One of the most substantial and established environmental risk factors for neurological and psychiatric disorders is stress exposure, whose detrimental consequences hinge on several variables including time. In this regard the gestational period is known to present an intrinsic vulnerability to environmental insults and thus stressful events during pregnancy can lead to severe consequences on the offspring’s brain development with long-term repercussions throughout adulthood. On this basis, we investigated the long-lasting impact of prenatal stress exposure on the susceptibility to the experimental autoimmune encephalomyelitis (EAE), a well-established murine model of multiple sclerosis. Although stress is considered a triggering factor for this chronic, progressive, autoimmune disease, little is known about the underlying mechanisms. To this end, EAE was induced by immunization with MOG35-55/CFA and pertussis toxin administration in adult female C57BL/6 mice born from control or stressed dams exposed to restraint stress during the last days of gestation. Our results demonstrate that gestational stress induces a marked increase in the severity of EAE symptoms in adulthood. Further, we highlight an altered maturation of oligodendrocytes in the spinal cord of prenatally stressed EAE mice, as indicated by the higher levels of GPR17, a marker of immature oligodendrocyte precursor cells. These behavioral and molecular alterations are paralleled by changes in the expression and signaling of the neurotrophin BDNF, an important mediator of neural plasticity that may contribute to stress-induced impaired remyelination. Since several already marketed drugs are able to modulate BDNF levels, these results pave the way to the possibility of repositioning these drugs in multiple sclerosis.The online version of this article (10.1007/s10571-020-01014-x) contains supplementary material, which is available to authorized users. Stress experience has been consistently established to be a major environmental factor in the etiology of several neurological and psychiatric diseases Gradus . Thus, lWith these premises, the aim of this study has been to evaluate the impact of a prenatal stress exposure on EAE course at adulthood. Specifically, given that MS affects women twice as often as men  pregnant mice at gestational day (GD) 14 were purchased from a commercial breeder (Charles River Laboratories). Upon arrival, the animals were singly housed with food and water freely available and were maintained on a 12-h light/dark cycle in a constant temperature (22 ± 2 °C) and humidity (50 ± 5%) conditions. All animal experiments were conducted according to the authorization from the Italian Health Ministry (n.1136/2016PR to RM) in full agreement with the Italian legislation on animal experimentation  and adherent to EU recommendation (EEC Council Directive 2010/63). Accordingly, all the in vivo procedures were carefully refined to minimize animal suffering and to reduce the number of animals used and conducted by staff with certified experience in the use and handling of laboratory animals and in adequately detect any sign of possible discomfort or pain in the animals used. Moreover, the two procedures that may represent a source of suffering for the animals, i.e. the stress exposure and the EAE induction, have been carefully refined as subsequently described. Animal sample size was calculated using the software Piface. The power analysis demonstrated that a sample of 12 mice per group will provide 80% detection power with a 5% type I error. With the inherent variations in mouse behavioral outputs (primary endpoint), we estimated to detect a 30% difference between groups, a standard deviation of 25% and an effect size of f = 1.2. For the molecular analyses (second endpoint) we estimated to detect a 15% difference between groups, a standard deviation of 10% and thus an effect size of f = 1.5.Adult female C57BL/6 (n = 10) were left undisturbed in their home cages. Witnessing stress was limited by blocking any visual and auditory cues, as the stress exposure took place in a different area of the colony room with white noise generators. It is important to underline that this stress protocol does not cause physical damage or severe suffering to the animal, as demonstrated by the absence of differences between the stressed and the control dams regarding the number of delivered pups or their aptitude for maternal care (see “n = 12), (ii) animals born from non-stressed dams and exposed to EAE induction NO PNS/EAE (n = 15), (iii) animals born from stressed dams PNS/CTRL (n = 15), (iv) animals born from stressed dams and exposed to EAE induction PNS/EAE (n = 16). All animals were socially housed with non-littermates (n = 4 per cage) under standard laboratory conditions. A graphic representation of the experimental paradigm can be found in Fig. Ten pregnant dams were randomly selected for exposure to restraint stress, from GD16 until delivery. Briefly, the animals were subjected to multiple daily stress sessions during the last three days of gestation: two sessions at GD16 and GD17 (10.00 a.m. and 14.00 p.m.) and three sessions at GD18 and GD19  during which they were placed in plastic cylinders (12 cm long and 4 cm diameter) for 45 min under bright light (3000 lx). Control pregnant females  was provided to all the pregnant females and, the day after the birth, the complexity of the nest has been scored by four different blind operators according to the following scale: 0 = the animal has not manipulated the building material; 1 = the material has been manipulated but the position of the nest is not clear (sparse paper on the bottom of the cage); 2 = flat nest, without vertical walls; 3 = "cup" nest with walls less than half the height of a nest with a full dome; 4 = nest with incomplete dome; 5 = nest with full dome.n = 3 (1 NO PNS/EAE and 2 PNS/EAE) mice died due to the severity of the EAE symptoms. At PND 106 (i.e. day post injection 50), one animal at a time was moved to a separate room to be quickly sacrificed by cervical dislocation, the spinal cord was dissected, frozen on dry ice and stored at − 80° until molecular analyses.EAE was induced in 8-week-old female by subcutaneous immunization in the flanks and at the base of the tail with 300 μg of myelin oligodendrocyte glycoprotein  per mouse in Incomplete Freund's adjuvant  supplemented with 8 mg/ml of Mycobacterium tuberculosis . Mice immunized received 500 ng of pertussis toxin  intravenously the day of the immunization and 48 h later. Animals were daily (11 a.m.) weighted and scored for clinical symptoms of EAE according to the standard EAE scoring system: 0 = healthy, 1 = flaccid tail, 2 = ataxia and/or paresis of hindlimbs, 3 = paralysis of hindlimbs and/or paresis of forelimbs, 4 = tetraparalysis, 5 = moribund or death  method, where ΔCT = CT target-CT β-actin and Δ(ΔCT) = CT exp. group-CT control group and CT is the threshold cycle. For graphical clarity, the obtained data were then expressed as percentage versus control group, which has been set at 100%.For gene expression analyses, total RNA was isolated from the whole cervical portion of the spinal cord by single step guanidinium isothiocyanate/phenol extraction using PureZol RNA isolation reagent  according to the manufacturer’s instructions and quantified by spectrophotometric analysis. The samples were then processed for real-time polymerase chain reaction (PCR) as previously reported  and then sonicated for 10 s at a maximum power of 10% to 15% (Bandelin Sonoplus). The homogenate was clarified  obtaining a pellet (P1) enriched in nuclear components, which was resuspended in a buffer  supplemented with protease and phosphatase inhibitors. The supernatant (S1) was then centrifuged  to obtain a clarified fraction of cytosolic proteins (S2). The pellet (P2), corresponding to the crude membrane fraction, was resuspended in the same buffer used for the nuclear fraction. Total protein content was measured according to the Bradford Protein Assay procedure (Bio-Rad Laboratories), using bovine serum albumin (BSA) as calibration standard.Whole cervical spinal cord samples were manually homogenized using a glass-glass potter in a pH 7.4 cold buffer , in the cytosolic fraction (targeting phospho-Akt at Ser473 and Akt), and in the crude membrane fraction (targeting MAG) of 6 mice/experimental conditions. Equal amounts of protein (12 or 16 μg) were run under reducing conditions on polyacrylamide gels and then electrophoretically transferred onto nitrocellulose membranes. Unspecific binding sites were blocked with 10% nonfat dry milk; then the membranes were incubated overnight with the primary antibodies and for 1.5 h at room temperature with a peroxidase-conjugated anti-rabbit or anti-mouse IgG. Specifically, the following primary antibody dilutions were used: against mature BDNF  1:500 in 3% nonfat dry milk; phospho-mTOR/mTOR  1:1000 in BSA 5%; phospho-Akt/Akt  1:1000 in BSA 5%; MAG  1:1000 in 5% non-fat dry milk and β-actin  1:20,000 in 3% non-fat dry milk. All the primary antibodies utilized were validated for western blot by the suppliers. Immunocomplexes were visualized by chemiluminescence using the ECL ETA C 2.0 (Cyanagen #XLS070) or ECL SUN . Results were standardized using β-actin as the internal control, which was detected by evaluating the band density at 43 kDa. Protein levels were calculated by measuring the optical density of the immunocomplexes using chemiluminescence ). To ensure that autoradiographic bands would be in the linear range of intensity, different exposure times were used.Three animals from each condition that displayed clinical scores representative of their experimental group were dedicated to immunofluorescence staining. Mice were anesthetized with ketamine (100 mg/kg) and xylazine (10 mg/kg) and perfused transcardially with 0.1 M EDTA  in saline followed by 4% neutral buffered formalin  in deionized water. Spinal cords were collected and post-fixed for 1 h in the same solution at 4 °C, cryoprotected in 30% sucrose for 24 h, embedded in OCT and then frozen at -80 °C. Spinal cords were cut transversally into 20 μm-thick sections with a cryostat and processed for immunofluorescence. Slides were incubated for 45 min at room temperature with a blocking solution composed by 10% goat normal serum  and 0.1% triton X-100 in phosphate buffered saline (PBS). Then, the sections were incubated with rabbit polyclonal anti-GPR17  overnight at 4 °C in PBS with 5% goat normal serum and 0.1% Triton X-100. Following primary antibody incubation, the sections were washed and incubated with the biotinylated secondary antibody  for 1 h at room temperature. GPR17 labeling was detected with the high sensitivity tyramide signal amplification kit  according to the manufacturer’s instruction. Hoechst 33,528 was used to visualize cell nuclei. After processing, sections were mounted on microscope slides with fluorescent mounting medium . The custom anti-GPR17 primary antibody used in this publication has been validated  were entirely reconstructed with Adobe Photoshop CC following acquisition of 8–10 images at 10× magnification for each section. GPR17 positive cells were counted manually with ImageJ software in the whole white matter of each section reconstructed and then normalized to the relative area.t test. The effects of PNS and EAE on the mRNA or protein levels of the molecular targets were conducted with a Two-way ANOVA followed—when appropriate—by a Single Contrast Post Hoc Test (Fisher’s Protected LSD). Differences in the GPR17 positive cell count and MAG protein levels were evaluated using two-tailed Unpaired t test. The Shapiro–Wilk normality test was performed to analyze the data distribution for each group. Homogeneity of variance was evaluated using Brown–Forsythe and F test for ANOVA and Unpaired t test analyses respectively. All the data presented in the manuscript passed both tests and were analyzed as normally distributed and with equal