However, the sources and mechanisms that contributed to this process remain unresolved. Here, we present evidence for substantial ancient terrestrial carbon remobilization in the Canadian Arctic following the Laurentide Ice Sheet retreat. Glacial-retreat-induced physical erosion of bedrock has mobilized petrogenic carbon, as revealed by sedimentary records of radiocarbon dates and thermal maturity of organic carbon from the Canadian Beaufort Sea. Additionally, coastal erosion during the meltwater pulses 1a and 1b has remobilized pre-aged carbon from permafrost. Assuming extensive petrogenic organic carbon oxidation during the glacial retreat, a model-based assessment suggests that the combined processes have contributed 12 ppm to the deglacial CO2 rise. Our findings suggest potentially positive climate feedback of ice-sheet retreat by accelerating terrestrial organic carbon remobilization and subsequent oxidation during the glacial-interglacial transition.The changes in atmospheric  Shrinking of the Laurentide Ice Sheet mobilized the underlying rock organic carbon. Together with permafrost carbon release, this may contribute 12 ppm to deglacial CO2 rise, underscoring the impact of cryospheric change on the carbon cycle. During the last deglaciation, atmospheric CO2 concentrations rose by ~75 ppm while the Δ14C values of CO2 declined3. Evidence from both data and models suggests that the pCO2 increase is driven mainly by changes in Southern Ocean ventilation, making the region a source of ancient carbon to the atmosphere5. However, the oceanic CO2 release alone cannot account for the full glacial/interglacial amplitude of CO2, or the rapid rise at 16.4, 14.6, and 11.5 cal. kyr BP, or the stable carbon isotopic anomaly of atmospheric CO2. Hence, terrestrial and marine carbon sources have been both invoked to explain the CO2 variations7.Identifying Earth system processes that have contributed to atmospheric 2 variations. Growing evidence of terrestrial carbon remobilization/oxidation related to ice-sheet retreat, however, has indicated the necessity of a careful re-evaluation of this paradigm9. One can also imagine that glacial retreat directly leads to exposure to the atmosphere of organic carbon (OC) that has been isolated for many millennia and the oxidation of which may be important for the OC-rich regions. More recently, ice-sheet retreat and the subsequent exposure of its underlying shales have received attention to explain the CO2 increases10.Ice sheets have traditionally been regarded as an inert component in the carbon cycle and thus have not been considered to explain the COpetro; rock-derived OC that is typically radiocarbon free) can be reintroduced into the active carbon cycle through chemical weathering or microbial utilization12. Such processes have been proposed to regulate atmospheric CO2 levels over geological timescales13. With more studies into this field, modern observations describe OCpetro oxidative weathering as a supply-limited process, oxidation flux depending on the rock erosion rate15. High OCpetro supply is found in glaciated regions today and glacial denudation of bedrock is a significant contributor. In the southern Alps of New Zealand, the OCpetro oxidative weathering fluxes in glacier-dominated watersheds (up to 50 tC km−2 yr−1) are 2–3 times higher than those in less-glaciated watersheds15. Along the southeast Alaskan coast, the mass accumulation rates (MARs) of OCpetro in glaciated fjords are significantly higher than those in non-glaciated fjords16. Notably, initial evidence of enhanced OCpetro mobilization during the ice-sheet retreat has been seen in a sedimentary record obtained from the Bering Sea17. The above lines of evidence support rather substantial OCpetro mobilization for the previously glaciated continents and imply extensive OCpetro oxidation during the last deglaciation. It further raises questions, depending on the magnitude of carbon release, whether the processes are connected to the millennial-scale CO2 increases during glacial terminations10.Oxidized petrogenic organic carbon  and Cordilleran Ice Sheet2 rise24. However, so far, most studies on permafrost carbon remobilization have been carried out along the shelves or slopes of the Laptev Sea, the East Siberian Sea, the Chukchi Sea, the Bering Sea, the North Pacific, and the Okhotsk Sea27. With the possible exception of the Bering Sea, the continental areas in the hinterland of these regions remained largely unglaciated during the LGM. Thus, a complex combination of processes during the last deglaciation, including water runoff, shelf flooding, and permafrost thawing in the interior, makes it difficult to unambiguously determine the process of coastal erosion. In contrast to the unglaciated regions, ice sheets in glaciated regions hindered vegetation development and the accumulation of carbon-rich permafrost deposits in the interior. This unique feature precludes signals from hinterland permafrost thawing and thus makes it an ideal region to study the process of coastal erosion.Another terrestrial carbon pool that may be remobilized during the ice-sheet retreat is permafrost carbon, which has been freeze-locked for thousands of years and is vulnerable to degradation once thaws. Coastal erosion during the rapid sea-level rise, as a result of ice volume reduction, has been proposed to remobilize permafrost carbon and contribute to the deglacial COpetro mobilization and the process of coastal erosion during the last deglaciation. In this work, we analyze biomarker contents and radiocarbon signatures of sedimentary OC and of specific terrigenous biomarkers in core ARA04C/37 from the Canadian Beaufort Sea  and radiocarbon-free OCpetro, pyrolysis and biomarker proxies are used as supporting evidence of OCpetro contributions. We demonstrate that ice-sheet retreat has caused substantial OCpetro mobilization during the last deglaciation. Additionally, rapid sea-level rise at ca. 14 and 11 cal. kyr BP most likely caused two events of strong coastal erosion. Based on our findings, we attempt to estimate carbon release from OCpetro oxidation and assess the impacts of oxidized OCpetro and flooded permafrost on atmospheric carbon pools by using the global carbon cycle model BICYCLE30. The simulations suggest that the two processes additively may have a long-term effect of an increase in atmospheric CO2 of 12 ppm and a decrease in atmospheric Δ14C of 12 permil.Our study area in the Canadian Beaufort Sea is ideally located to elucidate both OCSea Fig. , spannin3 yr−1 and sediment flux of 124–128 Mt yr−1 . The OC delivered into the Canadian Beaufort Sea was much older between 14.5 and 10 cal. kyr BP compared to the Holocene input. When compared to the mean age of modern Mackenzie River particulate organic carbon (6.6 ± 1.2 kyrs) . The pre-depositional ages of bulk OC were oldest (20–30 kyrs) between 14.5–10 cal. kyr BP while values decreased throughout the Holocene Fig. . We notepetro34, and the increased carbon age may suggest an even increased OCpetro input in the past. Multiple proxies, i.e., carbon preference index of high molecular weight n-alkanes , the fractional abundance of “biological” homohopane to its diagenetic isomers (fββ), and temperature at which pyrolysis yields the maximum of hydrocarbons (Tmax), are used as support for large OCpetro input between 14.5–10 cal. kyr BP. These proxies have been proposed to indicate carbon thermal maturity (see methods) and thus are indicative of OCpetro input. However, as these proxies have limitations to specifically indicate OCpetro input, interpretation of their variations warrants caution. Nevertheless, the overall low values of CPIalk and fββ, as well as high Tmax values, are consistent with OCpetro input typical for the Mackenzie River basin and support increased OCpetro contribution between 14.5–10 cal. kyr BP  coincides with finely laminated sediments .The period of enhanced OCnts Fig. , implyin28. The increased TOC MARs at the onset of the Younger Dryas (YD) can be explained by flood mobilization/transport of OC since multiple sedimentary records have documented the high-energy YD flood draining through the Mackenzie River to the Arctic Ocean , while δ18O values during the putative post-YD flood are even higher than 2‰  and the diol proxy  peaked during the YD flood, whereas no such clear