Muscle biopsies were obtained from the vastus lateralis muscle. Three populations of muscle fibres were identified according to their specific Sr2+-activation properties: slow-twitch (type I), fast-twitch (type II) and hybrid (type I/II) fibres. All three fibre types were sampled from the biopsies of 66 to 72 years old women, but the muscle biopsies of women older than 80 years yielded only slow-twitch (type I) fibres. The proportion of hybrid fibres in the vastus lateralis muscle of women of circa 70 years of age (24%) was several-fold greater than in the same muscle of adults (< 10%), suggesting that muscle remodelling occurs around this age. There were no differences between the Ca2+- and Sr2+-activation properties of slow-twitch fibres from the two groups of elderly women, but there were differences compared with muscle fibres from young adults with respect to sensitivity to Ca2+, steepness of the activation curves, and characteristics of the fibre-type dependent phenomenon of spontaneous oscillatory contractions (SPOC) (or force oscillations) occurring at submaximal levels of activation. The maximal Ca2+ activated specific force from all the fibres collected from the seven old women use in the present study was significantly lower by 20% than in the same muscle of adults. Taken together these results show there are qualitative and quantitative changes in the activation properties of the contractile apparatus of muscle fibres from the vastus lateralis muscle of women with advancing age, and that these changes need to be considered when explaining observed changes in women’s mobility with aging.The single freshly skinned muscle fibre technique was used to investigate Ca There have been a large number of reports of a loss of skeletal muscle mass and force generation capacity as a result of the aging process —and strontium (Sr2+)—activation properties of freshly dissected single skeletal muscle fibres from elderly women (60–90 years) using the skinned muscle fibre technique. Strontium (Sr2+) was also used as an activator because it allows unequivocal differentiation between type I, type II and hybrid (type I/type II) fibres  isoform  expressed in the respective fibre, which in turn, is tightly correlated with the myosin heavy chain (MHC) expressed (MHCI or MHCII) in the fibre . We split the data obtained from the 28 freshly dissected muscle fibres into two age bins; (1) a circa 70 year old age group which contained five women 66–70 years of age (mean 69.80 ± 1.11 years), in this group the statistics were performed on 16 fibres and (2) a ≥ 80 year age group (mean 85 ± 5 years) containing two women, in this group the statistics were performed on 12 fibres. Each fibre segment was carefully dissected from the muscle biopsy under oil by an experienced operator under a high-powered dissection microscope (magnification × 40–100), fibres were only selected if they were free from any visual imperfections and were supple and flexible, any fibres with signs of mechanical damage from the surgery or were fragile and showed signs of damage when manipulated between the fine jewellers forceps were discarded.Single muscle fibres were dissected from fresh muscle biopsies obtained from elderly women undergoing orthopaedic surgery for total hip replacement or repair of a fractured neck of femur. Each woman's activity profile was obtained from interview and medical records data prior to the scheduled surgery. Care was taken to select only women with an active lifestyle prior to surgery.The muscle sample was dissected by an orthopaedic surgeon from the vastus lateralis muscle in elderly women undergoing orthopaedic surgery. The muscle biopsy was obtained within 5–15 min of the commencement of the surgery. The muscle biopsy was blotted thoroughly on Whatman's filter paper (No. 1) immediately upon its dissection from the vastus lateralis muscle to remove any excess interstitial fluid, then placed in a jar of cold paraffin oil at 2 °C. The muscle biopsy was then placed in a thermos flask containing ice and transferred immediately to the laboratory.2+ activated specific forces than fibres obtained from biopsies stored at − 20° for days or weeks.The dissection of the muscle fibres from the muscle biopsy was generally commenced within 60 min of its removal from the vastus lateralis muscle. The muscle biopsy was transferred from the cold paraffin into a Petri dish containing cold paraffin. Lynch et al.  showed tThe length of the fibre was adjusted such that the preparation was just taut, and the diameter of the skinned muscle fibres was measured under oil. The sarcomere length (SL) of the skinned muscle fibres was then measured by laser diffraction  and Ca-EGTA-containing solution (solution B). The strongly buffered Sr2+ solutions of different free [Sr2+] were prepared by mixing specific proportions of EGTA-containing solutions (solution A) and Sr-EGTA-containing solution (solution C). It was important that solution B did not have excess total Ca compared with EGTA to ensure that the pH did not change when solution A was mixed with solution B. An excess Ca compared with EGTA in solution B inevitably causes a decrease in the pH of a mixture of solution A and solution B because the excess Ca coming from solution B will bind to EGTA coming from solution A, releasing two protons for each Ca that becomes bound to EGTA in the mixed solution. A change in pH must be avoided when mixing two EGTA containing solutions because the ionised [Ca2+] is very sensitive to pH. Note that solution C contained 40 mM total Sr and 50 mM EGTA to ensure that the concentration of ionised Sr2+ was < 0.3 mM and would not significantly affect the pH when solution C was mixed with solution A.. The apparent binding constants for Ca2+ (KappCa) and Sr2+ (KappSr) to EGTA at pH 7.10 and in the presence of 1 mM Mg2+ used to determine the pCa (− log [Ca2+]) and pSr (− log [Sr2+]) values in our solutions were KappCa = 4.78 × 106 M−1 n) where n is the Hill co-efficient for Ca2+ and [Ca50] is the calcium concentration required for half-maximal tension activation. An equivalent equation was used for the Sr2+ activation curves. The following activation properties were measured from the force activation curves generated for each muscle fibre from the two age groups, when all data points fell within 5% of the fitted curves: Ca2+ and Sr2+ threshold for contraction , sensitivity to Ca2+ and Sr2+  and related differential sensitivity (pCa50-pSr50) and steepness of the activation curves (Hill co-efficient: nCa and nSr).Assessment of the effects of Cance Fig. . The cur2+-data points for some fibres could not be well fitted by simple Hill-curves . In such instances, the Sr2+-data points were well fitted by a biphasic curve generated by the following equation: Relative tension (%) = α/(1 + ([Sr501]/[Sr2+])n1 + β/(1 + ([Sr502]/[Sr2+])n2, where α and β represent the percentage of the two phases (α + β = 100%) and Sr501, Sr502 are the strontium concentrations corresponding to the half-maximal activation of the two phases. For the hybrid fibres we do not provide Hill parameters as there aren’t enough data points (distinct pSr’s) to determine pSr501/pSr502 and two Hill coefficients.As described by Bortolotto et al. , the Sr22+-dependent activation properties of individual muscle fibres identifies three groups which are commonly accepted to relate directly to the type of myosin isoform expressed (Schiaffino and Reggiani 2+ of fibres expressing the TnC slow isoform (and MHC I), than the TnC fast isoform (and MHC II isoforms)  present in the fibre  eliminates the possibility that the force oscillations were in any way caused by oscillations in Ca2+ or Sr2+ concentration. Indeed, in previous studies, we have shown that these oscillations are maintained even after treatment of the fibres with detergent to disrupt and extract all membrane compartments (Stephenson and Williams All slow-twitch (type I) fibres and some fast-twitch (type II) and hybrid fibres displayed spontaneous oscillatory contractions or ‘SPOC’ of myofibrillar origin at submaximal levels of force activation. The highly Ca2+-activated specific force it makes sense to express the maximum Ca2+-activated force developed by the fibre per unit cross-sectional area before the fibre swells. The maximum Ca2+ activated specific force was, therefore, calculated only for fibres where the fibre diameter was measured in oil, as described by Fink et al.  changing inverse-proportionally with the square root of sarcomere length. In contrast, the diameter (transverse spacing of filament lattice) changes little when a skinned fibre is stretched . Results were analysed with a one-way analysis of variance  and/or Student t-test where appropriate, according to levels of significance. The Mann Whitney rank order test was applied when the sample size was small (n < 6) and the variance quite marked , type II (fast-twitch) and hybrid (type I/II). The slow-twitch fibres were 10 times more sensitive to Sr2+ than the fast-twitch fibres  and fibres from women older than 80 years, all fibres investigated from women older than 80 years were of type I (100%), while all three fibre types were present in women of circa 70 years  fibres.2+ and Sr2+ thresholds for contraction , sensitivity to Ca2+ and Sr2+ , related differential sensitivity (pCa50–pSr50) and steepness of the activation curves (Hill co-efficient: nCa and nSr). As shown in Fig. 2+-activation curves lie much closer to the respective Ca2+-activation curves in slow-twitch fibres compared with the fast-twitch fibres.Representative force-pCa and force-pSr activation curves for slow-twitch (type I) fibres from the two age groups (circa 70 years and > 80 years) of women together with the activation curves of a representative fast-twitch (type II) fibre from a 70 years old woman are shown in Fig. 2+- and Sr2+-activation characteristics of slow-twitch (type I) fibres from the two age groups (circa 70 years and > 80 years) are summarized in Table 2+- and Sr2+- activation parameters of type I fibres from the two groups. However, as we point out in the “2+ compared with slow-twitch fibres from the vastus lateralis muscles of young adults, mean age 24 years  fibres from the circa 70 years old group. There were no type II (fast-twitch) fibres sampled from the muscle biopsies of women older than 80 yrs. The fast-twitch fibres from the circa 70 years old women have significantly higher Sr2+ and Ca2+ thresholds for contraction , lower sensitivity to Sr2+ , larger differential sensitivity (pCa50-pSr50) and higher Hill coefficients  than the slow-twitch fibres from the circa 70 years old women. The sensitivity to Ca2+ and Sr2+ of fast-twitch (type II) fibres sampled from the circa 70 years old women are higher than in