Danio rerio. We exposed zebrafish from embryonic stage to either control (28 °C) or elevated temperature (30 °C) for seven days. Overall, warming reduced routine swimming activity and caused upregulation of metabolism and neuron development genes. When exposed to olfactory cues, namely catfish cue, a non-alarming but novel odour, and conspecifics alarming cue, warming differently affected the larvae response to the two cues. An increase in locomotory activity and a large transcriptional reprogramming was observed at elevated temperature in response to novel odour, with upregulation of cell signalling, neuron development and neuron functioning genes. As this response was coupled with the downregulation of genes involved in protein translation and ATP metabolism, novel odour recognition in future-predicted thermal conditions would require energetic trade-offs between expensive baseline processes and responsive functions. To evaluate their learning abilities at both temperatures, larvae were conditioned with a mixture of conspecifics alarm cue and catfish cue. Regardless of temperature, no behavioural nor gene expression changes were detected, reinforcing our findings that warming mainly affects zebrafish molecular response to novel odours. Overall, our results show that future thermal conditions will likely impact developing stages, causing trade-offs following novel olfactory detection in the environment.Temperature is a primary factor affecting the physiology of ectothermic animals and global warming of water bodies may therefore impact aquatic life. Understanding the effects of near-future predicted temperature changes on the behaviour and underlying molecular mechanisms of aquatic animals is of particular importance, since behaviour mediates survival. In this study, we investigate the effects of developmental temperature on locomotory behaviour and olfactory learning in the zebrafish,  One famous example is the accidental discovery of fear reaction to alarm cues in fish: when a minnow (Phoxinus phoxinus) is injured, an alarm cue is released and nearby conspecifics drastically change their behaviour by swimming away and moving in tighter schools2. Such olfactory-mediated behaviours are common in fish3 and positively affect survival not only in adults but also in immature life stages, and many fish larvae can assess risks by sensing cues from predators or other prey4. While some of the olfactory processes important for survival are innate, others involve associative learning: if during a conditioning phase two odours occur together, later in life the second odour will be associated with the same events and situations as the first odour5. This is the case with predator recognition, which has been described in the European minnow. After sensing the odour of a natural predator mixed with alarm cues released by the skin of conspecifics, minnows would start hiding and schooling upon smelling the pike’s odour alone6. Such an association of odours causing antipredator behaviours to otherwise neutral stimuli occurs in a diverse range of prey fishes7, notably zebrafish8.Olfaction is one of the main ways fish gather information about their environment. A wide variety of behaviours is influenced by the detection of olfactory stimuli, such as feeding, migration, reproduction and predator escape response9, with temperature arguably one of the main environmental variables influencing the performance of fish11 including effects on olfactory triggered feeding12. Global warming, which is happening at an unprecedented rate in aquatic environments14, may therefore alter crucial processes in fish, including olfactory and behavioural responses. Olfaction in fish is mediated by olfactory sensory neurons that converge on the olfactory bulb, where there is an exchange of information to second-order neurons, that are likely involved in the learning process15. Physiological changes in the olfactory bulb may occur due to temperature17 and warming can impair fish associative learning due to alterations in memory formation19. Despite previous evidence of temperature altering gene expression involved in olfaction20, it is unclear to what extent or how near-future thermal conditions will impact the sensory system and overall cue processing in fishes21, particularly at the molecular level. For this reason, understanding how warming modulates the behaviour and learning experiences that fish need for survival is of crucial importance, especially in light of rapid climate change.Environmental factors have the potential to influence olfactory responsesIn our study, we investigate the effects of developmental temperature on the locomotory behavioural and genome-wide transcriptomic responses of zebrafish larvae to two different olfactory cues: an alarm substance (Conspecifics Alarm Cue) and a non-alarming odour (catfish cue). We hypothesize that future predicted thermal conditions for the end of the century will impact the molecular state in sensory processing during the behavioural response to different cues. By performing classical conditioning, we assess whether a climate change-driven increase in temperature influences the olfactory learning experience, both at behavioural and molecular levels. Overall, by characterizing temperature-specific whole body transcriptomic and behavioural changes in response to olfactory cues, we aim to determine how future predicted temperature will affect the environmental perception of zebrafish and their learning experience through olfaction.22) were collected in the morning and then placed in Petri dishes filled with Danieau’s solution embryo medium 2, 1.5 mM HEPES) in DSI-060D incubators (Digisystem) at either control (28 °C) or elevated (30 °C) temperature. Temperature inside the incubators was adjusted every 60 s. We selected this control temperature as it is the optimal rearing temperature of zebrafish in laboratory settings and chose the treatment temperature as + 2 °C as current IPCC scenarios estimate that because of climate change temperatures will globally increase between 1.5 °C and 2 °C above pre-industrial levels by the end of the century13. The embryo medium was changed daily. Embryos were reared under a 14/10 h light–dark cycle and from five days post fertilization (dpf) onwards they were fed a larval diet (Zeigler Bros) daily until seven dpf, which is a critical life stage23 during which larvae become active in their environment22 and can detect olfactory information with a functional sensory system24. Temperatures between treatments differed significantly  and did not follow a normal distribution : the “treatment” temperature over the experimentation period was 30.1 ± 0.3 °C, whereas the mean control temperature was 28.2 ± 0.3 °C  were obtained from the Hong Kong University of Science and Technology zebrafish husbandry facilities. Wild-type zebrafish were kept at 28 °C and housed in two recirculating systems (80 × 37 × 32 cm) with six males/four females in one and four males/six females in the other, with a 14/10 h light–dark cycle. The thermal conditions were measured, adjusted and recorded every 60 s with heaters (Schego) and a STC-1000 Thermostat (Elitech). Fish were fed twice a day with TetraMin pellets. pH and nitrate levels were measured weekly using a WP-91 pH meter (TPS) and a HI97728 nitrate photometer (Hanna Instruments), respectively. Fertilized eggs (at the cleavage period of development25. The catfish cue (Catfish C) was chosen to assess the larval response to the odour of a fish species that zebrafish do not innately fear, as used in previous research26. Because lab-reared zebrafish were not previously exposed to catfish or Catfish C, catfish odour would not elicit anti-predation responses, since recognition of this species by zebrafish would only occur from associative learning. The CAC was produced by sacrificing zebrafish larvae reared together with the experiment subjects by head concussion, and homogenizing their bodies in water at a concentration of one donor larva/mL with a sterile mortar and pestle, 5 min before cue exposure time26. For Catfish C, water in which two shark catfish fed with Algae wafers (Hikari) were maintained for 24 h  was used, following the methodology by Lucon-Xiccato et al.26. Seven dpf larvae were transferred to experimental acrylic chambers (40 × 40 × 9 mm each) with a transparent bottom filled with six mL of Danieau’s solution that had been maintained at the corresponding larval rearing temperature and gradually reached a common room temperature of 26 °C during an acclimation period. Larvae were given 40 min acclimation time, then recorded from above using a Canon EOS M50 camera. After a baseline observation period of 12 min, larvae were exposed to either CAC , Catfish C  or control water  for another 12 min , a substance that is known to trigger an alarm response such as reduced locomotion or increased freezing, which consists in a total suppression of the swimming activity26. On the following day, larvae were placed back in individual chambers, where they were given 40 min to acclimate and were then video recorded. After a baseline activity period of 12 min, larvae were exposed to either control water  or Catfish C alone  for another 12 min, as in experiment 1  and Catfish C (0.5 mL), prepared as described above. The conditioning phase lasted 40 min, then the larvae were placed back into the incubation chambers for 24 h, following the methodology by Lucon-Xiccato et al.27 for body coordinates tracking of multiple animals per video. For a training dataset for machine learning of a network  body parts were manually labelled in 20 frames per video among a representative set of 10 videos across dates and treatment. Incorrect tracklets were manually corrected post-analysis in DeepLabCut and positions through time of each larva were extracted in R v 4.2.128 using the trajr package v 1.4.029. Trajectories in which position was retrieved in less than 80% of all frames were discarded  by each larva’s body length (mm), to account for body length potentially driving differences in swimming performance.To standardize the length of all videos to 12 min, raw videos were cut in Adobe Premiere 2019. The videos were then processed in DeepLabCut v 2.2.0ed Table . With th29 Table . Finally31 with the following parameters: “ILLUMINACLIP: all_adapters.fa:2:30:10:8:TRUE LEADING:4 TRAILING:3 SLIDINGWINDOW:4:20 MINLEN:36”. High quality reads  and the R package “FindMyFriends”36.In order to assess the broad transcriptomic response of zebrafish to olfactory cues and the potential influence of temperature, total RNA was extracted from whole larvae (n = 10 per treatment) using a TRIzol™ Plus RNA Purification Kit with Phasemaker tubes (Thermo Fisher) due to the small size of the larvae. RNA concentration was measured using Qubit™ RNA HS Assay Kit (Thermo Fisher Scientific) and quality assessed using TapeStation (Agilent). RNA was sequenced at 150 bp paired end on an Illumina NovaSeq at the Centre for PanorOmic Sciences (CPOS) of the University of Hong Kong. After sequencing, raw sequence data  between control larvae and treatment larvae between samples from the same experiment (innate or learning). The larvae’s date of fertilization (df) was found to be an important factor influencing the differential expression of genes, so it was kept in the statistical model of both experiments . The formula contained a combination of the two factors (temperature and cue) with therefore six possible levels, allowing to make specific pairwise comparisons between the most specific groups of the experimental design (“ ~ df + combination”). Differentially expressed genes with a baseMean under 10 and/or an absolute value of log2foldchange inferior to 0.3 were discarded to ensure that differential expression was not an artifact of low counts, and to increase stringency.Finally, differential expression analyses were conducted using DESeq2 v 1.3838 below the 0.05 threshold were considered enriched and reduced to most specific.For the significantly differentially expressed (DE) genes, functional enrichment analyses were performed in OmicsBox v 1.4.11 (Fisher’s Exact Test). The GO terms get associated with the gene IDs because of their correspondence with either one of the three other types of IDs: if there was no documented Ensembl ID, the Entrez ID would be used and if the two former ones were absent, then the ZFIN ID would be used. The Gene Ontology (GO) terms with an FDR adjusted p-valueWe hypothesized that warming would alter the swimming behaviour of zebrafish larvae. There was a significant effect of rearing temperature on baseline swimming distance in the innate experiment , with larvae swimming on average 332.4 ± 202.3 body lengths if reared in control temperature (n = 67) but only 176.2 ± 78.9 body lengths when reared at elevated temperature (n = 62), during the baseline activity period Table  & Fig. 2Overall, there was no significant innate effect of any olfactory cue exposure on swimming activity at control temperature Tables , SFig 2.