The results map out the local carbon and nitrogen baselines and define isotopic ranges of local terrestrial, avian and aquatic fauna. We also demonstrate the potential application of sulfur stable isotope analysis in archaeological research. The results demonstrate a clear distinction between δ13C and δ34S values of marine and terrestrial species, however, freshwater fish display notable overlaps with both marine and terrestrial ranges for both δ13C and δ34S values. Herbivores show variation in δ34S values when grouped by region, explained by differences in the local biotopes. This study is the first attempt to connect the Eastern Baltic isotopic baselines and provides more detailed temporal and geographical references to study the local ecologies and interpret the human data.To better comprehend the dietary practices of past populations in the Eastern Baltic region we have created temporally and geographically restricted baselines for the time period of 200–1800 CE. In this multi-isotopic analysis, we report new δ The adoption of stable isotope analysis to study archaeological questions has revolutionized the field by providing new insight into topics as varied as diet, social equality, palaeoecology, and past movements of people and animals. It has become a staple of multidisciplinary investigations, however, some regions such as the eastern part of Europe have been trailing behind in regards to fully embracing the method, as the arrival of modern scientific methods have reached the area with a certain delay. During recent years, there has been a sizeable increase in the number of publications of stable isotope analyses from the Baltic country of Estonia, yet most data have focused on analyzing human skeletal remains –5 with l13C, δ15N and δ34S values from two historic period burial sites in northern Estonia [Proper baseline information is required to accurately reconstruct the nuances of prehistoric and historic dietary habits in the region. The authors of this study have highlighted this need in various papers about the dietary habits of hunter-gatherers , Bronze  Estonia ,8. HowevThis trend of terrestrial carbon signals coupled with high nitrogen isotope values has also been observed in other Medieval populations from Northern Europe –13 and i34S values from two historic period cemeteries displayed a surprisingly wide variation, indicating either very diverse food sources or migration between areas with different sulfur isotope baseline values. While the application of sulfur isotope analysis has shown great potential [34S values between different ecosystems  and/or regions. Having a good overview of the local faunal baseline is therefore crucial for the successful utilization of sulfur stable isotope analysis. It is also necessary to differentiate sulfur isotope variation caused by dietary differences  from that caused by differences in origin.The Medieval case-study from northern Estonia  also demotential ,17–24, tvs aquatic, and domesticated vs wild species in the later part of Iron Age (200–1225 CE), Medieval (1225–1560 CE) and Early Modern (1560–1800 CE) periods. While this approach is limited in directly following temporal continuity, the main goal is to obtain a regional overview, thus observing temporal or site-specific patterns is of secondary importance. Our research ties into the wider discussion on the need for isotopic baseline datasets for the eastern Baltic Sea region [This study incorporates the largest and most comprehensive set of faunal bone collagen stable isotope data from prehistoric and historic Estonia. The dataset covers the whole geographical area of present-day Estonia, including 197 faunal skeletal samples (ca. 700–1800 CE) collected during a multidisciplinary project on the foodways of Medieval Estonia (Estonian Research Council grant No PRG29), and 54 samples from the Georeferenced dataset of stable carbon and nitrogen isotope values of prehistoric Estonia and its neighboring areas (ca. 200–1650 CE). By characterizing temporal and geographical trends in isotopic baselines in the area of present-day Estonia we aim to provide an interpretative framework for human paleodietary reconstructions. We will identify the respective local isotope ranges of terrestrial ge 200–12 CE, MediAs the northernmost of the three Baltic States, today Estonia enjoys a humid, continental climate with clearly defined seasons and ample forests, rivers and lakes . SurrounThe Baltic Sea, one of the largest brackish-water inland seas in the world, has a diverse hydrological history and has fluctuated between freshwater and marine conditions since the onset of the glacial retreat at the end of Pleistocene. In its present Limnea Sea stage  it is characterized by minor inflow of Atlantic saltwater through the narrow Danish Straits and abundant freshwater runoff from the large catchment area of the Baltic Sea ,31. The Estonia has a moderately varied topography with the main features being an extensive limestone plateau in the northern part of the country, a relatively flat low-lying area in the west and islands, and gently sloping hills in the south . The preThe basic principles of stable isotope analysis and its use in archaeology are well established ,37. It i13C) are used to distinguish between marine and terrestrial sources of carbon, but also between diets based on either C3 or C4 plants [13C of about 5‰ between plants and herbivorous animals, and about 1‰ between carnivores and their prey [13C anywhere between -12‰ and -28‰ [Carbon isotope ratios  broadly reflect the trophic level of the individual, as δ15N values increase by about 3–6‰ with every step up the food chain [15N values. Several factors can influence the nitrogen isotopic composition of plants and animals, e.g., climatic conditions such as precipitation and temperature [Nitrogen isotope ratios  in terrestrial plants have been shown to vary significantly due to different sulfur sources in the local geology, with additional sulfate sources from the hydrosphere  and atmosphere  all contributing to the average δ34S values of the local biologically available sulfur [34S values so that there is a lot of potential overlap between the terrestrial and freshwater ecosystems [34S values of marine organisms living in the ocean are fairly constant and fall within a relatively narrow range between 17‰ and 21‰ [34S values, resulting in plants grown on these soils having sulfur isotope values similar to the marine ecosystem [Sulfur isotope ratios  specimens are listed under ‘wild animals’, it is possible that some of these were likely domestic birds [Individual sample selection was based on availability of identified faunal remains in the chosen zooarchaeological assemblages. Altogether 251 samples representing the main sources of animal protein available to the local people were collected, including the most common domestic and wild terrestrial and avian species, and various marine and freshwater fish . Althougic birds .Temporal parameters of each sample are assigned based on archaeological context and, where possible, radiocarbon dating . The rural societies from the Iron Age until the Early Modern Period were small agrarian villages by their structure that formed larger parishes . In esseAll necessary permits were obtained for the described study, which complied with all relevant regulations. Sampling permission was granted by the Archaeological Research Collection at Tallinn University, Estonia , Institute of History and Archaeology at the University of Tartu, Estonia  and Tartu City Museum, Estonia . Sampling protocols (with photographs before and after sampling) are stored with the respective collection holders. Specimen numbers and other contextual information can be found in 13C, δ15N and δ34S isotope analysis for these samples was conducted at the Scottish Universities Environmental Research Centre (SUERC) Radiocarbon Laboratory in East Kilbride, United Kingdom. Radiocarbon ages were obtained from selected samples (n = 13) at the Poznań Radiocarbon Laboratory in Poland. For the remaining 54 samples, collagen extraction and radiocarbon dating was performed at the Leibniz Laboratory for Radiometric Dating and Stable Isotope Research, at the Christian-Albrechts-University of Kiel, and stable isotope measurements done at the Isolab GmbH, Germany. Thirteen (n = 13) samples were further analyzed with Zooarchaeology by Mass Spectrometry (ZooMS) in the BioArCh lab at the University of York, United Kingdom, to differentiate between goat and sheep  had a C:N ratio of 3.7 but satisfactory elemental concentrations, so was included in the dataset. The other (hare–GUsi10812) had a ratio of 3.8 but since this sample also had problematic δ34S quality indicators, it was discarded from further analysis. For carbon and nitrogen concentrations, most samples were above 30% for %C and more than 10% for %N, indicative of good quality collagen [To check sample quality, routinely used criteria were followed . A few s9 to 3.6 ,69, excecollagen . Seven scollagen .13C and δ15N. Arguably, the research concerning these criteria is still in progress as the number of controlled, large-scale studies on δ34S isotopes is relatively low. In our study, mammalian and avian samples have an average C:S atomic ratio of 482 ± 96 (1-sigma standard deviation), N:S atomic ratio of 144 ± 29 (1SD), and sulfur concentration (%S) of 0.24% ± 0.1% (1SD), consistent with results reported by other researchers [13C and δ15N values for these samples were not excluded as the other collagen quality indicators were acceptable.Quality indicators for sulfur stable isotopes are not as established as for δearchers ,23,71. W34S to argue whether the reported values may be influenced by contamination. Since it seemed to us that these data were still meaningful, we chose to include them in our study.Fish atomic C:S and N:S ratios reported here  are somewhat higher than those seen in other studies ,23,71 anStatistical analysis was applied to determine whether differences between groups of data were  significant. A non-parametric Mann–Whitney U test was preferred due to the presence of outliers and non-normally distributed data . When more than two groups were compared, the non-parametric Kruskal–Wallis H test was applied. The rejection of the null hypothesis for the Kruskal–Wallis test was automatically followed by a post hoc analysis using Dunn’s procedure with a Bonferroni correction for multiple comparisons. Statistical uncertainty was set at 95%.Results of stable isotope analyses are summarized in Due to the diverse dataset, it was not possible to follow a rigid sampling procedure, e.g., only sampling specific skeletal element(s) or only adult (mature) animals. We acknowledge that these factors may result in data that are not entirely comparable due to minor isotopic differences caused by intraskeletal and interspecies variation in bone collagen turnover rates –75 and a13C and 5.9 ± 1.3‰ for δ15N, domestic omnivores –21.3 ± 1.0‰ and 8.9 ± 1.6‰, wild mammals –22.6 ± 0.6‰ and 5.1 ± 1.7‰, and geese –22.7 ± 0.3‰ and 9.9 ± 2.1‰  due to the inclusion of animal protein in the diet of omnivorous animals.Domestic herbivores have average values of –21.7 ± 0.5‰ (1SD) for δ9 ± 2.1‰ . These r13C and δ15N values. δ13C values range from –20.1‰ to –23.1‰. There are no statistical differences in δ13C values between domestic herbivores found from urban vs. rural contexts  were likely due to forested environments [13C values can be associated with animals raised in open areas, probably close to human settlements. However, there are no statistically significant differences between domestic herbivore δ13C values by region, nor when only comparing coastal vs. inland samples. Although terrestrial