fast-twitch (type II) fibres sampled from young adult males   than from the women under 70 years of age , but statistically, the results are not significantly different.The average value for the maximum Ca2+ activated specific force in fast-twitch (type 2) skinned muscle fibres from the circa 70 year old women  and the slow-twitch (type I) fibres from either group of women.There was no statistically significant difference between maximum Ca2+ activated specific force in hybrid muscle fibres, found only in the circa 70 years old group of women, varied between 16.3 to 40.0 N/cm2 and was not statistically different from the values of either the slow- or the fast-twitch fibres in the two groups of women.The maximum Ca2+ activated specific force in the pooled data from this study was significantly lower by about 20% than the pooled data for young adults from a study from the same laboratory using similar solutions.As detailed in the “Figure The SPOC phenomenon was observed in a small number of fast-twitch (type II) skinned muscle fibres from elderly women, circa 70 years old. As shown in Table 2+ the fibres could be grouped into three distinct categories: slow-twitch (type I), fast-twitch (type II) and hybrid (type I/II) fibres. All three fibre types were present in the biopsies of women of circa 70 years of age, but no fast-twitch or hybrid fibre was sampled from biopsies of women older than 80 years (> 80 years). This may be a consequence of taking one small sample from a specific region in the women of advanced age, where there are slow motor units containing large numbers of slow-twitch muscle fibres all present in one area rather than being distributed throughout the muscle as is the case with younger subjects  and fast-twitch (type II) fibres from young adults were 5.93 ± 0.01 (n = 40) and 5.83 ± 0.01 (n = 30) respectively. In comparison, the slow- and fast-twitch fibres from the vastus lateralis muscle of elderly women (both our groups circa 70 years of age and > 80yrs) had significantly greater pCa50 values . On average, the results show that muscle fibres from elderly women (circa 70 years of age and > 80yrs) produce 50% of their maximum Ca2+-activated force at Ca2+ concentrations that are lower by a factor of 1.4 for slow-twitch fibres and 1.7 for fast-twitch fibres compared with fast- and slow-twitch fibres biopsied from the vastus lateralis muscle of young adults  than in fibres from young adults of both sexes (mean 24 years)  vs 4.4 (young adults both sexes pooled) for slow-twitch and 3.38  vs 5.3 (young adult both sexes pooled) (for fast-twitch fibres). Lamboley et al.   appears to be several-fold higher in the circa 70 years of age group of elderly women (24%) than in muscle fibres sampled from the vastus lateralis muscle of young adults  fibres from all elderly women (24.3 N/cm2) compared with the average value for adult fibres from the vastus lateralis (30.0 N/cm2) obtained in a previous study from the same laboratory using similar procedures and solutions, but where the solutions contained, in addition, 10 mM caffeine (Fink et al. The average maximum Ca2+ activated specific force in chemically skinned fibres of the same type from young and elderly women. However, Trappe et al. (Note that when the force measurements were made at 15 °C (Trappe et al. e et al.  found thThe spontaneous oscillatory contractions, or force oscillations that originate from the interaction of myofibrillar proteins (SPOC, see Fig. Taken together the results described in this paper show that with advancing age, in women, there are changes in the activation properties of the contractile apparatus of muscle fibres from the vastus lateralis muscle. There is also an increase in the number of slow-twitch fibres and hybrid fibres and a decrease in fast-twitch fibres. These observed changes occur on the background of a robust capacity of old and senescent muscle to regenerate functional architecture (Lee et al.


Trends may be further influenced by an unexplored factor—changes in the seasonal timing of 6 because biological effects dominate thermal effects. Here we show that 27 Earth system models simulate similar timing under historical forcing but generally project that the summer low, relative to the annual mean, eventually becomes a high across much of the Arctic Ocean under mid-to-high-level CO2 emissions scenarios. Often the greater increase in summer 7 from earlier retreat of seasonal sea ice8. Warming and changes in other drivers enhance this century’s increase in extreme summer Long-term stress on marine organisms from ocean acidification will differ between seasons. As atmospheric carbon dioxide (CO Simulations suggest that the partial pressure of carbon dioxide in the Arctic Ocean will shift from a winter to a summer maximum owing to enhanced summer sea surface warming from earlier sea-ice retreat. Theory suggests that seasonal variations in ocean pH and CO2 partial pressure .More than a decade ago, it was recognized that the ongoing increase in atmospheric carbon dioxide (CO2 system variables in the Arctic Ocean using a suite of 27 Earth system models (ESMs) that participated in the two most recent phases of the Coupled Model Intercomparison Project . Both appear to be tied to earlier retreat of seasonal sea-ice cover. These projected tendencies are consistent with observations in some Arctic regions that are already experiencing earlier reductions in sea-ice cover, where phytoplankton blooms occur earlier in the year16 and there is greater surface warming8. Observed summer 17, has grown over recent decades as sea ice retreats18 and is particularly high under exceptional warming21.Under high-end emissions, the models project that by 2100, the thermally driven, summer maximum in The projected sign reversal in the summer extreme of entclass1pt{minimaT, which exhibit little or no timing change ). Simultaneously, the timing of the annual low retreats from August to June, crossing over the advancing annual high at 827 ppm. The same abrupt transition is found for the CMIP6 model mean but crossover occurs at 571 ppm, and the advance of the timing of the annual high to September reverses itself at about 700 ppm and then recedes to August  and higher area-averaged, summer maximum sea surface temperature in 2091–2100 , assuming that the former affects the driver anomalies, whereas the latter affects the sensitivities. This climate–CO2 separation was used to distinguish the combined effects of the sensitivities from those of the driver anomalies in terms of how they affect the total change in A first framework, three idealized experiments run in two CMIP5 models, suggests that the mentclass2pt{minim091–2100 . For breThis timing change also affects the seasonal amplitude and trends in seasonal means. With the timing change, the seasonal amplitude of entclass1pt{minimaCT term, as in the subarctic27  changes relatively little and that of CT′ (sCT′) even declines  and rearrange to3−] is the bicarbonate ion concentration, K0 is the CO2 solubility, Cf is the fugacity coefficient (which remains very near unity), and [CO2*] is the sum of aqueous [CO2] and [H2CO3]. At constant temperature, the relationship between +] is nearly proportional because the denominator in equation 2*] do not resemble those for ocean 2 exchange, the relative sensitivity of 2*] 33, the main link between zooplankton and marine mammals, seabirds and other fish34. These organisms are sensitive to different CO2 system variables35.Ocean acidification is expected to adversely affect life-sustaining processes across various groups of marine organisms3 depends on [CO32−], whereas CaCO3 production may be only correlated with that variable. That is, many marine calcifiers appear to take up HCO3−, suggesting that increasing [HCO3−] from ocean acidification would stimulate calcification (Ca2+ + HCO3− → CaCO3 + H+) provided the proton is removed from body fluids by acid–base regulation; conversely, increases in body fluid [H+] would inhibit calcification38. Thus the [HCO3−]/[H+] ratio in seawater and body fluids may be more physiologically relevant from a thermodynamic perspective; however, kinetic constraints still imply that [CO32−] is a fundamental controlling variable39. Projected lower [CO32−]′ and higher [H+]′ in summer are proportionally much larger than the increase in [HCO3−]′, relative to background levels  and to 10.8 ± 2.7 °C in CMIP6 , beyond the upper thermal limits of certain fish and other fauna endemic to the Arctic46. Thermal vulnerability will be heightened further by simultaneous ocean acidification, particularly in summer, based on observations and experiments with boreal to Arctic crustaceans, bivalves and fish50.Ocean acidification is concerning, but it is warming that is likely to most affect Arctic marine organisms during this century. Between 1996–2005 and 2091–2100, the summer maximum surface temperature averaged over the Arctic shelf seas is projected to increase from 3.0 °C (after model debiasing) to 8.5 ± 1.2 °C in CMIP5  and when computing integrated quantities such as averages over the Arctic domain (basin-wide mean) or the Arctic’s individual regional seas.Following previous studies52 while providing a test to check whether conclusions hold across model generations. One improvement in CMIP6 that could be important for the Arctic is that some models have much finer lateral resolution.To assess potential changes while accounting for regional differences, physical climate change, and the carbon cycle, we used a suite of 9 ESMs that participated in CMIP5 and 18 ESMs that participated in CMIP6 , referred to as RCP2.6, RCP4.5 and RCP8.5, respectively. Likewise, the CMIP6 results for 1850–2014  were combined with those for four projections for 2015–2100 under the Shared Socioeconomic Pathways (SSPs) that reach radiative forcings of 2.6 W m−2, 4.5 W m−2, 7.0 W m−2 and 8.5 W m−2 , referred to as SSP1-2.6, SSP2-4.5, SSP3-7.0 and SSP5-8.5, respectively.The CMIP models were used to assess monthly variations and trends in surface ocean 54 of the monthly mean times series at each grid cell. Decadal mean climatologies were compared between either 1996–2005 and 2091–2100 or 2006–2015 and 2091–2100, and tendencies were assessed as a function of the atmospheric CO2 level. The driving mechanisms were assessed with (1) Taylor-series expansions to quantify contributions from each of the four main input variables  and (2) idealized scenarios from CMIP5 with multiple simulations under different forcing to separate the direct chemical consequences attributable to the increase in atmospheric CO2  from the indirect consequences of physical climate change (radiative effect). Error bars given in the text are reported as ±1 s.d about the multimodel mean.Fields were regridded