Pinus sylvestris L. dominated forest with a novel analytical approach,allowing the first comparison of: (i) magnitude and δ13C of shoot, stem andsoil CO2 fluxes , (ii)concentration and δ13C of compound-specific and/or bulk non-structuralcarbohydrates (NSCs) in phloem and roots and (iii) growth of stem and fine roots. Resultsshowed a significant effect of phloem NSC concentrations on tracheid growth, and bothvariables significantly impacted Rstem. Also, concentrationsof root NSCs, especially starch, had a significant effect on fine root growth, although noeffect of root NSC concentrations or root growth was detected onRsoil. Time series analysis between δ13C ofAshoot and δ13C ofRstem or δ13C ofRsoil revealed strengthened C allocation to stem or rootsunder high C demands. Furthermore, we detected a significant correlation betweenδ13C of Rstem and δ13C of phloemsucrose and glucose, but not for starch or water-soluble carbohydrates. Our resultsindicate the need to include C allocation dynamics into tree growth models. We recommendusing compound-specific concentration and δ13C analysis to reveal C allocationprocesses that may not be detected by the conventional approach that utilizes bulk organicmatter.Incomplete knowledge of carbon (C) allocation dynamics in trees hinders accurate modelingand future predictions of tree growth. We studied C allocation dynamics in a mature However, ourknowledge of the C allocation dynamics in trees is incomplete (Forests assimilate carbon dioxide (COcomplete . One of complete .These hcomplete  and thus2 efflux (Rstem), is driv (Rstem) and, alb (Rstem). The lat (Rstem). There h (Rstem), and the (Rstem).However (Rstem). For exa (Rstem). More ac (Rstem), which,  (Rstem).2 efflux (Rsoil). Bothcomponents of soil respiration, autotrophic (root and rhizosphere) respiration andheterotrophic respiration, are driven by a seasonally variable supply of recentphotosynthates from leaves to belowground , which serve as both energy carriersand building blocks for amphibolic processes , includi13C) of the assimilates from leaves to respiredCO2 or tree biomass  may provide more accurate knowledge of the temporal dynamics of down-stem allocationof assimilates and its linkage to Rstem orRsoil. CSIA has been applied together with13CO2-pulse labeling to explore C allocation patterns in trees uponchanges in environmental conditions, such as elevated CO2 and soil warming  interacts with C allocationdynamics during a growing season and how this determines the magnitude and δ13Cof Rstem and Rsoil in a borealforest. For the first time, we combined continuous CO2 flux measurements forshoot, stem and soil with high temporal resolution analysis of stem and root growth, whichwere determined by micro-coring technique and root scanners, respectively. Ourinterpretations were further supported by data on dimensional growth of shoots and needlesand by compound-specific and/or bulk concentration and δ13C analysis of NSCs inphloem and roots. We had the following hypotheses:In this study, we applied a novel methodological approach to explore how organ growth ofmature Scots pine  Karst) and birches (Betulapubescens Ehrh. and Betula pendula Roth) in the understory.The Scots pine trees were 56-years-old in 2018. In summer 2016, the stand density for alltrees taller than 1.3 m was 1177 ha−1, and the dominant height 18 m , is a managed Scots pine dominated boreal forest stand mixed with Norwayspruce . During 2018, this site experienced a dryperiod lasting from 16 August to 11 September , Rstem andRsoil from May to October in 2018 (see Tree Physiology Online). A transparent shoot chamber of 2.1 l wasinstalled in the top canopy of a mature Scots pine tree (‘cuvette tree’), with a debudded1-year-old shoot inserted  standard, defined as13C/12C ratios in a sample and standard, respectively. Theδ13C values of CO2 were calibrated by reference CO2gases  with δ13C of −19 and −3.1‰.The shoot chamber was intermittently closed 50–80 times per day for 65 s, the stemchamber 48 times per day for 90 s and the soil chamber eight times per day for 840 s.Sample air was taken to gas analyzers  that measurednd13CO2  during tAshoot, nighttimeRstem and daily Rsoil werecalculated. Nighttime Rstem was used in subsequent analysis toavoid the influence of the upward transport of stem respired CO2 via sapstreams at daytime . As the contribution ofCO2 released from xylem storage pools to Rstemwas suggested to be insignificant . Fine roots(<2 mm) were excavated from locations about 100 m away from the cuvette tree butwithin the same stand. This was done in order to avoid any disturbance to the soil orharm to the roots of our study tree and to prevent any disturbance to other on-goingobservations conducted at this site. In the root sampling spots, the tree and soilcharacteristics equal those at our main study site. Roots were sampled from three randomspots (see Tree Physiology Online), approximately 5–15 cmdepth from the soil 11 times from May to October every 2 or 4 weeks. All samples weremicrowaved at 600 W for 1 min within 2 h to stop enzymatic and metabolic activities(Stem phloem at 1.3-m height was collected from five mature trees nearby the cuvettetree with a 2-cm diameter corer six times: twice in May and once per month from June toSeptember (see tivities. SamplesExtraction and purification of water-soluble carbohydrates (WSCs) were performedaccording to Starch was extracted from the pellet of the hot water extraction by enzymatichydrolysis . In brieTree Physiology Online).δ13C values of WSCs and starch were measured using an elemental analyzer coupled to an isotope ratio mass spectrometry at the Stable Isotope Laboratory of Luke. The δ13C values of bulk samples were calibrated againstIAEA-CH3 , IAEA-CH7  and in-house  reference materials. Measurement precision was 0.1‰ (SD), determined fromrepeat measurement of a quality control material.Aliquots of WSC and starch samples were pipetted into individual tin capsules, freeze-dried and wrapped. Concentrations ofWSCs were determined using the weights of samples in tin capsules and the weights ofplant materials used for extraction. Similarly, starch content was calculated using aconversion factor accounting for the efficiency of the enzymatic conversion of starch tohydrolyzed glucose  of external compound-matched standard solutions  were analyzed between every 10 samples tocalculate sample concentrations and to correct δ13C values  with aFinnigan LC Isolink interface following C values . Only δ1C signal .The meaTreePhysiology Online). The monitored shoots were at the top or the middle of thecrown. The percentage of shoot and needle length to their final length was calculatedfor each observation, and the averages were presented.To trace the timing of shoot and needle growth, length increment of 15 shoots fromthree trees and the length of one needle of each shoot were measured two or three timesa week during 2018, according to Tree Physiology Online), to avoid damage to thecuvette tree. Micro-cores were extracted at 1.3-m height once or twice a week from Mayto early August, and once every 2 weeks thereafter till October 11. In laboratory,micro-core sections were prepared and analyzed according to Tree Physiology Online, see TreePhysiology Online). The Gompertz fitting function  werecollected using Trephor corer .Micro-cores were sampled from five mature trees nearby the cuvette tree δ13C of Rstem on δ13C of phloem NSCs.δ13C of Rstem was tested against the averageδ13C values of individual phloem NSCs from five trees using linear models.(iv) root growth on root NSC concentration. As no repeated measurements were done for rootNSC concentration, root growth and Rsoil, we applied linearmodels with average values of the response variables and the independent variables,assuming that the average values represent the conditions of the stand. To remove thetemperature and soil moisture effects on growth of fibrous root growth, we tested theeffect of root NSC concentration on the residual of the regression between root growth andsoil temperature and soil moisture (Rsoil on root growth and root NSCconcentration. As in (iv), we tested the residual of the regression betweenRsoil and soil temperature and soil moisture against theindependent variables: the residuals of fibrous root growth (see iv) and concentrations ofroot NSCs. For all analyses from (i) to (v), time  was originallyincluded as a covariate and removed from the final model when not having a significanteffect on the response variable.We examined the dependence of: (i) tracheid growth on phloem NSC concentration. Sinceboth variables were performed repeatedly on the same sampling trees, a linearmixed-effects model was applied for analysis (i), using R package ‘NLME’ , with saperature  as the rmoisture . (v) Rso13C ofAshoot and δ13C ofRstem or δ13C ofRsoil, we applied the wavelet coherence analysis, using theR package ‘WaveletComp’ (Rsoil (Rstem (13C ofAshoot and daily δ13C ofRstem or δ13C ofRsoil at different time periods or frequencies. Any gaps(2%) in the input data were linearly interpolated. The output results includecross-correlation between x (daily δ13C ofAshoot) and y (daily δ13C ofRstem or δ13C ofRsoil) time series at any given time period (or frequency)and phase difference (or time lag) of x over y. Asδ13C signal is transported from photosynthesis to respiration, we consideredonly the phase differences when δ13C of Ashoot ledδ13C of Rstem or δ13C ofRsoil as meaningful.To test the temporal variability in the correlation between δletComp’ . WaveletletComp’ . This me’ . Earlywood (EW) growth period of year 2018 wasfrom May 7 to July 14, latewood (LW) growth period from August 2 to October 11 and EW-LWtransition period from July 15 to August 1 (Tree Physiology Online).Tracheid growth periods were defined as follows : trachei−1 and an increase in phloem sucrosecontent were observed, indicating significant re-mobilization of phloem starch during thisperiod  by The nighttime n period , showingRstem residuals . In contrast,phloem starch concentration was positively correlated withRstem residuals (P = 0.01).Tracheid growth rate was positively correlated with the concentration of glucose,negatively to that of sucrose in phloem .Tracheiesiduals , whereasesiduals . For ins13C of Ashootand δ13C of Rstem via wavelet coherence analysis isshown in 13C of Ashootand δ13C of Rstem were not constant throughout thegrowing season. The phase differences when δ13C ofAshoot led changes in δ13C ofRstem with significant coherence levels (marked by arrows)mainly appeared in the maximum tracheid growth period, maximum tracheid maturation periodand dry period. It indicates intensified correlations between δ13C ofAshoot and δ13C ofRstem during these periods, compared with other periods.The temporal correlation between δThree fibrous root growth periods were identified : period r = 0.64, P = 0.05, Root NSC concentration shared a similar seasonal pattern with fibrous root growth . In periRsoilcaptured by the automated chamber were in agreement with that observed by the manualchambers  mainly appeared in the fibrous rootgrowth period I and period III, which included the dry period. It indicates a tighterrelationship between δ13C of Ashoot andδ13C of Rstem for these periods than otherperiods.The temporal dynamics of C allocation to soil was tested by wavelet coherence analysisbetween δofRsoil . Thetem13C of Rstemvaried 18.7‰, whereas δ13C of phloem WSCs and δ13C of phloem sucrosevaried only 0.9 and 1.3‰, respectively  and glucose(P = 0.01), but not with δ13C of WSCs or starch in phloem was much higherthan that of root WSCs (1.8‰) during the studied period .Similar to δd period . δ13C ofyperiod . Overall2 of stem and roots based on fieldobservation of mature field-grown trees. We identified (i) negative correlations betweenphloem sucrose concentration and tracheid growth and Rstemresiduals, (ii) a positive correlation between concentration of root starch and fibrous rootgrowth rate, (iii) strengthened couplings between δ13C ofAshoot and δ13C ofRstem or Rsoil under high stem orroot growth demand periods and (iv) a significant correlation between δ13C ofRstem and δ13C of phloem sucrose and glucose, butnot for starch or WSCs. Our results provide evidence that C allocation dynamics in trees arehighly coupled with growth demands of sink organs via regulations on NSC pools, and suggestthat a better knowledge about these dynamics would improve the current presentation of Callocation scheme in land surface models.To the best of our knowledge, we present the first quantification of the interactionbetween NSC pools, organ growth and respired CORstem . The agreement of theresults across calculating methods supported the reliability of our data, although theday-to-day variation in δ13C of Rstem was ratherhigh. We also had only one automated soil chamber to determineRsoil. However, we used manual soil chamber data to validatethe seasonal course of Rsoil and found good agreement betweenthe two ,together with compound-specific and/or bulk concentration and δ13C analysis ofNSCs in phloem and roots of Scots pine (Pinus sylvestris L.) trees over agrowing season. The results demonstrate that the allocation of newly assimilated C to stemand roots increases under high growth rate of stem and roots, respectively. The pieces ofevidence include: (i) phloem sucrose content, which was conversely linked to phloemunloading rate, had a significant negative correlation with tracheid growth; (ii)δ13C of phloem sucrose had a significant correlation with δ13C ofRstem; (iii) concentration of root starch, which mainlyoriginated from new assimilates, had a significant positive effect on fine root growth and(iv) time-series analysis revealed significant temporal correlations between δ13Cof Ashoot and δ13C ofRstem or δ13C of Rsoilfor the periods when stem or roots were under high C demands. Increased C allocation andassociated growth contributed to higher Rstem, which however wasnot observed for Rsoil likely due to the disturbance ofheterotrophic soil respiration. We suggest that the dynamics of C allocation in response totree organ growth should be considered in models based on whole tree C allocation forprojecting forest growth under climate change. Our results also emphasize the need tocarefully evaluate the composition of the substrates, which are used for concentration andδ13C analysis, to study tree growth and C allocation dynamics. Where possible,compound-specific concentration and δ13C analysis should be used, as thesesignals can provide more detailed and accurate information on C allocation and utilizationprocesses in trees.In this study, we aimed to examine the interaction between tree organ growth and Callocation dynamics on field-grown mature trees. With this aim, for the first time, wetraced the magnitude and δSI_tpac079Click here for additional data file.