plants display geographical variation in stable carbon isotope ratios due to climatic conditions such as water availability, temperature, and sunlight exposure [Among domestic herbivores, there is a particularly large variation in both δcontexts . Lower δronments ,79, e.g.exposure ,80,81, t15N values range from 2.7‰ to 10.3‰. The large variation can be explained by various scenarios which are not necessarily mutually exclusive. For example, atypically high δ15N values in herbivores can be caused by nursing, i.e. suckling animals literally feeding off their mothers [15N (and δ13C) values  with the latter having on average higher δ15N values  values compared to Medieval ones, although the differences between chronological contexts are not statistically significant . We are not sure why Medieval herbivores would have had lower δ15N values compared to Iron Age and Early Modern animals , having been preceded by relatively warmer conditions in Northern Europe during the so-called Medieval Warm Period (ca. 9–14th centuries) [15N trend to what is observed here. It thus seems unlikely that climate had a significant effect on terrestrial herbivore nitrogen isotopic values in our dataset.A general trend in global soil δperature . Similars milder . The onls milder ,83, whicnturies) . As such15N values when analyzed by species  and δ15N values from 5.3‰ to 11.7‰ . The range of omnivore δ15N values is in fact smaller than was reported for domestic herbivores . There are no statistical differences between urban and rural omnivore δ13C and δ15N values. Statistical comparisons between omnivores from different regions and periods were run  tend to plot in-between. There is a positive significant correlation between pig δ13C and δ15N values , suggesting that variation in pig isotope values can be best explained by increased reliance on higher trophic level protein. Pigs sampled here range from almost fully herbivorous (possibly left to roam freely in forests) to those similar to chicken and dog. However, most pigs show little overlap with ruminants when compared with samples from the same site , suggesting that those on predominantly herbivorous diets were not consuming the same plants as (most) cattle and caprids were.Pigs show the most variation in δ13C values above –20‰. Dogs’ isotopic values can sometimes be used as a proxy for human diet due to their role as companions and pets. Indeed, published human isotopic data from two historic period sites in northern Estonia [th–18th century) have mean values of –20.0‰ and 11.2‰ for δ13C and δ15N compared to –20.0‰ and 10.7‰ for urban dogs in this study. For rural dogs, the mean values of –20.5‰ and 9.6‰ for δ13C and δ15N are more distinct from rural humans buried at the Kaberla village cemetery (12th–17th century), who have mean values of –19.8‰ and 10.4‰. The larger discrepancy between rural dogs and humans may be due to the fact that the cemetery is from northern coastal Estonia whereas the majority of rural dogs sampled for this study are from inland sites further south. However, the close similarity of urban commoners’ and dogs’ isotope values from similar contexts supports the assumption that dogs were likely fed household scraps and leftovers, including some aquatic resources as evidenced by two dogs  with δ13C values of –17.9‰ and –18.3‰.Dogs are the most distinct of all omnivores, indicating a unique diet, and are the only terrestrial species with δ Estonia  exhibit 13C and δ15N values compared to most domesticated animals. Statistical comparisons between wild and domestic herbivores demonstrate significant differences in their δ13C values , but not for nitrogen . No similar comparisons were run for omnivores due to their fewer numbers in the dataset. The isotopic range of wild mammals reported here is characteristic of forested environments and the consumption of wild (i.e. non-cultivated) plants. There is a noticeable range of isotopic variation observed for hares, most of which are from similar contexts , probably reflecting differences in habitat and food availability. One hare is a clear outlier  .Terrestrial animals display a remarkably wide range (17.8‰) in their δ8‰) Figs . There i34S values similar to the surrounding terrestrial vegetation. Because of this and how the local sulfur isotopic baseline has remained relatively constant in (pre)history, the observed variation in our dataset is unlikely to have been caused by species- or period-specific differences. For this reason, sulfur isotopic data should be analyzed by region.Animals obtain their sulfur through dietary protein  with only a minor (on average +0.5‰) trophic level change between consumer and food source ,61,85. T34S values from the four regions are compared with each other, demonstrating noticeable and statistically significant  differences between them  and only omnivorous animals (including geese). While geese are predominantly herbivorous, their δ34S values cannot be considered a reliable indicator of the local terrestrial baseline due to their preference for aquatic plant consumption, in addition to the possibility that some sampled geese may have been wild (i.e. migratory) birds. However, removing the geese samples from analysis altogether does not significantly change the outcome, as most specimens actually plot near the regional mean δ34S value, which may suggest that they were locally raised.Since the terrestrial fauna also includes omnivorous animals, whose δ34S values remain consistent even if only terrestrial herbivores are included in the analysis  differences between omnivore and herbivore mean δ34S values, with the former having on average around 2‰ higher values compared to the latter. This variance is best explained by the consumption of aquatic protein  by omnivorous animals, which has resulted in an increase of local terrestrial δ34S values. Inland regions do not show these differences. It is unlikely that this is due to inland omnivores not consuming any aquatic protein; the lack of difference is rather caused by the local terrestrial δ34S baseline already being higher there.Omnivore mean δ34S values may also reflect an inclusion of dietary sources affected by the ‘sea-spray effect’, which results in increased δ34S values due to the effects of airborne marine sulfates on coastal soils and plants [34S values in the whole dataset, although some herbivores from coastal areas do have noticeably high δ34S values. The absence of a consistent sea-spray effect can be taken to suggest that either its range is relatively limited and/or that most of the sampled terrestrial fauna were not feeding close to the shoreline. However, without sampling local geology, the true extent of the sea-spray effect is difficult to estimate. The terrestrial baseline may theoretically be highly negative but dampened by various proportions of marine sulfates.The increase in average coastal omnivore δd plants ,63. Howe34S values by region  and both herbivorous and omnivorous domesticates. It is noteworthy that two dogs with clear signals of marine resource consumption  also have some of the highest δ34S values in this region. This can be compared to another dog sample from the same context that displays much more ‘terrestrial’ isotopic values , coupled with a very low δ34S value of –2.2‰. Based on the size of the sampled bone, this individual may have also been a wolf. It would thus seem that the lower end of δ34S values reported for ‘northern coastal’ may actually represent the local terrestrial baseline, whereas higher δ34S values can be explained by the influences of the sea-spray effect (for herbivores and omnivores) and consumption of aquatic resources (for omnivores).Looking at individual terrestrial faunal δy region , ‘northe34S values, albeit with a slightly smaller range compared to the northern coast ‒ 13.8‰, from –2.9‰ to 10.9‰. There are also notably less samples that fall outside the 1SD range for ‘western coastal’. A few domestic herbivores have δ34S values below 0‰. These animals may have been herded in areas closer to the northern coastline. On the other hand, herbivores with the highest δ34S values were likely raised on or near coastal soils influenced by the sea-spray effect . Interestingly, several geese (sampled from a single context) all have very similar δ34S values . These particular geese were probably domestic and kept for food since their high δ15N values and large bone size were indicative of fattening [34S values may be considered a good representation of the local baseline .Terrestrial fauna from the ‘western coastal’ region displays equally marked variation in δattening . It seem34S values again show a rather substantial range  but the results are much more concentrated compared to coastal regions. A few animals with values below 0‰ are likely from areas closer to the coast, and likewise samples with very high δ34S values may originate from other areas .In ‘central inland’, δ34S values is narrow compared to other areas . Several wild hares, which likely were local specimens, were sampled here and most fall within the 1SD range of the regional average, including the outlier with atypical carbon and nitrogen isotope values. A few herbivores have δ34S values around or above 10‰ which may suggest that the local terrestrial baseline might be even more positive further south/southeast. The highest reported δ34S value  is from an elk (11.5‰). On the other hand, a beaver has a rather low δ34S value of 3.7‰, similar to two geese and a few other samples with δ34S values below 5‰. Fauna with such low δ34S values was probably non-local, brought to the ‘southern inland’ region through trade or hunting activities.For the ‘southern inland’ region, the range of δ34S values of herbivores (both wild and domestic) are compared based on site or local region (if too few samples from one site), with the 1SD range of the herbivore average for each of the four main regions marked with a rectangle. This graph is supported by 34S values plotted on the map of Estonia based on sampling area. Even though bedrock is thought to be only one of many components influencing the δ34S baseline of a certain region, it is clear from our data that geology seems to be a major factor behind the observed sulfur isotopic variation in this region. Further studies on rock, soil and plant δ34S values would be beneficial in supporting this hypothesis.In The fact that there exists such a gradient in local terrestrial faunal sulfur isotope ratios from the north-west to south-east can be extremely useful for studies of human migration and animal trade. However, this assumes that we understand all the factors influencing terrestrial faunal sulfur isotope values and can determine the local baseline with as much accuracy as possible.34S terrestrial baselines in coastal regions requires additional research, as the current variation among sampled herbivores is far too great and cannot be reliably used as an indicator for sulfur isotope values of local plants. However, it is reasonable to assume that the lowest reported δ34S values from coastal regions likely reflect the local terrestrial baseline and the remaining variation can be explained by marine influences (i.e. sea-spray). We do not know the true extent of the sea-spray effect, but in the ‘northern coastal’ region most animals with δ34S values below 0‰ originate from sites to the south and east of Tallinn which can be considered to represent the rural hinterland, whereas herbivores from the urban center of Tallinn have an average value of 3.3‰. In fact, all samples from the ‘northern coastal’ region with δ34S values above 6‰ are from Tallinn, a town situated right on the coastline.The exact range of δ34S values are from another coastal town ‒ Pärnu. It is