to a 1° × 1° regular grid for model evaluation and comparison. Monthly mean anomalies relative to the annual mean were computed by subtracting a cubic-spline fit55), sea surface temperature56 and sea-ice concentration57. Both the 57 data products are provided on a 0.25° × 0.25° regular latitude–longitude grid. For comparison, these data products and all model fields were regridded to the same World Ocean Atlas 1° × 1° regular latitude–longitude grid, that is, that of the sea-surface-temperature data product. Regridding was done using the nearest-neighbour algorithm in the cdo package (cdo remapnn)58. A common land mask was applied from the World Ocean Atlas over the Arctic Ocean domain.CMIP5 and CMIP6 seasonal climatologies constructed from the 1996–2005 model output years of each historical experiment were compared over the Arctic Ocean domain to observation-based products of surface ocean 56 to obtain the model bias. The bias, at each grid point and month, was then removed from the 2091–2100 climatology. Then the annual maxima were computed and the area-weighted average taken over all grid points in the Arctic shelf seas (bottom depths <500 m). Results are reported as the CMIP5 and CMIP6 multimodel means ±1 s.d. In the same way, the observational database was masked and the maxima computed to obtain the modern data-based reference for the area-weighted summer maximum for the Arctic shelf seas. For other analyses, models were not debiased.Models were debiased only to compute the maximum summer temperature in the shelf seas for 2091–2100 under RCP8.5 as well as under SSP5-8.5. The individual models were debiased by computing the 1996–2005 climatology for each model and then subtracting from that the observational climatology2 that increases at the same rate, 1% per year , but how that is felt by the Earth system differs. The 1pctCO2 simulation considers both the direct ‘geochemical’ effect of increasing CO2 on the carbon cycle and the ‘radiative’ effect of CO2 on physical climate, which drives physical changes, thereby affecting the carbon cycle indirectly. The esmFixClim1 simulation has identical forcing but considers only the direct effect , whereas the esmFdbk1 simulation considers only the indirect effect (radiative).Three of the CMIP5 models each provided a set of three idealized experiments: 1pctCO2, esmFixClim1 and esmFdbk1. All three experiments are forced by atmospheric CO2 is larger than in the historical and high-end RCP8.5 scenarios. Second, the separation between the three experiments is imperfect. In the esmFixClim1 simulation, intended to eliminate physical climate change effects, there are slight increases in ocean temperature linked to the response of the terrestrial biosphere, because the higher CO2 reduces stomatal conductance, thus causing greater surface fluxes of sensible heat. Third, only three models provided results for the full set of experiments, and only two of those (IPSL-CM5A-LR and MPI-ESM-LR) continued the 1% per year atmospheric CO2 increase until the end of the 140-year simulation, whereupon atmospheric CO2 had quadrupled relative to the pre-industrial starting point (284 ppm). Conversely, the third model (GFDL-ESM2M) stopped that increase after the first 70 years, the point at which atmospheric CO2 had doubled, holding the same level over the remaining 70 years. Given the limited number of models, no attempt was made to provide quantitative estimates of model uncertainty.These CMIP5 idealized experiments allow one to deconvolve the geochemical and radiative contributions, but they also come with limitations. The most obvious is that the rate of increase in atmospheric COPT and SiT. Typically, that equation is used to compare contributions from each of the four drivers12, but here we use it in a broader way to distinguish the effects of the atmospheric CO2 increase from those of physical climate change. Thus the effects from the combined sensitivities were separated from those of the combined driver anomalies to ascribe general causes for differences between the modern reference state, defined as the 2006–2015 decadal climatology of surface X =  and the corresponding sensitivities γ = . The first right-hand side term (in parentheses) in equation , which affects the sensitivities, whereas the second and third terms (each in separate parentheses) would be null without the effect of physical climate change, which affects the driver anomalies.As mentclass2pt{minimIn practice, the normal Taylor expansion for the modern state is made using modern sensitivities and driver anomalies, whereas that for the future state is made using future sensitivities and driver anomalies. The total difference between those two states is due to changes in both the sensitivities and the driver anomalies. To isolate the effect of the changes in the sensitivities , the sum of the four terms in equation  is compu2 separation is a simplification of a more elaborate regrouping of terms that was derived to analyse contributions to the amplitude of the annual cycle of 4 that excluded the Arctic Ocean and did not address seasonal timing. Nor have previous studies emphasized that changes in sensitivities come mainly from the increase in atmospheric CO2, whereas changes in driver anomalies come from physical climate change. This climate–CO2 Taylor-series expansion requires results from just one model experiment. Hence, we were able to use it here to assess all nine CMIP5 models forced under the RCP8.5 scenario, unlike the approach described in the previous section that relies on multiple idealized simulations carried out with less realistic forcing and for which only two CMIP5 models have provided a complete set of results.This climate–COAT and CT terms in equation . Thus equation . In our case, S0 is the annual mean salinity in each grid cell because the focus is on monthly anomalies relative to the annual mean, a choice also adopted previously1 that should minimize known problems with salinity normalization62. Thus each of the two original terms for AT and CT in equation  were computed numerically using derivnum2, curves were fit with a cubic spline to suppress interannual variations.Plots are shown detailing the evolution in timing of the annual high and low for multiple variables. That timing  is represented as an average across a basin or region, which is computed in one of two ways. For monthly anomalies of +], 2*] shown in Extended Data Fig. 53 and the constants recommended for best practices with AT = 2,130 µmol kg−1 and CT = 2,000 µmol kg−1. Total dissolved inorganic phosphorus and silicon were set to zero.Equilibrium calculations for [HAny methods, additional references, Nature Research reporting summaries, source data, extended data, supplementary information, acknowledgements, peer review information; details of author contributions and competing interests; and statements of data and code availability are available at 10.1038/s41586-022-05205-y.Supplementary InformationSupplementary discussion, figures, tables and references.Peer Review File


For both molecules, dissociative chemisorption proceeds through cleavage of carbon−oxygen bonds. The dissociation rate increases exponentially with temperature and stress. When the rate−temperature−stress data are fitted with the Bell model, both molecules have similar activation energies and activation volumes and the higher reactivity of tri(s-butyl)phosphate is due to a larger pre-exponential factor. These observations are consistent with experiments using the antiwear additive zinc dialkyldithiophosphate. This study represents a crucial step towards the virtual screening of lubricant additives with different substituents to optimise tribological performance.The molecular structure of lubricant additives controls not only their adsorption and dissociation behaviour at the nanoscale, but also their ability to reduce friction and wear at the macroscale. Here, we show using nonequilibrium molecular dynamics simulations with a reactive force field that tri( Antiwear additives are crucial to ensuring the reliable operation of lubricated machine components, but virtual screening to obtain new additives has hardly been explored. Here, the authors use nonequilibrium molecular dynamics simulations with a reactive force field to investigate the mechanochemical dissociation of phosphate esters with different alkyl substituents to inform future molecular design. It could soon play a central role in many important industrial processes1, such as ammonia production2. Currently, the most economically valuable application of mechanochemistry is for the formation of friction- and/or wear-reducing films by lubricant additives on rubbing surfaces3. These ‘tribofilms’ are critical to maintaining the efficient and reliable operation of the majority of lubricated machine components. Zinc dialkyldithiophosphate (ZDDP) is the most popular antiwear additive; it is included in almost all engine oils, as well as many other types of lubricant4. It forms relatively thick (~100 nm), patchy tribofilms on rubbing steel surfaces, which are mostly composed of zinc and iron polyphosphates. Due to environmental concerns with ZDDP, there has been a sustained global research effort over several decades to develop alternatives that are metal-free, form lower amounts of sulfated ash when combusted, and contain less phosphorus and sulfur5. In macroscale tribometer experiments, metal-free dialkyldithiophosphates (DDPs)6, sulfur-free zinc dialkylphosphates (ZDPs)7 and metal- and sulfur-free trialkylphosphates8 have all been shown to form protective tribofilms on steel surfaces; however, these are generally thinner and grow more slowly compared to those formed by ZDDP. Consequently, low-sulfated ash, phosphorus, and sulfur (SAPS) additives generally show poorer antiwear performance than ZDDP5.Mechanochemistry describes a diverse range of phenomena where chemical reactivity is influenced by mechanical load9. This information is challenging to obtain from macroscale tribometer experiments in the mixed/boundary lubrication regime10. In these experiments, numerous solid−solid asperity contacts occur, resulting in local conditions that are difficult to measure and control. In recent years, in situ experiments of single nanoscale asperities have enabled the study of additive behaviour under more controlled conditions11. For example, Gosvami et al.12 showed using atomic force microscopy (AFM) that the tribofilm formation rate of ZDDP is exponentially dependent on both temperature, T, and normal stress, σzz. These observations are consistent with a mechanochemical driving force for tribofilm formation12. Tribofilm growth in these experiments can be modelled as a stress-augmented thermally activated (SATA) process13. The