Thomas Lecocq
email: thomas.lecocq@seismology.be

Stephen Hicks

Koen Van Noten

Kasper Van Wijk

Paula Koelemeijer

Raphael S M De Plaen

Frédérick Massin

Gregor Hillers

Robert E Anthony

Maria-Theresia Apoloner

Koen Van Noten

Maria- Theresia Apoloner

Mario Arroyo-Solórzano

Jelle D Assink

Pinar Büyükakpinar

Andrea Cannata

Flavio Cannavo

Sebastian Carrasco

Corentin Caudron

Esteban J Chaves

David G Cornwell

David Craig

Olivier F C Den Ouden

Jordi Diaz

Stefanie Donner

Christos P Evangelidis

Läslo Evers

Benoit Fauville

Gonzalo A Fernandez

Dimitrios Giannopoulos

Steven J Gibbons

Társilo Girona

Bogdan Grecu

Marc Grunberg

György Hetényi

Anna Horleston

Adolfo Inza

Jessica C E Irving

Mohammadreza Jamalreyhani

Alan Kafka

Mathijs R Koymans

Celeste R Labedz

Eric Larose

Nathaniel J Lindsey

Mika Mckinnon

Tobias Megies

Meghan S Miller

William Minarik

Louis Moresi

Víctor H Márquez- Ramírez

Martin Möllhoff

Ian M Nesbitt

Shankho Niyogi

Javier Ojeda

Adrien Oth

Simon Proud

Jay Pulli

Lise Retailleau

Annukka E Rintamäki

Claudio Satriano

Martha K Savage

Shahar Shani-Kadmiel

Reinoud Sleeman

Efthimios Sokos

Klaus Stammler

Alexander E Stott

Shiba Subedi

Mathilde B Sørensen

Taka'aki Taira

Fatih Turhan

Ben Van Der Pluijm

Mark Vanstone

Jerome Vergne

Tommi A T Vuorinen

Tristram Warren

Joachim Wassermann

Han Xiao

Global quieting of high-frequency seismic noise due to COVID-19 pandemic lockdown measures

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

ABSTRACT: Human activity causes vibrations that propagate into the ground as highfrequency seismic waves. Measures to mitigate the COVID-19 pandemic caused widespread changes in human activity, leading to a months-long reduction in seismic noise of up to 50%. The 2020 seismic noise quiet period is the longest and most prominent global anthropogenic seismic noise reduction on record. While the reduction is strongest at surface seismometers in populated areas, this seismic quiescence extends for many kilometers radially and hundreds of meters in depth. This provides an opportunity to detect subtle signals from subsurface seismic sources that would have been concealed in noisier times and to benchmark sources of anthropogenic noise. A strong correlation between seismic noise and independent measurements of human mobility suggests that seismology provides an absolute, real-time estimate of population dynamics.

ONE SENTENCE SUMMARY: Global changes in social and economic activity following COVID-19 lockdown measures caused significantly lower anthropogenic seismic noise levels.

Seismometers record signals from more than just earthquakes; interactions between the solid Earth and fluid bodies, such as ocean swell and atmospheric pressure (1,2), are now commonly used to image and monitor the subsurface (3). Human activity is a third source of seismic signal. Nuclear explosions and fluid injection/extraction result in impulsive signals, but everyday human activity is recorded as near-continuous signal especially on seismometers in urban environments. These complicated signals are the superposition of a wide variety of activities happening at different times and places at or near the Earth's surface, but are typically stronger during the day than at night, weaker on weekends than weekdays, and stronger near population centers (4,5,6,7). Seismometers in urban environments are important to maximize the spatial coverage of seismic networks and to warn of local geologic hazards (8), even though anthropogenic seismic noise degrades their capability to detect transient signals associated with earthquakes and volcanic eruptions. Understanding urban seismic sources is therefore vital. However, research studies have been limited to confined areas or distinct events, such as road traffic (9,10), public transport (11,7), and "football quakes" (11,12). Broad analysis of the longterm global anthropogenic seismic wavefield has been lacking. The impact of large, coherent changes in human behavior on seismic noise is unknown, as is how far it propagates and whether seismic recordings offer a coarse proxy for monitoring human activity patterns. Answering these questions has proven challenging: datasets are large, monitoring network heterogeneous, and the many possible noise sources likely vary spatially and overlap in time (13).

The COVID-19 outbreak was declared a global health emergency in January 2020 (14) and a pandemic in March by the World Health Organisation. The outbreak resulted in emergency measures to reduce the basic reproduction rate of the virus (R0) (15), beginning in China, Italy, and then followed by most countries. These measures disrupted social and economic behavior (16), industry (17), and tourism (18). In this paper, we use "lockdown" to broadly encompass many types of emergency measures, such as full quarantine (e.g. Wuhan, China (19,20,21)), enforced physical distancing (e.g. Italy; UK), travel restrictions (22), widespread closure of services and industry, or any other emergency measures. These drastic changes to daily life provide a unique opportunity to study their environmental impacts, such as reductions in nitrous oxide emissions in the atmosphere (23). Recordings of human-generated seismic vibrations that travel through the solid Earth provide insights into the dynamics of pandemic lockdowns.

We assessed the effects of COVID-19 lockdowns on high-Frequency (4-14 Hz) Seismic Ambient Noise (hiFSAN; [START_REF]Materials and Methods, and Network Citations are available as supplementary materials on Science Online[END_REF]). We compiled a global seismic noise dataset using verticalcomponent seismic waveform data from 337 broadband and individually-operated citizen seismometer stations [START_REF]Materials and Methods, and Network Citations are available as supplementary materials on Science Online[END_REF], such as Raspberry Shakes (RS), with a self-noise well below the ground motion generated by anthropogenic noise [START_REF] Anthony | [END_REF], and flat responses in the target frequency band (Fig. 1). For 268 seismic stations, we obtained usable data (e.g. no large data gaps, working sensors) and found significant reductions in hiFSAN during local lockdown measures at 185 stations (Fig. 2). Periods that are often seismically quiet include weekends, and the Christmas / New Year holidays for those locations where these are celebrated. We found a near-global reduction in noise, commencing in China in late Jan 2020, then followed by Europe and the rest of the world in Mar to Apr 2020. The noise level we observe during lockdowns lasted longer and was often quieter than the Christmas to New Year period.

In China (Fig. 3A), the COVID-19 outbreak and subsequent emergency measures occurred during Chinese New Year (CNY). In Enshi city, Hubei province, where the outbreak began (26), hiFSAN in 2020 clearly diverges from the normal annual reduction during CNY. The hiFSAN level remained at a minimum for several weeks after CNY. This minimum was demarcated by the start and end of quarantine in Hubei. While such strict quarantine measures were not enforced in Beijing, local hiFSAN reductions are stronger and longer than recent years. As of the end date of our analysis, Beijing has still not reached the average hiFSAN level of previous years, suggesting the impact of COVID-19 is still restricting anthropogenic noise there. We noticed a later hiFSAN lockdown reduction in Apr 2020 in Heilongjiang, in NE China, near the Russian border. While we see seismic effects of lockdown in areas with low population density estimates (<1 person per km², Fig. 1), the strongest hiFSAN reduction occurs in populated environments. For a permanent seismic station in Sri Lanka, a 50% reduction in hiFSAN occurred after lockdown, the strongest we observed in the available data from that station since at least July 2013 (Fig. S2). In Central Park, New York, on Sunday nights, hiFSAN was 10% lower during the lockdown compared to before it (Fig. S3).

Seismic networks in populated areas allow us to correlate hiFSAN with other human activity measurements, such as audible recordings and flight data [START_REF]Materials and Methods, and Network Citations are available as supplementary materials on Science Online[END_REF]. At a surface station in Brussels, Belgium (Fig. 3B), we found a 33% reduction in hiFSAN after lockdown. We compared this with data from a nearby microphone, located close to a major road, that mainly records audible traffic noise. We found a high correlation between pre-lockdown hiFSAN and audible noise, both showing characteristic diurnal and weekly changes. However, during lockdown, audible noise reductions are more pronounced, suggesting that seismometers are sensitive to a wider distribution of seismic sources, not solely to the nearby traffic. Audible and hiFSAN levels then gradually increase after Apr 2020. Independent mobility data [START_REF]Materials and Methods, and Network Citations are available as supplementary materials on Science Online[END_REF] provide insights into what cause these changes. Mobility correlates with hiFSAN at lockdown, with correlation coefficients exceeding 0.8 [START_REF]Materials and Methods, and Network Citations are available as supplementary materials on Science Online[END_REF], except for time spent at places of residence (Google's "residential" category), which is expected given the increased number of people spending more time at home due to government restrictions.

Citizen seismometers provide a different urban ground motion dataset, with denser coverage in some places. Large hiFSAN drops especially occurred at schools and universities following lockdown-related closures (e.g. in Boston and Michigan (US) and Cornwall (UK)), Fig. S4). The hiFSAN level is even 20% lower than during school holidays, indicating sensitivity to the environment outside of the school.

The pandemic impacted tourism, for example, during the holiday season in the Caribbean. In Barbados (Fig. 3C), hiFSAN decreased by ∼45% following lockdown on 28 March 2020, through April 2020 and stayed ∼50% below levels observed in previous years for the same period. However, seismic noise levels started to decrease 1-2 weeks before a local curfew started. Local flight data [START_REF]Materials and Methods, and Network Citations are available as supplementary materials on Science Online[END_REF] imply travel to Barbados started decreasing after 21 March 2020 and the overall reduction in hiFSAN might be due in part to tourists repatriating. We also observed noise reductions due to reduced tourist activity at ski resorts in Europe (Zugspitze) and the US (Mammoth Mountain) (Fig. S5).

While we saw lockdown effects most strongly at surface stations, we also detected them underground. Seismometers installed in boreholes to minimize the effects of anthropogenic noise on the data monitor potential hazards associated with the Auckland Volcanic Field, New Zealand (27,8,6). Station HBAZ is 380 m below the city, while MBAZ is at 98 m depth, 14 km from the city center on the uninhabited Motutapu island (Fig. 3D). The hiFSAN level at both stations varies between weekdays and weekends before the lockdown, suggesting that both are sensitive to anthropogenic activity. While the island station is quieter overall, the lockdown instigated a reduction in hiFSAN by a factor of two for both stations. We attribute the remaining hiFSAN maxima on the island (mid Apr 2020; early May 2020) to strong winds and high waves. On 27 April 2020, New Zealand lifted restrictions, with hiFSAN increasing to the pre-lockdown levels.