very likely that livestock from Tallinn and Pärnu were sometimes herded on coastal meadows  δ periods ,87) whic34S values specific to towns and smaller regions shown in 34S values ± 1SD. The 1-sigma standard deviation is much higher for coastal fauna but we do not believe this needs correcting since animals herded on coastal soils  were also routinely consumed and thus the larger variation would also be reflected in local human δ34S values. This has significant implications for using δ34S for palaeodietary reconstructions in this region, especially in terms of marine resource consumption, as it would be difficult to fully distinguish whether increased δ34S values of humans are due to consumption of aquatic resources or terrestrial resources influenced by the sea-spray effect.In the context of using sulfur isotope analysis to reconstruct diet and origin of humans from these periods, average δ34S values (on average 3.7‰) compared to southern central sites (6.0‰), although the difference is not statistically significant .For samples from ‘central inland’ region, a distinction should be made between northern and southern sites , but not for δ13C  coupled with relatively low δ15N values (ca. 10‰). We presume these fish to be caught locally, i.e. to represent the isotopic signal of the Baltic Sea. This would be in accordance with previously published data [13C values around –16‰ to –18‰, whereas cod from western Baltic and the North Sea have carbon isotopic values around –13‰ to –15‰. Since carbon isotope ratios are directly correlated with water salinity [13C values compared to ‘typical’ marine environments [Five cod samples  are clearly separate from the rest of the fish, displaying a ‘typical’ marine signal with δorth Sea . The remhed data ,88–90 thsalinity , variousronments .vs. from the North Sea are distinguished by both their δ13C and δ15N values. While the former variation is due to the brackish conditions  of the Baltic Sea, lower δ15N values of locally caught cod may be an indication of their trophic position. North Sea cod have higher δ15N values because of the increased number of trophic levels in the oceanic food web. They also have faster growth rate, resulting in oceanic cod being generally larger in size [15N values [15N values.Cod caught from the Baltic Sea  in size ,93. SincN values . Among t15N values  and high δ13C values (similar to cod from the North Sea). In these instances, the δ13C values probably do not reflect variations in seawater salinity, but rather changes in water turbidity. For example, δ13C of aquatic species varies based on whether they are from faster moving open water areas (offshore) or from slower moving waters (nearshore), so that very high δ13C values are often seen in fish living in stale waters [Two marine samples in our study (a cod and a turbot) display a combination of low δe waters . Turbot,e waters , wherease waters .KIA-55657) which has higher δ13C and δ15N values  compared to the other three seals . This range of values is similar to those of imported cod and is somewhat higher than reported for Bronze and Iron Age harp seals that were feeding and breeding in the Baltic Sea [Seals sampled in our study have generally uniform isotope values, suggestive of feeding on local  marine fish, except for the harp seal from Rebala  [For freshwater fish, which are characterized by even greater variation in both their δs, etc.) .13C values (from –23‰ to –25‰) and δ15N values between 10‰ and 14‰. These fish probably originated from fast flowing rivers in inland regions. The noticeable variation in δ15N values even within one species  may reflect individual differences in size. While fish samples that were identified as having belonged to large individuals had higher than average δ15N values, high nitrogen isotope values were also seen in those specimens that were identified as medium-sized. Most freshwater species with low carbon isotope values are from inland sites.One of the two niches  is characterized by carbon isotopic values typically associated with freshwater fish, with low δ13C values (up to –11‰). These include pike, perch, bream and ide. The carbon and nitrogen isotope values for this group partially overlap with those from locally caught cod , suggesting that these samples represent freshwater fish living in the brackish conditions of the Baltic Sea. The highest δ13C values are probably influenced by a littoral habitat, i.e. living in shallow waters close to the shore, as also suggested by Eriksson et al. [13C (between –13‰ and –10‰) values for pike and perch from the Baltic Sea island of Öland (Sweden). The low δ15N values of species such as bream and ide reflect their feeding habits and lower trophic position compared to piscivorous species such as pike and perch. Most freshwater species with carbon isotope values higher than –20‰ are from coastal sites.The other group of freshwater fish is set apart by their high δn et al. , who rep34S values of aquatic species plotted against their respective δ13C and δ15N values. Marine species in our study are well distinguished by their δ34S values, generally falling between 15‰ and 18‰. This range of δ34S values was also measured for modern cod caught from the Baltic Sea [34S to distinguish between fully marine and coastal environments, with another cutoff point of 10‰ to signify marine environments with substantial riverine freshwater influx such as estuaries [Figs ltic Sea . A cutofstuaries ,98–100.13C and δ15N values between cod from the Baltic Sea and North Sea is not reflected in their δ34S values. While this may be an effect of the small sample size, it seems that marine δ34S values are not correlated with salinity the same way that δ13C values are, or that there are other factors behind the observed variability. The latter seems probable as even among cod thought to be imported from the North Sea or beyond  there is noticeable variation in δ34S values, from 12.2‰ to 17.6‰. The Rebala harp seal with isotope values similar to imported cod also has a δ34S value not reflective of the ‘typical’ marine sulfur isotope range (14.8‰), while the other seals believed to be local have much higher values (from 16.8‰ to 17.4‰).Interestingly, variation in δvs. Baltic Sea δ34S values is all the more surprising considering that local freshwater fish living in brackish conditions have statistically significantly different δ34S values  compared to purely marine species from the Baltic. While this may again be affected by the size of our dataset, the majority of brackish freshwater fish have δ34S values in the range of 10‰ to 15‰. This suggests that the freshwater fish mostly occupied coastal waters whereas cod and seals preferred offshore areas unaffected by freshwater sulfates. This may also explain why some of the specimens most depleted in 34S are also the most enriched in δ13C, as both of these instances occur in near-shore waters which likely experienced significant mixing of marine sulfates with freshwater and terrestrial sulfur sources.The apparent overlap in oceanic et al. [34S values of fish caught from the Thames estuary to those from adjacent coastal regions in southeast England, they observed a clear gradient of increasing δ13C and δ34S values that resulted from the mixing of marine and freshwater, with δ34S values ranging from –5‰ to 15‰ across the gradient. In our dataset, no similar gradient is evident when comparing freshwater species from purely freshwater  to brackish  waters. In fact, ‘freshwater’ and ‘brackish’ fish show significant overlap and no statistical differences in their respective δ34S values  paleodietary research of material from related contexts. Our results demonstrate that domestic omnivores and herbivores are well distinguished by their δvs. terrestrial δ34S values and the existence of a north-west/south-east gradient in terrestrial δ34S values influenced by local geology. Low terrestrial δ34S values (ca. 0‰) can be interpreted as originating from coastal regions , whereas highly positive δ34S values can be caused by various factors such as aquatic resource consumption, marine sulfate influence on coastal soils, or originating from the southern inland regions. These differences can potentially be exploited to study migration at a local level, e.g., to shed more light on exogamous practices that were common in (pre)history.This study has demonstrated the importance of sulfur stable isotope analysis in local archaeological research by showing clear differences in marine 34S values of freshwater fish partly overlapping with both terrestrial and marine sulfur isotopic ranges. However, δ13C values of freshwater species seem to be a good indicator of their habitat, e.g., whether they originated from inland  or coastal  regions. Since aquatic resources with such diverse isotopic signals were all routinely consumed, identifying their respective signals in consumer (i.e. human) isotope values is going to be challenging.Although some researchers have successfully used sulfur isotope analyses to identify freshwater resource consumption, this is problematic in our study area due to δ34S values in the territory of Estonia, supporting this with other isotopic proxies  to help distinguish between sulfur isotopic variation caused by origin and that caused by marine influence.Future studies should take advantage of the regional distribution in δS1 Fig(TIF)Click here for additional data file.S2 Fig(TIF)Click here for additional data file.S3 Fig(TIF)Click here for additional data file.S1 Appendix(XLSX)Click here for additional data file.S2 Appendix(XLSX)Click here for additional data file.S3 Appendix(DOCX)Click here for additional data file.S4 Appendix(XLSX)Click here for additional data file.


In this work, wehave developed two novel unit-specificevent-basedmixed-integer linear programing models for scheduling multipurposebatch plants. The concept of indirect and direct material transferis introduced to rigorously sequence and align tasks in differentunits. A batch after production is allowed to be partially transferredto storage and downstream processing units or held in processing unitsover multiple event points. The computational results demonstratethat the proposed models require a smaller number of event pointsin many cases to achieve optimality than existing unit-specific event-basedmodels. It is interesting to find that no task is required to spanover multiple event points to reach optimality for all addressed examples.The best variant developed is superior to existing unit-specific event-basedmodels with the same or better objective values by a maximum improvementof 67%. The computational effort is significantly reduced by at least1 order of magnitude in some cases. These models can also be classified intosingle- and multiple-time grid models.23 For more details about these models, the readers are referred tothe excellent review papers.24Multipurpose batch plantswidely exist in the chemical industryfor production of a large number of low-volume, high-value products.To achieve higher utilization of resources, lower inventory costs,and better responsiveness to a fluctuating manufacturing environment,optimal scheduling of multipurpose facilities is desirable and hasattracted much interest of both academia and industry in the pastdecades. Many mathematical models have been developed based on eithera state task network (STN)16 observed that if there areenough materials in their dedicated storage for consumption, somesequence constraints related to different tasks in different unitscould be relaxed. They also implied that if there is sufficient storagespace to hold materials, all related production and consumption tasksare not necessary to be rigorously aligned. Although their formulationdid