variances. All the molecular analyses were carried out in individual animals (independent determinations) and for graphic clarity, data are presented as means percent ± standard error (SEM) of control group, with significance threshold set at P < 0.05. We removed EAE mice that did not show symptoms at day post injection 50 from the molecular analyses . Otherwise, outliers that were more than two standard deviations away from the mean were removed, as they likely resulted from technical errors.This study was not pre-registered. Mice were randomized into the experimental groups (stratified randomization). Biochemical assays were performed using blinding codes and counterbalancing to ensure that treated and untreated conditions appear in adjacent lanes to mitigate regional assay variance (e.g. gel edge effects). All the molecular analyses were repeated 2/3 times and the results confirmed. Analyses of body-weight gain—of the mothers and of the pups before and after the EAE induction—and EAE clinical score were performed with Two-way analysis of variance (ANOVA) with repeated measures (RM). Sphericity was not assumed and Geisser-Greenhouse correction was used. Comparisons between stressed animals or non-stressed mice in nest building assessment test score, number of pups, ratio between female and male newborn, EAE cumulative disease score (CDS), maximum score (CS max) and day of EAE onset were analyzed by two-tailed Unpaired th day post-partum, we monitored the body weight of control and stressed pregnant mice as well as their capability to build a nest, using the nest test as an indicator of animal well-fare. As shown in Fig. To establish whether restraint stress exposure affected proper gestation course, starting from GD17 until the 38F1,56 = 25.78, P < 0.0001; Fig. Subsequently, to establish the lasting effects of prenatal stress (PNS) in the offspring after weaning, we monitored the weight of female pups from PND 24 to PND 56, finding that early stress reduced the body weight of female pups born from stressed dams compared to the non-stressed counterpart . It is noteworthy that PNS also reduced the body weight of non-immunized control mice throughout adulthood  and the following recovery phase . The cumulative disease score (CDS) was also greater in the PNS/EAE group  and a key modulator of OPC maturation and myelination , as summarized in Fig. 2 . Although these data may represent explorative results, given the small sample size, they suggest a defect in oligodendrocyte maturation that potentially leads to impaired remyelination.The count of GPR17 positive cells (GPR17 +) in the whole white matter of the cervical spinal cord highlighted a greater number of OPCs in EAE animals prenatally exposed to stress compared to non-stressed EAE mice  and EAE . More in detail, as shown in Fig. P = 0.0371) that appeared to be exacerbated in mice previously exposed to PNS  that results in a broad reduction trend in all EAE mice .These explorative results suggest that intrauterine stress exposure had a negative impact on mTOR activation in EAE animals.The statistical analyses of Ser2448-phosphorylated-mTOR revealed a significant effect of both PNS . However, multiple comparisons analyses depicted a significant decrease due to PNS exposure alone  and we did not observe any specific modulation of phospho-Akt in EAE animals compared to NO PNS/CTRL mice  that resulted in a reduction of the total form of the protein only in PNS/EAE animals . Overall, our results confirm the implication of Akt/mTOR pathway in the impaired neurological score of these animals.Next, we analyzed the levels of the protein kinase Akt which is known to stimulate mTOR activity  and EAE effect . Indeed, as displayed in Fig. P = 0.0074) as well as in EAE animals . Interestingly, the decrease was exacerbated in EAE mice prenatally exposed to stress . Normality and equal variances assumptions were not violated .The Akt-mTOR pathway is one of the three main signaling cascades triggered by the binding of the neurotrophin BDNF to its high-affinity tropomyosin receptor kinase B (TrkB), alongside the mitogen-activated protein kinase (MAPK) and the phospholipase Cγ (PLCγ) pathways , which contains the protein coding region. Moreover, two alternative polyadenylated transcription stop sites are located within the common 3′ exon IX, which generate two distinct pools of mRNA with either short or long 3′untranslated regions (3′-UTRs). It is known that BDNF transcripts characterized by short 3′-UTR are restricted to the soma, whereas long 3′-UTR mRNAs are mainly localized in dendrites  and by a significant PNS x EAE interaction . As a result, the mRNA levels of total BDNF  and reduced by the encephalomyelitis  an effect even higher in PNS/EAE animals . A partially different profile was observed for the gene expression of the long 3′-UTR pool of transcripts  and PNS x EAE interaction  displayed by a strong reduction of long 3′-UTR BDNF only in PNS/EAE mice compared to control mice , to prenatally stressed mice  and to EAE animals not exposed to stress . The analysis of isoform IV gene expression displayed a significant EAE  and PNS  effect. Similar to what was observed for the total form of the neurotrophin, we found an increase in PNS mice  paralleled by a decrease after EAE in both non stressed  and prenatally stressed mice  that resulted in a decrease only in the EAE mice prenatally exposed to stress .We found that the gene expression of total BDNF was significantly modulated by EAE Below is the link to the electronic supplementary material.


We show that luminescence cannot be totally neglected in that case, since photon absorption lies at the root of the chemical reaction. We propose two coupled simple and appropriate analytical approximations enabling the estimation of absorptance with a relative error below 6% in every tested situation: the zero-order scattering approximation and the gray single-scattering approximation. Finally, this theoretical approach is used to determine and discuss the overall quantum yield of a bio-inspired photoreactive system with Eosin Y as a photosensitizer, implemented in an experimental setup comprising a photoreactor dedicated to hydrogen production.Most chemical reactions promoted by light and using a photosensitizer (a dye) are subject to the phenomenon of luminescence. Redistribution of light in all directions (isotropic luminescence emission) and in a new spectral range (luminescence emission spectrum) makes experimental and theoretical studies much more complex compared to a situation with a purely absorbing reaction volume. This has a significant impact on the engineering of photoreactors for industrial applications. Future developments associated with photoreactive system optimization are therefore extremely challenging, and require an in-depth description and quantitative analysis of luminescence. In this study, a radiative model describing the effect of luminescence radiation on the calculation of absorptance is presented and analyzed with the multiple inelastic-scattering approach, using Monte Carlo simulations. The formalism of successive orders of scattering expansion is used as a sophisticated analysis tool which provides, when combined with relevant physical approximations, convenient analytical approximate solutions. Its application to four photosensitizers that are representative of renewable hydrogen production  We can cite first of all applications in industrial photochemistry using artificial light sources 32+) , 29. TheRegarding the application, we considered a homogeneous reaction medium with luminescent species implemented in a photoreactor modeled as a slab whose radiative configuration and boundary conditions are detailed in section 2.1. In particular, heterogeneous photoreactive systems with particles leading to elastic scattering are not discussed in this article. First we will focus on situations where the luminescent photosensitizer is the only species that interacts with radiation—there is no other absorbing species—and results will subsequently be extended to configurations where the catalyst also absorbs radiation. Extension is quite straightforward and the conclusions are not modified, since absorption by catalyst is not desirable (it does not lead to reaction) and is therefore low when working with efficient molecular photoreactive systems.The corresponding steady-state Radiative Transfer Equation (RTE) will be presented in section 2.2 and is rigorously solved using the Monte Carlo method. Efforts are then essentially focused on the analysis of luminescence effects on MVRPA, and as a result on the construction of relevant analytical approximate solutions. The collision term that describes luminescence in the radiative transfer equation can either be interpreted as an emission source in the volume , 31, or The overall effect of luminescence on absorptance is quantified, indicating that luminescence can hardly be neglected in applications concerning solar fuel production. We therefore analyzed the respective influence of two characteristics of luminescence: multiple scattering and inelasticity. For this purpose, the weight of the successive scattering orders was first analyzed, and then the effect of inelasticity in scattering was quantified by comparing the reference results with those obtained thanks to equivalent gray or elastic scattering models. From these developments important conclusions decribing the impact of luminescence on MVRPA quantification are given, and rules of thumb for reasoning from well-defined optical thicknesses are proposed for any application using photosensitizers. Various useful analytical approximations for MVRPA assessment, also valid for any photosensitized reactive process in the absence of particles, are fully developed and compared to rigorous calculations in section 4 in order to discuss their validity in detail.2 in photoreactors, where the fluorescence of Eosin Y was neglected ifξ < Φ (scattering event) thenStep 4a.1: Scattering counter is incremented: j = j + 1.Step 4a.2: Scattering direction u is sampled according to the isotropic phase function.Step 4a.3: Wavelength λ is sampled according to the luminescence spectrum pL(λ) and the extinction coefficient kλ = CEλ is interpolated from the spectral database.Step 4a.4: Extinction length l is sampled over  where the studied photosensitizers are active . MVRPA X. Note that the relative difference for relative differencer PA see ,Pj) computed with X ≡ (Φ = 0).Here we compare absorptance values +, between 20% and 50% for Eosin Y and larger than 100% for Rhodamine B. The only photosensitizer for which Δ(Φ = 0) is constant and lower than 10% is x = 0 and exit the medium through the front face of the reactor .Neglecting luminescence always leads to an overestimation of absorptance: Δ(Φ = 0)>0. Indeed when luminescence is not taken into account, each interaction with photosensitizers necessarily leads to absorption, whereas luminescence interaction has a probability Φ of leading to scattered photons that might exit the medium. We record Δ(Φ = 0) values between 10% and 20% for TATAOverall, these results indicate significant luminescence effects that should not be neglected when studying photosensitized systems.