Lava domes exhibit highly unpredictable and hazardous behavior, which is why imaging their morphological evolution to decipher the underlying governing mechanisms remains a major challenge. Using high-resolution satellite radar imagery enhanced with deep-learning, we image the repetitive dome construction-subsidence cycles at Popocatépetl volcano (Mexico) with very high temporal and spatial resolution. We show that these cycles resemble gas-driven rise and fall of the upper magma column, where buoyant bubble-rich magma is extruded from the conduit (in ~hours-days), and successively drained back (in ~days-months) as magma degasses and crystallizes. These cycles are superimposed on a progressive decadal crater deepening, accompanied by heat and gas flux decrease, which could be partially explained by gas depletion within the magma plumbing system. Results reinforce the idea that gas retention and escape from the magma column play a key role in the short- and long-term morphological evolution of low-viscosity lava domes and their associated hazards. Satellite imagery enhanced with deep learning sheds light on the mechanisms driving lava dome construction-destruction cycles. Results suggest that gas retention and escape from the magma system control the dome and crater morphological evolution. Morphologies span from tall and steep domes  to flat and circular domes , with a broad variety of intermediate shapes and extrusive features4. These two end-members are thought to be driven by two different growth mechanisms: exogenous , and endogenous 5. The associated volcanic hazards, of both exogenously and endogenously growing domes, are highly dependent on the resulting dome morphology6, as instabilities may trigger rockfalls and collapses, potentially generating deadly pyroclastic density currents8. Moreover, rapid changes in the dome permeability can lead to sudden transitions from passive degassing to violent explosive events13. Due to the hazardous and unpredictable nature of growing lava domes, the study of dome morphology and extrusion dynamics have been essentially approached through modeling  and remote sensing, including photogrammetry from ground-18, air-20, and satellite-based sensors using both optical and infrared bands24. However, lack of visibility is a major limitation to photogrammetry techniques. Synthetic Aperture Radar (SAR) is therefore a unique method to track dome growth and deformation, as radar microwaves penetrate clouds with little interference, therefore allowing imaging independently of cloud cover, volcanic steam or ash obstructing the view. Although interferometric processing (InSAR) has been widely used to quantify volcano-wide deformation25 or even summit deformation27, the small spatial extent of domes and their tendency to be incoherent in InSAR imagery (due to rapidly changing surface and morphology) have made this technique less suited for studying lava dome emplacement. Instead, the reflected SAR intensity has been used to track the dome and crater morphology31. Nonetheless, while SAR imaging has the advantage of sensing through clouds, visual interpretation of the resulting intensity images is hindered by both the intrinsic radar viewing geometry and intrinsic granular noise (speckle). Indeed, unlike geocoded images which are displayed with respect to cardinal directions, images in radar geometry are displayed with respect to the sensor itself, i.e., along the satellite motion direction , and along the radar look direction . Although such imaging geometry is subject to geometric distortions , it can be used to our advantage to recover quantitative measurements of the surface topography. In particular, slopes facing away from the satellite with an angle steeper than the radar incidence angle will cast a shadow, from which vertical depths can be estimated from trigonometry31. The method is applied here to track the variations of Popocatépetl volcano (Mexico) inner-crater depth  and MODIS (Moderate Resolution Imaging Spectroradiometer), which confirm that magma volumes required to sustain the gas and thermal fluxes largely exceed the actual erupted magma volumes. This unique combination of observations offers a new comprehensive view of the eruptive dynamics and magma conduit processes operating at Popocatépetl, where gas retention and escape could explain the short- and long-term ups and downs of the magma column. The results are consistent with observations at other low-viscosity lava dome volcanoes, and point to unexpected similarities with magmatic processes operating in the upper magma column of more basaltic open-systems. This study opens new perspectives to constrain the overarching characteristics of open-vent volcanic activity42, and paves the way to improved multidisciplinary satellite volcano monitoring43 and hazard assessment.Here we investigate the shallow magma dynamics governing the repetitive dome cycles and peculiar excess degassing at Popocatépetl using multiparametric satellite datasets. We use high-resolution TerraSAR-X (TSX) and medium-resolution Sentinel-1 (S1) SAR images acquired over 8 years (2012–2020) to: (1) quantify vertical variations of the inner-crater depth, revealing both short-term dome construction-subsidence cycles and long-term crater deepening and widening, and (2) analyze dome morphological evolution, revealing magma emplacement and withdrawal mechanisms with exceptional temporal and spatial detail, thanks to a deep-learning image enhancement approach. We compare this data with 15 years (2005–2020) of SO3 (±0.5 Mm3). Ground-based observations indicate that dome growth episodes are commonly accompanied with strombolian-like activity, characterized by continuous emission of ash and incandescent ballistics11  recovered from the MODIS satellite images  and losses  are estimated by taking, respectively, positive and negative differential crater volumes ΔVc, and show that from mid 2016 onwards the excavation rate increases with respect to the extrusion rate , this results in a very rough estimate of 2.8 Mm3 (±1 Mm3) of pyroclasts deposited on the main crater floor during ~8 years, which is far less than the inner-crater volume loss.Alongside the repeated cycles of dome construction and destruction, a progressive enlargement and deepening of the inner-crater is observed throughout the past decade Fig. , which cMm3 Fig. , assuminMm3 Fig. . Inner-cate Fig. . The mai23. In the long-term, however, thermal radiation shows a striking correlation with gas fluxes. Figure 2 fluxes recorded over a 15-year period (2005–2020), smoothed with a 365-day running average to remove both seasonal and eruptive transients. The cross-plot of VRP and SO2 fluxes  given by: VRP = 10.5 · SO2 + 1.8, where VRP is expressed in MW and SO2 flux in kilotons/day. The period associated with high SO2/VRP ratios , and the volume of lava expelled outside the crater as tephra products . We hereafter quantify the shallow magma budget following ref. 21 (see “Methods” for details), by estimating the following magma volumes  derived from the SO2 emissions, volume of radiating magma  derived from the thermal VRP, and volume of extruded magma (Vextruded) derived from the SAR images. Because we have no estimate of the long-term volume of magma ejected as tephra outside the crater (Vtephra), we use a semi-empirical approach assuming that Vtephra = 1/3·Vextruded . These volumes are then smoothed and converted to monthly averaged fluxes Qdegas, Qthermal, Qextruded, and Qtephra  required to sustain the measured gas emissions is far greater than the average magma output rate Qout (=Qextruded + Qtephra = 0.06 m3/s). Likewise, the average magma flux required to sustain the measured thermal radiative power Qthermal is far greater than the average magma output rate Qout. This suggests that unerupted magma is degassing and cooling at shallow levels in the plumbing system.Magma volumes coming in and out of the system are estimated from the satellite dataset to infer on the subsurface magma dynamics. The magma input supply rate in particular is inferred from the SOmes Fig. : volume 2 and halogen emissions45, (iii) surface strombolian activity11, and (iv) fluid flow inside the conduit revealed by characteristic seismic tremor signal47. The destruction phase on the other hand is characterized by two processes: a progressive dome subsidence lasting weeks to months, which is punctuated by sporadic vulcanian explosions , and (ii) the drainage of extruded magma back into the conduit48. Evidence of this is provided by the subsiding dome center , the peripheral bulge, the development of concentric ring fractures accommodating the downward sag, as well as sub-circular piston collapse structures. Such ring fractures and piston-like subsidence of the crater floor have been previously described at Popocatépetl34 and other volcanoes such as Láscar12 (Chile) and Mount Cleveland24 (USA). These combined observations remind a gas-driven upward and downward advection of magma: an initial increase in the gas content leads to an increased buoyancy resulting in magma extrusion from the conduit, and the subsequent gas/heat loss and crystallization leads to a buoyancy decrease resulting in the drain-back into the conduit. The subsidence, in turn, is thought to reduce the permeability of the system through temporary closure of gas escape pathways, promoting episodes of pressurization leading to vulcanian explosions12. Modeling of the magma column density36 over a range of pressures, temperatures, and dissolved water contents, has shown that the column height is very sensitive to small changes in the dissolved volatile content, and it has therefore been suggested that the dome growth (and collapse) at Popocatépetl could be buoyancy-driven49. The dataset presented here provides further evidence supporting this idea, which we extend by suggesting that variations in the exsolved gas fraction of the upper magma column can explain the observed depth variations. Indeed, the dome emplacement is followed by rapid dome subsidence, reaching ~30–60 m drop in the ~30 days after dome emplacement /(1−Xgas) – Hf, where Xgas0 is the initial gas fraction at the time of the dome emplacement, and R the conduit radius (see “Methods”). Following previous work36 at Popocatépetl, we assume Xgas0 = 0.5 and Hf = 100 m ± 75 m, and we consider for simplicity that the gas fraction decreases linearly until reaching values comparable to the mean porosity of erupted pyroclasts during dome-forming eruptions 57. Figure H calculated during the first ~30 days can explain the observed dome subsidence rates  in the column/reservoir, as a function of constant gas flux, constant conduit radius, initial reservoir volume, and magma/host rock properties. In turn, the magma level variations ΔH in the conduit expected from the pressure changes can be recovered from ΔP(t)/, where ρm,c is the mean density of melt  in the column, assuming that the mass of melt in the conduit is much larger than the mass of gas, and that the conduit radius and melt density are constant. We contemplate the model scenario in which gas exsolution occurs at low pressures via magma convection in the conduit60, in agreement with both petrological studies at Popocatépetl40 and excess degassing/excess thermal radiation reported here. The degassing rate is in turn directly controlled by this convection (parametrized in the model following refs. 60), whereby the gas-rich magma upflow rate (Q) loses a fraction (nc) of its dissolved volatile content, before sinking back into the conduit due to increased density. We here consider two end-member cases of the magma input flux Q = 10 m3/s and Q = 1 m3/s  as input to the model. The conduit radius (R) is constrained from these magma input fluxes according to the convection parametrization60, and result in R = 14.8 m and R = 8.3 m, respectively. The remaining parameters necessary to calculate ΔP(t) are fixed based on previous studies, namely the