The reduction of hiFSAN is weaker in less populated areas, such as at Rundu which is located along the Namibia-Angola border (Fig. 3E). After COVID-19 was confirmed in Namibia, an emergency was declared on 17 Mar 2020 to restrict mobility, followed by full lockdown on 27 Mar 2020. These measures are reflected in >25% hiFSAN reduction compared to pre-lockdown. Despite Rundu having a population roughly eight and five times less dense than Brussels and Auckland, respectively [START_REF]Gridded population of the world, version 4 (GPWv4): Population density[END_REF], we observed a similarly high correlation between seismic and mobility data. The Black Forest Observatory in Germany is an even more remote station, located 150-170 m below the surface in crystalline bedrock. Considered a reference low-noise laboratory [START_REF] Zürn | [END_REF], even there we found a small hiFSAN reduction during lockdown nights (Fig. S6), corresponding to the lowest hiFSAN since at least 25 Dec 2015.

We have provided a global-scale analysis of high-frequency anthropogenic seismic noise. Global median hiFSAN dropped by as much as 50% during March to May 2020 (Fig. 4). The length and quiescence of this period represents the longest and most coherent global seismic noise reduction in recorded history, highlighting how human activities impact the solid Earth. A globally high correlation exists between changes in hiFSAN and population mobility [START_REF]Materials and Methods, and Network Citations are available as supplementary materials on Science Online[END_REF], with correlations exceeding 0.9 for many categories.

This distinct low-noise period will help to optimize seismic monitoring (4). Analyzing the full spectrum of seismogenic behavior, including the smallest earthquakes, is essential for monitoring fault dynamics over seismic cycles, and for earthquake forecasting and seismic hazard assessment. Small earthquakes should dominate datasets (30), but typical operational catalogues using amplitude-based detection lack many of the smallest earthquakes (31). This detection issue is especially problematic in populated areas, where anthropogenic noise energy interferes with earthquake signals. This problem is exemplified by recordings of a M5.0 earthquake at 15 km depth SW of Petatlan, Mexico during lockdown (Fig. S7). An earthquake with this magnitude and source mechanism occurring during daytime could typically only be observed at stations in urban environments by filtering the signal. However, the reduction of seismic noise by ∼40% during lockdown made this event visible without any filtering required at a RS station in Querétaro city, 380 km away. Low noise levels during COVID-19 lockdowns could thus allow detection of signals from new sources in areas with incomplete seismic catalogues. Such newly identified signals could be used as distinct templates (30) for finding similar waveforms in noisier data pre-and post-lockdown. This approach also works for tremor signals masked by anthropogenic noise, yet vital for monitoring potential volcanic unrest (6). Although broadband sensors in rural environments are impacted less by anthropogenic noise, any densification of and reliance on lowcost sensors in urban areas, such as RS and low-cost accelerometers (32), will require a better understanding of anthropogenic noise sources to suppress false detections. As populations increase globally, more people become exposed to potential natural and induced geohazards (33). Urbanization will increase anthropogenic noise in exposed areas, further complicating seismic monitoring. Characterizing and minimizing anthropogenic noise is increasingly important for accurately detecting and imaging the seismic signatures of potentially harmful subsurface hazards.

Anthropogenic seismic noise is thought to be dominated by noise sources less than 1 km away (34,5,6,7,11). Because population mobility generates time-varying loads that radiate energy through the shallow subsurface as Rayleigh waves (11), local effects, such as construction sites, heavy machinery, can impact individual stations. However, the unique 2020 seismic noise quiet period reveals that when considering multiple stations or whole networks over longer timescales, the anthropogenic seismic wavefield affects large areas. With denser networks and more citizen sensors in urban environments, more features of the seismic noise, rather than just amplitude, will become usable and will help to identify different anthropogenic noise sources (35,10). Characterizing these sources will be useful for imaging the shallow subsurface in 3D in urban areas using high-frequency anthropogenic ambient noise (36,37). Our finding of a distributed noise field is supported by the strong correlations with independent mobility data (Fig. 4). In contrast to mobility data, publicly available data from existing seismometer networks provide an objective absolute baseline of human activity levels. Therefore, hiFSAN can serve as a near-real-time technique for monitoring anthropogenic activity patterns with fewer potential privacy concerns than mobility data. In addition, industrial activities may not be captured in mobility data, but leave a seismic noise signature. The 2020 seismic quiet period is a baseline for using seismic properties (34) to identify and isolate the sources contributing to the anthropogenic noise wavefield, especially when combined with data indicative of human behavior. The seismic observations of human activity during the COVID-19 lockdown allow us to assess the impact of mitigation policies on daily life, especially the time to establish and recover from lockdowns. As such, hiFSAN may provide important constraints for health and behavioral science studies.

Figure 1 :

 1 Figure 1: Worldwide seismic station locations. Locations of the 268 global seismic stations with usable data (e.g. no long data gaps, working sensors) we analyzed. Lockdown effects are observed (red) at 185 out of 268 stations. Symbol size is scaled by the inverse of population density (28) to emphasize stations located in remote areas. The stations we labelled are discussed in detail in the text.

Figure 2 :

 2 Figure 2: Global temporal changes in seismic noise. Global daily median hiFSAN based on displacement data (24), normalized to percentage variation of the baseline before lockdown measures, and sorted by lockdown date. Data gaps are colored white. Location and country code of the station are indicated, while Fig. S1 also includes the network and station code.

Figure 3 :

 3 Figure 3: Regional examples of the 2020 seismic noise quiet period. Examples showing different features of the lockdown seismic signal changes in regional settings. We filtered the hiFSAN data between 4 and 14 Hz and present temporal changes either as displacement (A), acceleration (D) or as percentage change compared to the baseline before lockdown (B, C and E) with the panels in (A) also comparing to the baseline of corresponding time periods in prior years. Individual seismic stations are identified by network.station codes (IC.ENH, BE.UCCS, etc.). The legends of (B-E) include correlation coefficients r with mobility data (24). (A) Lockdown effects at three stations in China compared to the Chinese New Year holiday in previous years. (B) Lockdown effects in hiFSAN compared with audible environmental noise and independent mobility data in Brussels, Belgium. (C) Lockdown effect in Barbados compared to noise levels in the last decade (in grey) and

Figure 4 :

 4 Figure 4: Global changes in seismic noise compared to population mobility trends. (A) Comparison between temporal changes in global daily median hiFSAN based on the 185 stations that observed lockdown effects and population mobility changes (24). (B) Scatter plot to illustrate the correlation between the binned (10% bins) time series of seismic noise changes and all categories of mobility data in (A). Percentage changes are given relative to a prelockdown baseline. All categories show a strong positive correlation, apart from time spent in residential premises, which is anti-correlated.

Acknowledgments

We sincerely thank the editor, two anonymous reviewers and Tarje Nissen-Meyer for their comments, which have improved the manuscript. We are extremely grateful to all seismic network managers, operators, and technicians who have helped to facilitate the raw global seismic dataset (24). We also kindly acknowledge all the passionate community seismologists for

Data and materials availability:

The raw data used to compute the hiFSAN was obtained from different networks and data providers [START_REF]Materials and Methods, and Network Citations are available as supplementary materials on Science Online[END_REF]. The computed data and codes used to analyze and plot the Figures 1,2, 3 and 4 are available from the companion repository: https://doi.org/10.5281/zenodo.3944739.

running their "home" seismometers and participating, indirectly, to a better understanding of the Earth. Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the U.S. Government. We dedicate this community-led study to all essential workers who have kept our countries going during these difficult times. Funding:

• P.K. was funded by a Royal Society University Research Fellowship (URF\R1\180377).


Yanghune Ha

Riccardo Spezia
email: riccardo.spezia@sorbonne-universite.fr

Kihyung Song
email: ksong@knue.ac.kr

Computer Simulation of Collision Induced Dissociation and Isolobal Analogy: The Case of Biotin and its Analogues

Keywords: theoretical mass spectrometry, chemical dynamics simulations, isolobal analogy, biotin

We have studied how collision induced dissociation (CID) products and associated mechanisms change when a chemical group is modified by isolobal substitution, and in particular the sequence S, O, NH and CH 2 . At this end, we have considered protonated biotin (vitamin B 7 ) and corresponding oxybiotin, N-biotin and C-biotin, which have the same structures except for one chemical group (the S in biotin which is substituted with the aforementioned isolobal ones). Collisional simulations with Ar were performed to model CID fragmentations and to have direct access to related mechanisms. Simulations show that the CID fragmentation of the four compounds are similar and the resulting fragments involve in a similar way the isolobal groups. Details on the mechanisms obtained from simulations are reported and discussed. This result shows that it is possible to predict, in principle and with a reasonable confidence, mass spectra of unknown molecules based on mass spectrum of a known one when isolobal modifications are done.

INTRODUCTION

The concept of isolobal analogy was introduced years ago by Hoffmann as a practical tool to understand and easily predict organic and organometallic reactions. [START_REF] Hoffmann | Building bridges between inorganic and organic chemistry (Nobel Lecture)[END_REF] In the original publication, discussing the properties of M(CO) 3 and M(C 6 H 6 ) (where M is a metal) they "mean to imply that the number, symmetry properties, extent in space and energy of the frontier orbitals of the fragments are similar -not identical, but similar". [START_REF] Elian | Comparative Bonding Study of Conical Fragments[END_REF] Thus, two compounds, where one chemical group is replaced by another with similar properties in the frontier orbitals, are expected to behave similarly. In mass spectrometry, this concept could be used to predict fragmentation patterns of molecules which are derived from a known one where a group is replaced by an isolobal one.