–3; baseline distance = 167.6 ± 81.6 body lengths, exposure distance = 216.4 ± 122.5 body lengths), with larvae swimming on average 29% more distance after exposure . Body length was found non-significantly different among thermal groups, although barely , with larvae reared at elevated temperature tending to be shorter than control larvae , are involved in peptide synthesis, while the gene protocadherin 2 alpha b2 (pcdh2ab2) codes for a subunit of protocadherin protein, that is involved in neuronal development.Being reared at elevated temperature resulted in eight genes being differentially expressed compared to control temperature, in larvae not exposed to any olfactory cues. All those genes were upregulated Table . Among tpcdh2ab2, in larvae exposed to catfish cue  and other types of G-protein, such as the alpha activating activity polypeptide, olfactory type . Furthermore, palmitoylation of proteins was also upregulated, enriching lipoprotein metabolism , contactin-associated genes (cntnap2a and cntnap5a) involved in organization of myelinated axons as well as axon growth associated genes of the semaphorin-plexin pathway . Additionally, genes involved in synaptic transmission were over-expressed upon exposure to catfish cue at elevated temperature. These genes belong to calcium, sodium and potassium voltage-gated ion channels  were downregulated  decreased routine swimming distance and increased expression of genes involved in peptide synthesis and neuron development. However, unexpectedly, CAC did not provoke a reduction in swimming activity, no matter the rearing temperature, despite elevated temperature mediating a behavioural and a large molecular response upon exposure to non-alarming catfish cue. Finally, we found that conditioned larvae did not react to catfish cue in a way consistent with associative learning neither behaviourally nor molecularly.39 and that zebrafish swimming capability was found to be comparable within the range of 26–30 °C40, our results suggest that reduced swimming activity is an effect of developmental thermal exposure. This is consistent with reports of swimming performance being influenced by developmental temperature in zebrafish juveniles tested at a common temperature41. Reduced swimming could be a behavioural trade-off caused by higher energy costs of maintaining homeostasis at 30 °C, as the thermal performance curve dogma predicts42. Concurrently, elevated temperature triggered an over-expression of genes involved in neuron development and protein synthesis. In particular, pcdh2ab2, which codes for a neuronal cell-surface protocadherin expressed throughout the developing nervous system44, is upregulated in larvae at elevated temperature. Similarly, genes such as an acid-amino acid ligase (gdhc), a ribosome constituent (mrps9) and tars2, which codes for an enzyme that performs the first step of translation, are found at elevated levels in elevated temperature. Upregulation of genes involved in peptide production and brain development at elevated temperature is consistent with the acceleration of metabolism and overall development due to high temperature45. Moreover, a 2 °C elevation was also reported to increase larval expression of growth hormone and insulin-like growth factor genes in other fish species46. Therefore, our results support that larvae exposed to 30 °C during embryogenesis had a faster development regarding molecular patterns, than larvae reared at control temperature.Elevated temperature during embryogenesis resulted in a reduction in swimming distance in zebrafish larvae. As previous findings found no swimming alteration when seven dpf zebrafish reared at control temperature were suddenly exposed to 30 °C47, which is likely a survival strategy to remain hidden from a predator. Therefore an absence of behavioural and molecular response to CAC is contrary to our expectations, as injured conspecific cues have been shown to reduce mobility of larvae from five to 24 dpf48. One of the possible explanations for the lack of freezing behaviour in our samples is that larvae could have responded with behaviours other than freezing, which however, were not measured here. Indeed, freezing is not the only possible behavioural response to alarm cues and zebrafish has also been shown to react to alarming cues by bottom swimming or escaping the area25. Alternatively, the concentration of the cue could have been under a threshold for a behavioural (and molecular) response to occur, despite the fact that we followed the methodology of Lucon-Xiccato et al.26, as 7 dpf larvae are smaller than 12 dpf ones. Indeed, previous research found that intensity of the alarm response is dose-dependent25.While elevated temperature elicited a behavioural change, neither of the cues provoked freezing behaviour at control temperature. A complete suppression of locomotory movement has been previously reported in response to alarming olfactory substances in zebrafishPangasianodon hypophthalmus) is not a known alarming presence to lab-reared zebrafish and its smell has not been found to trigger a freezing response26, therefore unchanged activity at control temperature following catfish cue exposure was consistent with our expectations. Interestingly, exposure to catfish cue elicited expression changes of pcdh2ab2 at control temperature. In seahorses (Hippocampus erectus), pcdh2ab2 is also changed in expression levels when faced with the visual and olfactory signal of a paired mate49. As pcdh2ab2 is involved in neuron development, it could play a role in the neuronal alterations in the context of odour detecting and olfactory memory. In our case, since this gene was not also upregulated in larvae exposed to CAC, the reason for upregulation of this gene upon smelling catfish cue might be due to the novelty of this specific cue in the larvae’s environment. Unlike CAC, which was prepared with larvae of the same school, catfish cue was never introduced before and this was the first exposure to this new smell for the larvae. Interestingly, exposure to elevated temperature caused an increase in swimming activity in response to catfish cue. Previous occurrences of increased locomotory activity were reported in zebrafish as a response to a variety of odours, such as food, social cues or decay odours51, as well as amino acids in larvae as early as 4 dpf52. Here, increased activity in the presence of the novel catfish cue at elevated temperature could be due to zebrafish larvae displaying an aversive response similar to decay odour avoidance53, with catfish cue possibly containing dead skin compounds. Since older larvae do not react to catfish odour alone at control temperature26, it is unlikely that the reason larvae only responded to this cue at elevated temperature is solely accelerated development. Rather, temperature-induced stress may increase the fish sensitivity to olfactory stimulation and therefore decrease the threshold for a behavioural response to occur.Catfish cue was used as a “neutral non-alarming cue” since the catfish  larvae respond to catfish cue by freezing after conditioning with CACSupplementary Figures.Supplementary Tables.


In molecular dynamicssimulations in the NPT ensemble at constantpressure, the size and shape of the periodic simulation box fluctuatewith time. For particle images far from the origin, the rescalingof the box by the barostat results in unbounded position displacements.Special care is thus required when a particle trajectory is unwrappedfrom a projection into the central box under periodic boundary conditionsto a trajectory in full three-dimensional space, e.g., for the calculationof translational diffusion coefficients. Here, we review and comparedifferent schemes in use for trajectory unwrapping. We also specifythe corresponding rewrapping schemes to put an unwrapped trajectoryback into the central box. On this basis, we then identify a schemefor the calculation of diffusion coefficients from NPT simulations,which is a primary application of trajectory unwrapping. In this scheme,the wrapped and unwrapped trajectory are mutually consistent and theirstatistical properties are preserved. We conclude with advice on bestpractice for the consistent unwrapping of constant-pressure simulationtrajectories and the calculation of accurate translational diffusioncoefficients. In the lattice view, each particle corresponds to a collection of infinitely many pointson a periodic lattice, whose lattice constants are determined by thebox size and shape. The toroidal view naturally leads to so-calledwrapped trajectories, where particles at every instance in time arecontained within the central box . By contrast, in the lattice view eachindividual marked point on the lattice representing a particular particlecan traverse the full three-dimensional space, resulting in an associatedunwrapped trajectory. For simulation boxes of constant volume in constant-energy(NVE) and constant-temperature (NVT) ensembles, the task of unwrappinga trajectory therefore corresponds to transforming from the toroidalview to the lattice view.Molecular dynamics (MD)simulations are performed by numericallysolving the classical equations of motion for every particle in agiven system. For systems in the condensed phase, such as proteinsin water, these simulations are usually conducted in volumes of finitesize subject to periodic boundary conditions (PBCs). In constant-volumesimulations, one can think of the periodic system either as a singlebox in which opposite faces are identified under what are also referredto as toroidal boundary conditions, or as an infinite periodic latticeof replicates of the central simulation box. In the 1 In the lattice view of PBCs, the periodic latticeis now fluctuating. Importantly, the motion of particles purely asa result of the barostat action depends on their distance from thecentral simulation box and is thus unbounded (see In constant-pressure (NPT) simulations,however, the task of unwrappingbecomes somewhat ambiguous, because the barostat constantly modifiesthe size and shape of the simulation box to keep the average pressurefixed. The positions of the particles within the box thereby get rescaled.nded see 1. By con2 preserves the statistical properties of the wrapped trajectoryand should therefore be preferred for the calculation of translationaldiffusion coefficients. However, because the scheme does not adhereto the lattice view, it does not preserve distances.3 Molecules should thus first be made “whole”and then unwrapped, e.g., according to their center of mass. We concludeby giving guidance to practitioners on how to extract reliable diffusioncoefficient estimates from constant-pressure MD simulations , which in one dimension(1D) can be cast into the following form:wi denotes thewrapped position of a particle inside the simulationbox of width Li at integrationstep i corresponding to time ti, uiHLAT is the correspondingunwrapped position predicted by the HLAT scheme ))trjconv . In ref , however2.223 Therefore,molecules should first be made “whole” and then unwrapped.After exposingthe shortcomings of the HLAT scheme, three of theauthors of the present paper proposed an alternative unwrapping scheme,which resolves the issues of D in terms of the autocorrelation function of the velocity v(t), which in one dimension leads to theGreen–Kubo relation6D = lim+ϵ→0∫0∞dt exp(−ϵt)⟨v(t)v(0)⟩. Fromthis expression, one obtains the Einstein relation D = limt→∞⟨[u(t)–u(0)]2⟩/(2t) by writing the position u(t) as a sum of infinitesimal displacements, u(t) = u(0) + ∫0tdt′v(t′).In analogy, the TOR scheme (u(t).We note that the TOR scheme 2 appealsR scheme 2 adds up2.37 software package. To ourknowledge, this scheme was never explicitly documented in the literatureprior to implementation, but the LAMMPS simulation software8 uses it to write out unwrapped coordinates.An alternative to the HLAT scheme, which takes a lattice view ofPBCs without succumbing to the known shortcomings of HLAT, is implementedin the qwrapni that indicate how many periodic images the currentwrapped coordinates are away from the original, unwrapped particle.The image number ni canbe obtained either by explicit bookkeeping of image changes due towrapping (as done by the remap function ofLAMMPS), or by detecting large jumps in the wrapped coordinates (asdone by the qunwrap feature of qwrap). In bothcases, the unwrapped coordinate can be obtained as a lattice imageof its wrapped counterpart, i.e.,9In the lattice view, crossing the periodic boundaries correspondsto shifting the identity of the particle in the central box to oneof its lattice images. The LAT unwrapping scheme keeps track of theseshifts using integer image numbers 3 proposeda correction to the TOR scheme with the aim to preserve the underlyinglattice structure. Their scheme takes the following form in 1D:Recently,Kulke and VermaasIn what follows, we restrict ourdiscussion to the comparison ofthe TOR and LAT schemes, as the HLAT scheme has already been establishedas faulty.3Here, wedescribe a minimal stochastic model of a diffusive particleinside a fluctuating box with PBCs, which we use to generate numericaldata and to highlight the differences between the unwrapping schemesvia analytic calculations. We also develop and identify appropriate(re)wrapping schemes for the TOR and LAT schemes, respectively. Finally,we derive an upper bound for the frequency with which particle coordinatesshould be sampled to make sure that all boundary crossings are accountedfor.3.1w that evolves between two periodic boundaries, located at ± Li/2 at time integration step i, which are themselves modeled as Gaussian white noise.Due to box length fluctuations, the value of the process gets rescaledin each time step, after which a diffusive displacement is performed.The model gives rise to the following wrapped trajectory:L is the average length of the 1D simulationbox, and σw and σL determine the noise amplitudes of the random processesdriving particle diffusion and box fluctuations, respectively.The 1D Gaussianmodel was introduced in ref  and provw of L ≪ L, where wehave w and u distinctivelydifferent from an ordinary Wiener process. Yet, because the noiseamplitude is only proportional to wi (and not ui),it remains bounded and does not overshadow the diffusive process.In the absence of wrapping events, the displacements resulting frombox rescaling and diffusion would give rise to a trajectory of thefollowing form:3.2wRi+1 ≪ Li+1 and |Li+1 – Li| < Li+1/2, whichare reasonable assumptions to make for MD simulations when the samplinginterval is sufficiently small. We therefore obtain Unwrapping the wrapped trajectory of Li+1/Li – 1) uiLAT that scales with theunwrapped coordinate. Its magnitude therefore grows without boundsas the particle diffuses away from the origin. The unbounded multiplicativenoise in the LAT scheme causes pathological particle dynamics, whichbecomes apparent when the LAT scheme is used to unwrap trajectoriesfrom Brownian dynamics (BD) and MD simulations, as demonstrated belowin By contrast,the LAT scheme evaluates to3.33 further claimed thatthe TOR scheme cannot be reversible, because a subsequent wrappingof uTOR using “conventional wrappingschemes” does not reproduce the wrapped trajectory w. While the authors did not explicitly specify which wrappingschemes they were referring to, we expect a lattice-view scheme, whichin 1D readsLi]  then α = 0, whereasfor cells fluctuating symmetrically around the origin, i.e., , one has α = 1 (this is the conventionthat LAMMPS8 and NAMD10 adhere to). The scheme in i the wrapped and unwrapped trajectories are identical upto an integer number of box lengths Li, consistent with the lattice view of n = wiLAT – uiLAT)/Li + 1/2uTOR.Besidescriticizing the undesired effect of intramolecular bond stretching,Kulke and Vermaasui+1TOR – uiTOR to reconstruct the wrapped trajectory inan iterative manner as follows:wiTOR + (ui+1TOR – uiTOR) crosses the periodicboundaries, it gets shifted backinto the central box with the help of the last term. Substituting To constructa (re)wrapping scheme consistent with the TOR unwrapping scheme, webacktrace the displacements 3.4wRi+1 ≪ Li+1 must hold, and argued for its validity for MD simulationsat sufficiently small sampling intervals Δt. Very roughly, for a particle with mass m and diffusioncoefficient D we require DΔt ≪ L2 and Δt2 ≪ βmL2 inthe regimes dominated by diffusion and inertia, respectively. Here,β–1 = kBT denotes the thermal energy scale, kB is the Boltzmann constant and T is the absolutetemperature. To obtain a quantitative estimate of an upper bound forΔt, we consider the probability P for one or more of the N particles in the simulationbox to travel a distance greater than L/2 within Δt along any of the threeCartesian coordinates, resulting in an incorrect unwrapping eventin at least one of the ttotal/Δt sampled frames, i.e.,ttotal isthe total simulation time and Pr(X > L/2) denotes the probability for a singleparticlein 1D to move either ballistically or diffusively in the time intervalΔt by more than L/2 in either direction. We can estimate this probabilityas follows: t, the probabilities P and Pr(X > L/2) are also small, which allows usto reduce P ≈ 3 NPr(X > L/2) ttotal/Δt and replace erfc(·) with its asymptoticexpansion for large arguments. Setting P = ε ≪ 1 results in the expressiont can be chosen for a specificMD simulation setup without skewing the resulting unwrapped trajectorydue to particles crossing the periodic boundaries.In t in the ballistic (σ2 = Δt2/βm) and diffusive limit (σ2 = 2DΔt) gives therequirementsW–1(·) denotes the lower branch of the Lambert W function, which can be expanded for small arguments togive W–1(z →0–) ∼ – ln(−1/z) – ln(ln(−1/z)) – ln (ln(−1/z))/ln(−1/z).11 For ε = 10–2 and N ≈ 33.3 nm–3L3 TIP3P water molecules with D ≈ 6 nm2 ns–112 and m ≈ 18 g mol–1 at T = 300 K, tballistic ≈ 0.48 ps, 0.94ps, 1.4 ps and Δtdiffusive ≈2.9 ps, 11 ps, 25 ps for cubic simulation boxes with edge lengths L = 2.5 nm, 5 nm, and 7.5 nm, respectively.For water at ambient conditions,2 one cansafely use the Δtdiffusive boundfor times Δt ≥ 1 ps.Solving 44.113 in a cubic boxwith an average edge length of L ≈ 2.5 nm, which was previously reported on in ref and the Parrinello–Rahman barostat17 (τp = 5 ps), respectively. Particlecoordinates were sampled every Δt = 1 ps. Forthe sake of comparison, we also considered a 1 μs constant-volumesimulation of the system described above, which was equilibrated andrun in an identical manner.2We made use of a 1 μs constant-pressure simulation of 515TIP4P-D water molecules4.218 at ambient conditionsusing the LAMMPS package stable release from September 29, 2021 (update3).19 The simulation was performed at constantpressure in a cubic box with an average edge length of L ≈ 2.5 nm. The SHAKE algorithm20 was used to constrain the intramolecular bondsand angles at an accuracy tolerance of 10–4. Theparticle-particle particle-mesh solver21 with a relative force error accuracy of 10–4 wasused to compute long-range Coulombic interactions, where the cutoffdistance in real space was set to 9.8 Å. Equilibration consistedof a 15 ns run in the NVT ensemble, followed by a 20 ns run in theNPT ensemble. Temperature and pressure were maintained at 300 K and1 bar using the Nosé–Hoover thermostat and barostat23 with damping coefficients of 100 and 1000 fs, respectively. The1 μs production run in the NPT ensemble was performed usingthe same thermostat and barostat coefficients, and a 1 fs integrationtime step. Particle coordinates of the wrapped and unwrapped trajectorywere sampled every Δt = 1 ps via the dump command.We generateda set of wrapped and unwrapped trajectories of 511SPC/E water molecules4.324 at ambient conditionsin a cubic periodic boxwith L ≈ 2.9 nm, usingNAMD version 3.10 A time step of 2 fs wasused. Temperature was maintained at 300 K using underdamped Langevindynamics with a damping time of 1 ps. Pressure was set to 1 bar usingthe Nosé–Hoover Langevin piston method as implementedin NAMD,25 with a piston period of 200fs and a decay time of 100 fs. Water molecules were kept rigid usingthe SETTLE algorithm.15 Long-range electrostaticinteractions were computed using the Particle-Mesh Ewald method, witha 12 Å cutoff for the real-space part. The same cutoff was appliedto Lennard-Jones potentials, with force-switching for a continuousdecay of the force to zero. Particle coordinates were sampled everyΔt = 1 ps for 900 ns in total, this slightlyshorter duration being the result of numerical instability  with L = 0.1L and σw = 0.05L .Toverify the analytic predictions of uLAT associated with the LAT scheme exhibits the same position-dependentfluctuations that can be found in u*  wrapped trajectory w⃗ = T. Theunwrapped trajectories u⃗TOR and u⃗LAT were generated by unwrapping eachcomponent of w⃗ separately using the TOR andLAT schemes, respectively. As shown, the apparent noise in the u⃗LAT trajectory not only grows with distancefrom the central simulation box but also becomes anisotropic. Supporting Movie S1 visualizes the evolutionof the trajectories and the fluctuations of the simulation box.The nondiffusivity of w when appliedto uTOR. Similarly, we find that uLAT back into the simulation box. It is thereforeunsurprising that Kulke and Vermaas3 onlyfound their own unwrapping scheme to be reversible with respect to“conventional wrapping schemes”  for the diffusion coefficient D, which accounts for the fact that a d-dimensional diffusive process X⃗(t) can be corrupted by static noise and dynamic motion blur,resulting in the following mean squared displacement (MSD):B is zeroand the vertical intercept a2 accountsfor nondiffusive dynamics at short times.27 Note that the MLE does not rely explicitly on estimates for theMSD, but instead exploits the statistics of the increments X⃗(ti+1) – X⃗(ti). We segmented our unwrapped oxygen trajectoriesfor TIP4P-D water into 1 ns blocks and extracted for each block (withindex i) estimates for the static noise ai2 and the diffusion coefficient Di. i, whereas the estimates for the LAT schemevary strongly with i and tend toward larger valuesat later times in the trajectory. This behavior is to be expectedas the diffusive spread of the water molecules moves them furtheraway from the central simulation box, where artifacts become morepronounced in trajectories associated with the LAT unwrapping scheme.To quantify the effect that boxfluctuations have on unwrappedtrajectories, we analyzed the diffusive behavior observed in differenttrajectory segments. We made use of a maximum likelihood estimatort = 1 pstime step. Consistent with the analysis of DTOR = 2.0602(2) nm2 ns–1 and DLAT = 4.64(3) nm2 ns–1 byapplying the MLE to the full 1 μs trajectory of each oxygenatom and then average over all water molecules, without correctingfor finite-size effects.28 By comparison, we obtainedthe global mean estimate D =2.0517(2) nm2 ns–1 for the correspondingNVT simulation  were estimated by assuming that the diffusion processesof individual water molecules were uncorrelated. Importantly, we expectthe discrepancy between DTOR and DLAT to grow if the MD simulations are extended beyond the 1 μsused here, because D estimates in It should be noted that our results imply a significantdifferencebetween global diffusion coefficient estimates obtained for the TORscheme and the LAT scheme with a Δ5.3trjconv or third-partysoftware, such as the PBCTools29 and qwrap7 plugins for VMD.30 Other MD simulation codes write out unwrapped trajectories directly,either by default or via user-specified settings, but this raisesthe question which unwrapping scheme these trajectories correspondto. We therefore analyzed