This paper presents a methodology for synchronizing noisy and nonnoisy multiple coupled neurobiological FitzHugh–Nagumo (FHN) drive and slave neural networks with and without delayed coupling, under external electrical stimulation (EES), external disturbance, and variable parameters for each state of both FHN networks. Each network of neurons was configured by considering all aspects of real neurons communications in the brain, i.e., synapse and gap junctions. Novel adaptive control laws were developed and proposed that guarantee the synchronization of FHN neural networks in different configurations. The Lyapunov stability theory was utilized to analytically derive the sufficient conditions that ensure the synchronization of the FHN networks. The effectiveness and robustness of the proposed control laws were shown through different numerical simulations. Generally, synchronization emerges when two or more dynamical systems have strong enough coupling strength –3. In 19τ time at the receiver side [Over the last few decades, several researchers have studied various synchronization schemes and methodologies for chaotic systems –14. Amonver side , 23. Thever side . The finver side . It is pver side , 28. Thuver side , 30. Prever side , 32. Furver side , 33–38. ver side .Taking into account, numerous efforts have been made in recent years to study the lag synchronization of delayed neural networks and chaotic systems , 40–44. In past research, researchers have investigated the interaction between neurons and their networks in different brain regions using techniques like neuroimaging systems –59 and un coupled neurons and all neurons in both networks are connected with other neurons of the same network via synapse and there is a special junction to communicate with target cells. The interactions between neurobiological coupled neurons, namely, the coupling junctions, have a great impact on the dynamical properties of the neurobiological network. Therefore, such configuration shows more challenging and intriguing dynamical characteristics and more intricate dynamical behavior than two, three, or n neurons within the same network. Various novel and diverse control schemes are proposed for both multiple coupled neurobiological networks under different scenarios. These scenarios may conclude neuronal networks with and without time delays for both drive and slave networks in addition to the absence/presence of noise. Using the theory of the Lyapunov stability, we derived the necessary and sufficient conditions that ensure the synchronization of both multiple with and without delay coupled FHN neurobiological networks. Furthermore, the proposed diverse control laws have been verified by using five neurons of each network in both neurobiological networks of coupled FHN neurons under the conditions of (with/without) external noises through numerical simulations. In the light of the above, this paper presents a methodology for lag synchronization of noisy and nonnoisy multiple coupled neurobiological FitzHugh–Nagumo (FHN) master and slave networks with and without delayed coupling, under EES, external disturbances, and different parameters for each state of the networks. Each drive and slave network contains The rest of the article is organized as follows. The model formulation of noisy and nonnoisy FHN multiple neurobiological networks and designing of adaptive controllers are briefly described in n neurons.This section describes the formulation of the synchronization problem for two multiple neurobiological noisy and nonnoisy FHN networks with and without delay in gap junctions under EES. Different parameters for each state of both FHN networks are considered. Consequently, four different multiple neurobiological networks with nonnoisy and noisy FHN neurons are formulated and utilized for the exploration of synchronization phenomena in coupled neural networks. Each network formulated in each case consists of In this section, multiple neuronal models are mathematically expressed without introducing a delay in the gap junctions dynamics, but noisy and nonnoisy networks are considered.n neurons. Mathematically,xi1, ∈ℜ represents membrane-potential and xi2 ∈ ℜ the recovery-variable of the ith neuron of neurobiological FHN drive network, respectively, where yi1 ∈ ℜ represents membrane-potential and yi2 ∈ ℜ the recovery-variable of the ith neuron of neurobiological FHN slave network, respectively, ri1, bi1, and ci1 are positive parameters, Ii1=(Α/ω)cos(ωt) is the EES with frequency ω and A amplitude, di1 is the ionic gate disturbance, uxi1 and uyi1 is the ith control parameter of the drive and slave networks respectively, and G=(gij)N×N representing the topology of the network and is known as coupling matrix whose elements are defined as below:Let us consider nonnoisy multiple FHN neurobiological nondelayed networks each composed of I11=I21=⋯=In1.In addition, we assumed that ξi1 is the Gaussian noise [Let us consider noisy multiple FHN neurobiological nondelayed networks composed of n neurons. Mathematically,an noise  sources The error states of the neurobiological FHN systems formulated in equations  and 2)  2) and  and 5)  5) can bui1=uxi1 − uyi1. Now, let us define the following terms for simplification:ex1, ey1, cd, sd, u ∈ ℜNx1, G ∈ ℜNxN, and T represents the transpose operator. As a result,  can converge to that of the drive system (1/4).It can be concluded that the problem of synchronization is substituted with the synchronized error system  with theNext, the Lyapunov stability and adaptive control theories are utilized to design a unique and simple control scheme that will guarantee the synchronization of the coupled FHN neurobiological without delay networks.ui1={2ex1(gi1+(A/w)sin(wt)+bi1+ci1) − 2ey1(gi2 − (A/w)cos(wt) − bi1 − ci1)} then the synchronization of the nonnoisy/noisy multiple FHN coupled neurobiological non-delayed networks can be achieved.Consider the nonnoisy/noisy multiple FHN neurobiological nondelayed networks described in equations  and 2)  2) and  and 5)  5) with V. In this study, it is chosen as follows:v/dt < 0 for all t.The proof of this theorem and sufficient conditions that ensured the synchronization can be obtained using the theory of the Lyapunov stability. According to the theory of the Lyapunov stability, the stability of a system can be proved by choosing a positive definite function called as the Lyapunov function candidate V is a positive definite function. After taking the time derivative of ,   2) and  and 5)  5) are b3 …, n),  results Correspondingly,I ∈ ℜN×N, is the identity matrix,Incorporating  and 17)17) into P should be a positive definite to ensure the asymptotic stability of the synchronized error system  using the method of determinants, i.e., determinants of all leading principal minors have positive values [It can be concluded that the matrix r system  at the oe values . AccordiMultiple neurobiological noisy and nonnoisy FHN networks are modeled with delays in gap-junction dynamics.n neurons. Mathematically,Let us consider nonnoisy multiple FHN neurobiological delayed networks composed of Let us consider noisy multiple FHN neurobiological delayed networks composed of n neurons. Mathematically,The error states of the neurobiological FHN systems formulated in equations –23 can bui1=uxi1 − uyi1. Now, let us define the following terms for simplification,ex1τ, ey1τ, cdτ, sdτ, u ∈ ℜN×1, G ∈ ℜN×N and T represents the transpose operator. As a result,  can converge to that of the drive system (19/21).It can be concluded that the problem of synchronization is substituted with the synchronized error system  with theui1={−gi1(bi1 − ci1)ex1τ − (bi1 − ci1)ey1τ}, then the synchronization of the nonnoisy/noisy multiple FHN neurobiological delayed networks presented in equations , ,  results Correspondingly,I ∈ ℜN×N is the identity matrix.Incorporating  and 34)34) into P should be a positive definite to ensure the asymptotic stability of the synchronized error system  using the method of determinants, i.e., determinants of all leading principal minors have positive values [It can be concluded that the matrix r system  at the oe values . Accordir11 = 10, r21 = 10.2, r31 = 10.4, r41 = 10.6, r51 = 10.8, b11 = 1, b21 = 1.001, b31 = 1.002, b41 = 1.003, b51 = 1.004, c11 = 0.001, c21 = 0.002, c31 = 0.003, c41 = 0.004, c51 = 0.005, d11 = 0.001 sin(0.2 × t), d21 = 0.002 sin(0.2 × t), d31 = 0.003 sin(0.2 × t), d41 = 0.004 sin(0.2 × t), d51 = 0.005 sin(0.2 × t), A = 0.1, f = 0.129, ω = 2πf and initial conditions are x11(0) = 0, y11(0) = 0, x12(0) = 0.1, y12(0) = 0.1, x21(0) = 0.05, y21(0) = 0.05, x22(0) = 0.2, y22(0) = 0.2, x31(0) = 0.05, y31(0) = 0.05, x32(0) = 0.2, y22(0) = 0.2, x41(0) = 0, y41(0) = 0, x42(0) = 0.1, y42(0) = 0.1, x51(0) = 0.05, y51(0) = 0.05, x52(0) = 0.2, and y52(0) = 0.2. The values of the gap junctions are listed in the matrix GIn this section, the results of the numerical simulations are discussed to analyze and validate the efficacy of the designed control laws for the synchronization of noisy and nonnoisy multiple neurobiological FHN networks with and without delayed gap junctions. To perform this, we considered five neurons of two noisy and nonnoisy multiple neurobiological FHN networks with and without delay gap-junctions and external noise. The parameter values used in this study are t = 150 and the temporal dynamics of the neurons is highly abrupt, but all the errors converged to zero, proving synchronization between both states of all neurons in both networks, as soon as the designed control laws are activated, showing the efficacy of the proposed scheme.Figures Furthermore, the unsynchronized activities of the networks could also be observed through the abrupt behavior of the phase plane diagrams for both states as shown in Figures t = 150 and the temporal dynamics of the neurons is highly abrupt, but all the errors converged to zero, proving synchronization between both states of all neurons in both networks, as soon as the designed control laws are activated, showing the efficacy of the proposed scheme. Furthermore, the unsynchronized activities of the network could also be observed through the abrupt behavior of the phase plane diagrams for both states as shown in Figures Figures t = 110 and the temporal dynamics of the neurons is highly abrupt, but all the errors converged to zero, proving synchronization between both states of all neurons in both networks, as soon as the designed control laws are activated, showing the efficacy of the proposed scheme. Furthermore, the unsynchronized activities of the network could also be observed through the abrupt behavior of the phase plane diagrams for both states as shown in Figures Figures t = 110 and the temporal dynamics of the neurons is highly abrupt, but all the errors converged to zero, proving synchronization between both states of all neurons in both networks, as soon as the designed control laws are activated, showing the efficacy of the proposed scheme. Furthermore, the unsynchronized activities of the network could also be observed through the abrupt behavior of the phase plane diagrams for both states as shown in Figures Figures This paper presents the design of different control schemes for the synchronization of noisy and nonnoisy multiple neurobiological FHN networks with and without delay coupling. Variable parameters have been used for each state of both FHN networks. The proposed control laws for both networks are different and unique to achieve synchronization. The robust adaptive control theory was utilized to propose robust and different adaptive control strategies to investigate the synchronization problem of the noisy and nonnoisy multiple neurobiological FHN networks with and without delay coupling. Control laws are designed to stabilize the error dynamics without direct cancelation and to synchronize all the states of both FHN neurobiological networks. Sufficient conditions for achieving synchronization in the multiple noisy and nonnoisy neurobiological networks were derived analytically using the Lyapunov stability theory. The results of numerical simulations demonstrated the efficacy of the designed control schemes. The most important contributions of this research consist of (i) examining the nondelayed multiple coupled FHN neurobiological networks under the conditions of external noise (with and without), different delayed gap-junctions, and external disturbance, (ii) examining the delayed multiple coupled FHN neurobiological networks under the conditions of external noise (with and without), different delayed gap-junctions and external disturbance, (iii) the development of novel and diverse control laws under the conditions of external noise (with and without) for both multiple FHN neurobiological delayed and nondelayed networks, and (iv) achieving the synchronization of multiple FHN neurobiological networks membrane states and recovery variables states for drive and slave networks using the proposed control schemes.