Understanding and even better predicting fragmentation patterns in collision induced dissociation (CID) is crucial in both fundamental and practical applications of mass spectrometry. One approach consists in library searching, for example using the extended NIST library. 3 Of course, libraries need experiments on all the species of interest and mechanisms can be proposed only for data for which experiments are available. Another approach uses machine learning algorithms to guess fragmentation patterns, like in the competitive fragmentation model (CFM) by Allen et al. which uses a probabilistic generative model. [START_REF] Allen | Competitive fragmentation modeling of ESI-MS/MS spectra for putative metabolite identification[END_REF] Another possibility to predict CID spectra independently from simulation is to use molecular simulations. [START_REF] Song | Theoretical Mass Spectrometry: Tracing Ions with Classical Trajectories[END_REF] This approach, pioneered by Hase and co-workers, [START_REF] Meroueh | Direct Dynamics Simulations of Collision-and Surface-Induced Dissociation of N-Protonated Glycine. Shattering Fragmentation[END_REF][START_REF] Liu | Direct Dynamics Study of Energy Transfer and Collision-Induced Dissociation: Effect of Impact Energy, Geometry, and Reactant Vibrational Modes in H 2 CO + -Ne Collisions[END_REF] was then extended in last 10 years to a variety of biological and organic molecules. [START_REF] Martin-Somer | Role of Chemical Dynamics Simulations in Mass Spectrometry Studies of Collision-Induced Dissociation and Collisions of Biological Ions with Organic Surfaces[END_REF] The same approach can be successfully used to model and predict surface induced dissociation and soft landing. [START_REF] Pratihar | Chemical Dynamics Simulations of Energy Transfer, Surface-Induced Dissociation, Soft-Landing, and Reactive-Landing in Collisions of Protonated Peptide Ions with Organic Surfaces[END_REF][START_REF] Pratihar | Perspective: Dynamics of Protonated Peptide Ion Collisions with Organic Surfaces. Consonance of Simulation and Experiment[END_REF] It is based on two alternative physical representations of the collisional activation: (1) by providing an excess energy equally distributed through the vibrational modes of the fragmenting molecule, (2) by direct simulating the collision with the inert gas. [START_REF] Spezia | Unimolecular Dissociation of Peptides: Statistical vs Non-Statistical Fragmentation Mechanisms and Time Scales[END_REF][START_REF] Martin-Somer | Unimolecular Fragmentation of Deprotonated Diproline [Pro 2 -H] -Studied by Chemical Dynamics Simulations and IRMPD Spectroscopy[END_REF] Since it is based on the generation of an ensemble of reactive trajectories, the chemical dynamics approach provides at the same time the fragmentation products and the related mechanisms. The most relevant drawback is that it requires significant computational effort, and thus for relatively large systems highly accurate quantum chemistry methods cannot be used. However, semi-empirical Hamiltonians have shown to be able to provide relatively good fragmentation patterns and mechanisms, [START_REF] Ortiz | Gas-Phase Collision Induced Dissociation Mechanisms of Peptides. Theoretical and Experimental Study of N-Formylalanylamide Fragmentation[END_REF][START_REF] Bednarski | A combined theoretical and experimental study of mechanisms of fragmentation active for PHB oligomers in negative-ion mode multistage mass spectrometry[END_REF][START_REF] Lucas | Modeling the Effects of O-sulfonation on the CID of Serine[END_REF][START_REF] Rodríguez-Fernández | Collision-induced dissociation mechanisms of [Li (uracil)] +[END_REF] in particular for organic and rigid molecules, like testosterone [START_REF] Lee | Gas phase fragmentation mechanisms of protonated testosterone as revealed by chemical dynamics simulations[END_REF] or methyl-guanine. [START_REF] Carrà | Fragmentation Spectra Prediction and DNA Adducts Structural Determination[END_REF] In this last study, a comparison with CFM machine learning prediction was done, showing that the chemical trajectory approach is comparable with it, providing at the same time more information on reaction mechanisms and physically ground results.

Here, we have investigated the CID fragmentation in relation with the isolobal analogy.

In particular we have considered protonated biotin (also called vitamin B 7 or H) and then substituted the S atom with O (oxybiotin), NH (N-biotin) and CH 2 (C-biotin), forming a set of compounds shown in Figure 1. These atoms and fragments fulfill the "isolobal analogy" prescription since their frontier orbitals have similar energy, shape and number of electrons. 1 Other than a chemical rationale in modifying the S atom of biotin, there is also a biological interest on it. In fact, biotin acts as a coenzyme for carboxylase enzymes, involved in the synthesis of fatty acids, isoleucine, and valine, and in gluconeogenesis. [START_REF] Obermayer | Structure of biotin enzymes[END_REF][START_REF] Attwood | The structure and the mechanism of action of pyruvate carboxylase[END_REF] (a) (b)

(c) (d)
If there is insufficient biotin in a higher organism, oxybiotin is the only analog capable of replacing it. [START_REF] Casutt | Vitamins, 9. Biotin. Ullmann's Encyclopedia of Industrial Chemistry[END_REF] In general, single site substitution is common in biology and it can be useful to predict mass spectra of possible analogs independently from experiments. We have thus considered these four molecules, activated by modeling explicit collision with Ar atom and analyzed product ions and mechanisms. In particular, we focused on how the fragmentation spectra is (eventually) modified in the isolobal analogs and which are the related mechanisms. This will provide a guide to possibly predict the CID of different isolobal species from the spectrum of a known one.

COMPUTATIONAL DETAILS

Reactant structures

Biotin has an imidazolidinone structure and thiolane ring (Figure 1a). The isolobal analogs considered here are: oxybiotin, N-biotin and C-biotin. They have the same structure as biotin but S is substituted by O, NH, CH 2 (also shown in Figure 1). Although The geometries of the different structures were optimized at Hartre-Fock (HF) and B3LYP PM6 [START_REF] Stewart | Optimization of Parameters for Semiempirical Methods V: Modification of NDDO Approximations and Application to 70 Elements[END_REF] and PM7. [START_REF] Stewart | Optimization of parameters for semiempirical methods VI: more modifications to the NDDO approximations and re-optimization of parameters[END_REF] The resulting optimized geometries of each tautomeric form are reported in Figures 2 andS1-S3. From these calculations, it was possible to obtain the proton affinities of all the structures considered at different levels of theory. HF and B3LYP calculations were performed using Gaussin 09 Rev D.01 software, [START_REF] Frisch | Gaussian 09, Revision D.01[END_REF] while semi-empirical Hamiltonians calculations with MOPAC 2016. 31

Ion-Ar interaction potential

The potential energy for the collisional system, consisting of the ion and the neutral Ar atom (the collision gas) is described by:

𝑉 = 𝑉 #$% + 𝑉 '()#$% (1)
where 𝑉 #$% is the intramolecular potential of the protonated molecule and 𝑉 '()#$% is the intermolecular potential between Ar and the ion. This last term is as a sum of two-body interactions between Ar and the atoms of the ion. We used the expression proposed by Meroueh and Hase : 32

𝑉 '()#$% = 𝑎 '()# exp -𝑏 '()# ×𝑟 '()# + 𝑐 '()# 𝑟 '()# 4 # (2)
where 𝑖 runs over all atoms of the ion and the parameters 𝑎 '()# , 𝑏 '()# and 𝑐 '()# are always positive as reported in the original publication and found in next studies. This interaction potential was able to correctly simulate the CID of a series of systems, like protonated urea, [START_REF] Spezia | Protonated urea collisioninduced dissociation. Comparison of experiments and chemical dynamics simulations[END_REF] protonated N-formylalanylamide [START_REF] Ortiz | Gas-Phase Collision Induced Dissociation Mechanisms of Peptides. Theoretical and Experimental Study of N-Formylalanylamide Fragmentation[END_REF] and testosterone. [START_REF] Lee | Gas phase fragmentation mechanisms of protonated testosterone as revealed by chemical dynamics simulations[END_REF] We used parameters of H, C, O, N as from the original works of Meroueh and Hase [START_REF] Meroueh | Collisional activation of small peptides[END_REF] and Ortiz et al. [START_REF] Ortiz | Galactose-6-Sulfate collision induced dissociation using QM+MM chemical dynamics simulations and ESI-MS/MS experiments[END_REF] Parameters for S were obtained previously for sulfate group, [START_REF] Ortiz | Galactose-6-Sulfate collision induced dissociation using QM+MM chemical dynamics simulations and ESI-MS/MS experiments[END_REF] but the electron density of sulfur in biotin is clearly different and thus we have re-parametrized the potential for this new atom type. We have used at this aim the interaction between Ar and thiolane molecule to obtain parameters for S atom. The thiolane molecule containing thioether group (R-S-R') is a good model to represent the short-range repulsive interaction between Ar and S of biotin. The interaction potential energy between Ar and S was calculated from the shortest possible distance up to 3.5 Å, and the parameters 𝑎, 𝑏 and 𝑐 of Eq. ( 2) were obtained by fitting ab initio interaction energy curves carried out on the QCISD(T)/6-31++G(d,p) level of theory, which is the same level of theory used in previous parametrizations. The fit was performed by means of the least squares method as in Kaleidagraph software. [START_REF] Kirsch | KaleidaGraph: Graphing and Data Analysis[END_REF]

Trajectory simulations

Direct dynamics simulations of the ion-Ar collision were performed for the most stable precursor tautomer of each molecule (biotin, oxybiotin, N-and C-biotin). As we will show in the results section, this will correspond to the tautomer (a) where the excess proton is on the oxygen of the carbonyl group of the imidazolidinone group. Initial conditions for the ions were obtained from most stable structures, and initial positions and momenta obtained from vibrational normal mode Boltzmann sampling at 300 K. [START_REF] Peslherbe | Monte Carlo Sampling for Classical Trajectory Simulations[END_REF] Rotational energy was also added corresponding to the same temperature. The collisional system was set as follows: (1) the ion was randomly rotated about its Euler angles; (2) the Ar was placed at 13 Å distance (ensuring no ion-Ar interaction at the beginning); (3) an initial relative velocity was impressed to Ar and ion, with velocity vectors connecting the two centers of mass, corresponding to a relative energy of 30 eV in the center of mass framework; (4) the Ar atom was shifted by a randomly obtained impact parameter in the 0-5.0 Å range. This maximum value was estimated by the maximum length of the protonated systems which was about 9.2 Å. These collisional simulation initial conditions were set as described in details by Hase et al. [START_REF] Hase | Dynamics of Ethyl Radical Decomposition. 3. Effect of Chemical Activation vs. Microcanonical Sampling[END_REF] Simulations were then run and stopped when the Ar-ion distance exceeds 300 Å and in any case with a maximum simulation time of 40 ps. Equations of motions were integrated using velocity Verlet algorithm with a time step of 0.2 fs. For each system, we performed between 10,000 and 20,000 trajectories in order to have enough reactive events for the given collision energy and simulation time. Namely, we have between 288 (for C-biotin) and 1003 (for biotin) reactive trajectories, as reported in Table S1 of the supporting information. The relative energy of 30 eV ensures also enough fragmentation to a have a statistical consistent number of products and it is what successfully used recently to model protonated testosterone fragmentation. 17

RESULTS AND DISCUSSIONS

Ar-S interaction potential parameters

The interaction potential between Ar and S bound to two carbon atoms (C-S-C) in thiolane was obtained by performing QCISD(T)/6-31++G(d,p) calculations along the Ar…S C 2v axis of thiolane. The resulting ab initio energy curve is plotted in Figure 3 together with the result of fitted Equation 2. Corresponding parameters for Ar-S interaction are reported in Table 1. 2. [START_REF] Hoffmann | Building bridges between inorganic and organic chemistry (Nobel Lecture)[END_REF] Units are in kcal/mol. [START_REF] Elian | Comparative Bonding Study of Conical Fragments[END_REF] Units are in Å -1 .