+, +), but the molar extinction coefficient is equal to zero over part of this spectral range =0.99  but thisange see . TherefoHere we analyze the effect of multiple luminescence scattering. In the previous paragraphs we discussed the fact that due to luminescence, interaction has a probability Φ of leading to scattered photons that might exit the medium. Therefore Pj)( of scattering orders and its tail cumulative Pj>q)( (see P(0) is the contribution of ballistic photons, P(1) is the contribution of photons absorbed after one scattering event (first order), P(2) is the contribution of photons absorbed after two scattering events (second order), etc., with decreasing contributions Pj)( > Pj+1)( = PS) . Furthermore, as regards luminescence contributions, the higher the j>q) see : P(0) isviaThe following case-by-case analysis is organized according to  see Eqs .P(0) = 1 and Pj>0)( = 0 in j = 0) = 0 for This case is illustrated here with izer see . The pho+, Eosin Y and Rhodamine B. In this situation the photosensitizer interacts with scattered luminescence radiation that can be absorbed after one, two, … j scattering events:This is the case for most fluorescent molecules, as illustrated here with TATA+ case, ballistic photons P(0) are responsible for at least 95% of absorption. The proportion of photons Pj>1) represent about 99% of photon absorption.Looking at the TATAPj>1) leads to 99%. For the higher optical thicknesses, ballistic photons represent 80 to 90% of absorption. For P(0) + P(1) are responsible for 99% of absorption. For In the case of Eosin Y, the photon proportion absorbed after more than one scattering event Pj>1) and Δ(elastic) in Inelastic scattering is another conceptual and numerical difficulty when describing photon transport in photosensitized and photocatalytic systems, in addition to multiple scattering. Indeed, wavelengths are redistributed according to the luminescence spectrum at each scattering event. Here we analyze the sensitivity of absorptance and MVRPA to inelastic scattering effects in order to determine if this difficulty must be tackled or can be partially bypassed. For this purpose, we constructed two equivalent models for luminescence radiation that we compared with the reference solution  intensity sity see . Gray apThe RTE in E¯LC see . Using tStep 4a.3 was replaced by:The Step 4a.3: Whatever the wavelength, the extinction coefficient for scattered photons is set to E¯LC see .gray) between gray) > 0  indicates that gray approximation for luminescence radiation overestimates absorptance  ≲ 5 since at least 95% of absorption is due to ballistic radiation that is not affected by inelastic scattering. For Eosin Y, the first and second scattering orders contribute up to 20% and Δ(gray) reaches 11%. For Rhodamine B, we record a significant contribution up to the third scattering order, and Δ(gray) reaches 70%.Δ(gray) rapidly increases with the scattering optical thickness ents see . For TATi.e.Eλ does not vary with λ in the spectral range pL(λ) ≠ 0), then the gray model and reference model are exactly identical, and therefore Eλ on gray) increases with Δ(gray) always increases with ange see .To conclude, for the typical cases tested in this paper, wavelength redistribution due to luminescence can hardly be put aside once scattering optical thickness exceeds 0.1. However, the results in The elastic-scattering model for luminescence radiation is simply obtained by replacing the inelastic collision term in the RTE for luminescence intensity (see sity see  by an elStep 4a.3 was replaced by:The Step 4a.3:ifj = = 1 thenpL(λ) and the extinction coefficient kλ = CEλ is interpolated.The wavelength λ is sampled according to the luminescence spectrum endi.e. for j = 1).The wavelength λ is sampled during the first scattering event only (elastic) and Δ(gray) in elastic) below 2% for TATA+ and Eosin Y. This is due to the fact that scattering orders j > 1 have little impact with these photosensitizers  to population (1). The comparison of Δ.With this model, the extinction coefficient th order scattering approximation.As discussed in Section 3.1, we observe serious Δ(Φ = 0) errors when neglecting luminescence see . A straiIn Section 3.2 we observed that the main contribution to absorption is due to ballistic radiation. The expansion in successive orders of scattering is therefore truncated here at order zero: j = 0) < 0 in j = 0) in P(j > 0) in j = 0).The solution for i.e. when Φ = 0). In this case e.g. Δ(Φ = 0) = 25% for Φ = 0.2. In these situations where Of course, when +, Eosin Y and Rhodamine B. As discussed in Section 3.1, the luminescence effect is significant in these cases and should not be neglected (Δ(Φ = 0) = 10% to 170%):In +, the zero-order scattering approximation provides accurate results with error Δ(j = 0) ≤ 5% in every tested situation. Indeed, For TATAFor Eosin Y and Rhodamine B, even if the zero-order scattering approximation is not sufficient to describe photon transport with accuracy below 5%, we nevertheless record a significant improvement in relative error compared to Δ(Φ = 0).Overall, we record the following accuracy levels for the zero-order scattering approximation as a function of scattering optical thickness j = 0) < 5% for Δ(j = 0) < 10% for 0.05 Δ(j = 0) < 30% for 0.3 < Δ in The gray approximation presented in Section 3.3 produces fairly accurate results for TATAions see .μ ∈  to obtain the local macroscopic balance:x. Afterwards, μ and then integrated over μ ∈ :τλ = kλL = EλCL and pi(λ) is the incident spectrum (see Section 2.1 and dλ = τλ/(mτL) andFirst the expression of 0,λe-kλxIn this +, which is accurately described by zero-order approximation and the gray model, relative errors are comparable: The results presented in 2.mol−1  and pL(λ) are the incident and luminescence spectrum respectively  andAn analytical expression of τL > 0.1 involving the strong impact of inelastic scattering. Double spectral integration in + and Eosin Y. Indeed, the two validity conditions for elastic) < 2%) and second, P1 approximation well describes multiple scattering in the framework of this elastic model (τL > 1), the elastic-scattering model at the root of the elastic) > 10%). This is due to high scattering optical thicknesses combined with significant inelastic effects, as discussed in Section 3.3.The relative error j > 1  because our elastic-scattering model includes spectral redistribution when ballistic photons move from population (0) to population (1). Thus the numerical evaluation of j ≤ 1) recorded with this model is reported in j ≤ 1) = −Pj>1) rapidly exceeds 10% when absorption optical thickness increases. Overall, single-scattering approximation is fairly accurate when τL < 1, which corresponds to a significant improvement compared to zero-order scattering approximation.Single-scattering approximation leads to an error below or equal to 5% for TATAThe above approximation provides valuable results but requires double numerical integration. Here, the gray approximation presented in Section 3.3 is applied to the first-order term, in order to eliminate spectral integration over the luminescence spectrum in A(1) see : PA(1)≃Pj = 1, leading to the following RTE for first-order intensity The same gray equivalent medium representation as in Section 3.3 is applied to Then the same approach as in Eqs The results in This remarkable accuracy results in fact from the compensation of two errors:j ≤ 1) in On the one hand, truncating scattering expansion always underestimates absorptance, as discussed in Section 2.3. The magnitude of this underestimation is provided by Δ, as discussed in Section 3.3.Therefore, even if this approximation is of great interest for the study of photosensitized and photocatalytic systems, we cannot be sure that these two antagonistic effects always have similar absolute values and compensate for each other. For example, if a photosensitizer were studied with a gray extinction cross section on the luminescence spectral range (see Section 3.3), then To conclude, the use of this gray single-scattering approximation requires some precautions, but provides accurate results for every typical case investigated in this paper.2 production implemented in a benchmark photoreactor was estimated without taking into account luminescence. Hereafter we revisit these results and discuss the effects of luminescence on quantum yield measurements. In particular, the method established in the previous sections will be implemented in order to identify a relevant analytical approximate solution based on optical thickness analysis.In a previous publication , the ove2−) as the photosensitizer and triethylamine (Et3N) as a sacrificial electron donor. Such a photoreactive system can operate in water with the mechanism  complex used as a proton reduction catalyst, fluorescent Eosin Y ,When EY3*EY2−),In the most favorable case for hydrogen production, electrons go through a spin conversion by intersystem crossing (ISC) into a triplet state  can be described as follow:1*EY2− can relax by non-radiative emission  and water  and scattered (fluorescent) photons emitted by Eosin Y in interval λ∈ , as presented in fλ to account for catalyst absorption : notation (•) ≡ (Φ = 0)Reference model taking fluorescence into account (see Section 2.5): notation where superscript (•) is droppedGray Single-scattering analytical approximation (see Section 4.3): notation Absorption by the catalyst is simply added to the models established in previous sections by modifying the radiative properties as follows:kλ → kλ + kcat,λ with the extinction coefficient of the catalyst kcat,λ = CcatEcat,λfλ that a photon absorbed is absorbed by Eosin Y molecules :f varies between 79% and 96% for the concentration range studied . Moreover, less than 10% of the incident radiation reaches the rear glass for the absorption optical thicknesses studied in Absorption and scattering optical thicknesses defined in Eqs φ (obtained with the reference MVRPA given by the Monte Carlo method) and the overall quantum yields φX)( obtained from the MVRPA models denoted (X) above.The relative differenceφ in φ when Eosin Y concentration decreases could be explained by quenching phenomena: collisions between Eosin Y excited states and other molecules (quenchers) such as Et3N, H2O, or Eosin Y itself, for instance, limits the singlet and triplet state yield required for hydrogen production  see : the grej decreases with j, and the higher j = 3 in the cases investigated;of course, the effect of multiple scattering increases with optical thickness: the contribution of scattering orders zero-order scattering approximation in +, representing half of the test cases investigated in this paper,inelastic single-scattering approximation in approximation in Eλ in + and Eosin Y, but require double numerical integration;grayapproximation in Eλ in gray single-scattering approximationEλ in the following analytical approximate solutions can be used to describe photon absorption with an error below 5%:Eλ in a priori that this is the case for every photosensitizer.Cases with high scattering optical thickness combined with strong spectral variations in 2 production was initially obtained without accounting for the fluorescence of Eosin Y in the treatment of experimental results [The work presented in this article also allows us to take another look at overall quantum yield estimation. The overall quantum yield of a photoreactive system composed of Eosin Y as the photosensitizer and a bio-inspired catalyst for H results . We revineglecting fluorescence on absorptance clearly affects the results of overall quantum yields, which are underestimated since absorptance is overestimated,according to the optical thickness of the experimental configuration, the gray single-scattering analytical approximation was selected. It provides results with a error of less than 4% on overall quantum yield estimation, enabling fluorescence to be taken into account without having to implement an advanced numerical method such as Monte Carlo.Some interesting perspectives can also be drawn up. First of all, this work could be extended to the evaluation of the mean volumetric rate of photon absorption ling law , 50. Thiling law , 56.Finally, many of the tools presented and discussed in this work could find interesting applications for the quantitative use of Fast Fluorescence Rate (FFR) or Pulse Amplitude Modulation (PAM) fluorescence measurements using microalgae in the field of photobioreactor engineering , as wellS1 Appendix(ZIP)Click here for additional data file.S2 Appendix(ZIP)Click here for additional data file.S3 Appendix(ZIP)Click here for additional data file.S1 Nomenclature(PDF)Click here for additional data file.