degassing scenario described by ref. 40 . The overall agreement of this model with our observations therefore suggests that progressive depressurization due to persistent degassing could contribute to the progressive deepening of Popocatépetl’s inner-crater observed over the past decade. The coeval crater widening which is observed, could instead be a direct consequence of this deepening, due in particular to the instability of the crater walls , as well as the repeated vulcanian explosions. Although the above mechanism is still speculative, the model suggests that within reasonable input values and assumptions, it can predict the overall long-term crater deepening trend.If the above model seems able to explain the short-term variations in the crater depth associated with individual dome cycles, the progressive deepening and enlargement of Popocatépetl’s inner-crater observed over the last decade raises the question of the driving mechanism, and its relationship with the dome construction-destruction cycles. Two processes can be considered: (i) the excavation due to repeated explosions, and/or (ii) the depressurization of the magma plumbing system due to persistent passive degassing and decreasing magma supply rates. Although both mechanisms likely operate and contribute to the progressive crater deepening, our observations suggest that the latter plays an important and previously unsuspected role Fig. . Indeed,2 degassing collected over 15 years (2005–2020), offers a new comprehensive view of the eruptive dynamics and magma conduit processes operating at Popocatépetl. The combined observations suggest that: (1) the short-term dome construction-subsidence cycles resemble gas-driven ups and downs of the uppermost magma column, where retention and escape of exsolved gas are responsible for magma extrusion and withdrawal from the conduit, (2) the long-term progressive inner-crater deepening and the concomitant decrease in heat/gas fluxes could reflect the progressive depressurization of the magma conduit and reservoir due to progressive gas depletion, (3) the excess degassing and excess thermal radiation of the system suggests that unerupted magma is degassing and cooling at shallow levels below the crater floor. These observations echo those reported at other low-viscosity lava domes24, and remind magmatic processes operating in the upper magma column of more basaltic open-systems41. Such multiparametric analyses could in the future be applied to other open-systems, and help constrain the overarching characteristics of open-vent volcanic activity and associated hazards42.The novel combination of observations presented here, including high-resolution radar imagery of the crater’s morphological evolution collected over 8 years (2012–2020), together with infrared thermal radiation and SO61, whereby image denoising is learned without requiring noise-free reference data. The network is an adaptation and improvement of the filter designed for Sentinel-1 SAR images acquired in volcanic settings62, which is used operationally by the volcano monitoring system MOUNTS43. The most important modifications were in the preprocessing and selection of the training data: since higher resolution requires more precise alignment, TSX crops were aligned individually, and discarded when alignment failed . The architecture is shown in Supplementary Fig. Speckle results from the interference of radar waves reflected by many elementary scatterers on the topography. It appears as granular noise in the SAR intensity images, which hinders their interpretation and reduces the ability to visualize small morphological features. To alleviate this problem, we have specifically designed and trained a convolutional neural network to remove speckle from SAR imagery acquired in volcanic settings, thereby gaining exceptional insights in fine structural details of the dome and crater , which implied that the shadow was not well defined but rather a succession of discontinued shadows. For this reason, in order to recover the maximum crater depth hcrater, we counted the maximum number of “shadow” pixels encountered across a sequence of horizontal profiles crossing the crater, and multiplied it by the cosine of the radar incidence angle . The reference point for the inner-crater calculated depth hcrater = 0 m in both TSX and S1 images is the main crater floor, so the progressive infilling of the main crater (due to progressive accumulation of pyroclastic deposits) is not affecting the measure. The main crater infilling , and 31 in stripmap-mode , with an incidence angle of 44°. The orbital repeat time of the satellite is 11 days, however, the acquisition occasionally suffered interruptions, so that 78.3% of the acquisitions had 11-day time interval, 11.5% 22-day interval, and the remaining ~10% had between 33- and 120-day interval , which is a measurement of the heat flux radiated by hot volcanic surfaces expressed in Watt, with a ±30% error on the measurement64. The combination of both satellites provide ~4 images/day of the entire Earth surface since 2000 and 2002, respectively, with a nominal spatial resolution of 1 km2/pixel in the infrared band.Thermal emissions were processed through the MIROVA system2 gas emissions were estimated from the analysis of the OMI sensor acquisitions on board the Aura satellite. The sensor measures solar backscatter radiation at wavelengths spanning from the visible to ultraviolet (270–500 nm), and provides daily global coverage since 2004, with nominal pixel spatial resolution of 13 × 24 km at nadir. The monthly SO2 fluxes were calculated from the monthly SO2 masses calibrated with the traverses method65 (±50% error). The OMI images of each month were gridded and stacked over a 0.05° grid, excluding data affected by a thick cloud cover, or by the row anomaly . The monthly cumulated SO2 matrix was then divided by a matrix containing the number of valid data over the month, to obtain a map of the monthly averaged SO2 around the volcano. A box was defined around the volcano to contain the monthly-averaged SO2 anomaly corresponding to the volcanic plumes, and the monthly averaged SO2 mass was calculated as the sum of the SO2 column density of every grid element multiplied by its area. The calibration to convert the monthly averaged SO2 mass into a flux, is obtained by performing a linear regression between a series of monthly masses (MM) and its corresponding series of monthly-averaged fluxes (MF) computed with the traverse method65. The regression plot between the two series obtained over 55 months at Popocatépetl is shown in Supplementary Fig. 2 = 0.759) given by MF = 0.751·MM. In the case of Popocatépetl, a seasonal effect is noted in the monthly mass time series, which was corrected by multiplying the time series with a square sinusoidal function fitted to smooth this 12-month periodic fluctuation.SO21. Volumes were calculated for Dense Rock Equivalent (DRE), assuming a DRE magma density ρDRE = 2400 kg/m3 40, and an extruded lava (dome) bulk density ρextruded = 2000 kg/m3. The volume of degassed magma Vdegas is derived from the SO2 OMI measurements using the “petrological method”37: Vdegas = MSO2 / (2·ρDRE·∆XS), where MSO2 is the measured mass of SO2 in kg, and ΔXS is the sulfur volatile loss. We used ΔXS = 1500 ppm, and tested two extreme cases ΔXS = 500 ppm (upper boundary for andesitic melt), and ΔXS = 2500 ppm (mafic melt mixed with andesitic melt). The volume of radiating magma Vthermal is derived from the MODIS measurements using the “thermal approach”66: Vthermal = VRE / crad · (ρextruded/ρDRE), where VRE (in J) is the volcanic radiant energy obtained from the integration of the VRP time series, and crad (in J/m3) is an empirical coefficient accounting for the rheology of the extruding lava. We used a value crad = 1.2 × 107 J/m3 consistent with andesitic lava domes, and tested two extreme cases crad = 0.6 × 107 J/m3 and crad = 1.8 × 107 J/m3. The volume of extruded magma Vextruded is derived from the crater volume Vc, which was calculated from the TSX intensity images (see dedicated section in “Methods”). More specifically, the extruded DRE volume was taken as Vextruded = {ΔVc > 0} · (ρdome/ρDRE), where ΔVc is the discrete crater volume difference computed from one acquisition to another. We used a value ρextruded = 2000 kg/m3, and tested the extreme cases 1500 kg/m3 and 2500 kg/m3. The extruded volumes calculated here should be considered as a proxy for the average extruded magma volume, which are partially biased by the crater shape which we assume to be a truncated cone with slope angle of 60°. The volume of tephra Vtephra expelled outside the crater is calculated from the semi-empirical equation Vtephra = 1/3·Vextruded. The factor 1/3 corresponds to the ratio between the extruded volumes of three distinct domes and the volume of tephra fall associated to their destruction , as reported by ref. 34 and ref. 67, respectively. This value is in agreement with the ratio of the cumulative volume of extruded lava to the cumulative volume of in-crater loss, shown by ref. 34 for the period 1996–2015. Although this factor is likely to vary significantly through time, it is an approximation used to give an order of magnitude to the tephra emissions Vtephra.The magma budget of Popocatépetl was estimated following the approach of ref. Qdegas, Qthermal, Qextruded, and Qtephra are then derived from the corresponding volumes, by smoothing values using a 365-day running time-window, and averaging over monthly time bins.Magma fluxes Hf and radius R is filled with magma and exsolved gases, with an initial volumetric gas fraction Xgas0. Decreasing gas fraction in Hf results in increasing column bulk density and decreasing column volume. The associated magma level variation ΔH can be recovered from ΔH = H – Hf, where H = (mf/ρDRE(1−Xgas))/πR2. If we assume the mass of gas to be negligible with respect to the mass of magma, and the mass of magma within the cylindrical portion to be constant, such that m(t) = mf = ρDRE(1−Xgas0)· πR2Hf, than after simplification ΔH = Hf·(1−Xgas0)/(1−Xgas) – Hf. We take Xgas0 = 0.5 and Hf = 100 m ± 75 m following ref. 36 at Popocatépetl, and assume for simplicity that the gas fraction in Hf decreases linearly until reaching values typical of pyroclast porosities erupted during dome-forming eruptions (~15–20%)57. The calculated magma level variations ΔH are compared to a selection of dome subsidence rates measured from TSX images . The good fit suggests that a decrease in gas fraction from 0.5 to 0.2 in the first 30 days  = −0.01(t) + Xgas0, where time is expressed in days) can explain the selected subsidence rates. Assuming a magma density ρDRE = 2400 kg/m3 40, this gas fraction decrease corresponds to a column density increase from 1200 kg/m3 to 1920 kg/m3. The selection criteria for the subsidence trends shown in Fig. The short-term fast subsidence observed after dome emplacements are explained by rapid variations in the volume fraction of exsolved gas in the upper magma column. We consider a simplistic approach where a cylindrical portion of the column of length ges Fig.  during t59. The model predicts pressure changes ΔP(t) in the magma reservoir due to steady gas loss , and the associated magma level variations ΔH(t) in the magma column are calculated following ΔP(t)/, where g is the acceleration due to gravity, and ρm,c is the mean density of melt  in the column. These magma level variations are used as a proxy to the observed crater depth . We here use a conduit of length L = 10 km following ref. 36, and an initial reservoir volume Vr0 = 2 km3. Note that the length of the conduit influences the initial reservoir pressure, but not the pressure variation ΔP. The system is embedded in a medium with viscoelastic rheology characterized by a bulk modulus k = 1010 Pa and effective viscosity μ = 1018 Pa s.A magma reservoir with initial volume 60, where convection is driven by the density