Figure 3. Potential energy for Ar/S(CH2)4 as obtained from QCISD(T)/6-31++G(d,p) calculations (crosses) and fitted Equation

(3) Units are in Å 9 kcal/mol.

Proton affinities

Proton affinities are calculated for each stable tautomer of biotin and isolobal analogs.

In this way, it is possible to determine the most stable pronation state which will be used as starting structure for the following chemical dynamics simulations. Results are reported in Tables 2345. In all systems, the (a) protonation site (on the carboxyl oxygen of imidazolidinone ring) is the most favorable one. Values are very similar for the different structures, which is reasonable since the protonation site is relatively far from the modified group. Interestingly, for N-biotin the proton affinity of N-analog atom -site (d)

-is much closer to site (a) than in biotin and oxybiotin, such that it becomes slightly higher when calculated at B3LYP/6-311++G(d,p), RM1 or PM7 levels of theory.

Fragmentation yields and products

Reactivity yield is about 10% for biotin, but then it decreases when moving to oxybiotin (7.8%), N-biotin (4.2%) and C-biotin (2.4%), which roughly reflects the increasing in C-X bond strength from S to C (where X = S, O, N and C). Details are reported in Table S1 of the supporting material.

Fragmentation products of biotin are compared with what reported from experiments [START_REF] Beisken | Metabolic differences in ripening of Solanum lycopersicum "Ailsa Craig" and three monogenic mutants[END_REF] in the MassBank database. 39 The two fragmentation spectra are shown in Globally, the match between experiments and simulations is quite good: the main experimental peaks are found also in simulations with some differences in relative intensity. In particular, experimentally, the most intense peak is m/z 227.08 which is found less intense in simulations. Simulations report ion m/z 199.09 more abundant, while it is found less in experiments. A possible explanation can be that in the experiments once that ion m/z 199.09 is formed it can further react. We did not have any direct evidence from trajectories, since our simulation time-length was not enough to observe a secondary fragmentation. We will discuss some possible secondary products in next section. The largest difference concerns peak m/z 85.04 which is very abundant in simulations while very small in experiments. This is one of the lightest peak observed and thus the difference in abundance can be due to several reasons. One possibility is that the energy in simulations is higher than in experiments (a direct comparison on energetics cannot be done since experiments were not done in a triple-quad or QQTof instrument), thus smallest fragments are more probable. Furthermore, we do not have information on how the detection range is set in experiments, which can impact the observed number of ions in the low mass range of the instrument if it was optimized for higher m/z peaks. In any case, this low mass peak is not a characteristic peak. Details on most important mechanisms will be reported in section 3.4, here we mostly remark that the characteristic peak is obtained (m/z 227.08) and the global pattern is in reasonable agreement with experiments. Note that collisional conditions are also different, so we do not expect a perfect match, in particular concerning intensities. In Figure 5 we show the theoretical MS/MS spectrum obtained as results of all collisional simulations. Details and corresponding formula are listed in Table S2 where in each raw we report m/z, formula and abundance of the ions of the different isolobal anolog fragmentation products. Globally, the fragmentation patterns are very similar, in particular concerning the characteristic peaks of biotin. The intensities show some differences. In particular, moving from biotin to C-biotin, the relative intensity of ion m/z 199.09 (which is m/z 183.11, 182.13 and 181.13 in oxybiotin, N-and C-biotin, respectively) becomes more intense, and also other peaks that are less intense in biotin become more relevant. As we have discussed previously, simulations of biotin report the low m/z ion 85.04 with high intensity. This same m/z ion was found in other isolobal analogs, because the modified groups are in the neutral fragments. Details on the mechanisms observed in simulations are reported in next section.

Fragmentation mechanisms

We now analyze in details reaction mechanisms for the formation of the most relevant reaction products. We discuss the mechanisms observed in biotin together with the equivalent ones for the other systems, leading to isolobal analog fragments. In some biotin and oxybiotin simulations, the neutral further breaks in two molecules Concluding, this work shows that it is possible to use the isolobal analogy to guess with a certain confidence the presence many fragmentation products, but for this the detailed mechanisms should be known for at least one system. This result paves the way of using in the future chemical dynamics simulations on one species and use simple mechanistic considerations to propose fragments of isolobal analogs. In the future, it will be thus possible to predict mass spectrum of unknown molecules based on mass spectrum of the known ones with the help of computer simulations also with the aim of building a theoretical MS/MS database which can support experiments and complement existent databases.

C

Figure 1 .

 1 Figure 1. Chemical structures of neutral (a) biotin, (b) oxybiotin, (c) N-biotin and (d) C-biotin.

N

  -biotin and C-biotin are hypothetical molecules, these two compounds provide optimal examples to study isolobal analogy on CID products and mechanisms. Protonation can occur on different basic sites: six for biotin, oxybiotin and N-biotin and five for C-biotin. We define the different protonation sites as follows: (a) protonated on oxygen in the carbonyl group of the ring; (b) protonated on the nitrogen atom of amide group located in the opposite direction of the carboxylic group; (c) protonated on the other amide group; (d) protonated on S, O or N for biotin, oxybiotin and N-biotin, respectively (this site does not exist by definition in C-biotin); (e) protonated on the carbonyl of the carboxyl group and (f) protonated on the hydroxyl group. In Figure 2 we show the resulting different tautomers for biotin, while in Figures S1-S3 of the supporting material we report the same for oxybiotin, N-biotin and C-biotin.

Figure 2 .

 2 Figure 2. Structures of the different tautomers of protonated biotin.

Figure 4 .

 4 From simulations, the theoretical MS/MS spectrum is obtained simply by counting the product ions at the end of each trajectory and normalizing the intensities with respect to the ion m/z 227.08 which is the same normalization reported in the experiments.

Figure 4 .

 4 Figure 4. CID spectra of biotin as obtained from simulations (upper panel, in black) and reported experimentally (lower panel, in red; the sign is inversed). Both spectra are normalized with respect to the first peak, m/z 227.08. Precursor ion is not reported.

Figure 5 .

 5 Figure 5. Comparison of fragmentation products obtained from CID simulations of biotin, oxybiotin, N-biotin and C-biotin. In y-axis relative intensity, where the normalization was set on the first fragmentation peak of each species. Precursor ions are not reported.

(CH 2 XScheme 8 .

 28 Scheme 8. Mechanism observed for the formation of m/z 85.04 as from CID simulations of biotin.

Table 1 .

 1 Intermolecular potential parameters of sulfur atom

	potential	𝑎 (1)	𝑏 (2)	𝑐 (3)
	Ar/S(CH 2 ) 4 (ArS)	21634.0	2.5991	739.11

Table 2 .

 2 Proton affinities for biotin a

		ion type	ion type	ion type	ion type	ion type	ion type
		(a)	(b)	(c)	(d)	(e)	(f)
	HF / 6-31G(d,p)	237.827 217.820 223.635 208.919 230.635 224.321
	HF / 6-311++G(d,p)	235.860 217.365 223.029 209.893 212.692 222.274
	B3LYP / 6-31G(d,p)	233.257 220.055 224.987 206.991 229.003 222.569
	B3LYP / 6-311++G(d,p)	229.203 216.975 221.778 206.434 223.698 218.001
	MNDO-d	168.318 145.957 148.263 161.202 157.071 137.742
	RM1	182.809 177.649 181.017 158.401 181.173 176.824
	PM3	202.598 191.167 190.578 182.970 182.814 172.221
	PM6	155.682 156.357 159.775 149.318 155.038 150.902
	PM7	152.531 149.646 151.436 142.566 151.382 149.319

a Units are in kcal/mol.

Table 3 .

 3 Proton affinities for oxybiotin a

		ion type	ion type	ion type	ion type	ion type	ion type
		(a)	(b)	(c)	(d)	(e)	(f)
	HF / 6-31G(d,p)	240.516 218.196 224.224 214.428 231.060 228.388
	HF / 6-311++G(d,p)	238.161 216.888 193.723 213.397 213.943 222.894
	B3LYP / 6-31G(d,p)	235.175 226.335 225.271 204.091 229.577 223.728
	B3LYP / 6-	230.962 216.836 221.573 185.463 227.396 218.707
	311++G(d,p)
	MNDO-d	167.439 145.622 147.426 139.601 155.568 136.016

a Units are in kcal/mol.

Table 4 .

 4 Proton affinities for N-biotin a

		ion type	ion type	ion type	ion type	ion type	ion type
		(a)	(b)	(c)	(d)	(e)	(f)
	HF / 6-31G(d,p)	240.469 224.928 227.665 240.371 234.100 229.235
	HF / 6-311++G(d,p)	238.829 210.509 226.882 238.758 216.545 227.104
	B3LYP / 6-31G(d,p)	235.884 227.754 228.457 235.132 232.183 226.714
	B3LYP / 6-311++G(d,p)	231.122 224.040 224.890 232.102 226.507 221.886
	MNDO-d	168.188 146.629 147.445 160.405 155.386 136.159
	RM1	186.119 182.625 183.743 190.428 183.195 179.376
	PM3	205.433 194.979 194.711 192.415 184.334 174.060
	PM6	156.195 160.384 161.702 166.231 156.058 152.228
	PM7	153.257 152.973 152.803 155.431 152.232 150.253

a Units are in kcal/mol.

Table 5 .

 5 Proton affinities for C-biotin a

		ion type	ion type	ion type	ion	ion type	ion type
		(a)	(b)	(c)	type (d)	(e)	(f)
	HF / 6-31G(d,p)	242.297 227.125 229.229	-	235.556 230.259
	HF / 6-311++G(d,p)	240.450 226.376 228.566	-	233.123 228.259
	B3LYP / 6-31G(d,p)	237.473 229.051 229.942	-	233.574 227.890

a Units are in kcal/mol. The semi-empirical methods globally underestimate the proton affinity, but they show similar trend as from HF and B3LYP calculations, except for PM6 which provides ion type (c) as the most stable in contrast with HF and B3LYP results. Given such poor performance of PM6 in proton affinity, we did not add any empirical dispersion, which is however implicit in PM7 parametrization. Between different methods tested, PM3 seems to better reproduce these values. We have thus used it in the following chemical dynamics simulations. Note that the same semi-empirical Hamiltonian was successfully used to study CID of other molecules, like notably galactose sulfate.