rate constant for SATA processes can be calculated through a modified Arrhenius equation,A is the pre-exponential factor, Ea is the activation energy, σ is the applied stress, ΔV* is the activation volume, and kB is the Boltzmann constant. This equation was first proposed in the context of molecular systems by Evans and Polanyi14, but it is now usually known as the Bell model15. Experiments at different scales have suggested that ZDDP tribofilm formation follows zero-order (rate = k)16 or fractional-order (rate = k[ZDDP]n)12 kinetics. These observations suggest that the ZDDP molecules adsorb onto the steel surface before they dissociate and form tribofilms16. Similar mechanochemical responses have also been observed for metal-free DDPs in AFM experiments by Dorgham et al.17, although these additives produced thinner tribofilms that formed more slowly than with ZDDP.An improved understanding of the atomic-scale behaviour of antiwear additives inside tribological contacts is required to rationally design new molecules with improved performance and reduced environmental impact18 showed that under full-film elastohydrodynamic lubrication (EHL) conditions, ZDDP tribofilms formed on tungsten carbide surfaces from high shear stress traction fluids, but not from low shear stress lubricant base oils18. Using Eq. (σxy), rather than the normal stress (σzz)18. Zhang et al.16 recently confirmed this finding using steel surfaces and ZDDPs containing different alkyl substituents. In similar tribometer experiments, Ueda et al.19 showed that tribofilm thickness was the largest for steel substrates, followed by silicon nitride and then tungsten carbide, with no tribofilm formation observed on silicon carbide or diamond-like-carbon (DLC). Along with accompanying quartz crystal microbalance (QCM) experiments, these observations suggested that strong surface adsorption is required to form a tribofilm and that the rate of tribofilm formation was faster on harder surfaces, which led to higher contact stresses19.Zhang and Spikes20 suggested that secondary dialkyl ZDDPs have lower thermal stability compared to primary dialkyl ZDDPs because the former are more susceptible to β−H elimination reactions. Jones and Coy21 showed that the thermal stability of ZDDPs increased in the order; secondary alkyl < primary linear alkyl < primary branched alkyl < aryl. They suggested that primary and secondary ZDDPs undergo different decomposition mechanisms; alkyl transfer and β−H elimination, respectively21. Fujita et al.10 noted that secondary ZDDPs formed thicker tribofilms more quickly than primary ZDDPs on steel substrates under mixed/boundary lubrication  conditions. Recently, Zhang et al.16 showed that ZDDPs with secondary dialkyl groups also form tribofilms much faster than those with primary dialkyl groups on steel surfaces under full-film EHL  conditions. Similar substituent effects have also been observed for other antiwear additives, such as ZDPs and phosphate esters. For example, triarylphosphates are known to be more thermally stable than trialkylphosphates22. Similar to ZDDP20, this could be due to the susceptibility of trialkylphosphates to β−H elimination reactions, which cannot occur for triarylphosphates24. Moreover, Hoshino et al.7 showed that secondary ZDPs form tribofilms more quickly than primary ZDPs on rubbing steel surfaces. These observations imply that the rate-determining step for tribofilm growth by ZDDP, ZDP, and phosphate ester antiwear additives on rubbing steel surfaces is the initial removal of the alkyl groups. This is perhaps unsurprising given that dissociative chemisorption is often the rate-determining step for heterogeneously-catalysed processes25. To design new antiwear additives with controlled tribofilm formation rates, it is therefore critical to obtain a detailed understanding of the effects of different alkyl and aryl substituents on mechanochemical reactivity.Antiwear additives with different alkyl and aryl substituents can show very different thermal, mechanochemical and tribochemical reactivity. Dickert and Rowe26. MD simulations have also been successfully applied to compare the thermal stability of different antiwear additives on steel surfaces. In particular, Ewen et al.27 have studied substituent effects on the thermal decomposition of phosphate esters on ferrous surfaces, reproducing the same order of reactivity as observed experimentally for ZDDP21. Moreover, nonequilibrium molecular dynamics (NEMD) simulations have provided unique insights into mechanochemical processes at molecule-solid interfaces inside tribological systems28. For example, NEMD simulations have recently been used to study the tribopolymerization of aldehydes between alumina surfaces29, phosphoric acid31, allyl alcohols32 and terpenes33 between sliding silica surfaces, and cyclopropane carboxylic acid between iron oxide surfaces34. They have also been used to study the mechanochemical decomposition of alkyl sulfides between sliding iron surfaces35 and perfluoropolyethers (PFPEs) between DLC surfaces36, the vapour phase lubrication of trialkylphosphates37 and trialkylphosphites39 between iron surfaces, and the ultralow friction of organic friction modifier additives between DLC surfaces40. Most of these NEMD simulations employed many-body empirical force fields36, while others use first principles methods39, or sometimes a combination of both of these techniques40.It has recently been demonstrated that molecular dynamics (MD) simulations can be used to virtually screen and even autonomously design new lubricant molecules with a high viscosity index40. Bond order potentials are several orders of magnitude cheaper than first principles approaches41, allowing much larger systems to be simulated under experimentally-relevant conditions. In particular, ReaxFF, which was originally developed by van Duin et al. to study hydrocarbon reactivity42, has been parameterised to model a wide range of chemical systems and processes43. Of particular relevance to this study, ReaxFF simulations are now routinely used to study tribochemical reactions44. The high parallel efficiency  of ReaxFF MD simulations allows the routine study of large systems  under conditions that are much closer to, or even the same as, those used experimentally41. For some systems, it has been argued that current ReaxFF parameterisations are incapable of accurately reproducing chemical reactions that are observed under tribological conditions using first principles methods45. However, for many important chemical processes , careful parametrisation has ensured that the accuracy of ReaxFF MD simulations is close to that obtained when using first principles methods43. This includes the adsorption and dissociation of phosphate esters on iron and iron oxide surfaces46.First principles methods are extremely computationally expensive and are therefore limited to single molecules, sub-nanosecond timescales, and very severe conditionsn-butyl)phosphate (TNBP), which contains primary linear alkyl substituents, compared to secondary tri(s-butyl)phosphate (TSBP), which contains secondary alkyl groups  and its dependence on temperature and stress. It also represents an important step towards the virtual screening and autonomous molecular design26 of antiwear additives with optimised molecular structures for tailored mechanochemical and tribological responses.In this study, we use NEMD simulations with ReaxFF to study the reactivity of trialkylphosphate esters heated and compressed between sliding iron surfaces. We compare the decomposition of tri, compression (σzz = 2 GPa), and sliding (vs = 10 m s−1) phase. Figure 3O4(001) surfaces27. The rate of C−O cleavage is faster for TSBP than TNBP, which is due to the greater stability of secondary alkyl cations or radicals compared to primary ones49. Note that heterolysis and homolysis cannot be differentiated using the standard ReaxFF approach because the electrons are not explicitly modelled. Previous experimental studies have suggested that heterolytic C−O fission is probably the dominant process during the thermal decomposition of trialkylphosphates50. For TSBP, some C−O cleavage reactions occur even during equilibration at relatively low temperature (300 K) and pressure (10 MPa). The higher reactivity of TSBP than TNBP can be rationalised through the inductive effect, because alkyl groups have more electron-donating character compared to hydrogen atoms51. There is also evidence in the literature suggesting that steric effects and hyperconjugation can also affect the susceptibility of phosphate esters to C−O bond cleavage;49 however, the substituent effect sobserved in the current simulations suggest that such effects are less important for these systems. In the current NEMD simulations, C−O cleavage through dissociative chemisorption is favoured over β−H elimination, which has previously been suggested to be the major route of C−O cleavage for both trialkylphosphates24 and ZDDPs21. Dissociative chemisorption is promoted by the stabilisation of the resultant ions or radicals formed by the iron surface39. Some of the broken C−O bonds reform for TNBP (blue dotted lines), whereas this is negligible for TSBP.Figure on σzz =  GPa, and50. However, there is some disagreement in the experimental literature regarding the thermal decomposition mechanism of trialkylphosphates on iron oxide surfaces. Some studies using TNBP have suggested that this proceeds through C−O cleavage24, while others have postulated that P−O cleavage dominates52. The latter suggestion was based upon the detection of gas-phase alcohols, rather than alkenes when TNBP was gradually heated to 800 K on an iron oxide surface52. However, recent MD simulations of TNBP showed that gas-phase alcohols could also be formed by oxidation of the surface-adsorbed alkyl groups (formed by C−O cleavage) by the iron oxide surface, followed by desorption27. The large substituent effects observed in previous MD simulations27 can only be accounted for if C−O cleavage, rather than P−O cleavage, is the rate-determining step for the thermal decomposition of trialkylphosphates on ferrous surfaces. More specifically, phosphate esters containing secondary alkyl groups (e.g. TSBP), that form more stable carbocations or radicals by C−O cleavage49, decomposed much faster than those with primary groups (e.g. TNBP)27. The current NEMD simulations show that the same dissociation mechanism dominates under mechanochemical conditions.The pyrolysis of TNBP is known to proceed mostly through C−O cleavage21. Figure 21. Inside lubricated contacts, these nucleophilic substitution reactions would eventually result in the formation of thick (~100 nm) polyphosphate tribofilms on the rubbing steel surfaces. This