Mathematical models at multiple temporal and spatial scales can unveil the fundamental mechanisms of critical transitions in brain activities. Neural mass models (NMMs) consider the average temporal dynamics of interconnected neuronal subpopulations without explicitly representing the underlying cellular activity. The mesoscopic level offered by the neural mass formulation has been used to model electroencephalographic (EEG) recordings and to investigate various cerebral mechanisms, such as the generation of physiological and pathological brain activities. In this work, we consider a NMM widely accepted in the context of epilepsy, which includes four interacting neuronal subpopulations with different synaptic kinetics. Due to the resulting three-time-scale structure, the model yields complex oscillations of relaxation and bursting types. By applying the principles of geometric singular perturbation theory, we unveil the existence of the canard solutions and detail how they organize the complex oscillations and excitability properties of the model. In particular, we show that boundaries between pathological epileptic discharges and physiological background activity are determined by the canard solutions. Finally we report the existence of canard-mediated small-amplitude frequency-specific oscillations in simulated local field potentials for decreased inhibition conditions. Interestingly, such oscillations are actually observed in intracerebral EEG signals recorded in epileptic patients during pre-ictal periods, close to seizure onsets. The concept of neural excitability for single neurons was introduced initially by Louis Lapique in 1907 [re-introduced the concept [Brain dynamics emerges from neural entities interacting at different levels, from single neurons to large-scale neural networks. At each level, transitions between different regimes, such as firing/resting states in single neurons and up/down states in neural networks, are associated with both physiological functions and pathological activity –3. One o in 1907 , 5. Alan concept , classif concept . At the  concept  and loss concept  are assoMathematical models of brain activity range from microscopic level of single cell dynamics to macroscopic level of interactions between large scale neural systems. Neural mass models (NMMs) consider the average temporal dynamics of interconnected neural subpopulations without explicitly representing the underlying mechanisms at the level of single cells. The mesoscopic level offered by the neural mass formulation has been used to model brain signals, from local field potentials (LFPs) to global electroencephalographic (EEG) recordings, and to investigate various cerebral rhythms –15. NMMsInteractions between slow and fast components of neural systems, hence, of their mathematical models, result in multiple time-scale complex oscillations, such as relaxation, bursting and mixed-mode oscillations. Geometric singular perturbation theory (GSPT) is a key tool for understanding the interaction between the geometry of the system and the emerging multiple time-scale dynamics. In particular, canard solutions, which can exist in multiple time-scale systems with a folded geometry, appear as building blocks of complex oscillations in both phenomenological and neurophysiologically plausible models ranging from single cell –26 to neW represents the average synaptic gain and A, B, G are the synaptic gains, the p is the mean of external input ξ is a random variable following a normal distribution with In this study we investigate critical regimes in the NMM initially presented in . This phmentclass2pt{minimquations . The parAs introduced in , under t, system –1h) can can\docuIn this manuscript, we will consider system –2h) for for2h) fsoftware . The stosoftware . Table 1fast form with spikes) followed by a slower oscillation  exp exp2h) efined in –(2h). Th Systems –(2h), (3t}δ→0 in –(2h) yie problem –2b) whi whit̃ isfined by –(2b) wit theorem .slow reduced problem, ε being the time-scaling parameter. The equilibria of the slow layer problem in the super-slow manifoldSetting t}δ→0 in –3h) giv giv\doculimit of –4h)..\documenIn order to investigate the super-slow flow on e system –6h) wit wit\docud system –(6h) as  F_{2}y_{}, \end{aFigure entclass1pt{minimafined by , i.e. \d0 within –6h); se; se\docudesingularized slow reduced system (DSRS), reading As being the usual strategy, we consider the desingularized version of the super-slow dynamics on mentclass2pt{minimibria of –8f), he, he\docuibria of –2h). Fi. Fi\docufolded saddle-node type II (FSN II) singularity [Stability of the equilibrium points of the desingularized (slow) reduced system on the fold set determines the type of the folded singularities of the original system. Classification of these equilibrium points is based on the linear stability analysis. When the desingularized (slow) reduced system is planar, this analysis can be done using the trace and the determinant of the Jacobian matrix at the fold equilibrium. If both are different from zero, the fold equilibrium can be a folded saddle, a folded node or a folded focus. If the determinant equals zero but not the trace, then the desingularized flow has a degenerate equilibrium point, which is a folded saddle-node. A folded saddle-node is either related to a saddle-node bifurcation of the folded equilibria or a transcritical bifurcation of a folded equilibrium with an ordinary equilibrium. The latter case refers to the gularity , 54, whegularity , 56.degenerate transcritical bifurcations where (The Jacobian matrix of –11b) ha ha11b) hp2)=0 in –(11b) arF7)=0 in –(11b) reB in the region of interest. Two straight lines of the equilibria Figure e system –8f) (an (anB in e system –2h)) ha) haB in e system –(8f) (ane system –(2h)) hadegenerate transcritical bifurcation points degenerate FSN II singularity. A degenerate FSN II singularity in  can candegensee Fig. d, as it arity in –(2h) stecanard point. In such case, the amplitude of the periodic orbits bifurcated at the singular Hopf point increases stiffly in a narrow interval of the parameter  that controls the transition from small amplitude to relaxation oscillations [canard explosion [canard-without-head solutions), large canards following the unstable branch of the critical manifold and two stable branches , and a maximal canard solution that follows the longest the repelling branch. In planar multiple time-scale systems, canard solutions are tightly connected to excitability and firing thresholds [Folded singularities can lead to canard solutions in the original system. In a planar slow–fast system, a singular Hopf bifurcation can occur near a folded singularity, which is then called a llations . This phxplosion , 58. A cresholds , 31. In resholds , 59–61. resholds , 36, 44.resholds , 42, 62.resholds , 63–65.In our problem, the critical manifold ument}S0  is hyperument}L0 –8f) has has\docuument}L0 –(8f). Asument}L0 –(8f) hastions in –(8f) (hetions in –2h)). O). O\docutions in –(8f) bections in –(8f) is l system –(2h)  whi whi2h) wnt}F7 in –11b)  undB for different values of B-space and eventually connects to Figures System –2h) doe doe2h) d saddles , 67). AsB, such as The Hopf bifurcations . System –2h) can can\docuB decreases the number of spikes while driving the oscillations one peak to the next one in the parameter space  for for\docuB indicates that the corresponding orbits are of relaxation type  can can2h) csee Fig. –(2h) is . System –(2h) is B for Figure For a parameter set ensuring the type-II excitability  emi emi\docu}H4 Fig. –11. A pakes Fig. a1–a3. Onion Fig. b1–b3. We}H3 Fig. c1–c3. SiFigures In Fig. In this article, we extended the multiple time-scale analyses previously initiated in . Here, wThese model predictions motivated a close analysis of SEEG recordings performed in epileptic patients. In this paper, results illustrative of both signatures are reported only in two patients. Interestingly, in brain structures clearly involved in the transition from interictal to ictal activity, we observed a narrow band activity between sporadic discharges before the seizure initiation, which strongly differed from the preceding background activity. Although the parameter set used in this paper was not aimed for modeling these recordings specifically, it is striking to see such a matching between the mathematical analysis and the actual recordings.It has been evidenced that impaired excitation–inhibition balance shapes the activity of neural networks and, therefore, causes the emergence of “pathological” electrophysiological patterns such as pre-ictal spikes and seizures in the context of epilepsy (see for a review ). IndeedAs epilepsy can be considered as a dynamic disease , 80, 81,