Autism spectrum disorder (ASD) is a neurodevelopmental disorder with strong genetic underpinnings. Microarray‐based comparative genomic hybridization (aCGH) technology has been proposed as a first‐level test in the genetic diagnosis of ASD and of neurodevelopmental disorders in general.We performed aCGH on 98 Tunisian children (83 boys and 15 girls) diagnosed with ASD according to DSM‐IV criteria.“Pathogenic” or “likely pathogenic” copy number variants (CNVs) were detected in 11 (11.2%) patients, CNVs of “uncertain clinical significance” in 26 (26.5%), “likely benign” or “benign” CNVs were found in 37 (37.8%) and 24 (24.5%) patients, respectively. Gene set enrichment analysis involving genes spanning rare “pathogenic,” “likely pathogenic,” or “uncertain clinical significance” CNVs, as well as SFARI database “autism genes” in common CNVs, detected eight neuronal Gene Ontology classes among the top 10 most significant, including synapse, neuron differentiation, synaptic signaling, neurogenesis, and others. Similar results were obtained performing g: Profiler analysis. Neither transcriptional regulation nor immune pathways reached significance.aCGH confirms its sizable diagnostic yield in a novel sample of autistic children from North Africa. Recruitment of additional families is under way, to verify whether genetic contributions to ASD in the Tunisian population, differently from other ethnic groups, may involve primarily neuronal genes, more than transcriptional regulation and immune‐related pathways. Array‐CGH confirms its satisfactory diagnostic yield in a novel sample of 98 Tunisian autistic children. Pathogenic and likely pathogenic CNVs were detected in 11/98 (11.2%) patients. Several recurrent CNVs were found also in this patient population. Preliminary gene pathway analyses suggest that in the Tunisian population, compared to Caucasian and Asian populations, neuronal gene pathways may be more involved with ASD as compared to genes related to transcriptional regulation and immune function. Addditional families are being recruited to verify this hypothesis. The purpose and protocol of the study were explained to parents by the child psychiatrist (N.G.) and the first investigator (F.C.). Written informed consent was obtained from parents of all patients.We enrolled 98 children and adolescents with ASD, including 83 boys and 15 girls (M:F = 5.5:1), ranging from 3 to 18 years old, and belonging to 91 simplex and four multiplex families with two autistic children . Patients were recruited between January and April 2017 at the Child and Adolescent Psychiatry Clinic of the Department of Psychiatry, Fattouma Bourguiba University Hospital, Monastir, Tunisia. Clinical diagnosis of ASD was based on the Diagnostic and Statistical Manual of Mental Disorders, Fourth Edition (DSM‐IV) .In reference to their frequency in the general population, CNVs were classified into “rare” or “common” using an R script developed ad hoc, based on the presence of ≤3 or >3 healthy subjects, respectively, in the Database of Genomic Variants  or similar  to pathogenic/likely pathogenic CNVs carried by patients listed in the DECIPHER database  , Simons Foundation Autism Research Initiative Gene  , Pubmed, Online Mendelian Inheritance in Man (http://www.ncbi.nlm.nih.gov/Omim), and GeneCards (http://www.genecards.org/). All chromosome coordinates refer to hg19 /GRCh37.In reference to their clinical significance, CNVs were classified into five categories: (a) pathogenic, (b) likely pathogenic, (c) uncertain clinical significance, (d) likely benign, and (e) benign, in accordance with the 2020 American College of Medical Genetics and Genomics (ACMG) and Clinical Genome Resource (ClinGen) recommendations  to perform Enrichment Analysis with the Gene Ontology Functional database .We selected all genes spanning rare CNVs classified as either “pathogenic,” “likely pathogenic,” or “uncertain clinical significance,” as well as all the “autism genes” spanning common CNVs and listed in the SFARI GENE database. We used the open‐access web platform Gene Set Enrichment Analysis (GSEA) (https://biit.cs.ut.ee/gprofiler/gost), a public web server for characterizing and manipulating gene lists .Patient n.41 is a 6‐year‐old boy carrying a large deletion of >500 kb in size, located in chr. 16p11.2 (“16p11.2 microdeletion syndrome”). This child shows severe deficits in social communication, language delay with echolalia, and other moderate symptoms of ASD, in line with prior clinical descriptions of this syndrome . This region comprises several OMIM genes, including SHANK3 gene. This deletion causes Phelan‐McDermid syndrome (PMS), a rare genetic disorder mainly characterized by ID, global developmental delay, muscle hypotonia, and motor coordination deficits, accompanied by ASD in approximately 40% of cases, and by several other systemic signs and symptoms . She carries a terminal deletion of approximately 178 kb located on chr. 22q13.33, involving the At least five individuals carry rare “pathogenic” or “likely pathogenic” dup/dels similar to CNVs listed in the Decipher database, although none is exactly overlapping Table . Three oSFARI GENE, and AutismKB databases, such as DMD, NEXMIF, NLGN4X, PRKN, and others (Table DMD) gene. DMD deletions, duplications, and mutations cause Duchenne muscular dystrophy (DMD), Becker muscular dystrophy (BMD), or cardiomyopathy [OMIM #300377]. This boy was referred for autistic behaviors and has not yet developed a clear DMD/BMD or cardiomyopathy phenotype, as previously observed in other young children  gene, while sparing the neighboring RLIM gene, which has recently been implicated in a mild neurocognitive phenotype in hemizygous males , which is associated with ASD especially in late‐diagnosed PKU patients, although full comorbidity remains a rare event  gene, located in the pseudoautosomal region 1 of the sex chromosomes  out of the 98 patients in the entire sample, underscoring the importance of CNVs involving ASMT in influencing sleep and circadian rhythms.Rare VOUS are listed in Table es Table . ASMT enATL1, one of the causative genes of spastic paraplegia (Table ATL1 encodes a protein involved in the regulation of endoplasmic reticulum (ER) morphology  carry the same 14q22.1 duplication encompassing ed Table .VAMP7 and CDH18, and contain highly conserved H3K27Ac marks often found near active regulatory elements (see http://genome.ucsc.edu). In principle, CNVs can influence gene expression by affecting epigenetically relevant regions encompassing long noncoding RNAs , where it stimulates dendritic growth and spine development, enhancing excitatory synaptic activity , which encodes a scaffolding protein that is enriched in postsynaptic densities of excitatory synapses and also in presynaptic axons and terminals  which in our case n. 24 displays a particularly severe phenotype. Pathogenic deletions and mutations typically involve the s Tables .Among other genes playing a “pathogenic” or “likely pathogenic” role, DMD is especially interesting, because duplications have been found in children diagnosed primarily with ASD and not with DMD/BMD. This may be due both to its earlier onset and at least in some cases due to a milder expression of the muscular phenotype, which can clinically overlap with the motor development delays and coordination deficits often seen in children with ASD  protein, crucial to neuronal migration, cell adhesion, neurite outgrowth, and branching  to identify recurrent CNVs and genetic syndromes associated with ASD, and (b) to detect rare or “unique” pathogenic and likely pathogenic CNVs. This level of genetic characterization can, at least in some cases, foster a better understanding of phenotype–genotype correlations and improved management at the clinical level . The purpose and protocol of the study were explained to parents by the child psychiatrist (N.G.) and the first investigator (F.C.). Written informed consent was obtained from parents of all patients.This study was approved by the Ethics Committee of Mahdia's University Hospital, Tunisia (Ref. n. SupinfoClick here for additional data file.Table S1Click here for additional data file.