require a smaller number of event points in some cases, it couldgenerate a schedule with real-time violation.17 Vooradi and Shaik17 noticed that if aconsumption task consumes a state from a specifically related productiontask, this consumption task should start only after the specificallyrelated production task instead of all related production tasks likeSeid and Majozi.16 They also required relatedproduction and consumption tasks not to be rigorously aligned forsufficient storage space. They improved their previous formulationof Shaik and Floudas,13 which indeed furtherreduced the number of event points required without real-time violationin comparison to the model of Seid and Majozi.16 However, they introduced an increased number of binaryvariables, leading to computational inefficiency. In addition, theirmodel can lead to a greater number of event points in many cases.All existing time-grid mathematical models divide the schedulinghorizon using time points/slots/event points on which a task, operation,or activity can start, finish, or both. Therefore, the number of timepoints/slots/event points directly affects the efficiency of thesemathematical models. More specifically, an increment in the numberof time points/slots/event points can lead to an exponential increasein the model size , which can potentially increase the computationaltime by at least 1 order of magnitude to generate the optimal solution.To reduce the required number of time points/slots/event points, Seidand Majozi25 and Mostafaei and Harjunkoski26 attempted to eliminate some big-M constraints in theirdeveloped models, which could lead to much more slots/event pointsrequired and sub-optimality. More importantly, the multi-grid modelof Mostafaei and Harjunkoski26 is applicableonly when the storage capacity is unlimited. With limited or finitestorage capacities, the schedules obtained from their models are ofteninfeasible due to violation of storage capacities. Shaik and Vooradi27 and Rakovitis et al.19 imposed related production and consumption tasks to start at thesame events. To improve the schedule accuracy for varying processingtimes from the discrete-time models, the combination of discrete-and continuous-time formulations was also investigated.29 In addition, machine learning techniques were also applied for onlineproduction scheduling.31Besides the abovementioned two attempts, Vooradi and Shaik19 They are also the basis for the development of decomposition algorithmsto solve industrial-scale scheduling problems. It is found that almostall existing unit-specific event-based models17 for scheduling of multipurpose batch plants still require a greatnumber of event points in many cases, leading to computational inefficiency.More importantly, almost all existing models did not allow a batchof materials to be temporarily stored in processing units or be partiallytransferred to downstream units after production, leading to sub-optimalityand inefficient utilization of processing units. Therefore, in thiswork, we have developed two novel multiple time-grid continuous-timeformulations using the unit-specific event-based modeling approachto address the abovementioned limitations. The concept of indirectand direct material transfer is explicitly introduced to sequencedifferent tasks in different units, which allow material transferto be monitored between units rather than specific tasks to reducethe number of discrete decision variables and improve the computationalefficiency. A batch of materials after production is allowed to bepartially transferred to storage and downstream processing units ortemporarily held in suitable processing units over multiple eventpoints. A new continuous variable denoting the time when a state producedin a processing unit is available at an event point is introducedto assist the sequencing of different tasks related to the same statesin different units, which overcomes the limitations in the existingunit-specific event-based models.17 Tofurther reduce the computational expense, some new tightening constraintsare proposed. A number of benchmark examples are solved to evaluatethe performance of the proposed formulations. The computational resultsdemonstrate that the best variant developed is superior to the existingunit-specific event-based models.In this work, we mainlyfocus on the existing multiple time-gridcontinuous-time models, especially the unit-specific event-based modelsfor short-term scheduling as their capabilities are well establishedin the literature.2I  tasks such as heating,reaction, and separation processed in J  units. The unit j can process Ij tasks. However, it can process at most one task at a time. All materialsincluding raw materials SR, intermediate products Sin, and final products SP aredenoted as states. There are S  states, subject to differentstorage policies such as finite intermediate storage (FIS), unlimitedintermediate storage (UIS), no intermediate storage (NIS), and zero-wait(ZW) policies. The proportion of a state s that atask i consumes or produces is known and denotedby a parameter ρsi.J units, suitable Ij tasks, minimum (Bijmin) and maximum(Bijmax) capacities; (b) S states,related Is tasks,initialamount, and storage capacities; (c) production recipes ; (d) economic data , scheduling horizon andproduct demands. It is to determine (a) optimal production scheduleincluding allocation, sequence, timings of tasks in a unit; (b) amountof materials being processed in each unit at each time; (c) inventoryprofiles of all material states. Assumptions include (i) all parametersare deterministic without batch/unit failures or operational interruptions;(ii) the processing time of a task depends on the batch size (bij), which is represented byαij + βij·bij; (iii)unlimited feed materials and other resources like utility and manpower;(iv) unlimited storage for raw materials and final products; (v) negligibletransfer time between facilities ;(vi) setup or changeover time is lumped into processing time; (vii)each state has its dedicated storage.The scheduling problem is statedas follows: Given(a) 14Two optimization objectivesare considered, including maximizationof profit over a given scheduling horizon and minimization of makespanto fulfill consumer demands. The detailed problem description canbe referred to Li and Floudas.3Supporting Information.We create threeexamples to illustrate the limitations of existingtime-grid continuous-time models for scheduling multipurpose batchplants. The STN representations and relevant data are provided inFigures S2, S3, and Tables S1–S5 in the 3.1–1. The objective is to maximizeprofit over a given scheduling horizon of 8 h. We use the models ofSusarla, Li, and Karimi,10 Li and Floudas,14 and Vooradi and Shaik17  to solve this example. These models are excellentrepresentations of existing multiple time-grid continuous-time models.Note that the multiple time-grid model of Mostafaei and Harjunkoski26 is not used as it is not suitable for limitedstorage capacities. The schedule with a maximum profit of $300 obtainedfrom these models is illustrated in 17  due to the factthat in In this example,state S2 is produced by task T1 in unit J1 and consumed by task T2in unit J2. It has a dedicated storage with a maximum capacity of10 mu (mass units) and no initial inventory. S3 is the final productpriced at $5 mu3.2Table S2. The objective is to minimize makespan with the demand ofS3 being 100 mu. Besides the abovementioned representative multipletime-grid continuous-time models,17 a representative discrete-time model32 proposed by Velez, Merchan, and Maravelias (referred as VMM) is used to solve this example. All these representativemodels generate a best schedule with a makespan of 11.5 h and VMM. Note that Δn is a parameterdenoting the maximum number of event points over which a task is allowedto span. The optimal schedule from V&S is illustratedin V&S and L&F.In this example,five intermediate states (S1–S5) are subject to FIS with amaximum capacity of 1000 mu and no initial inventory. Demands forproducts P1 and P2 are 100 and 200 mu, respectively. The objectiveis to minimize makespan. The optimal makespan of 19 h is generatedfrom All these examples motivateus to develop a newmathematical modelto address the abovementioned limitations of existing multiple time-gridcontinuous-time models especially the unit-specific event-based models,which may lead to a significant increase in solution quality.424 the well-established unit-specific event-based time representation19 is adopted in this work  as it is more flexible and efficient, comparedto other continuous-time representations. It is often more efficientand accurate than the discrete-time variant in handling variable processingtimes.26 For more details about this timerepresentation, the readers can refer to Ierapetritou and Floudas.12It is ofgreat importance to represent the time horizon beforedeveloping a mathematical formulation. Although there are severalexisting time representations,4.1n and n′ are event points with n ≤ n′ ≤ n + Δn. The parameter Δn denotes the maximum numberof event points that a task is allowed to span over. As discussedbefore, a state is allowed to be held in a processing unit over consecutiveevent points after production, if it is neither unstable nor subjectto ZW policy. We introduce new binary variables ysijn to denote holding operations as followsWe introducefour-index binary variables 4.1.1j at a time.IP denotes tasks producingstates that can be temporarily heldin processing units.At most,one task is allowed to be processed or temporarily held in a processingunit 4.1.2Bijmin) and maximum (Bijmax) capacities.The batchsize , plus the amount produced at the end of event point(n – 1), minus the amount consumed at thebeginning of event point n , while ρsi < 0, task i consumes state s .Wedefine positive variables nt n see 3 and 4.3s held in processingunits should not exceed its total amount stored.The amount of state 4.1.4Tjns and Tjnf as the startand end times of unit j at event point n, respectively. Then, the duration of event point n on unit j must exceed the processing time, as indicatedby We define 4.1.5n + 1) onunit j must start after event point n on this unit ends, as given by Event point (Tsjn to denote the time when state s produced in unit j is available at eventpoint n. The time when state s isavailable at (n + 1) is always after the time whenit is available at n.JsP denotes the processing units that can process tasksto produce state s.To correctly sequence different tasksin different units, we define new continuous variables s is produced in unit j at event point n, then the time whenthis state s is available at event point n shouldalways be after the end time of this event point n on unit j. In other words, this state s is available for storage or consumption only after it is produced.If state s is producedor temporarily held inunit j at event point n, then thetime when this state s is available at n, must be before the start time of event point (n + 1) on this unit j.If state 4.1.639 Non-instantaneous material transfer,35 zero-wait materialtransfer,37 and non-zero transfer times39 are also implicitly or explicitly taken into account. However, thedifferentiation of these material transfers based on the availabilityof the storage is not explicitly discussed. In this work, we explicitlyintroduce the concept of indirect and direct material transfer, whichallows us to differentiate material transfer between processing unitsand storage based on the availability of storage capacity and rigorouslysequence and align tasks in different units. As shown in Material transferbetween processing units and storage in batch scheduling has beenstudied in the literature.4.1.6.1Inthis