signals were found during the post-YD flood  MAR shows three distinct peaks during the last deglaciation and the early Holocene Fig. 28. The iean Fig. 28,29. Ho 2‰ Fig. 29, the bood Fig. , suggestterr-bio41. The pre-depositional ages of HMW-FAs were the oldest  between 14.5 and 10 cal. kyr BP and values decreased during the Holocene  in the Mackenzie River basin34. Because the remobilized OCterr-bio is always a mixture of constituents of different carbon ages, e.g., young biospheric organic carbon synthesized by plants and pre-aged biospheric carbon from relic permafrost or deeper soil profiles, the older mean age of HMW-FAs likely indicates lower contributions from young constituents. This can be attributed to the fact that the LIS has restricted vegetation and reduced contributions from freshly produced biospheric carbon during the last deglaciation. It implies that the mean age of OCterr-bio during the last deglaciation is different from the modern one.The high molecular weight fatty acids (HMW-FAs) are synthesized by terrestrial higher plants and are widely found in plants and soils. Since they are expected to be largely absent in mature petrogenic materials, HMW-FAs are commonly taken to represent OCene Fig. . Furtherterr-bio transported by freshwater discharge. However, the pre-depositional ages of HMW-FAs sharply increased at 14 and 11 cal. kyr BP  14C dates at the base of core ARA04C/37 (see methods) or an incomplete record of this event.The pre-depositional ages of HMW-FAs were not uniformly old between 14.5 and 10 cal. kyr BP. Ages were much younger during the YD, indicating a younger inland OC BP Fig. . As perm BP Fig. , indicat BP Fig. e, f. Sin13C, CPI, fββ, and Tmax did not show significant changes  continuously high OCpetro supply from the hinterland and (2) significant contributions from the eroded coastal deposits containing OCpetro debris42.Although the distinct increases in TOC MAR were likely linked to coastal erosion during the MWP 1a and 1b, parameters of bulk OC, i.e., δges Fig. . This supetro following the LIS retreat. Towards quantitative estimates, a three-endmember mixing model based on a Markov chain Monte Carlo Bayesian approach was used to apportion relative contributions of OCpetro, OCterr-bio, and marine biospheric carbon  were ~six times higher than those in the late Holocene (~0.06 g cm−2 kyr−1) (see more information in petro MARs were 6–18 (or 12 ± 6) times higher during the last deglaciation.The records of core ARA04C/37 present direct evidence for substantial remobilization of OCbon Fig. . More inene Fig. . The estpetro exhumation during the last deglaciation is currently uncertain and depends on the fate of remobilized carbon. Through a simple pathway, the remobilized OCpetro escaped remineralization and translocated from sedimentary rocks to oceanic storage which has negligible impacts on atmospheric CO2 levels, while when through an oxidation pathway the remobilized OCpetro was reintroduced into the carbon cycle which may affect atmospheric carbon chemistry. Emerging evidence couples OCpetro oxidation flux with rock erosion rate13, and particularly, the recent study observed higher CO2 emissions in glaciated areas than in unglaciated areas15. The evidence provides us with the basis to explore an alternative scenario of large OCpetro oxidation during the last deglaciation. Reconstructing oxidation of exhumed OCpetro for past time periods is not possible from direct observations, but insights might be gained by studying sedimentary records. When postulating that our core record is representative of the process of petrogenic carbon mobilization in response to the deglaciation of North America, the record provides us with the opportunity to explore the effect enhanced rock erosion might have had on atmospheric CO2.The climate impact of OCpetro are oxidized, percentages varying in different regions, whereas OCpetro buried in river/marine sediments is unoxidized and may be chemically and physically resilient13. Regarding the increased OCpetro MARs as a consequence of enhanced rock erosion and assuming a constant burial efficiency, the OCpetro oxidized should always keep pace with that accumulated in marine sediments. Therefore, the increase in OCpetro MARs indicates an increase in OCpetro oxidation flux by 6–18 (12 ± 6) times during the last deglaciation when compared to the modern oxidation flux. In the Mackenzie River basin, the modern OCpetro oxidation fluxes are estimated to be ~0.45 ± 0.19 tC km−2 yr−1 for the Mackenzie River and a mean value of 0.89 ± 0.32 tC km−2 yr−1 for its main tributaries 43. The oxidation flux along the Mackenzie River is moderate in comparison to its tributaries. This can be explained by the fact that only 54% of the entire basin is on shales while all the tributaries drain through the shales-dominated mountain regions44. Therefore, the mean value (0.89 ± 0.32 tC km−2 yr−1) from the main tributaries is taken to represent the OCpetro oxidation flux in shales regions, which is estimated to be 11 ± 7 tC km−2 yr−1 during the last deglaciation.Modern observations suggest that ~10–90% of the exhumed OCpetro MAR. Organic carbon burial efficiency increases with higher sedimentation rates46. On a larger spatial scale, global TOC MARs during the LGM were 147 ± 18% relative to the Holocene and then gradually decreased to the Holocene level47. This may indicate more efficient OC transfer from the sea surface to the seafloor and better preservation in marine sediment during the last deglaciation. In the study area, the meltwater-induced high discharge and shorter pathways from glaciers to the ocean may have further shortened the transport time, reducing OC oxidation during transport, and thus increased the OC burial efficiency in marine sediments. Besides, lower sea-level and closer distance of the study site to the coast may have caused higher OCpetro MARs during the last deglaciation. While in opposite to the extensive shelves in the Laptev Sea or the East Siberian Sea, the offshore distance may change less in the Beaufort Sea due to the narrow shelf. Because the OCpetro burial efficiency might have increased via multiple processes during the last deglaciation, the estimated OCpetro oxidation flux must therefore be regarded as an upper limit.One should keep in mind that physical erosion was not the only factor responsible for the increases in OCpetro oxidation flux even at the same rate of physical erosion15. Besides, not all of the exhumed OCpetro was transported to the ocean, and much of the glacially eroded material may have been deposited on land  or trapped in an intermediate pool of glacial lakes48. The enhanced OCpetro MARs in marine records thus only reflect part of the exhumed OCpetro. These characteristics in the glacial watersheds imply that extrapolating oxidation flux from an unglaciated modern environment to a glaciated paleo scenario may cause an underestimate.On the other hand, there are reasons that we would argue to expect even larger oxidation fluxes than we predicted. Glacial processes appear to enhance OC2 into the atmosphere. Estimating OCpetro oxidation flux in such regions allows for a quantitative estimate of carbon release. The carbon yield (Jcarbon) from OCpetro oxidation can be estimated based on the exposed area (Aexposure), oxidative weathering fluxes (Foxidation), and the exposure time (Texposure) using the equation:Outcropping shales that were exposed by glacial retreat after long-term isolation may have released additional COAexposure is defined as freshly exposed areas with outcropping shales during the ice-sheet retreat. The area changes through time with regard to ice-sheet retreat, we, therefore, calculate Aexposure based on shales distribution and the changes in ice-sheet extent49 in North America  to be 11 ± 7 tC km−2 yr−1 during the last deglaciation. From the last deglaciation towards the present, the large decrease in Foxidation may reflect processes such as soil formation and vegetation development, which reduce Foxidation with increasing exposure time. To include such processes in the calculation, we assume that Foxidation decreases with increasing substrate age in a similar manner as in silicate weathering 51. F0 is the oxidation flux of freshly exposed substrate (10-year-old), and Foxidation denotes the oxidation flux of the substrate at