process has recently been observed experimentally for systems lubricated by a secondary tri(i-propyl)phosphate dissolved in a hydrocarbon base oil8. Comparing the green dotted lines in Fig. 53. However, since nucleophilic substitution is not the rate-determining step, we restrict our detailed rate analysis to the C−O cleavage process.The polyphosphate tribofilms formed from trialkylphosphates and ZDDP grow through nucleophilic substitution reactions. After C−O cleavage has occurred, the resultant dialkylphosphate or monoalkylphosphate anion or radical is more nucleophilic than the corresponding trialkylphosphate. Moreover, the central P(V) atom is susceptible to nucleophilic attack by neighbouring molecules due to reduced steric hindrance18.We also performed a subset of MD simulations under identical conditions to those shown in Fig. T = 400 K) and variable pressure (σzz = 1–4 GPa). Fig. σzz = 2 GPa) and variable temperature (T = 300−500 K). The results for some of the other conditions considered are shown in Supplementary Fig. 36. The NEMD simulation data (dashed lines) during the production phase are therefore fitted with an exponential function (solid lines) to determine the reaction rate. In previous experiments for ZDDP17 and DDP17, the rate of tribofilm formation has followed either zero-order or fractional-order kinetics. The main reason for this difference is the finite number of additive molecules in the NEMD simulations, which means that the dissociation rate inevitably decreases as fewer molecules are available to react. In the experiments, the additive molecules are continually replenished from the base oil solution and the bulk concentration does not significantly decrease16. The rate of tribofilm formation does not change appreciably over the course of the experiments16, meaning that the rate-determining step is zero-order and involves surface-adsorbed molecules54.The dissociation rate of TNBP and TSBP molecules between the sliding α-Fe(110) surfaces was investigated over a wide range of temperature and stress conditions. Figure 27, the dissociation rate is much higher for TSBP  fits the data using Eq.  in ΔV* we observe cannot be completely accounted for by the change in contact stiffness of the solid surfaces. As expected for SATA processes13, the dissociation rate also increases exponentially with temperature, as shown in the Arrhenius plots in Supplementary Fig. Figure Ea, calculated from the 2D fits to Eq. (−1 for TBNP and 11 ± 7 to 22 ± 10 kJ mol−1 for TSBP between 1−4 GPa (Supplementary Table A), also increases with increasing pressure from 24 ± 1 to 26 ± 4 for TNBP and 25 ± 2 to 28 ± 2 for TSBP over the same range (Supplementary Table Ea ∝ ln[A]) is known as the kinetic compensation effect  and TSBP (R2 = 0.82). The parameters for Eq.    and TSBP (16.7 ± 4.0 Å3) within the uncertainty of the calculations. From previous macroscale tribometer experiments16, ΔV* was also found to be identical (15 Å3) for ZDDPs with primary and secondary substituents. The slightly larger ΔV* values calculated for trialkylphosphates compared to ZDDPs suggest that the former are more mechanochemically susceptible. If the normal stress, σzz, rather than the shear stress, σxy, is used as the variable in Eq.  using AFM12. The fact that the ΔV* values are similar for primary and secondary trialkylphosphates and ZDDPs suggests that, although the former dissociates and forms tribofilms much more slowly, the differences cannot be attributed to their relative mechanochemical susceptibilities.From the 3D fits, ΔV* values can also be compared to the molecular volumes60, which were calculated for TNBP and TSBP molecules relaxed using the MM2 force field61. Using a probe size of 3 Å3, TNBP has a molecular volume, V ≈ 440 Å3 and for TSBP, V ≈ 390 Å3. Thus, ΔV* represents a ~4% deformation of the molecule for both TNBP and TSBP. This percentage deformation is comparable to that calculated from previous NEMD simulation results for α-pinene (~3%)33 and allyl alcohol (~7%)32 oligomerisation between sliding silica surfaces, as well as the decomposition of PFPEs (~2%)36 between DLC surfaces.The Ea, calculated from the 3D fits to Eq. (−1) and TSBP (17.5 ± 3.6 kJ mol−1). The thermal decomposition of TNBP in an inert atmosphere (170 kJ mol−1)50 and with a steel catalyst in the air (80 kJ mol−1)22 yielded higher Ea values, suggesting that the application of stress alters the reaction pathway to considerably reduce the energy barrier62. The calculated values of Ea for TNBP and TSBP are within the range observed from AFM experiments using DDP (10−25 kJ mol−1)17. However, the Ea values are somewhat lower than those obtained from AFM experiments for mixed primary/secondary ZDDPs (77 ± 19 kJ mol−1)12 and full-film EHL experiments for primary (59 kJ mol−1) and secondary (84 kJ mol−1) ZDDPs16. This implies that there is a lower energy barrier for removal of the alkyl groups in trialkylphophates than ZDDPs under mechanochemical conditions.The activation energy, s to Eq.  in Fig. ΔV* and Ea values from the 3D fits for TNBP  than TNBP (5.0 ± 3.0 × 1011 s−1), as shown in Table A values  using AFM12. However, much larger differences in A were observed between primary (6 × 105 s−1) and secondary (2 × 1010 s−1) ZDDPs in previous full-film EHL experiments16. This is probably because the primary  and secondary (β−H elimination) ZDDPs are believed to undergo different initial decomposition mechanisms to remove the alkyl groups21, whereas the primary and secondary phosphate esters studied here both follow the same decomposition mechanism (C−O cleavage).The NBP Fig.  and TSBPNBP Fig.  are almoNBP Fig. . Thus, tA = Z ρ, where Z is the frequency or collision factor, and ρ is the steric factor, which is usually less than unity14. The rate of molecule−surface collisions (Z) has been quantified previously from NEMD simulations of solid−gas interfaces;63 however, this is more challenging for solid−liquid interfaces. Given that their molecular structure only differs by the position of the C−O bond along the butyl chain, Z is expected to be very similar for TNBP and TSBP. Previous experiments have shown almost identical adsorption behaviour for n-butyl and s-butyl ZDDPs from a hydrocarbon base oil onto iron oxide64. Therefore, the much higher reaction rates observed experimentally16 and in the current NEMD simulations for additives containing secondary alkyl groups arise mostly from variations in ρ. This implies that the cleavage of the C−O bond in TNBP on the α-Fe(110) surface is more strongly dependent on the molecular conformation and a smaller fraction of molecule−surface collisions result in a reaction. Indeed, the through-film number density profile for the C atoms in TNBP  is unimolecular, the rate constant can be calculated as,h is Planck’s constant, R is the molar gas constant, κ is the transmission factor (assumed to be unity), ΔG‡ is the Gibbs free energy of activation, and ΔH‡ is the activation enthalpy54. For SATA processes13, ΔU‡ is the internal activation energy67. Using the 3D fits shown in Fig. ΔV‡ = 16.4 ± 2.7 Å3, ΔH‡ = 14.2 ± 2.6 kJ mol−1 and TΔS‡  = −16.9 ± 1.9 kJ mol−1 for TNBP at T = 400 K. From the 3D fits in Fig. ΔV‡ = 16.7 ± 4.0 Å3, ΔH‡ = 14.4 ± 3.5 kJ mol−1 and TΔS‡ = −12.6 ± 2.8 kJ mol−1 for TSBP at the same temperature. Negative entropy values are expected given that the phosphate esters are transformed from liquid molecules to surface-adsorbed species, which means that the transition state is more ordered than the reactants. The above values suggest that the smaller activation entropy penalty is mostly responsible for the higher reactivity of TSBP than TNBP. Previous DFT calculations have also highlighted the importance of entropic contributions to the mechanochemistry of phosphate esters68. Dissociative chemisorption for TNBP has a larger activation entropy penalty than TSBP, implying that the former has a more restricted transition state, in which translation and rotation are hindered69. This is due to the lower stability of the primary carbocation49, which means that TNBP has a narrower reaction path along the potential energy surface because there are fewer low-energy states in the vicinity of the transition state. Although the difference in activation entropy between TNBP and TSBP is relatively small (~4 kJ mol−1), the exponential dependence of the rate on this quantity in the Eyring equation leads to much faster reactivity for TSBP under all of the conditions studied.According to transition state theory, 15) equation, the higher rate of TSBP than TNBP originates from a higher steric factor  for the former. Using the Eyring equation66, the higher reactivity of TSBP can be attributed to a smaller activation entropy penalty, due to a less restricted transition state.In summary, the higher mechanochemical reactivity of secondary TSBP compared to primary TNBP can be interpreted through different, although not contradictory, perspectives through either collision theory or transition state theory. Using the modified Arrhenius 70. In addition to tribology, we anticipate that NEMD simulations with reactive force fields44 will be useful to elucidate mechanochemical synthesis pathways by mimicking the conditions inside ball mills1.The general agreement between the mechanochemical parameters obtained from experiments and NEMD simulations with ReaxFF suggests that the latter are suitable for the virtual screening of antiwear additives with different alkyl substituents. This paves the way for the autonomous molecular design of new lubricant additives with optimised molecular structures for tailored tribological performance, as has recently been achieved for base oilsWe have used NEMD simulations with ReaxFF to compare the mechanochemical responses of primary (TNBP) and secondary (TSBP) trialkylphosphates heated and compressed between sliding iron surfaces. For both TNBP and TSBP, decomposition proceeds through dissociative chemisorption, during which one of the C−O bonds is broken. The rate of this process increases exponentially with temperature and shear stress, which implies that this is a SATA process. 2D fits to the Bell model suggest that the activation energy and pre-exponential factor both increase with pressure, which is indicative of a kinetic compensation effect. The activation volume increases with temperature, which can only partially be explained through a reduction in contact stiffness. 