difference between degassed and undegassed magma. This parametrization states that the mean gas flux is related to the volumetric magma upflow rate Q, which depends on the conduit radius R and magma viscosity. Magma convection in the conduit has been considered a plausible assumption at Popocatétpetl40, and the long-term excess degassing and excess thermal radiation reported here provide additional credit to it. The density difference between the degassed melt density ρ1 and the undegassed melt density ρ2 in the conduit is defined as Δρ1,2 = 59 kg/m3 following ref. 40. Because the descending degassed melt is replaced by ascending undegassed melt, the mean conduit melt density ρm,c is assumed constant, and defined as the average density between ρ1 and ρ2. The model assumes the gas mass in the conduit to be much smaller than the mass of incompressible melt (liquid and solid phase), and assumes the mean gas density in the conduit to be much smaller than the mean melt density. Complex bubble dynamics such as foam collapse70, which can cause short-term magma level variations, are not considered by the model.Magma convection in the conduit is parametrized following ref. Qdegas  as the magma upflow rate Q. Three distinct values are considered to compute the pressure variation ΔP: high Q = 10 m3/s . According to the convection parametrization of ref. 60 , these values equate to conduit radii of 14.8, 8.3, and 13.5 m, respectively. Conduit radius is held constant in the model.Magma degassing rate is held constant through time. The degassing rate is controlled by the magma upflow rate, as per the convection parametrization described above. We use values of 40 at Popocatépetl: the parent melt is a mixture of silicic and mafic end-members , having a non-degassed density ρnd = 2400 kg/m3, a non-degassed viscosity μnd = 104 Pa s, and containing α = 3 wt% of dissolved H2O prior to degassing. Separation of gas and magma occurs in the upper conduit, where nc = 2 wt% of H2O is exsolved. The remaining 1 wt% H2O retained in the melt is equivalent to depth of ~600 m (~150 bar), above which rests a permeable lava cap. Degassing results in a density difference Δρ1,2 = 59 kg/m3 between the undegassed and partially degassed melt, and in a degassed melt viscosity μ1 = 105.3 Pa s. Sensitivity of the model to varying initial reservoir volume Vr0 and mass fraction of exsolved gas in the conduit nc is shown in Supplementary Figs. Further parametrization of the model follows the degassing scenario (1) proposed by ref. The long-term crater deepening observed on the timescale of years is reproduced using the theoretical model proposed by ref. pth Fig. . We consSupplementary InformationPeer Review FileSupplementary Video 1Supplementary Data 1


Iridium based C–H borylationcatalysts in particular are established as one of the foremost methodsin the field of C–H functionalization.3 Main group compounds also have been applied as catalysts for areneC–H borylation, with the greater abundance, lower cost, andhigher permitted exposure limits of most main group elements relativeto precious metals one key driver for this research.4 A second driver stems from the fact that main group catalysisgenerally proceeds at a fixed oxidation state thus requiring distinctborylation mechanisms. This can lead to complementary regioselectivityand functional group tolerance to that using transition metal basedcatalysts. However, significant challenges remain in main group catalyzedarene borylation, particularly around expanding the substrate scopeand generating operationally simple methodologies.5 Most systems reported to date use (pre)catalysts that arechallenging to handle (due to their sensitivity to protic speciessuch as H2O) and that are limited in substrate scope tonucleophilic (hetero)arenes  > 1, for reference,2-Me-thiopheneand furan have N ≈ 1.3).6 Identifying a single catalytic system that addresses bothof these challenges is essential for the wider uptake of main groupcatalyzed arene C–H borylation.C–H borylation is anefficient method to generate organoboranes that are powerful intermediatesin synthesis, due in large part to the Suzuki–Miyaura reaction.7 andintramolecular C–H borylation, the reader is directed to recentreviews.8This viewpoint summarizesthe general approaches used to date inmain group catalyzed intermolecular arene C–H borylation. Itis not a comprehensive survey of the area; instead, it focuses onanalyzing common key steps and through this seeks to highlight someof the current challenges and future opportunities in the field. Forstoichiometric (in strong Lewis acid)EAr type process9 and thus can be termedelectrophilic borylation reactions. Inthese, controlling the fate of the byproduct from SEAr,[H]+, is vital.10 Indeed, theeffective sequestering of [H]+ was recognized as crucialeven in the early stoichiometric electrophilic borylation studiesfrom the 1960s.11 The generation of [H]+ as a byproduct also provides a route to using substoichiometricelectrophilic activators in arene borylation. Combining [H]+ with a hydroborane  or pinacolborane(PinBH) derivatives) or another hydridic species can lead to H2 evolution and (re)generate a reactive electrophile for performingfurther C–H functionalization. Virtually all main group catalyzedborylation reactions reported to date rely on this as a key step toclose the catalytic cycle. To facilitate analysis, these reactionshave been divided into two types based on the nature of the electrophilethat effects C–H functionalization. Specifically, it separatessystems based on whether or not a σ-bond metathesis step isrequired to form the target aryl-borane post C–H functionalization.These two classes are discussed separately as they have distinct challenges.For example, approach (i) requires converting a hydroborane into anelectrophile that effects SEAr . This study highlighted a numberof important factors: (i) the need for a robust (toward electrophiles)hydroborane as pinacolborane decomposed under the reaction conditions;(ii) the necessity for the correct anion, with key considerationsbeing low anion coordinating ability and high anion stability. Inthis work the highly reactive nature of the electrophile(s) necessitateduse of the extremely robust [closo-CB11H6Br6]− anion.14 The reactive boron species was termed [CatB(closo-CB11H6Br6)], 1 . The identity of this ligating species, termedL, is a key variable in approach (i) as it has a significant effecton multiple steps in the catalytic cycle.This approach generally uses substoichiometricadditives to convertCatBH (or a derivative) into an electrophile that then effects areneC–H borylation. In our early work CatBH was combined with 5mol % of CatBBr/+ cations,such as 3 L can also be the Brønsted base that deprotonates arenium cationintermediates; (iv) the conjugate acid, [LH]+, then isinvolved in the dehydrocoupling step forming H2 and regeneratingthe electrophile and L. A number of these processes are shown in 16a It shouldbe noted that L also can lead to off-cycle species, such as [CatB(L)2]+ boronium cations , andto substituent redistribution of CatBH to form Cat3B2 and L–BH3.17 Furthermore, in some systems competing reactivity  can occur to generate a “hidden”L in situ which can also play a crucial role.18Subsequent reports from multiple groups utilized CatBH/PinBH inthe presence of exogenous L (which forms a dative bond with the hydroborane)to borylate arenes using a substoichiometric Lewis acid activator t+. Furthermore, a weakly Brønstedbasic L will lead to less exothermic deprotonation of arenium intermediatesbut generate a stronger conjugate Brønsted acid ([LH]+), thereby impacting the energetics of the dehydrocoupling step.The above only consider minima on the potential energy surface; clearly,altering L will impact the energy of the transition state involvedin each step. Thus, it is challenging a priori topredict an optimal L for electrophilic borylation even when ignoringcompeting off-cycle reactivity, e.g., substituent scrambling and Lbinding to the activator. Nevertheless, given the range of bases studiedto date, particularly with CatBH and using fluoroaryl-borane activators,there is limited potential to significantly improve reactivity incatalytic electrophilic borylation by utilizing other monofunctionalbases.Changing L can impact differentsteps in opposite ways; e.g., whenL is a weak Lewis base it will bind weakly to CatBH and make hydrideabstraction less favored enthalpically, but it will enhance the electrophilicityof [CatB–L]1+/0 systems, bifunctional derivatives, e.g., 2-DMAP, alsohave beenexplored. While this was initially in stoichiometric C–H borylation,19 later work with compound 5  three coordinate and sufficiently electrophilic to interactwith arenes. The bifunctional nature of L is crucial as it introducesa basic site proximal to the electrophilic boron center (thus is apreorganized FLP). This facilitates C–H borylation via a six-memberedtransition state  species via TS2. This again emphasizes that the selection of L requiresa balancing act to prevent any one transition state becoming too highin energy. To date the systems in N values ≥ −1.5;however, benzothiophene (N = −2.6) did notundergo borylation. With fewer reports using bifunctional bases, itis possible that improved bifunctional base/hydroborane combinationsexist that will increase the scope further. The studies using 6 also highlight the complementary nature of catalytic electrophilicborylation, with groups often challenging in precious metal catalyzedborylation  tolerated. Furthermore,hindered sites can be borylated with 6 ,21 whereas iridium catalyzed borylation proceedsunder steric control.Moving beyond monofunctional bases in [CatB–L]mpound 5 420 and moracycle4, top.19ate TS1, 4 which i1+/0 species as the key electrophile effectingC–H functionalization. An alternative route to generate reactiveelectrophiles from CatBH is by binding a Lewis acid to an O or theB–H. As the Lewis acidity in dioxaborolanes is significantlyaffected by the π donor ability of the oxo groups,22 attaching a Lewis acid at O will modify theLewis acidity at boron. Our recent work utilized this approach incatalytic arene borylation with low coordinate zinc cations calculatedto prefer binding to O over the B–H unit (7-O vs 7-H).23 Using 10 mol % of compound 8 [CatB–L]mpound 8 5 as a prhe cycle 5, bottom10 (1510 activated 4-chloro-CatBH25 to form an electrophile that was highly effective in arene borylation.Compound 10 (5 mol %) was even sufficient to borylatebenzene  in high yield with ClCatBH. A highly electrophilic borenium cation is essentialwith B(C6F5)3, and a less Lewis acidicborenium cation not effective. 10 was proposed to interactwith the B–H of ClCatBH to generate electrophile 11 .26 Furthermore, stericallyhindered arenes, e.g., mesitylene, also underwent borylation using 10 in good yield; note, these hindered substrates are challengingfor iridium catalysts. This work combined with the zinc-catalyzedsystems indicates that electrophile binding to CatBH (and derivatives)to generate borocation equivalents is an underexplored area that maylead to further advances in catalytic borylation.In recent work, Wang and co-workers reportedthe use of the boreniumcation 10 6 as the phile 11 6. 