age t. Calculation of F0 requires a given Foxidation with a known substrate age t. Since Horan et al.43 have estimated the modern oxidation flux (0.89 ± 0.32 tC km−2 yr−1) for the shales-dominated region and the region is known to have been exposed between 15 and 10 cal. kyr BP19, we thus assume for 104 years old substrates (t) an oxidation rate of 1 tC km−2 yr−1 (Foxidation) and obtain for newly exposed shales a rate of 21 tC km−2 yr−1 (F0). Uncertainty bands are added to this approach by assuming that the modern Foxidation (~1 tC km−2 yr−1) is alternatively valid for substrate ages of 5 kyrs or 15 kyrs  fall well within the range and correspond to a substrate age of <100 to 2000 years  is calculated in steps of 100 years for entire North America and has been integrated over all time steps. The annual carbon release for entire North America is shown in Fig. The yrs Fig. . Althougpetro during the last deglaciation, the events of increased TOC MARs also provide evidence for coastal erosion of permafrost that occurred in well-defined pulses. Because inland permafrost formation was restricted in the Mackenzie River basin, the maxima in accumulation occurring in the PreBoreal (MWP1b) and at or around MWP 1a were most likely attributed to the erosion of non-glaciated coastal permafrost , OC-rich deposits from the eastern coast, and residual permafrost/soil deposited in coastal regions. Within dating uncertainties, these two events were broadly coeval with those found in other records across the North Pacific and the Arctic Ocean26. Therefore, our records confirm that coastal erosion induced by rapid sea-level rise was a major process of aged permafrost carbon release in (sub-)Arctic coasts and shelves.Besides the exhumation of OC52. The authors demonstrate that substantial amounts of OC are quickly re-mineralized in all incubations, and the CO2 production is even higher when seawater is added, indicating potentially substantial CO2 emissions from erosion of permafrost onshore and within the nearshore waters. Estimates from Herschel Basin, a shelf basin in the Beaufort Sea, suggest that only ~40% of the eroded permafrost carbon from adjacent Herschel Island is buried locally in the basin32, where it may, however, be further degraded. Another study based on OC concentrations of thawed samples from eroded bluffs estimates that ~66% of the OC contained in Yedoma deposits is released as CO2 in one thawing season, prior to reaching a water body downslope53. Accordingly, the eroded permafrost carbon may have contributed to rapid deglacial CO2 rises.Remobilized permafrost carbon has been proposed to be highly bioavailable. A recent study mimics coastal permafrost erosion by incubating permafrost with and without seawater for the duration of one Arctic open-water seasonpetro and destabilization of coastal permafrost deposits, are both related to ice-sheet retreat. Ice-sheet retreat directly led to erosion, exposure, and oxidation of OCpetro which released, depending on assumed substrate age, 84 ± 30 Pg of carbon. At the same time, the reduction in ice volume resulted in sea-level rise leading to coastal erosion/shelf flooding of permafrost from the Arctic shelves, which is estimated to release 85 Pg of carbon24. We applied the most recent version of the global carbon cycle model BICYCLE30 in order to assess the impacts of ice-sheet retreat via the combined processes mentioned above on atmospheric CO2 and Δ14C. The carbon release rate from OCpetro oxidation is shown in Fig. 24, i.e., the release of 10 kyr-old permafrost carbon is restricted to a time window of 200 years for three pulses: 170 TgC yr−1 (or 34 PgC) at 11.5 and 14.6 cal. kyr BP each and 85 TgC yr−1 (or 17 PgC) at 16.5 cal. kyr BP. All carbon is released as CO2 and directly enters the atmosphere in the model.The two processes of carbon release, i.e., exhumation of OC2 peak of 6 ppm at 16.5 cal. kyr BP and two more CO2 peaks of ~12 ppm at 14.6 and 11.5 cal. kyr BP  glacial erosion of sedimentary rocks may have strengthened oxidative weathering, (2) lower temperature may have weakened CO2 drawdown by silicate weathering, and (3) limited vegetation and soils may have resulted in lower OCterr-bio stock in the landscape and weakened CO2 drawdown by OCterr-bio burial. Our study presents direct evidence of substantial OCpetro remobilization that may support the strengthened OCpetro oxidative weathering during the last deglaciation. Besides, the very old OCterr-bio in our sediment archive most likely reflects limited vegetation in the glaciated environment  and oxygen index (mgCO2/gC). In a van Krevelen-type diagram, a classification illustrating carbon types is possible57. Furthermore, the temperature at which pyrolysis yields the maximum of hydrocarbons (Tmax) is used as an indicator of the thermal maturity of the kerogen. Immature organic matter usually has Tmax values of <435 °C.Rock-Eval pyrolysis was performed on bulk sediment samples according to Espitalie et al.n-alkanes and hopanes) and an alcohol fraction via open column chromatography with silica gel (6 mm i.d.*4.5 cm). Hydrocarbon fractions were eluted with 5 ml n-hexane, followed by alcohol fraction elution with 9 ml ethyl acetate:n-hexane .Freeze-dried sediments (~5 g) were extracted with DCM:MeOH , and an internal standard  was added prior to analytical treatment. Total lipid extracts were concentrated and separated into a hydrocarbon fraction  coupled to a flame ionization detector (GC-FID). Homohopane isomers were analyzed with an Agilent 6850 gas chromatograph (GC) coupled to an Agilent 5975 C VL MSD quadrupole mass spectrometer operating in electron impact ionization (70 eV) and full-scan (m/z 50–600) mode.The n-alkanes were identified with external standards, and the carbon preference index of n-alkanes  was calculated as follows  can further indicate contributions from thermally mature OC.The lows Eq. :2\docume31) were identified by relative retention times and mass spectra17. The relative abundance of the “biogenic isomer” 17β,21β(H) 22 R (C31ββR) to the “diagenetic isomers” 17β,21α(H) 22 R (C31βαR), 17β,21α(H) 22 S (C31βαS), 17α,21β(H) 22 R (C31αβR), and 17α,21β(H) 22 S (C31αβS) is described as Eq. 17:Homohopane isomers C1 were idValues of 1 indicate the absence of “diagenetic isomers”, whereas values of 0 indicate the absence of “biogenic isomer”.59. Briefly, according to the respective TOC contents, sediment samples containing ~1 mg OC were weighed into silver capsules and were acidified with 6 N hydrochloric acid (HCl) to completely remove the inorganic carbon. Acid evaporation was conducted on a hot plate at 60 °C, and the dried samples were then stored in an oven (60 °C) until the analysis. Samples including the silver capsules were packed into tin capsules and combusted individually via an Elementar vario ISOTOPE EA . Oxidized carbon (CO2) was directly graphitized by the Ionplus AGE3 system (Automated Graphitization System)60. Radiocarbon contents of samples were analyzed using the Ionplus MICADAS dating system62.Radiocarbon dating was performed following methods described in Mollenhauer et al.2O  at 80 °C for 2 h. The neutral lipids were extracted with n-hexane, and the n-alkanoic acids were then extracted with DCM after adjusting the pH to a value of around 2 by the addition of 37% HCl. The extracted n-alkanoic acids were methylated with 37% HCl and MeOH with a known 14C-signature in a nitrogen atmosphere at 80 °C for over 12 h. The fatty acid methyl esters (FAMEs) were extracted with n-hexane and subsequently separated from polar compounds by silica gel chromatography.For compound-specific (HMW-FAs) radiocarbon dating, sediment samples (~50–70 g) were extracted with DCM:MeOH  using a Soxhlet for over 48 h. The total extracts were hydrolyzed with potassium hydroxide  in MeOH:H24 were purified by preparative capillary gas chromatography (PC-GC) using an Agilent 6890 N GC equipped with a Gerstel Cooled Injection System (GIS) and connected to a Gerstel preparative fraction collector63. The GC was equipped with a Restek Rxi-XLB fused silica capillary column . All samples were injected stepwise with 5 µL per injection. Afterwards, the purified individual FAMEs were transferred into tin capsules and packed. Samples were combusted via the Elementar vario ISOTOPE EA , and the isotopic ratios (14C/12C) of produced CO2 were