Here we explore the effects of pulsed carbon release from the Karoo LIP on atmospheric pCO2 and δ13C of marine sediments, using the GEOCLIM carbon cycle model. We show that a total of 20,500 Gt C replicates the Toarcian pCO2 and δ13C proxy data, and that thermogenic carbon (δ13C of −36 ‰) represents a plausible source for the observed negative CIEs. Importantly, an extremely isotopically depleted carbon source, such as methane clathrates, is not required in order to replicate the negative CIEs. Although exact values of individual degassing pulses represent estimates, we consider our emission scenario realistic as it incorporates the available geological knowledge of the Karoo LIP and a representative framework for Earth system processes during the Toarcian.The emplacement of the Karoo Large Igneous Province (LIP) occurred synchronously with the Toarcian crisis (ca. 183 Ma), which is characterized by major carbon cycle perturbations. A marked increase in the atmospheric concentration of CO The emplacement of the Karoo LIP occurred synchronously with the Toarcian crisis, which is characterized by negative carbon isotope excursions. Here the authors use carbon cycle modelling to show that thermogenic carbon released during LIP emplacement represents a plausible source for the negative excursions. The carbon cycle disturbances are evidenced by increases in the atmospheric concentration of CO2  and negative carbon isotope excursions (CIEs) recorded in both carbonate and organic matter in marine and terrestrial archives14. A prominent negative CIE marks the onset of the T-OAE, and varies in magnitude in both carbonate and organic matter . High-resolution δ13C curves from multiple sections show a stepwise character of the excursion, with several abrupt negative shifts making up the full body of the CIE17.The Toarcian crisis (ca. 183 Ma) is characterized by extinctions in both the marine and terrestrial realm, localized ocean anoxia , global warming and major carbon cycle perturbations21). This has led to the hypothesis that Karoo-derived emissions were responsible for the carbon cycle perturbations ; however, the negative shift in δ13C is of such magnitude that mantle-derived carbon alone is unlikely to have been the source22. Alternative suggestions include marine methane clathrate dissociation , permafrost melting23, terrestrial organic matter25, or thermogenic carbon release generated by sill emplacement into organic-rich sedimentary rocks of the Karoo Basin .High-precision U-Pb geochronology demonstrates that the Karoo LIP in South Africa and Lesotho Fig.  was empl27,), leading to pulsed contact metamorphism and fluid release. Notably, a stepwise decrease in δ13C is suggestive of isotopically light carbon supplied in pulses to the ocean-atmosphere system28. Field investigations, borehole studies, and numerical modeling suggest thermogenic carbon generation on the order of several thousand gigatons within the Karoo basin31. The presence of thousands of explosion pipes and hydrothermal vent complexes rooted in the contact metamorphic aureoles represent a plausible release mechanism, and attests to rapid emissions of the thermogenic gases32. Available high-precision U-Pb ages of the sills and thermogenic emission estimates from the Karoo Basin allows to identify detailed and realistic emission scenarios from the Karoo LIP; however, these have not yet been tested by carbon cycle modeling.Volcanic basins, such as the Karoo, are characterized by a pulsed emplacement of sills , the T-OAE lasted for 500 kyr, and overlaps with the full extent of the carbon isotope perturbations . Following our correlations, the pCO2 peak coincides with the peak negative δ13C values .In order to investigate the consequences of carbon release from the Karoo LIP, it is essential to constrain the timing between the negative CIEs, 36, Fig. 37. As this CIE is not systematically recorded, and there is no evidence for pCO2 increase or Karoo activity at this time, it is not considered in this study. Furthermore, we stress that there are alternative correlations and interpretations for the Toarcian carbon cycle perturbations that differ from those used here, particularly with respect to the duration of the full extent of the T-OAE CIE, which varies from 120 to 2400 kyr (Supplementary Note 43).The Karoo intrusives postdate a ∼1–2‰ negative CIE that occurs around the Pliensbachian-Toarcian (Pl-T) boundary in some sections  = 30 and 262 kyr  is set to 8000 Gt, following average estimates for the Karoo LIP , which overestimates the pCO2 , with a total negative shift (δ13Cmax – δ13CpreT-OAE) of ~−4‰. Following the δ13Ccarb data, the modeled δ13Corg curve also decreases in seven steps (between ~0.5 and ~3.7‰), but with larger magnitudes, as well as a larger a total negative shift of ~−6‰. Both the modeled δ13Ccarb and δ13Corg curves generally plot within the range of observed data considering both the magnitude and shape of the negative shift  the modeled δ13Corg curve does not replicate all of the short-lived negative CIEs making up the prolonged interval of negative δ13C values following peak negative values. Note that all observed δ13C curves are from shallow marine stratigraphic sections, and is accordingly compared to model δ13C data representing a shallow ocean epicontinental sea or shelf environment .The pulsed release of a total of 20,500 Gt C leads to a stepwise increase in CO2 Fig. . The mod13C, including several negative steps, and a total negative shift (δ13Cmax – δ13CpreT-OAE) of ~−4‰ for δ13Ccarb and ~−6‰ for δ13Corg. This is comparable to observed Toarcian carbonate δ13C records showing generally lower CIE magnitudes compared to those of organic matter, with mean total CIE values of ~−3 vs. ~−5‰, respectively15. Globally, the total magnitude of the T-OAE CIE ranges considerably , however, the largest excursions are likely exaggerated due to local effects43. Furthermore, all high-resolution Toarcian carbon isotope curves show a stepwise character of the T-OAE excursion, and a series of at least five prominent negative shifts is recognized in numerous carbonate and organic matter Toarcian sections . δ13C curves showing one main long-lived T-OAE CIE, or a limited number of negative shifts, have likely failed to record the full extent of the stepped descent due to low sample or stratigraphic resolution. We chose not to take the observed prolonged interval of negative δ13Corg values following peak negative values into account, because it is uncertain whether or not this represents a global trend. It has been suggested that, due to improved preservation of marine organic matter under oxygen-depleted conditions, artificial Toarcian δ13Corg excursions have been produced40. This could potentially explain why there is an apparent prolonged interval of δ13Corg CIEs, while δ13Ccarb values instead return to background levels . Although Toarcian δ13C curves vary with respect to the magnitude, number, timing, and durations of the negative CIEs, we consider our modeled δ13Ccarb and δ13Corg curves to be representative for the overall global trend of Toarcian carbon cycle changes.The emission scenario presented here replicates an overall global trend in δ13C data is compared to several observed δ13C curves, available reconstructed Toarcian pCO2 curves are scarce. As seen in Fig. pCO2 curve generally plots within the range of observed Toarcian pCO2 data from ref. 1, but potential target pCO2 values represent quite a wide range due to data points with large error bars. Consequently, the magnitude of released carbon could vary greatly and still replicate the observed pCO2 data within the range of uncertainties. However, by respecting both observed pCO2 and δ13C curves simultaneously, the possible magnitude of carbon release is narrowed down considerably. Furthermore, based on Toarcian seawater pH (ref. 2) and Δ13C data , a pCO2 increase from ~800–850 ppm to ~1750–1800 ppm has been calculated . As seen in Fig. pCO2 data. The overestimation of pCO2 at t = 111 kyr shown by the modeled curve . The ratio of trapped versus released thermogenic gases from volcanic basins is poorly constrained, although 100% degassing from intrusive LIP components is considered unrealistic . Consequently, the magnitude of released carbon must be lower than the magnitude of carbon generated. The lowermost thermogenic carbon generation estimates are lower than the release value constrained by our modeling. However, these numbers are likely significantly underestimated as they have been upscaled based on a much smaller area of affected host rock compared to that of ref. 31, and do not include devolatilization of Ecca coals or Beaufort, Dwyka and Stormberg organic-bearing rocks in the Karoo strata . In contrast, sills are rare in the Stormberg Group, while devolatilization of Dwyka sedimentary rocks was likely restricted to the upper parts of the series based on the distribution of the sills. The Ecca shales have the highest TOC contents, reaching locally as much as 18 wt.%, while maximum values within the Stormberg, Beaufort and Dwyka Group sedimentary rocks range from 3 to 6 wt.%53. Although the TOC contents are overall lower compared to the Ecca Group, the presence of closely spaced large sills  in the Beaufort Group with TOC up to ~6 wt.