[START_REF] Ortiz | Galactose-6-Sulfate collision induced dissociation using QM+MM chemical dynamics simulations and ESI-MS/MS experiments[END_REF]

  10 H 15 N 2 O 2 S + (m/z=227.08) and isolobal analog ions. Fragment m/z 227.08 is the most abundant peak in experiments and, as discussed previously, obtained also in simulations, but with less relative abundance. Analog fragments m/z 211.11, 210.12 and 209.13 are Collisional simulations are limited in time-length and this is clearly at the origin of the missing of these secondary and tertiary product ions in simulations.C 9 H 15 N 2 OS + (m/z=199.09) and isolobal analog ions. The peak m/z 199.09 corresponds to HCOOH lost and is observed in both simulations and experiments as an intense peak. The mechanisms are the same for the different species, leading to ions m/z 183.11, 182.13 and 181.13 for oxybiotin, N-biotin and C-biotin, respectively. For simplicity, we report in Scheme 2 only the mechanism observed in biotin simulations. As discussed in section 3.2, this ion was much more abundant in simulations than in experiments. This can be due to secondary fragmentations, which unfortunately we did not observe from trajectories which are too short to allow such further reactions. Based on the structure of the product ion we can suggest a H 2 O loss providing ion m/z 181.09 which is observed in experiments but not in trajectories. Ion m/z 185.07 observed in biotin corresponds to CH 3 COOH neutral loss and the same mechanism is reported for the other systems. As previously, the mechanism does not involve the S, O, NH or CH 2 isolobal modified groups and thus they are the same (in Scheme 3 we report for simplicity only the case of biotin).In the case of N-biotin the corresponding product ion C 5 H 8 N 3 O + (m/z 126.07) is formed with a different mechanism, where the hydrogen atom on the NH isolobal group is abstracted, as reported in Scheme 6. Other two mechanisms in common with biotin and oxybiotin (abstraction of H from the breaking C-C bond and from the other NH group) are also observed. For C-biotin the product ion C 6 H 9 N 2 O This product was observed in all simulations and with a very high intensity. It is the most abundant product in biotin, oxybiotin and Nbiotin, while it is not reported in experiments. The mechanism is reported in Scheme 8.

	of N-biotin (upper) and C-biotin (lower), respectively, as from CID simulations.
	C 4 H 7 N 2 OS + (m/z 131.03) and isolobal analog ions. The formation of m/z 131.03 in
	biotin involves the breaking of S-C bond, as reported in Scheme 7. The analog
	mechanism is found also in oxybiotin (ion C 4 H 7 N 2 O 2	+ , m/z 115.05), but not in N-biotin
	and C-biotin. The final product for biotin and oxybiotin contains SH and OH group,
	Scheme 2. Mechanism observed for the formation of m/z 199.09 as from CID simulations respectively. Together with the difference in C-X bond (X = S, O, N, C) this can be at the
	of biotin. Scheme 5. Mechanism observed for the formation of m/z 127.05 specific of oxybiotin as origin of the absence of this product ion in simulations of N-and C-biotin.
	from CID simulations.
	Differences in the reactivity of isolobal analogs for this and other products are minor since they concern ions for which we obtained only few reactive trajectories, so any conclusion is not statistically ground. They are reported for completeness in the C 8 H 13 N 2 OS + (m/z=185.07) and isolobal analog ions. Scheme 3. Mechanism observed for the formation of m/z 185.07 as from CID supporting information. Moreover, they are in a region of the spectrum which shows
	simulations of biotin. experimentally very low signals.
	C 5 H 7 N 2 OS + (m/z 143.02) and isolobal analog ions. The mechanism responsible for the C 3 H 5 N 2 O + (m/z 85.04) product ion.
	formation of these ions involve the isolobal moieties. They have in common the cleavage
	of C-C bond, but then a hydrogen atom is taken from a different site. The mechanisms
	observed in the case of biotin are reported in Scheme 4: hydrogen is released from one C
	atom of the broken C-C bond, from NH in the imidazolidinone ring or from the CH group
	in common between the two rings. Similar mechanisms are obtained for the oxybiotin
	Scheme 1. Mechanisms observed for the formation of m/z 277.08 as from CID simulations (product ion C 5 H 7 N 2 O 2 + , m/z 127.05), with the exception of this last mechanism which is
	of biotin. not observed, while a new one is. This corresponds to a proton transfer from the
	protonated carbonyl and it is reported in Scheme 5. For both biotin and oxybiotin the 07 specific

obtained in simulations of oxybiotin, N-biotin and C-biotin, respectively. The product ion corresponds to water loss with three possible mechanisms, shown in Scheme 1, where for simplicity we report only what was observed in biotin, the others being similar given the isolobal substitution. The water loss can be obtained from the two oxygen atoms, from carbonyl in the imidazolidinone ring or from the carboxylic tail. In the first case, the mechanism is rather complex, while for the latter the OH can pick a hydrogen from either the NH group of imidazolidinone or a vicinal CH. The last mechanism is the most abundant (about 67%) while the first two have lower abundance (12 and 21%, respectively). We should note that the product ion m/z 209.07, observed experimentally in biotin but not in simulations, corresponds to the subsequent water loss from the product ion m/z 227.08. Another ion, m/z 192.05 observed experimentally, but not in simulations, is likely coming from further ammonia loss from m/z 209.07. + (m/z 125.07) is also formed with a mechanism in which the hydrogen is taken from the isolobal modified group (see Scheme 6). These new mechanisms typical of N-and C-biotin cannot be observed by definition in biotin and oxybiotin, but, since the proton can be abstracted also from other sites, finally we do not observe any difference in the product ions. Scheme 6. Mechanism observed for the formation of m/z 126.07 and 125.Scheme 7. Mechanism observed for the formation of m/z 131.03 as from CID simulations of biotin.

S.Grimme. Accurate description of van der Waals complexes by density functional

ACKNOWLEDGMENTS

The authors dedicate this article to the memory of Prof. William (Bill) L. Hase. He inspired us for many years, and we had many fruitful collaborations and scientific discussions. He was a reference and a friend.


Abdul Malik

Laurence A Angel

Riccardo Spezia
email: riccardo.spezia@sorbonne-universite.fr

William L Hase

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

Chemical dynamics simulations are performed to study the collision induced gas phase unimolecular fragmentation of a model peptide with the sequence acetyl-His 1 -Cys 2 -Gly 3 -Pro 4 -Tyr 5 -His 6 -Cys 7 (analogue methanobactin peptide-5, amb 5 ) and in particular to explore the role of zinc binding on reactivity. Fragmentation pathways, their mechanisms, and collision energy transfer are discussed. The probability distributions of the pathways are compared with the results of the experimental IM-MS, MS/MS spectrum and previous thermal simulations. Collisional activation gives both statistical and non-statistical fragmentation pathways with nonstatistical shattering mechanisms accounting for a relevant percentage of reactive trajectories, becoming dominant at higher energies. The tetra-coordination of zinc changes qualitative and quantitative fragmentation, in particular the shattering. The collision energy threshold for the shattering mechanism was found to be 118.9 kcal/mol which is substantially higher than the statistical Arrhenius activation barrier of 35.8 kcal/mol identified previously during thermal simulations. This difference can be attributed to the tetra-coordinated zinc complex that hinders the availability of the sidechains to undergo direct collision with the Ar projectile.

Introduction

Zinc plays an important role in biological systems 1 where it can either aid in catalysis or provide structural support to maintain the protein conformation. 2 These functions are performed by incorporating zinc as a cofactor into proteins or peptides usually via thiolate groups of cysteine and the imidazole groups of histidine in a distorted tetrahedral coordination geometry. [3][4][5][6][7] For example, matrix metalloproteinases are zinc-dependent enzymes that catalyze the hydrolysis of structural proteins in the extracellular matrix 8 and their inhibition has been investigated for slowing the progression of cancers. 9 The eukaryotic zinc finger proteins have conformations that are specific for binding to DNA 10,11 and the zinc ion is most commonly tetrahedrally coordinated via 2Cys-2His. 2,[11][12][13] Ion mobility -mass spectrometry (IM-MS) 6,14,15 with molecular modelling and novel ion activation methods can be used to determine the accurate structure of these zinc containing metallopeptides. Previous studies of methanobactin 16,17 from Methylosinus trichosporium and analogue methanobactin (amb) peptides 6,14,15,[18][19][20][21] show the IM-MS analyses in negative ion mode is particularly informative because it shows a distinct pH dependence for the metal binding and provides the protonation state of the acidic and basic binding sites, the charge of the metal ion, and the collision cross section of the conformer. The primary structures of the amb peptides include Pro as a hinge to position the His and Cys substituent groups for coordinating the metal ion (Figure 1).

After decades of development, collisional activation is still one of the most popular activation methods and is routinely used in peptide science. 22 Collision induced dissociation (CID) involves energetic collisions between ions and neutral gas atoms which result in the transfer of translational energy to the internal energy of the ion. 23 This excess ro-vibrational energy causes dissociation of the precursor ion and generates product ions which are mass analyzed (the so-called MS/MS).

