory can shed additional light on this fascinating result. Our calculations provide evidence for both the increased flexibility of pipecolic-acid-containing peptides, and structural changes in the transition structures necessary to produce the sequence ions. The most striking computational finding is inversion of the stereochemistry of the transition structures leading to "proline effect"-type amide bond fragmentation between the proline/pipecolic acid-congeners: R (proline) to S (pipecolic acid). Additionally, our calculations predict substantial stabilization of the amide bond cleavage barriers for the pipecolic acid congeners by reduction in deleterious steric interactions and provide evidence for the importance of experimental energy regime in rationalizing the spectra. Graphical Abstract ᅟ.

Difference of Electron Capture and Transfer Dissociation Mass Spectrometry on Ni(2+)-, Cu(2+)-, and Zn(2+)-Polyhistidine Complexes in the Absence of Remote Protons

Electron capture dissociation (ECD) and electron transfer dissociation (ETD) in metal-peptide complexes are dependent on the metal cation in the complex. The divalent transition metals Ni(2+), Cu(2+), and Zn(2+) were used as charge carriers to produce metal-polyhistidine complexes in the absence of remote protons, since these metal cations strongly bind to neutral histidine residues in peptides. In the case of the ECD and ETD of Cu(2+)-polyhistidine complexes, the metal cation in the complex was reduced and the recombination energy was redistributed throughout the peptide to lead a zwitterionic peptide form having a protonated histidine residue and a deprotonated amide nitrogen. The zwitterion then underwent peptide bond cleavage, producing a and b fragment ions. In contrast, ECD and ETD induced different fragmentation processes in Zn(2+)-polyhistidine complexes. Although the N-Cα bond in the Zn(2+)-polyhistidine complex was cleaved by ETD, ECD of Zn(2+)-polyhistidine induced peptide bond cleavage accompanied with hydrogen atom release. The different fragmentation modes by ECD and ETD originated from the different electronic states of the charge-reduced complexes resulting from these processes. The details of the fragmentation processes were investigated by density functional theory. Graphical Abstract ᅟ.

Unimolecular dissociation of peptides: statistical vs. non-statistical fragmentation mechanisms and time scales

In the present work we have investigated mechanisms of gas phase unimolecular dissociation of a relatively simple dipeptide, the di-proline anion, by means of chemical dynamics simulations, using the PM3 semi-empirical Hamiltonian. In particular, we have considered two activation processes that are representative limits of what occurs in collision induced dissociation experiments: (i) thermal activation, corresponding to several low energy collisions, in which the system is prepared with a microcanonical distribution of energy; (ii) collisional activation where a single shock of hundreds of kcal mol⁻¹ (300 kcal mol⁻¹ in the present case) can transfer sufficient energy to allow dissociation. From these two activation processes we obtained different product abundances, and for one particular fragmentation pathway a clear mechanistic difference for the two activation processes. This mechanism corresponds to the leaving of an OH⁻ group and subsequent formation of water by taking a proton from the remaining molecule. This last reaction is always observed in thermal activation while in collisional activation it is less favoured and the formation of OH⁻ as a final product is observed. More importantly, we show that while in thermal activation unimolecular dissociation follows exponential decay, in collision activation the initial population decays with non-exponential behaviour. Finally, from the thermal activation simulations it was possible to obtain rate constants as a function of temperature that show Arrhenius behaviour. Thus activation energies have also been extracted from these simulations.