%52 suggests significant gas generation potential at these stratigraphic levels as well. Sill thicknesses and vertical spacing are important factors influencing the gas generation potential; gas generation can increase by up to ~35 % for more closely spaced sills, compared to separate sills emplaced into the same host-rock27.Considering the TOC content and sill distribution in the Karoo Basin, sill emplacement into Ecca and Beaufort shales volatilized significantly more carbon-bearing gases compared to sill emplacement at other stratigraphic levels. Within the Ecca and Beaufort series, sills are abundant and can be traced almost continuously with depth, as well as between the basin margins Fig. ; ref. 4713C curves. Importantly, however, the U-Pb geochronology links sill emplacements within organic-rich sedimentary rocks  to the entire interval of Toarcian carbon cycle perturbations . We therefore consider the magnitudes of the individual pulsed thermogenic carbon releases to represent realistic values.According to our emission scenario, the magnitudes of the individual thermogenic carbon pulses vary throughout the model run Table , which ions Fig. . Further13C-depleted carbon, which can explain the observed negative CIEs. As the lowest δ13C value of the released thermogenic carbon in our model is −36‰, an extremely isotopically depleted carbon source  is not a required component  and their associated isotopic cycles , to the 3D FOAM general circulation climate model57. COMBINE consists of one atmospheric box and nine ocean boxes, including 1) an epicontinental surface reservoir divided in two boxes , 2) three mid-latitude ocean boxes , and 3) two polar oceans both divided in two boxes (surface and deep). A full description of the GEOCLIM model can be found in refs. 34 and 56.GEOCLIM couples the 10-box model COMBINE58. The background volcanic degassing rate was set to 4 × 1012 mol/yr so that the pCO2 equals ~ 650 ppm at t = 0 (prior to any Karoo degassing), which represents an average value of observed pCO2 data .Boundary conditions for the simulations presented here include a Jurassic (180 Ma) paleogeography, which is derived from a synthesis of paleomagnetic data, hot spot tracks and geological constraints13C of the various carbon species  in each reservoir/box . The isotopic fractionation between H2CO3* (H2CO3 + CO2; Supplementary Note 2CO3* concentration at each timestep for each oceanic reservoir. As shown in Supplementary Fig. 2CO3* and the POC increases during the interval of carbon injections, but then decreases towards “background values”. A decrease in fractionation reduces the difference between the δ13C of carbonate and POC, which allows the δ13Corg to increase faster compared to δ13Ccarb59. This could potentially explain the apparent decoupling between the δ13Corg and δ13Ccarb modeled curves (Fig. 13Corg curve recovers faster and reach observed values during the recovery interval at the end of the model run, the modeled δ13C carb curve predicts slightly lower δ13C values compared to observed values.GEOCLIM calculates the δves Fig. ; while tSupplementary Information


This study evaluated oxygen uptake (VOn = 21) and 12 months (n = 14) after transplantation and a control group of healthy young adults (n = 16) underwent cardiopulmonary exercise testing on cycle-ergometer. The protocol consisted in two subsequent constant, moderate-load exercise phases with a final incremental test until exhaustion.Two groups of KTRs enrolled 3 . Peak VO2 was lower in KTRs evaluated 3 months after transplantation compared to patients evaluated after 1 year . Blood haemoglobin (Hb) concentration was higher in KTRs evaluated at 12 months . Among KTRs, τ showed a moderate negative correlation with Peak VO2 (ρ = − 0.52) and Oxygen uptake efficiency slope (OUES) (r = − 0.57) while no significant correlation with Hb and peak heart rate.The time constant of VO2 kinetics compared to healthy controls. Hb and peak VO2 seem to improve during the first year after transplantation. VO2 kinetics were significantly associated with indices of cardiorespiratory fitness, but less with central determinants of aerobic capacity, thus suggesting a potential usefulness of adding this index of muscular oxidative metabolism to functional evaluation in KTRs.KTRs show slower VOThe online version contains supplementary material available at 10.1007/s00421-021-04672-x. Scientific evidence clearly shows that cardiorespiratory fitness is a strong predictor of all-cause and cardiovascular mortality independent of age, sex, ethnicity, and comorbidities , i.e., the rate of adjustment of the oxygen consumption to a sudden increase in workload during the transition from rest to constant, moderate intensity exercise, is thought to reflect the oxygen utilization at a peripheral muscular level . All procedures were conducted in accordance with the Declaration of Helsinki and patients provided written informed consent. The evaluation was performed during routine clinical exercise testing, as previously described for other patient population . To overcome the possible drop-outs that could have arisen testing patients on two different days, a specific protocol was designed to obtain both constant load and incremental exercise testing data in a single clinical evaluation Fig. . The pro2 kinetics during the transition from unloaded pedalling to moderate intensity exercise. First, the VO2 responses were linearly interpolated using a mathematical software  to provide one value of VO2 per second; thereafter the values of the two bouts were averaged. Iterative nonlinear regression (Levenberg–Marquardt procedure) was used to characterize the primary VO2 response after removing the first 20 s of data , fitting the resting 5 min in a mono-exponential function according to the following equation:2(t) is the VO2 at time t; VO2(bl) is the baseline VO2 measured in the 30 s preceding the transition to exercise; and Ap, TDp, and τ are the amplitude, time delay, and the time constant of the primary (phase 2) response of VO2 kinetics, respectively.The first two constant load bouts were used for the determination of the VO2 at peak exercise (peak VO2) was determined during a final, incremental ramp testing until patients’ exhaustion, defining peak VO2 as the highest average VO2 recorded during a 30-s period of testing. The first ventilatory threshold (VT1) was estimated using the V-slope method and evaluating the ventilatory equivalent of VO2  with post hoc analysis (Tuckey’s post hoc test) was performed on all normally distributed variables. For parameters that violated the assumption of homogeneity of variances, a Welch test was performed and Games-Howell post hoc tests were used for multiple comparisons. For variables that showed a non-normal distribution in at least one of the three groups, a Kruskal–Wallis H test was performed and pairwise comparisons were conducted using Dunn’s (1964) procedure with a Bonferroni correction for multiple comparisons. A statistical significance level of 0.05 was used for all tests; pairwise comparisons results were expressed as adjusted P values. Controlling data for outliers, the analysis was performed also removing the outliers and their presence was tolerated if they did not alter the significance of the results obtained. To assess correlations between variables, Pearson’s r or Spearman’s rho correlation indexes were used for normally and non-normally distributed variables, respectively. Statistical analysis was performed using SPSS .Normality of variables was checked using the Shapiro–Wilk test. For comparisons between two groups, a chi-square test was used to assess the differences between categorical variables. In the case expected cell frequencies were greater than five a Fisher’s exact test was used. For continuous variables, a 2, maximal power output, VO2 at the VT1 and peak heart rate. The VO2/Work Rate slope was, however, comparable between all groups , maximal power output  and OUES  were found higher 1 year post-surgery. This was also confirmed by a more efficient ventilation as shown by the lower VE/VCO2 slope 12 months after transplantation  , peak power output , VO2 at the VT1 , power output at the VT1  and the OUES . No significant correlation was found between τ and Hb  or percentage-predicted peak heart rate (HR) . Conversely, Hb was more strongly correlated with main parameters of cardiorespiratory fitness, similarly to what found for patients’ peak HR . This value seems to improve 1 year after transplant . These results confirm existing data on VO2 improvement after kidney transplant  , which were comparable for KTRs of the 12-month group  . Although these data cannot provide information regarding the underpinning pathophysiological mechanisms affecting VO2 kinetics, study outcomes may suggest that also peripheral adaptations occur after kidney transplantation. As previously mentioned, current evidence supports the hypothesis that slowed VO2 kinetics during moderate intensity cycling mainly reflect an impaired oxidative capacity of the muscle. Even if this assumption is still debated, particularly for patients with chronic diseases  Below is the link to the electronic supplementary material.