Migraine frequency increases after the cessation of successful preventive treatment with CGRP(-receptor) monoclonal antibodies (mAbs). In this study, we aimed to evaluate the course of migraine after treatment resumption.Patients with migraine, who started treatment with the same CGRP(-R) mAb after a three-month drug holiday were included in this analysis. We collected headache data at four prospective visits: 1) during the four weeks before the initial mAb treatment (baseline); 2) during the four weeks before the last mAb injection; 3) in weeks 13–16 of the drug holiday; 4) in weeks 9–12 after treatment restart. Outcomes were the changes in monthly migraine days (MMD), monthly headache days (MHD), monthly days with acute medication use (AMD) and Headache Impact Test-6 (HIT-6) scores across the observation period.n = 16; galcanezumab/ fremanezumab n = 23). MMD decreased from 12.3 ± 6.3 at the end of the drug holiday to 7.8 ± 5.5 three months after treatment restart (p = 0.001). The improvement after treatment resumption was similar to the response in the initial treatment period (baseline: 12.3 ± 6.3 MMD vs. 7.5 ± 5.2 MMD before treatment interruption). MHD and AMD showed a significant improvement after treatment restart. HIT-6 scores decreased, indicating a diminished impact of headache on everyday life.This study included 39 patients (erenumab Reinitiation of treatment with CGRP(-R) mAbs after a drug holiday leads to a significant reduction of migraine frequency and medication use as well as improvement in quality of life. Three monoclonal antibodies (mAbs) targeting the Calcitonin Gene-Related Peptide (CGRP) pathway are currently available in Germany as specific migraine preventive treatments: erenumab binds to the CGRP-receptor (CGRP-R), while galcanezumab and fremanezumab target CGRP directly .The efficacy and tolerability of CGRP(-R) mAbs have been demonstrated in large trial programs and confirmed in numerous real-world studies –13. HoweOne key issue is the optimal treatment duration and the need for treatment discontinuation after a period of successful therapy. The expert consensus of the European Headache Federation (EHF) recommends a discontinuation attempt after 6–12 months to reevaluate the need for preventive therapy . CurrentBased on our experience, approximately 90% of patients resume treatment within three months after discontinuation . HoweverFrom a clinical point of view, treatment resumption would ideally lead to an improvement of migraine frequency similar to the initial treatment. A predictable good response after restart would facilitate the decision to temporarily stop treatment and begin again in case of disease deterioration. Alternatively, a second treatment cycle after a long pause could potentially be less effective than the first one, for example due to habituation effects. The evaluation of headache parameters during a second treatment cycle is therefore a crucial step towards improved care of patients with migraine. We have recently published data on migraine frequency and quality of life after mAbs discontinuation . We now We conducted a longitudinal cohort study at the Headache Center of the Charité – Universitätsmedizin Berlin.Eligible patients were selected from a previous study cohort . All patrestart of preventive treatment with CGRP(-R) mAbs after three months of treatment interruptiontreatment with the same CGRP(-R) mAb as in the first treatment cyclecomplete headache documentation for three months after treatment restart.Inclusion criteria for this analysis were:The start of a concomitant migraine preventive treatment led to exclusion from the analysis.Depending on the mAb they received patients were divided in a CGRP-R mAb group (i.e. treatment with erenumab 140 mg s.c. per month) and a CGRP-ligand mAb group .Study procedures up to the end of the medication pause were described in detail elsewhere . In brieFor this analysis, patients’ data were acquired from an additional visit 12 weeks after treatment reinitiation. Patients had to provide headache data for four consecutive weeks prior to this visit (weeks 9–12 after restart) , monthly headache days (MHD) and monthly days with acute medication use (AMD). A migraine day was defined as any calendar day fulfilling the ICHD-3 criteria of a definite or probable migraine. We considered both triptans and non-specific pain medication  as acute medication.Patients with an improvement in MMD of ≥ 30% after treatment restart were considered responders, patients with < 30% improvement non-responders to the second treatment cycle.At each visit except baseline, patients also completed the Headache Impact Test-6 (HIT-6). The HIT-6 is a validated questionnaire to assess the impact of headache on everyday life . The achThe primary endpoint of the study was the change in MMD between the last four weeks of treatment discontinuation and weeks 9–12 after restart. Secondary endpoints were the changes in MMD across the other observation points and the changes in MHD, AMD, and HIT-6 sum scores. The changes in headache parameters and HIT-6 scores in the receptor and ligand group were considered exploratory outcomes.Further exploratory outcomes were the changes in headache parameters in responders and non-responders as well as patients with episodic and chronic migraine separately.Statistical analyses were performed using SPSS 27 . We summarized demographic data using descriptive statistics .p value < 0.05 was considered statistically significant. P values were adjusted for multiple comparisons using the Bonferroni method. For exploratory endpoints we provided only descriptive values.Since all outcomes of interest  were not normally distributed, we used the Friedman test with post-hoc pairwise comparisons to assess primary and secondary endpoints. A two-tailed n = 39 patients  mAb. During therapy, MMD decreased to 7.5 ± 5.2 in the last treatment month. The discontinuation of mAbs led to an increase of MMD to 12.3 ± 6.3 at the end of the three-month discontinuation attempt similar to the data of the entire cohort .By using CGRP(-R) mAbs, MHD decreased from 13.8 ± 6.4 to 7.7 ± 5.2 days. During the drug holiday, a MHD increase to 12.8 ± 6.1 was observed. In parallel, AMD were reduced from 11.0 ± 5.3 to 5.9 ± 4.6 under mAb treatment and increased again to 9.5 ± 5.3 after treatment discontinuation.p < 0.001) .The reinitiation of CGRP mAb therapy after the discontinuation period led to a significant reduction of MMD by -4.5 ± 4.9 after 9–12 weeks of therapy  responded to the same mAb, in more than one-fourth of patients  migraine frequency did not improve to a significant extent (> 30%) after mAb restart compared to the last month of the drug holiday. Patients were equally distributed between groups . Demographic characteristics or headache data at baseline did not reveal any significant difference between non-responders and the remaining cohort . However, the non-responders showed a significantly higher reduction of MMD during the first mAb treatment period than the responders did .While In line with the entire cohort, patients with episodic and chronic migraine showed a worsening of MMD, MHD, and AMD to baseline levels after treatment discontinuation Table . Three mp < 0.001), indicating a significant reduction of headache impact on everyday life. The HIT-6 scores after treatment reinitiation were very similar to those during the initial treatment cycle .The HIT-6 sum scores decreased from 63.9 ± 4.5 in the third month of the drug holiday to 57.9 ± 5.6 in weeks 9–12 after treatment restart  mAb after a three-month drug holiday experienced a significant reduction of migraine frequency and acute medication use. HIT-6 scores improved, indicating a reduction of headache impact on everyday life. Migraine frequency after three months of mAb therapy following the drug holiday was similar to the frequency that was reported at the end of the first treatment period.This data is relevant for clinical practice as most patients treated with a CGRP(-R) mAb in Europe undergo a drug holiday after 6–12 months as recommended by national and international guidelines, or even forced by the healthcare systems of some countries , 15, 19.n  = 10 patients restarted erenumab treatment after only one month of treatment pause and showed a significant improvement of MMD and AMD in the first month after restart [n = 32 patients reported significantly improved MMD, AMD and HIT-6 scores in the first month of retreatment with erenumab or galcanezumab compared to the third month of treatment discontinuation [Headache data after a mAb drug holiday is only available for two small Italian cohorts: In the study by De Matteis et al.,  restart . In the inuation . Our resOur findings are reassuring for patients who are advised to stop treatment with CGRP(-R) mAbs. The confirmation that almost 75% of patients have a favorable response after treatment resumption with the same mAb medication might reduce the fear of a drug holiday.A lack of improvement after a drug holiday was described for other diseases. Multiple reports described a decreased effectiveness of lithium in patients with bipolar disorders after a treatment interruption, a phenomenon called “lithium-discontinuation-induced refractoriness” –25. A poThe general recommendation of a drug holiday is based on the treatment with oral migraine preventatives. Oral drugs are commonly discontinued due to lack of efficacy or side effects, only 20% of patients continue treatment for one year . Data frThis is the longest prospective analysis on treatment resumption with CGRP(-R) mAbs after a drug holiday. The inclusion and exclusion criteria allow for a very homogenous population. The small sample size constitutes a limitation and enables only exploratory analyses for the subgroups of patients with CGRP and CGRP-R mAbs. Given the real-world character of our investigation, we cannot control for placebo or nocebo effects during discontinuation or after restart.In conclusion, we showed a significant reduction of migraine frequency after re-initiation of treatment with CGRP(-R) mAbs. While over 70% of patients returned to the same migraine frequency comparable to the end of the first treatment cycle, in 30% of patients the response was not sufficient. Further research should aim to better characterize these patients and design personalized treatment regimens.