11 theEAr. In contrast, the borylation of ethylbenzene with ClCatBH/10 gave ca. 1:1 mixtures of C4 and C3borylated products.15 This is potentiallydue to isomerization at the borylated arenium cation stage prior todeprotonation as observed in stoichiometric electrophilic borylation.27 Controlling the rate of deprotonation relativeto that of isomerization therefore offers a route to obtain distinctborylation products. Analogously, if deprotonation of the “kineticborylated-arenium cation” is reversible, then the thermodynamicborylated product could be accessed selectively. The latter was observedin our work on borylations using NHC-BH3/10 mol % I2.28 This forms NHC–BH2I that reacts with activated arenes by SEAr, withreaction of the HI byproduct with NHC–BH3 regeneratingNHC–BH2I. With N-Me-indole, theonly product observed was the C2 borylated product 12  Brønsted base. However,in the absence of a base 13 was formed reversibly, ultimatelyleading to formation of 12 as the only borylated product,consistent with 12 being calculated to be the thermodynamicproduct. Hatakeyama and co-workers also noted that, in borylationsusing BI3 in the absence of a base, reversible borylationoccurs, presumably enabled by the HI byproduct from SEAr.29Alongside increasing the scope, switching theregioselectivityin catalytic electrophilic borylation is also of interest. To date,the vast majority of reports generate the products expected from Soduct 12 7, withC3/hindered amine FLPsto borylate activated arenes. This enabled formation of trifluoroorganoboratesby electrophilic borylation. Notably, the addition of 5 mol % tetramethylthiourea(TMTU) catalyzed this borylation process, possibly by providing alower barrier deprotonation pathway or by enabling formation of differentreactive electrophiles, e.g., [(TMTU)BF2]+ cations.30These studies with NHC boranes also emphasizethat boranes otherthan dioxaborolanes can be useful in catalyzed electrophilic borylations.This is an underexplored area and one that may lead to distinct reactivity/products.This is exemplified by the use of BF31 in 2015 Fontaine and co-workersreported an FLP that catalyzedarene C–H borylation with PinBH.32 Vital to this process was linking a C–H functionalizationstep with a σ-bond metathesis step , which canbe viewed as a concerted SEAr type process.9 The concerted transition states accessible in systems containingpendant bases enables what are relatively weak (compared to boreniums)boron electrophiles to effect C–H functionalization. Presumably,this is due to the preorganized nature of unimolecular FLPs circumventingarenium intermediates and a separate deprotonation step with an exogenousbase . It should be notedthat an initial endergonic step to form the active FLP 14 is required, which can be termed a FLP preparation step. This stepis also present in derivatives of 14 and when using 6 and 9. It is associated with dimer dissociation/cleavageof a dative bond to access the FLP. This step has the effect of makingthe subsequent energy profile more endergonic, with the preparationenergy required generally greater the lower the steric bulk is inthe FLP. Therefore, developing systems where the active FLP is theresting state would be attractive for increasing the substrate scope.Building on breakthroughs inFLP chemistry,sis step 8. C–H fu20 and Fontaine34 revealed thattuning the boron substituents and/or reducing the steric bulk aroundN can reduce the barrier to C–H functionalization. A significantimpact on this step was observed by altering the substituents at boronto generate more Lewis acidic FLPs, with 15  and is a key obstacle that has preventedsignificant substrate expansion via this approach. This is also highlightedby the nucleophilic heteroarene thiophene proving challenging to borylatecatalytically using 14 and PinBH.12a In this case double C–H functionalization occurs,e.g., to form 17, but 17 does not undergoσ-bond metathesis with PinBH. To date successful σ-bondmetathesis, and thus turnover via approach (ii), has been limitedto FLP catalysts containing BH2 units . Finding alternative hydroboranes (to PinBH or CatBH) that undergoselective σ-bond metathesis with compounds such as 16 could significantly expand the substrate scope via this approach,as would identifying distinct BH2-containing FLPs thatare more Lewis acidic than 14  but still undergo metathesis with PinBH.Structure activity studies from the groups ofRepo with 15 9 able to14 based on aluminum, e.g., 18  does catalyze terminal alkyne C–H borylationwith PinBH.36 However, many main groupcompounds have been reported that catalyze alkyne C–H borylation,and this conversion is in general less challenging than arene C–Hborylation. Finally, in this section, it is noteworthy that a zinccatalyzed C–H functionalization/metathesis mechanism also wasexplored computationally starting from compound 8.24 This had an overall free energy span for theborylation of N-Me-indole of 26.6 kcal mol–1 (–1 for that via approach(i)  step. Thus, exploringother hydroboranes may facilitate this step and enable catalytic borylation via thisapproach.Analogues of al mol–1 10 bottomshown in 5. Note, 2Cat3); thus, PinBH is clearly preferable. In this area,Fontaine and co-workers have progressed from their initial sensitive(pre)catalysts to bench stable zwitterionic precursors of generalformula 20 could be synthesized on a >100 g scale and was effective in theborylationof a range of activated heteroarenes on scales up to 1 kg (for 21).For a process tobe widely used, it not only requires broad applicability,but it also needs to be operationally simple. This requires (pre)catalystsand reagents that are easy to handle . Thisactually excludes CatBH due to its sensitivity (to moisture) and itstendency to undergo substituent scrambling : (a) utilizing bifunctional bases; (b) accessing boronelectrophiles by binding the activator to an O or the B–H toform borenium equivalents; (c) minimizing the preparation energy requiredto access active FLPs; (d) controlling the relative rates of deprotonationversus isomerization to access alternative borylation regioisomers.For approach (ii) many of the considerations are the same as in (i),but this approach would also benefit from more diverse FLPs  being explored. This may help solve thecurrent challenge associated with the σ-bond metathesis stepthat currently limits the substrate scope in catalytic electrophilicborylation via approach (ii). Breakthroughs have also been reportedusing boron electrophiles outside of the usual dioxaborolane basedsystems. While this is an underexplored area that can enable novelchemistry, it does introduce an additional consideration—theprimary products from C–H borylation need to be syntheticallyuseful in their own right, or they must be able to be converted readilyinto useful organoboranes, e.g., pinacol boronate esters.Given the short timespan since the 2010 report using iPr)3  in the presence ofPMDETA  to effect C–Hborylation.40 The borylation proceeds viaa C–H metalation step to form an aryl–sodium complexthat then arylates B(OiPr)3, with the latterstep key to drive the C–H metalation to completion. This workis an extension beyond the classical stepwise ArylC–H metalation/B(OR)3 trapping—as NaTMP and B(OiPr)3 are mutually compatible, i.e., they do not react irreversibly witheach other. If a related system could be made to turnover, then itwould be complementary to catalytic electrophilic borylation methods.The complementarity is indicated by the stoichiometric NaTMP/B(OiPr)3 system being able to borylate the highly deactivated(in term of nucleophilicity) arene PhCF3. However, thereare still significant challenges to overcome to combine metalationwith a subsequent step 41 that would regenerate the strong base and closethe cycle.Movingforward, the fact that the catalytic approaches discussedabove all rely on electrophile based C–H functionalizationsteps is a limitation. It would be extremely interesting if fundamentallydifferent main group catalyzed arene borylation routes could be developed.For example, is a strong Brønsted base mediated catalytic borylationprocess feasible? Conceptually this would proceed via a strongly basicmain group compound metallating (deprotonating) an arene, and thiswould be followed by reaction of the Aryl-M product with an appropriateborane to form the arylborane, ideally with concomitant regenerationof the strong Brønsted base. A step toward this has been reportedrecently by Hevia and co-workers left, 12 who us42 This proceeds via a C–H/B–H σ-bondmetathesis type transition state , it does indicate thatwith the right system main group catalyzed electrophilic alkane borylationis possible, which would be a highly notable breakthrough.Finally, Vedejs’ seminal work on intramolecularborylationoffers a different mechanistic pathway to achieve C–H borylation.e inset, 12. This n right, 12.44 Whi


A comparison of the results with the availableexperimental data shows that the relaxation mechanism we obtain byour theoretical-computational model is reliable, reproducing ratheraccurately all the experimental observables.In this paper, wereconstruct in detail the dynamicsof the emittingelectronic excited state of aqueous indole, investigating its relaxationmechanism and kinetics to be related to the time-dependent fluorescencesignal. Taking advantage of the results shown in a very recent paper,we were able to model the relaxation process in solution in termsof the transitions between two gas-phase singlet electronic states( Upon excitation, bothgeometrical and solvent relaxation occurs, thus resulting in the loweringof the energy of La and Lb states, in some casesleading even to their inversion in a polar environment, because ofthe higher dipole moment of the La state with respect toLb.3 This is at the basis ofthe complexity in the interpretation of the radiative deactivationprocesses of the electronic excited states that are responsible forthe large, solvent-polarity dependent Stoke’s shift shown byindole  and its high quantum yield.These properties have been exploited to probe local changes of polarityin proteins containing this amino acid upon denaturation5 or ligand binding,7 even though proteins, in general,contain more than one tryptophan residue, making it often extremelydifficult to unambiguously assign the changes in fluorescence to aparticular protein domain/site. This has led to the proposal in theliterature of several analogues of this important amino acid, variouslysubstituted on the indole moiety, in order to increase the sensitivityof this spectroscopic method in probing the protein structure anddynamics.8Indolesee 1 represe12 and theoretical point of view,16 some unclear aspects still remain. For example, the exact mechanismof the excited electronic state relaxation (energy transfer) in polarsolvents, such as water is still a matter of debate.Even though indole photophysicshas been deeplyinvestigated byseveral authors, both from an experimental18 to address the above-mentioned relaxation of the excited electronicstates of aqueous indole, focusing on the thermodynamics and kineticsof the deactivation processes at the basis of the fluorescence propertiesof this model molecule. Such an approach has provided accurate resultsat significantly less computational expense when compared to the morecommonly used strategies relying on the calculation of an ensembleof QM/MM trajectories.21 In fact, the high cost of this latter approach usuallylimits its applicability to the picosecond time scale, making it unsuitablefor the current study. Even though Machine Learning-based approachesenable longer simulations,24 our method offers a much reducedoverall computational cost permitting an extended phase space sampling,an easier implementation, and a robust and coherent quantum treatment,making it an appealing alternative, especially when the other approachesare not feasible.This paperwill exploit the general model for treating electronicstate transitions, focused specifically on charge transfer and intersystemcrossing reactions, developed by our group in the past,25 we studied indetail both the absorption and emission vibronic spectra of aqueousindole , as reconstructed by means of a theoretical–computationalmodel based on the Perturbed Matrix Method (PMM) approach28 and MD simulations, providing at each MD frame the QC electronicHamiltonian matrix H̃e representingthe electronic Hamiltonian operator Ĥe within the unperturbed electronic eigenstate basis set Φj0  via28jth unperturbed electroniceigenstate , N runs over theQC atoms with positions RN, qN,j0 is the Nth atomic charge in the j unperturbed eigenstate, Nth atom position, the scalar function ΔV (independent of the electronic states) approximates allthe higher order terms of the diagonal elements, E(r0) is the perturbing electric field at the referenceposition r0 , μ̂ is the dipole operator, and δj,l is the Kronecker delta. By meansof the eigenvectors and eigenvalues of the Hamiltonian matrix providedby In a previous paper,25 wasthat the first perturbed electronic excited state ofaqueous indole can be conceived as fluctuating among the first threegas-phase  singlet electronic excited states: thespectroscopically active Lb and La states andthe dark state πσ*. The perturbed first excited electronicstate is largely corresponding to the Lb electronic statejust after the excitation ,subsequently relaxing to a population mixture largely characterizedby the La electronic state, thus providing an emissionspectrum essentially corresponding to the La ensemble one.In this paper, we characterize in detail the transitions and processesoccurring within the population of the perturbed electronic firstexcited state, reconstructing its relaxation kinetics and inherentreaction scheme in terms of the emission decay and of the interconversionrates among Lb, La, and πσ* .It is worth noting that the Lb, πσ* and La electronic states correspond to the gas phase first three electronic excited states, respectively, at the groundstate optimized geometry where each of such excited states is characterizedby well distinguishable diagonal and transition dipoles. We then definedthe Lb, πσ*, or La electronic stateat each QC nuclear configuration via one of the unperturbed firstthree electronic excited states: the one best corresponding to theground state optimized geometry Lb, πσ*, orLa state ,regardless of its position within the energy order. When consideringthe unperturbed electronic excited state optimized geometries, providingthe equilibrium structure/structures for each excited state, we obtainedthat while the Lb state is always corresponding to thefirst unperturbed electronic excited state, the πσ*, andLa states exchange their energy position: i.e., the unperturbedsecond electronic excited state has two energy minima where it correspondsto either the La or the πσ* state. Note, however,that all such unperturbed excited state minima correspond to threedifferent energy minima for the aqueous indole electronic first excitedstate (the perturbed electronic first excited state): i.e., in eachminimum well  the perturbed first electronicexcited state corresponds to either the Lb, πσ*,or La state, respectively.25One of themain results of our previous paper18 we derived in detaila generalmodel for treating diabatic state transitions, focusing specificallyon charge transfer reactions17 modeledvia using the unperturbed electronic states as the proper diabaticstates. In this paper, we apply the same theoretical–computationalmodel using the Lb, πσ*, and La unperturbedelectronic states as the appropriate diabatic states to reconstructthe kinetics of the perturbed electronic first excited state relaxation(energy transfer) in aqueous indole.In previous papers,25 wherewe modeled the absorption and fluorescence spectra due to the singletvibronic state transitions . Briefly, for each electronic excitation/emissionof the chromophore, i.e., the quantum center (QC), by extracting theMD frames of the ground/excited state simulation with the ith perturbed electronic excited eigenstate best correspondingto a given jth unperturbed one and for a flexibleQC also belonging to a single conformation (MD subensemble), we obtainthe corresponding excitation or emission vertical electronic spectrumby means of the electronic vertical energy hν and transition dipole μi0, as provided by the Perturbed MatrixMethod28 (PMM), via290 beingthe vacuum dielectric constant, ℏ = h/2π the summation running over the frequency bins identified by the vertical electronic transition referencefrequencies νref, n(νref) the number of (extracted) MD frames with the verticalelectronic transition frequency within the bin centered in νref, |μi0,|refν2 the corresponding electronic vertical transition dipole mean squarenorm as obtained averaging over the bin MD frames, Nf the total number of extracted MD frames, and the Gaussiandistributions providing the broadening due to the QC semiclassicalvibrations disregarded by the PMM calculations . Note that withconformation we mean a configurational region of the QC internal semiclassicalcoordinate space  where all the QC electronic vertical transition properties,except the vertical transition energy, can be obtained at a singlereference structure corresponding to a local energy minimum of theunperturbed ground state (excitation) or of the jth unperturbed electronic excited state best corresponding to theperturbed ith excited state (emission). On the basisof the assumed negligible perturbation effects on the vibrationaleigenstates and eigenvalues, we can reconstruct for each subensemblethe mth vibronic spectral peak by multiplying theabsorption and emission vertical electronic spectrum by |⟨φ0,00|φj,m0⟩|2 and |⟨φj,00|φm0,0⟩|2, respectively, with φ0,00, φm0,0 being the ground and mth vibrational states ofthe unperturbed ground electronic state and φj,m0, φj,00 the mth and ground vibrationalstates of the unperturbed jth electronic excitedstate (the unperturbed electronic state best corresponding to the ith perturbed electronic excited state within the subensemble),as well as by substituting in ref with the binreference frequencies of the mth vibronic transitionνrefm, given by25m0 is the frequency ofthe unperturbed mth vibronic transition (unperturbed mth vibronic frequency) possibly corrected to match theexperimental gas-phase value, νel0 is the frequency of the unperturbedvertical electronic transition ,and clearly n(νrefm) = n(νref). Note that we evaluate the vibrational stateoverlaps via the simplified very efficient procedure described inthe previous paper25 based on consideringidentical vibrational modes and frequencies for the ground and excitedelectronic states, with the vibrational wave functions of correspondingmodes only differing for their minimum energy positions. The sum ofthese vibronic peaks provides the subensemble vibronic spectrum, andthus summing such spectra over all the subensembles, each statisticallyweighted by the corresponding probability as provided by the ground/excitedstate MD simulation, and then over all the relevant electronic transitionswe obtain the complete vibronic spectrum.We reconstructedthe aqueous indole emission properties by means of the procedure describedin detail in our previous paperb, La, and πσ*unperturbed electronic states), the rate equations for the R →P reaction can be obtained when considering all the reaction stepsdue to the crossing of the R vibronic energy surface with all theP vibronic ones involved in each reaction event (see R1 → Rn reactionsteps as completely irreversible with stationary intermediates (irreversiblereaction step approximation17), RA corresponding to the R1 substate of 17G is the reactiontransmission coefficient,17 as obtainedby the transition region (TR) crossings via the Landau–Zenerapproximation, and RA]0 being the RA concentration atthe beginning of the reaction. In the following, we will always considerthe electronic state transition as occurring according to the previousequations: i.e., RA is the initial reactantstate and hence for each reactive trajectory the transition energy is always positive before thefirst crossing is achieved. It is worth noting that the R and P diabatic electronic energies, furnishingvia their difference the relevant transition energy of the processand providing when vanishing the first crossing of the RA trajectories, are provided by the corresponding (perturbed)electronic Hamiltonian matrix diagonal elements  each as obtained at the proper unperturbed electronicstate minimum energy geometry17 .Defining for a rigid/semirigidQC, or for a conformational basinof a flexible QC, with A and B the two adiabatic energy surfaces see 2 involvevent see 3. Note tR and P diabatic state couple, to evaluate the distributionof the time-lengths needed by the QC for reaching the first diabaticenergy surface crossing in the reactant ensemble and thus to reconstructthe kinetic trace of [RA] providing thecorresponding kinetic constant 17 Moreover, by means ofthe Landau–Zenerapproximation, we can estimate the reaction transmission coefficientfor the subset of reactive trajectories unidirectionally traversing a given identical number nP of P (subsequent) vibronic states and characterizedby a virtually identical electronic adiabatic fraction χe that we consider roughly constant over the reaction steps,via17e corresponds to the electronic adiabatic fraction as obtainedatthe first crossing encountered by the reactive trajectories and ξi2 = |⟨φR,00|φP,i0⟩|2 is the squared(unperturbed) vibrational state overlap of the R (ground)and P (ith) vibrational states ,we obtain by averaging over all the crossing trajectories∑ΩNΩ = N is thetotal number of crossing trajectories , the anglebrackets mean as usual averaging over all the crossing trajectories,and the angle brackets with subscript Ω indicate averaging overthe NΩ crossing trajectories irreversiblytraversing a given identical number of P (subsequent)vibronic states. Note that when dealing with typical charge transferprocesses each reaction event may involve the irreversible traversingof roughly the complete set of the productive P vibronicdiabatic energy surfaces , thus providing for all the crossing trajectories Ω ≈1 . Differently,for electronic state transitions with reaction events involving theirreversible traversing of only a subset of the productive P vibronic diabatic energy surfaces, we necessarily haveξ02 ≤ Ω < 1 with ξ02 the squared vibrational state overlapof the first relevant R, P vibroniccrossing encountered by the R ensemble trajectories. In such more general cases, either we use le, and Ωl) or we can employthe approximatione,Ω = ⟨χe⟩Ω is the electronictransmissioncoefficient as obtained by evaluating the electronic adiabatic fractionχe at each of the NΩ first crossings and then averaging over all these crossings andαe = ⟨χe⟩ is the electronictransmission coefficient as obtained averaging over all the N first crossings sampled by the MD simulations. Finally,the electronic adiabatic fraction χe, as providedby the Landau–Zener and the dipolar approximations, can beobtained via17E beingthe perturbing electricfield at each (first) crossing as obtained at the QC mass center and H̅e,R,P and μ̅R,P0 beingthe arithmetic mean of the R, P electroniccouplings and electronic reactant–product unperturbed transitiondipoles as obtained at the R and P energy minima.ates see 3, as obtRA trajectories (note that the RA subscript of the angle brackets indicatesthat averaging is performed in the RA equilibriumensemble). In fact, considering that within each TR we have a virtuallyunidirectional flux, we obtain18RA2 is the variance ofthe transition energy within the RA equilibriumensemble and ⟨vcr⟩TR is the equilibrium average ofthe crossing velocity norm vcr, whichcan be evaluated by averaging the norm of the transition energy timederivative v within the RA equilibrium ensemble .In the unfortunate case that the kinetics istoo slow to obtaina proper crossing sampling from MD simulations (as for some of theelectronic state transitions investigated in this paper), we can stillreasonably well evaluate G ≈ 1 –(1 – αe)⟨Ω⟩ (with ξ02 ≤ ⟨Ω⟩ ≤ 1), by using theelectronic transmission coefficient αe = ⟨χe⟩ as provided by the crossing mean coupling approximationbased on expressing 1 – ⟨χe⟩= ⟨exp⟩ viaμR0, μP0 are the electronicenergies and diagonal dipoles of the R and P diabatic (unperturbed) states (eachas obtained at the corresponding unperturbed electronic state energyminimum), E∥ provides the perturbingfield along the unit vector η∥ at each first crossing event, following from17E⊥ is the perturbing field along the unit vector