Ipomoea batatas L.) cultivation in Turkey is concentrated in one province situated in Mediterranean region only, which would not fulfill the domestic needs of the country soon. Therefore, cultivation of the crop in other provinces/climatic regions should be initiated to fulfill the domestic needs. The cultivation in other provinces requires thorough assessment of yield and quality traits of target crop. Therefore, yield and quality characteristics of four sweet potato genotypes  were assessed in the current study in Kazova and Niksar counties of Tokat province of the country having middle Black Sea climate in field experiments during 2018 and 2019. The cuttings of the genotypes were planted in Niksar during the second fortnight of April and first week of May in Kazova. The planting density was kept 90 × 45 cm. Data relating to number of storage roots, storage root weight, storage root yield per hill and storage root yield per hectare were recorded. Furthermore, quality traits, including dry matter ratio (%), protein ratio (%) and antioxidant ratio (%) of storage roots were also determined. The highest total storage root yield was recorded for ‘Havuc’ genotype during both years and locations, followed by ‘Hatay Yerlisi’ and ‘Hatay Kırmızısı’ genotypes. Overall, storage root yield (60.06 and 62.40 tons ha-1 during first and second year) recorded for the experiment at Niksar was higher than the storage root yield recorded for Kazova experiment . The highest dry matter was produced by ‘Kalem’ and ‘Hatay Yerlisi’ genotypes during both years and at both locations, followed by ‘Hatay Kırmızısı’ and ‘Havuc’ genotypes. The storage roots of the tested genotypes accumulated higher dry matter at Kazova during both years. The highest protein content was obtained from the ‘Kalem’ genotype, and the protein contents of the ‘Hatay Yerlisi’ and ‘Hatay Kırmızısı’ genotypes were close to the ‘Kalem’ genotype. The results indicated that tested genotypes can successfully be cultivated in middle Black Sea climate. Therefore, production of sweet potato can be initiated in the future to meet the domestic needs for sweet potato in the country.Sweet potato ( Ipomoea batatas L.), a member of the ivy (morning glory) family (Conconvulaceae), is of Latin American origin [th century [Sweet potato  of Tokat province, Turkey. Experimental site in Niksar was situated between 40.534167°N, and 36.929167°E longitude (290 m asl) during first year (2018) and between 40.5625°N latitude and 36.913889°E longitude (281 asl) during second year (2019). Similarly, the experimental field in Kazova was situated between 40.331944°N latitude and 36.473333°E longitude (595 m asl) during first year (2018), and between 40.330278°N latitude and 36.391389°E longitude (567 m asl) during second year (2019) of the experiment.2O5; 1.04–1.31 kg ha−1) and rich in exchangeable potassium content  [Composite soil samples were taken from 0–30 cm depth and analyzed at soil testing Laboratory, Faculty of Agriculture, Tokat Gaziosmanpasa University. Soils of the experimental sites were clay-loam in texture and alkaline . Soils had sufficient organic matter content (2.04–2.02%), high lime content (21.00–21.42%), poor in available phosphorus (Pkg ha−1) .Monthly average temperature and total precipitation received at both experimental sites are given in -1 15N-15P2O5-15K2O fertilizer was applied before planting, and additional 80 kg N ha-1 was applied one month after planting. Mechanical weed control was carried out to prevent weed competition. Plants were irrigated by drip irrigation system at an average of ten days intervals. The crop was harvested during first fortnight of October in the Kazova, and in last week of October at Niksar.Experimental design was randomized complete block with three replications and each plot consisted of four rows of 3.6 m. Planting density in each plot was 90 × 45 cm. Planting in both years was carried out during second fortnight of April at the Niksar and in the first week of May at Kazova. In all locations, 80 kg haThe plants in the central two rows of each plot were removed one by one and the number of storage roots per plant, average storage root weight and the total storage root yield were determined. Dry matter ratios, protein ratios and antioxidant contents of the storage roots were calculated for both years and locations. Four g of storage root sample was weighed and placed on a watch glass in order to determine dry matter ratio. The samples were kept in an oven at 105°C for 48 hours, weighed and the dry matter ratios were calculated.The samples were ground and powdered with the IKA A11 Basic model blender and dried in a BINDER brand oven for 48 hours at 65°C for determining protein ratio. A calibration curve was drawn using aspartic acid standard according to the sample category to be analyzed from the Thermo Cookbook before starting the analysis, samples were weighed in specified amounts and analyzed. Protein analysis was performed with the Thermo Scientific flash 2000 N-protein analyzer device.Various methods are available to evaluate the antioxidant activity of natural compounds in food or biological systems. The 1,1-diphenyl-2-picrylhydrazyl (DPPH) and 2,2-azinobis-(3-ethyl benzo thiazoline-6-sulfonate) (ABTS) are two commonly used methods for antioxidant analysis. The mechanism of both methods is similar because the absorption spectra of stable, free radicals change when the molecule is reduced by an antioxidant or a free radical species. The ABTS can dissolve in aqueous and organic solvents and react readily compared to DPPH, which normally takes several hours for the reaction to complete. The color of the DPPH test can interfere with samples containing anthocyanins, which leads to an underestimation of antioxidant activity. However, this problem does not arise in the ABTS test, especially when the absorbance value is measured at 734 nm. However, DPPH procedure can be successfully used to determine antioxidant activity of sweet potatoes .• free radical scavenging effect of sweet potato varieties was determined according to Blois [• scavenging capacity. The DPPH kit was purchased from Merck SA (Pty) Ltd. . The DPPH scavenging activity was measured according to The DPPH assay is used as a substrate to evaluate the activity of antioxidant enzymes. The DPPHto Blois . In this1 is the control and A2 is the sample absorbance.Where, AThe data were subjected to two-way analysis of variance (ANOVA) . The datAverage number of storage roots per plant significantly (p<0.05) differed among tested genotypes during both years at Niksar . The higThe number of storage roots reported by Arslanoğlu and Hendekçi  ranged b-1 by Arslanoğlu and Hendekçi [The tested genotypes significantly differed for weight of storage roots per plant during both locations and years. The highest storage root weight per plant at both locations was noted from ‘Havuç’ genotypes during both years. Overall, storage root weight at Niksar was higher than Kazova during both years. Storage root yield for 3 different sweet potato local genotypes was reported between 2219.4 and 2523.3 g plantHendekçi , whose rHendekçi .Storage root yield of sweet potato is related to the number of plants per unit area, number of storage root per plant, and weight of the storage roots, which may vary across environments . AverageThe ‘Havuç’ genotype produced the highest storage root weight during both years and locations followed by ‘Hatay Kırmızisı’ genotype. The storage root weights reported by Yıldırım et al.  are in aStorage root yield of local genotypes grown at Niksar was higher than those grown in Kazova . LewthwaThe highest storage yield during both years was obtained from ‘Havuç’ genotype followed by ‘Hatay Yerlisi’, ‘Hatay Kırmızısı’ and ‘Kalem’ genotypes at both locations. The results for storage root yield indicated that ‘Kalem’ genotype did not adopt well to the ecological conditions of the experimental sites, while other 3 genotypes adapted well to the environmental conditions of Tokat-Kazova.-1 in Diyarbakır province, 19.36 and 85.60 ton ha-1 in Şanlıurfa province, 12.14 and 79.72 ton ha-1 in Adana province and 16.33 and 61.16 ton ha-1 in Hatay province. They concluded that sweet potato genotypes have successfully adapted to the South and Southeastern regions of Turkey. The storage root yield values obtained from ‘Havuç’, ‘Hatay Yerlisi’ and ‘Hatay Kırmızısı’ genotypes under Tokat conditions are similar to the yield values of the same genotypes reported by Çalışkan et al. [’.Sweet potato is a sensitive plant to environmental variation. Several studies have revealed that changes in environmental conditions might have significant impact on its yield and quality –25. Çalın et al.  obtainedDry matter and protein ratio of storage roots were significantly affected by different sweet potato genotypes . GrowingThe highest dry matter content of storage roots at Niksar during 2018 was recorded for ‘Hatay Yerlisi’ followed by ‘Kalem’, ‘Hatay Kırmızısı’ and ‘Havuç’ genotypes, respectively. During 2019, the highest dry matter content was recorded for ‘Kalem’ genotype. Oduro  and GurmDry matter content of sweet potato genotypes at Kazova location during 2018 ranged from 8.11% (‘Havuç’ genotype) to 33.36% (‘Hatay Yerlisi’). The highest dry matter content during second year of the experiment at Kazova location was obtained for ‘Hatay Yerlisi’ followed by ‘Kalem’, ‘Hatay Kırmızı’ and ‘Havuç’ genotypes, respectively.The highest protein ratio of storage roots during both years at both locations was observed for ‘Kalem’ genotype, while the lowest for ‘Havuç’ genotype.Carbohydrates, vitamins, minerals, and protein content of sweet potato were higher compared to the other root and tuber crops . YıldırıAntioxidant activities of genotypes at Niksar during 2018 were moderate compared to the standards. The antioxidant activity was not significantly different between sweet potato genotypes . The higThe genotypes significantly differed for yield and quality response and could adapt new climatic conditions as hypothesized. Temperature conditions in Kazova and Niksar were good enough for the sweet potato to complete the vegetation period. Temperature requirements of sweet potato plants in the experimental area could met 180 days from planting. The results of the study indicated that sweet potato can easily adapt to the climatic conditions of this region.