simulation trajectories for SPC/E and TIP3Pwater generated via the software packages LAMMPS and NAMD, respectively nm2 ns–1 for SPC/E waterin the LAMMPS simulation, whereas early and late blocks give valuesaround 2.7 nm2 ns–1 and 4 nm2 ns–1, respectively [see DNAMD = 6.50(2) nm2 ns–1, with early andlate blocks around 5 nm2 ns–1 and 7 nm2 ns–1, respectively [see DTOR = 2.7078(2)nm2 ns–1 obtained after TOR unwrappingof the wrapped LAMMPS trajectory is consistent with the respectiveblock estimates, as is DTOR = 5.0132(3) nm2 ns–1 obtainedfor the NAMD trajectory. Note that we did not correct for system-sizeeffects on the self-diffusion coefficients.28We find that the diffusion coefficientscalculated directly fromthe unwrapped trajectories steadily diverge to ever larger valuesas a function of time. By contrast, the wrapped trajectories, whichwere unwrapped using the TOR scheme, produce robust diffusion coefficientestimates. The behavior in wrapAll or wrapWater options, resulting in all coordinates or specifically water moleculesbeing wrapped at every restart.The NAMD simulation became numerically unstable as particlecoordinatesand their barostat-induced fluctuations became large. While such asmall box with less than 1000 water molecules can be seen as an extremeexample, this phenomenon highlights a benefit of propagating wrappedcoordinates internally during the simulation, which is to make thebest use of limited floating-point precision, especially in mixed-precisionGPU software. In NAMD this behavior can be approached by enablingthe 5.4D estimates were calculatedfrom ordinary least-squares (OLS) fits of straight lines to the MSD.The fit region is usually chosen “by eye” to cover awindow in which the MSD grows more or less linearly with time. Consideringthe fact that, to a rough approximation, LAT trajectories make everlarger jumps about TOR trajectories, it is conceivable that simple D estimates obtained from OLS fits to the MSD are less impactedby LAT unwrapping than the more sophisticated MLE used in the analysisabove.To assessthe possible impact of LAT unwrapping on diffusion coefficients obtainedfrom NPT simulations in earlier studies, it is important to recognizethat the vast majority of mΔt for the TIP4P-D water data analyzed in N = 106 datapoints for a time step of Δt = 1 ps. The MSDobtained from the LAT unwrapped trajectories oscillates at short lagtimes and then approaches a straight line. Halving the simulationtime to 500 ns reduces the magnitude of the oscillations at shorttimes, consistent with the observation that the amplitude of oscillationsin the LAT unwrapped trajectories tends to increase with their duration(DTOR and DLAT in ref (27 (GLS) and a covariance-based estimator31 (CVE). The resulting estimates of the diffusioncoefficient of TIP4P-D water (without correcting for system-size effects28) are listed in t = 1 ps. This wasdiscovered and extensively discussed in ref  and Y⃗(t), isalso diffusive with the following diffusion coefficient:DZ⃗ denotes the diffusion coefficientof the process Z⃗(t).Finally, one mightspeculate whether the nonpreservation of distances in the TOR unwrappingscheme affects other observables that rely on unwrapping, such aspair diffusion coefficients. According to theory, the distance vector X⃗, Y⃗, and X⃗ – Y⃗, as described in To test whether pair diffusion is preservedfor the TOR scheme, the LAT scheme, or both, we considered two randomlyselected TIP4P-D water molecules from the GROMACS MD simulation andanalyzed the diffusive behavior of A special case of restricted pair diffusion isthe end-to-end relaxationof long (bio)polymers. Any motions that extend over the scale of thebox will require care in unwrapping of PBCs. For polymer end-to-endrelaxations and similar properties, one should first make the molecule“whole” across PBCs using the instantaneous box sizeand then calculate the relaxation dynamics of, say, the end-to-enddistance.62 Another7 takes a lattice view of the PBCs and tracesthe trajectory through the fluctuating lattice of image particles.As a consequence of the fluctuations in box size and shape, and theassociated fluctuations in the lattice parameters, the two approachesproduce different unwrapped trajectories. We have shown here thatthe toroidal approach embodied in the TOR algorithm2 sacrifices the preservation of interparticle distancesto preserve the statistical properties of the wrapped trajectory.In particular, a trajectory created by a diffusion process retainsits diffusive character. By contrast, the lattice view taken in theLAT algorithm3 preserves distances betweenparticles, but distorts the statistical properties of local dynamicsand thus destroys the diffusive character of a wrapped diffusion trajectory.Unwrappingtrajectories of constant-pressure MD simulations isa nontrivial task. One school of thought takes a toroidal view ofthe PBCs to construct an unwrapped trajectory by adding up minimaldisplacement vectors at each time step.Our analytic calculations 3.2, as wA surprising conclusion is that the“unwrapped” trajectorieswritten out by MD simulation software like NAMD and LAMMPS for NPTsimulations should not be used to calculate diffusion coefficients5.3. TheIn light of the fact that particle dynamicsin constant-pressuresimulations is always affected by a (bounded) barostat-induced multiplicativenoise, even in the wrapped trajectory, one might be tempted to constructa postprocessing scheme to remove this noise altogether. However,such sanitation is highly nontrivial and its advantage over performingsimulations at constant volume is not evident. For this reason, weinstead take a toroidal view of the PBCs and treat the wrapped particledynamics as the “true” dynamics corresponding to thegiven simulation ensemble, despite the presence of multiplicativenoise. If the multiplicative noise associated with barostat positionrescaling is considered an issue, we recommend constant-volume simulationsinstead of the complex and somewhat arbitrary postprocessing of trajectoriesgenerated at constant pressure.Reassuringly, we expect publishedstudies of diffusion coefficientsto be minimally affected by the choice of unwrapping scheme. For one,early simulations tended to be short, making diffusion far beyondthe central box and thus unwrapping artifacts rare, in particularfor larger molecules. In addition, diffusion coefficients were usuallyestimated by least-squares fitting to the MSD, which we found to bequite robust at sufficiently long times 5.4.V with system size, namely β⟨(V –⟨V⟩)2 ⟩ = χT⟨V ⟩, whereχT denotes the isothermal compressibility.32Although current MD simulationsof large biological molecules areonly minimally affected by the shortcomings of the LAT scheme reportedhere, we expect our findings to become crucial for the proper analysisof future simulation trajectories on the time scales of millisecondsand beyond. For NPT simulations, we recommend the use of large boxes,for which the time to diffuse over multiple box dimensions is largeand the position rescaling effects are small. The latter follows fromthe decay in the relative fluctuations of the box volume 34 An added advantage of workingat constant volume is that the box size and shape entering the largefinite-size corrections of translational diffusion coefficients28 are well defined, whereas for NPT conditions one usually resortsto averages.For precision calculations of diffusioncoefficients and relatedquantities, one may want to resort to NVT simulations. The choiceof an NVT ensemble is advisable in particular for long simulationswith small boxes of highly compressible systems with low viscosity,where the relative box-size fluctuations are large and particles candiffuse over many box widths. At constant volume, the lattice andtoroidal view of PBCs coincide and unwrapping is unambiguous. If needed,the results from NVT simulations at different volumes can be interpolatedto the targeted pressure or rigorously combined into weighted samplesof an NPT ensemble.


The quadrupolar excitons exhibit a quadratic dependence on the electric field, distinctively different from the linear Stark shift of the dipolar excitons in heterobilayers. This quadrupolar exciton stems from the hybridization of WSe2 valence moiré flatbands. The same mechanism also gives rise to an interlayer Mott insulator state, in which the two WSe2 layers share one hole laterally confined in one moiré unit cell. In contrast, the hole occupation probability in each layer can be continuously tuned via an out-of-plane electric field, reaching 100% in the top or bottom WSe2 under a large electric field, accompanying the transition from quadrupolar excitons to dipolar excitons. Our work demonstrates a trilayer moiré system as a new exciting playground for realizing novel correlated states and engineering quantum phase transitions.Transition metal dichalcogenide (TMDC) moiré superlattices, owing to the moiré flatbands and strong correlation, can host periodic electron crystals and fascinating correlated physics. The TMDC heterojunctions in the type-II alignment also enable long-lived interlayer excitons that are promising for correlated bosonic states, while the interaction is dictated by the asymmetry of the heterojunction. Here we demonstrate a new excitonic state, quadrupolar exciton, in a symmetric WSe 2-WS2-WSe2 trilayer moiré superlattice, originating from the hybridization of the WSe2 valence moiré flatbands. They further use electrostatic gating to reveal a hybridized interlayer Mott insulator state, with holes shared between the two WSe2 layers but laterally confined in moiré superlattices.The authors observe the signatures of quadrupolar excitons in a WSe For example, TMDC heterojunctions in a type-II alignment host long-lived interlayer excitons6, with electrons and holes residing in different layers4. These interlayer excitons possess the valley degree of freedom, as well as a large Stark shift due to the permanent dipole moment, rendering them promising candidates as tunable quantum emitters6. Recently, angle-aligned TMDC moiré superlattices exhibit strong Coulomb interactions in the electronic flatbands, leading to correlated states19 such as Mott insulator and generalized Wigner crystal17. The moiré coupling also gives rise to flat excitonic bands23 that could potentially be utilized to realize correlated bosonic states24, such as Bose-Einstein condensation (BEC) and superfluidity27. The interaction between interlayer excitons is dominated by the repulsive force between their permanent dipoles, whose alignment is dictated by the asymmetry of the heterostructure, with electrons and holes separated in two different layers.Monolayer TMDCs, as atomically thin direct bandgap semiconductors, offer a unique playground to explore novel optoelectronic phenomena2/WS2/WSe2 trilayer. The interlayer excitons in the top and bottom bilayers have opposite polarities, which restores the symmetry. Their hybridization then forms a superposition state of interlayer excitons, canceling the dipolar moments and giving rise to a quadrupolar exciton, which has been predicted to enable intriguing quantum phase transition30. In the presence of moiré coupling, this hybridization further gives rise to a new type of correlated electronic state, hybridized interlayer Mott insulator, in which the correlated holes are shared between the two WSe2 layers, and the layer population can be continuously tuned by an electric field.In this work, we report a new interlayer quadrupolar exciton in a symmetric TMDC heterostructure: angle-aligned WSe2 over the bottom WSe2, which we denote as WS2/b-WSe2; (II) top WSe2 over WS2 (t-WSe2/WS2); and (III) the t-WSe2/WS2/b-WSe2 trilayer. The whole device is gated by the top and bottom gate electrodes made of few-layer graphene (FLG), which provides independent control of the electric field and doping.The typical device structure is schematically shown in Fig. 2/WS2 moiré superlattices host both correlated electrons and interlayer excitons due to the type-II band alignment  spectra in these regions .In the trilayer region III, we expect quadrupolar excitons as schematically plotted in Fig. 2/b-WSe2 (region I) and 0.66 2/WS2 (region II), consistent with the previous results39. In contrast, the PL