η⊥ orthogonal to η∥ ,and according to Similarly, when no crossingsampling is present we can also estimatethe transmission coefficient according to μ̅R,P0·η∥ and μ̅R,P0·η⊥, just like E∥ and E⊥ can be considered as statistically independent variables , then we can assumethat the distribution of E⊥ withinthe RA equilibrium ensemble be virtuallyidentical to the one obtained over all the crossing events where From e using the equilibrium RA ensemble, via ⟨E⊥⟩RA,⟨E⊥2⟩AR, and ⟨vcr⟩RA once we have evaluated μ̅R,P0·η∥), .b, La, and πσ* (unperturbed)excited states using CCSD and EOM-CCSD, and 6-311+G(d) as the basisset. The optimization of the unperturbed electronic ground state andof the Lb and La electronic states was performedin vacuo, whereas the minimized geometry of the dark πσ*state was estimated in aqueous solution (modeled using IEFPCM30): i.e., we assume for these unperturbed electronicstates identical minimum energy structures, at least for the quantumnuclear coordinates, for the isolated or the perturbed QC, with avirtually identical perturbed and unperturbed dark state at the correspondingminimum energy geometry. Note that for the dark state, we were notable to reach convergence of the calculation in vacuo, possibly dueto the very shallow minimum of this unperturbed electronic state inthe isolated indole.31 The excited stateminima were obtained by using the standard procedure of the Gaussianpackage,32 starting the calculation fromthe ground state optimized geometry where the first three gas-phase(unperturbed) electronic excited states correspond to the Lb, πσ*, and La state, respectively. The procedureused by Gaussian minimizes over the electronic energy surfaces, conservingthe character of the electronic state initially selected, by performingstate-tracking procedures.33 Therefore,in our case we find a minimum for each of the three starting electronicstates: the Lb minimum corresponding to the first unperturbedexcited state minimum and the πσ* and La stateminima corresponding to two different minima of the second unperturbedexcited state. However, all such minima correspond to three differentminima of the electronic perturbed first excited state: i.e., in theLb, πσ*, and La conformational basins(corresponding to the three optimized geometries) the perturbed firstexcited state is basically identical to the Lb, πσ*,and La electronic state, respectively. For each of theoptimized geometries (reference geometries), the electronic propertiesof the unperturbed ground and the lowest-lying six singlet excitedstates were calculated using CCSD and EOM-CCSD, and using 6-311+G(d)as the basis set. Like in our previous work,25 the calculated gas phase vibronic transition energies involvingthe Lb and La states were corrected to matchthe experimental gas phase 0–0 transitions reported in theliterature:34 the shifts of −0.32eV for GS → Lb and −0.57 eV for GS →La were used to correct the corresponding spectral signalsand furnished the energy corrections for the Lb⇌ La reaction rate calculations. Sincesuch gas-phase experimental data is not achievable for the πσ*(dark) state, no corrections have been applied when considering thetransition energies involving the dark state .The reference QM geometries usedfor the PMM calculations wereobtained by optimizing the structure of indole in the electronic groundstate and L35 functional and 6-311+G(d) basis set. The corresponding vibronictransitions were calculated using the simplified treatment we proposedin a recent paper.25 In fact, the highcomputational cost of the more accurate QM methods did not allow usto use EOM-CCSD for both the optimization and calculation of the vibrationalfrequencies, a condition required with the commonly used algorithms.37 In our approach, the use of different levels of theory was rigorouslyjustified by separating and uncoupling the vibrational modes betweenclassical-like  and the quantum modes . Vibrational modes belonging to different electronicstates with similar frequencies were approximated as being virtuallyidentical, differing only in the positions of their minimum energy,an assumption that is further validated by the quasi-diagonal Duschinskymatrices obtained for the considered electronic transitions . Moreover, the efficiencyof our treatment allowed us to explicitly consider more than a millionvibronic transitions without necessarily requiring the calculationsbeing performed in a local minimum, as is mandatory by the commonlyused method implemented in Gaussian.36 Note thatthe harmonic approximation for the vibrational states at each referencegeometry is applicable even when dealing with a shallow minimum. Infact, by separating classical-like and quantum vibrational coordinatesas allowed by our treatment, we can express the vibronic states ateach reference geometry via only the quantum vibrational subspacedefined by the vibrational modes with excitation energy higher thanthe thermal energy , with all the lower frequencymodes treated as classical-like (possibly anharmonic) coordinatesand determining parametrically the vibronic wave functions. Therefore,in order to ensure an accurate harmonic approximation in modelingthe vibrational wave functions involved in the vibronic states, weonly have to assume no mixing of the classical-like and quantum nuclearcoordinate subspaces with no significant coupling between them. Inour previous paper,25 such an approachhas already been applied to calculate both the absorption and emissionvibronic spectra of indole providing accurate results when comparedto the experimental data, therefore fully justifying its applicationin the present work. The benchmarking which led to the choice of functionalsand basis sets is described in our previous work.25 The geometry optimizations, the calculation of the vibrationaleigenstates and of the ESP charges39 of all theunperturbed electronic states were performed using Gaussian 16,32 while all the other electronic properties werecalculated using Q-Chem 5.3.40Furthermore, the vibrationaleigenstates were calculated for eachreference geometry using TD-DFT with M06-2Xb,La, and πσ* excited states. Each excited stateMD simulation was performed using the atomic charges of the diabaticexcited state corresponding at each reference geometry to the perturbedfirst electronic excited state, with all the other force field parametersidentical to those of the ground state force field .This choice is motivated by the tiny structural changes among theexcited state minima and between these and the ground state (GS) one,providing for indole virtually indistinguishable geometries in theMD simulations . Note however thatall the PMM calculations and reaction rate evaluations are obtainedby using at each MD frame the proper excited state reference geometrywith the corresponding unperturbed quantum states: at each MD framethe proper QC excited state reference structure is (mass-weighted)fitted to the instantaneous QC MD configuration to obtain the correctcalculations involving the perturbing field.NVTMD simulations were performed for indole and 1276 TIP3P watermolecules in a cubic box with sides of 3.37589 nm using periodic boundaryconditions, at 300 K, for the ground state and the L41 The force field used was CHARMM36,43 and for the simulations of indole in the diabatic excited states the atomiccharges were replaced with the ESP charges obtained using EOM-CCSD/6-311+G(d). The canonicalsampling was achieved using the velocity rescaling thermostat.44 Each equilibrium simulation used to obtain the RA equilibrium ensemble was carried out for 400ns with a time step of 2 fs, using for the MD-PMM calculations 20,000frames taken every 20 ps. Additional MD simulations, 500 trajectoriesof 3 ps for the Lb ensemble and 500 trajectories of 10ps for the La ensemble, with 1 fs of time step were performedfor obtaining the nonequilibrium simulations providing the explicitcrossing sampling. The starting configurations of the nonequilibriumsimulations were extracted from their corresponding equilibrium simulationby dividing the latter into 500 subtrajectories of 40 frames eachand by randomly selecting a frame. For each subtrajectory, frameswere randomly chosen and discarded until the resulting transitionenergy of the considered process  was positive  electronicexcited state is largely coinciding with the Lb electronicdiabatic state, with the excited state population subsequently relaxingvia transitions to the La and the dark (πσ*)electronic diabatic states. According to the theoretical model describedin the theory section, we estimated all the relevant kinetic propertiesfor each of the diabatic state transitions  by means of MDsimulations performed in the corresponding reactant ensemble . By using the La, Lb, and πσ* MD ensembles, we then obtained the kineticproperties for all the possible transitions, as summarized in b⇌ La interconversion, and thus we obtained thecorresponding transmission coefficients via αG ≈1 – (1 – αe)⟨Ω⟩ with ⟨Ω⟩ = ξ02.It is worth remarking thatgiven the large tate see 1, we alwa, Lb interconversion, the valuesof αG ≅ 1 – ⟨(1 – χe)Ω⟩ and related τ were evaluatedby the simulation crossing sampling . For comparison, the Gaussian and crossing mean coupling approximationswith either ⟨Ω⟩ = ξ02 or ⟨Ω⟩= 1 were also used to estimate αG ≈ 1 –(1 – αe)⟨Ω⟩ and τ values. It is worth noting that the Lb⇌ La reaction involves insufficientlylarge RA inner distribution due to RA innerrelaxations kinetically comparable to the Lb⇌ La reaction. However, the τ0 and αG values obtained by means of the Gaussian and crossing meancoupling approximations (the latter when using ⟨Ω⟩= ξ02) are reasonably close to the corresponding values as provided bythe simulation explicit crossing sampling, reproducing the correctorder of magnitude of the reaction mean lifetimes and thus confirmingthe reliability of these approximations needed when no crossing samplingis achievable , with the latter being a virtuallyirreversible transition which leads to the overall relaxation mechanismof aqueous indole first (perturbed) electronic excited state representedin b⇌ La interconversion, their radiative relaxations to theground state, and the Lb → πσ* and La → πσ* (irreversible) transitions −1 are compared to the corresponding experimentalvalues. From these last two tables, it is evident that our theoretical–computationalapproach rather well reproduces the experimental relaxation rate constantsas obtained by the fluorescence signal , thus showingthat the model employed captures the essential features of the aqueousindole excited state relaxation mechanism. It is worth noting thatin our theoretical–computational model we disregarded any La → triplet and Lb → triplet transition,possibly contributing to the nonradiative relaxation involved in thesinglet first (perturbed) excited state fluorescence time-dependentsignal. However, such intersystem crossing (ISC) processes are characterizedby very slow kinetics due to the tiny diabatic state coupling of theISC reactions , typically resulting in a tiny adiabatic fraction. Therefore,given the high computational costs for including all the possibleLb and La to triplet state transitions and relyingon their relevantly slower kinetics compared to the La →πσ* and Lb → πσ* reactions,in our model we did not include the ISC transitions as they can beconsidered negligible for reconstructing the essential features ofthe relaxation mechanism. Indeed the only experimental (indirect)estimate of the overall ISC rate constant involved in the aqueousindole singlet first perturbed excited state relaxation we found inthe literature48 , when included in our calculations provides τnr = 3.1 ns and τF = 2.7 ns deviating for only a coupleof standard errors from the corresponding values as obtained neglectingthe ISC reactions  based on assuming a fastrelaxation of the chromophore–quencher complex compared tothe chromophore–quencher association and dissociation ratesmight be inaccurate to treat the slow ISC relaxation, thus possiblyresulting in an overestimated kISC .The resulting relaxation propertiesare shown in ions see 4: i.e., b⇌ La interconversionfollowed by the much slower Lb and La radiativerelaxations competing with the (nonradiative) virtually irreversibletransitions to the dark state  excited staterelaxation largely characterized by the La radiative andnonradiative competing decays. It is worth noting that the final relaxationfrom the dark state to the ground state, being a nonradiative process,cannot be detected by fluorescence experiments and thus disregardedin our calculations. Finally, the results obtained, confirming theaccuracy of the theoretical approach used for modeling the electronicstate transitions, show that the use of a coherent theoretical–computationalmodel can provide a quantitative description of a complex molecularprocess, unveiling its still controversial and not fully clarifiedessential features.In this paper, we investigatedin detailthe relaxation processof aqueous indole first excited electronic state. By means of a theoretical–computationalmodel, we reconstructed all the relevant paths involved in the relaxationkinetics, evaluating all the corresponding rate constants. Comparisonwith all the available experimental data  shows that the model employed rather well reproducesboth the radiative and nonradiative mean lifetimes, demonstratingits reliability in elucidating the essential features of the relaxationmechanism. Our results indicate that the relaxation process involvesa very fast L