3D fits of the entire dataset to the Bell model over a wide range of temperature and stress conditions give reduced uncertainty in the model parameters compared to individual 2D fits. TSBP shows much faster dissociation rates than TNBP; however, both molecules have similar activation energy and activation volume. The much higher reactivity of TSBP is driven mostly by the pre-exponential factor, which is approximately four times larger than for TNBP. This is due to the higher stability of the secondary carbocation formed from the former following C−O cleavage. The additional stability enables a higher proportion of molecule−surface collisions to result in a reaction. This can also be interpreted as a smaller activation entropy penalty because of a less hindered transition state. Many of the observations from these NEMD simulations, as well as the parameters obtained from fits to the Bell model, are similar to those obtained from AFM and macroscale tribometer experiments using the ubiquitous antiwear additive ZDDP. The results provide further evidence that the initial dissociative chemisorption is the rate-determining step for tribofilm formation by antiwear additives. They also highlight the central role of the pre-exponential factor (or activation entropy) in distinguishing the mechanochemical reactivity of antiwear additives containing different alkyl groups. This study represents an important step towards the virtual screening and autonomous design of antiwear additives to optimise their molecular structure for tailored mechanochemical and tribological responses.71, trialkylphosphates are also used as vapour phase lubricants72. The molecular structures of the two phosphate esters considered are shown in Fig. 18, no direct solid−solid contact occurs and the stress is applied through the confined molecules.We compare the reactivity of two trialkylphosphates; TNBP, which contains primary linear alkyl groups and TSBP, which contains secondary alkyl groups. In addition to their primary application as antiwear additives for liquid lubricants73. However, during rubbing, nascent iron will be exposed, which will quickly react with phosphorus-containing antiwear additives73. To obtain sufficient reaction events in the accessible simulation time under experimentally-relevant conditions, we employed iron, rather than iron oxide surfaces. Previous ReaxFF MD simulations showed that, for TNBP and TSBP, the same initial thermal decomposition process (C−O cleavage) occurs on iron and iron oxide surfaces27. We selected the α-Fe(110) surface due to its higher thermodynamic stability than the other cleavage planes74.Surface analysis of steel surfaces following tribometer experiments using a lubricant with phosphorus-containing antiwear additive suggests that iron oxide is present at the surfacex = 5.1, y = 4.8 and z = 1.1 nm. Periodic boundary conditions are applied in the x and y directions. Before compression, the surfaces were initially separated by 4.0 nm of vacuum in the z-direction. A snapshot of a representative system is shown in Fig. All of the systems were constructed using the Materials and Processes Simulations (MAPS) platform from Scienomics SARL. The two α-Fe(110) surfaces had dimensions of 75 for all of the NEMD simulations. We employed velocity Verlet integration76 with a time step of 0.25 fs46. First, the systems were energy minimised using the conjugate gradient method. Equilibration simulations were then performed at an ambient temperature of 300 K and low pressure of 10 MPa for 0.1 ns. The temperature (T = 300−500 K), pressure (σzz = 1−4 GPa), and sliding velocity (vs = 10 m s−1) were then simultaneously increased to their target values. The selected temperature and pressure ranges align with those used in previous macroscale tribometer16 and AFM experiments12 of antiwear additive mechanochemistry. The temperature in the NEMD simulations was controlled with a Langevin thermostat77 using a damping parameter of 25 fs. The thermostat was only applied to the middle layer of atoms in the slabs78. The pressure was increased by adding a constant normal force to the outer layer of atoms in the top slab, while the outer layer of atoms in the bottom slab was fixed in the z-direction79. The sliding velocity was imposed by adding equal and opposite velocities (±5 m s−1) to the outer layer of atoms in the slabs in the x-direction  softwaresee Fig. . These h75 was first outlined by Chenoweth et al.80 and was described in more detail by Aktulga et al.81. The general form is given by43:Ebond is a continuous function of the interatomic distance and describes the energy associated with bond formation . Eangle and Etors are the energies associated with three-body angle and four-body torsional angle strain, respectively. Eover is an energy penalty to prevent over-coordination of atoms and is based on atomic valence rules. ECoulomb and EvdW represent the electrostatic and dispersive interactions between all of the atoms in the system, irrespective of their connectivity and bond order. Especific represents system-specific terms required to capture particular properties of the system of interest, such as lone-pairs, conjugation and hydrogen bonding43. The point charges on the atoms vary dynamically during the MD simulation and are calculated using the charge equilibration (Qeq) method83.The functional form of ReaxFF that is implemented in LAMMPS46. They used the Fe/O/H parameters due to Aryanpour et al.84, the Fe/C parameters due to Zou et al.85, the P/O/C/H parameters due to Verlackt et al.86 and the C/H/O parameters due to Chenoweth et al.80. The ReaxFF parameters for Fe have been shown to accurately reproduce the experimental lattice parameters for α-Fe (within 1%)85 and they have also been shown to perform favourably compared to other many-body force fields in describing its mechanical properties, including the elastic modulus87. The C/H/O/Fe/P ReaxFF parameterisation has recently been successfully applied to study the thermal decomposition of phosphate esters with different alkyl and aryl substituents on several ferrous surfaces88. The ReaxFF parameters have also been validated against DFT calculations for the adsorption energy and dissociation energy (including the energy barrier) for TNBP on α-Fe(110)27. Chemical bonding information was output every 1.0 ps, using a bond order cutoff of 0.3 to identify covalent bonds80. The choice of bond order cutoff only affects the post-processing analysis and does not influence the ReaxFF energy or force calculations during then NEMD simulations27.We employed the ReaxFF parameterisation developed for C/H/O/Fe/P-containing systems by Khajeh et al.Supplementary InformationDescription of Additional Supplementary FilesPeer Review FileSupplementary Data


Species with sympatric distribution influence ecosystem dynamics and are impacted by the presence of other co-existing species. Assessing the coexistence and the role of interspecific interactions with the landscape variables is necessary to know the species co-occurrence in space. In the Indian Himalayan region, such studies are completely lacking due to limited efforts being made, mainly because of complex terrains and inaccessible landscape features. We used camera trapping and sign survey in a multi-species occupancy framework to understand the influence of environmental variables on occupancy and detection probability of species-specific and pair-wise interaction of the three ungulates in Uttarkashi. Our results concluded that individual species' occupancy probabilities were related both to the environmental variables and the presence or absence of other interacting species. Our top model showed evidence of interspecific interaction among species pairs, and the occupancy probability of species one varied in the presence or absence of another species. The overall activity patterns were similar among all the three species and were found active throughout the day. The activity overlap between sambar—barking deer  was considerably higher than barking deer—goral . The findings of the present study will be useful for the conservation and management of ungulates in the Indian Himalayan and adjoining regions. Conservation strategies are primarily focused on the concept of multiple-species conservation in protecting endangered species and assessing biodiversity within entire communities4. Moreover, several studies demonstrated that ecological communities are composed of multiple interacting species, and species occurrence can be influenced by environmental factors and even the presence of other species6. Hence understanding those factors  which influence the distribution of species is of fundamental interest in wildlife conservation and management. Multi-species occupancy modeling provides a method for assessing biodiversity while accounting for multiple sources of uncertainty, imperfect detections and sampling designs8. However, several studies highlighted that species occupancy probabilities are often influenced by many factors such as environmental factors and the presence or absence of interacting species, e.g. Predator’s presence for prey10, or habitat utilization may be impacted by the presence of other species11.In the Himalayas, the ungulates form the major prey base for the large predators and are good ecological indicators, more prone to anthropogenic disturbance and habitat qualityMuntiacus vaginalis), Himalayan goral , and Sambar deer (Rusa unicolor) have sympatric distribution in Himalayan regions and play an essential role in shaping ecosystems by influencing vegetation structure, forming a major prey base for carnivores and act as ecological indicators13. However, these species are threatened due to habitat loss, illegal poaching, climate change and interspecific competition16. Among the three studied species, the barking deer is widely distributed from eastern Pakistan, India, Nepal and up to south-east Asian countries, and mostly prefers high understory dense tropical and sub-tropical forest19. Barking deer also have a wide elevation distribution (100–3000 m) and are mostly found at the edge of forested habitats20. Whereas the Himalayan goral adapted to high elevation (900 to 2750 m) areas, it is a cliff-dwelling, solitary, sexually monomorphic mountain ungulate. Its distribution encompasses the Himalayan range of India, Nepal and Bhutan with densely forested areas to the sub-alpine scrub, alpine meadow and grassland22. The sambar is a large mesoherbivores deer native to South and South-East Asia and distributed in habitats with high tree and shrub densities23.Among the ungulates, Barking deer  Act, 1972, and are seriously threatened because of illegal poaching. Since all three species are symmetrically distributed in Himalayan regions, such sympatric distribution of species may face exclusion25, avoidance26 or sometimes extinction due to increasing inter-specific competition27. Furthermore, limited studies on habitat use28, behaviour29, distributions33, genetics23 of these ungulates species is available but completely lacking evaluations on their occupancy and