determined via the directly connected AMS, the MICADAS system, which is equipped with a gas-ion source.FAMEs with chain lengths >C64. All results are reported as fraction modern carbon (F14C).Radiocarbon contents of the samples were analyzed along with reference standards  and blanks  and in-house reference sediments. Blank correction and standard normalization were performed via the BATS software14C of the blank and the size of blank. For this purpose, radiocarbon analyses of in-house reference samples from 14C-free Eocene Messel Shale (F14COC = 0) and modern apple peel (F14COC = 1.029 ± 0.001) processed in the same way as the compound-specific samples were conducted to determine the F14C and mass of blank, following the method of Sun et al.65. All radiocarbon data were corrected for the procedural blank and, to remove the contribution of the methyl group added during the derivatization process, a methyl correction was further performed through isotopic mass balance. Uncertainties were fully propagated.Compound-specific samples analyzed for radiocarbon are sensitive to contamination during processing (procedure blank), for example, the carbon introduced via column bleed and carry-over as well as from the tin capsules. Blank correction of compound-specific samples requires careful determination of F14Cinitial; radiocarbon content prior to the OC deposition to marine sediment), which has been calculated based on the following equation:66The pre-depositional age of OC can be derived from the initial radiocarbon content .F14Catm) was taken from the atmospheric Δ14C record of IntCal13 67. The apparent conventional 14C age  thus has been calculated by the following equation:66The radiocarbon content of the past atmosphere differed from the modern atmosphere, and thus the atmospheric radiocarbon content at the time of deposition  and a process-based sediment model, which calculates as function of the depth-dependent carbonate ion concentrations the accumulation or dissolution of CaCO3 in the deep ocean sediments. The core of the model still consists of a 10-box ocean, a 1-box atmosphere, and a 7-box terrestrial biosphere. We calculate the contribution from OCpetro released from a retreating LIS on shales  terrestrial carbon pool. This has been chosen to make simulation results comparable to Winterfeld et al.24, in which a similar setup, but using an older model version, has been applied. The 14C production rate is kept constant at 25% higher than preindustrial levels in order to obtain at LGM an atmospheric Δ14C of ~400 permil, comparable to reconstructions. Simulations are initialized with interglacial conditions, and the state variables of the sediment are taken after an 800 kyr-long spinup, and started at 210 cal. kyr BP to give the model enough time to run into a reasonable state which is largely independent from initial conditions and spinup.We use the most recent version of the global carbon cycle model BICYCLEles Fig.  and permpetro depending on the assumed substrate age , we use only one version of the permafrost-based carbon release related to coastal erosion. Here, 17, 34, and 34 Pg of 10 kyr-old carbon are released in three 200-year-long pulses starting at 16.5, 14.6, and 11.5 cal. kyr BP24. The carbon released from both processes is entering the model as ingoing CO2 fluxes to the atmosphere. The time-dependent forcing—the changes in climatic boundary conditions —is otherwise identical to what is described in Köhler and Munhoven30.While we use three different versions of the fluxes for OCSupplementary InformationPeer Review File


Cardiac cephalalgia is an unusual condition that occurs during an episode of myocardial ischemia. Information about cardiac cephalalgia is scarce and its characteristics and physiopathology remain unclear. Our aim is to provide a narrative review of clinical characteristics and physiopathology of cardiac cephalalgia and to evaluate the current diagnostic criteria. th September 2022. We summarized the literature and provide a comprehensive review of the headache characteristics and possible mechanisms. We also evaluated current International Classification of Headache Disorders third edition diagnostic criteria based on prior reported cases. A search through PubMed was undertaken for studies on cardiac cephalalgia published until 20In total, 88 cases were found. Headache characteristics were variable. Occipital location and throbbing pain were the most frequently reported. Headache was accompanied in most cases by cardiac symptoms. Criterion B was fulfilled by 98% of cases, criterion C1 by 72%, and criteria C2a and C2b by 37 and 93.2%, respectively. Regarding headache features described in diagnostic criterion C3, ‘moderate to severe intensity’, ‘accompanied by nausea’, ‘not accompanied by photophobia or phonophobia’ and ‘aggravated by exertion’, were reported in 75, 31, 55 and 55% of cases, respectively.Cardiac cephalalgia characteristics are variable and the headache features described in the diagnostic criterion C3 might not be adequate. Given that cardiac cephalalgia can be the manifestation of a life-threatening condition it is important to increase the knowledge about this entity.The online version contains supplementary material available at 10.1186/s10194-022-01508-7. Comorbidities of primary headache disorders include cardiovascular conditions and ischemic heart disease prevalence is higher in patients with primary headache that in general population 7% vs. 2.6%) . Nonethe.6% . NonCardiac cephalalgia is an unusual condition that occurs in relation to an episode of myocardial ischemia. This term was first proposed by Lipton et al. in 1997  and, sinSince cardiac cephalalgia can be the main or even the only clinical manifestation of a myocardial infarction, a life-threatening condition, recognizing this entity is of great importance. Therefore, our aim is to review the clinical characteristics of cardiac cephalalgia and the proposed pathogenic mechanisms and to evaluate the current International Classification of Headache Disorders third edition (ICHD-3)  diagnostWe performed a literature search in Pubmed database on 20 September 2022. We used the following search lines: “Cardiac”[Title/Abstract] and “Cephalgia”[Title/Abstract], “Cardiac”[Title/Abstract] and “Cephalalgia”[Title/Abstract], “Acute myocardial infarction”[Title/Abstract] and “Headache”[Title/Abstract], “Myocardial Infarction”[MeSH] and “Headache”[MeSH], “Myocardial Ischemia”[MeSH]) and “Headache”[MeSH], “Acute Coronary Syndrome”[MeSH] and “Headache”[MeSH], “Angina”[MeSH] and “Headache”[MeSH]. Only manuscripts written in English and Spanish were included. We applied no time limits. We selected all publications relevant to our topic and we also reviewed the references of these papers in order to find other useful material to our review.We identified 227 records of which, after deduplication, 155 remained for further analysis. A total of 66 articles were screened by abstract. After a further screening process, 50 publications were finally included, three of them from the review of the references of selected papers  as a secondary headache in the category of ‘headache attributed to disorder of homeostasis’ . ICH-2 dIn 2004, Chen et al.  performeIn the ICHD-3 , cardiacn = 36; 62.1%). These data are in line with the study from Xu et al. that reported a mean age of 64.6 years (± 11.9) and a predominance of male patients (53.3%) [We found a total of 88 cases of cardiac cephalalgia, 58 from case reports –53 a co and 30 p (53.3%) . History (53.3%) . History (53.3%)   [n = 14, 46.6%) [n = 8, 13.8%) and pressing pain  were the most frequent but in one-half of the cases headache quality was not specified. Xu et al. found that pulsating quality was the most frequent (33.3%) followed by dull (16.7%) and stuffy pain (16.7%) [Regarding headache features, location of pain was variable and occipital pain was the most frequently reported among previous case reports n = 16, 2,6% [7–53, 46.6%) . Bilater (16.7%)  n = 51, 57.9%), moderate intensity was described by 15 cases (17%), mild intensity by 6 (6.8%) and variable intensity by 3 (3.4%). In 13 patients (14.7%) headache intensity was not specified. Headache was accompanied by nausea in 28 cases (31.8%), was not accompanied by photophobia or phonophobia in 49 patients (55.7%) and was aggravated or induced by exertion in 49 (55.7%). It is also interesting that two cases reported tearing and one case reported rhinorrhoea [In total, more than half of the 88 cases reported severe intensity  and the right coronary artery  were the most frequently affected . In one case of headache with and without exertion relieved by nitrates myocardial ischemia was not demonstrated because patient died suddenly without electrocardiogram and cardiac enzymes determination  Table 55.Table 5To evaluate criterion C1 `Headache has developed in temporal relation to the onset of acute myocardial ischaemia’ it is necessary to observe the temporal relationship of headache and cardiac symptoms but it can only be confirmed if we observe the onset of headache during a stress test. We considered that 34 patients from the case reports met this criterion. 