Among all analyzed factors, the percent of forest cover influenced the carbon isotopic composition most significantly, and decreasing forest cover caused an increase in δ13C values. The δ15N was positively related to the proportion of open area and  negatively related to the distance to the seashore. Using rigorous statistical methods and a large number of samples, we confirmed that δ13C and δ15N values can be used as a proxy of past habitats of red deer.Stable isotope analyses of bone collagen are often used in palaeoecological studies to reveal environmental conditions in the habitats of different herbivore species. However, such studies require valuable reference data, obtained from analyses of modern individuals, in habitats of well-known conditions. In this article, we present the stable carbon and nitrogen isotope composition of bone collagen from modern red deer  dwelling in various habitats (N = 15 study sites) in Europe. We investigated which of the selected climatic and environmental factors affected the  Since herbivore tissues record the δ13C values of their plant food, it is possible to identify the type of environment in which the studied animals fed: closed (forested) or open habitats . Plant δ15N values can vary according to the same abiotic factors as plant δ13C values ). Therefore, we were not able to include supplementary feeding or crop availability as variables in our analyses. Seasonally, in study sites located in uplands and mountains , red deer migrated between lower and higher altitudes.In all study sites in Poland and Slovenia, game animals (including red deer) were supplementarily fed mainly for harvest purposes. Additionally, they were fed during the winter time (more intensively in severe and snowy than in mild winters) and potentially had access to agricultural crops located near forest areas. However, it was impossible to assess the amount of supplementary food or crops consumed by each of the studied individuals, and there were also no data available concerning the amount of supplementary food provided in each of the study sites. Red deer rarely caused any damage to agricultural crops, and such losses were not recorded. Additionally, there are no formal recommendations concerning the amount of supplementary food that should be provided for wild ungulates in Poland. Such food usually is not isotopically homogenous as it may consist of hay, straw, dried shoots with leaves as well potatoes, beets, carrots, cabbage, silage, and cereal grains  notation as follows:Before analyses, the collected bone samples were frozen at −20°C. Prior to collagen extraction, the samples were rinsed in water and dried at 70°C for 6 hours. Bone collagen was extracted using the classical Longin method  with addδ13C and δ15N values are presented in units of parts per thousand and communicated in per mil shown as ‰ , where δ13Catm is the correction added to the δ13C value and t is the year of the individual’s death [δ13C, atmospheric correction values and corrected values of δ13C are provided in The analyzed samples originated from deer that died in different years, and the ver time . Due to ’s death . UncorreWe georeferenced the locations of red deer samples . When precise data were not available, we assumed the centroid of the hunting district, where the animals were culled or found dead, to be the sample location. For each location, we described the following environmental variables: (1) the proportion of forest cover , (2) the proportion of open area , (3) the mean annual temperature, (4) the mean January temperature, (5) the mean July temperature, (6) the annual precipitation, and (7) the altitude. Additionally, for individuals from study sites situated in coastal areas, we measured the distance to the seashore or coastal salt lake (later referred to as distance to the seashore).The proportion of forest cover and open area at the sample locations were estimated within circular buffers of 3 km and 5 km radii for females and males, respectively. The buffer size corresponded to the mean annual home range size of does and stags of red deer in Europe . The resδ13C and δ15N for all analyzed samples with Pearson’s correlation analysis. We calculated the mean ± SE (standard error of the mean) of δ13C and δ15N values for red deer inhabiting each of the study sites  and the following variables: percentage of forest cover, percentage of open area, mean January temperature, annual precipitation, and altitude. As we sampled red deer from the same locations multiple times, we set location and year as random factors in all our LMMs. The homoscedasticity in distribution of final model residuals was checked by visual inspection of plots presenting model residuals against fitted values (estimated responses). We ran separate models with δ13C and δ15N values as the response variables. All LMM models were performed using the lme4 package [We used linear mixed-effects models (LMMs) with a Gaussian error structure to test for associations between stable isotope composition  of competing models. Each model consisted of the uncorrelated independent variables (predictors). We assumed that the predictors were uncorrelated when Pearson’s correlation coefficients were below |0.6| (MuMin package [c) and with ΔAIC < 2 were considered to have substantial empirical support.To test which set of variables best explained the observed variance in ow |0.6| . Next, t package  implemen package . All modδ13C or δ15N values and the distance to the seashore. We performed additional LMMs for δ13C and δ15N values on selected samples (N = 61) of red deer individuals inhabiting areas at a distance ≤ 40 km from the seashore in the Rum, Flevoland, G. Pomerania, W. Pomerania, and Goleniów study sites.Since the coastal habitats could represent enriched carbon nitrogen stable isotope values , we testδ13C or δ15N values between red deer occurring in habitats differing in forest cover, we assigned sampled individuals to four forest cover classes  and compared the variance of δ13C or δ15N values among those forest cover classes with ANOVA fitted on residual values and Tukey’s post hoc HSD test. These analyses were completed in R version 4.0.2 [To check for significant differences in the variability of on 4.0.2 .δ13C ranged from −24.83 to −19.50‰, and those of δ15N from 0.60 to 9.29‰, respectively. Values of δ13C and δ15N were significantly correlated  was detected in individuals from the Rum covered mostly by heathlands, while the lowest mean value (−23.13 ± 0.08‰) was observed in red deer from the Ustrzyki study site–a mountainous area covered by forests  was observed in deer from the Flevoland–a fenced wetland covered mostly by grasslands, and the lowest mean value of δ15N (2.76 ± 0.42‰) was detected in bone collagen of deer from Hru&Jav–a mountainous area covered mostly by forests . With the increasing percentage of forest cover from 0 to 100%, δ13C values decreased from −21.75‰ to −23.15‰ . The selected model predicted a 2.76‰ increase in the δ15N value in bone collagen between red deer inhabiting 0 and 100% open area . In the case of the nitrogen model, distance to the seashore had a significant effect on δ15N values . With increasing distance to the seashore from 0 to 40 km, δ15N values decreased from 5.91‰ to 2.82‰ , distance to the seashore did not explain the variation in to 2.82‰ .δ13C and δ15N values, respectively  in red deer buffers (δ13C was detected in the group with the lowest forest cover (SD = 0.47), and the highest in groups with 21–50% (SD = 0.78) and 81–100% (SD = 0.76) forest cover. However, the differences in variability of carbon isotopic composition between all pairs of groups were not significant (P > 0.05). The highest variability of nitrogen isotopic composition were observed in the group with 0–20% of forest cover (SD = 2.05) and the lowest in the groups with 21–50% and 81–100% forest cover . The difference in variability of δ15N was significant only between the first (0–20% forest cover) and the three other groups (P < 0.001)  .δ13C values in the bone collagen of red deer. Individuals from forested areas, dwelling under the canopy, showed lower δ13C values than deer from more open areas. These results are concordant with the results of previous stable isotopic studies, including those one modern free-ranging cervids and bovines [13C abundance in plants growing under a closed canopy, in poorly ventilated, more humid and shaded conditions, compared to those from open habitats [δ13C values of red deer bone collagen analyzed in this study.Among all analyzed climatic and environmental factors, the percentage of forest cover best explained the variability of  bovines , 47. Thehabitats , 48. Sinδ15N values than deer inhabiting forested areas. Similar results were reported in the study on the European bison (Bison bonasus). The variability of δ15N in bone collagen of European bison was negatively influenced by forest cover and positively associated with the average annual temperature and the use of agricultural crops [Hippocamelus bisulcus) inhabiting the Patagonian Andean forest presented lower δ15N values than the guanaco (Lama guanicoe) occupying Patagonia’s continental steppe [δ15N values were reported in a study performed in South Africa [δ15N values, while other variables such as altitude, annual precipitation, or mean January temperature were not significant.The general pattern of nitrogen stable isotope composition in bone collagen presented in this study was as follows: deer from open lands showed higher al crops . Also, il steppe . The auth Africa , but thi15N in red deer from coastal areas relative to those from inland areas, we tested the hypothesis that distance to the seashore significantly influenced the nitrogen isotopic composition of bone collagen. Bone collagen δ15N values of deer living in coastal areas (<40 km from the seashore) decreased significantly with increasing distance from the seashore. A possible explanation may be given by the sea spray effect or soil salinity. Sea spray contains marine nitrogen, which affects forage in coastal areas. Such nitrogen is enriched in 15N in comparison to terrestrial nitrogen and is deposited near the seashore and taken up by plants [15N enrichment in plants from such saline areas and is later recorded in the herbivores which consume them [δ15N values also in Pampas Deer (Ozotoceros bezoarticus) in Eastern Central Argentina [Due to the presumed enrichment in y plants . Soil saume them . The seargentina .13C depletion may not be present [e.g., δ13C values than native plants  were depleted in 13C relative to hair of individuals from open environments  [In general, carbon isotopic values were highly variable among red deer from a single study site and within groups determined by the percentage of forest cover. There are several potential explanations for such variability. Firstly, regardless of whether red deer inhabited the same study site, they could have fed in areas with different percentages of forest cover, as most of our studied sites were not homogenous according to the available habitats. Moreover, the proportion of forest cover does not always reflect the closeness of the canopy and condition of the understory, which may determine the “canopy cover effect”. For instance, in managed forests, where clear-cuts are practiced, nt e.g., . Secondlg., corn ), the cag., corn . Despite tundra) , 57. Fin tundra) ; therefoδ13C, δ15N values were highly variable among red deer from a single study site, and within groups determined by the percentage of forest cover. Again, there are a number of potential explanations for this variability. Firstly, we cannot exclude the possibility that the sampled individuals (except red deer from the Rum and Flevoland study sites) fed on agricultural crops or supplementary food provided by hunters or foresters. The consumption of cultivated plants by red deer (as in the case of δ13C) increased the δ15N values in their tissues [δ15N values in hair increase during nutritional stress [δ15N values in the Flevoland deer, which were in poor condition due to starvation [δ15N abundance can be relatively low in the soil and plants [Similar to  tissues . Secondll stress , it is parvation . On the arvation , the δ15d plants  and, in d plants .δ13C of red deer confirmed the presence of the “canopy cover effect.” The variability of δ15N values was best explained by the proportion of open area. Additionally, in coastal areas located less than 40 km from the shore, the variability of δ15N values was influenced by the marine environment. However, the variance of the carbon and nitrogen isotopic composition of bone collagen was high among individuals inhabiting similar environmental conditions, so it can be concluded that they were influenced by additional factors, which were not identified and analyzed in our study.On the whole, the results of our study confirmed that the carbon and nitrogen stable isotope compositions of red deer bone collagen across a wide range of environments are shaped by habitat conditions. Using rigorous statistical methods, we identified forest cover  as the factor that best described the isotopic composition of carbon and nitrogen in the bone collagen of modern red deer in Europe. The association of forest cover and δ15N and δ13C values, the present large-scale study showed a general association between bone collagen isotopic composition and the habitat.In the context of palaeoecological studies, we highly recommend the use of additional sources of information about past habitats of studied herbivore species. e.g., palynological data, for more accurate interpretation of the results of stable isotopic analyses. Despite this high variation in S1 Table(DOCX)Click here for additional data file.S2 Table(DOCX)Click here for additional data file.S3 Table(DOCX)Click here for additional data file.S4 Table(DOCX)Click here for additional data file.S5 Table(DOCX)Click here for additional data file.S1 Fig(TIF)Click here for additional data file.