Chronic liver disease (CLD) is a serious condition where various toxins present in the blood affect the brain leading to type C hepatic encephalopathy (HE). Both adults and children are impacted, while children may display unique vulnerabilities depending on the affected window of brain development.1H MRS) to study longitudinally the neurometabolic and behavioural effects of Bile Duct Ligation  on rats at post-natal day 15 (p15) to get closer to neonatal onset liver disease. Furthermore, we compared two sets of animals (p15 and p21-previously published) to evaluate whether the brain responds differently to CLD according to age onset.We aimed to use the advantages of high field proton Magnetic Resonance Spectroscopy . When compared to rats that acquired CLD at p21, p15 rats did not show any significant difference in plasma biochemistry, but displayed a delayed increase in brain glutamine and decrease in total-choline. The changes in neurotransmitters were milder than in p21 rats. Moreover, p15 rats showed an earlier increase in brain lactate and a different antioxidant response. These findings offer tentative pointers as to which neurodevelopmental processes may be impacted and raise the question of whether similar changes might exist in humans but are missed owing to  Chronic liver disease (CLD) is a serious condition that can develop in adults or children. In CLD, various toxins present in high concentrations in the blood stream  affect the brain and lead to a neuropsychiatric disorder called type C hepatic encephalopathy (HE)  at post-natal day 21 (p21) (still during a period of brain development) suffered from more pronounced changes in many brain metabolites  compared to adult BDL rats  to analyze the longitudinal changes of brain metabolites in vivo measured in the hippocampus of rats having undergone BDL at p15 together with plasma biochemical parameters and behavioural tests. The final goal was to compare the two sets of animals .Eight (8) male Wistar pups underwent bile duct ligation (BDL) surgery and 8 male Wistar pups were sham operated at p15. One BDL pup was removed from the study as it recovered from surgery  leading to a total of 7 BDL pups entering the study. The progression of CLD and HE was monitored longitudinally in each animal until post-operative week 6. The BDL rat model is an animal model of type C HE recognized by the International Society for Hepatic Encephalopathy and Nitrogen Metabolism. In this model, biliary cirrhosis is associated with hyperammonemia, jaundice and portal hypertension . Nevertheless, mammalian species develop at different rates, particularly when it comes to neurodevelopmental processes and brain regions, so determining when all neurodevelopmental processes in rats translate in a specific time window in humans is complex and challenging  for total bilirubin, and blood ammonium meter (PocketChemTM BA PA-4140) for blood ammonium as markers of biliary obstruction and liver function . In the p21 study  for the 1H MRS scans was placed in dorsal hippocampus localized on axial and sagittal anatomical T2 weighted images  = 4000/52 ms, echo train length = 8, field of view = 23 × 23 mm2, slice thickness = 1 mm, 2 averages, 256 × 256 image matrix). Hippocampus, as a part of limbic system, was chosen for 1H MRS measurements due to known problems with learning and memory in patients with type C HE  spectroscopy sequence   interfaced to a Varian Direct Drive console  using a home-built quadrature surface coil as a transceiver (17 mm diameter for each loop). The volume of interest  and in % difference between BDL rats and shams at each time-point in order to account for ongoing development.Spectra were fitted and metabolite concentrations were calculated by LCModel  test to test the presence of fine motor deficits characteristics of type C HE. It involved placing the rat in an open circular arena   in the measured parameters. If only two sets of data were compared, Student’s t test was used. Pearson correlation analysis was performed on all longitudinally acquired data to test for correlations between the measured parameters.All results are presented as mean ± standard deviation ). One-way analysis of variance (ANOVA)  with the Bonferroni’s multi-comparisons post-test were used to assess significance  in BDL p15 and p21 rats at week 4 and 6 after BDL surgery is shown in Fig. 4+ increase between p15 and p21 rats. An approximate ~ 2-fold average increase at week 4 and ~ 3-fold increase at week 6 was observed for p15, while the increase was slightly lower for p21.Figure Gln, in contrast to p21 BDL rats that had significantly higher Gln at week 2 after BDL surgery. Gln increase, for p15 BDL rats, was significant at week 4  and further increased at week 6 after BDL   Fig. A,B. The 01) Fig. C.Ins decreased in p15 BDL rats significantly at week 2 after BDL surgery  and reached a decrease of -45 ± 23% (p < 0.01) at 6 weeks after BDL  decreasing further to -35 ± 9% (p < 0.001) at week 6 , reaching − 17 ± 7% (p < 0.01) at week 6  Fig. .Cr and PCr, which are considered both as being involved in energy metabolism and Cr also in osmoregulation  decreased significantly in p15 BDL rats week 4  and further to -16 ± 7% (p < 0.01) at week 6  and remained high at week 6 (16 ± 16%) without reaching significance  without reaching significance  showed any significant decrease throughout the study in p15 BDL rats. BDL Fig. A,B in coBDL Fig. C. Asp dik 6 Fig. G,H, insik 6 Fig. I.The correlations between Gln increase and decrease in neurotransmitters were much weaker in p15 BDL rats compared to p21 BDL rats. The correlation between Gln and Glu was present in p15 BDL rats but the slope was not as steep as in p21 BDL rats Fig. A. There Ala, NAA, NAAG and PE did not show any significant difference between p15 BDL rats and their shams throughout the study.In the Open Field test, there was no difference in the distance moved between p15 BDL and their shams Fig. A, in con1H MRS methodological limitations in field strength in clinical magnets.The present work showed for the first time that when CLD was acquired in rats at p15, the rats presented the typical signs of CLD, i.e. rise in plasma bilirubin and ammonium, and developed the characteristic brain metabolic changes associated with type C HE namely an increase in brain Gln which correlated with the decrease in the other main osmolytes . When compared to the group of rats that acquired CLD at p21, p15 rats did not show any significant difference in plasma biochemistry (bilirubin and ammonium) but did display a delayed increase in brain Gln and decrease in tCho. In addition, the changes in neurotransmitters were milder than in p21 rats. On the other hand, p15 rats showed an earlier increase in brain Lac and a different antioxidant response than p21 rats, and a decrease in exploratory behaviour. The cellular and enzymatic underpinnings remain unknown, yet these differences suggest that the brain of younger pups does respond differently to the metabolic insults of CLD. Whether this is due to maturing enzymes and metabolic pathways remains to be elucidated. Nonetheless, these novel findings raise the question of whether similar changes might exist in humans but are missed owing to 1H MRS in humans during infancy and early childhood and connected with the increase in the number of neurons, formation of dendritic arborizations and synaptic connections  – the enzyme that allows astrocytes to detoxify ammonium by condensing Glu and ammonium. GS seems not to be fully active until p26  – Ca2+ signalling pathways in the CNS are contributing to the synaptic plasticity and thus learning and memory . Whether tCho decreased as a part of an osmoregulatory process or as a result of impaired phospholipid metabolism is not clear. However, it could be argued that its decreased concentration in the brain during development could significantly impact membrane metabolism. PCho and GPC are the main sources of choline for phosphatidyl-choline ) in developing brain cell 3D cultures . In p21 BDL rats, Asc showed a continuous decrease, significantly stronger at week 4 after BDL surgery than for p15. On the other hand, GSH in p15 BDL rats decreased gradually showing a more pronounced change than GSH in the brain of p21 BDL rats. GSH in p21 BDL rats stayed stable until week 6.As Asc is known to be predominantly in neurons and GSH to be in glial cells , p15 BDL rats showed significantly increased latency to enter the centre of Open Field arena during the test. Indeed, this difference in the decrease of motor activity in p21 BDL rats and decrease in the exploratory behavioural in p15 BDL may simply be related to behavioural development. Exploratory activity dominates over locomotor activity between p20 and p30 and they interchange afterwards . However, this approach did not allow a direct comparison of the animals at the same age, meaning that p15 BDL operated rats are at p29  at week 2  after surgery while p21 BDL operated rats are at p35  at week 2  after surgery.In conclusion, we showed that the neurometabolic changes of rats that developed CLD at p15 display many similarities with p21 BDL rats and even adult rats, for example in the osmoregulatory response to CLD. There are however a few notable differences such as a less rapid increase in Gln and decrease in tCho, Asc concentrations; and a more significant and earlier Lac increase and GSH decrease. Importantly, Gln concentrations were slightly higher in p15 rats at the end of the study. Effect of the disease on the concentrations of neurotransmitters was minor in p15 BDL rats. These findings offer tentative pointers as to which neurodevelopmental processes may be impacted. Ultimately it is the fine balance of how osmotic shifts and molecular fluxes impact membrane formation, neuro- and synaptogenesis, as well as the proliferation and differentiation of other cell types which will lead to the behavioral or neurological or neurocognitive phenotype. Here we compared neurometabolic changes between p15 and p21 BDL rats in the hippocampus. Knowing that brain regions are enriched in different molecules to perform their different functions, it seems reasonable to extrapolate that different brain regions will respond differently to the metabolic insults of CLD not just longitudinally but also spatially, something important to explore if we are to progress in our understanding of the vast phenotypic spectrum of type C HE.