However, the mechanism of megatemperature affecting gill osmoregulation has not been fully elucidated.Maintaining osmotic equilibrium plays an important role in the survival of cold-water fishes. Heat stress has been proven to reduce the activity of NaAcipenser baerii) was used to analyze histopathological change, plasma ion level, and transcriptome of gill tissue subjected to 20℃, 24℃and 28℃. The results showed that ROS level and damage were increased in gill tissue with the increasing of heat stress temperature. Plasma Cl− level at 28℃ was distinctly lower than that at 20℃ and 24℃, while no significant difference was found in Na+ and K+ ion levels among different groups. Transcriptome analysis displayed that osmoregulation-, DNA-repair- and apoptosis-related terms or pathways were enriched in GO and KEGG analysis. Moreover, 194 osmoregulation-related genes were identified. Amongst, the expression of genes limiting ion outflow, occluding (OCLN), and ion absorption, solute carrier family 4, member 2 (AE2) solute carrier family 9, member 3 (NHE3) chloride channel 2 (CLC-2) were increased, while Na+/K+-ATPase alpha (NKA-a) expression was decreased after heat stress.In this study, Siberian sturgeon (This study reveals for the first time that the effect of heat stress on damage and osmotic regulation in gill tissue of cold-water fishes. Heat stress increases the permeability of fish’s gill tissue, and induces the gill tissue to keep ion balance through active ion absorption and passive ion outflow. Our study will contribute to research of global-warming-caused effects on cold-water fishes.The online version contains supplementary material available at 10.1186/s12864-022-08969-9. Since the 1850s, global warming has aggravated climate change –4. In Ch+/K+-ATPase) activity in gill tissue [Freshwater makes fish hypoosmotic, which allows ions in the blood to passively diffuse into the surrounding freshwater. Internal osmotic pressure equilibrium is the foundation to maintain cells and physiological processes. To maintain the osmotic pressure, fish requires coordination of multiple organs, including gill, intestine, and kidney tissues –10. The l tissue , 26. HowSturgeon, widely distributed throughout the Northern Hemisphere , is an iPrevious studies have showed that the optimal water temperature was around 20 °C for survival and growth of Siberian sturgeon , 32. HowThe histopathological change of the gill tissue subjected to heat stress was observed via H&E staining Fig. . The resROS level of gill tissue was measured via immunofluorescence after heat stress. As shown in Fig. +, K+ and Cl− ion contents were measured after heat stress in Siberian sturgeon  but no significant change at 24℃ than the control group.Plasma Naeon Fig. . The resde novo assembly. All the unigenes were annotated by five databases, including NR, GO, eggNOG, KEGG and Swiss  Short Read Archive (SRA) database under accession number PRJNA765171). After sequencing and filtering with raw data, 30 to 44 million clean reads were acquired in each library, whose Q30 values ranged from 94.29% to 96.04% in the libraries. Clean reads from all groups were mapping with the corresponding unigene, the mapping rate is 69.09%-74.76%  ≥ 2)were identified in 24℃ vs 20℃group, containing 4,593 up-regulated genes, and 4,275 down-regulated genes  and apoptosis  , cellular components (CC), and molecular functions (MF). In both 24℃ vs 20℃ and 28℃ vs 20℃ groups, many DEGs related to osmoregulation were enriched in “regulation of metal ion transport”, “inorganic ion homeostasis”, “cellular ion homeostasis”, “inorganic ion transmembrane transport”, and “regulation of ion transport” Fig. .Fig. 6GOIn 24℃ vs 20℃ and 28℃ vs 20℃groups, top 10 KEGG pathways were shown in Fig. SAE2, CLC-Kb, ATP1a, ATP2a, CLC-2, NHE3 and ATP4a), three resistance ion loss  and one water molecules' transport (AQP3) genes were changed after heat stress at 24℃ or 28℃. The seven ion absorption genes showed different expression changes, of which the expression level of ATP2a was significantly downregulated but upregulated in other genes, after heat stress at 24℃ or 28℃. The expression levels of three resistance ion loss genes were significantly increased at both 24℃ and 28℃, but the expression level of water molecules' transport gene was only increased at 28℃.The expression of osmoregulatory DEGs at 24℃ vs 20℃ and 28℃ vs 20℃ groups were visualized by heat map Fig. . AmongstOCLN, NHE3, CLC-2 and AE2 genes were upregulated, while the expression level of NKA-a gene was significantly downregulated at 24℃ or 28℃. The mRNA expression of these genes was consistent with the RNA-Seq results, indicating the transcriptome data is reliable.The expression levels of 5 osmoregulatory DEGs were detected by qPCR in gill tissue after heat stress. As shown in Fig. Global warming has increased average summer temperatures and the frequency of extreme weather, posing the thermal threat to cold-water fishes . Gill tiThe gill tissue is particularly sensitive to environmental temperature changes, making it be a perfect organ to study the effect of heat stress on cold-water fishes , 34. In +, K+, and Cl− are the major ions in the blood, and the change of their content has a great influence on the internal homeostasis of fish [+ and K+ in the blood of Siberian sturgeon did not alter after the heat stress, while the content of Cl− reduced dramatically at 28 °C compared to the control group  and Atlantic salmon  exposed to rising temperature [− reabsorption in fish [Na of fish , 37. Theperature , 26, 38, in fish .Temperature is an important environmental factor affecting the physiological function of fish –42. OsmoOCLN expression was increased at 24℃ and 28℃  tended to increase with temperature rising  three times per day  and bred at least one week of acclimatization before temperature administration. The handling of animals was performed in accordance with the protocols approved by the Animal Protection Committee of Sichuan Agricultural University.A total of 300 healthy Siberian sturgeon  were purchased from Sichuan Runzhao Fisheries Co., Ltd., Sichuan, China. All fishes were bred in 40 × 80 × 50 cmn = 90): the control group (at 20℃) and two heat stress groups . The fishes of two heat stress groups underwent an increasing temperature of 1 ± 0.5℃/day within 8 days to 24℃ and 28℃, respectively, then were maintained at the heat stress temperature for 12 days . Blood was collected in tube with heparin sodium for detection of plasma ion contents, and gill tissues were sampled for histopathological observation, ROS immunofluorescence, transcriptome analysis, and qPCR analysis.The acquired gill tissues were fixed with 10% formaldehyde solution for at least 24 h, then dehydrated in graded ethanol solutions, cleared in xylene, embedded in paraffin wax and sectioned into 3–5 μm sections. Sections were prepared, then mounted on slides for hematoxylin and eosin (H&E). After staining, the sections were observed and imaged by a Motic BA400Digital microscope .The refrigerant gill tissues were embedded by OCT , then sliced by freezing microtome . The slice thickness was 8–10 μm. The frozen slides were restored to room temperature, then incubated with spontaneous fluorescence quenching reagent . ROS staining solution  was used to stain slides at 37℃ for 30 min in dark place, following washing three times with PBS (pH 7.4) and then incubating with DAPI solution  at room temperature for 10 min in dark place. Finally, the sections were observed by Fluorescent Microscopy .+, Cl− and K+ contents were measured by detection kits . All the procedures were performed following strict adherence to the manufacturer’s instructions.The blood was centrifuged at 4000 × g for 10 min, the plasma was collected and frozen at -80℃ until for use. Plasma NaTotal RNA was extracted from the gill tissue by TRIzol® Reagent according to the manufacturer’s instructions , and genomic DNA was removed by DNase I . Then, RNA quality was determined by 2100 Bioanalyser ) and quantified by ND-2000 . The high-quality RNA sample  was used to construct sequencing libraries. RNA-seq transcriptome libraries were prepared following TruSeqTM RNA sample preparation Kit from Illumina . Libraries were selected for cDNA target fragments of 200–300 bp on 2% Low Range Ultra Agarose followed by PCR amplified using Phusion DNA polymerase (NEB) for 15 PCR cycles. After quantified by TBS380, paired-end libraries were sequenced by Illumina NovaSeq 6000 platform .de novo assembly with Trinity (http://trinityrnaseq.sourceforge.net/). All the assembled transcripts were annotated against NR, GO, eggNOG, KEGG and Swiss databases. NR database was used to identify the proteins that have the highest sequence similarity with the given transcripts. BLAST2GO (http://www.blast2go.com/b2ghome) program was used to get GO annotations of unique assembled transcripts for describing biological processes, molecular functions, and cellular components.The raw paired-end reads were firstly trimmed, and quality was controlled by Trim Galore and Fast QC software. Then, clean data from all samples was used to p < 0.005, |log2 (foldchange)|≥ 2. The acquired DEGs then underwent GO and KEGG enrichment analysis [After assembly, the gene expression abundance was calculated as FPKM (Fragments Per Kilobase of transcript per Million mapped reads) values that were used to analyze the expression change of genes in the gill tissues of Siberian sturgeon after heat stress. The DEGs of heat stress groups than the control group were identified via identified by DEseq R packages within adjusted analysis –54.5 DEGs were selected to verify the RNA-Seq results. These genes were measured by qRT-PCR. The Primer 6.0 software was used to design primers Table . Total R−△△Ct method was used to calculate relative changes in mRNA transcript expression from the qPCR results .To distinguish between specific and nonspecific reaction products, a melting curve was obtained at the end of each run Table . The 2−△p < 0.05.All data were expressed as mean ± standard deviation. Differences between groups were analyzed by one-way analysis of variance (ANOVA) followed by Bonferroni’s Multiple Comparison Test with the significance as Additional file 1: Fig.S1. Temperature control Day1 to 7: temperature acclimation; Day7 to 14: Reaching targeted temperature. Day15 to 27: Summer water temperature exposure. Fig. S2. DEGs analysis.  DEGs analyzed in 24℃-vs-20℃.  DEGs in 28℃-vs-20℃. Each dot represents one gene. Red dots represent up-regulated genes and blue dots represent down-regulated genes. Gray dots represent genes with no differential expression. Fig. S3. KEGG pathway of osmoregulation DEGs. (A) 24℃-vs-20℃. (B) 28℃-vs-20℃. Table S1. The sequence quality and mapping results in the nine samples.