However, the growth of the cnb1Δ/Δyvc1Δ/Δ mutant was recovered and its cell vitality was better than the cnb1Δ/Δ strain. Meanwhile, the cellular calcium concentration was decreased and its fluctuation was weakened under ER stress in the cnb1Δ/Δyvc1Δ/Δ strain. To verify the regulation role of Yvc1 in the calcium concentration, we found that the addition of CaCl2 led to the worse viability, while the growth state was relieved under the treatment of EGTA in the cnb1Δ/Δ strain. In conclusion, the deletion of YVC1 could reduce the cellular calcium and relieve the ER stress sensitivity of the cnb1Δ/Δ strain. Thereby, our findings shed a novel light on the relationship between the Yvc1-governed cellular calcium concentration and ER stress response in C. albicans.Transient receptor potential (TRP) channel Yvc1 was related with hyphal growth, oxidative stress response, and pathogenicity. Calcineurin subunit Cnb1 was activated immediately in yeasts when exposed to severe stimulation. However, the relationship between Yvc1 and Cnb1-governed calcium ions and endoplasmic reticulum (ER) stress response remains unrevealed. In this study, we found that the mutant  Candida albicans, as the most well-known pathogenic fungi, may cause lethal systemic infection of humans  . TunicamR stress . In mammR stress . BesidesR stress .cnb1Δ/Δ was sensitive to ER stress, which was related with the overexpression of cytoplasm membrane channel CCH1 and irrelevant to the oxidative stress reaction. Besides, we found that the growth of the cnb1Δ/Δyvc1Δ/Δ strain was faster than that of the cnb1Δ/Δ strain, and the cell death rate, vacuolar membrane permeability, and mitochondrial activity were relieved in the double mutant. Interestingly, the classical UPR pathway was activated normally in all of the strains, indicating that the mechanism of relieving the growth in cnb1Δ/Δyvc1Δ/Δ was unrelated with the UPR pathway. However, the calcium flux was enhanced and its concentration was increased in the cnb1Δ/Δ strain under ER stress, and their level decreased obviously in the cnb1Δ/Δyvc1Δ/Δ strain. CaCl2 or its chelating reagent EGTA was added to verify the regulatory role of Yvc1 in the calcium ion concentration, and we found that the addition of CaCl2 led to poor viability and weakened the functions of vacuole and mitochondria under ER stress of the cnb1Δ/Δ strain. However, the growth state or organelle activity was relieved under the treatment of EGTA, indicating that Yvc1 alters the cellular calcium concentration in response to ER stress to improve the cnb1Δ/Δ growth. Overall, our work shed a novel light on the interaction between Yvc1-mediated calcium homeostasis and ER stress response in C. albicans.In this study, we found that cnb1Δ/Δ, yvc1Δ/Δ, and cnb1Δ/Δyvc1Δ/Δ mutant strains by the PCR-mediated homologous recombination method. The ARG4 cassettes were amplified and transformed into the WT. The heterozygous mutants (cnb1:ARG4/CNB1) were identified by PCR. After that, the URA3 fragment was transformed into the heterozygous mutant above to construct the cnb1Δ/Δ mutant strains (cnb1:ARG4/cnb1:URA3). The yvc1Δ/Δ and double mutant cnb1Δ/Δyvc1Δ/Δ were constructed with a similar method.The strains and primers used in our study are listed in CCH1-GFP plasmid was digested with StuI for 1 h and transferred into the WT and other mutant strains to measure the CCH1 expression level. In general, the strains were cultured in YPD  medium. The SC  medium without uracil was used to separate and select the URA3-tagged strains.Besides, the pPThe YPD plates containing different concentrations of TN, β-mercaptoethanol, dithiothreitol (DTT), or calcofluor white (CFW) were used to measure the sensitivity to ER stress or cell wall stress . Besides51H50F2N2O23, Beyotime, Shanghai, China, dissolved in DMSO) probe , and resuspended with PBS buffer. The 2-mM Fluo-4 probe was added and incubated with 70 r/min at 30°C for 1 h. The fluorescence intensity  was detected using a fluorescent microplate reader  probe . Log-phae reader . The sca25H14Cl2O9, Heowns, Tianjin, China, dissolved in DMSO) or 1 mg/ml CMAC . The cells were incubated for 10 min and observed by fluorescence microscopy. At least 1,000 cells for each group were photographed to count the percent of VMP-positive cells.5-(6)-Carboxy-2′,7′-dichlorofluorescein diacetate (C-DCFDA) or 7-amino-4 chloromethyl coumarin (CMAC) was used to measure the vacuolar membrane permeability (VMP) . In the The log-phase cells treated with 2 μg/ml TN were collected, washed, and resuspended in PBS buffer. Two micrograms per milliliter of JC-1  was added into the suspension. The cells were incubated for 1 h, and the mitochondrial membrane potential (MMP) was recorded with the flow cytometer . The red fluorescence  with J-aggregates could be detected in the cells with normal MMP. The green fluorescence  with J-monomer was detected in the cells with decreased MMP .TM Total RNA Extraction Kit  and transcribed reversely to cDNA. The HAC1 splicing assay was detected by the PCR method with primers HAC1-5RT and HAC1-3RT. The PCR product was separated in agarose gel electrophoresis for 3 h -dimethylthiazo(-z-y1)-3,5-di-phenytetrazoliumromide, 4 mg/ml, Beyotime, China] . The logPropidium iodide (PI) was used to measure the cell death rate for the PI-positive cells which were stained with red fluorescence completely . The strCCH1 and UPR response-related genes PMT4 and PRB1. Cells were collected, and the total RNA was extracted with EastepTM Total RNA Extraction Kit  and transcribed reversely to cDNA  strain, while cnb1Δ/Δ could hardly grow on the 2-μg/ml TN plate (600 of cnb1Δ/Δ was always maintained at 0.8 and the maximum value at 24 h was just 3 (CCH1 (CNB1 might have an impact on the CCH1 expression. It was interesting that under TN treatment, the expression level of the CCH1 promoter in the cnb1Δ/Δ strain was near as 1.5 times as WT (CCH1 was upregulated in the transcription level of cnb1Δ/Δ in response to ER stress (CNB1 leads to the sensitivity to ER stress and overexpression of CCH1.Firstly, we constructed the TN plate . Besidess just 3 . Since c 3 (CCH1 , we assues as WT . MoreoveR stress . In genecnb1Δ/Δ strain was related with the overexpression of CCH1, we speculated that the inhibition of the plasma membrane calcium channel might improve its growth status. Verapamil or nifedipine, as the universal calcium channel blocker, was usually applied to cure the hypertension or angina. A different concentration of verapamil or nifedipine was added into the YPD plates containing 2 μg/ml TN. The spot assay result showed that the colony of cnb1Δ/Δ could grow in both the plates treated with verapamil and nifedipine (cnb1Δ/Δ under ER stress (cnb1Δ/Δ growth under ER stress.Now that the sensitivity to ER stress of the fedipine . MeanwhiR stress . These rcnb1Δ/Δ and Yvc1 was the unique vacuolar membrane calcium channel in yeast, we doubted whether the deletion of YVC1 could improve the growth status of cnb1Δ/Δ under ER stress. We constructed yvc1Δ/Δ and cnb1Δ/Δyvc1Δ/Δ strains and measured their susceptibility to environmental stress. CFW and caspofungin could cause the cell wall stress. Besides, both β-mercaptoethanol and DTT could interfere the formation of disulfide bonds, and TN could inhibit glycosylation. These three reagents could lead to ER stress. We found that similar with the WT strain, cnb1Δ/Δ, yvc1Δ/Δ, and cnb1Δ/Δyvc1Δ/Δ strains were resistant to CFW, β-mercaptoethanol, and DTT (cnb1Δ/Δ and cnb1Δ/Δyvc1Δ/Δ strains were sensitive to caspofungin and TN. Since Yvc1 regulated the OSR in yeast (Since the inhibition of the cytosolic calcium concentration recovered the growth of in yeast , the antyvc1Δ/Δ strains grew rapidly to the log phase and eventually maintained with the maximum quantity. Although cnb1Δ/Δ and cnb1Δ/Δyvc1Δ/Δ mutants grew slowly, cnb1Δ/Δyvc1Δ/Δ grew marginally faster than the cnb1Δ/Δ strain did (yvc1Δ/Δ strains were still with the small dead cells, and the death rate was 26.8% in the cnb1Δ/Δyvc1Δ/Δ strains, which was increased to 39.72% in the cnb1Δ/Δ strain (cnb1Δ/Δyvc1Δ/Δ showed sensitivity to TN, the cell death rate was lower than that of the cnb1Δ/Δ strain, indicating that the deletion of YVC1 recovered the cell vitality of cnb1Δ/Δ.Under TN treatment, we measured the strain growth in the liquid medium during the 24-h cultivation. WT and rain did . Besidesrain did , controlΔ strain . These rCNB1 caused the damaged vacuolar membrane under TN treatment, with the whole cells stained by CMAC or failing to be stained (yvc1Δ/Δ strains maintained the integrity of vacuoles, with a low percentage of the VMP-positive rate. However, the positive rate was up to 70% in the vacuolar severely impaired cnb1Δ/Δ strain, although for the cnb1Δ/Δyvc1Δ/Δ strain with impaired vacuolar membrane, the VMP-positive rate was lower than cnb1Δ/Δ, just about 45% (Normally, the vacuole cavity could be dyed by CMAC, while the damaged cells were stained in the whole cell or failed to be stained . The vac stained . Besidesbout 45% .cnb1Δ/Δyvc1Δ/Δ, cnb1Δ/Δ, and yvc1Δ/Δ strain, as the WT strain, maintained the normal mitochondrial function, with the low percentage of damaged rate (cnb1Δ/Δ strain, and the rate of decreased MMP was up to 41.72%. Nevertheless, the rate of impaired mitochondria of cnb1Δ/Δyvc1Δ/Δ was just 16.71% (YVC1 recovered the function of vacuole and mitochondria of the cnb1Δ/Δ strain.The mitochondrial activities under ER stress were measured as well. In the control group, the ged rate , controlt 16.71% . In concYVC1 recovered the cell vitality of cnb1Δ/Δ under the treatment of TN, we speculated whether the UPR pathway was overactivated in this mutant. To verify the possibility, the total RNA of these three mutants and WT strains was extracted and transcribed reversely to cDNA (PRB1 and PMT4 were measured. However, much unexpectedly, similar with the WT or yvc1Δ/Δ mutants, the UPR pathway was activated in cnb1Δ/Δ and cnb1Δ/Δyvc1Δ/Δ effectively. The unspliced HAC1 was 581 bp in the WT and mutant strains of the control group (HAC1 was spliced normally in the cnb1Δ/Δ and cnb1Δ/Δyvc1Δ/Δ strains and other strains with the size at 562 bp (The UPR pathway is the classical response process in the ER stress of yeast strains . Since t to cDNA . The Hacol group . Moreovet 562 bp .PMT4 and PRB1 in the cnb1Δ/Δ and cnb1Δ/Δyvc1Δ/Δ strains were similar with WT, which were all upregulated in the transcriptional level under ER stress (Besides, qPCR analysis indicated that the expression levels of R stress . In summCCH1 to decrease the cytosolic calcium content could improve the growth status in the cnb1Δ/Δ strain. Therefore, we speculated whether the disruption of YVC1 reduces the vacuolar calcium release to improve the cell vitality. Moreover, the results showed that calcium fluctuation was enhanced in the cnb1Δ/Δ strain under ER stress. In the detected period, the calcium fluctuation was increased within 3 min, and the maximum concentration was higher than other strains. Nevertheless, the calcium flux of the cnb1Δ/Δyvc1Δ/Δ strain was steady with a low peak value like the WT strain (Yvc1 and Cnb1 were related with the cellular calcium regulation , and