scheme, the storage capacity is usually large enough. A statesubject to UIS policy is always indirectly transferred to downstreamprocessing units. For a state with FIS policy, indirect material transferof the state works only when there is enough storage capacity. Tomodel this indirect material transfer scheme, we define new binaryvariables j to unit j′ atevent point (n + 1), the start time of event point(n + 1) on unit j′ shouldexceed the end time of event point n on unit j.CJj denotes units consuminga state produced in unit j, that is, JsC denotes the processing units that can processtasksto consume state s.If indirect material transfer happensfrom unit j and unit j′. Specifically, the state is produced by a task i in unit j at event point (n – 1) and then indirectly transferred to a downstream unit j′ in which task i′takes place and consumes the transferred state at event point n. The total amount of state s requiredby downstream tasks at event point n should not exceedthe amount stored at the previous event point (n –1) plus the amount through indirect transfer.SB denotes the statesthat are initially held in the processingunits performing production tasks of the state, that is, We also define continuousvariables s produced by task i in unit j throughindirect material transferat event point n should not exceed the batch sizeproduced by this task at the previous event point (n – 1). When there is indirect material transfer from a unit j to a downstream unit j′ at thefirst event point, the transferred material comes from the batch ofthe state that is initially held in unit j .The amount of state s indirectlytransferredto a downstream unit j′ where task i′ taking place at event point n should not exceed the amount required by this task i′.Similarly, the amount of state When there isno indirect materialtransfer between two processingunits, the amount through the indirect material transfer should bezero, which is ensured by j and unit j′ at eventpoint (n + 1). The indirect material transfer isnot monitored from unit j to unit j′ at event point (n + 2) or higherevent points. If a state produced in unit j at eventpoint n is consumed by a task in unit j′ taking place at event point (n + 2) orhigher event points, then the unit j′ that consumes state s at event point (n + 2) or higher event points should always start after the stateis available on unit j at event point n to avoid storage violation. This logic condition is ensured by The abovementioned constraints areused to monitor indirect materialtransfer as well as the correct timing sequence between unit 4.1.6.2j to unit j′ where it is consumed. To model directmaterial transfer, binary variables Fora state subject to FIS policy, if there is no storage space, thisstate cannot be transferred to a dedicated storage tank. Instead,it must be transferred directly from unit j to j′ at (n + 1), unit j′ at event point n must finish before unit j finishes at the same n to avoid overlappingon j′, as indicated in If direct materialtransfer takes placefrom unit j where it is produced by atask i or temporarily held at event point (n – 1) to a downstream unit j′ where it is consumed by a task i′ at event point n. Direct materialtransfer of a state from its producing task i onunit j at event (n – 1) tothe consuming task i′ on unit j′ at event point n should be activated whenthere is no sufficient storage space to settle the amount of the stateprovided (produced or temporarily held in unit j)at event point (n – 1). n – 1) exceeds the maximum storage capacity, directmaterial transfer should be non-zero. We define continuous variables n must not exceed the amount of this state provided by task i on unit j at the previous event point(n – 1).Similar to indirect material transfer, s through direct materialtransfer to unit j′ where task i′ takes place at event point n should not exceed the amount of this state consumed bytask i′ at event point n.The amount of state When there is no direct material transferbetween two related processingunits, the amount through this direct material transfer should bezero.4.1.7s produced in unit j is available at event point n must be after the finish time of event point (n – 1) on unit j′ where a task consumes state s at event point n. This is to ensure that when state s isavailable, there is enough space to hold this state, as illustratedin S1 is available at the end of event point n, thereis no enough storage space for S1 because S1 is available at the end of event point n, it can be stored in the dedicated storage as S1 stored in the storage tank is transferred to unit J2 for processing, as shown in To avoid storage violation in real time, constraint30 is also imposed to ensure that the time when state s storedis enforced by s storedat a time must not exceed the maximum storage capacity plusthe maximum allowable holding amount in all processing units.An upper bound for the excess amount of state 4.1.8i thatis temporarily held in unit j at event point n must be zero if the binary variable ysijn = 0.The amount of a stateproduced by task The amount of a state heldin a processingunit at the first event point must be smaller than the initial holdingamount, as ascertained by 4.1.9ysijn with j′ processes a task consuming intermediate state s, and indirect material transfer happens between units j and j′ at event point (n + 1), unit j must process a task producing s or temporarily hold s at event point n.CJ0j includes units j′∈CJj except those in which multiplestates produced in j are consumed by a task in j′ or multiple states consumed by tasksin j′ are produced by a task in j.Some newtightening constraints are introduced to improve the performance ofthe proposed model. Constraints (34)–(37) relate j processesa task producing state s at event point n, and there is indirect material transfer between units j and j′ at event point (n + 1), then unit j′ must processa related consumption task starting at event point (n + 1) according to constraint (35).Similarly, if unit When direct material transfer betweentwo units takes place  and j′ must process a task at event point n.When indirect material transfer takesplace between units 4.1.10j at event point n must be smaller than the time horizon (H), as ascertainedby H would be replacedby M while addressing minimization of makespan, asthe scheduling horizon (H) may be unavailable.The start andend times of unit i are subject to UIS policy, ysijn and bsijn should be zero.If all statesproduced by task i in unit j starting at eventpoint n cannot finish at event point n′ when n′ < n, While If there is no initial amountof astate held in a processing unit,the variables related to temporarily holding materials and materialtransfer are fixed as zero at the first event point.4.1.11As alreadydiscussed, two objective functions are considered. While constraint(45) is used for maximization of profit, constraint (46) is used forminimization of makespan.In minimization of makespan, it shouldbe also ensured that the total demand is satisfied.The tightening constraint 48 is addedfor minimization of makespanonly.Finally, (49) and (50) denote all thecontinuous and binary variablesof the model.M1, which consistsof constraints M2) plus the amount through indirect transfer.Similar to s through indirect materialtransfer at event point n should not exceed its availableamount produced from task i or held in the processingunit at event point (n – 1).The amount of state n – 1) exceeds themaximum storage capacity, direct material transfer should be non-zero.s with FIS must notexceed the maximum storage capacity.The inventory level of state TsnM2 to denote thetime when a state s is available at event point n instead of using Tsjn. This is because the computational performance becomes worsewhen Tsjn is used, asdemonstrated in the Supporting Information through comparing the performance of this model M2 withmodel M3 using Tsjn presented in Section S8 of Supporting Information. The difference between TsnM2 and Tsjn is depicted in Figure S16 of the Supporting Information.We define s is availableat event point (n + 1) should be always after itsavailable time at event point n, as indicated by We require that the time when a state s is availablefor transfer only afterit is produced, which is enforced by A state j at event point n is consumed by a taskin unit j′ taking place at event point (n + 2) or higher event points, the unit j′ that consumes state s at (n+ 2) or higher event points should always start after thestate is available on unit j at n to avoid storage violation. This logic condition is ensured by Similar to constraint(20), if a stateproduced in unit j that processes or temporarilyholds one batch of a production taskfor state s at event point n shouldfinish after the end time of unit j′ at the previous event point (n – 1), wherea task consumes the state s at event point n, to avoid real-time storage violation. Here, ttsnM2 are intermediate variables. Handled by j′ consumes or pre-processesa state s before its production in unit j at the same event point to avoid the inventory level of state s after production in units at n beyondthe maximum storage capacity.The available time of anystate atthe last event point shouldbe smaller than makespan while addressing the minimization of makespan.M2 as better computational performanceis obtained based on our computationalexperience. Batch size of tasks and amount for one batch of materialsheld in a suitable processing unit should be always smaller than themaximum unit capacity, as handled by Some upper bounds arealso imposedto this model s through indirect or directmaterial transfer cannot exceed its maximumproduction amount from a task i at unit j and the maximum consumption amount by a task i′at unit j′.M2 are denotedby All continuous variables of model M2 consists of constraints, –19M2 constraints, 24–29)–29M2 constraints–45, straints, 32–45)–45M2 constraints, 46–48)–48M2 con4.3M1 can be extended to address the following situations likevariable recipes, and states subject to NIS and ZW policies. We usemodel M1 for this extension due to its better computationalperformance than M2  is no more than its amount providedby the task i at n.For task si·bsijn) for task i∈IV shouldbe replaced by bsvsijn, respectively.To handle variable production recipesfor some tasks, constraintsconcerning material balance and material transfer should be modified.Specifically, variables  should immediately start after thisstate is produced at n, as pre-processing unit waitis not permitted.For a state withZW policy, a taskconsuming this state at eventpoint (n – 1) shouldbe consumed, or partially held in the processing units at event point n. Given that a state for ZW cannot be held in processingunits, For a state subject to NIS or ZW policy,the amount of this stateconsumed must be from direct material transfer.For a state subject to ZWpolicy, excessamounts of this statemust be zero.j for NIS after production. Similarly, materialsused by consuming tasks at event n must be transferreddirectly from production tasks finished at the previous event (n – 1), given by EM1, which is providedin Section S9 of the Supporting Information. Note that models M1–M2 aredeveloped for scheduling multipurpose batch plants for FIS and UIS,while the extended model EM1 can solve problems withvariable proportion of states produced/consumed and four types ofstorage policies . It should also benoted that although many sets are defined, most of them can be automaticallydetermined based on sets SR, Sin, SP, SFIS, SUIS, SNIS, SZW, IV, Ij and the parameter ρsi.The complete modelwith all extensions is denoted as 5M1–M2, we solve 16 examples including three motivatingexamples, 11 benchmark examples from the