A formally exact density functional theory (DFT) determinationof the average electron energy is presented. Our theory, which isbased on a different accounting of energy functional terms, partiallysolves one well-known downside of conventional Kohn–Sham (KS)DFT: that electronic energies have but tenuous connections to physicalquantities. Calculated average electron energies are close to experimentalionizationpotentials (IPs) in one-electron systems, demonstrating a surprisinglysmall effect of self-interaction and other exchange-correlation errorsin established DFT methods. Remarkable agreement with ab initio quantummechanical calculations of multielectron systems is demonstrated usingseveral flavors of DFT, and we argue for the use of the average electronenergy as a design criterion for density functional approximations. Self-interaction is related to moregeneral delocalization and static correlation errors,2 which, together with incorrect asymptotic behaviors ofexchange-correlation (XC) potentials,3 areimportant limitations of DFT. A clear physical interpretation of orbitalenergies is also missing in DFT.4 It isonly the highest occupied molecular orbital (HOMO) energy that allowsfor an interpretation via Janak’s theorem,5 as a sudden photoionization excitation energy (the firstIP).6 Resolution of the frontier-orbitalenergy problem (getting the first IP right) is in practice linkedto a correct functional description of the derivative discontinuityand fractional-particle occupations7 aswell as to the gap renormalization at the molecular-metal interfaces.8 Significant advances have been made in thesedirections through, for example, the development of screened and range-separatedhybrid XC-functionals.13 Impressive agreements with semiconductor band gaps16 and low-order experimental IPs of molecules17 arepossible in a generalized Kohn–Sham (GKS), range-separated-hybrid21 framework.Kohn–Sham (KS) density functionaltheory (DFT) is the veritableengine of computational chemistry, physics, and materials science.The linchpin idea behind this successful theory is the descriptionof an in principle exact electron density using a set of fictitiouslynoninteracting electrons, the occupied KS-orbitals. The associatedwell-known challenges with this approach are several. For example,a self-interaction error arises as a consequence of describing thetotal energy as a nonexact functional of the electron density,average electronenergy, χ̅. We then point to the use of χ̅as a design criteria and quality indicator for density functionalapproximations. The DFT-based theory we outline is formally exactand does not directly relate to individual photoionization processesnor orbital energies, as is discussed in In this work,we present a DFT determination of the ab initio quantum chemistry in terms ofone-electron energies (Ee1) and multielectron energies (Eee),N is the total numberof electrons. In Ee1 sums the totalkinetic energy and the attraction to nuclei of all electrons, while Eee quantifies all repulsionbetween electrons in the fully interacting system. In nonrelativisticquantum mechanics, the Ee1 and Eee energies canbe interpreted as expectation values of corresponding one- and two-electronoperators:0 isthe ground state wave function, i and j denote electrons, A denotes nuclei, M is the total number of nuclei, ZA is nuclear charge, and ∇i2 is the Laplace operator.Note in N of electrons.The average electron energy is aninherent physical property ofany system of electrons, for example molecules, and it can be generallydefined in 33 followed by coordinate-based representation in 35There exist many other ways of expressing χ̅ exactly.For example, in formal many-body physics χ̅ equals theintegral of the so-called spectral function weighted by the frequencyand the Fermi occupation (see refs −25). In 36 which we will return to discuss, have been productivelyused to predict properties like Hammett constants,38 polarizability,39 hardness,40 electronegativity,42 electrophilic reactive sites,46 general chemical reactivity,49 pKa,50 and solubility.51 The average electron energy appears in the theoreticalframework of moments of the electron distribution, which is usefulfor predicting solid state structure (where χ̅ is thefirst moment).52 Interest in χ̅in chemistry is also rooted in its association with electronegativity,57 and to its relation with changes in the total energy E asVNN is the nuclear repulsion energy.55 The energy partitioning of 55 and has even been usedto study the effect of compression on the electronegativity of atoms.58The use of χ̅in chemistry and physics is broad. Approximationsto χ̅ based on orbital energy averaging,ab initio methods such as multireferenceconfiguration interaction (MRCI) offers a near-exact evaluation ofthe average electron energy. However, in practice, such calculationsare often prohibitively costly. Most studies of χ̅ arequalitative and rely on some form of approximation separate from theformally exact nocc is the number of occupied spin orbitals, and εi is the eigenvalue associated with the ith spin orbital. Ee1 in Eee in 59 The latter interpretationallows χ̅ to be estimated also from experiment,as an average of photoionization energies,m is the number ofpeaks analyzed, εi,IP and wi are, respectively,the vertical ionization energy and the integrated spectral weightassociated with the ith ionization peak.In the estimates of χ̅IP that follows we have assumed wi = 1 and averaged only the ionization peaks of whatformally can be viewed as occupied levels in a 1-determinantal picture.The ability to estimate Δχ̅ experimentally, alongwith ΔVNN frommolecular structures and ΔE from thermochemicaldata, has merited some of us to label experimental quantum chemistry energy partitioning.55Accurate viz. 60 However, the average of the correspondingKS orbital energies is, as we shall outline, not equal to χ̅.We now returnto DFT, for which the prevailing approach of evaluating χ̅,by averaging conventional KS-DFT orbital energies viz. 5, can beT⟩ is in KS DFT described asa sum of two terms,TKS[ρ] is the kinetic energy of the noninteracting system and where the remainder Tc[ρ] is the kinetic correlation energy.In other words, Tc[ρ]is the difference in kinetic energy between the real interacting electronswe aim to describe and the noninteracting (fictitious) KS orbitals.The division of 63 but is alsoa consequence of there being no direct way to exactly compute theactual kinetic energy ⟨T⟩ in DFT. Thecorrelation component of the kinetic energy is typically handled implicitly,as part of the total XC energy Exc.62 Undoing the division expressed as Our approach for calculating an in-principle exactand physically motivated χ̅ boils down to a sum of energyterms that does not involve KS orbital energies. We look first atthe components of the exact ENe[ρ]energy can be evaluated exactly asr) is the potential experienced by electrons interacting with a setof nuclei. The expectation value of the Eee energy in J[ρ] denotesthe Hartree or mean-field approximation to Eee as calculated in DFT,The second expectationvalue at the right-hand side of Exc[ρ] energyis to compensate forthe inclusion of electron-self-interaction in J[ρ].In other words, whereas there is a criterion i < j in 64 The formulation of Eee in Exc[ρ] = ⟨T⟩ + ⟨Vee⟩ – J[ρ] – TKS,65 since Tc[ρ] isjust the difference between the actual kinetic energy and TKS, the kinetic energy of asingle Slater determinant of KS orbitals.62We remind that one part of the functionof the By combining mostly given in termsprovided by generic molecular andperiodic DFT codes. We do, however, need a separate step for computingthe Tc[ρ] term,which we outline in the SI. Fortunately,the Tc[ρ] termis often small compared to the total XC energy in molecules, whereexchange dominates. In cases where this assumption holds in practicewe may proceed with an approximate characterization,Tc and Exc is at most 6% (Table S1).χ̅DFT and χ̅DFT* quantitiesare both notably different from HF and KS orbital-basedapproximations, χ̅orbHF and χ̅orbKS, commonly computed in chemistry from 67identical at the HF level. However, an averaging over KSorbital energies also reflects a density-weighted integral of theXC potential, υxc(r),61The 68υxc(r) is given as the functionalderivative of the exchange-correlation energy Exc[ρ] that can itself be expressed asa product of the density and the so-called exchange correlation hole ρxc.72 One part of υxc(r), often termedυxcresp(r), isset by the functional derivative of ρxc and should produce a discontinuity when the electronoccupation is changed across integer values.32 All standard functional approximationsmore-or-less fail in correctly describing υxcresp(r)—i.e., they fail to have a properaccount of the derivative discontinuity. Nonetheless, that componentof the effective potential helps to set the orbital energies in Kohn–ShamDFT calculations.68 Effectively, the last term ofthe right-hand side of orbKS.χ̅DFT isonly weakly sensitive to derivate-discontinuity limitationsin the υxc(r) description since we base our evaluation of χ̅DFT directly on Exc[ρ]. Of course, χ̅DFT is still sensitive to errors thatexist in the electron density ρ and to those that remain inpresent-day XC functional Exc[ρ]. Use of a hybrid functional, like in refs  and B3LYP10 (providing χ̅DFT*B3LYP and χ̅orbB3LYP). We will at times refer to our χ̅DFT*-values as XC corrected average electron energies. We extract χ̅DFT* values from conventional outputfiles of standard quantum-chemistry codes . We havemade an in-house update of the postprocessing ppacf code65 of the Quantum Espresso (QE) suite68 for planewave computations of both the kinetic-correlationenergy Tc and χ̅DFT for molecularand extended systems. This ppacf code update is available upon requestand will be released to the open-source QE suite.In what follows, we focus on the analysis of J[ρ].1 For one-electron systems χ̅ should equal the total energy of the system.The self-interaction error ofDFT is most apparent in systems of only one electron. The XC energyfunctional must here produce an effective local XC potential thatexactly cancels what is clearly a spurious Hartree or mean-electron-fieldenergy contribution to +, and H2+. Also shown are experimental references, χ̅IP, which in thesecases are nothing more than the single ionization potential of themolecule or ion in question. Note in orbPBE and χ̅orbB3LYP are here the negative of the energies of occupiedKS energy levels). For example, the KS-orbital of H is attributedan energy of 7.6 and 8.8 eV with PBE and B3LYP, respectively. Theactual energy of an electron in H is exactly the ionization potentialof the atom, 13.598 eV.