theT strain .cnb1Δ/Δ, in which the concentration was much higher than those of other strains. The calcium content of the cnb1Δ/Δyvc1Δ/Δ strain was close to that of yvc1Δ/Δ, lower than that of cnb1Δ/Δ (cnb1Δ/Δyvc1Δ/Δ strain, indicating that the disruption of YVC1 could reduce the cellular calcium concentration, thereby improving the vitality.Next, we measured the specific concentration of cellular calcium, which showed a similar tendency with the calcium flux. We found that the calcium concentration was increased significantly with TN treatment for 2 h of  cnb1Δ/Δ . In concYVC1 could decrease the cytosolic calcium concentration and recover the cell growth, CaCl2 or its chelating agent EGTA was added into the culture medium in the presence of TN. Although TN treatment in cnb1Δ/Δ caused a decreased MTT level, the supplement of EGTA recovered the cellular vitality, in which the MTT level was increased. Moreover, the supplement of CaCl2 led to significantly decreased vitality level in cnb1Δ/Δ (2 group. It indicated that the addition of EGTA improved the cell growth as well (2 caused severely damaged VMP in the cnb1Δ/Δ strain (2 led to a 60% positive rate of the mutant, while under EGTA treatment, the positive rate was down to 48% (cnb1Δ/Δ strain, and the disruption of YVC1 reduces the cytosolic calcium and improves the cell vitality (To test and verify our hypothesis that the deletion of  cnb1Δ/Δ . Moreove as well . The VMPΔ strain . Furthern to 48% . In concvitality .YVC1 recovered the growth defect of cnb1Δ/Δ in the regulation of calcium ions in response to ER stress (cnb1Δ/Δ was hypersensitive to TN, which was relevant with the overexpression of the cytoplasm membrane channel CCH1 (cnb1Δ/Δ strain. Although cnb1Δ/Δyvc1Δ/Δ was sensitive to TN, the growth was recovered and the death rate was obviously decreased (In this study, we found that the deletion of R stress . cnb1Δ/Δnel CCH1 , 2. Thisecreased . In the ecreased .cnb1Δ/Δ strain. Also, the calcium flux was steady with a lower content in the cnb1Δ/Δyvc1Δ/Δ strain, indicating the effect of the deletion of YVC1 on the decrease in cellular calcium (The UPR pathway was a classical regulation method in response to ER stress; much unexpectedly, the UPR pathway was evoked in all of the tested strains, indicating their normal activation . However calcium . The fur calcium .S. cerevisiae, ER stress upregulated the expression of Ptp2 tyrosine phosphatase and Cmp2 calcineurin phosphatase; the former was mediated by Mpk1 MAP kinase, and the latter could downregulate the activity of Hog1 MAP kinase (C. albicans is the catalytic subunit which maintains the principal role for the stress response. Besides, calcineurin is essential for cells in many biological processes and for the long-term survival of cells undergoing ER stress (Endoplasmic reticulum stress leads to the activation of the IRE1/Xbp1 signal pathway in mammalian cells. Regulated by Hac1, Pmt4 is expressed in the nucleus to alleviate the misfolded or unfolded proteins. In P kinase . The CmpR stress . ConnectIt was reported that for humans, the nephrotic syndrome was associated with the activation of the ER calcium release channel, which led to podocyte injury . MoreoveCNB1 or YVC1 deletion was interesting since the sensitivity to TN was irrelevant with the UPR pathway; indeed, it was the ROS-independent and UPR-independent calcium overloading. Connected with our previous cognition, it was subversive and enlightening.Verapamil and nifedipine are the cytoplasm membrane channel blockers in mammalian cells, used as the clinical drugs in curing heart diseases like angina pectoris and supraventricular arrhythmias . In our CCH1 in C. albicans. Besides, the specific regulation site of CCH1, the mechanism by which deletion of Cnb1 and Yvc1 caused cellular calcium ions to be increased under TN treatment, and the sensitivity to other environmental stimulus of the mutant are still unknown. Furthermore, we will work in-depth to figure out more mechanisms about the calcium signal pathway regulation under environmental stress.Moreover, the relationship between the calcium signaling pathway members and the environmental stress response needs further investigation, for instance, the relationship between Cch1 and Yvc1 for their regulation role in calcium ion content. Since Cnb1 regulates the ER stress response, does the transcription factor Crz1 or the other subunit of calcineurin Cna1 regulate In summary, our study revealed a novel interaction between the Yvc1-regulated cellular calcium ions and ER stress response, which was independent on the antioxidative reaction or UPR pathway . This woThe original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author/s.LP and ML conceived and designed the experiments and wrote the manuscript. LP, JD, and RZ performed the experiments. HZ, NZ, and QZ analyzed the data. ML and QY did supervision. All authors have read and agreed to the published version of the manuscript.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.


Orthodontic tooth movement (OTM) is facilitated by two events; bone resorption on the compression side and bone formation on the tension side simultaneously termed bone remodeling. Osteocytes play a critical role in bone remodeling during OTM, as they have been described as the critical source of nuclear factor-κB ligand (RANKL) necessary for bone remodeling during OTM. Tumor necrosis factor (TNF)-α is a cytokine that acts by amplifying RANKL expression in osteocytes. In this study, we evaluated the effects of TNF-α on RANKL expression in osteocyte during OTM.We assessed whether TNF-α influenced RANKL expression in osteocyte during orthodontic tooth movement by using wild-type (WT) and TNF receptor I and II deficient (TNFRsKO) mice. A Nickel-titanium closed coil spring was attached to the maxillary alveolar bone near the incisors and the upper left first molar, and the first molars were moved mesially in WT and TNFRsKO mice. After OTM, the number of RANKL-positive osteocytes in the alveolar bone was evaluated by immunohistochemistry.The number of RANKL-positive osteocyte in the alveolar bone significantly increased in WT mice than in TNFRsKO mice after OTM.The results indicate that TNF-α induces the expression of RANKL in osteocyte during OTM. The external force induces growth factor, cytokine, and neurotransmitter release, which signals to enhance osteoclastogenesis with compressive forces and osteoblast formation with tension, leading to the coupling of bone resorption and bone formation which are prerequisites of bone remodeling.The role of osteocytes in OTM is revealed in transgenic mice which osteocytes express the diphtheria toxin receptor under the control of the Dmp1-promoter. After diphtheria toxin injection to these mice, OTM was hindered when compared to wild type mice. Both tooth movement and osteoclast formation decreased on the compression side.In this study, we evaluated the effect of TNF-α on the expression of RANKL in osteocytes during OTM by using TNF receptor I and II deficient (TNFRs KO) mice.tm1lmxTnfrsf1btm1lmx) were obtained from  aged eight to ten-week-old. The mice were maintained with a 12/12-h light/dark cycle at 21–24 °C. The mice were provided with a granular diet  to ease eating during OTM without the use of excessive chewing force.Male C57BL6/J mice were purchased from  and TNFRs KO mice  closed coil spring  was hooked to the left maxillary first molar, and the maxillary alveolar bone underneath the incisors, which resulted in a 10 g force according to manufacturer's instructions moving the maxillary left first molar in a mesial direction. For appliance fixation, a hole was made by drilling with a slow-speed handpiece and a tungsten carbide bur underneath each of the two incisors at the alveolar bone level; then the appliance was tied to a 0.1 mm stainless steel wire through this hole, this facilitated the secure attachment of the appliance to both the left maxillary first molar and the alveolar bone .25, 26, 2O2 in PBS for 15 min and treated with 3% skim milk for 30 min at 37 °C for blocking. The treated sections were treated with anti-RANKL antibody  1:50 in Can Get Immunostain solution B  overnight at 4 °C for immunohistochemistry. After washing, the sections were treated with Histofine® Simple Stain™ Mouse MAX PO (R)  at room temperature for 1 h. The sections were counterstained with hematoxylin. The number of RANKL-positive osteocytes at the alveolar bone on the compression side of the distobuccal root on day 6 and on day 12 during OTM was evaluated.The mice were sacrificed by an overdose of 5% isoflurane in an inhalation chamber. The maxillae were cut off from the skull and fixed in 4% paraformaldehyde at 4 °C overnight. Maxillae were decalcified in 14% EDTA for 3 days at 4 °C. Decalcified maxillae were dehydrated in graded ethanol and embedded in paraffin blocks. The samples were cut into horizontal sections at a thickness of 4 μm from a starting point of approximately 150 μm from the root furcation of the maxillary left first molar as described previously.All data are presented as the mean ± standard deviation of independent biological replicas. Statistical analysis was performed using Scheffe's F-test. Statistical significance was assumed at a threshold of p < 0.05.After 6 days and 12 days of orthodontic tooth movement in mice, the mice were sacrificed, and the maxillae were prepared for immunohistochemical analysis. After 6 and 12 days of OTM there was significantly a fewer number of RANKL-positive osteocytes in the alveolar bone at the compression side of the distobuccal root in TNFRsKO mice when compared to WT mice, however there was no appreciable difference at the opposite right control (non-OTM) side . Thus, OIn the present study, we showed that RANKL expression increased in WT mice, but not TNFRsKO mice during OTM. We found that TNF-α stimulated RANKL expression in osteocytes during OTM. The results suggested that orthodontic force mediated-TNF-α release is a significant factor for facilitating the expression of RANKL in osteocytes. This is the first experiment to examine an interaction between TNF-α stimulation and RANKL expression in osteocytes during OTM.in vivo.,,in vivo.We previously reported that TNF-α injection to supracalvariae of mice induced osteoclast formation in calvaria ,in vitro and in vivo.,,,A recent report where mice lacking RANKL in osteocyte were used reported that these mice experienced a severe osteopetrotic phenotype as they aged. The results considered that osteocyte RANKL is most relevant to physiological bone remodeling.In our pervious study, we analyzed target cell contribution to the TNF-α pool and subsequent osteoclast formation during OTM using TNFRsKO and WT chimeric mice. The chimeric mice were generated by transplanting the marrow of either TNFRsKO or WT mice into lethally irradiated WT and TNFRsKO mice, resulting in four mice types. The results showed that TNF-α-responsive stromal cells (including osteocytes) in mice that were transplanted with TNFRsKO marrow are most contributing to osteoclast formation in OTM setting.The authors have no conflicts of interest relevant to this article.