17 patients reported headache onset in relation to onset of cardiac symptoms and in 17 cases stress tests confirmed the temporal relationship between myocardial ischemia and headache. All 30 patients from the study from Xu et al. met this criterion  Table 55.Regarding criterion C2 most patients (93.2%) fulfilled criterion C2b ‘Headache has significantly improved or resolved in parallel with improvement in or resolution of the myocardial ischaemia’. However, evaluate criterion C2a is difficult because it is hard to determine the worsening of myocardial ischemia. For this reason, we considered that only three cases who presented worsening of headache in relation to confirmed worsening of the myocardial ischemia during the coronarography met criterion C2a , 14, 52.Criterion C3 is the criterion that describes headache characteristics. Criterion C3a ‘moderate to severe intensity’ was met by 75%, criterion C3b ‘accompanied by nausea’ by 31.8%, criterion C3c ‘not accompanied by photophobia or phonophobia’ by 55.7% and criterion C3d ‘aggravated by exertion’ by 55.7%. Considering these findings, nausea is not a frequent accompanying symptom in cardiac cephalalgia. This finding is in line with the results of the literature review by Chen et al.  that fouFinally, among those cases that reported nitrates administration, Criterion C4 ‘Headache is relieved by nitroglycerine or derivatives of it’ was fulfilled by 100% of cases. However, it must be considered that in 36 case reports the use of nitrates was not specified and that in the study by Xen et al. all 12 patients did not receive nitrates .Taking into account the present evaluation and in order to improve ICHD-3 diagnostic criteria, we might suggest removing criterion C3b ‘accompanied by nausea’ given that it was the least commonly fulfilled criterion.Even though the pathophysiology of cardiac cephalalgia is not known, four hypotheses have been proposed to illustrate its mechanisms , 53–56.The first hypothesis states that cardiac cephalalgia could be the result of the convergence of afferent autonomic visceral fibers, which carry nociceptive cardiac stimuli, and somatic sensory fibers onto a common pool of spinothalamic tract (STT) and spinoreticular tract (SRT) neurons. Thus, according to this hypothesis, cardiac cephalalgia would be a referred pain produced because the brain interprets that cardiac pain is originated in the somatic structures –59.Foreman et al.  proposedThe concentration of cardiac afferent autonomic visceral fibers can vary for each cardiac region . AlthougThe second theory states that the abrupt decrease of cardiac output during myocardial ischemia would cause a rising of pressure in the left atrium and left ventricle hindering cerebral venous return. Hence, cardiac cephalalgia would be the result of an increased intracranial pressure secondary to a reduction of cerebral venous drainage , 53–56.The third hypothesis suggests that the release of inflammatory mediators during cardiac ischemia including bradykinin, serotonin, substance P and histamine could cause vasodilation in brain arteries leading to headache , 53–56.Finally, Wang et al.  proposedWe provide an updated overview on cardiac cephalalgia from the physiopathology to the diagnostic criteria. The major limitation of our review is that the description of headache characteristics of cardiac cephalagia in a high proportion of previous reports were scarce and that there were a large number of terms to describe headache quality. Another limitation is that headache history was rarely reported. Thus, patients with a worsening of a preexisting headache may have been misdiagnosed as cardiac cephalalgia. To further elucidate the characteristics of cardiac cephalalgia and its pathophysiology it would be of great interest to conduct further studies with standardized data collection of patients with demonstrated myocardial ischemia in order to investigate cardiac cephalalgia prevalence and characteristics.Cardiac cephalalgia characteristics are variable and the proposed headache features in the diagnostic criterion C3 might not be adequate, especially nausea which was the least commonly met criterion. Given that it can be the manifestation of a life-threatening condition it is important to increase the knowledge about this entity. Further prospective studies are warranted to assess its prevalence and to describe in detail its clinical features in order to better understand and manage patients with cardiac cephalalgia.Additional file1. Cardiac cephalalgia case reports. Summary of data from previous case reports of cardiac cephalalgia.


Thanks for Crimi et al.’s comment . The fol2/min (FiO2 0.4–0.6) to achieve the target SpO2 (≥90% for nonpregnant patients and ≥92–95% for pregnant patients) [We recommend HFNC as a first-line treatment for patients with “severe” COVID-19 in the small discussion chapter of this review article. We are sorry for not giving clear definition of severe COVID-19 in our discussion chapter. The definition of severe COVID-19 here is to use 6–15 L OIndeed, a personalized and stepwise approach is important in treating COVID-19 patients with hypoxemic respiratory failure. Although there is still uncertainty about optimal oxygen strategy in COVID-19 patients with hypoxemic respiratory failure, HFNC may play an important role in a stepwise approach because of its great comfort for the patients.We have learned much from your comment. Thank you again.


It is not entirely clear which amino acid (AA) residues and sites in the protein are preferred for binding. The understanding of NC-protein interactions and how they evolve in the polypeptide templates is the key to designing Au NCs. In this work, binding of gold ion Au+ and diatomic neutral gold nanocluster Au2 with a full set of α-proteinogenic amino acids is studied using Density Functional Theory (DFT) and the ab initio RI-MP2 method in order to find the preferred sites of gold interaction in proteins. We demonstrated that the interaction of gold cations and clusters with protonated and deprotonated amino acid residues do not differ greatly. The binding affinity of AAs to the Au2 cluster increases in the following order: Cys(−H+) > Asp(−H+) > Tyr(−H+) > Glu(−H+) > Arg > Gln, His, Met ≫ Asn, Pro, Trp > Lys, Tyr, Phe > His(+H+) > Asp > Lys(+H+) > Glu, Leu > Arg(+H+) > Ile, Val, Ala > Thr, Ser > Gly, Cys, which agrees with the available experimental data that gold cluster synthesis occurs in a wide range of pH – amino acid residues with different protonation states are involved in this process. The significant difference in the binding energy of metal atoms with nucleobases and amino acids apparently means that unlike on DNA templates, neutral metal atoms are strongly bound to amino acid residues and can't freely diffuse in a polypeptide globula. This fact allows one to conclude that formation of metal NCs in proteins occurs through the nucleation of reduced Au atoms bound to the neighboring amino acid residues, and the flexibility of the amino acid residue side-chains and protein chain as a whole plays a significant role in this process.Metal nanoclusters (NCs) have gained much attention in the last decade. In solution, metal nanoclusters can be stabilized by proteins, and, thus, exhibit many advantages in biocatalysis, biosensing, and bioimaging. In spite of much progress in the synthesis of polypeptide-stabilized gold (Au) clusters, their structure, as well as amino acid-cluster and amino acid–Au Our calculations showed that amino acids stabilize