Theoretical mass spectrometry, in the form of direct dynamics simulations, 24,25 combined with experimental IM-MS and MS/MS can be used to obtain atomistic level information about biomolecules. The dissociation pathways and products found through experimental and theoretical studies can be used to illuminate the main fragmentation features of the peptides. Due to their high efficiency, collisional activation methods are routinely used in most of the tandem mass spectrometry instruments (ion traps, Fourier-transform ion cyclotron resonance, quadrupole time-of-flight, etc.). [26][27][28][29] There are certain details in the CID fragmentation mechanisms that are still of interest including the role of the side chains, [30][31][32][33][34] or the effect of the collisional activation mode on the fragmentation products. 35 Theoretical simulations can be used to answer these queries. 25,36,37 There are two main activation methods employed in chemical dynamics simulations of biomolecules. One involves thermal (internal energy) excitation to reflect multiple collisions and the other is the single collision excitation with an inert gas molecule. 24,25 In experimental MS/MS spectra, product ions due to both statistical and non-statistical mechanisms appear but their ratio depends on the experimental conditions. 38 For example, fragmentation occurring in tandem mass spectrometers and extrapolated to the single collision CID can provide reaction cross sections as a function center-of-mass collision energy. 39 Simulations of single collision CID can be useful to understand fragmentation mechanisms of peptides. 22,37,40 For the fragment dissociation of large molecules, efficient energy transfer during the collision is required. 41 Similarly to what was recognized by the previous studies on surface-induced dissociation (SID) [42][43][44][45][46][47] the dynamics for the ions excited by this CID mode experience key differences with respect to randomized unimolecular fragmentation, 45 which relies on the well-known Rice-Ramsperger-Kassel-Marcus (RRKM) theory. [START_REF] Baer | Unimolecular Reaction Dynamics. Theory and Experiments[END_REF] This theory is based on statistical assumption requiring that translation to vibration energy transfer during the collision occurs within intramolecular vibrational energy redistribution (IVR). For these non-random dynamics, the decay of the initial population will be non-exponential, as recently shown in the case of di-proline anion CID simulations. 38 One relevant nonstatistical mechanism observed in CID is the so-called shattering: [START_REF] Spezia | [END_REF]50 the collision activates one (or more) vibrational mode(s), leading to fragmentation within one vibrational period of the bond which breaks. Shattering fragmentation during CID has been observed in previous chemical dynamics simulations and experiments for protonated urea, [START_REF] Spezia | [END_REF]51 protonated uracil, 52,53 CH 3 SH + , 54,55 and Cr + (CO) 6 56 and more recently in polypeptides. [36][37][38]57,58 To have a better estimate of the expected ions from an excitation method during experimental mass spectrometry, it is important to compare fragmentation pathways and product ions for different excitation methods using direct dynamics simulations.

Direct chemical dynamics simulations [START_REF] Bolton | Modern Methods for Multidimensional Dynamics Computations in Chemistry[END_REF][START_REF] Sun | Reviews in Computational Chemistry[END_REF] were recently [START_REF] Malik | [END_REF] used to analyse fragmentation of thermally excited [amb 5 -3H+Zn(II)] -and can be now used to study non-random CID fragmentation as has been used in the past to analyse e.g. protonated poly-glycines, 57,58 and a diproline anion 38 and TIK(H + ) 2 . 36,37 During thermal excitation, [START_REF] Malik | [END_REF] [amb 5 -3H+Zn(II)] -ion was excited at temperatures ranging from 1600 to 2250 K and the energy was randomly distributed in the vibrational modes of the ion. The kinetic analysis showed that fragmentation probability of [amb 5 -3H+Zn(II)] -follows RRKM theory. Out of the three lowest energy conformers of [amb 5 -3H+Zn(II)] -, that were thermally excited in ref. 51, chemical dynamics simulations are here performed on conformer a (structure shown in Figure 1) since its fragmentation pattern most closely matched with the experiment. We now investigate how the same peptide will fragment under explicit collision simulations with Ar. In this case, the ion will be excited nonrandomly and the site of collision will have a major impact on fragmentation dynamics. Differently to peptides studied previously via CID, the one reported here is the first presenting a tetracoordination binding to a transition metal. This could result in substantial differences. To have a more detailed picture of the effects of explicit collision, we compared the results reported here with those obtained in the previously reported study under thermal excitation conditions. 61

Computational Methodology

Electronic Structure Theory. Previous simulations [START_REF] Malik | [END_REF] of the thermal fragmentation of [amb 5 -3H+Zn(II)] -used PM7, 62 semi-empirical electronic structure theory method. In this same previous work, the PM7 method was shown to be able to correctly describe the reactivity of this system. We have thus employed PM7 in the present work. Here, PM7 was used also to describe the interaction between the peptide and Ar atom. With respect to previous semi-empirical Hamiltonians of the same family, PM7 implicitly addresses dispersion by including non-covalent systems in the training set during the parameterization and is thus able to describe also Ar, for which parameters are reported in the litteraure. 62 As initial structure of the ion for subsequent collisional dynamics simulation, we used the lowest energy structure of the peptide found previously, [START_REF] Malik | [END_REF] notably conformer a.

Direct Dynamics Simulations.

[amb 5 -3H+Zn(II)] -collisional direct dynamics simulations were performed with a VENUS/MOPAC software package which consists of an interface between the VENUS 63 chemical dynamics computer program and the MOPAC 64 electronic structure theory computer program.

Quasi-classical initial conditions 65 were selected for the ion, with its initial vibrational energies chosen from 300 K normal mode Boltzmann distribution. For rotational energy, a classical Boltzmann sampling at 300K was used. To set the collisional system (ion + Ar), the ion was randomly rotated about its Euler angles. The initial distance between the ion and Ar was set at 15 Å, in order to have no initial interaction between the ion and the neutral projectile. The impact parameter was randomly chosen between 0 to 9.5 Å. This maximum value was chosen on geometrical consideration: the maximum radius of the ion is about 8.8 Å and thus at 9.5 Å no noticeable interactions occur. Collisional simulations were performed for relative translational energies (E rel ) of 10.8, 13.0, 26.0 and 39.0 eV between Ar and [amb 5 -3H+Zn(II)] -. These values were chosen in order to have increasing fragmentation yields. In fact, 10.8 eV is the lowest energy for which 1. Fragmentation pathways, probabilities of total reactive trajectories, and probability that the pathway followed a shattering mechanism for E rel = 10.8, 13, 26, and 39 eV. In parentheses is the probability that the pathway followed a shattering mechanism.

a The percentage probability of this pathway against the total reactive trajectories. b Percentage probability of all the other pathways with respect to the reactive trajectories. The uncertainties are the standard deviations of the percentages. some fragmentation is observed. The higher collision energies are chosen to get a clear energy dependent picture of shattering as well as non-shattering mechanisms. Once a fragmentation occurs, Mulliken population analysis was performed on the atoms of the system at the final geometry and charge localized on one fragment. The total spin of the system was conserved (and singlet) in all calculations. Finally, a trajectory is considered as shattering if the fragmentation occurs in less than 40 fs after the collision, which is an arbitrary limit assuming that the bond dissociation occurs within this time period before IVR could take place. (similar time limit was used in a previous study 37 ). 2000 trajectories were run each for 10.8 and 13 eV, and 1000 trajectories each for 26 and 39 eV. For all the collision energies, trajectories were integrated up to 20 ps.

Simulation Results

Primary Dissociation Pathways. The dissociation dynamics of [amb 5 -3H+Zn(II)] -subsequent to collision with Ar projectile are discussed here in detail. In particular, we first report in Table 1 the probabilities (as percentage over the total reactive trajectories) of the most abundant primary dissociation pathways (23), specifying if the fragmentation occurs on the backbone or the sidechain. The nomenclature 66 used previously [START_REF] Malik | [END_REF] to represent peptide fragments in mass spectrometry is employed here and is shown in Figure 2 for analogue methanobactin peptide-5, amb 5 . In Table 1 (in parentheses) the probability that the pathway follows a shattering mechanism is also specified. Pathways 1-20 are shown in the supporting information in Figure S1. Pathways For simulations at higher collision energies (26 and 39 eV) there are 69±5 % and 85±6 % shattering pathways, respectively. The shattering percentage is less than that for similar collision energies of TIK(H + ) 2 36,37 mainly because of the unavailability of the sidechains due to the tetra-coordinated zinc complex. Both thiol groups of cysteine and imidazole groups of histidine are bonded to zinc: they are less exposed to projectile and more importantly, if the collision breaks the bond with zinc, this does not always lead to a fragmentation. Since thiol side chains are bound to the zinc, the percentage of overall reactive as well as shattering trajectories is lowered with respect to a free peptide. Loss of the sidechain of the Tyr residue which is not bound to zinc (corresponding to pathway 11) is on the other hand observed for collision energies of 13 eV and higher almost exclusively as a result of a shattering mechanism. Product ion [y 5 +Zn(II)] -with m/z 636.1, labelled pathway 12, was observed at 10.8, 13, and 39 eV. Pathway 13 was the loss of terminal methyl group which was observed for three higher energies exclusively due to shattering. Pathway 14, due to the loss of SCH 2 , was observed at 13, 26, and 39 eV almost exclusively because of shattering. Product ion [b 3 +x 3 +Zn(II)] -with m/z 849.1, pathway 15, was found at 13, 26, and 39 eV. Pathway 16 involved a proton transfer from terminal carboxyl group to thiol group of Cys 7 followed by the loss of HS radical to generate product ion with m/z 885.2. Pathway 17 gave [a 6 +Zn(II)] -ion with m/z 771.2 and was observed at 13, 26, and 39 eV. Loss of CO+COOH with m/z 845.2, shown as pathway 18 in Figure S1, was observed at 13, and 39 eV. Pathway 19 for product ion m/z 889.2 was observed due to the loss of CH 2 NH at 26 and 39 eV. Pathway 20 (product ion m/z 840.2 for the loss of (H 2 S+CO 2 )) is observed for collision energies of 10.8 and 13 eV. The same m/z 840.2 is also observed due to the loss of (SCO+H 2 O) at 10.8 eV but is not shown here.

In the CID of amino acids and peptides, the loss of (CO+H 2 O), CO 2 H 2 , CO, and the iminium ion [CH 2 =NH 2 ] + are a few of the most common fragmentation pathways. [67][68][69][70][71][72][73] All of these pathways were observed here at one or more collision energies. The loss of CO 2 H 2 , shown in Scheme 1, was observed at E rel = 13 eV: the carboxyl group at the C-terminus picks the proton on the phenol of Tyr and then the C-C bond dissociation occurs. The loss of (CO+H 2 O) was found for E rel = 13 eV. Loss of CO, pathway 4 in Figure S1, is one of the most common pathways for each E rel . The loss of the iminium ion is shown as pathway 19.

Scheme 1. Schematic diagram of formation of CO 2 H 2 .