χ̅DFT* is already with a conventional generalized-gradient-approximation(GGA) functional, such as PBE, in near perfect agreement with experiment.The value of χ̅DFT*PBE for H is, likelysomewhat fortuitously, only 16 meV different from experiment. Thehybrid XC functional B3LYP is less affected by self-interaction erroroverall but overestimates the electron energy in H by 0.14 eV.The improvement provided by 2, and H–. With a second electron correlationenergy is introduced, and we here expect the mean-field picture ofHF to fail to some degree. In principle, the energy of two explicitlycorrelated electrons should be better described by DFT.In DFT*PBE and χ̅DFT*B3LYP-values are all slightly larger than the negativeof the HF orbital energies, χ̅orbHF.In other words, our χ̅DFT* evaluations correctly describe electrons that are more bound compared to the mean field description. Addingthe Tc contributionsto extract χ̅DFT increases the values only marginally (Table S1). The improvements provided by the near exact χ̅DFT* is furtherhighlighted when comparing to MRCI results. MRCI introduces, at considerablecomputational costs, correlation energy contributions which are missedin HF theory. Going forward, χ̅MRCI (and not χ̅IP) represents our reference values for validating Indeed, whereas the estimates based on averaging KSorbital energiesare far off the mark and sometime predict unbound electrons, the correctedχ̅rginally S1. The iχ̅IP is only approximatelyequal to χ̅for systems of more than one electron . Ionization of single molecules can,of course, be calculated very accurately, especially with MRCI. However,averaging of such accurate ionization energies, cf. not equal the average electron energy, χ̅. Weexplain in There are several reasons for why electron . Relaxat19 We again stress, due to the ease of misinterpretation,that we do not discuss ionization, but a single-state property, χ̅,which is only approximately related to electron binding, and strictlyobservable  only for one-electronsystems  of 0.9998, implying that relative measures, Δχ̅,can be productively approached experimentally .Complementary estimates to χ̅ obtainedfrom the averagingof photoionization peaks, i.e., χ̅DFT* , is as a metric of quality of density functional approximations.DFT methods are today primarily evaluated against total energies and,to a lesser degree, properties.77 The averageelectron energy χ̅ contains all the terms most challengingin DFT functional design twice, those describingelectron repulsion and correlation effects. All density functionalapproximations are associated with errors in both the density andin the computed XC energy for that density. Computations of totalenergies may therefore appear accurate because of fortuitous cancellationsof these kinds of errors. By relying on χ̅ as a qualityassessment, we offset such cancellations. Tables 1–3 . Our testset is not exhaustive and relies on the omission of Tc in the definition of χ̅DFT*. Consequently, One way to use more physically motivated average electron energies,such as Etot but also, independently, on the average-electronenergy χ̅. Having two independent assessments providesan option to separate out density-driven functional errors.78 The comparison is not only possible for molecules, but also, aswe show in the SI for general extendedsystems.Nevertheless, our formal theory now makes it possibleto evaluatefunctional quality not only on DFT total-energy results 79 The absolute energy position of KS levels cannotbe rigorously defined unless we make assumptions for the charge distributionsat the far-away bulk-system surfaces. It is a subtle but importantpoint that we here present an exact theory for average electron energyand an evaluation-scheme that is independent of the arbitrarily chosenreference for the KS-orbital energy. Instead, it suffices to knowthe kinetic energy and the density, which are both set by the shapesof the orbitals (and hence of the electron density), as we detailin the SI. We can therefore complete theformally exact characterizations of χ̅ and analysis ofchemical bonding also in general materials.The opportunity for general-system testing presentsitself becauseour theory addresses a fundamental challenge of handling the well-knowndivergence of Coulomb terms in infinite (ionic) crystals:The usefulness of conventional KS DFT derivesfrom the constructionof correlated electron densities from fictitious noninteracting electronicorbitals. Several of the known problems with this successful theoryare, in one way or another, interpretative in nature and related tothe tenuous connection between KS orbitals and physical electrons.The purpose of this work is to partially address this issue, by presentinga formally exact KS-orbital-energy-free evaluation of physical electronenergies in DFT. Our inspiration for considering the average electronenergy derives from chemistry, where more qualitative KS-orbital-energy-basedapproximations to this quantity have proven useful for analyzing chemicalbonding, reactivity, and electronegativity.+, and H2+ compute as only fractions of an eV away fromexperimental ionization potentials using conventional GGA functionals.Our approach provides a more bound description of the average electroncompared to HF theory in larger molecules, and values consistentlyresemble those obtained at accurate ab initio MRCIlevel of theory, but at drastically reduced computational costs. Thisagreement is a testament to how well self-interaction errors are handledin KS DFT. We therefore suggest that the average electron energy canbe used as a physically motivated  indicatorof quality, and as a constraint, in the design of DFT functionals.A more physicaldescription of electrons is demonstrated in severalways: The average electron energies of H, HeOur theory is straightforwardly implementable together with standardDFT functionals and software and comes at no additional computationalcost. Potential utility abounds: More physically motivated electronenergies will, for example, provide better predictions of chemicalreactivity. Implementation is here exemplified on molecular calculations,but applicability is being developed also for extended systems. Apromising avenue to be explored is using average electron energiesto constrain KS electronic levels. Such developments may lead to furtherimprovements in the modeling of light-matter interactions, spectroscopy,electron transport, and a range of material properties. Our formaltheory is important in the broader context of developing general-purposeXC energy functionals.


Our findings may provide new insights into the etiologies and pathology for IDD, further, targeting of microtubule acetylation may be an effective strategy for the treatment of IDD.Intervertebral disc degeneration (IDD) is the cardinal pathological mechanism that underlies low back pain. Mechanical stress of the intervertebral disc may result in a change in nucleus pulposus cells state, matrix degradation, and degeneration of the disc. Microtubules, which are components of the cytoskeleton, are involved in driving or regulating signal pathways, which sense and transmit mechano-transduction. Microtubule and the related proteins play an important role in the development of many diseases, while little is known about the role of microtubules in nucleus pulposus cells. Researchers have found that type II collagen (COL2) expression is promoted by microtubule stabilization in synovial mesenchymal stem cells. In this study, we demonstrated that microtubule stabilization promotes the expression of COL2 in nucleus pulposus cells. Stabilized microtubules stimulating Hippo signaling pathway, inhibiting YAP protein expression and activity. In addition, microtubules stabilization promotes the expression of COL2 and alleviates disc degeneration in rats. In summary, our study for the first time, identifies microtubule as a promising therapeutic target for IDD, up-regulating the synthesis of COL2  Intervertebral disc degeneration (IDD) is considered to be the principal cause of low back pain, which brings a heavy economic and social burden to the global healthcare system . The bio in vivo . In addi in vivo . TherefoMicrotubules (MT), filamentous actin (F-actin) and intermediate filaments (IFs) together form a three-dimensional cytoskeleton, which mediates force transmission. Most microtubules are not static, they exhibit cycles of growth, shortening and regrowth. This dynamic instability allows MT responding to changes in internal or external conditions, and thus allows a cell to alter its cytoskeleton accordingly. Dynamic MT can generate pushing forces, which could maintain the cell shape under compressive forces . HoweverYes-associated protein (YAP) and transcriptional coactivator with PDZ-binding motif (TAZ) serve an important role in biomechanical and mechanical signaling that affects cell proliferation and differentiation. YAP/TAZ read diverse biomechanical signals and transduce them into biological effects in a manner that is specific for each type of cell and mechanical-stress, which highlights the central role of YAP as universal mechano-transducers and mechano-effectors. Studies reveal that F-actin plays such an important role in the mechano-transduction between extracellular matrix and intervertebral disc cells . MoreoveHence, we investigated the role of MT stabilization in the synthesis of COL2 in NP cells, using docetaxel (MT stabilizer) and nocodazole (MT destabilizer). Our results suggest that MT stabilization of NP cells would be a potential therapeutic target for enhancing the synthesis of COL2 and alleviating IDD.All the experimental protocols were approved by the Ethics Committee of Nanjing Drum Tower Hospital, the Affiliated Hospital of Nanjing University Medical School. With the informed consent of the patients, normal NP tissues were obtained from eight patients  who underwent surgery for congenital scoliosis. Degenerative NP tissues were collected from eight patients  who underwent posterior spinal fusion surgery. The human NP tissue samples were classified according to their degenerative grades . After cNP tissue and NP cells were lysed in the radioimmunoprecipitation assay (RIPA) buffer. The protein concentration was determined using a BCA kit (Thermo Scientific). 5% skim milk  was added to TBST  for 60 min to block membranes. After blocking, the membranes were incubated overnight at 4°C with the corresponding primary antibodies of Ace-tubulin , Collagen 2 , SOX9 , Smad3 , YAP , p-YAP , TAZ , LATS1 , LATS2 , and GAPDH . Then, HP-linked secondary antibodies  were applied. The immunoblotting was detected by UVP ChemiDoc-It Imaging System  with the enhanced chemiluminescence detection kit  added to the membranes. Each blot was measured using ImageJ software for its integrated density.A total RNA extract was prepared with Trizol . Following reverse transcription, the RNA was converted into cDNA using PrimeScript RT Master Mix Kit . Real-time polymerase chain reactions (RT-PCRs) were carried out using the TaKaRa SYBR Premix Ex Taq (RR420A) and the ABI StepOnePlus Real-Time PCR System . By normalizing by GAPDH, fold changes of interested mRNAs were calculated. The primers were designed as follows:Col2: 5′-AAGGGACACCGAGGTTTCACTGG-3′, 5′-GGGCCTGTTTCTCCTGAGCGT-3′; SOX9: 5′-AGCGACAACTTTACCAG-3′; 5′-GGAAAACAGAGAACGAAAC-3; GAPDH: ACAGCAACAGGGTGGTGGAC-3′, 5′- TTTGAGGGTACAGCGAACTT-3′; YAP: 5′-GCTAGATAAAGAAAGCTTT-3′, 5′-CCAATAGTTCCGATCCCTT-3′; TAZ: 5′- GAATCAGCCTCTGAATCAT-3′, 5′-GTCTGAAGATCTGATCCCT-3′; LATS1: 5′-CCACCCTAC CCAAAACATCTG-3′, 5′- CGCTGCTGATGAGATTTGAGTAC-3′; LATS2: 5′-GCCAAAGACTTTTCCTGCCA-3′, 5′- TCTTTGCTCCCCAGGACTTT-3′.Using Ribobio’s EdU Reagent Kit , the manufacturer’s instructions were followed to investigate cell proliferation. Following treatment with nocodazole and docetaxel for 3 days, the degenerative NPCs were exposed to 10 μM EdU for 2 h. Fluorescence images were captured using a fluorescence microscope .In accordance with the manufacturer’s instructions, the viability of NPCs was evaluated by using CCK8 assay ((Solarbio). We subsequently incubated each well for 2 h at 37°C with DMEM/F12 containing 10% (v/v) CCK-8 