literature,17 a variant of benchmark example 3 (denoted as example 12), and theKallrath example.43 Relevant data, STNrepresentations, and values of M in big-M constraintsfor all examples are provided in the Supporting Information. It should be noted that we only compare the performanceof our models with model V&S due to the addedflexibility allowing materials produced to be held in the processingunits over consecutive event points to share storage burden. For motivatingexample 2, our models lead to a 30.4% smaller makespan (8 vs 11.5h) than the existing continuous-17 and discrete-time32 models.For motivating example 3, our models generate the optimal makespan(19 h) using 10 event points compared to V&S with18 event points and Δn = 6, resulting in areduction in the numbers of event points by 44% (10 vs 18) and binaryvariables by 84% (114 vs 732). In addition, V&S requiresmore than 1 h to generate the optimal solution using 18 event pointswith Δn = 1 and 2. As a result, the total CPUtime required to generate the optimal makespan of 19 h using our modelsis significantly decreased by 3 orders of magnitude according to theiterative procedure. This is mainly because V&S imposesif task i produces state s at eventpoint n, it must finish after a task i′ starts to consume this state s∈SFIS at n and before a task i″ starts toconsume this state s∈Sin at (n + 2), regardless of whethertask i′ or i″ actually takes place at n or (n + 2), which is overcome by M1 and M2.We revisit themotivating examples 1–3. The computational results are providedin nd SLK2 $0 due to 5.214 are presentedin V&S are different from thosereported in Vooradi and Shaik17 as somebinary variables are not fixed based on STN. If we fix them, we doget the same model statistics. We do not present results with tinycomputational efforts in these tables. The complete results are providedin Section S3 of the Supporting Information.The computationalresults from solving 11 benchmark examples and a variant example ofexample 3 V&S. Specifically, the computational time forexample 1a is reduced by 84% (133.7 vs 833.2 s) using M1 with 14 event points compared with V&S. In addition, M1 proves the optimality in 1 h  when 15 eventpoints are used, while V&S and M2 cannot.The relative gap from M2 is 0.47%, which is much smallerthan that from V&S (4.64%). M1 outperforms M2 with a reduction of CPU time by over 28% while solvingexample 1a with 15 event points, even though it has a relatively largernumber of continuous variables and constraints.M1, M2, and V&S require the same number of event points to generate the optimalsolution without allowing a task to span over multiple event points.However, our proposed models require a smaller number of binary variablesfor examples 2 and 3. This is because our models only examine if thereis material transfer between processing units, while V&S tests if there is material transfer from a task to another. As multipletasks share one processing unit in examples 2–3, our modelslead to smaller model size and less computational time. Specifically,the computational time is reduced by 1 order of magnitude (721 vs42 s from M1) using our models to find the best resultof $1583.442 for Example 3a. Similar reduction in the computationaltime can also be observed in examples 3b and 3d. Although more constraintsare involved in the proposed models, less computational effort isrequired due to additional tightening constraints imposed. Finally, M1 shows better performance than M2 as it canprove optimality for example 3b using 8 event points within 1 h, while M2 cannot.V&S. This is becausethe batch of materials is permitted to be temporarily held in thesuitable processing units over consecutive event points in our models(see the schedule in n = 0) due to allowing processing units to hold materialsover multiple event points. Therefore, all proposed models lead tosignificantly smaller model size with less numbers of binary and continuousvariables. For instance, our models require 40.2% (79 vs 132) and56.0% (139 vs 316) fewer binary variables than V&S to generate the optimal solution for examples 8 and 9, respectively.As the iterative procedure is often conducted to estimate the appropriateevent points, the total test time would be significantly reduced iftasks do not require to span over multiple events using our models.The results for examples6, 8, and 9 listed in M1 proves optimality using dramatically decreased computationaltime for example 1a and leads to a 16.9% (2.06 vs 2.48%) reductionin the relative gap for example 1b, compared with V&S. For example 2b, all the proposed models M1–M2 can yield the optimal solution of 47.68 h without any task spanningover multiple event points, but V&S reaches the optimalsolution with Δn = 2. Decrease in the numberof binary variables by 40% (648 vs 1080) and computational time bya factor of 43 (82 vs 3600) are realized by M1 comparedwith V&S. Comparing with M2, M1 always shows better performances due to low relative gaps and shortcomputational times. Specifically, Examples 1a and 2b are not solvedto optimality by M2 within 1 h, while M1 finds the optimal solution in less than 2000 and 100 s, respectively.In addition, M1 reports a smaller relative gap for example1b.5.343 using the extended model EM1, V&S,17 and VMM to find the optimal solution for instance 3. VMM shows better computational performance, especially in computationalefficiency, while solving instances 1–4 as all tasks have fixedand integer processing times in these instances. However, its dominanceis diminished with the incremental customer demands. EM1 finds the best feasible solutions with optimality gaps smaller than17% within 40,000 s compared with VMM and V&S for larger instances 6–9. For instance, a better solutionwith 18% (334 vs 408) lower makespan is generated using EM1 for instance 7 within the same time resource compared to VMM. This is mainly attributed to the huge number of time intervalsrequired in VMM, leading to a dramatic rise in the modelsize and computational effort. For instance 10 with decimal processingtimes of tasks (see Table S30 in the Supporting Information), VMM is hard to find any feasiblesolution within 40,000 s using the greatest common divisor  of processing times due to the excessive number ofdiscrete variables required. EM1 leads to 7.6% (91.9vs 99.6 and 99.5) smaller makespan and over 45% (11.01 vs 20.23 and25.5%) lower relative gap than V&S and VMM with δ = 0.5.We solve the industrial-scaleKallrath example7 and VMM with a rSupporting Information. Similar conclusions can be made when using CPLEX 12.8.0.Tofurther illustrate the robustness and efficiencyof the proposedmodels, we also solve all motivating and benchmark examples usingCPLEX 12.8.0/GAMS 25.1.3. The computational results are provided inSection S3 of the 6In this work, we presentedtwo novel unit-specific event-basedMILP models for short-term scheduling of multipurpose batch plants.We introduced the concept of indirect and direct material transfer,allowing efficient sequence or alignment of different tasks in differentunits. A batch was allowed to be partially transferred to downstreamfacilities and held in processing time over multiple event points.A new continuous variable denoting the available time of one statewas introduced to avoid the limitations in the existing unit-specificevent-based models. New tightening constraints were proposed to reducecomputational expense.M1. In some cases, it was reduced by at least1 order of magnitude. More importantly, the proposed models can generatethe same or better objective values for all solved examples. The increasein profit can range from 21.5 to 67% and the reduction in makespancan vary from 1.05 to 30.4%. This is due to the added flexibilitythat materials are allowed to be temporarily stored in the suitableprocessing units. In other words, additional storage space from processingunits is provided. Therefore, the proposed models especially model M1 are superior  to all existing unit-specificevent-based models. Additionally, model M1 outperforms M2 on both solution optimality and computational efficiency.The computational results for the motivatingexamples and benchmarkexamples demonstrated that the proposed models require fewer numbersof discrete variables in most cases, especially where a processingunit can process multiple tasks, compared with the existing unit-specificevent-based formulation. Interestingly, all tasks do not need to spanover multiple event points to yield optimal solutions for all solvedexamples. As a result, the computational effort was significantlyreduced by a factor ranging from 1 to 43 using the proposed modelsespecially EM1 leadsto a reduction in the CPU time over 45% for medium instances and bettermakespan for large instances. Additionally, for large instances, EM1 yields competitive solutions with maximum improvementin makespan by 18% compared with the discrete-time formulation,32 while the discrete-time formulation shows32 better computational performance especiallyin computational efficiency for medium instances where all tasks havefixed and integer processing times. In the future, we will integratethe proposed model M1 into the rolling-horizon decompositionframework or develop a more efficient decomposition algorithm to solvelarger-scale scheduling problems.The industrial-scale Kallrath example is more complicated comparedto the benchmark examples due to variable recipes and three storagepolicies involved. Results show that compared with the existing unit-specificevent-based formulation, the extended variant


Billions of cells die in the body every day, and cell-free chromatin particles (cfChPs) which are released from them enter into the extracellular compartments of the body, including into the circulation. cfChPs are known to readily enter into healthy cells to damage their DNA and activate apoptotic and inflammatory pathways. We have hypothesized that lifelong assault on healthy cells by cfChPs is the underlying cause of ageing, and that ageing could be retarded by deactivating extra-cellular cfChPs. The latter can be effected by oxygen radicals that are generated upon admixing the nutraceuticals resveratrol and copper (R–Cu). The present study investigated whether prolonged administration of R–Cu would retard biological hallmarks of ageing. C57Bl/6 mice were divided into 3 equal groups; one group was sacrificed at age 3 months, and which acted as young controls. The remaining mice were allowed to age, and at age 10 months the experimental ageing group was given R–Cu by oral gavage twice daily for further 12 months at a dose of 1 mg/kg of R and 0.1 μg/kg of Cu. The control ageing group was given water by oral gavage twice daily for 12 months. Animals of both groups were sacrificed at age 22 months. R–Cu treatment led to reduction of several biological hallmarks of ageing in brain cells which included telomere attrition, amyloid deposition, DNA damage, apoptosis, inflammation, senescence, aneuploidy and mitochondrial dysfunction. R–Cu treatment also led to significant reduction in blood levels of glucose, cholesterol and C-reactive protein. These findings suggest that cfChPs may act as global instigators of ageing and neurodegeneration, and that therapeutic use of R–Cu may help to make healthy ageing an attainable goal. The United Nations General Assembly has declared 2021–2030 as the Decade of Healthy Ageing, with the ultimate goal to find therapeutic interventions which will simultaneously delay the many conditions associated with ageing2. It is argued that healthy ageing should be considered as the ultimate preventive medicine3. Ageing is characterised by a myriad pathological processes which lead to gradual deterioration of structure and function of all cells