A prerequisite for their emergence is the existence of robust gapped phases, which are difficult to find in extended graphene systems. Here we show that semi-metallic chiral GNRs (chGNRs) narrowed down to nanometer widths undergo a topological phase transition. We fabricated atomically precise chGNRs of different chirality and size by on surface synthesis using predesigned molecular precursors. Combining scanning tunneling microscopy (STM) measurements and theory simulations, we follow the evolution of topological properties and bulk band gap depending on the width, length, and chirality of chGNRs. Our findings represent a new platform for producing topologically protected spin states and demonstrate the potential of connecting chiral edge and defect structure with band engineering.Precise control over the size and shape of graphene nanostructures allows engineering spin-polarized edge and topological states, representing a novel source of non-conventional  Graphene nanoribbons are potential systems for engineering topological phases of matter, but the pre-required gapped phases are difficult to find. Here, the authors show that chiral graphene nanoribbons undergo a transition from metallic to topological insulators, and then to trivial band insulators as they are narrowed down to nanometer widths. The potential of this classification relies on the protection of the topological order by a symmetry, that can undergo a topological phase transition when the symmetry is changed. Symmetry Protected Topological (SPT) phase transitions were observed in artificial semiconducting systems such as two-dimensional quantum wells of HgTe5 and one-dimensional organic polymers6. The key element is the existence of two gapped SPT phases, the traditional  band insulator and the nontrivial topological insulating state, separated by a metallic state.Band topological classification of materials has been successfully applied to predict and explain the emergence of exotic states of matter such as Quantum Spin Hall (QSH) edge states in topological insulators7. For example, one-dimensional SPT phases were engineered inside the bandgap of armchair GNRs by modelling a one-dimensional Su-Schrieffer-Heeger (SSH) chain8 with edge moieties containing localized in-gap states13. In zigzag GNRs (ZGNRs), however, the existence of zero-energy edge bands15 prevents the appearance of gapped topological phases. As proposed by Kane and Mele3, the presence of spin–orbit interaction can open a gap in bulk graphene and turn the zero-energy modes into QSH edge states. However, the expected gap induced by spin–orbit interaction in graphene is very small, and this effect could only be present at very low temperatures16.In spite of being a semimetal, graphene has the potential to build up SPT phases by opening an energy gap around the Fermi level and endowing the lattice with an additional chiral symmetric interactionn, m) of graphene. The genuine zero-energy edge bands of ZGNRs persist in chGNRs via the accumulation of states around zero energy over zigzag sites, including their spin polarization in the presence of Coulomb electron–electron interactions18. However, chiral ribbons are more sensitive to a reduced width than ZGNRs, allowing to easily produce gapped GNRs with inherited chirality from the edge reconstruction.Here, we demonstrate that sizeable topological insulating phases emerge in narrow chiral GNRs driven by the interaction between the opposing edges. The term chiral GNRs (chGNRs) refers to the large set of ribbons extending along low-symmetry crystallographic directions (z (number of zigzag unit cells) and width w (number of carbon atoms across), blue-shadowed in Fig. n, m) can be obtained simply by repeating and shifting these blocks along their armchair edges an amount of a − 1/2 armchair unit cells, and connecting them with C–C bonds. The edges of the resulting chGNR alternate z zigzag and a-1/2 armchair sites to accommodate its orientation to the chiral vector, such that  =   simulations in Fig. We consider a family of chGNRs customized from a basic rectangular aromatic block of length γz = π20 of the occupied bands, using a rectangular unit cell enclosing the blue block in Fig. However, this metallic phase vanishes in narrow ribbons due to hybridization of bands at opposing edges. Interestingly, the emergent gapped phase corresponds to a SPT insulating phase characterized by an invariant mentclass2pt{minimn = 3, m = 1) and  chiral vectors, by plotting their evolution of the energy gap with the width w. First, a sizable energy gap opens up as the ribbons are narrowed down, which corresponds to a one-dimensional topological insulating phase, and at a critical width of w ~ 6, the gap closes, and reopens, now in a trivial phase.Our simulations also find that the topological phase vanishes upon further reducing the width of the ribbon. The gap closes and reopens again as a trivial band insulator, characterized by mentclass2pt{minim22. Our strategy started with the synthesis of poli-[n’]anthracene precursor molecules 1, 2, 3, and 4 shown in Fig. z = 3 edge structure. Their customized structures, composed of an increasing number of anthacene units and different Br functionalization sites a, were designed for obtaining  chGNRs with increasing width  and chiral angle  chGNR, using 4) through a sequence of OSS steps. For a fixed z, the Br-substitution site, labelled a in Supplementary Note n, m) chiral vector by steering the Ullmann-like connection between molecular precursors with a shift of a − 1/2 armchair unit lengths  followed by reduction with a mixture of HI and H3PO2. Similarly, the tetrakisanthracene 3, precursor of 3,1,8-chGNRs, was synthesized by reaction of compound 8 with organolithium 7, followed by a reduction step. Finally, compound 4, precursor of 3,2,8-chGNRs, was prepared from derivative 9 following a similar procedure (see Methods for further details). In the OSS step, each precursor was independently sublimated onto a clean Au(111) surface held at room temperature and step-wisely annealed to T1 to induce their Ullmann-like polymerization. Subsequently, a further annealing to T2 activated the cyclodehydrogenation (CDH) of the polymers into the targeted chiral graphene nanoribbons with chiral vectors  and  and with different widths  reproduce the hexagonal ring patterns of the different ribbons, in agreement with the chemical structures in Fig. dI/dV) on the different ribbons, as shown in Fig. dI/dV signal around zero bias, with a peculiar substructure  of the 3,1,4-chGNR closes abruptly for the wider ribbons, whose valence and conduction bands (VB and CB) apparently merge at zero energy and flatten, being these the edge-localized states resolved in the experiments. However, as we show in the inset of Fig. w ≥ 12 the gap closes definitively , revealing a band inversion at k = 0. As a consequence, the wavefunction acquires a net phase as it disperses along the Brillouin space. To connect these differences in parity with topological classes, we computed the Zak phase γz20 of the occupied band structure for every ribbon and obtained their γz = 0 and, hence, are in a trivial topological phase, i.e., γz = π in accordance with a nontrivial SPT phase . This chiral interaction pattern causes a gapped phase with negative sign, defined from the ti dominates over the others, leading now to a gapped phase with positive sign (w = 6 case.The presence of band gaps in narrow chGNRs and the SPT phase transition can be explained using the modified Su-Shrieffer-Heeger (mSSH) modelmentclass2pt{minim=0) Fig. b, with az,a,w-chGNR family. We computed the band structure and the total Zak phase γz of occupied bands for the set 0 < z ≤ 10, a < 6, and w ≤ 12, comprising ribbons with chiral angle from 4.5° to 80°  length, while vanish completely in chGNRs with three PUs or less, whose spectra is fully gapped  substrate32. The first peak above the VB corresponds to the CB onset, and no subgap features neither signal at the chGNR ends is observed, in agreement with their trivial semiconducting character.Contrasting with the topological character of 3,1,8-chGNR, end states are absent in narrower ribbons, proving their trivial insulating phase and confirming the existence of a width controlled topological phase transition in this family of chGNRs. For 3,1,6-chGNRs, low-bias peaks are spaced by tens of meVs, with a central one pinned close above the Fermi level  steers the formation of 3,2,8-chGNRs on a Au(111) surface at elevated temperatures. These ribbons are oriented along a  vector of the graphene lattice, and alternate three zigzag with one and a half armchair sites along the edges. The bond-resolved STM current image in Fig. dI/dV spectra measured over the chGNR ends show sharp peaks pinned at zero bias, while over the bulk region of the ribbon a bare ~300 meV bandgap is found , respectively. Low-resolution electron impact mass spectra were determined at 70 eV on a HP-5988A instrument. High-resolution mass spectra (HRMS) were obtained on a Micromass Autospec spectrometer. NALDI-TOF spectra were determined on a Bruker Autoflex instrument. Experimental details for the synthesis of the precursors and spectroscopic data can be found in All reactions for the synthesis of the precursors were carried out under argon using oven-dried glassware. TLC was performed on Merck silica gel 60 F254; chromatograms were visualized with UV light (254 and 360 nm). Flash column chromatography was performed on Merck silica gel 60 (ASTM 230–400 mesh). + ion sputtering and subsequent annealing to 730 K. The three molecular precursors were separately sublimed from Knusden cells onto a clean Au(111) substrate kept at room temperature. The sublimation