solution after washing with PBS. Microplate readers  were used to measure absorbance at 450 nm.Analyses of immunofluorescence were performed as previously described . We fixeAccording to the manufacturer’s instructions, immunohistochemical staining and immunofluorescent analysis were performed. The serial sections were incubated overnight at 4°C with primary antibodies against Col2  and Ace-tubulin . The slides were stained immunohistochemically with secondary antibodies conjugated with HRP, incubated at 37°C for 1 h. Photographs of sections were taken using a Zeiss fluorescence microscope .The siRNA sequence was designed and synthesized to target the human YAP1 gene: 5-GGUGAUACUAUCAACCAAATT-3 (Hippobio). We seeded NPCs in 6-well plates and grew them to a confluence of about 70%. Transfecting the cells with either 50 nM siRNA-YAP or a negative control, as directed by the manufacturer, took place for 12 h in Lipofectamine 3,000 (Thermo Fisher Scientific).In accordance with the guidelines of the Institutional Animal Care and Use Committee at Nanjing University Medical School, all experiments were reviewed and approved by the committee. In the study, SD-Rats (10 weeks) were anesthetized with 10% chloral hydrate (0.3 mL/100 g) injected intraperitoneally. After placing the animals in a prone position, ethanol was applied to the tail skin for disinfection. A 21 G needle with a stopper was used to percutaneously puncture the discs Co6-7, Co7-8, and Co8-9 to the depth of 5 mm, after which the needle was rotated 360 degrees and held for 30 s. Four weeks after acupuncture, the caudal intervertebral discs of rats were examined by microCT and MRI. This study used MicroCT instead of X-ray to calculate the intervertebral disc height index (DHI), which is conducive to more intuitive indication of the changes in intervertebral disc height. The calculation method of DHI is as previously reported . DegenerUsing CO2 inhalation, all animals were sacrificed and the vertebral segments were dissected from the coccygeal segments 6–7, 7–8, and 8–9. Specimens were fixed in 10% formalin for 20 h at room temperature, then decalcified in an ethylenediaminetetraacetic acid (EDTA)-glycerol solution for 4 weeks. An embedding of decalcified tissue in paraffin, sectioning sagittally to a thickness of 5 μm. Hematoxylin-eosin was used to stain the slides of each disc, and a histological grading system was used to grade them . Meanwhip < 0.05.The means and standard deviations were calculated for all data. In GraphPad Prism 8, one-way ANOVA was used for the statistical analysis. In this study, statistical significance was defined as a In order to harvest the degenerated NP cells, we collected human NP tissue samples from patients who underwent posterior transforaminal lumbar interbody fusion surgery due to lumbar spinal stenosis. The degenerated intervertebral discs all demonstrated low signal intensity (Pfirrmann grade Ⅳ or Ⅴ) in T2 Weight images of Magnetic Resonance . The norMicrotubules are involved in secretory transport mechanisms in collagen and proteoglycan synthesis. Thus we explored the stability of microtubules in degenerated NP cells. As previously reported, acetylated tubulin (Ace-tubulin) was used as a marker and quantitative index for microtubule stabilization since tubulin acetylation was found mainly on stable microtubules resistant to depolymerization . TubulinSince the microtubule stability may regulate the cellular function of NP cells, we then investigated the effect of upregulation and the downregulation of microtubule stability on NP cells. Docetaxel, the microtubule stabilizer, and nocodazole, the microtubule depolymerizer, were used for the stabilization and destabilization of the microtubules, respectively. Regarding the cytotoxicity induced by high concentrations of docetaxel and nocodazole, we evaluated the proliferation and cell viability of NPCs treated with different concentrations of docetaxel and nocodazole using the CCK-8 and EdU staining. The EdU staining showed that the proliferation of NP cells was not significantly affected by docetaxel  or nocodazole , but was significantly inhibited by docetaxel at higher concentrations (5 and 10 nM) and enhanced by nocodazole at higher concentrations (50 and 100 nM) . NP cellAfter treating NP cells with docetaxel and nocodazole for 1 week, the expression of Ace-tubulin was enhanced in NP cells treated with docetaxel compared to the untreated group, but no difference was found in NP cells treated with nocodazole, according to the results of Western blot and cell immunofluorescence . As the YAP/TAZ plays a critical role in response to mechanical stress, perturbation of the cytoskeleton and matrix remodeling . YAP/TAZDrosophila (via regulating Hippo pathway.Hippo pathway regulates YAP/TAZ primarily through LATS kinases (LATS1 and LATS2)-mediated phosphorylation. Moreover, Hippo pathway is regulated by actin cytoskeletal factors, including capping proteins and cofilin . A recenosophila . Therefoosophila , which wosophila . In addivia the regulation on YAP.To clarify whether YAP plays a role in the up-regulated COL2 expression promoted by MT stabilization, YAP was knocked down by small interfering RNA (siRNA). As the total and phosphorylated YAP both decreased following YAP siRNA transfection, the nucleus pulposus related proteins, including COL2, SOX9 and Smad3, were all upregulated with and without docetaxel treatment; while the expression of LATS1, LATS2 and Ace-tubulin were not significantly altered . MoreoveTo further investigate the therapeutic effects of MT stabilization on IDD, we used a classic rat caudal intervertebral disc acupuncture animal model for this study. PBS, nocodazole and docetaxel were injected into three consecutive independent intervertebral discs of each rat 4 weeks after acupuncture. MRI and microCT examinations of rat IVD were performed at 4 weeks after the modeling and 4 weeks after the treatment to determine the degree of degeneration. A percent disc height index (%DHI) was calculated based on the microCT results. With a low percent DHI in all rats 4 weeks after needle puncture, the intervertebral disc showed intervertebral space stenosis or collapse, indicating degenerative changes of IVD . After 4in vivo in rats  could suppress the synthesis of Col2 while YAP knockdown promoted synthesis in NP cells. Increased YAP expression levels has been reported to increase osteogenesis and decrease adipogenesis of mesenchymal stem cells and initiate dedifferentiation of chondrocytes , and thuIt is very interesting that we observed increased ace-tubulin in degenerated NP tissues derived from patients with IDD, which has not been reported in previous studies. The acetylation of tubulin is a consequence of microtubule stabilization since artificially chemical stabilization of microtubules leads to acetylation of tubulin . The mecIn summary, our study for the first time, identifies microtubule stabilization as a promising therapeutic target for IDD, up-regulating the synthesis of Col2. Moreover, Hippo-Yap pathway participates in the regulation of Col2 in the context of stabilized microtubule. Our findings may provide new insights into the etiologies and pathology for IDD, further, targeting of microtubule acetylation may be an effective strategy for the treatment of IDD.


Halorubrum lacusprofundi functions in extremely cold and hypersaline conditions. To better understand the basis of polyextremophilic activity, the enzyme was studied using steady-state kinetics and molecular dynamics at temperatures ranging from 10 °C to 50 °C and salt concentrations from 1 M to 4 M KCl. Kinetic analysis showed that while catalytic efficiency (catk/Km) improves with increasing temperature and salinity, Km is reduced with decreasing temperatures and increasing salinity, consistent with improved substrate binding at low temperatures. In contrast, catk was similar from 2–4 M KCl across the temperature range, with the calculated enthalpic and entropic components indicating a threshold of 2 M KCl to lower the activation barrier for catalysis. With molecular dynamics simulations, the increase in per-residue root-mean-square fluctuation (RMSF) was observed with higher temperature and salinity, with trends like those seen with the catalytic efficiency, consistent with the enzyme’s function being related to its flexibility. Domain A had the smallest change in flexibility across the conditions tested, suggesting the adaptation to extreme conditions occurs via regions distant to the active site and surface accessible residues. Increased flexibility was most apparent in the distal active sites, indicating their importance in conferring salinity and temperature-dependent effects.The polyextremophilic β-galactosidase enzyme of the haloarchaeon  The mechanism of polyextremophilic protein function is of significant interest for pushing the limits of protein evolution and the design of novel enzymes for biotechnology. Of particular interest are proteins from extremely halophilic Archaea , salt-loving microorganisms in the third Domain of life. Enzymes from haloarchaea typically function optimally in salt concentrations of 2–4 M or higher, reflecting the internal milieu of cells . The halHalorubrum lacusprofundi, isolated from Deep Lake in the Vestfold Hills of Antarctica, which grows under both high salinity and low temperatures [w/v) with a temperature range of −18 to 11.5 °C. The high concentration of salts results in freezing-point depression which prevents the lake from freezing even in the coldest months. H. lacusprofundi has been found to be capable of growth in the laboratory at temperatures as low as −2 °C and its enzymes are consequently adapted to function under such low temperatures and high salinity conditions and has even been of interest for astrobiological studies [In the case of enzymes of haloarchaea inhabiting perennially cold environments, both cold temperatures and high salinity must be tolerated simultaneously . An exceeratures . The sal studies ,8.H. lacusprofundi, the genome was sequenced and the predicted proteome analyzed in relation to cold activity [H. lacusprofundi was found to be highly acidic with a mode of 4.4 for the pI, similar to other sequenced haloarchaea. Its highly acidic proteome is the hallmark of haloarchaeal proteomes, observed originally with sequencing of the Halobacterium sp. NRC-1 genome and subsequently confirmed in many other related species [H. lacusprofundi proteome was compared to twelve haloarchaea from temperate climates [H. lacusprofundi proteins belonging to fully conserved haloarchaeal orthologous groups (cHOGs) [H. lacusprofundi cHOG protein positions invariant in homologous proteins from the mesophilic halophiles [To better understand the function of polyextremophilic enzymes of activity ,10. The  species ,4. In orclimates . A total (cHOGs)  were alilophiles . The moslophiles .H. lacusprofundi bga gene which codes for its cold- and salt-active β-galactosidase was selected for further investigation. The H. lacusprofundi β-galactosidase has a high negative net charge located primarily on its surface, typical of haloarchaeal proteins, and its amino acid alterations compared to mesophilic homologs are similar to those observed at the whole proteome level [H. lacusprofundi β-galactosidase, the enzyme was expressed using Halobacterium sp. NRC-1 as host, which lacks an endogenous