CH of oxide–electrolyte interfaces usingdensity functional theory-based finite-field molecular dynamics simulations.It is found that the dipole of interfacial adsorbed groups  at the electrified SnO2(110)/NaCl interfaces significantly modulates the double layerpotential which leads to the asymmetric distribution of CH. We also find that the dissociative water adsorptionprefers the inner sphere binding of counterions, which in turn leadsto a higher Helmholtz capacitance, compared with that of the nondissociativecase at the interface. This work provides a molecular interpretationof asymmetric EDLs seen experimentally in a range of metal oxides/hydroxides.The structure ofelectric double layers (EDLs) dictates the chemistryand the physics of electrified interfaces, and the differential capacitanceis the key property for characterizing EDLs. Here we develop a theoreticalmodel for computing the differential Helmholtz capacitance  Some of thefundamental questions therein are the following: What are the surfacecomposition and ions distribution in the EDL? How would adsorbed watermolecules respond to the electric field?9 How would the dissociation and the recombination of interfacialwater molecules affect the double layer potential ΔU? What would the differential capacitance look like, that is, thechange of the Helmholtz capacitance with respect to the surface chargedensity?10 In this regard, experimentalmethods such as X-ray photoelectron spectroscopy and X-ray standingwave provide the ion adsorption and the surface potential information;12 the sum-frequency generation spectroscopy probes the polarizationof water at charged interfaces;14 and titration experimentsreveal the change of surface charge density versus pH.16 Nevertheless, the analysis and extraction of this microscopic interfacialinformation on EDL is rather difficult if not impossible.19EDLs play an important role in electrochemistry,21 Recently, it has been shown thatthe finite-field DFTMD is a promising technique for modeling EDLsat electrified solid–liquid interfaces.24 Finite-fieldDFTMD simulations relies on the constant electric displacement D Hamiltonian introduced by Stengel, Spaldin, and Vanderbilt,25 and the corresponding expression of the averageHelmholtz capacitance CH is shown to be22Lz is the dimension of the supercellperpendicular to the interface, q is the introducedsurface proton charge, A is the area of the x, y crosssection, and ⟨Pz⟩ indicates the ensemble averaged supercell polarization.Because ⟨Pz⟩converges rapidly in the finite-field simulations, this makes CH a new observable within the accessible time-scaleof DFTMD. Note that in conjugation with This calls for density functional theory-based molecular dynamicssimulation (DFTMD), which is a suitable computational method for describingthe microscopic structure and the dynamics of water and ions nearan interface.23 it was found that the Helmholtz capacitanceat electrified rutile TiO2(110)/NaCl interfaces is muchhigher at high pH than that at low pH for the given surface chargedensity, and the interfacial proton transfer at low pH increases significantlythe capacitance value. Compared with rutile TiO2, the isostructuralcassiterite SnO2 has a characteristic dissociative wateradsorption,27 which involves terminal adsorbedwater Sn5cOwH2 to bridge oxygen siteSn2Obr asIn the first work of applying finite-field DFTMD for modeling EDLs,2(110)/NaCl electrolyte interfacesat different surface charge densities σ were simulated withfinite-field DFTMD, using the CP2K/Quickstep package29 with the PBE functional.30 Detailed descriptionsof the computational setup are given in the Supporting Information.Then, the question naturallyarises: how would the proton transferaffect the differential capacitance and vice versa? To answer that,herein the electrified SnO2(110) surfaces are positively chargedby adsorbing protons to Sn2Obr sites, and thedirection of dissociative proton transfer is opposite to that of theelectric field E in the EDL (2(110)surfaces are negatively charged by the desorption proton from terminalSn5cOwH2, and the direction of thedissociative proton transfer is the same as that of the electric fieldE in the EDL  over DFTMD trajectories (see Supporting Information). Meanwhile, we find the free energy of water dissociation(Adiss decreases with the pH (see Supporting Information).At low pH,the SnO the EDL 2 α incre the EDL 1b, when ociation2 ΔAdiss When looking at the orientation of interfacial water, itis foundthat the adsorbed water molecules point toward the electrolyte solution1c, with 33 As shown in Supporting Information), the band edge is shifted upward with reference to the standardhydrogen electrode (SHE) scale34 when goingfrom the vacuum surface, to the water monolayer (ML) adsorption andthe fully solvated SnO2(110)/H2O interface.This effect is also manifested when restraining water molecules adsorbedon the left side of the SnO2 slab not undergoing dissociationreactions at the PZC. In this case, interfacial water molecules wouldhave different orientational distributions on the two sides of theSnO2 slab , which is a function of D.Fromthe equation above, it is clear that we will have a constantterm Pw as a descriptor, theΔPw includes the contribution ofadsorbed water molecules in both molecular and dissociative forms.One may scale ΔPw by the dielectricconstant of the double layer ϵH° to accountfor the electrostatic screening. This recasts Mw(D) = Ω · ΔPw(D), the volume Ω = A · lH. Here ΔMw(D) is the total dipole momentdifferenceof interfacial groups (including the molecular and dissociative formsof adsorbed water) with respect to PZC. We can get ΔMw = (Mw · Nw – Mw0 · Nw0) + (Mdis · Ndis – Mdis0 · Ndis0). Mw, Mdis, Nw, and Ndis are the dipole moment and number of adsorbedwater molecule and dissociated (OH–+H+) groups . Note that inthe model introduced here, there is only one free parameter ϵH° in lH and ΔMw(D) can be determined from finite-field DFTMD simulations.This allows us to obtain the differential capacitance rather thanapplying the one-shot estimator . In the case of SnO2(110),ΔMw(D) includesthe contribution of adsorbed water molecules in both molecular anddissociative forms as shown in lH is about 2.6 Å, which estimates from the surfacenormal projected distance between the counterions and the nuclei ofObr sites averaged over all surface charge densities.Then, we applied the ue35 see S6a. In tU(σ) – UPZC is given in H° turns out to be 24, which is quite close to the commonlyassumed values for rutile structures.36 This agreement further justifies the theoretical model we formulatedfor the differential Helmholtz capacitance at oxide–electrolyteinterfaces.The fitting result of U(σ)– UPZC, we obtain the differentialcapacitance CH of the Helmholtz layeras shown in CH shows a maximum of∼151 μF/cm2 at the negatively surface chargedensity −10 μC/cm2, and it decreases to ∼100and ∼60 μF/cm2 when the surface charge densitymoves away to −40 and 40 μC/cm2, respectively.In addition, we find that CH at the negativelycharged surface is about 50% higher than that at the positively chargedsurface for the same value of |σ|, and this finding of asymmetricdistribution of the differential CH isin accord with what has been seen at electrified TiO2(110)/NaClinterfaces from finite-field DFTMD simulations23 and in agreement with titration experiments of SnO2 at higher ionic strength.37 In fact, theasymmetric Helmholtz capacitance has been also seen in a range ofmetal oxides/hydroxides, such as ZnO,38 TiO2,16 α-Al2O339 and γ-FeOOH.40By taking the analytical derivative of U(σ) – UPZC with ΔMw as theinput, this points to the asymmetric orientation of adsorbed surfaceO–H groups as the determining factor. At the metal oxide surfaces,water molecules have preferred orientations because of the chemisorption,where dipoles are pointing to the liquid phase, i.e. ⟨Mw⟩> 0 at PZC (DPZC into the Debye-type Hamiltonian– μ · (D + DPZC) cos(θ), where μ is the dipole moment of noninteractingwater molecules.This common feature observed in differentoxides suggests thatthere should be a fundamental reason behind its cause. Because themodel given in 0 at PZC 1c. This Mw⟩ with referenceto the PZC , the interaction between dissociated OH–, H+ and counterions in electrolyte is directand strong, forming the inner sphere coordination. For example, atthe positively charged interfaces, as shown in – is stabilized by two neighboring Sn2ObrH+ and two Sn5cOwH– groups.Similarly, at the negatively charged interfaces, the counterion Na+ is stabilized by two neighboring Sn5cOwH– or two Sn2Obr groups asshown in The final question is how the chemical specificity of surfacescomes into play. Clearly, the magnitude and the sign of CH of SnO2 withdissociatively adsorbed water molecules is about 109 μF/cm2, which is 45% larger than that of SnO2 with watermolecules restrained to the molecular adsorption ∼61 μF/cm2 . Overall, they indicatethat theoretical models connecting the macroscopic property and themicroscopy information are essential for interpreting the differentialcapacitance CH of oxide–electrolyteinterfaces.In contrast, the outer spherecoordination is preferred when restrainingadsorbed water molecules not undergoing the dissociation 5c,d. Con2(110)was established. It has been shown that the general phenomenon ofasymmetric electric double layers seen in a range of metal oxides/hydroxidescan be explained by the specific orientation of chemisorbed watermolecules at the point of zero charge.In summary, through a combination of finite–finiteDFTMDsimulations and a theoretical model, the quantitative relationshipbetween interfacial water orientation, proton transfer and differentialcapacitance at the charged water interface of SnO


OB) is largely unknown despite evidence that higher level processing is different than orthonasal. To this end, we use multi-electrode array in vivo recordings of rat OB mitral cells (MC) in response to a food odor with both modes of stimulation, and find significant differences in evoked firing rates and spike count covariances . Differences in spiking activity often have implications for sensory coding, thus we develop a single-compartment biophysical OB model that is able to reproduce key properties of important OB cell types. Prior experiments in olfactory receptor neurons (ORN) showed retro stimulation yields slower and spatially smaller ORN inputs than with ortho, yet whether this is consequential for OB activity remains unknown. Indeed with these specifications for ORN inputs, our OB model captures the salient trends in our OB data. We also analyze how first and second order ORN input statistics dynamically transfer to MC spiking statistics with a phenomenological linear-nonlinear filter model, and find that retro inputs result in larger linear filters than ortho inputs. Finally, our models show that the temporal profile of ORN is crucial for capturing our data and is thus a distinguishing feature between ortho and retro stimulation, even at the OB. Using data-driven modeling, we detail how ORN inputs result in differences in OB dynamics and MC spiking statistics. These differences may ultimately shape how ortho and retro odors are coded.The majority of olfaction studies focus on orthonasal stimulation where odors enter via the front nasal cavity, while retronasal olfaction, where odors enter the rear of the nasal cavity during feeding, is understudied. The coding of retronasal odors via coordinated spiking of neurons in the olfactory bulb ( Olfaction is a key sense for many cognitive and behavioral tasks, and is particularly unique because odors can naturally