from the trilayer region III is symmetric about the electric field, and the resonance energy exhibits a quadratic dependence on the electric field, as shown in Fig. 2/MoSe2/WSe2)29. We have also reproduced similar quadrupolar exciton behaviors in other angle-aligned WSe2/WS2/WSe2 devices, which show a 29) is missing in Fig. 40 of the quadrupolar exciton, which leads to the absence of PL.The quadrupole nature of the excitons in the trilayer region is confirmed by the electric field-dependent PL spectra. In regions I Fig.  and II , the intentclass1pt{minimaThe quadrupolar excitons show distinctively different power dependence compared with that from dipolar excitons, as shown in Fig. Snt and nb, respectively, and the total filling factor n = nt + nb. We focus on the low energy mode of the trilayer quadrupolar exciton and observe two main features in its PL spectra, at n = −1 and n = −2, respectively. At n = −1, the PL peak energy exhibits a kink , the same as those in the moiré bilayer regions I and II. However, since the trilayer consists of two moiré superlattices, both of which can be filled with carriers, we define their individual filling factors as ink Fig. , and theink Fig. . At n = 2 layers will be different due to carrier populations and layer chemical potentials . Therefore, the observed change in the PL spectra signals the transition from a quadrupolar exciton to a dipolar exciton. Similar results were reproduced in another device with the same structure (device D3), as shown in Supplementary Information Section The behaviors at these two fillings evolve systematically as a function of the external electric field. Since the device structure is symmetric, the observed PL behaviors are also symmetric with respect to the electric field direction. Figure n = −1 and −2 states and their evolution under electric fields. Figure n = −1, the PL energy and intensity both change abruptly above a certain threshold external electric field n = −2, the PL blueshift disappears when the external electric field exceeds n = −1 state, in the absence of an external electric field, each hole is hybridized between the top and bottom WSe2 layers with equal probability, i.e., the hole wavefunction is a superposition of the top and bottom WSe2 valence moiré bands. Laterally it is confined such that there is one hole in the two overlapping moiré unit cells combined , leaving the top WSe2 layer empty (nt = 0). This state now becomes a Mott insulator in the WS2/b-WSe2 interface only, similar to that in a WS2/WSe2 moiré bilayer. The system should remain insulating, as seen in the behavior of the PL peak energy in Fig. 2 layers. Based on the threshold electric field, we estimate the overall potential difference between the two WSe2 layers is about 0 meV at the transition, which suggests that With the understanding of the quadrupolar to dipolar exciton transition, we now discuss the nature of the ned Fig. . This stn = −2, the transition is different. Initially, at zero field, there is one hole per moiré unit cell in each of the two WSe2 layers, forming two separate Mott insulator states at both t-WSe2/WS2 and WS2/b-WSe2 interfaces  will remain stable until the UHB of the top WSe2 layer starts to overlap with the lower Hubbard band (LHB) of the bottom WSe2 layer  and n = −2 (Mott insulator). In particular, the quadrupolar excitons and interlayer Mott insulator both originate from the valence band hybridization and interact with each other. Here, the flat valence band hybridization, combined with the large spin-orbit coupling, is promising for generating nontrivial topological states and engineering quantum states such as quantum anomalous Hall43. The quadrupolar excitons in this unique trilayer moiré system are not only promising for realizing the quantum phase transition of bosonic quasiparticles but also strongly interact with correlated electrons, setting up an exciting platform for engineering new correlated physics of fermions, bosons, and a mixture of both44. We also envision that further development in aligning the moiré trilayer to allow different stacking of moiré sites (high symmetry points45) such as AAA, ABA, or ABC will usher in unprecedented opportunities in electronic and excitonic band engineering.In summary, our study demonstrates a unique trilayer moiré system that hosts both quadrupolar excitons and correlated states at 46, ref. 47, and reference 29 in ref. 47).Note: During the submission of this work, we became aware of other works on quadrupolar excitons  flakes are exfoliated on silicon chips with 285 nm thermal oxide. It is worth noting that typical large TMDC flakes with one dimension exceeding 50 µm were chosen for the device structure shown in Fig. 2 and bottom WSe2 are aligned with a 0-twist angle (R-stacked configuration). This is achieved either through angle-aligned layer stacking and checking the second harmonic generation (SHG) afterward or using the same WSe2 flake and splitting it into two pieces via the tear and twist technique. The alignment of each layer is achieved under a home-built microscope transfer stage with the rotation controlled with an accuracy of 0.02 degrees. The PC is then removed in the chloroform/isopropanol sequence and dried with nitrogen gas. The final constructed devices were annealed in a vacuum (<10−6 torr) at 250 oC for 8 h.We used the same dry pick-up method as reported in our earlier workDuring the optical measurements, the sample was kept in a cryogen-free optical cryostat (Montana Instruments). A home-built confocal imaging system was used to focus the laser onto the sample (with a beam spot diameter of ~2 µm) and collect the optical signal into a spectrometer (Princeton Instruments). During the measurements, the samples were kept in a vacuum and cooled down to 6−10 K. The PL measurements in Figs. The external electric field is defined as The electric field in Fig. Supplementary InformationPeer Review File


As OMP is a methane source in direct contact with the atmosphere, a better understanding of its extent and drivers is necessary to constrain the atmospheric methane contribution by inland waters.Contrasting the paradigm that methane is only produced in anoxic conditions, recent discoveries show that oxic methane production  occurs in oxygenated surface waters worldwide. OMP drivers and their contribution to global methane emissions, however, are not well constrained. In four adjacent pre-alpine lakes, we determine the net methane production rates in oxic surface waters using two mass balance approaches, accounting for methane sources and sinks. We find that OMP occurs in three out of four studied lakes, often as the dominant source of diffusive methane emissions. Correlations of net methane production versus chlorophyll- Methane production was thought to be an exclusively anaerobic process. This study shows that methane production occurs in oxygenated surface waters of four pre-alpine lakes and is often the main contributor to their methane emissions Methane production in oxic conditions  has been reported for an increasing number of lakes8. While recent studies have shown that OMP may have contributed up to 80% of lake-diffusive CH4 emissions8, other researchers suggest that CH4 produced in anoxic littoral sediments is enough to resolve the CH4 paradox12. Thus, the drivers and OMP contribution to global lake CH4 emissions remain unclear.The widely reported methane , the global warming potential (GWP) of CH4 is ~80 times higher than CO2 over a 20-year period14. Its GWP combined with its ~12-year lifetime means that reducing CH4 emissions is a priority for mitigating climate change15. Lakes represent ~25% of natural CH4 atmospheric sources, but large uncertainties remain about the contribution of internal sources and sinks18. Methane in lakes can be emitted to the atmosphere through bubbles (ebullition) and diffusive fluxes at the air-water interface (AWI)17. Ebullition is driven by high CH4 production rates in anoxic sediments19 and the diffusive fluxes at the AWI are driven by CH4 concentrations and turbulence in surface waters20. As OMP occurs in surface waters, the CH4 can be quickly emitted to the atmosphere2.Atmospheric CH23, however, recent studies have shown correlations between CH4, oxygen, and phytoplankton concentrations6, suggesting a direct role of phytoplankton in OMP25. Although the mechanisms remain unclear, OMP has been shown to follow light-dark cycles in different phytoplankton cultures25. It is likely that multiple pathways produce CH4 in oxic lake environments, and that these may vary from lake-to-lake and seasonally based on trophic properties and light conditions.Several mechanisms have been proposed for OMP25, in-lake mesocosms8, a physical lateral transport model26, and lake mass balances8. OMP has also been reported from different freshwater environments, including both temperate27 and polar regions28, high altitude lakes (above 2500 m.a.s.l)29, tropical latitude lakes12, and across a range of trophic states30. While these studies show the occurrence of OMP in lakes across geographic and trophic gradients, OMP has not been investigated in pre-alpine lakes.OMP rates have been reported using different methodologies, such as laboratory and in-situ water incubations4 sources31 and, with air temperature increasing two times faster in the European Alps than the global mean32, these lakes are disproportionately experiencing climate change34. Such an increase in air temperature can induce limnological change in pre-alpine lakes with implications for aquatic CH4 emissions35 such as: (1) a longer ice-free season that allows CH4 to be emitted for a longer period36; (2) an increase in surface water temperature that enhances littoral production rates of CH437; and (3) a longer stratified season that allows for more CH4 accumulation in the hypolimnion38. These impacts will differ across lakes depending on the light regime and trophic state39; therefore, the precise impact of climate change on the CH4 budget in pre-alpine lakes needs further investigation.Pre-alpine lakes (from 1300 to 2000 m.a.s.l) are atmospheric CH4 production rate  and CH4 oxidation  in the surface mixed layer (SML)40. Pnet in the SML was estimated using two independent mass balance approaches: a 0-D full-scale mass balance following Donis et al.7 and a 1-D lateral transport model adapted from Peeters et al.9. In the latter, we included two additional terms—diffusive CH4 flux across the thermocline and CH4 bubble dissolution , but would be required to calculate OMP. Here, we determine Pnet (Pnet = OMP − MOx) as this is the component that contributes to the diffusive emissions.This study focuses on four adjacent Swiss pre-alpine lakes under identical climate forcing but with different trophic states. The net CH42. Instead, we used direct flux measurements from floating chambers and found the two models agree well with each other (R2 = 0.97). The results indicate that Pnet contributes between 30 and 90% to diffusive emissions during the stratified period of pre-alpine lakes with different trophic states. Moreover, we performed a sensitivity analysis using five diffusive flux literature parameterizations and surface flux measurements to analyze the impact that modeled versus measured atmospheric diffusive fluxes have on Pnet estimation. Finally, we present a Pnet upscaling approach based on chlorophyll-a concentrations (Chla), light penetration, and SML depth. Ultimately, our findings highlight the need for Pnet to be included in CH4 lake budgets and for more research to understand OMP(Pnet) drivers and its response to climate change.In previous studies, the two models have shown contradictory results mainly due to the use of literature parameterizations to estimate surface diffusive emissions4 , nutrients and Chla concentrations reflect the trophic gradient of the study lakes , Lac Noir (NOI), Lac des Chavonnes (CHA), and Lac Lioson (LIO)—are located between 1650 to 1850 m.a.s.l in the Swiss Alps and are eutrophic, meso/eutrophic, mesotrophic and oligotrophic, respectively , although only 40% of the time this difference was significant (Table −3) than the oligo/mesotrophic lakes LIO and CHA (0.15 ± 0.13 mmol m−3)  at the air-water interface (AWI) were