temperatures of molecular precursors 1–4 in Fig. 1 and 300 °C for 2–4.) of molecular precursors. The annealing time for each step is 10 min for all the precursors. A tungsten tip was used in the experiment. High-resolution images were constant-height current maps acquired with a CO-functionalized tip at very small voltages, and junction resistances of typically 20 MΩ. The dI/dV signal was recorded using a lock-in amplifier with a bias modulation of Vrms = 4 mV  scanning tunneling microscope (STM) operating at 5 K. The Au(111) single crystal was cleaned in UHV by repeated cycles of Nesp2 carbon atoms, as implemented in the SISL python package45:ci  model with t1 = 2.7 eV, t2 = 0.2 eV, and t3 = 0.18 eV that has successfully described other synthesized sp2 carbon systems35. For completeness, we also have compared the band structures, gaps and SPT phase with simulations with a first-nearest neighbor (1NN) model -chGNRs within the mean-field Hubbard (MFH) model, the Hamiltonian H of Eq. (U parameter:47 (See Supplementary Note To analyze the effect of the electron–electron interactions in the (H of Eq.  incorpor48. The nanoribbons were relaxed until forces on all atoms were smaller than 0.01 eV/Å, and the dispersion interactions were taken into account by the non-local optB88-vdW functional49. The basis set consisted of double-ζ plus polarization orbitals for all species, with an energy shift parameter of 0.01 Ry. A 1 × 1 × 101 Monkhorst-Pack mesh was used for the k-point sampling of the Brillouin zone, where the 101 k-points are taken along the direction of the ribbon. A cutoff of 300 Ry was used for the real-space grid integrations.The optimized geometry and electronic structure of free-standing chiral GNRs were calculated using density functional theory, as implemented in the SIESTA codeSupplementary InformationPeer Review File


Fundamentally, this is because of differences in redox potentials and gearing. Biology adds kinetic constraints that tune the oxidation of NADH and succinate to ensure that the resulting mitochondrial pmf is suitable for meeting cellular needs without triggering pathology. Tuning within an optimal range is used, for example, to shift ATP consumption between different consumers. Conditions that overcome these constraints and allow succinate oxidation to drive pmf too high can cause pathological generation of reactive oxygen species. We discuss the thermodynamic properties that allow succinate oxidation to drive pmf higher than NADH oxidation, and discuss the evidence for kinetic tuning of ATP production and for pathologies resulting from substantial succinate oxidation  The operation of a biological system is like the operation of a factory: each machine (enzyme) in the factory performs one or more linked tasks. At steady-state, the rate of each reaction in the system is the same. This rate is not, as is sometimes stated, set by the capacity of the slowest machine (the ‘rate-limiting step'). Instead, it is dynamic and responsive; adjustment of the concentrations of the intermediates by the system coordinates the rate of each machine with the rates of all the others linked to it. This coordination helps to avoid the accumulation of too much of one thing or the depletion of another and keeps the factory running smoothly.Seeing the molecular machines present, and what each one does, is clearly necessary to understanding the system. However, you can only understand how the factory operates when the machines are all running and material is flowing between them. In steady-state, all the machines run at a rate that keeps all intermediates at constant and appropriate levels, and the factory is supported by the supply of raw materials and meets economic demand for the product.Mitochondrial energetics is an excellent model factory, whose primary function is to transform energy released from substrate oxidation into the transferable currency of ATP. Standard textbook descriptions of this ‘energetic factory' carefully present the architecture of the molecular machines but tend to minimize the factory's moving parts — the thermodynamic and kinetic properties that drive these machines. The goal of this short review is to discuss why and how understanding the moving parts is crucial to understanding the system, and to examine the kinetic tools used by biology to manage the thermodynamic challenges specific to succinate oxidation.2•−, and hydrogen peroxide, H2O2), it is an indirect modulator of any process sensitive to ATP/ADP or to ROS. Pmf itself may also drive cell signaling-related responses  with different tendencies to donate electrons  behave differently from one another. Specifically, why does the less-powerful reductant, succinate, deliver a higher resting  mitochondrial protonmotive force  ? What biitophagy )in vivo, perhaps due to different (and stronger) upstream kinetic constraints.Why succinate? As an intermediate in the tricarboxylic acid (TCA) cycle, succinate is a small component of normal cellular metabolism. However, there is abundant evidence that succinate accumulates during tissue ischemia ,5, and tIn the classic complete tricarboxylic acid cycle oxidizing pyruvate, the ratio of NADH to succinate production is fixed at 4 : 1, predicting pmf generation >80% by NADH oxidation. However, by diverting carbon into and out of the cycle, biology can shift reducing equivalent generation entirely to NADH oxidation (e.g. by running pyruvate to citrate and using the citrate for fatty acid synthesis) or strongly to succinate oxidation . In this way, pmf, phosphorylation potential, and superoxide and hydrogen peroxide production will change with the proportion that each substrate contributes to total oxidation. We discuss how such changes would result from systems oxidizing NADH or succinate.+) pumping by Complexes I, III, and IV of the electron transport chain to generate the electrical and chemical separation of H+ across the mitochondrial inner membrane. The energy to pump these H+ derives from electron transfer from an initial donor through the chain of redox centers in the respiratory complexes, ending with reduction in O2 to H2O. For an electron pair (2e−) to enter the respiratory chain, the electron donor must be more reducing than the initial acceptor.Mitochondrial protonmotive force is established through proton (H2/NAD (2e− enter at Complex I) and FADH2/FAD (2e− enter at succinate dehydrogenase/Complex II). However, they are not exactly analogous — whereas NADH is an intermediate 2e− carrier between substrates (e.g. pyruvate) and Complex I, FADH2/FAD is embedded within succinate dehydrogenase and receives its 2e− directly from succinate oxidation to fumarate — making the FADH2/FAD couple more analogous to the FMN moiety of Complex I than to NADH. Therefore, succinate/fumarate is the more appropriate redox couple to compare with NADH2/NAD.The two electron donor couples generally presented together are NADH2/NAD couple is more reducing than the succinate/fumarate couple, yet succinate oxidation can drive pmf higher than NADH2 oxidation can [2, multiplied by number of e− transferred  pumped across the mitochondrial inner membrane multiplied by the pmf they are pumped against. The higher the ΔE/n ratio, the higher the pmf.The NADHtion can . The then protons pumped. For a hypothetical system at equilibrium under standard conditions, flow between connected tanks is unrestricted and each of the donor redox couples is 50% reduced . The redox potential  under tved from ). The ΔEn protons pumped; for NADH oxidation through Complex I, n = 10. Since succinate-derived electrons are not reducing enough to enter at Complex I , they enter at Complex II and therefore drive proton pumping only from Complexes III and IV, so n = 6 [Because the systems in so n = 6 ,14.2, pmf solves to (2 × 1124)/10 = 225 mV. For succinate it solves to (2 × 785)/6 = 262 mV. Thus, even though succinate is a weaker reductant than NADH, its available ΔEm is divided by fewer protons pumped (different gearing), so the resulting pmf is higher. A good analogy is pressure (force distributed over surface area). Compared with succinate oxidation, NAD-linked oxidation is ‘heavier' (greater ΔEm) but is distributed over a larger ‘area' (H+ pumped), resulting in a smaller ‘pressure' (pmf). Consider how lying on a bed of vertical nails is preferable to lying on one nail.The pmf generated by proton pumping can increase to thermodynamic equilibrium with ΔE, as described by the equation2/NAD pool ∼10% reduced [h) from the midpoint potential Em. In Although standard equilibrium conditions  clarify  reduced ,16, and  reduced ,17. This2/NAD and succinate/fumarate pools to the pmf sustained by each, NADH oxidation operates further from equilibrium than succinate oxidation, further limiting the pmf established by NAD-linked flux. For succinate-linked flux, the pipe is wider, flux is higher  and the potentials therefore are closer to equilibrium [Connecting pipes between the left and right tanks are different diameters in the two systems. A smaller pipe diameter represents greater kinetic constraint imposed by the enzyme machinery, holding flow between tanks further from equilibrium. ilibrium .In isolated mitochondria with saturating substrates, the observed rate of uncoupled NADH-linked respiration (via Complex I) is about half the rate of succinate-linked respiration (via Complex II) , and aboThe turnover number (moles substrate transformed per second) for isolated Complex I is not much faster, and may be slower, than Complex II. There are few valid literature comparisons — the turnover numbers of succinate dehydrogenase (SDH) and Complex I have been rarely determined side by side, and experimental conditions  varied