and tissues of the body4, and is associated with a multitude of degenerative disorders such as Alzheimer’s disease5, cardiovascular diseases6, diabetes7, and cancer8. Although many theories of ageing have been advanced10, none can comprehensively explain the numerous changes that accompany this multidimensional process.With progressively increasing longevity, the human race is facing a parallel increase in ageing related degenerative disorders which can severely compromise quality of life. It is predicted that, globally, the number of people age 60 years or above will grow by 38%, from 1 billion to 1.4 billion, outnumbering the youth during the next ten years12. In this context, we have reported that cell-free chromatin particles (cfChPs) that are released from the billions of cells that die in the body every day, and enter into the extracellular compartments of the body, can be readily internalised by healthy cells wherein they inflict dsDNA breaks, activate apoptotic pathways and induce inflammatory cytokines14. This has led us to hypothesise that repeated lifelong assault on healthy cells by cfChPs may be the underlying cause of ageing16. Our group has successfully isolated and characterised cfChPs from human serum, which upon EM examination revealed extensive size heterogeneity ranging between ~ 10 and ~ 1000 nm13. We have also reported that blood levels of cfChPs increase with age17.DNA damage and chronic inflammation are two cardinal features of ageing20. R is a well-known anti-oxidant which has been extensively researched for its health benefits21. However, and surprisingly, it acts as a pro-oxidant in presence of Cu, which is also a widely researched nutraceutical22. Fukuhara et al.23 were the first to report that oxygen radicals are generated when R and Cu are admixed. They showed that R acts as a catalyst to reduce Cu (II) to Cu (I) resulting in generation of oxygen radicals which cleaved plasmid pBR322 DNA24. We have extended these findings to show that a combination of R and Cu can degrade genomic DNA and RNA25, and can deactivate cfChPs in vivo by degrading their DNA component25. We have further observed that, paradoxically, the DNA degrading activity of R–Cu increases as the molar concentration of Cu is gradually reduced with respect to R25. On the basis of this finding, in the present study, we kept the molar ratio of R:Cu at 1:10–4.Our pre-clinical studies have led to the identification of a novel pro-oxidant combination of the nutraceuticals resveratrol (R) and copper (Cu) which deactivates cfChPs via the medium of oxygen radicals–4, has therapeutic effects in several pre-clinical conditions associated with elevated extracellular levels of cfChPs20. For example, orally administered R–Cu can ameliorate toxic side effects of chemotherapy18, and radiation therapy19, and prevent bacterial endotoxin induced cytokine storm and fatality in mice20. Our early results also suggest that R–Cu is therapeutically effective in humans. An observational study showed that orally administered R–Cu to patients with severe Covid-19 led to reduction in mortality by nearly 50%26. We have also reported that grade III-IV mucositis could be significantly reduced by orally administered R–Cu in patients receiving high dose chemotherapy and bone marrow transplant for multiple myeloma27. R–Cu treatment also led to significant reduction in blood levels of inflammatory cytokines in that study.We have reported that a combination of R and Cu, when used at a molar ratio of 1:1027. In the present study, we have taken advantage of cfChPs deactivating property of R–Cu to investigate whether prolonged administration of R–Cu to ageing mice will retard the hallmarks of ageing and neurodegeneration. The dose of R used in our study was 1 mg/kg, and that of Cu was 0.1 μg/kg, given by oral gavage twice daily. This dose of Cu was 20,000 times less, and that of R 5 times less, than those that have been used in pre-clinical studies to investigate their health promoting properties by other investigators29.Oxygen radicals that are generated upon oral administration of R–Cu are apparently absorbed from the stomach to have systemic effects in the form of deactivation/eradication of extracellular cfChPsUsing confocal microscopy and antibodies against DNA and histone we detected copious presence of extra-cellular cfChPs in brain of ageing mice, and observed that cfChPs were deactivated/eradicated following prolonged oral administration of R–Cu. Deactivation/eradication of cfChPs was associated with down-regulation of multiple biological hallmarks of ageing in brain cells. At a systemic level, R–Cu treatment led to significant reduction in blood levels of glucose, cholesterol and C-reactive protein. Taken together, our results suggest that cfChPs act as global instigators of ageing and neurodegeneration, and that therapeutic use of R–Cu may help to make healthy ageing an attainable goal.The experimental protocol of this study was approved by the Institutional Animal Ethics Committee (IAEC) of Advanced Centre for Treatment, Research and Education in Cancer (ACTREC), Tata Memorial Centre, Navi Mumbai, India under permission No.16/2015. The experiments were carried out in compliance with the IAEC animal safety guidelines, and with those of ARRIVE guidelines.ACTREC- IAEC maintains respectful treatment, care and use of animals in scientific research. It aims that the use of animals in research contributes to the advancement of knowledge following the ethical and scientific necessities. All scientists and technicians involved in this study have undergone training in ethical handling and management of animals under supervision of FELASA certified attending veterinarian. Animals were euthanised at appropriate time points under CO2 atmosphere by cervical dislocation under supervision of FELASA trained animal facility personnel.https://www.biotivia.com/product/transmax/); Copper .The sources of R and Cu were: Resveratrol  were allowed to age until they were 10 months old and divided into two groups: (1) Ageing control mice (N = 4 of each sex), and (2) R–Cu treated ageing mice (N = 4 of each sex). Animals of both groups were sacrificed after 12 months when they were 22 months old.20.R–Cu was administered twice daily by oral gavage for 12 months (from 10 to 22 months) at a dose of 1 mg/kg of R and 0.1 μg/kg of Cu. R, being insoluble in water, was administered as water suspension (100 μL), and Cu was administered as a water-based solution (100 μL). The ageing control mice were given water (100 μL) twice daily by oral gavage. Our previous studies have shown this dose of R–Cu is therapeutically effective in multiple other pre-clinical conditionsReduced physical activity and weight loss of mice were used as humane endpoints of the study and were scored twice every week. At appropriate time points as indicated above, blood was collected via retro-orbital route under isoflurane anaesthesia for serum separation. Animals were then euthanised under CO2 atmosphere by cervical dislocation under supervision of FELASA trained animal facility personnel. After euthanasia, brain was harvested from all animals, fixed in 10% formalin and paraffin blocks were prepared for further analysis.Details of commercial sources and catalogue numbers of reagents, antibodies and analytical kits used in this study are given in supplementary table 20. Briefly, FFPE sections were deparaffinised, rehydrated in alcohol series, incubated in 0.01 M citrate buffer (pH 6.0) at 95 °C for 20 min and washed in 1X PBS. Sections were immune-stained using primary antibody against SOD and corresponding secondary antibody .Expression of SOD in brain cells was estimated using immunofluorescence (IF) technique as described by us earlierSerum SOD activity was measured by ELISA using a commercial kit  according to manufacturer’s instructions.20. Fluorescence intensity of five randomly chosen confocal fields (~ 50 cells in each field) was recorded, and mean fluorescence intensity (MFI) (± S.E.M) was estimated.Immune-staining for DNA and histone H4 followed by confocal microscopy was performed on formalin fixed paraffin embedded (FFPE) sections of brain as described in detail by us earlier31. Genomic DNA was isolated from brain tissue using DNeasy blood & Tissue Kit . DNA quantification was performed using a Nanodrop™ spectrophotometer . Ten nanogram of DNA was used in 5 µl of 1 × SYBR Select Master Mix , 250 nM of both telomere specific primers or 350 nM of 36B4 primers to a total volume of 10 µl reactions. The thermal cycling conditions for both Telomere and 36B4 are: initial denaturation of 95 °C for 10 min followed by 40 cycles of 95 °C for 15 s, 60 °C for 30 s & 72 °C for 30 s. The sequence for telomere-specific forward and reverse primers (Sigma-Aldrich) are 5’ CGG TTT GTT TGG GTT TGG GTT TGG GTT TGG GTT TGG GTT 3’ & 5’ GGC TTG CCT TAC CCT TAC CCT TAC CCT TAC CCT TAC CCT 3’. The sequences for acidic ribosomal phosphoprotein (36B4)—specific forward and reverse primers are 5′ ACT GGT CTA GGA CCC GAG AAG 3′ and 5′TCA ATG GTG CCT CTG GAG ATT 3′, respectively). Genomic DNA isolated from the spleen of an individual mouse was used as a reference DNA and serially diluted for telomere and 36B4 PCR. All samples were assayed in duplicate on a QuantStudio™ 12 K Flex Real-Time PCR System (ThermoFisher) using 384-well block. Standard curves were generated and the relative input amount for both telomere and 36B4 were calculated. The average of the ratio of telomere and 36B4 was reported as the average telomere length.The average telomere length from the brain tissue was estimated using a highly sensitive quantitative real-time PCR (qRT-PCR) techniquehttps://spectral-imaging.com, Applied Spectral Imaging, Israel) in a multichannel 3-D mode with a constant exposure of 1000 ms for Cy3 (telomeres) and 150 ms for DAPI (nuclei) throughout the experiments. Each 3D image comprised of a stack of 11 focal planes per cell with a sampling distance of 500 nm along the z direction and 107 nm in the xy direction. Images were de-convoluted and telomere numbers per nucleus was estimated using Spot Count algorithm in SpotView software 8.1 . Number of telomere aggregates per nucleus was estimated visually.Quantitative telomere FISH was performed using Cy3-labeled peptide nucleic acid (PNA) telomere probes  co-localisation of telomere and γ-H2AX IF signals using Immuno-FISH; (2) co-localization of 53BP1 and pro-myelocytic leukemia-nuclear bodies (PML-NBs) IF signals; (3) p16Aneuploidy was assessed with respect to chromosome numbers 7 and 16 by FISH using chromosome specific probes on FFPE sections of brain tissues. Sections were de-paraffinised and dehydrated in alcohol series (70–100%) followed by antigen retrieval in sodium citrate buffer (pH 6) at 90 °C in water bath and then cooled to room temperature. Sections were hybridised with chromosome 7 and 16 specific DNA probes overnight at 37 °C. Unbound probes were washed off with 2X SSC followed by 0.4X SSC at 70 °C for 3 min each. The sections were finally washed in 4X SSCT and mounted in VectaShield DAPI. Images were acquired and analysed using Applied Spectral Bio-imaging system . Number of fluorescent signals per nucleus was counted, and signals more or less than 2 N were considered as evidence of aneuploidy. Five fields containing ~ 500 nuclei were analysed and average number of signals per nucleus was calculated.http://www.bitplane.com, Bitplane Technologies, AG). Mean volume (in x–y–z planes) was calculated for 5 images  for each brain section.Mitochondrial dysfunction was analysed by IF on FFPE sections of brain tissue to assess the expression of the mitochondrial trans-membrane protein TOMM20. Estimation of volumetric changes in TOMM20 expression