Effect of Impact Parameter on Fragmentations. A previous study 36 has shown that in collision dynamics it is important to correctly set the maximum value of the randomly chosen impact parameter (b max ). In particular this is crucial when investigating the shattering mechanisms, since one should obtain both backbone and sidechain shattering. A very small b max would disproportionately give more backbone shattering and a very large b max would result in many nonreactive trajectories, with insufficient internal energy transfer, increasing the computational cost. Figure 3 shows the distributions of impact parameters versus the number of shattering trajectories for the collision dynamics simulations at E rel = 13 eV. Shattering Fragmentations. As shown in Figure 4, the percentage of shattering fragmentation increases with increase in E rel : from 36 ± 1 % to 85 ± 6 % when the energy increases from 10.8 to 39 eV. It is thus interesting to follow how the localization of fragmentations behaving with a shattering mechanism changes as a function of collision energy. Table 2 shows the percentage of backbone and sidechain fragmentation out of total reactive trajectories as well as the percentage of the shattering fragmentation mechanisms. Note that reactive trajectories resulting in loss of H or H 2 (which occur with a shattering mechanism) are not considered and thus the sum of backbone plus sidechain is not 100%. Similar to a previous study, 36 backbone fragmentation is more important at lower energies, in fact it goes down from 84% at 10.8 eV to 58% at 39 eV whereas sidechain fragmentation hovers around 20% for 13-39 eV and is only 11% for 10.8 eV. Percentage of backbone shattering trajectories goes from 64% to 74% when energy is increased from 10.8 to 13 eV but goes down to 49% and 52% for 26 and 39 eV primarily due to the fact that these percentages do not include the fragmentation due to the loss of H atom or H 2 molecule both of which are exclusively due to shattering. The loss of H and H 2 comprise 5%, 10%, 18% and 21% of total reactive trajectories for energies of 10.8, 13, 26, and 39 eV, respectively. simulations can also provide the energy transferred to the internal energy of the ion. Figure S2 shows the distribution of change in internal energies in kcal/mol versus the number of trajectories for all the collision energies. Table 3 lists the summarized properties of the energy transfer to the internal energy of [amb 5 -3H+Zn(II)] -at different collision energies. In each case, the average energy for the reactive trajectories (<E> react ) is way higher than that of non-reactive trajectories (<E> non-react ). We can obtain, for each E rel , the minimum energy value for which a fragmentation is observed, E min (Table 3). We can thus define P(E > E min ) as the percentage of non-reactive trajectories with transferred energy greater than E min . The high values of P(E > E min ), which varies from 27-36% for different E rel , and minimum fragmentation energies is also due to the fact that the nonreactive trajectories include those that undergo a proton transfer or one or more bond dissociations without generating two or more fragments.

Energy Transfer. In addition to providing information about the fragmentation products and mechanisms, collision activated

Table 3. Summarized energy transfer properties for CID of [amb 5 -3H+Zn(II)]

-a a E rel is in eV and all the other energies in kcal/mol. <E> react is the average energy transferred for reactive trajectories. <E> non-react is the average transferred energy for non-reactive trajectories. E min is the minimum energy required to undergo dissociation. P(E > E min ) is the percentage of non-reactive trajectories with internal energy transfer greater than E min . <E> shattering is the average transferred energy for shattering trajectories. 𝐸 "#$%%&'()* +() is the minimum energy required for shattering. The reported uncertainties are one standard deviation In our previous work, [START_REF] Malik | [END_REF] Arrhenius activation energies were calculated from direct dynamics simulations of thermally excited [amb 5 -3H+Zn(II)] -. Following the statistical redistribution of the ion's vibrational energy and RRKM unimolecular kinetics, the minimum activation energy was found to be 35.8 kcal/mol for pathway 1. From the analysis of non-shattering trajectories, we found a minimum value which is substantially higher, notably: 115.4 kcal/mol. In CID, nonshattering trajectories should follow statistical fragmentation when they are run for longer times. Here, the trajectories were integrated for a short time of 20ps, hence, non-shattering trajectories do not correspond to the thermal statistical limit of 35.8 kcal/mol. In other words, non-reactive trajectories with energy transferred less than 115.4 kcal/mol during CID may react if they are run on longer time scales, which is computationally unaffordable for [amb 5 -3H+Zn(II)] -. On the other hand, our simulation time is long enough for an accurate study of shattering trajectories.

The minimum energy threshold for shattering of [amb 5 -3H+Zn(II)] - is 118.9 kcal/mol, as also reported in Table 3. Since sidechains of cysteine and histidine are bound to Zn(II), when they break right after collision with Ar, this will not lead to a direct fragmentation. This reduces considerably the shattering probability and increases the shattering threshold. The nature of the complex also reduces the number of hydrogen atoms exposed to the projectile. The unavailability of the side chains is probably another reason that no reactive trajectories were observed at collision energies lower than 10.8 eV.

The shattering threshold of 118.9 kcal/mol is substantially higher than the lowest threshold of 35.8 kcal/mol obtained during the thermal dissociation [START_REF] Malik | [END_REF] of [amb 5 -3H+Zn(II)] -. It reaffirms the previous finding 37 that due to the higher energies required for shattering as compared to the statistical fragmentation, the former may not play a big role in determining fragmentation products in threshold-CID experiments.

Thermal versus CID Fragmentation of [amb 5 -3H+Zn(II)]

-. In this section, the relevant fragment ions for collisional and thermal simulations are compared. In previous studies 36,38 it has been discussed that both statistical (thermal fragmentation) and nonstatistical (single collision simulations) mechanisms contribute to the peaks observed in an experimental mass spectrum. All dissociations in thermal excitation simulations are by definition non-shattering whereas in CID simulations both shattering and non-shattering fragmentation can occur.

Table 4 reports the results for the most abundant product ions obtained in thermal simulations to be compared with collisional simulation results summarized in Table 1. In particular, for collisional simulations we discuss the percentages of shattering vs non-shattering mechanisms from Table 1 for E rel = 10.8 and 13 eV. Here we describe in detail the different behaviours.

The ion [x 6 +Zn(II)] -, m/z 766.1 corresponding to pathway 1 in Figure S1, was one of the most abundant ions for thermal excitation and it was also found for all the E rel during CID simulations.

Fragmentation Ions Unique of CID Simulations and Experiments.

Detailed comparison between the results of thermal simulations of three conformers of [amb 5 -3H+Zn(II)] -and the experiment 6 has been performed in a previous work [START_REF] Malik | [END_REF] and a comparison of thermal and CID simulation results has been performed in previous section. Here, we discuss only two product ions which are unique in collisional simulations with respect to experiments (as in Ref 51), namely m/z 885.2 and 840.2. Ion m/z 885.2 (pathway 16) corresponded to the loss of SH radical and was observed for collision energies 13 eV and higher. The experiment found m/z 884.2 corresponding to the loss of H 2 S molecule. This pathway was not observed in simulations, probably because one needed a second H-transfer to sulfur atom, not observed in simulation time. In simulations, loss of H 2 S is observed only with loss of a second neutral, CO 2 . This led to ion m/z 840.2 which was the second product ion observed in collisional simulations and not in thermal ones. This ion was observed in experiments and attributed to CO 2 + H 2 S or SCO + H 2 O loss. Interestingly, both these mechanisms were observed for CID simulations: at 13 eV we observed loss of CO 2 + H 2 S, while at 10.8 eV loss of SCO + H 2 O. This supported the experiment that both neutral losses are possible.

Conclusions

In this article, we report chemical dynamics simulations of collisions between a Zn(II) containing oligopeptide (acetyl-His 1 -Cys 2 -Gly 3 -Pro 4 -Tyr 5 -His 6 -Cys 7 labelled here [amb 5 -3H+Zn(II)] -) and Ar atom at different energies. From simulations, we obtained and studied in detail the fragmentation products and their corresponding mechanisms. The results are compared with previous thermal simulations [START_REF] Malik | [END_REF] as well as multiple collision ion mobility MS/MS experimental spectrum. 6 The collisional simulations are able to provide details on the first pico-seconds subsequent to the collision with Ar.

The collisional and thermal simulations show similar product ions with differences in some abundances and mechanisms. This is due to the fact that in collision induced dissociation there is both statistical and non-statistical fragmentation as compared to only statistical dissociation in thermal excitation. In particular, we have analysed carefully the so-called shattering fragmentations, which are characteristic examples of non-statistical fragmentation and which can occur in CID simulations and not in thermal ones by definition.

From the energy transfer analysis, we obtained that the minimum energy required to undergo shattering is 118.9 kcal/mol which is substantially higher than the Arrhenius activation barrier of 35.8 kcal/mol found using direct dynamics of statistical thermal fragmentations. [START_REF] Malik | [END_REF] Note that in a previous work on a linear peptide we have also found that the shattering threshold is higher than the Arrhenius barrier (55 vs 15 kcal/mol, respectively). Remarkably, the shattering threshold is in both cases about three times higher than Arrhenius activation energy.

The tetrahedral nature of the zinc complex determines the fragmentation mechanisms of CID simulations. The unavailability of sidechains of both cysteine and histidine due to covalent bonding with Zn(II), results in higher collision energy needed for fragmentation and increased internal energy transfer to undergo either backbone or sidechain dissociation with respect to what observed in similar free peptides. 36,37,55,74 Note that, in most of the pathways, due to the tetracoordinated Zn(II) complex, two or more bonds must be broken to generate fragments. When Ar atom hits on cysteine or histidine sidechains it can break a bond but without any resulting fragment. To obtain a fragment a second bond must be broken, which can happen after that the energy flows through the molecule. This by definition does no correspond anymore to a shattering mechanism. The nature of the complex also reduces the number of hydrogen atoms exposed to the projectile making them less susceptible to undergo shattering.

For these reasons there are no reactive trajectories below E rel = 10.8 eV and the minimum energy required for shattering is 118.9 kcal/mol. Furthermore, the threshold for non-shattering fragmentations is also high (115.4 kcal/mol, only 3.5 kcal/mol lower than the shattering one). This can be due to the limited simulation time not allowing for enough efficient intramolecular vibrational energy redistribution. For this reason, thermal simulations provide a more accurate description of statistical fragmentations, which is complementary to the present one.

In conclusion, the tetra-coordinated nature of the zinc complex guides the CID simulations. Since the sidechains of both cysteine and histidine are covalently bound to zinc, they are not readily available to dissociate. This not only results in higher collision energy required to achieve fragmentation but also increases the internal energy transferred to have either backbone or sidechain dissociations. The tetra-coordinated complex also implies that not every bond dissociation ends up in fragmentation with most of the pathways reported requiring at least two or more bonds to be broken to generate fragments.

Figure 1 .

 1 Figure 1. Schematic diagram of conformer a of [amb 5 -3H+Zn(II)] - and 3D structure of its optimized geometry. grey, Zn; yellow, S; cyan; C, blue, N; red, O; white, H.