between laboratories. Ackrell and colleagues reported a 2-fold higher turnover number for Complex I than for Complex II using the same electron acceptor . ConversComplex II is more abundant than Complex I. In mammalian mitochondria SDH was 1.2–2 fold more abundant than Complex I, based on electron microscopic ,27, specLow control of pathway flux is associated with near-equilibrium operation . The conAltogether, considering the turnover number and stoichiometry of NADH to succinate oxidation (4 : 1 per complete turn of the TCA cycle oxidizing pyruvate), SDH activity is in excess (parity being a 4-fold lower rate). The relative abundance of Complex II activity may help it operate closer to equilibrium, allowing the generation of high pmf [What empirical evidence  oxidation can only sustain a pmf up to 170 mV under the same conditions [in vitro can sustain a higher pmf on succinate, by ∼10 mV. In mitochondria isolated from cultured cells, the electrical portion (Δψm) differed by ∼15 mV [2, the variation in these differences may at least partially reflect tissue specificity.So, what is the net effect on pmf when these biological kinetic constraints modulate the underlying thermodynamics? As nditions . Thus, iy ∼15 mV ,56. In my ∼15 mV ,58. Whil− entry are compared, demonstrating how predominantly the thermodynamics of the mitochondrial machine predict its operation. Brown et al. found that in isolated liver mitochondria, feeding 2e− at Complex IV (via sulfite oxidation) gave 2ΔEh of 987 mV, ∼65% of the value for succinate oxidation, yet drove a resting pmf of 187 mV, ∼10 mV higher than the 176 mV driven by succinate oxidation [The same principle applies when different sites of 2exidation .in vivo is extensive, and why so much regulation exists on this enzyme has remained an open question. A tentative model, drawing from the thermodynamic properties above, is that such regulation exists to rein in this powerful machine in cells, by decreasing its activity (narrowing the pipes) when ATP demand slackens and preventing pmf from being driven too high. Multiple regulatory mechanisms are summarized below.Biological regulation of Complex II activity Complex II/SDH exhibits conformational changes through interaction with many metabolites, including the TCA intermediates succinate, malate and oxaloacetate, ATP, reduced ubiquinone, protons (i.e. low pH), and certain anions . These c2/NAD will increase malate/oxaloacetate ratio, decreasing oxaloacetate concentration. This interaction may exist to increase SDH activity when Complex I is unable to oxidize NADH, e.g. at very high pmf [Three endogenous metabolites competitively inhibit SDH: oxaloacetate, itaconate, and malonate. The keto-tautomeric form of oxaloacetate produced by malate dehydrogenase (MDH), is a tightly binding competitive inhibitor . Since Mhigh pmf , though high pmf . Oxaloachigh pmf ,64,65. Thigh pmf ,67. Itachigh pmf . Itaconahigh pmf ,58. Malohigh pmf . Endogenhigh pmf .2O2, but not O2•−. A corresponding matrix-localized phosphatase, PTPMT1, is reported [SDH is also subject to posttranslational phosphorylation and succinylation. Mitochondrial Fgr tyrosine kinase phosphorylates SDH on the A subunit and activates the enzyme . Phosphoreported . Succinyreported . Desuccireported .Complex I also undergoes reversible conformation changes (activation/deactivation A/D transition). One putative function of deactivation is to mitigate reperfusion injury during anoxia . In tissHow cells consume ATP is partly dependent on cellular phosphorylation potential . This foAs an analogy, when your paycheck is high, you might spend more on luxuries than when times are lean. However, your rent stays about the same. Some categories of your spending (luxuries) are more dependent on your income than others (rent). In biology, the implication is that sustained high pmf through oxidation of succinate drives proportionally more protein synthesis. Pmf is therefore not just an intermediate to be charged and discharged; in the light of an ATP consumption hierarchy, pmf becomes an important director of cellular activity.As an aside, a common oversimplification is that high pmf is ‘functional', and low pmf is ‘dysfunctional'. A model that better fits the available data is that both extremes carry the risk of dysfunction; too low a pmf leaves a cell under-powered and unable to run essential functions, whereas too high a pmf drives high rates of superoxide production and leads to damage and pathology (section 6). What defines ‘extreme' remains to be determined but it likely cell type-specific. Plausibly, pmf values between these extremes are neither strictly functional nor dysfunctional; the biological outcome depends on how pmf supports cellular functions and viability in the environment occupied by the biological system (defined as narrowly or as broadly as appropriate). For example, in both neurons and pancreatic β-cells the pmf can change by up to 50 mV as a part of apparently normal function ,722•−/H2O2 production than NADH oxidation [2•−/H2O2 production rate increases at high pmf when the ubiquinone pool is highly reduced (sink full of water) and single electrons more readily reduce O2 to form O2•− (water pooling on the floor). In isolated mitochondria O2•−/H2O2 production increases non-linearly with respect to pmf; between pmf values of ∼180 (achieved by NADH oxidation) and 220 mV (achieved by succinate oxidation) O2•−/H2O2 production can increase 5- to 10-fold [As well as driving high ATP/ADP, high pmf also slows electron flow, reducing redox centers, which drives faster mitochondrial production of superoxide and hydrogen peroxide. Succinate oxidation can therefore drive faster mitochondrial Oxidation . Like wa 10-fold .in vivo to prevent damage and pathology. Are there conditions in cells and in vivo that approximate the unconstrained state achievable in vitro, and are they pathological?Considering the framework presented above, isolated mitochondria can be exposed to conditions (such as exclusive oxidation of abundant succinate) that bypass the biological constraints that would presumably be present 2•−/H2O2 production when mitochondria are within cells or in vivo? Yes — mitochondria are a major contributor to cellular H2O2 production, with the majority emanating from site IQ of Complex I and site IIIQo of Complex III, the sites are routinely driven in isolated mitochondria by the oxidation of excess added succinate [2•−/H2O2 production by sites IQ and IIIQo is not restricted to cell models; substantial pathological effects of H2O2 production from sites IQ and IIIQo can also be demonstrated in vivo when endogenous mitochondrial superoxide dismutase is knocked out [First, can high pmf drive Ouccinate . O2•−/H2cked out . Under ccked out ,93, but cked out .in vivo that succinate oxidation could drive high rates of O2•−/H2O2 production? The answer is yes, with the best-studied model being ischemia/reperfusion (I/R) injury [KM of SDH for succinate  injury . Estimat) injury , in the 0–400 µM ,87 in ma0–400 µM . Reperfuresponse , suggest2 can lead cellular reductants to drive SDH in reverse, pulling fumarate from different sources and reducing it to succinate. Alternatively, succinate may accumulate through forward SDH activity, supported partially by aminotransferase anaplerosis [Two plausible models explain why succinate accumulates under ischemia. The absence of sufficient Oplerosis ,6.2•−/H2O2 production from sites IQ and IIIQo occurs in vivo, and that succinate can accumulate in vivo, it needs to be demonstrated that oxidation of accumulated succinate is associated with high rates of O2•−/H2O2 production from these sites. Strong evidence comes from experiments showing that tissue damage due to I/R is attenuated when different elements required for succinate oxidation-associated O2•−/H2O2 production are disrupted, by inhibiting succinate oxidation [2/Q pool) using chemical uncouplers [Q [2•−/H2O2 production at site IQ using SIQELs, which impedes electron leak to O2•−/H2O2 but not electron flux to H2O [2•−/H2O2 derived from site IQ has broad biological effects, S1QELs modulate many different physiological and pathological conditions in vivo [Having evidence that Oxidation ,90, disscouplers ,92, inhiplers [Q ,94, or bx to H2O ,96. Supp in vivo ,95.2•−/H2O2, metabolite levels) but minimizes oxidative damage by O2•−/H2O2. If these controls are compromised, pathology can follow.Oxidation of succinate supports a higher pmf than oxidation of NADH. This is not because of some specific molecular property of succinate or NADH, but because of the thermodynamics , gearing (numbers of protons pumped) and kinetics of the components of the pathways by which energy from NADH and succinate oxidation is captured as pmf. In the absence of kinetic constraints, thermodynamics enables succinate to drive a pmf high enough to cause significant biological damage. This may explain the extensive regulation of SDH: biology has responded to the thermodynamic hazard created by succinate oxidation by tightly controlling SDH activity to maintain pmf within a range that allows optimal ATP production and signaling (by ATP/ADP, OWe discuss the importance of thermodynamic and kinetic properties in explaining the mitochondrial protonmotive forces that result when different substrates are oxidized.Current thinking is complicated when the molecular properties of different substrates and substrate oxidation pathways are emphasized; models of mitochondrial function can be unified and simplified by considering these thermodynamic and kinetic properties.Predicting how mitochondrial oxidation of succinate may contribute to physiology and to pathology can be simplified by applying these considerations.