measured in each lake using a floating chamber44 at the deepest point of the lake and along the transects. Average surface fluxes measured in the eutrophic lakes  were an order of magnitude higher than in the oligotrophic lakes . Surface diffusive fluxes of CH4 remained relatively similar between sampling dates in each lake (Table Diffusive CHk600) used along with CH4 concentrations to estimate atmospheric diffusive emissions (Klaus & Vachon45 and references therein). We compared CH4 mass transfer coefficients based on our chamber flux data , MA10-MB (mixed buoyancy), and MA10-PB (positive buoyancy) based on MacIntyre et al.20; and VP13 based on Vachon & Prairie47  in the littoral zone (Fs) were estimated using benthic chambers and porewater measurements of dissolved CH4 , followed by NOI (eutrophic), CHA (mesotrophic) and LIO (oligotrophic) with the lowest value (0.3 ± 0.1 mmol m−2 d−1)  were obtained using a discrete bubble model48 (Methods). The spatially averaged ebullitive fluxes (Feb) for BRE and NOI , resulted in bubble dissolution rates between 17 and 51 μmol m−3 d−1 (Table CHFz) is determined with Fick’s 1st Law using the turbulent vertical diffusivity (Kz) and concentration gradients at the base of the epilimnion. Kz values at the top of the thermocline ranged between 0.03 and 14.4 × 10−6 m2 s−1 , except in BRE and NOI at the end of the summer when fluxes were 13.3 and 3.1 mmol m−2 d−1, respectively.The vertical transport from/to the epiliminion (KH) for each lake using Peeters & Hofmann49 parametrization (Methods). Water level fluctuations were minimal in BRE, NOI, and LOI (± 1 m). In CHA, the highest water level was observed at the beginning of summer after ice-off and slowly decreased during the summer by about 4 m  and thus KH , which adds and removes CH4 to the SML, respectively. Thus, when Pnet is positive the true OMP rate is actually higher than Pnet.The full-scale mass balance (0-D) proposed by Donis et al.7 (Eq. ) and a m (9 (Eq. ) were usPnet rates calculated with both models under steady-state conditions correlated well with each other . Monte Carlo simulations were applied to assess uncertainties using all sources and sinks in both models during the stratified period (Methods). The average Pnet rates for the three sampling dates were 305, 1504, 22, and 246 μmol m−3 d−1 for BRE, NOI, CHA, and LIO, respectively  were about seven times higher than in the oligotrophic lakes (CHA and LIO). A decrease of Pnet rates from the beginning to the end of the summer was observed in NOI and BRE, whereas in CHA and LIO Pnet remained relatively consistent across campaigns.Despite the different modeling approaches and underlying assumptions, the k600 literature parameterizations to estimate Fa , although other studies have shown that these estimates often do not correspond with field measurements , or without any addition from Pnet . We also used five different mass transfer coefficient parameterizations (k600) to model diffusive CH4 emissions to the atmosphere in the lateral transport model  when compared with chamber-based estimations for CH4 (Since the del (Eq. ), we simel Table . Thus, tzations k00 to mod4 concentrations was found using Pnet from the full-scale mass balance  and Pnet-Pnet set to zero  resulted in an overestimation of CH4 concentrations (Table Pnet was set to zero (Pnet0-MA10-NB and Pnet0-CC98) with those k600 parameterizations, the average CH4 concentrations along the transect were underestimated  and Pnet were the two major sources of CH4 in the SML. Using the results obtained from the full-scale mass balance we found that Pnet contributed ~30% of the CH4 emissions in BRE and CHA, while it reached up to 60% and 90% for NOI and LIO, respectively  were found in all lakes in September 2019, except for LIO (91%). On average, Fs contributed about 10, 30, 50, and 65% to the CH4 emissions in LIO, NOI, BRE, and CHA, respectively. For CHA and NOI, the Fs contribution increased at the end of the summer and reached up to 90% for CHA in September. For BRE and LIO, the Fs contribution remains relatively constant during the different months. On average, Fs contributed about the same in the oligotrophic and eutrophic lakes. The vertical turbulent flux (Fz) contributed about 50% of the atmospheric CH4 emission from BRE and NOI in September and about 30% from CHA in July, but was negligible (<9%) for the other campaigns. The contribution from bubble dissolution (Rdis) was negligible (<4%) in BRE and NOI and absent in CHA and LIO.The sediment flux .In most of our study lakes, the son Fig. . Pnet waPnet rates were temporally variable in each lake and varied between study sites. While Pnet and Pnet rates at the beginning of the summer indicated that OMP was an active source of CH4 to the atmosphere in the eutrophic lakes. By the end of the stratified season, Pnet became negative indicating that MOx was dominating, which was corroborated by isotopically enriched CH4 , suggesting that Pnet may also be related to trophic state. From this perspective, productive lakes in general may experience higher Pnet rates than less productive ones.mentclass2pt{minim4 to the surface waters of our lakes were Pnet and Fs, although individual rates of these sources varied across campaigns. Despite eutrophic lakes have generally higher Pnet rates compared to more oligotrophic ones, the Pnet contribution fraction to surface diffusive CH4 emissions were independent of the trophic status of the lake. For example, the fraction of Pnet contribution to emissions was similar and even higher in oligotrophic LIO than that in eutrophic NOI. This was mainly due to the substantial contribution of CH4 from the littoral sediments to the SML in the eutrophic lakes. Therefore, our results suggest that there is no relationship between the contribution of the two dominant CH4 sources (Pnet and Fs) and trophic state, even though each of these sources are higher in more productive systems.The dominant sources of CHPnet are limited by the accuracy of the boundary conditions of the mass balance . These boundary conditions are often based on a few measurement locations and are naturally variable. The variability and uncertainty of such estimations led to the observed range of Pnet in mass balance approaches obtained with the Monte Carlo simulations  with literature values and examined how their variability may alter the outcome of the two mass balance models.The methodologies for determining ons Fig. . Therefo4 emissions to the atmosphere are temporally and spatially variable. We accounted for the spatial variability by using the average of ten surface flux measurements along a lake-wide transect for each Pnet calculation. In addition, the average diffusive CH4 emissions estimated for NOI, CHA, and BRE are well within the range reported for the stratified season of these lakes in previous studies . There are no previous data for LIO.Diffusive CH4 emissions is due to the parameterization of mass transfer coefficient (k600). Therefore, we applied five alternative k600 parameterizations to estimate CH4 diffusion at the AWI in the four pre-alpine lakes and compared these fluxes with direct measurements using floating chambers. The comparison of the chamber-based mass transfer coefficient (R2 < 0.38) and clear underestimation of the measured k600 values . We hypothesize that the presence of oxygen microbubbles produced by photosynthesis in the water column51 might enhance the mass transfer coefficient44. This phenomenon would be more relevant in high altitudes lakes, such as our study lakes, due to the lower air pressure and oxygen saturation concentration.A large uncertainty in the estimation of surface diffusive CHk600 parameterizations for the lateral transport model, we observed that when using the literature parameterizations for surface CH4 fluxes, the simulated surface CH4 concentrations were underestimated when Pnet was not included in the simulations . This is explained by the fact that these parameterizations underestimate k600 values provided the best results. To further corroborate this finding, we calculated the Pnet error due to an over- or underestimation of kCH4 caused by using k600 parameterizations instead of Pnet error and the Fa and the Pnet rates estimated using the measured values , the slope varied between 0.5 to 2.9 with an average value of 1.3, meaning that the Pnet error is on average 30% higher than the k600 in a mass balance as suggested by various researchers .In our analysis of the mentclasspt{minima−2 d−1 53). In the full-scale mass balance, we assumed that the initial lateral flux towards the center of the lakes was equal to the diffusive CH4 flux coming from the littoral sediment . As the CH4 production rates in sediments increase with increasing temperature37, it has been hypothesized that sediment CH4 diffusion will also follow this relationship9. As most of our sediment flux measurements in the littoral zone were performed in July when the temperatures were highest in all lakes  in the full-scale mass balance, the littoral sediment fluxes would have to be two to three times higher than our measured fluxes to compensate for the diffusive CH4 emissions measured at the AWI . In fact, in BRE we measured one of the highest littoral sediment fluxes yet reported (8.3 ± 6.7 mmol m−2 d−1)54, and we still required one of the highest Pnet rates ever reported in the literature (June 2018: 2314 ± 2046 μmol m−3 d−1) to close the CH4 budget. Therefore, littoral sediment CH4 flux alone cannot account for diffusive CH4 emissions in our lakes and OMP needs to be included to close their CH4 budget.Assuming that OMP does not occur . Assuming that OMP does not occur in the SML, the measured ebullitive fluxes would have to be 42 and 770 times higher for BRE and NOI in June 2018, respectively, to close the mass balance   biodegradation could lead to CHPnet contribution to atmospheric CH4 emissions, it is necessary to derive approaches to estimate and upscale Pnet. Günthel et al.8 proposed that the OMP contribution to diffusive CH4 emissions from lakes can be estimated as a function of littoral sediment area and SML volume. In our study, the Pnet contribution to diffusive CH4 flux to the atmosphere was highly variable and disagreed with this simple upscaling approach   Fig. a. LC defPnet versus LC relationship strongly depends on the trophic state of each lake and thus cannot alone be used to upscale Pnet in different lake ecosystems. We suggest an empirical approach using additional trophic state parameters  are dependent on trophic state, as indicated by higher CH4 concentrations typically observed in eutrophic lakes relative to oligotrophic lakes27. Therefore CH4 concentration in the SML can be used as a proxy to reflect the trophic state of each lake and to normalize Pnet rates found in the eutrophic and oligotrophic lakes .The ers Fig. b. CH4 cokes Fig. . This inPnet rates of CH4  in the oxic SML of four pre-alpine lakes using two models that have previously produced contradictory results when resolving OMP in lowland lakes42. The good agreement between the adaptation of these approaches used in our study shows that there are no methodological issues with the models themselves when the appropriate boundary conditions are used to estimate OMP . We also conducted a thorough sensitivity analysis on the three main parameters that lead to the highest uncertainties. This analysis shows that measured surface fluxes must be used instead of literature k600 parameterizations to estimate the diffusive CH4 flux to the atmosphere. Our results indicate that in three out of four lakes a positive Pnet  needs to be included in the SML CH4 budget. In fact, up to 85% of atmospheric CH4 emissions that occurred at the beginning of summer resulted from Pnet, and even in systems with some of the highest recorded littoral sediment fluxes, we still obtained some of the highest reported Pnet (or OMP) rates.In this study, we quantified the 25) show that light and photoautotrophs may play a significant role in OMP. Consequently, future changes in light availability and temperature may induce positive feedbacks by promoting algal species capable of producing CH4. Although the contribution of OMP to total diffusive emissions from