β-galactosidase enzyme. The enzyme had measurable activity below 0 °C, and surprisingly above 60 °C, with an optimum of 50 °C, and functioned under extremely high salt conditions: 2.0–4.5 M NaCl or KCl, with an optimum of 4.0 M for either salt [H. lacusprofundi β-galactosidase was initially modeled using the published structure of the homologous Thermus thermophilus family 42 β-galactosidase (pdb: 1KWK) and the model was subsequently validated by an X-ray crystal structure (pdb: 6LVW) [H. lacusprofundi [To analyze the mechanism of extremophilic protein function experimentally, the me level ,12. To eb: 6LVW) ,14. The profundi .H. lacusprofundi β-galactosidase, six residues were found to be diverged in the cold-active enzyme compared to mesophilic haloarchaeal homologs [In subsequent structure–function analysis of homologs ,15. Sitehomologs . These rH. lacusprofundi β-galactosidase enzyme function with varying temperatures and high-salt conditions through a combination of steady-state kinetics and molecular dynamics simulations. Through this interdisciplinary approach, we correlated kinetic effects under different salt concentrations and temperatures with protein dynamic predictions, to address the fine-tuning required for optimal enzyme activity in two extremes.In the current investigation, we addressed the mechanism of H. lacusprofundi β-galactosidase activity at various temperatures and salinity, we initially conducted steady-state kinetic analysis of the wild-type enzyme expressed in Halobacterium sp. NRC-1. Using the classic chromogenic substrate o-nitrophenyl-β-galactoside (ONPG), we carried out kinetic measurements from 1–4 M KCl in one-molar increments and temperatures of 10–50 °C in ten-degree increments. The catalytic rate constant (kcat) and Michaelis constant (Km) were determined from Lineweaver–Burk plots and used to calculate the catalytic efficiency (kcat/Km). The largest relative effect of salinity on catalytic efficiency was observed at the lowest temperature, consistent with the requirement of high salinity for improved low-temperature activity   a. An exce enzyme a.kcat of an enzyme can be described byBk is Boltzmann’s constant, T is the temperature, h is Planck’s constant, R is the gas constant, ∆H‡ is the activation enthalpy, and ∆S‡ is the activation entropy. Psychrophilic enzymes often have lower activation enthalpies and activation entropies than their mesophilic and thermophilic homologs, resulting in a catalytic rate that is less temperature dependent [It has been proposed that psychrophilic enzymes achieve cold adaptation through a reduced temperature dependence of their catalytic rates . Accordiependent ,19,20. TH. lacusprofundi β-galactosidase catalysis changes with salt concentration, we used a Bayesian inference method  to estimate the activation enthalpy ∆H‡ and activation entropy ∆S‡ at each KCl concentration, from the temperature dependence of the measured kcat values . Consequently, this analysis is consistent with H. lacusprofundi β-galactosidase exhibiting psychrophilic character only at high salinity (2–4 M KCl) and behaving more like a mesophilic enzyme at 1 M KCl. To examine how the apparent activation enthalpy and entropy of t values . The resH. lacusprofundi β-galactosidase in atomic detail, and its role in halophilic and temperature adaptation, we constructed a homology model of the enzyme, and performed molecular simulations at 1 M, 2 M, 3 M, and 4 M KCl . For each salt concentration, five different temperatures were used: 10, 20, 30, 40, 50 °C, resulting in 20 sets of conditions. Parallel simulations were performed on the Folding@home distributed computing platform, to produce a collection of trajectories ranging in length from ~20–80 ns, for a total aggregate simulation time of 422 µs. Each set of conditions contains 494 trajectories. To avoid bias, trajectory lengths were curated to achieve the same distribution of trajectory lengths across all sets of conditions , as well as the results of 100 ns simulations of this structure .The average root-mean-square fluctuation (RMSF) of backbone alpha-carbons observed in the simulations shows striking differences in flexibility for different regions of the protein. Across all conditions, the catalytic core (domain A) containing the active site and TIM barrel has the lowest RMSF values  of the three domains. Domain B displays more flexibility , and domain C the most flexibility . Domain B contains three long and flexible loops, corresponding to residues 485–503, 519–551, and 555–577, which can be identified from the peaks of the RMSF profile . Domain As the KCl concentration increases, there is a clear increase in flexibility across all domains, with the largest contribution to the average RMSF coming from domain C , inset. The low RMSF values observed in domain A and the relatively unperturbed RMSF values in the eight catalytic core residues suggested that flexibility of the solvent-exposed residues of the protein might be correlated to solvent exposure. To test this idea, we defined the surface of the protein as the set of residues that contain an atom which exceeds a solvent-accessible surface area (SASA) cutoff value. This SASA cutoff value was set as the 80th percentile of the average SASA per atom values for each set of conditions . The moskcat values are all considered together. When comparing across salt concentrations, the protein in 1 M KCl has a lower SASA compared to in 2–4 M KCl across all temperatures  of the enzyme in all of the conditions would be valuable. An MSM is likely to provide insights into conformational changes associated with substrate binding, and allow us to compare predictions of ablished . The larablished ,30,31. TInteractions between protein subunits in solution can also be greatly altered by salts. Electrostatic screening from salt may enhance hydrophobic interactions, causing aggregation between macromolecules . As a re4 buffer at pH 6.5 was used for all kinetic reactions. The assay solution was preincubated at the desired temperature for 2 min before the addition of ONPG. Changes in absorption at 420 nm over 2 min and 30 s were recorded. Three different concentrations of ONPG were used: 1, 2.5, and 5 mM. All experiments were run in triplicate and values were averaged. V0, the Michaelis constant (Km), and Vmax values were determined using Lineweaver–Burk plots with UV Probe ver. 4.23 software (Shimadzu). kcat values were calculated from Vmax and enzyme concentrations. The RSQ function in Microsoft Excel was used to determine R2 values of linear regression. The LINEST function in Excel was used to determine SEs for Km, Vmax, and kcat.Kinetic experiments were performed at temperatures from 10 to 50 °C in 10 °C increments, using a Shimadzu UV-VIS 1601 spectrophotometer with a customized temperature control system designed to prevent condensation at lower temperatures using the same method described in Laye et al. . A solutH‡ and ∆S‡ and their uncertainty, assuming the temperature-dependent kcat measurements can be modeled by the Eyring equation: kcat = κ (kBT/h) exp(–∆H‡/RT + ∆S‡/R), where the transmission coefficient κ is set to 1. In contrast to a simple maximum-likelihood approach (which minimizes a weighted sum of squared errors), our Bayesian approach estimates the ∆H‡ and ∆S‡ as the maximum a posteriori (MAP) of the Bayesian posterior distribution of these parameters given the experimental data D. Our model for the posterior probability isP is the likelihood of observing the data given ∆H‡, ∆S‡, and γ, which is an unknown nuisance parameter describing the quality of the fit. The remaining terms are prior distributions: P(∆H‡) and P(∆S‡) are uniform priors, and P(γ) ~ 1/γ is the non-informative Jeffreys prior. As a model of the likelihood, we use a multi-variate Gaussian,iy and iy* are the predicted and experimental values of kcat at each temperature, and σi are the reported uncertainties in the kcat measurements. A Bayesian inference algorithm was implemented to estimate the values of ∆H‡, ∆S‡, a Markov chain Monte Carlo (MCMC) algorithm was used to sample over a fixed grid of 500 ∆H‡ values ranging over 100 kJ mol−1, 500 ∆S‡ values ranging over 100 J K−1 mol−1, and 1000 values of γ ranging from 0.01 to 100. Values of γ were logarithmically spaced to enforce the Jeffreys prior. Proposed moves were simultaneous nearest-neighbor changes in ∆H‡, ∆S‡, and γ, with acceptance determined by the Metropolis criterion. A total of 107 MCMC steps were performed, with a typical acceptance ratio of 0.80. The best-fit ∆H‡, ∆S‡ were chosen as the values that maximized the marginal distribution P = ∫P dγ. The uncertainties in best-fit ∆H‡ and ∆S‡ were calculated as the standard deviations of marginal distributions P(∆H‡|D) and P(∆S‡|D), respectively. To find the MAP values of ∆H. lacusprofundi β-galactosidase from the closely related thermophilic Thermus thermophilus β-galactosidase structure (PDB ID: 1KWK) as a structural template, following previous similar efforts [The MODELLER (v9.21) software package  in UCSF  efforts . This hoH. lacusprofundi [The recent publication of the X-ray crystallographic structure of β-galactosidase from profundi  confirmse. Molecular simulation topologies were constructed by solvating the homology model with TIP3P waters in a (10.98 nm)3 periodic box, and adding neutralizing K+ and Cl- counterions at concentrations of 1M, 2M, 3M, and 4M. The Amber14sb force field [The protonation states of ionizable residues were determined using PROPKA ,37, resuce field  was usedce field  via Ambece field . The totThe enzyme was simulated as a monomer instead of its published trimeric form in an effort to closely match our kinetic experiments, which were conducted with the monomeric enzyme. Additionally, Karan et al. found no significant difference in backbone RMSD when they simulated their X-ray crystallographic structure in its monomeric and trimeric forms .−1 at 300 K. The LINCS algorithm was used to constrain the hydrogen bond lengths. PME electrostatics were used with Fourier spacing 0.16 for production run. The systems were minimized and equilibrated on Temple University’s Owlsnest High-Performance and Scientific Computing Cluster. Production runs were performed on the massively parallel distributed computing platform Folding@home [Simulations were performed using the GROMACS 5.1.4 software package . Systemsing@home ,43, withc+ 1 ≈ 21 ns (every 210th frame), where τc is the autocorrelation time. Additionally, the first 20 ns of each simulation were removed to ensure the sufficient equilibration. Finally, the averages of RMSF values of the trajectories were found for each condition.Root-mean-square fluctuation (RMSF) values were calculated for each of the 20 conditions using the MDTraj Python library (McGibbon 2015). After superposition with the first frame of the trajectory, its RMSF values were calculated for every alpha-carbon. To remove time-correlation from the trajectories, trajectories were subsampled at an interval of 2τSASA values were calculated using the Shrake and Rupley algorithm from the MDTraj Python library. Default parameters  were used for the calculation, in “atom” mode. Each trajectory was superposed to the first frame, the first 20 ns of each simulation were removed, and then the SASA values of all atoms in the protein were calculated for every 21 ns. The average SASA values were calculated for each condition.