species interactions throughout their distribution ranges, including the Himalayan regions.As per the IUCN Red List, barking deer is listed as ‘Least concern’35. These events lead to rapid habitat loss, fragmentation, and population decline of various species. Therefore, understanding habitat association, occupancy and interspecies interaction are imperative for conservation and management. A better understanding of the ecology of the ungulate community may allow managers to more fully balance gains against losses when managing the diversity of wildlife36. Additionally, our research was motivated by the lack of broad-scale ungulate studies from the study area. This study explores the utility of camera trap surveys to understand species-specific and pair-wise interaction between three ungulate species using multi-species hierarchical models in the Uttarkashi district. These devices are helpful in areas with rugged topography or dense vegetation and, in recent years, have been used to study activity patterns, habitat use, density and occupancy of ungulates39. Modern cameras record the time of the photo, and researchers have used this to investigate diel activity patterns and compared activity patterns among species to see how overlapping patterns may relate to competition or predation43.The Himalayan region is under tremendous pressure because of infrastructural development, climate change and other anthropogenic activitiesOur specific objectives were to evaluate species-specific responses to environmental variables and pair-wise interaction and the pattern of activity of the three ungulate species in Uttarkashi. We aimed to understand better how the environmental factors and interspecific interaction influence the occupancy of the three ungulates, which is vital for effective conservation and management implications.f12, f13, (f23). The top model assumed the occupancy of the three species at different sites varied as a function of habitat variables ψ (FT 188 + Distance to the village) when detection probability was kept as constant p(.) (Table f1) was positively influenced by distance to the village (β = 2.62 ± 1.13) and negatively influenced by FT 188  (β = − 7.79 ± 0.00) (Table f2) exhibits a positive relationship with variable FT 188 (β = 5.76 ± 0.00) and a negative relationship with variable distance to the village (β = − 2.43 ± 1.17). In contrast, marginal occupancy of sambar (f3) was positively influenced by FT 188 (β = 22.80 ± 0.00) and negatively influenced by distance to village (β = − 0.22 ± 0.59) (Table f12) and barking deer-sambar (f13) varied markedly. The relationship between the occurrence of barking deer (f1) and variable FT 188 varied markedly depending on whether goral (f2) and sambar (f3) were present. This model suggests that barking deer (f1) was more likely to occur together at sites where sambar (f3) was present (β = 12.80 ± 0.00), having FT 188  as a variable function of occupancy, while both barking deer (f1) and goral (f2) (β = − 13.38 ± 0.00), and goral (f2) and sambar (f3) (β = − 11.05 ± 0.00), are less likely to occur together at sites with FT 188  (β = 34.67 ± 163.39) were more likely to occur together than barking deer and goral (f12) (β = 16.50 ± 188.68) and goral and sambar (f23) (β = − 13.21 ± 188.68). This model also suggests barking deer–goral (f12) is negatively influenced by the variable (FT 188). The FT 188 showed negative influence on co-occurrence of barking deer-goral (f12) (β = − 13.38 ± 0.00) and goral-sambar (f23) (β = − 11.05 ± 0.00), while showed positive influence on occupancy of barking deer-sambar (f13) (β = 12.80 ± 0.00). The model also showed that the probability of two species occupying the same site as a function of covariates provided insight into factors driving marginal occupancy probabilities that might not have been evident otherwise. Our results concluded that individual species' occupancy probabilities were related both to environmental variables and the presence or absence of other interacting species  of each species. Our top model suggests evidence of interspecific dependence of the three species  and pair-wise interaction  of three ungulate species in Uttarkashi. The top model assumed the occupancy of the all thethree species at different sites varied as a function of habitat variables ψ (FT 188 + Distance to village) when detection probability was kept as constant p(.) (Table f1) was positively influenced by distance to the village and negatively influenced by FT 188  (Table f2) exhibits a positive relationship with variable FT 188 and a negative relationship with variable distance to the village. In contrast, marginal occupancy of sambar (f3) was positively influenced by FT 188 and negatively influenced by distance to the village  among three ungulate species that varied along with environmental variables in the present study. Nonetheless, we observed the anticipated negative association of FT 188 with pair-wise interaction of f12  and f23 . However, pair-wise interaction showed; that occupancy of f13 (barking deer-sambar) was positively influenced by FT 188. Of the three species, goral (f2) showed the broadest elevation range covering up to 3600 m. Other studies on the ecology and distribution of goat-antelopes also indicated a broad elevation range for goral49 in western Himalayas. These studies indicated that goral could be found from very low elevation (500 m) to the tree line (4000 m). Since FT 188 is negatively influencing the pair-wise interaction of barking deer-goral and sambar-goral, we suggest that this might be because of resource partitioning, which leads the species to occupy different habitats. Goral inhabits steep mountainous areas and sometimes use forests near cliffs but primarily stays within rugged rocky terrain covering a broad elevation range. Whereas sambar and barking deer are forest dwellers, sambar (f3) prefers hilly areas with high tree density and showed the least affinity towards human settlement, while barking deer prefers plain areas51.This is the first attempt to model multi-species occupancy of ungulates from Uttarkashi, Uttarakhand, and the entire Himalayan region. We found evidence for pair-wise interactions (. Since species-specific occupancy of barking deer (f1) was negatively influenced by FT 188 whereas FT 188 positively influenced the pair-wise interaction of barking deer-sambar (f13) which suggested barking deer (f1) was more likely to occur together at sites where sambar was present. Many species occur in sympatry where intraguild competition is frequent. Further, intraguild competition is an important determinant in structuring ecological communities, as it can lead to spatial or temporal segregation among species. Since we found evidences that the interaction between barking deer and sambar in FT 188 is positive, we suggest that the dietary overlap and resource competition of the two species might be small enough to allow coexistence.The model provides the probability of pair-wise interaction that two species occur together as a function of covariates. FT 188 positively influenced the marginal occupancy of goral and sambar and negatively influenced the marginal occupancy of barking deer52, which suggests barking deer also showed a positive association towards distance to the village, although barking deer (f1) prefers dense forest with high understory53. However, barking deer (f1) are also reported to occupy degraded tracts of forest ranges near human settlements. Their inability to live on rugged steep mountain slopes allows them to occupy forested habitats close to human habitations53. At the same time, goral (f2) and sambar (f3) showed a negative association toward distance to the village. Both the species are shy and mostly solitary thus, avoidance of villages was quite normal, similar to the results of54. The goral (f2) occupancy was associated with a wide variety of habitats throughout the mountain range28, and predominately, it is adapted to steep slopes with rugged mountain terrain56.Moreover, our findings were similar to that off2) was active throughout the day with decreased activity in the early morning and evening hours  is probably associated with more tree cover in winter because of their vulnerability to predation and food availability during heavy snow conditions. Such factors could influence the increased use of tree cover by the goral in summer as the need to find shelter during the monsoon or the need to secure cover for parturition. The biotic and abiotic conditions are essential for understanding the interspecific interactions as they determine the site utilization by the species. Hence, researchers have recognized their imperatives as covariates for modelling the space use, habitat selection57, and distribution58 assessment of a species. Accounting for the interspecific interactions may be necessary when predicting future distributions, predominantly in understanding the impacts of global warming and climate change on the distribution of species and communities. Hence, the present multi-species occupancy model provides a strategy for understanding the interspecific interactions for imperfectly detected species.The activity pattern results suggested that the goral f was acti58. The long-term survival of wildlife depends on sufficiently large areas of suitable habitat and decreasing anthropogenic pressure. The present findings may be helpful for the better conservation and management of the mountain ungulates in the Indian Himalayan Region and other adjoining areas. Hence, we propose that areas supporting suitable habitats for all three mountain ungulates should seldom have anthropogenic activity for proper management and conservation of the species given the influence of FT 188 on the occupancy of the three species, we would recommend plantation and assisted natural regeneration of the local plant species in suitable gap areas for supporting the ungulates in the landscape.Moreover, it may help in evaluating how the interspecific interactions shape habitat selection and species distributions. Among the three ungulate species studied, sambar and goral are threatened according to the IUCN category. Habitat loss, anthropogenic pressure, and wildlife hunting pose a formidable challenge for conserving wildlifeComplex terrain, inaccessibility and heavy snowfall are the limitations which make it difficult to study the species in the landscape. Due to weather conditions, heavy rainfall, landslides and snowfall during winters, we were not able to do sampling throughout the year, which is the major limitation of the study. Inferences have been made on the basis of short sampling effort, however, long-term study with intensive sampling is required for proper conservation and management of the