inland waters is still not well constrained, we have shown that it can be a dominant source from lakes in the pre-alpine region where climatic changes occur at higher rates than the global average34. It is thus crucial to continue quantifying the contribution of Pnet from various aquatic systems and identifying the main drivers of OMP that will help to better understand the impact of OMP on the global CH4 cycle and how to predict or possibly mitigate its impact in a changing climate.Finally, while the mechanisms behind OMP need further investigation, this study (in agreement with previous onesLac de Bretaye (BRE), Lac Noir (NOI), Lac des Chavonnes (CHA), and Lac Lioson (LIO) are pre-alpine lakes (above 1600 m.a.s.l) located in Canton Vaud, Switzerland  to measure total Chla concentrations.During each campaign, water column profiles were measured at the deepest point of each lake 59 and DSIL by Acidic molybdate with ANSA reduction60. A Shimadzu carbon analyzer (TOC-LCPH/CPN) measured TC.Total (TP) and dissolved phosphorus (DP), dissolved inorganic nitrogen as nitrate plus nitrite (DIN), dissolved silica (DSIL), and total carbon concentration (TC) were measured at each campaign in the upper mixed layer (from the surface to the bottom of the thermocline) and in the hypolimnion , bubble dissolution rates (Rdis) in the SML, and hypolimnetic fluxes (Fz) were used as boundaries conditions  (Supplementary Table HSML) was defined when ∂T/∂z becomes smaller than −1 °C m−1 61 (Table 4 production (Pnet) in the SML was estimated using Eq.  is the spatially varying thickness of the SML. The mass transfer coefficient for CH4 was calculated based on the average gas transfer coefficient obtained from the flux chambers . The SML thickness (H(r)) is equal to the mixed layer depth in the pelagic region and, within the littoral zone, H(r) decreases linearly with r from the mixed layer depth to zero at the shore. The littoral sediment flux is zero in the pelagic zone (r < rs) and equal to the measured average littoral sediment flux (r≥rs) as:Two regions were defined in the model, the littoral zone (Rdis(h(r))) as a function of lake depth (h) were included in the SML. At the boundaries, horizontal fluxes were assumed as zero. To estimate the horizontal dispersion coefficient (KH) we used Peeters & Hofmann49 parameterization:L [m] was calculated as L = rs  and their standard deviation (SD) retrieved from the field measurements. Given the small contribution of Rdis to the CH4 in the SML, its variability was not included in the Monte Carlo simulations of the lateral transport model. To prevent negative values, Fa and Fs were chosen from a gamma distribution defined by shape (κ = μ2/SD2) and the scale (θ2 = SD2/μ). Here the gamma distribution has the density 63 in Python were used for each normal and gamma distributions, respectively.To assess uncertainties, Monte Carlo simulations were performed  when solving the full-scale mass balance and the lateral transport models. 4 and At each sampling campaign CHmentclass2pt{minimmentclass2pt{minim4 concentration profiles were performed at a maximum depth resolution of 0.5 m where the metalimnetic CH4 gradient was expected. For the profile, the water samples were obtained with a 5-L Niskin bottle and then gently transferred into a 1-L glass bottle  while for the transect the samples were obtained directly with a 1-L glass bottle . For both methodologies, the water was overflowing to replace the volume three times. CH4 concentrations and 7. The samples were measured on a Cavity Ring-Down Spectrometer analyzer  for CH4 concentrations in the gas phase (ppm) and stable isotope ratio  in the bottle.Dissolved CH4 emissions to the atmosphere (Fa) were measured using a floating chamber attached to a portable GHG analyzer . Instrument-specific precision at ambient concentrations (1 − σ of 100 s average) for [12CH4] is 0.25 ppb. The floating chamber consists of an inverted plastic container with foam elements for floatation . To minimize artificial turbulence effects, the buoyancy element was adjusted that only ~2 cm of the chamber penetrated below the water level. The chamber was painted white to minimize heating. Two gas ports (inflow and outflow) were installed at the top of the chamber via two 5 m gas-impermeable tubes (Tygon 2375) and connected to the GHG analyzer measuring the gaseous CH4 concentrations in the chamber every 1 s. Transects were performed with the chamber deployed from a boat. The chamber was allowed to freely drift to minimize artificial disturbance. Fluxes were obtained by the slopes of the resolved CH4 curves over the first ~5 min when the slopes were approximately linear (R2 > 0.97).Diffusive CH44 as:Cw is the CH4 concentration in the surface water, Sc is the Schmidt number for CH4 and the exponent is taken as n = 2/3 for wind speed < 3.7 m s−1 and n = 1/2 for wind speed > 3.7 m s−1 44.To simulate the fluxes to the atmosphere in the lateral transport model, chamber-based mass transfer coefficient , temperature, headspace ratio, and assuming a porosity of 0.9. The location and depth of each core are shown in Supplementary Fig. Littoral sediment cores were taken in most of the lakes, except for LIO where the rocky bottom made it impossible to take a sample. Sampling was performed with a gravity sediment corer  equipped with an acrylic liner of 70 cm in length and with an internal diameter of 6 cm. 3 mL of sediment was sub-sampled at 1–2 cm depth intervals with headless 3 mL syringes through the pre-drilled holes from the selected depths. The sediment sub-sample was immediately placed into 1 L glass bottle  containing 500 mL of lake water previously bubbled with air to reach equilibrium with the atmosphere. The subsequent procedure followed the same as for the water column headspace method. Porewater CH4 sediment flux (Fs) at each lake was determined as the average flux provided by two independent methods. On average, three cores above the thermocline depth were taken in the epilimnion on September 2018 and July 2019 , 4 in water 66 and ∂C/∂z the measured vertical concentration gradient.Methane fluxes at the sediment-water interface were calculated using the CH4 (4 concentrations (Cw) were measured at the beginning and at the end of the deployment. Each deployment lasted about 1 h while the surface water was gently stirred to increase the mass transfer coefficient (kbc) at the air-water interface without producing sediment resuspension. The sediment flux was calculated using three methods:Fs is obtained using the beginning and final air and gas CH4 concentration and performing a mass balance in the water and the air phase as:Vw and Vair are the volume of the water and air phases, respectively. R is the ideal gas constant, Ta is the air temperature and Abc is the surface area of the chamber.Integrated mass balance: b = (w − HcpRTaa). The sediment flux is estimated fitting kcb and Fs to the measured curve fit function from Scipy62 in Python. The kbc boundaries were set from 0–40 m d−1 for the fitting.Transient mass balance: solving the mass balance over time we obtain that:Fs can be estimated with the last 5 min of the CH4 partial pressure as:Equilibrium mass balance: after ~ 1 h of measurements, we assume that the exponential part of the curve of Eq.  becomes Benthic fluxes were measured directly in sediment cores retrieved from the littoral sediment or core liners deployed in situ connected to a portable GHG analyzer . The core was covered leaving ~5 cm of headspace and ~30–50 cm of water. The lid was connected to a GHG analyzer creating a closed loop and partial pressure of CHThe flux from the benthic chamber was calculated as the average of the results of the three methods described above.4 dissolution from a single bubble released from the sediment was calculated using McGinnis et al.48. For each bubble we considered a diameter of 5 mm and the water column CH4, CO2, and O2 concentrations and temperature profiles. The initial bubble composition at each depth was estimated from a linear interpolation from bubble content obtained following the same methodology as Langenegger et al.19. The total bubble dissolution rate (Rdis(z)) was calculated considering the contribution from all bubbles released below that depth as:ri is the bubble dissolution from an individual bubble at depth i (μmol bub−1), Fieb,SWI, is the CH4 ebullition flux released at the sediment-water interface (SWI) at depth i (mmol m−2 d−1) and ni0, is the initial amount of CH4 in a single bubble (μmol bub−1). ΔAised, is the sediment area between the depth interval i to i + 1 (m2). Fieb,SWI, was estimated using Langenegger et al.19’s model. Using a mass balance in the sediment, this model predicts CH4 ebullition if the following are known: (1) the bubble CH4 content, (2) the water depth where the bubble was collected and (3) the diffusive CH4 flux from the sediment. In our study, we used the measured Fs to estimate Feb,SWI using Langenegger et al.19 approach. The mass balance model can be described by:Wi(z) (mol m−3 d−1) is the gas production rates as a function of the sediment depth , Di the molecular diffusion corrected by tortuosity, C(z) is the dissolved concentration (mol m−3), E(z) the total gas ebullition per bulk volume (mol m−3 d−1), KiH, is Henry’s law volatility constant (Pa m−3 mol−1), and P is the local critical gas pressure (Pa).The CH4 ebullition fluxes needed  to compensate the Pnet rates. We selected Pnet rates for BRE and NOI for June 2018, where we estimated the percentage of Feb that is dissolved in the SML (β) using McGinnis et al.48’s model assuming a bubble diameter of 5 mm. Then Feb,need was estimated using Eq. , Kz) was determined at each lake for each campaign , N is the Brunt-Väisälä buoyancy frequency and LT is the Thorpe scale estimated from the maximum displacement length (69:70.To estimate the transport of CHSi is each source term (mol d−1) such as bubble dissolution (Rdis∀SML), sediment flux (FsAs), net production (Pnet∀SML), and vertical diffusive fluxes (FzAz). If Si ≤ 0 then Si = 0 where i is each source term.We studied the importance of each source contribution (SC) to the diffusive surface flux by computing:Supplementary InformationPeer Review File


CBVF) and oxygen saturation (O2S) in unanesthetized, freely-moving mice. Then, we analyzed basal CBVF and O2,S and CVR of 5-month-old C57BL/6 mice during hypercapnia as well as during basic behavior such as grooming, walking and running. Moreover, we analyzed the CVR of freely-moving AD mice and their wildtype (WT) littermates during hypercapnia and could find impaired CVR in AD mice compared to WT littermates. Our results suggest that this optomechanical approach to reproducibly getting light into the brain enabled us to successfully measure CVR in unanesthetized freely-moving mice and to find impaired CVR in a mouse model of AD.Many Alzheimer’s disease (AD) patients suffer from altered cerebral blood flow and damaged cerebral vasculature. Cerebrovascular dysfunction could play an important role in this disease. However, the mechanism underlying a vascular contribution in AD is still unclear. Cerebrovascular reactivity (CVR) is a critical mechanism that maintains cerebral blood flow and brain homeostasis. Most current methods to analyze CVR require anesthesia which is known to hamper the investigation of molecular mechanisms underlying CVR. We therefore combined spectroscopy, spectral analysis software, and an implantable device to measure cerebral blood volume fraction ( Impaired CVR has been implicated in Alzheimer’s disease (AD) (O2S) during verbal fluency tasks  is a primary mechanism that enables adjustment of cerebral blood flow to maintain proper metabolic supply for brain tissues and is coordinated by the interaction of neurons, glia, endothelium, smooth muscle cells, and pericytes . The parduce CVR . Increasase (AD) . AD paticy tasks  and a facy tasks . Impairepatients , and blopatients . Howeverpatients . Furtherpatients . TherefoSeveral diagnostic modalities, including fMRI , and lasCBVF), the percent volume of blood in the measured volume of brain tissue, and oxygen saturation (O2S), the ratio of oxygenated hemoglobin to total hemoglobin, in freely moving animals using fiberoptic