gold nanoclusters; binding energy between organics and gold is higher than between organics and silver. In particular, DNA-stabilized8,9 and protein-protected6,7 NCs exhibit many advantages for biosensing and bioimaging: ultrasmall size, photostability, biocompatibility, and brightness. Noble metal NCs, in particular, silver (Ag) and gold (Au) clusters, in comparison with other NCs, exhibit excellent stability, facile synthesis, and low toxicity.10 Metal clusters emitting in the visible range have been synthesized using DNA,8,9 amino acids,11,12 peptides,13,14 and proteins such as bovine serum albumin,15–19 human serum albumin, egg albumin,20,21 lysozyme,22 and immunoglobulin.5Metal nanoclusters (NCs) have gained much attention in the last decade in biocatalysis, biosensing, and bioimaging due to their high biocompatibility, small size, and high sensitivity to molecular environment.23 We showed that deprotonated amino acid residues are preferable for binding with silver clusters, which is in line with experimental data: the formation of silver clusters on protein templates occurs predominantly at alkaline pH. On the contrary, gold clusters are synthesized in a wide range of pH.24 Several factors may influence this process: the ability of different amino acid functional groups to reduce gold, charge, and binding energy with gold.In spite of much progress in the synthesis of a wide variety of NCs, their structure, as well as ligand–cluster interactions, remains poorly understood. For protein-stabilized NCs, it is not entirely clear which amino acid residues and sites in the polypeptide are preferred for binding. The understanding of NCs–polypeptide interactions and how they evolve in the polypeptide matrices is the key to design the functional fluorescent biolabels. We have investigated earlier the interactions of amino acids with silver ions and clusters.2 cluster/amino acid (AA) interactions and on the Au+/AA interactions as a precursor of the cluster. In a typical synthesis, hydrogen tetrachloroaurate is usually taken as a source of gold Au3+ ions. At the first stage, proteins reduce most of the Au3+ to Au1+.25 It is generally believed that at the first step of Au NPs synthesis Au+–thiolate complexes are formed.26–28 In proteins, Au ions may bind to various AAs able to interact with gold. Many AAs can reduce the ions.29–33This paper focuses on the Au34It is known that Au can interact with O, N and S atoms. At the same time, it is believed that gold in protein templates interacts most effectively with sulfur, especially with cysteine. Indeed, cysteine is considered as the preferential binding site for gold in proteins, which is confirmed by theoretical calculations.+) and gold nanoparticles with individual amino acids and proteins has been investigated earlier.29–33,35–37 It was shown experimentally that low temperature and acidic pH favors the growth of gold nanoparticles on protein template.35 On contrary, we showed that deprotonated amino acid residues are preferable for binding with silver clusters,23 which is in line with experimental data: the formation of silver clusters on protein templates occurs predominantly at alkaline pH.5,18,38–40 Gold clusters are synthesized in a wide range of pH.24,41–44 The synthesis of gold nanostructures through the photo-reduction of amino acids in water is also possible: the most stable structures are produced by arginine, cysteine, threonine, methionine, tryptophan, and phenylalanine.36 The interaction of gold cation (Au+), gold clusters, and nanoparticles with individual amino acids and proteins was investigated theoretically earlier.37,45–47 Using molecular dynamics, it was shown that negatively charged atoms play a significant role in adsorption of amino acids on the gold nanoparticles.37 It was shown that the interaction energy with neutral Au3 cluster is higher for the glycine bearing a negative charge than for glycine with charge 0 or +1, the same is true for cysteine.45 In the case of neutral and negatively charged glycine, the interaction occurs with the nitrogen atom, while in the case of protonated glycine interaction with Au3 cluster proceeds through the carboxyl. In the case of cysteine, neutral amino acid interacts with the cluster through the nitrogen, negatively charged amino acid forms a bond between Au and sulfur, while for positively charged Gly interaction with Au occurs through both sulfur and hydroxyl of the carboxyl group. They also showed that two major bonding factors are: (1) Au–N, Au–O, and Au–S anchoring bonding; and (2) nonconventional OH⋯Au and NH⋯Au hydrogen bonding.45 Rai and co-authors performed theoretical calculations for proline and Au3 cluster. The interaction of gold cluster with proline occurred predominantly through amide terminal.46 Investigation of the interactions of Au8 and Au20 clusters with alanine and tryptophan showed that these clusters prefer single-site interactions through the amino-group for the amino acids.47 In these works, the authors regarded only alanine, cysteine, glycine, proline, and tryptophan interaction with gold nanoclusters and how the interplay of gold with the remaining 15 amino acids occurs was still unknown.The interaction of gold cation  analysis.In our quantum-chemical investigation we focused on the interactions of the neutral Au15–17,22 In contrast, DNA-stabilized NCs are positively charged clusters.50–52 We performed the calculations for gold and silver ions and clusters with cytosine and adenine, the preferred binding residues for Ag and Au clusters in DNA,53,54 and compared them with the literature data on Au and Ag interactions with DNA.There is a certain interest to compare the binding energies of gold and silver clusters with protein and DNA matrices. It was shown experimentally that both Au and Ag NCs on protein matrices consist mostly of neutral metal atoms.2.55 level, and resolution-of-the-identity second order Moller–Plesset perturbation theory (RI-MP2) realized in Orca 3.0 program package.56 Since DFT does not include dispersion forces, the atom-pair wise dispersion correction with Becke–Johnson damping was used.57 Karlsruhe basis set def2-TZVP was used in all the calculations, gold atoms were treated with def2-TZVP effective core potential (ECP).58 The initial geometries of amino acid–Au2 complexes for optimization were constructed by placing gold atoms near the active sites of amino acids. The active sites of the amino acids are the amino group, the carboxyl group, and sulfur. These groups possess electron-rich nitrogen, oxygen, and sulfur, which may donate electron density to Au from their lone electron pairs. Binding Gibbs free energies (ΔG) were calculated for the reactions:Equilibrium geometry optimizations and corresponding hessian calculations of complexes were done with usage of density functional theory (DFT) at the PBE59 was performed for the amino acid–Au2 complexes using NBO.5 program at the RI-MP2/def2-TZVP level of theory. The NBO analysis was done in order to obtain natural charges and Wiberg bond indices. The NBO orbitals of several complexes were plotted using the Chemcraft program. The atoms-in-molecules (AIM) analysis was performed with the Multiwfn program package60 to calculate the properties of bond critical points (BCPs).The NBO analysis3.61 In our next study, we showed that PBE-D3 method along with RI-MP2 give fruitful results when calculating Gibbs free energy of interaction between silver and amino acid residues.23 Thus, in this study we used both PBE-D3 and RI-MP2 method with def2-TZVP basis set and def2-TZVP ECP for another noble metal–gold.In our previous study, we showed that RI-MP2 method in combination with def2-TZVP basis set gives reasonable results predicting Gibbs free energy of interaction between simple organic molecules and silver.3.1+. Among the neutral amino acids, arginine had the highest binding free energy (ΔG) with Au+: −130.7 kcal mol−1 and −140.7 kcal mol−1, according to RI-MP2/def2-TZVP and PBE-D3/def2-TZVP, respectively  while RI-MP2 was used for the precise calculation of the final geometries and Gibbs free energy.We started with the analysis of amino acid interactions with gold cation Auectively . ΔG was +) had the highest ΔG among all amino acids (see +) > Tyr(−H+) > Asp(−H+), Glu(−H+) > Arg, Lys > Trp > Met > His > Tyr > Phe > Gln > Cys > Asn > Glu > Pro > Asp > Thr, Ser > Ile, Val, Leu, Ala > Gly. Obviously, we may conclude that Au2 will preferably bind to the deprotonated residues of the amino acids rather than to the protonated ones in a peptide or protein. Aliphatic AAs are less preferable for Au+ binding. It is also evident that the binding order (preferred binding sites) depends strongly on the pH conditions. Neutral cysteine attaches Au+ to both the nitrogen of the amino-group and the sulphur atom while deprotonated through the side-chain anionic cysteine (pK = 8.3) forms a monodentate complex with Au+ and attaches gold atom solely to the sulphur. ΔG rises from −74.9 kcal mol−1  to −194.1 kcal mol−1  during the deprotonation of the cysteine side-chain. Neutral Asp and Glu attach Au+ solely to the nitrogen of the amino-group while deprotonated anionic variants of these amino acids attach Au+ to the nitrogen and one of the oxygens of the carboxylate group  to −169.8 kcal mol−1  during the deprotonation of the Asp side-chain (pK = 3.7). For Glu (pK = 4.3), ΔG rises from −69.0 kcal mol−1  to −150.0 kcal mol−1  upon deprotonation of the side-chain. Both neutral Tyr and Tyr(−H+) with deprotonated side-chain (pK = 10.5) attach Au+ to the amino-group and form a cation–pi interaction with the six-membered ring  to −177.2 kcal mol−1  upon deprotonation.Cys, Asp, Glu, Pro, Ser, and Thr form a monodentate complex with Au+. Cys and Met form a bidentate complex while second bond occurs between sulphur and Au. For Arg, His, and Lys, the second site is the nitrogen of the radical side chain; this second site of Au+ attraction may become single in a polypeptide since the first site, amino-group, will participate in the formation of a peptide bond. Trp attaches Au+ to one of the carbon atoms of the six-membered ring. Phe, Tyr, and Tyr(−H+) form a cation–pi interaction between Au+ and a six-membered ring. Asn and Gln attach Au+ to the carbonyl of the side chain ), the Laplacian of electron density (∇2ρ(r)), the Lagrangian kinetic energy term (G(r)), the potential energy density (V(r)), and the energy density (H(r)).Next, we used AIM analysis2ρ(r) indicates depletion of electronic charge along the bond, which is typical for electrostatic interaction, while a negative value of ∇2ρ(r) indicates that electronic charge is located between the nuclei, which is a feature of electron-sharing and covalent interaction. All bond critical points (BCPs) in 2ρ(r) value, which means that all interactions are electrostatic.A positive value of ∇H(r) is a sum of kinetic and potential components:The electronic energy density term G(r) and V(r) are related to Laplacian through the equation:The virial theorem states that H(r) is positive then accumulation of charge at this point is destabilizing. If H(r) is negative then accumulation of charge is stabilizing. The negative value of H(r) indicates the presence of a covalent bond. From H(r) values are negative. The positive value of ∇2ρ(r) and negative value of H(r) mean that Au–X bonds are partially covalent and partially electrostatic. That is true for the complexes with both neutral and deprotonated amino acids. For example, AIM parameters calculated for the Au–N bond in the Gly–Au+ complex are following: ρ = 0.11226 hartree, ∇2ρ = 0.40289 hartree, and V(r) = −0.17388 hartree. The V(r) values allow to calculate the energy of Au–X bond as follows:63If −1 for the Au–NH bond) among the regarded complexes. This in line with the Gibbs free energy calculations, which show that Au2–Arg complex possesses the highest binding energy among neutral AAs. In Au2–Arg complex Au interacts both with the nitrogen of the NH2 group  and with the NH group of the side chain  and 39.6 kcal mol−1 for Au+–Cys, Au–C bond energy was equal to 41.9 kcal mol−1 for Au+–Tyr(−H+) and 35.4 kcal mol−1 for Au+–Tyr.As expected, arginine had the highest Au–X bond energy value  was equal to 2.465 Å, according to RI-MP2/def2-TZVP method. This bond length tends to slightly diminish in the complexes: for example, r(Au1–Au2) was equal to 2.461 Å in Au2–Gly.Next, we studied the complexes of amino acids with a minimal neutral cluster Au2 . Also, in the case of arginine gold plays the role of a proton acceptor and forms a nonconventional H-bond with the hydroxyl group (O–H⋯Au) of the carboxyl  undergoes a blue shift with respect to that of the uncoordinated C–N group: from 1730.5 cm−1 to 1635.5 cm−1.Thus, arginine forms an Au–N coordination bond with a length of 2.040 Å and a valence angle N–Au–Au equal to 170.5° . For ArgG values of the neutral amino acids while Cys(−H+) possesses the highest ΔG among the deprotonated amino acids. Cys(−H+) attaches the cluster through the sulfur atom. Cys(−H+) forms the Au–S bond with a length of 2.260 Å and a valence angle C–S–Au equal to 102.6° (+)–Au2 complex, the C–S bond stays intact after the interaction with Au2 cluster: the C–S bond is equal to 1.821 Å for the Cys(−H+)–Au2 complex and the same C–S bond is equal to 1.821 Å for the free Cys(−H+).Amino acids with deprotonated side chain surpass Δo 102.6° . For Cys+) had the highest ΔG among all amino acids (see 2 cluster increases in the following order: Cys(−H+) > Asp(−H+) > Tyr(−H+) > Glu(−H+) > Arg > Gln, His, Met ≫ Asn, Pro, Trp > Lys, Tyr, Phe > His(+H+) > Asp > Lys(+H+) > Glu, Leu > Arg(+H+) > Ile, Val, Ala > Thr, Ser > Gly, Cys. Obviously, we may conclude that Au2 will preferably bind to the deprotonated residues of the amino acids rather than to the protonated ones in a peptide or protein. Surprisingly, neutral cysteine has the lowest binding energy among all the amino acids, which results in the highest ΔG difference between the neutral and deprotonated amino acid. Generally, the interaction of Au2 with protonated and deprotonated AAs do not differ greatly.Cys, and for deprotonated cysteine it was found to be −53.5 kcal mol−1  . The interaction energy of Au2 with methionine, which also occurs through the sulfur, was equal to −28.1 kcal mol−1 , which was one of the highest ΔG among the neutral amino acids. The disulfide bond is less favorable for the formation of a complex with the gold cluster: the energy of the interaction between dimethyldisulfide and Au2 was equal to −23.4 kcal mol−1, according to RI-MP2/def2-TZVP method  . Cystein+), Glu(−H+), and Tyr(−H+) attach Au2 to the side chain namely to the oxygen atom and have high ΔG values: −41.1 kcal mol−1 , −35.4 kcal mol−1 , and −39.4 kcal mol−1 , respectively  in the unionized form and that means that alkalization of the solution with Tyr and Au2 from neutral to alkaline pH would give an increase in the interaction energy equal to 16.3 kcal mol−1 . These data show why alkalization of the solution with the protein containing Tyr residues is advantageous when a gold cluster is formed.Deprotonated anionic amino acids Asp(−Hectively . TyrosinKa 6.0) has ΔG equal to −28.3 kcal mol−1  in the unionized form and −22.9 kcal mol−1  with the protonated side chain. Alkalization of the solution with His and Au2 from acid to alkaline and neutral pH would give the increase of interaction energy equal to 5.4 kcal mol−1 . For lysine (pKa 10.5) ΔG rises from −22.2 kcal mol−1  for the cationic amino acid with protonated side chain to −23.3 kcal mol−1  for the neutral molecule. For arginine (pKa 12.5) ΔG changes from −22.0 kcal mol−1  for the cationic form with the protonated side-chain to −34.3 kcal mol−1  for the unionized molecule.Histidine , Glu(−H+) and chloroaurate anions frustrate the reduction reaction. However, some experimental protocols allow Asp and Glu residues to play significant role in the synthesis of gold nanoclusters.24 Moreover, the stability of Au2 complexes of all neutral and protonated amino acid residues is rather high , which indicates that all 20 proteinogenic AAs can stabilize gold NCs.In general, our results are in agreement with experimental results showing that gold nanoparticles have the highest binding affinity with the peptides containing Cys, His, Met, and Tyr residues.3.42 cluster in terms of electron density and its derivatives: the density of all electrons ρ(r), the Laplacian of electron density ∇2ρ(r), the Lagrangian kinetic energy term G(r), the potential energy density V(r), and the energy density H(r) are presented in We used Bader's AIM analysis to study the nature of amino acid interactions with AuH(r) value is negative. The positive value