ungulates. Though our data was collected relatively from a small area, information on the environmental factors governing the distribution of the ungulates would establish the baseline information on the distribution of ungulates in the landscape.2, covering primarily hilly terrain with an altitudinal range of 715–6717 m  Uttarkashi Forest Division (ii) Upper Yamuna Badkot Forest Division and (iii) Tons Forest Division) with two Protected Areas (PAs) (i) Gangotri National Park and (ii) Govind Pashu Vihar National Park. The forested habitats of the study landscape are home to top conservation priority species, including Asiatic Black bear (Ursus thibetanus), Musk deer (Moschus spp.), Common leopard (Panthera pardus), Himalayan brown bear (Ursus arctos isabellinus) and Western Tragopan , Himalayan monal (Lophophorus impejanus). The study was conducted after a study permit issued by the Chief Wildlife Warden, Forest Department, Uttarakhand government, vide letter no. 848/5-6 dated 31/08/2019, we have not handled the species for doing research. Instead, remote camera traps have been used for collecting the data with the permission of the Chief Wildlife Warden, Government of Uttarakhand. Further, informed consent was taken before interviewing the local communities. The data was collected according to the institutional guidelines and approved by the Research Advisory and Monitoring Committee of the Zoological Survey of India.The present study was conducted in Uttarkashi district, Uttarakhand, located between 38° 28′ to 31°28′ N latitude and 77°49′ to 79°25′ E longitude with an area of about 8016 km7. Briefly, a set of 62 intensive sites, were randomly selected, and each site i was surveyed j times. During each survey, detection/non-detection of S focal species was recorded. Additionally, direct or indirect evidences of species presence from the different areas were also recorded.The basic sampling protocol and assumptions for multi-species occupancy modelling are identical to the single-species casehttps://browningtrailcameras.com) camera traps were used to detect the presence/absence of ungulate species. The cameras were mounted 40–60 cm above ground on natural trails without lures.The complete study area was divided into 10 × 10 km grids, consisting of n = 60 grids. Based on the reconnaissance survey, out of these 60 grids, we selected 25 girds that were accessible to conduct the survey and have the species presence. Further, these grids were divided into 2 × 2 km grids to maximize our effort so that all logistically accessible grids could be covered, and we conducted intensive sampling in N = 62 grids after excluding the grids with human settlements. T The field surveys were conducted during 2018–2019, and a team of researchers systematically visited selected grids to collect data on the detection/non-detection of these ungulates. A total of 62 camera traps were deployed in selected grids, and 650 km were traversed, accounting for N = 54 trails in these sampled grids. These camera traps were visited once in every fifteen days for replacing the batteries as well as documenting the presence of the species through the sign surveys. The ultra-compact SPYPOINT FORCE-11D trail camera  and Browning trail camera . The habitat/ land cover classification was carried out using Landsat 8 satellite imagery  downloaded from Global Land Cover Facility by following the methodology suggested by61 using the ArcGIS v. 10.6 software . The study area was classified into nine Land use/land cover (LULC) classes viz., West Himalayan Sub-alpine birch/fir Forest (FT 188), West Himalayan upper oak/fir forest (FT 162), West Himalayan Dry juniper forest (FT 180), Ban oak forest (FT 152), Moist Deodar Forest (FT 155), Western mixed coniferous forest (FT 156), Moist temperate Deciduous Forest (FT 157) which were used for further analysis considering their importance to species ecology and behavior60. The values for all the covariates were extracted at 30 m resolution, and a single value per site was obtained by averaging all the pixel values within each sampling site (camera trap locations).We hypothesized that habitat variables may influence these ungulates' occupancy and detection probability. A total of 21 variables were extracted either from the field or using the ArcGIS v. 10.6 software , and only 14 were retained after collinearity testing60 Table . These c62 of barking deer, goral and sambar to estimate the probability of the species (s) occurred within the area (i) sampled during our survey period (j), for accounting the imperfect detection of the species8. Distinguishing the true presence/absence of a species from detection/non-detection  requires spatially or temporally replicated data. We used camera stations to record the presence/absence of species along with sign survey in all the studied grids. The camera traps were placed along the trail/transects in the studied grids hence each grid needs to be visited once in every fifteen days to check the camera traps as well as to document the presence of the studied species. Therefore, we treated 15 trap nights as one sampling occasion at a particular camera station resulting in ~ 7 sampling occasions per camera station.Our aim was to record the presence/ absence of the species at a particular gird hence we incorporated sign survey data if the species was not detected in camera station but recorded through sign survey. We pooled the presence/absence data in a single sheet of each species following6 and fitted occupancy and detectability models using programme Mark64. We model the species (s) presence (ysij = 1) and absence (ysij = 0) at site i during survey j, and the sampling protocol was identical to single species case65, where the Bernoulli random variable was conditional on the presence of species s (Zs = 1) following6sij represents the probability of detecting species S during replicate survey j at site i and Zsi = presence or absence of species s at site i.We used multi-species occupancy modellings at site i as a multivariate Bernoulli random variable:i = {Zi1, Zi2….., ZSi} is an S-dimensional vector of 1’s and 0’s denoting the latent occupancy state of all S species and (ψi) is a 2S-dimensional vector denoting the probability of all possible sequences of 1’s and 0’s Zi can attain such that ∑ ψi = 1 with corresponding probability mass function (PMF) adopted from64.Furthermore, we model the latent occupancy state of species f = log (ψi1/ψi0), is the log odds species S occupies a site often referred to as a ‘natural parameter’.The quantity S = 23 the possible encounter histories included in the dataset were eight, if neither of the two species were detected the value of ‘00’ was assigned; similarly ‘01’ indicates detection of species 1; ‘02’ indicates detection of species 2; ‘03’ indicates detection of both the species; ‘04’ indicates detection of species 3; ‘05’ indicates detection of species 1 and species 3; ‘06’ indicates detection of species 2 and species 3 and ‘07’ indicates detection of all the three species. We modelled constant occupancy and detection probability for each of the three species. Hence, we specified 6 f and p parameters, an intercept (β) for each of one-way f parameter and detection parameter p following64.Since we are modeling three ungulate species (S = 3), 2We fit a set of models including the detection probability as a constant, p(.), and variable function to occupancy ψ(covariate) for site-specific covariates and models include occupancy as constant ψ(.) and variable function of the detection p(covariates) for the respective site covariates.f1: occupancy of species 1, f2: occupancy of species 2, & f3: occupancy of species 3) and detection probabilities using a generalized linear modelling approach42. This requires 9 parameters: an intercept  and slope  coefficient for each 1-way f parameter f1, f2, f3 and an intercept parameter for each detection parameter . Below mentioned is the model for 1-way f parameters.As we have assumed the independence among all three species, the model shows marginal occupancy probabilities of species 1, species 2 and species 3 varies as a function of environmental variables. We incorporated site-level characteristics affecting species-specific occurrence  and pair-wise interaction  parameters. We modeled pair-wise interaction of species varies as a function of environmental variables keeping detection probability constant. Hence, we specified 15 f and p parameters, an intercept and slope coefficient for each of the one-way  and the two-way f parameters ; as well as an intercept parameter for each of the detection models. The model equation below implies for 2-way f parameters:Since multi-species occupancy simultaneously model environmental variables, & interspecific interactions. Further it also allows to understand the influence of environmental variables on one species occupancy, in the presence or absence of other sympatric speciesf and p parameters, an intercept and slope coefficient for each of one-way  and two-way f parameters ; and an intercept as well as the slope parameters for each of the detection models. The model equation below implies for 2-way f parameters:We also fitted models including co-occurrence and detection probability of a species varies as a function of environmental variables. Hence, we specified 18 f1, f2, f3) and pair-wise interaction of the three ungulate species. The best-supported model was identified by selecting the model with the lowest AICc value and highest model weights66, where higher model weights indicate a better fit of the model to the data. Second-Order Information Criterion (AICc)67 values were used to rank the occupancy models, and all the models whose ΔAICc < 2 were considered as equivalent models. The Akaike weight represents the ratio of ΔAICc values for the whole set of candidate models, providing a strength of evidence for each model. The sign of the logistic coefficient of each variable (positive or negative) was used to determine the direction of influence of the variables on the occupancy and detection probability of the three ungulate species.A total of 38 models were run to test the influence of environmental variables on occupancy and detection probability of species-specific (68. We used a Daily Activity Index (DAI) of half an hour duration to examine the daily activity. The coefficient of overlap is denoted by “Dhat1” values, ranging between zero (no overlap) and 1.0 (complete overlap).We have compared activity patterns among species to see how overlapping patterns may relate to the competition using the package “Overlap” in R (R Development Core Team). The time and date printed on the photographs have been used to determine the daily activity pattern of individual species