spectroscopy. Cerebrovascular tone and cerebral blood oxygen level are critical parameters of cerebral circulation that can be measured with CBVF and O2S using visible-light diffuse-reflectance spectroscopy. These measurements depend on the balance of blood flow and oxygen consumption by the tissue, making them attractive candidates to monitor cerebral circulation as used in functional magnetic resonance imaging (fMRI) and functional near-infrared spectroscopy (fNIRS). The measurement of CBVF is closely linked to cerebrovascular reactivity in the brain. When exposed to hypercapnic conditions, blood vessels in the brain dilate to match the tissue’s increased demand for blood, a process known as CVR to CO2. One way to investigate CVR is by measuring the changes in CBF or cerebral blood volume (CBV) induced by vasodilation  illuminated the cerebral cortex through an illumination fiber bundle of 8 fibers  in 7-around-1 mated to a solid core fiber in the tip , or a solid core plastic polymer fiber  mated to the same fiber material in the tip, while an identical detection fiber tip and bundle directed the measured diffuse reflectance to a spectrometer . Our system was controlled through Matlab (Mathworks) software by a laptop computer running Windows 10. Spectra were fit for real-time readout of C(λ) were acquired using measurements of a 99% reflectance standard  while holding the fiber probe 3 cm from the standard. The dark noise of the spectrometer was also measured (dark) with the illumination lamp off. Calibrated spectral measurements M(λ) of tissue were calculated from the raw tissue spectral measurements R(λ) and the calibration measurements C(λ) according to Calibration spectra p(λ)M was created by multiplying the predicted reflectance, p(λ),R by a scaling factor K: p(λ)M = p(λ)KR as in p(λ)M and λ)M( specified the endpoint metrics O2S and CBVF. pλ),z diffusion constant λ)D( and the effective attenuation coefficient MFP’ = 0.39 mm), calculated using scattering spectra (MFP’) is effectively the probing depth of optical penetration. spectra ,B and fowhere “Tissue” denotes the approximate mixed brain tissue type to be 1/3 white matter and 2/3 gray matter as in A) that accounts for the refractive index mismatch at the boundary between the tissue and the external medium is calculated based on (ir).An internal reflection parameter (0z) within the tissue.Diffuse reflectance (light escaping the tissue surface) emanates as if from an equivalent point source depth (D) is calculated:The diffusion constant (The effective attenuation coefficient is derived from the diffusion constant and the absorption.r) uses two geometrical factors (1r) and (2r).The Greens function describing fluence at a point separated from the source fiber by a distance (Two other variables—pM) based on diffusion theory is a constant (K) multiplied by the predicted diffuse reflectance pRThe predicted fiberoptic measurement , or plastic polymer fiber (npolymer = 1.49) and tissue (ntissue = 1.4) was n = nglass/ntissue = 1.09 or n = npolymer/ntissue = 1.06 a(λ)μ and s’(λ)μ were the absorption and reduced scattering coefficients of the tissue, respectively. The spectral absorption coefficient, a(λ)μ, was calculated as a weighted sum of the absorption spectra of oxygenated whole blood [a_oxy(λ)μ], deoxygenated whole blood [a_deoxy(λ)μ], and water [a_water(λ)μ], according to The fiber separation (distance between the source fiber tip and the detector fiber tip) was MFP, which is 0.39 mm , the fminsearch in Matlab. Fitting adjusted 3 variables: CBVF, SO2, and K where CBVF = 1 specifies 150 g/L hemoglobin. W, the fractional tissue water content, was fixed at an assumed value of 0.78, which has been reported for the mouse cortex  × μa_deoxy = 0.1103 cm−1. a_waterμ = 0.0025 cm−1, which is 44-fold lower than μa_blood.The difference between M  and Mp = KRp see  was minie cortex . Absorpts(λ)μ [cm−1] and scattering anisotropy λ)g( [−]), which were constant across all experiments, were spectral functions λ)( fit to the previous measurements of fresh human brain tissue (s(λ)μ and λ)g( were used as interpolated functions of wavelength (s’(λ) = μs(λ)μ × (1 − g(λ)) used in The absorption of the tissue due to blood was specified by the fitting described above while the scattering optical properties  and the anisotropy of scattering (g). The combination of sμ and g yields the reduced scattering coefficient [sμ’ = sμ(1 − g)] shown in sμ’(λ) spectrum was assumed when using least-square fitting of the data to specify K, CBVF, and O2S. After spectral fitting, the values for CBVF and O2S were output as a function of time over time periods where spectroscopic measurements were made on mice under various experimental conditions. These optical properties were also used to model the photon transport in the mouse brain.The The connection between the mouse brain and the spectrometer consisted of an implanted brain probe (~1 cm fiber) and a spectrometer connector (~2 m fiber). The connector  is fiberDuring assembly, the connector’s flat surface was pressed against the glass, and the ferrules and magnets were inserted and also pressed against the glass for alignment (friction fit). The male side connector was fabricated using a similar process of press-fitting the cannulae and magnets, but the assembly was pressed against an alignment tool see , insteadIn order to maintain alignment, so that the fibers in the brain probe and spectrometer connector mated precisely, the brain probe surface was printed with 6 small 4-sided pyramids while the connector surface was printed with complementary mating holes. This design configuration enabled the secure mating of the two connecting parts during measurements. Finished fiber probes were visually inspected under a 20X stereomicroscope for polish level and analyzed through a series of signal and noise tests using the spectroscopy probe in a dark room and the light source targeted at human skin.R1) at the 650 nm wavelength. A second count readout (R2) was measured with the probe contacting human skin. The ventral skin surface is less pigmented and the easily accessible, finger pad has little unwanted influence of melanin. The signal-to-noise ratio was then [R1 – R2]/R1 and the manufacturing quality control threshold was set as a 60-1 signal-to-noise ratio so that, as a first-order approximation, an extra 1/60th of an optical measurement of the brain consisting of leaked white light would erroneously decrease the absolute CBVF no more than 100%/60 = 1.6%.The quantitative performance parameter for magnetic coupling was the amount of white light that leaked directly from the source fiber bundle to the detector fiber bundle. This amount defined the noise and was measured with the surgically-implantable tip magnetically coupled and the illumination light going from it toward the Vantablack target in a dark room. The quantitative spectrometer readout, in counts, was read out .5-month-old C57BL/6 mice (The Jackson Laboratory) were used to measure basal cerebrovascular dynamic properties of the cortex while freely moving. The AD model mice studied were 13-month-old Tg6799, also called 5xFAD (Jackson Laboratory) double transgenic mice overexpressing both human amyloid precursor protein (APP) gene with KM670/671/NL, V717I, and I716V mutations and human presenilin 1 (PSEN1) harboring M146L and L286V mutations under the Thy1 promoter . WildtypAfter anesthesia with isoflurane mixed with pure oxygen (3% isoflurane and 1 L/min oxygen for induction and 1.5% isoflurane and 1 L/min oxygen for maintenance), mice were mounted on a stereotactic frame. After the removal of hair over the scalp, the scalp was cleaned with sterile alcohol and Betadine three times. We performed a minimal-sized midline scalp incision (~5 mm). We then drilled two small holes in the skull using a 0.7 mm diameter stainless steel micro drill burr (Fine Science Tools). The coordinates of the two holes in reference to Bregma were anterior = −1 mm, lateral = 1.5 mm and anterior = −3.5 mm, lateral = 1.5 mm. Brain probes were fitted to the holes and immobilized using dental cement. The skin incision was sutured and animals were monitored throughout the recovery period. A week after surgery, mice were placed into a chamber (22.8 cm × 20.3 cm × 15 cm) and we measured cerebral perfusion in the freely moving state.CBVF and O2S while video recording the animal. After the measurement, we classified the animal activity seen in the video recording as grooming, resting, or walking activity. In order to assert more control over animal behavior during fiberoptic measurements, we measured CBVF and O2S during an accelerating rotating rod (Rotarod) behavior test. For the Rotarod behavior test, we allowed the animal to rest on the Rotarod device for 60 s and then started the device for 180 s. The initial speed during the running period was set to 1 rpm and ramped up to 10 rpm over 60 s, staying at the top speed for another 120 s. After the 180 s running period, the animal was allowed to rest for 120 s for a total measurement period of 360 s. For the hypercapnia study, we injected 10%CO2/10% O2/80%N2 mixture into the induction chamber and measured changes in CBVF and O2S during and after hypercapnia.For the free moving recording study, we allowed the animal to freely move in an open field and measured O2S and CBVF  and a spectrometer connector (~2 m fiber). The device  fiber-opand CBVF . These vand CBVF .CBVF and O2S in mixed arterial and venous blood of the cortex of freely moving 5-month-old C57BL/6 mice yielded values of ~1.9% and ~35%, respectively  and O2S (17.5% ± 2.6%) values over the course of the running period as compared to the percent change of the average CBVF and O2S values of the baseline , which is a typical hyperaemic response to increased CO2 through vasodilation. O2S decreased (−31.8% ± 2.4%) slowly during hypercapnia but normalized rapidly after stopping CO2 injection and releasing CO2 at 300 s, while CBVF increased before returning to a basal level  littermates and also analyzed the difference in vascular reactivity between Tg6799 mice and WT littermates during and after hypercapnia using fiberoptic spectroscopy (CBVF and O2S between the two groups (CBVF of the cortex of AD mice during hypercapnia was significantly higher than that of WT littermates (CBVF of AD mice in comparison to WT littermates (To investigate the cerebrovascular properties of AD (Tg6799) mice, we measured the baseline of troscopy ,B. Whileo groups ,D, the itermates . In additermates .To assess longitudinal measurement and repeatability, we performed several measurements over time in the same animal and found that repeated measurements were stable between 1 and 3 weeks after the brain probe implantation surgery. O2S and the CBVF in the brains of freely moving mice when implemented with a magnetic coupling tip. The present study showed that our fiberoptic method detected changes in freely moving mice and measured cerebrovascular impairment in a mouse model of AD. Previous studies on O2S in the cortex of anesthetized rodents  exhibits high heterogeneity based on the types of blood vessels, such as arterioles, venules, and capillaries. Moreover, Sakadzic et al. observed a decline in vascular 2pO with an increase in cortical depth. Considering that our device measured mixed arterial and venous blood of the cortex at a depth of 0.3–0.7 mm  was ~1.7% , which other studies mainly used  can be found at: The animal study was reviewed and approved by Rutgers University and Rockefeller University.DG, NR, AC, MB, JZ, and HA performed the experiments. DG, NR, AC, AY, SJ, and HA analyzed the data and wrote the manuscript. DG, MS, SS, JK, and HA designed the study. DG and HA participated in the interpretation of data and manuscript preparation. All authors contributed to the article and approved the submitted version.Research reported in this publication was supported by the National Institute on Aging of the National Institutes of Health under Award Number RF1AG078245 (HA), by the National Institute of Neurological Disorders And Stroke of the National Institutes of Health under Award Number R01NS104386 (HA), and the Robertson Therapeutic Development Fund (HA). The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.