enter the nasal cavity from the front or rear, i.e., ortho- and retro-nasal, respectively. Yet little is known about the differences in coordinated spiking in the olfactory bulb with ortho versus retro stimulation, let alone how these different modes of olfaction may alter coding of odors. We simultaneously record many cells in rat olfactory bulb to assess the differences in spiking statistics, and develop a biophysical olfactory bulb network model to study the reasons for these differences. Using theoretical and computational methods, we find that the olfactory bulb transfers input statistics differently for retro stimulation relative to ortho stimulation. Furthermore, our models show that the temporal profile of inputs is crucial for capturing our data and is thus a distinguishing feature between ortho and retro stimulation, even at the olfactory bulb. Understanding the spiking dynamics of the olfactory bulb with both ortho and retro stimulation is a key step for ultimately understanding how the brain codes odors with different modes of olfaction. Orthonasal olfaction is essential for avoiding predators , for cells j and k detailed by j and k, and The ORN input rates can be pairwise correlated, which is achieved by the parameter each parameter set to accurately simulate the spike count statistics. After model parameters were set, the only manual tuning we did was to consider several Poisson input rates λO/R(t)  that we arbitrarily chose were fixed throughout.The biophysical OB model described thus far was adopted directly from Li & Cleland, aside from our single-compartment simplification where we lumped all ionic currents into one compartment and used the sum of the  conductances from all compartments. Here we describe how the network model was tuned to capture the salient features of our experimental data. We did not systematically consider large volumes of parameter space due to the enormous computational resources required for 50,000 simulations of the model for (see Eqs –12)) fo) foeach , wM←Gc = 0.3 (common inhibition to MC), wG←M = 1 , wGc←M = 0.5 (inhibition to common GC), wP←M = 1 and wM←P = 2 . These coupling strengths were chosen in part from results in Ly et. al [wGc←M ≤ wG←M ≤ wM←G). The coupling strengths were never tuned, they were fixed throughout.We used the same equations for the synaptic variables as Cleland , but setw see  to: wM←Gy et. al  who usedy et. al   between the following cell pairs: MC and PGC pair within a glomerulus have cj,k = 0.3 because they receive inputs from the same ORN cells; the two MCs have correlated ORN input [cj,k(t) time-varying as in cj,k = 0.3 for all 3 different pairs of GCs). All other pairs of cells have no ORN input correlation. Note that input correlation for the 2 MCs increased with odor to mimic increased correlation of glomeruli activity. In cR(t) < cO(t). This is based on prior imaging studies that show retronasal stimulation activates spatially smaller regions of glomeruli inputs than orthonasal, and that the activation regions from retro are subsets of ortho [cR/O(t), please refer to code on GitHub.The ORN inputs (Eqs –12)) co) co12)) RN input  of ortho , 17. ForO/R(t), the inhomogeneous Poisson input rate of tk in O/R(t), are constrained such that λO(t) increases faster and more abruptly than λR(t) with odor, and λR(t) decays slower than λO(t); this is all based on ORN imaging studies [O/R(t)) and inhibitory synapses (with rate 0.75λO/R(t)) to capture other unmodeled inhibitory effects.We considered several different λ studies , 17. Inpt) without any consideration for ortho or retro, we used a simple alpha-function form in the evoked state: λ(t) = tet/τ−, surveying 6 different τ (see O/R(t) we tried, notice that they all satisfy the constraints described above. Via trial and error with 2,000 realizations, we only looked at the resulting firing rates (PSTH), insuring the simulations matched the ortho data well. We were fortunate in fitting the retro firing rate data, trying only 2 λR(t). The other spike statistics  were never accounted for in our consideration of different λO/R(t), which is perhaps why the fit to the spike covariance data is so bad.To first understand how MC firing rates depends on λ, μS(t):Here we describe a method to capture the effects of ORN input statistics of synapses to the biophysical OB model, in the limit of infinite realizations. These methods are very useful as inputs for the LN model, without which one would have to use averages from Monte Carlo simulations that contain deviations from finite size effects. Taking the expected value of To derive the equation for variance Recall that Equivalently, Sj(t)Sk(t) correlated synapses, we have:Similarly for By our model construction Sj(t), Sk(t)) equivalently satisfies the ODE:Cov(τX). The quasi-steady-state approximation is:The calculations for the dynamic (time-varying) synapse statistics are important for capturing realistic statistics because a steady-state approximation can be very inaccurate, especially when the time-varying correlation and ORN spiking rate change quickly relative to the time-scales (≈τXaXλ(t)σS2(t)≈τk(t)λ¯(t)25) can k) and shift (b), that are used with the ORN input statistics (Y) to the biophysical OB network model’s output MC spike statistics (PSTH(t), R1, R2)). The LN model is summarized as:f as an exponential, and we can approximate the integral numerically as follows:n denotes the number of time points included in the linear filter, and j denotes the points in time of input statistic A is the Toeplitz matrix of size (Lt − n + 1) × n of our input statistic  of the MC spike statistic is calculated as follows:K denotes the convolutional matrix constructed from the truncated linear filter k.We use the above described ODEs , a, a18), aWe decided to use recordings from a single rat, with recordings from 3 sessions. We took this conservative approach to control differences in nasal cavity structure that can vary across rats , 61, whiRattus Norvegicus, Sprague-Dawley outbred, Harlan Laboratories, TX, USA) housed in an environment of controlled humidity (60%) and temperature (23°C) with 12h light-dark cycles. The experiments were performed in the light phase.All procedures were carried out in accordance with the recommendations in the Guide for the Care and Use of Laboratory Animals of the National Institutes of Health and approved by University of Arkansas Institutional Animal Care and Use Committee (protocol #14049). Data were collected from 11 adult male rats  dissolved in saline, intraperitoneal injection (ip)). Dexamethasone  and atropine sulphate  were administered before performing surgical procedures. Throughout surgery and electrophysiological recordings, core body temperature was maintained at 37°C with a thermostatically controlled heating pad. To isolate the effects of olfactory stimulation from breath-related effects, we performed a double tracheotomy surgery as described previously [Anesthesia was induced with isoflurane inhalation and maintained with urethane . We note that the full experimental data set included additional odors, but here we consider only EB.μm deep from dorsal surface of OB targeting tufted and mitral cell populations. The MEA probe consisted of 4 shanks , each with eight iridium recording sites arranged in two tetrode groups near the shank tip . Simultaneous with the OB recordings, we recorded from a second MEA placed in anterior piriform cortex. Voltage was measured with respect to an AgCl ground pellet placed in the saline-soaked gel foams covering the exposed brain surface around the inserted MEAs. Voltages were digitized with 30 kHz sample rate . Recordings were band-pass filtered between 300 and 3000Hz and semiautomatic spike sorting was performed using Klustakwik software, which is well suited to the type of electrode arrays used here [A 32-channel microelectrode array  was inserted 400 sed here .S1 Figα = 0.01) between ortho and retronasal firing rate (A) after and for the duration of odor stimulation (0.3 ≤ t ≤ 1 s with 100 ms time windows and 0.5 ≤ t ≤ 1.1 s with 200 ms time windows) as well as spike count covariance (C) for the entirety of the evoked state (0 ≤ t ≤ 2 s excluding t = 0 s with 200 ms time window). Spike count variance (B) is not found to have any statistical significant differences between ortho and retro. For completeness, significance of Fano Factor (D) and Pearson’s correlation (E) are also significantly different for ortho and retro in the evoked state (0 < t ≤ 2 s for Fano Factor and 0 ≤ t ≤ 2 s excluding t = 0 s with 100 ms time window for correlation).We performed two-sample t-tests assuming unequal variances for each point in time to assess whether the spike count statistics are significantly different with ortho and retro stimulation. We find statistical significance ((TIF)Click here for additional data file.S2 Figd value for the nondirectional (two-tailed) case to measure effect size index for t-tests of means  and medium  effect size of statistical significance between ortho and retronasal firing rate (A) as well as small (0 ≤ t ≤ 2 s excluding t = 0 s with 200 ms time windows) effect size of spike count covariance (C). Spike count variance (B) does not have a measure of effect size since it is not found to have any statistical significant differences between ortho and retro. For completeness, effect size of Fano Factor (D) and Pearson’s correlation (E) are also found to be small  and medium (0.2 < t ≤0.4 ∪ 1 < t ≤1.4 s for Fano Factor and 0.2≤ t ≤ 0.5 ∪ 0.8 ≤ t ≤ 2 s for correlation).We calculated Cohen’s eans see  in stand(TIF)Click here for additional data file.S3 FigA) Left: initial set of ORN inputs λ(t) (with evoked λ(t) = (t + 1)et+1)/τ− we surveyed to better understand the MC firing rate (right), calculated with 2,000 realizations. B) Fitting the ortho firing rate well enough required considering many λO(t), and we even shifted the spontaneous input rate up slightly at some point. However, the only 2 retro inputs we tried (pink and red) were relatively accurate.(TIF)Click here for additional data file.S4 FigA) Ortho-like input (fast rise and decay of Poisson rate) with same amplitude as retro (high), but with low input correlation used to capture data. Notice how the theory captures the fine structure of the covariance (double-hump). B) Retro-like input (slow rise and decay) with same amplitude as ortho (high), but with high input correlation used to capture data. C, D) Demonstrating accuracy of dynamic theory with much slower  time-scales: τ1 = 50 ms and τ2 = 100 ms and faster relative change in Poisson rate . Showing the quasi-steady-state approximation (Eqs (C) Sinusoidal input and time-varying amplitude: evoked λ(t) = 0.2 + 0.8(1 − 0.8 sin(−15t))(1 − et−2), with synapse jump sizes a1 = 2, a2 = 5. D) Here the jump sizes have opposite signs to get negative covariances: a1 = 2, a2 = −1, with λ(t) = 2(t + 2.25)2 * (1 − 0.9 sin(10t))et−1|/0.35−|. Gray curves (Monte Carlo) are much harder to see in C,D than in A,B because of the much larger magnitudes.Our theory for the ORN synaptic input statistics  an an18) anion (Eqs –25)) in) inA) Or(TIF)Click here for additional data file.S5 FigWe consider 8 total different combinations of ORN inputs varying: temporal profile, amplitude height, input correlation (2 ways each). Despite the simplistic LN model, the resulting fits to the OB model are generally very good. The only exceptions are when the input correlation is relatively smaller, in which case the LN model does not accurately capture the evoked spike count covariance after several hundred milliseconds.(TIF)Click here for additional data file.