This paper examines the effect of pandemic vaccination on asset prices in a simple asset pricing model à la Lucas 1978. In this model, asset prices depend on susceptible individuals’ saving motives to insure against a reduction in labour income due to getting they get the virus. Hence distributing vaccine reduces precautionary saving motives and asset prices. This implies that reducing the income gap between susceptible and infected individuals, such as by cash handouts, eases the negative effect of vaccine supply on asset prices. This study examines the effect of vaccination during a pandemic on asset prices and its economic implications. We employ a simple susceptible-infected-recovered-deceased (SIRD) model  with an The main results are two folds. First, an increase in vaccine supply decreases asset prices. Increasing vaccine distribution reduces the susceptible individuals’ saving motive to insure against future reduction in labour endowment. Hence, as more vaccines are distributed, the asset prices fall.Second, cash handouts reduce the negative impact of vaccine supply on asset prices. The level of precautionary saving motives depends on the difference in the labour endowments of susceptible and infected individuals—a higher gap induces more saving motives. Thus, reducing the income gap, such as cash handouts to infected individuals, decreases the negative impact of vaccine supply on asset prices. We also show that equal amount of cash handouts to every individual reduces the negative effect of vaccine supply when the utility functions are concave.Several studies have theoretically investigated asset prices during a pandemic. Studies such as –5 investSaito and Sakamoto  study thSeveral empirical studies have been conducted to investigate the financial markets during the COVID-19 pandemic. These studies include –17. 13]13] conteThis section illustrates our modelling of a pandemic and describes the individual economic behaviours in equilibrium.t. In each period t, population (N) is divided into four groups—susceptible (St) infected (It), recovered individuals (Rt), and deceased individuals (Dt). HenceN to be 1. Susceptible individuals have not had immunity to the virus; infected individuals have been infected and not recovered or dead yet; recovered individuals are either those who had recovered from the disease or have been vaccinated; deceased individuals have died due to the virus.We study asset prices in a modified version of the SIRD epidemic model. Periods are indexed by t, susceptible individuals will be infected at a rate of δ > 0 and be vaccinated at a rate of τt ≥ 0; infected individuals will recover with probability γ > 0 and will die with probability ρ > 0. Here, we assume that the parameters are constant as it does not affect the implication of our main results. In reality, the emergence of a variant of the virus can change the parameters. The laws of motions are as follows:In each period τt = 0 for all t.Note that the laws of motions t, there are kt trees, with each generating dt > 0 dividend. In period t, there are kt trees, with each generating dt > 0 dividend. Individuals in state θt ∈ {S, I, R, D} at t face the following budget constraint:ct denotes consumption, pt is the market price of a tree, and w(θt) is nonstorable exogenous labour endowment. We assume that infected individuals receive a smaller amount of labour endowment than susceptible and recovered individuals; susceptible and recovered individuals receive the same amount of labour endowment, i.e. wt(S) = wt(R) > wt(I) ≥ wt(D) for all t; deceased individuals cannot consume, save or earn, i.e ct(D) = wt(D) = kt+1(D) = 0 for all t.The economy is based on the asset pricing model of Lucas . The onlθt at period t will be in state θt+1 at period t + 1. Then the laws of motions t is as follows:β ∈  is the discount factor; t; u is an instant utility from consumption, which is increasing, concave, twice continuously differentiable, and u(0) = 0. Individuals maximise the intertemporal utility Let t+ω))]],where β Stct(S) + Itct(I) + Rtct(R) = dtkt + wt, where kt = Stkt(S) + Itkt(I) + Rtkt(R) and wt = Stw(S) + Itw(I) + Rtw(R). To obtain the results, we assume that the number of susceptible individuals is large enough at the initial period t, i.e. St ≈ N.Since all endowments are nonstorable, in equilibrium, the aggregate dividend and income are all consumed—it holds that St ≈ N, arranging the Euler Under the assumption of t, m is independent from u(ct(D)) for all t. Asset prices are determined by the expected value of the stream of future endowments. The vaccination measures  affects asset prices by impacting the transition probabilities. Intuitively, asset prices reflect the degree of susceptible individuals’ precautionary saving motives. If individuals get infected, they receive less labour income; thus, they have the incentive to insure against the possibility of getting infected.Note that since Proposition 1. A higher vaccination measure decreases the current asset prices:Proof. Sinceandwe have:ct+1(S) = ct+1(R) implies that Δt+1 = 0. Since ct(D) < ct(I) < ct(R) for all t and u is concave, we have u′(ct(D)) > u′(ct(I)) > u′(ct(R)) for all t. Sinceandare both positive for all t, we obtain Δt+ω < 0 for all ω ≥ 2. Sincewe obtain the result.τt) reduces susceptible individuals’ possibility of getting infected  − w(I)) decreases, the impact of vaccination on asset prices (i.e. decreases. If w(S) = w(I), thenSusceptible individuals’ precautionary saving motives depend on the income gap between susceptible and infected individuals; hence, a smaller income gap reduces their precautionary saving motives. Thus, the demand for the asset and its price decreases.w(S) = w(I), the vaccination measure does not affect asset prices. In such a case, the state of individuals does not affect their consumption levels; thus, the susceptible ones do not have precautionary saving motives. Hence, the vaccination measure does not affect individuals’ consumption and asset prices.In an extreme scenario where the income gap is zero, bt > 0, which is irrelevant to individuals’ states. Now the budget constraint is given by:Corollary 1 implies that a simple cash handout policy can eliminate the negative effect of vaccination on asset prices. Let suppose individuals receive an unstorable cash handout, Corollary 2. Proof. Since individuals cannot store bt, we have ct(θt) = bt + dtkt + w(θt). u″ < 0 impliesu′ > 0, u″ < 0, and w(R) > w(I) implyThe desired result follows.ct(I) = 0), we have Intuitively, lump-sum cash handouts reduce the marginal utility gap between susceptible and recovered individuals, which decreases precautionary saving motives. However, the result depends on the assumption that infected individuals can freely consume their endowments. If we assume that the health impact of virus is more severe and infected individuals cannot participate in economic activities (i.e. This study investigates the impacts of vaccination on asset prices in a simple model à la Lucas . The mai


We report a novel strategy for the front passivation of solar cells via aluminum-doped zinc oxide (AZO) films in the case of CIGS solar cells, leading to the highest efficiency of 15.07% without alkali metal post treatment and anti−reflective layer. The good passivation of CIGS solar cells via AZO films is attributed to the field passivation simulated by the SCAPS−1D software. The AZO films also exhibit high optical transparency both in visible and near infrared wavelength region, high conductivity, and cost−effective fabrication advantage. Importantly, the AZO films are deposited at room temperature via radio−frequency magnetron sputtering, showing that the AZO films are also applicable to other solar cells such as perovskite solar cells. Our work is of significance for advancing the development of CIGS−based photovoltaics devices by the well front passivation of AZO. The wide application of AZO in other solar cells such as perovskite solar cells and related tandem solar cells may also accelerate the development of these solar cells because of potential passivation of AZO, low deposition temperature, and high optical transparency of AZO. Low depJ−V curve. The J−V curve of a solar cells follows the single exponential diode Equation (1),J0 is the diode reverse saturation current, q is the elemental charge, A is the diode ideality factor, kT is the thermal energy, and LJ is the photo-generated current. The sR (series resistance) and G (shunt conductance) can be obtained based on the following equations,The parasitic optical absorption is further determined from the r(J)~(J + Jsc)−1 yields a straight line when RG << 1 and JL is independent of the voltage, see Rs is as low as 0.09 Ω·cm2, which is partly due to the strong carrier conductivity ability of AZO. The obtained AkT/q from the linear fit of the curve of r(J)~(J + Jsc)−1 yields a A value of 1.6, indicating a low interface recombination and thereby a high interface quality. The shunt resistance (Rsh) and G (1/Rsh) is 0.057 ± 0.006 kΩ·cm2 and 17.42 kΩ−1·cm−2 derived from the dJ/dV~V curve, see C−f curve measured on the Keithley 4200−SCS Semiconductor Characterization System with a DC bias of 0.6 V and an AC amplitude of 30 mV. The measured capacitance (Cm) shows little change in the whole frequency region, indicating that Cm is mainly composed of the frequency−independent junction capacitance (Cj) because the Cm is comprised of frequency independent Cj and frequency−dependent trap capacitance (Ct). Thus, the C−f result further confirms the low interface defects and thus the low interface damage during AZO deposition.The plot of C−V measurement. The carrier concentration (cNv−) and depletion width (Wd) are derived from the C−V curves according to the following equations,q, A, C, and V is the electronic charge (1.60 × 10−19 C), device area (0.25 cm2), vacuum dielectric constant, dielectric constant of CIGS, junction capacitance, and applied measured voltage, respectively. The built−in field (Vbi) for the CIGS solar cell is obtained from the slope of the C−2~V curve based on the Equation (6),C is the measured capacitance. From the 1/C2~V curve, the c−vN are obtained, as listed in 15 cm−3 (300 kHz) and 5.45 × 1015 cm−3 (400 kHz), respectively. The largest doping concentration of 9.37 × 1015 cm−3 is obtained at 300 kHz and the smallest value of 2.63 × 1015 cm−3 is obtained at 400 kHz with a +1 V DC voltage pre−treatment. The doping concentration decrease at high frequecy is mainly due to the slow change of the carrier. In addition, the carrier concentration is different at forward bias and reverse bias. The forward DC voltage bias only induces the shallow level concentration while the reverse DC voltage bias induces both shallow and deep levels [Vbi is 0.42−1.04 V (100 kHz~500 kHz). c−vN~Wdep curve  results, see 20 cm−3 (20–1022 cm−3) of AZO  of AZO . In conclusion, AZO films were observed to passivate CIGS solar cells by field passivation, along with the transportation of light and current. The maximum PCE was 15.07% for the CIGS solar cells free of alkali metal post treatment and anti-reflective layer due to the high optical transparency and high conductivity of AZO, and well front passivation by AZO. Our results open a novel strategy for front passivation of CIGS-based solar cells via AZO, which is also potentially applicable to other solar cells such as silicon hetero-junction, perovskite, and related tandem solar cells ,23,29.