Figure 3 .

 3 Figure 3. Distribution of impact parameter trajectories resulting in the shattering fragmentation of total, sidechain, and backbone [amb 5 -3H+Zn(II)] -at 13 eV collision energy. The figure shows the distributions for shattering (total, backbone and sidechain, where sidechain includes the H and H 2 loss). Table 1 lists the dissociation sites for the most important pathways. The probability of total shattering increases with b in the 2-5 Å range, while it decreases for b between 6-8 Å. Notably, only sidechain shattering is observed for b > 7 Å and the maximum b at which backbone shattering occurs is 7 Å. The average b for total, backbone, and sidechain shattering trajectories is 3.9, 3.8, and 4.3 Å, respectively. This result

Figure 4 .

 4 Figure 4. Percentage of shattering trajectories with respect to the total reactive trajectories versus relative translational energy (eV). The error bars show one standard deviation.

  21-23 correspond to the loss of H, H 2 , and OH.As expected, the number of open pathways increases as the collision energy increases: they are 22, 59, 60 and 63 for 10.8, 13, 26 and 39 eV collision energy, respectively. Also, the percentage of the reactive trajectories increases with the collision energy: there are 6.2, 12.8, 20.9, and 23.3 percent reactive trajectories for E rel of 10.8, 13, 26, and 39 eV, respectively. Some trajectories involve a H atom transfer Probability a for E rel (eV) Primary structure of amb 5 without Zn(II) and abbreviation used to characterize the fragments.66 following a bond dissociation; however, the tetra-coordinated nature of the zinc complex implies that a single bond dissociation may not result in formation of two or more fragments. Such trajectories are characterized as non-reactive, at least in the time-length available from our simulations. For example, for E rel = 13 eV 2.2 % of the total trajectories resulted in a H atom transfer that did not lead to fragmentation. H atoms most susceptible to be transferred are the ones bonded to either oxygen or nitrogen and they are most likely to be transferred to either of the thiol groups following the breaking of Zn-S bond. -, was observed only for collision energies of 10.8, 13 and 26 eV. Pathway 6 with product ion m/z 821.2 for [a 3 +x 3 +Zn(II)] -was found for all four collision energies. Pathway 7 for the loss of terminal acetyl group occurred at all energies and mostly due to shattering at 13, 26, and 39 eV. Pathway 8 with product ion m/z 860.2 for the loss of terminal amide group was observed mostly as a result of shattering for 10.8, 13, and 26 eV. Pathway 9 with product ion m/z 738.1 for [y 6 +Zn(II)] -was observed for all four E rel . Pathway 10 involved multiple bond dissociations to generate [x 5 +S+Zn(II)] -with m/z 696.1. It was found for energies of 10.8, 13, and 26 eV.

	Pathway	m/z	Dissociation Site	10.8	13	26	39
	1	766.1	Backbone	21.0 ± 5.2 (7.7 ± 5.7)	7.6 ± 1.8 (37.5 ± 4.3)	6.7 ± 1.9 (41.7 ± 4.4)	4.7 ± 1.4 (63.6 ± 3.4)
	2	873.2	Backbone	12.9 ± 4.3 (37.5 ± 10.3) 5.7 ± 1.6 (58.3 ± 4.4)	4.5 ± 1.6 (75.0 ± 3.9)	4.7 ± 1.4 (54.5 ± 3.7)
	3	837.2	Sidechain	6.5 ± 3.1 (75.0 ± 9.2)	3.3 ± 1.2 (57.1 ± 4.4)	5.1 ± 1.6 (77.8 ± 3.7)	5.2 ± 1.4 (100.0)
	4	890.2	Backbone	8.1 ± 3.5 (40.0 ± 10.4)	6.6 ± 1.7 (78.6 ± 3.7)	6.2 ± 1.8 (90.9 ± 2.6)	4.3 ± 1.3 (90.0 ± 2.1)
	5	723.1	Backbone	6.5 ± 3.1 (50.0 ± 10.7)	0.9 ± 0.7 (50.0 ± 4.5)	4.5 ± 1.6 (75.0 ± 3.9)	-
	6	821.2	Backbone	3.2 ± 2.2 (0.0)	2.4 ± 1.0 (20.0 ± 3.6)	1.7 ± 1.0 (0.0)	3.4 ± 1.2 (87.5 ± 2.4)
	7	875.2	Backbone	3.2 ± 2.2 (0.0)	3.3 ± 1.2 (42.9 ± 4.4)	4.5 ± 1.6 (75.0 ± 3.9)	5.2 ± 1.4 (91.7 ± 2.0)
	8	860.2	Backbone Figure 2.	3.2 ± 2.2 (50.0 ± 10.7)	4.7 ± 1.5 (90.0 ± 2.7)	1.1 ± 0.8 (100.0)	-
	9	738.1	Backbone	1.6 ± 1.6 (100.0)	1.4 ± 0.8 (33.3 ± 4.2)	2.8 ± 1.2 (40.0 ± 4.4)	3.0 ± 1.1 (85.7 ± 2.5)
	10	696.1	Backbone	3.2 ± 2.2 (0.0)	3.3 ± 1.2 (28.6 ± 4.1)	1.1 ± 0.8 (0.0)	-
	11	811.2	Sidechain	-	6.2 ± 1.7 (84.6 ± 3.2)	2.2 ± 1.1 (100.0)	3.0 ± 1.1 (85.7 ± 2.5)
	12	636.1	Backbone	1.6 ± 1.6 (0.0)	0.5 ± 0.5 (0.0)	-	0.4 ± 0.4 (100.0)
	13	903.2	Backbone	-	5.2 ± 1.5 (100.0)	3.4 ± 1.4 (100.0)	1.3 ± 0.7 (100.0)
	14	872.2	Sidechain	-	1.9 ± 0.9 (100.0)	1.7 ± 1.0 (66.7 ± 4.3)	0.9 ± 0.6 (100.0)
	15	849.1	Backbone	-	0.5 ± 0.5 (0.0)	1.1 ± 0.8 (0.0)	1.3 ± 0.7 (100.0)
	16	885.2	Sidechain	-	0.5 ± 0.5 (0.0)	0.6 ± 0.6 (0.0)	0.4 ± 0.4 (0.0)
	17	771.2	Backbone	-	1.4 ± 0.8 (66.7 ± 4.2)	0.6 ± 0.6 (0.0)	2.6 ± 1.0 (66.7 ± 3.4)
	18	845.2	Backbone	-	1.9 ± 0.9 (25.0 ± 3.9)	-	0.9 ± 0.6 (50.0 ± 3.6)
	19	889.2	Sidechain		1.4 ± 0.8 (33.3 ± 4.2)	0.6 ± 0.6 (100.0)	0.4 ± 0.4 (100.0)
	20	840.2	Backbone	1.6 ± 1.6 (0.0)	1.4 ± 0.8 (0.0)	-	-
	21	917.2	H atom	3.2 ± 2.2 (100.0)	8.1 ± 1.9 (100.0)	14.6 ± 2.6 (100.0)	15.9 ± 2.4 (100.0)
	22	916.2	H 2 molecule	1.6 ± 1.6 (100.0)	1.9 ± 0.9 (100.0)	3.4 ± 1.4 (100.0)	4.7 ± 1.4 (100.0)
	23	901.2	Sidechain	3.2 ± 2.2 (0.0)	1.9 ± 0.9 (100.0)	3.4 ± 1.4 (100.0)	-
	Other			21.0 ± 5.2 (30.8 ± 9.8)	27.0 ± 3.1 (42.4 ±	30.3 ± 3.4 (51.9 ±	38.2 ± 3.2 (80.9 ±
					4.4)	4.5)	2.8)

Pathway 1 resulting in m/z 766.1 product ion for [x 6 +Zn(II)] -was the most frequent pathway for E rel = 10.8 eV (lowest collision energy considered) and the second most abundant following pathway 21, which was the loss of H atom, at all three higher collision energies. Pathway 2 with product ion m/z 873.2 was observed due to the loss of terminal COOH molecule, at four collision energies, which also had a coincidental mass loss with two other distinct fragmentation mechanisms. For example, at E rel = 10.8, 13, and 26 eV it was found for the loss of (CO 2 +H) and at 13 eV the loss of (CO+OH) gave the same m/z final ion product. Pathway 3 with m/z 837.2 for product ion with the loss of (CH 2 +imi) was observed at all four collision energies almost exclusively due to shattering. Pathway 4, m/z 890.2 for the loss of CO molecule, was seen for all E rel . Pathway 5, resulting in product ion m/z 723.1 for the fragment [z 6 +Zn(II)]

Table 2 . Percentages of backbone and sidechain dissociation and shattering fragmentation

 2 Percentage of backbone and sidechain fragmentation out of the total reactive trajectories. b Percentage of total reactive trajectories that are shattering excluding hydrogen atom/molecule loss. The standard deviation of the percentage is also provided.

		% fragmentation a	% shattering b
	E rel (eV) Backbone Sidechain	Backbone	Sidechain
	10.8	84 ± 3	11 ± 2	64 ± 1	23 ± 2
	13	71 ± 4	19 ± 4	74 ± 3	23 ± 3
	26	60 ± 3	22 ± 2	49 ± 3	25 ± 2
	39	58 ± 3	21 ± 4	52 ± 3	24 ± 4

a

Table 4 . Relative abundances of dominant fragment ions for thermal simulations.

 4 13 eV collision energies. Pathway 6 (ion m/z 821.2 with fragment [a 3 +x 3 +Zn(II)] -) happened mostly due to non-shattering mechanism and it is also observed at four temperatures in thermal simulations. Ion with m/z 875.2 could refer to the loss of either one of CONH molecule or COCH 3 . Here, as shown in pathway 7, it corresponded to the loss of COCH 3 molecule. It was found for the four higher temperatures and all the collision energies and happened mostly due to non-shattering in CID simulations.

	It was not

-.

Acknowledgments

The research at Texas Tech University (TTU) was supported by the Robert A. Welch Foundation under Grant No. D-0005. The research at Texas A&M-Commerce was supported by the National Science Foundation under grant 1764436, and the Welch Foundation (T-0014). The simulations were performed with the computer clusters Chemdynm of the Hase Research Group and Quanah of the TTU High Performance Computing Center. The authors would like to dedicate this work to the memory of Prof. W.L. Hase, who passed away too soon few days before the submission of this work.

Conflicts of interest

Authors declare no conflict of interest in this work.