was performed using IMARIS software 7.2.3 . Serum C-reactive protein (CRP) levels were measured using a commercial ELISA kit . The results of aged control mice were compared with young controls and aged + R–Cu treated mice. Mean (± SEM) values for four mice in each group for both sexes were compared using non-parametric unpaired student’s t test, separately for both sexes.Statistical analyses were performed using GraphPad Prism 6.0  of Advanced Centre for Treatment, Research and Education in Cancer (ACTREC). ACTREC IAEC adheres to ARRIVE guidelines. The experiments in this study were undertaken in compliance with ARRIVE guidelines      and anti-histone (green) antibodies. Upon superimposing DNA and histone fluorescent images, copious presence of cfChPs  were detected in the extracellular spaces of brain of ageing mice Fig. . cfChPs es) Fig. .Figure 232. Telomere attrition, telomere loss and telomere aggregation are cardinal features of ageing33. We estimated telomere length in brain cells by qRT-PCR and observed a significant reduction in telomere length in mice of both sexes  , but not in male mice , which was again significantly restored following R–Cu treatment in female (p < 0.01) but not in male mice , but was significantly reduced following R–Cu treatment only in female mice (p < 0.01) . One year of R–Cu treatment resulted in significant reduction in extra-cellular amyloid in mice of both sexes   protein deposition in extra-cellular spaces of brain cells is classically associated with Alzheimer’s disease36, was greatly reduced in sera of ageing mice of both sexes as measured by ELISA   , which plays an important role in neuronal survival and growthly) Fig. B. R–Cu tly) Fig. B.39. DNA damage was examined using phosphorylation of H2AX as a marker of dsDNA breaks40. γ-H2AX levels were markedly increased in ageing mice . R–Cu treatment reduced γ-H2AX levels  . R–Cu treatment significantly reduced the degree of apoptosis in mice of both sexes  . R–Cu treatment significantly reduced NF-kB levels in both sexes  —a classical hallmark of senescence43—in ageing mice of both sexes (p < 0.001). Quantification of co-localising signals revealed a marked reduction following R–Cu treatment (p < 0.01 in both sexes)  which has been shown to be significantly correlated with DNA damage associated senescence in ageing mice46. We show that the number of co-localizing signals of 53BP1 and PML were markedly increased in ageing mice of both sexes (p < 0.0001). Co-localising signals were significantly reduced following R–Cu treatment for 1 year  INK4a47, which was elevated in ageing mice of both sexes (p < 0.0001 for both sexes). R–Cu treatment significantly reduced levels of p16 INK4a   ) . R–Cu treatment significantly restored mitochondrial volume  52. As anticipated serum glucose levels was significantly elevated in ageing mice53 (p < 0.01 for both sexes), which was reduced to levels seen in young controls following one-year treatment with R–Cu (p < 0.01 for both sexes)  but not in male mice  but not in male mice . CRP was highly significantly elevated in ageing mice of both sexes (p < 0.0001) and was reduced by R–Cu treatment (p < 0.05 in both sexes)  Fig. A. Serum ice Fig. B. Serum ice Fig. B. Nonethes) Fig. C.Figure 54. ROS induced oxidative stress is known to have multiple deleterious effects on host cells55. However, we have reported that, paradoxically, when ROS is artificially generated outside the cell in the extracellular spaces of the body, they can have wide ranging therapeutic effects27. Admixing R with Cu leads to generation of oxygen radicals by virtue of the ability of R to reduce Cu (II) to Cu (I)25. Oxygen radicals that are generated in the stomach upon oral administration of R–Cu are apparently absorbed to have systemic effects in the form of deactivation/eradication of extracellular cfChPs. We have shown that cfChPs have wide-ranging damaging effects on host cells. For example, cfChPs can readily enter into the healthy cells to damage their DNA, activate inflammatory cytokines and promote apoptosis via the mitochondrial pathway14. Given that 1 × 109–1 × 1012 cells die in the body every day57, we have hypothesised that repeated and lifelong assault on healthy cells by cfChPs derived from the dying cells may be the underlying cause of ageing16. In support of this hypothesis we show in this article that prolonged oral administration of R–Cu to ageing mice down-regulated multiple biological hallmarks of ageing and neurodegeneration by virtue of its ability to deactivate cfChPs. Our results suggest that R–Cu may qualify as an ideal anti-ageing agent since it has the potential to simultaneously retard or delay the many conditions that are associated with ageing2. To be globally applicable, an ideal anti-ageing agent should also be inexpensive and non-toxic—the two criteria that are also met by R–Cu. The latter can be easily administered orally, and both R and Cu are already approved for human use. An illustrated summary of the study design and the mechanisms by which R–Cu generated oxygen radicals eradicate cfChPs from brain micro-environment leading to down-regulation of ageing hallmarks is provided in Fig. ROS are short lived molecular species containing an unpaired electron which makes them highly reactive as they search for another electron to pair with, and in the process can damage biomolecules such as DNA, proteins and lipids43. The bare chromosomal ends can fuse with each other to lead to chromosomal instability and aneuploidy48, as was detected in our study. With respect to mitochondrial dysfunction, we have recently reported that internalised cfChPs, in addition to inflicting damage to genomic DNA, can inflict physical damage to mitochondria58. One of the indicators of mitochondrial damage detected in that study was up-regulation of TOMM2058. Our finding in the present study of TOMM20 over-expression in ageing mice, and its reversal by R–Cu is consistent with the possibility that mitochondrial damage in ageing mice is induced by cfChPs that are released from dying brain cells. However, reduction in amyloid plaque formation following prolonged R–Cu treatment would suggest an unknown role of cfChPs which calls for further research. Similarly, the mechanism(s) by which R–Cu reduced metabolic dysfunction in ageing mice leading to reduction in serum levels of glucose, cholesterol and CRP remains unknown at present. Taken together, it can be concluded that cfChPs have pleiotropic effects with wide ranging implications in ageing and neurodegeneration which remain open to future research.The mechanism(s) by which R–Cu down-regulates the multiple biological hallmarks of ageing and neurodegeneration needs elaboration. Reversal of telomere shortening by R–Cu may suggest that telomere shortening could be a consequence of DNA damage inflicted by cfChPs which shear off telomere ends causing them to shorten. We observed differential effects between female and male mice with respect to telomere abnormalities. R–Cu effects in preventing telomere abnormalities in female mice were statistically significant for all parameters tested, while this was not the case in male mice. The biological explanation for this discrepant finding remains to be determined. Breakage of telomere ends may also help to explain our detection of persistent γ-H2AX signals in telomere regions of brain cells (DNA-SCARS)—an established signature of senescenceWe did not detect any evidence of damage to genomic DNA of brain cells that could be attributed to oxygen radicals that are generated following one year of R–Cu treatment. The markedly up-regulated antioxidant enzyme SOD in R–Cu treated mice apparently neutralised the invading oxygen radicals and prevented damage to cellular genomic DNA  to Cu(I). Deactivation of cfChPs in extracellular spaces of brain that we observed assumes that this is effected by oxygen radicals; we do not actually demonstrate the presence of oxygen radicals in mouse brain. However, our finding of increased SOD activity in serum of R–Cu treated mice leads to the assumption that oxygen radicals might have also been generated in the brain. We also did not examine the mechanism by which oxygen radicals are absorbed from stomach or whether they were reactive against cfChPs. Finally, we observed that R–Cu treatment leads to increase in expression of SOD in brain cells. This does not necessarily imply increased SOD activity.Our study has some limitations. For example, it does not address the effects of R–Cu on physiological functions such as memory or behavioral aspects of the animals, or whether it extends survival. The effects of stopping exposure to R–Cu was also not investigated; whether the observed changes would revert or disappear remains unknown. The study also does not address whether the phenomenon of hormesis is involved in the biological effects that we observed64. However, antioxidant therapy to retard ageing in animal models has produced conflicting results66, and those in humans have been equivocal67. Of all anti-oxidants, resveratrol has been the most widely investigated as an anti-ageing agent68. Our current results raise the hypothesis that the reported anti-ageing effects of resveratrol may in fact be due to its pro-oxidant activity in the presence of copper. The conflicting results may reflect the inconsistent availability of copper in the stomach for resveratrol to have a sustained pro-oxidant activity in order to effectively deactivate extra-cellular cfChPs and to have a protective effect against ageing.It is believed that ageing is a consequence of oxidative stress leading to progressive loss of tissue and organ function resulting from accumulation of ROS-induced damage69. We propose that the latter, together with other yet unknown harmful pleiotropic effects of cfChPs, are the underlying processes that define ageing. Our results suggest that these harmful effects can be prevented by deactivation/eradication of the offending cfChPs via the medium of oxygen radicals. We propose that oral administration of a combination of small quantities of R and Cu holds the promise of being an effective anti-ageing therapeutic combination. Whether R–Cu will be effective in retarding ageing and neurodegeneration in humans will have to await clinical trials in appropriate populations. It is to be noted in this context that our early results have shown that R–Cu is therapeutically effective in humans, albeit in relation to other pathological situations27.We demonstrate for the first time that cfChPs derived from dying brain cells are abundantly present in the extracellular spaces of the ageing brain. We also show that extra-cellular cfChPs are virtually eliminated by oxygen radicals that are generated following prolonged treatment with R–Cu. The fact that elimination of cfChPs was associated with down-regulation of multiple biological hallmarks of ageing and neurodegeneration makes a strong case for a direct role of cfChPs in the aetiology of these pathological processes. We propose that cfChPs released from dying brain cells initiate a vicious cycle of more DNA damage, apoptosis and inflammation, setting in motion a low grade and unrelenting “cytokine storm”10, but none can comprehensively explain the myriad changes that accompany this multidimensional process. While we acknowledge that there may be other factors at play, our results suggest that cfChPs may be global instigators of ageing and neurodegeneration, and that therapeutic use of R–Cu may help to make healthy ageing an attainable goal.Over the past fifty years of biogerontological research, many theories and causes of ageing have been advancedSupplementary Figure S1.Supplementary Figure Legend.Supplementary Table 1.Supplementary Table 2.