of ∇2ρ(r) and negative value of H(r) in all cases means that Au–X bonds are partially covalent and partially electrostatic.One can see that in each case the electrostatic interaction is stabilizing since for each complex V(r) values we can calculate bond energies. Arginine had the highest Au–X bond energy value equal to 63.1 kcal mol−1 . When Au and X both have positive charges (the case of Cys–Au2 complex), it obliquely indicates that Au–X bond has a covalent nature. When Au and X have opposite charges , it indicates that Au–X bond has an electrostatic nature. In all the cases Au2 cluster had a negative charge (qcluster), which means that it oxidizes the coordinated amino acid. The bond orders were evaluated by using Wiberg's bond indices, which are presented in 2 than for the neutral complexes: WAu1–X is equal to 0.366 for Cys–Au2 and is 0.580 for Cys(−H+)–Au2, WAu1–X is equal to 0.206 for Tyr–Au2 and is 0.247 for Tyr(−H+)–Au2. On contrary, the Au–Au bond order is lower for deprotonated amino acids.Next, we performed the NBO analysis. Natural charges of gold atom and amino acid atom to which the cluster is attached are presented in E(2) obtained from the second-order perturbation theory analysis, are reported in E(2) value, the more intensive the interaction between i electron donor orbital and j electron acceptor orbital, which means the more donating tendency from electron donor to electron acceptor. Delocalization of the electron density from occupied bonds or lone pair NBO orbitals to formally unoccupied antibond NBO orbitals indicates a stabilizing donor–acceptor interaction. The intramolecular interaction is formed by the orbital overlap between n, n*, σ and σ* bond orbitals, which leads to the intramolecular charge transfer (ICT) permitting the stabilization of the system. These interactions are observed as an increase in the electron density in anti–bonding orbital that weakens the respective bonds.NBO analysis gives useful information when analyzing intramolecular bonding and interaction between bonds. The electron donor orbital and electron acceptor orbital occupancies, as well as the interacting stabilization energy E(2) of the i → j delocalization was calculated according to the following formula:ei and ej are NBO orbital energies, and F̂ is the Fock operator.For each i donor orbital and j acceptor orbital, the stabilization energy The amount of transferred charge from i donor orbital to j acceptor orbital was also calculated using the Fock operator and NBO orbital energies as follows:E(2) and qCT for the Au–X and Au–Au bonds of some complexes are presented. The charge is transferred from the lone pair of nitrogen and oxygen or σ Au–Au bond to n* orbital of Au, Au–S or Au–Au σ* anti-bond. In the case of Arg–Au2 complex, the charge is transferred from the nitrogen lone pair to the lone pair of Au. In the Gly–Au2 complex, the charge is transferred from the nitrogen lone pair to Au–Au σ* anti-bonding orbital –Au2, the same ICT contributes to the stabilization energy of 65.1 kcal mol−1. In the Tyr–Au2 complex, ICT of the electron from the nitrogen lone pair to the σ* Au–Au anti-bond leads to delocalization of 36.3 kcal mol−1. In the Tyr(−H+)–Au2 complex, ICT of the n electron of oxygen lone pair to the σ* Au–Au anti-bond leads to delocalization equal to 37.8 kcal mol−1.We focused on the complexes of cysteine and tyrosine with the gold nanocluster since deprotonation of these amino acids gives the strongest energy gain when the AA–Aus formed . Moreove3.5+ and Au+), neutral metal atoms (Ag0 and Au0), and diatomic metal clusters (Ag2 and Au2) with nucleobases, namely cytosine (Cyt) and adenine (Ade). Later, we compared the interaction energies between silver and gold, between different types of metal particles, between nucleobases and selected amino acids ). Interestingly, Cyt(+H+) tends to form nonconventional hydrogen bonds with metal atoms Me0 and diatomic clusters (+) and Au0_Cyt(+H+) complexes have positive ΔG values and highly likely are not formed: 1.9 kcal mol−1 and 1.1 kcal mol−1, respectively. ΔG values are negative for Ag2_Cyt(+H+) and Au2_Cyt(+H+) complexes: −6.1 kcal mol−1 and −5.0 kcal mol−1, respectively. The latter complexes are stabilized by Me–O bonds, as well as by nonconventional Me⋯H hydrogen bonding.Also, we analyzed silver and gold complexes of protonated cytosine  while the binding energy of deprotonated cysteine with Au+ is equal to −194.1 kcal mol−1. Probably, the reason is that negative charge of the amino acid residue is favorable for high ΔG. For the neutral Cys, ΔG is comparable with Cyt: −74.9 kcal mol−1 , ∇2ρ(r), G(r), V(r), and H(r) are presented in H(r) value is negative for most of the complexes, which means that the electrostatic interaction between metal atoms and cytosine is stabilizing. The positive value of the Laplacian of electron density ∇2ρ(r) and negative value of H(r) in most of the cases means that Me–X bonds are partially covalent and partially electrostatic. In the case of Ag0_Cyt(+H+) with Ag⋯HN1 interaction and Ag2_Cyt(+H+) with Ag–O interaction the local kinetic energy G(r) outweighs V(r): internuclear charge concentration is destabilizing, which is typical for a nonbonded situation, which in the case of Ag0_Cyt(+H+) is also confirmed by positive ΔG value .We used Bader's AIM analysis to study the nature of nucleobase interactions with metal ions, atoms, and nanoclusters in terms of electron density and its derivatives: +_Cyt complex attracted our interest since silver cation forms bonds with both nitrogen and oxygen atoms while Au+ forms a bond only with N1 atom of cytosine. The higher energy of potential energy density for Au–N BCP results in the higher energy of the bond equal to 70.4 kcal mol−1 as compared with Ag–N  and Ag–O , which is supported by Gibbs energy calculations , which indicates that practically all 20 amino acids can stabilize gold NCs and nanoparticles. The binding affinity of AAs to the Au2 cluster increases in the following order: Cys(−H+) > Asp(−H+) > Tyr(−H+) > Glu(−H+) > Arg > Gln, His, Met > Asn, Pro, Trp > Lys, Tyr, Phe > His(+H+) > Asp > Lys(+H+) > Glu, Leu > Arg(+H+) > Ile, Val, Ala > Thr, Ser > Gly, Cys. Generally, the interaction of gold atoms with protonated and deprotonated amino acid residues do not differ greatly, which is in agreement with the experimental evidences that gold cluster synthesis occurs in a wide range of pH.24,67 The fact that deprotonated cysteine has the highest binding energy with both Au2 and Au+ among all the amino acids explains the fine synthesis of gold nanoclusters on thiolates.68,69Binding energies between 19 amino acids and gold nanoparticles have been studied previously using molecular dynamics.G is equal to −1 to −9 kcal mol−1) as compared to charged particles . This is in line with experimental fact that DNA-templated metal clusters are positively charged.50–52 The interaction between Au0 atoms and nucleobases is also rather weak ; however, the binding energy between diatomic cluster and DNA is higher . This obstacle explains the existence of neutral gold nanoclusters stabilized by poly-cytosine and poly-adenine.54Our results suggest that binding energy between neutral silver clusters and DNA is rather weak (Δ15–17,22Speaking about protein templates, the interaction of neutral metal atoms and diatomic clusters with amino acid residues is high for both silver and gold. This is in agreement with the fact that a large part of protein-templated nanoclusters consists of mostly reduced metal atoms.Moreover, the significant difference in the binding energy of neutral gold and silver atoms with nucleobases and amino acids apparently means that unlike DNA template neutral metal atoms are strongly bound to amino acid residues and can't freely diffuse in a polypeptide globula. This fact allows to make a conclusion that formation of metal nanoclusters in proteins occurs through the nucleation of Au atoms located on the neighboring amino acid residues, and the flexibility of the amino acid residue side chains and protein chain as a whole plays a significant role in this process.2 bonds are partially electrostatic and partially covalent, the same is true for amino acid complexes with Au+.Finally, based on the AIM analysis, we have found that for all complexes amino acid–AuThere are no conflicts to declare.RA-010-D0RA06486F-s001