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Let G = ( V , E ) be a simple graph. The inverse sum indeg index of G is defined as I S I ( G ) = ∑ u v ∈ E ( G ) d ( u ) d ( v ) d ( u ) + d ( v ) , where d ( u ) is the degree of u . This index has a nice predicting ability for the total surface area of octane isomers. A cactus is a connected graph in which all of its blocks are either edges or cycles. Let C n , k be the set of cacti of order n and with k cycles. In this note, we characterize all cacti with minimum inverse sum indeg index among C n , k when n ≥ 6 k − 3 .

Zika virus (ZIKV) infection during pregnancy can cause microcephaly in newborns, yet the underlying mechanisms remain largely unexplored. Here, we reveal extensive and large-scale metabolic reprogramming events in ZIKV-infected mouse brains by performing a multi-omics study comprising transcriptomics, proteomics, phosphoproteomics and metabolomics approaches. Our proteomics and metabolomics analyses uncover dramatic alteration of nicotinamide adenine dinucleotide (NAD+)-related metabolic pathways, including oxidative phosphorylation, TCA cycle and tryptophan metabolism. Phosphoproteomics analysis indicates that MAPK and cyclic GMP-protein kinase G signaling may be associated with ZIKV-induced microcephaly. Notably, we demonstrate the utility of our rich multi-omics datasets with follow-up in vivo experiments, which confirm that boosting NAD+ by NAD+ or nicotinamide riboside supplementation alleviates cell death and increases cortex thickness in ZIKV-infected mouse brains. Nicotinamide riboside supplementation increases the brain and body weight as well as improves the survival in ZIKV-infected mice. Our study provides a comprehensive resource of biological data to support future investigations of ZIKV-induced microcephaly and demonstrates that metabolic alterations can be potentially exploited for developing therapeutic strategies.

The association of Zika virus (ZIKV) infection with microcephaly has raised alarm worldwide. Their causal link has been confirmed in different animal models infected by ZIKV. However, the molecular mechanisms underlying ZIKV pathogenesis are far from clear. Hence, we performed global gene expression analysis of ZIKV-infected mouse brains to unveil the biological and molecular networks underpinning microcephaly. We found significant dysregulation of the sub-networks associated with brain development, immune response, cell death, microglial cell activation, and autophagy amongst others. We provided detailed analysis of the related complicated gene networks and the links between them. Additionally, we analyzed the signaling pathways that were likely to be involved. This report provides systemic insights into not only the pathogenesis, but also a path to the development of prophylactic and therapeutic strategies against ZIKV infection.

The global COVID-19 epidemic has spread rapidly around the world and caused the death of more than 5 million people. It is urgent to develop effective strategies to treat COVID-19 patients. Here, we revealed that SARS-CoV-2 infection resulted in the dysregulation of genes associated with NAD+ metabolism, immune response, and cell death in mice, similar to that in COVID-19 patients. We therefore investigated the effect of treatment with NAD+ and its intermediate (NMN) and found that the pneumonia phenotypes, including excessive inflammatory cell infiltration, hemolysis, and embolization in SARS-CoV-2-infected lungs were significantly rescued. Cell death was suppressed substantially by NAD+ and NMN supplementation. More strikingly, NMN supplementation can protect 30% of aged mice infected with the lethal mouse-adapted SARS-CoV-2 from death. Mechanically, we found that NAD+ or NMN supplementation partially rescued the disturbed gene expression and metabolism caused by SARS-CoV-2 infection. Thus, our in vivo mouse study supports trials for treating COVID-19 patients by targeting the NAD+ pathway.

The global COVID-19 epidemic has spread rapidly around the world and caused the death of more than 5 million people. It is urgent to develop effective strategies to treat COVID-19 patients. Here, we revealed that SARS-CoV-2 infection resulted in the dysregulation of genes associated with NAD

Let G = ( V , E ) be a graph. A vertex u in G totally dominates a vertex v if u is adjacent to v in G . The total domination game played on G consists of two players, named Dominator and Staller, who alternately take turns choosing vertices of G such that each chosen vertex totally dominates at least one vertex not totally dominated by the vertices previously chosen. Dominator wishes to totally dominate the graph as fast as possible, while Staller wishes to delay the process as much as possible. The game total domination number γ t g ( G ) (resp. the Staller-start game total domination number γ t g ′ ( G ) ) of G is the number of vertices chosen when Dominator starts the game (resp. when Staller starts the game) and both players play optimally. In this paper, we determine the exact value of γ t g ( G ) and γ t g ′ ( G ) when G is a cyclic bipartite graph.

The global COVID-19 epidemic has spread rapidly around the world and has already caused the death of more than one million people. As there is yet no vaccine, it is urgent to develop effective strategies to treat COVID-19 patients. Here, we used a mouse-adapted SARS-CoV-2 infection model to explore potential therapeutic targets for SARS-CoV-2 pneumonia. Global gene expression analysis of infected mouse lungs revealed dysregulation of genes associated with NAD+ metabolism, immune response and cell death, similar to that in COVID-19 patients. We therefore investigated the effect of treatment with NAD+ and found that the pneumonia phenotypes, including excessive inflammatory cell infiltration and embolization in SARS-CoV-2 infected lungs were significantly rescued by boosting NAD+ levels. Most notable, cell death was suppressed substantially (>65%) by NAD+ supplementation. Thus, our in vivo mouse study supports trials for treating COVID-19 patients with NAD+ or its precursors.

Zika virus (ZIKV) infection during pregnancy can cause microcephaly in newborns, yet the underlying mechanisms remain largely unexplored. Here, we reveal extensive and large-scale metabolic reprogramming events in ZIKV-infected mouse brains by performing a multi-omics study comprising transcriptomics, proteomics, phosphoproteomics and metabolomics approaches. Our proteomics and metabolomics analyses uncover dramatic alteration of nicotinamide adenine dinucleotide (NAD

Zika virus (ZIKV) has evolved into a global health threat because of its causal link to congenital Zika syndrome. ZIKV infection of pregnant women may cause a spectrum of abnormalities in children. In the studies in Brazil, a large cohort of children with perinatal exposure to ZIKV is followed, and a spectrum of neurodevelopmental abnormalities is identified. In parallel, it is demonstrated that infection of the mouse neonatal brain by a contemporary ZIKV strain instead of an Asian ancestral strain can cause microcephaly and various abnormal neurological functions. These include defects in social interaction and depression, impaired learning and memory, in addition to severe motor defects, which are present in adult mice as well as in the prospective cohort of children. Importantly, although mouse brains infected later after birth do not have apparent abnormal brain structure, those mice still show significant impairments of visual cortical functions, circuit organization, and experience‐dependent plasticity. Thus, the study suggests that special attention should be paid to all children born to ZIKV infected mothers for screening of abnormal behaviors and sensory function during childhood., A spectrum of neurodevelopmental abnormalities is identified in children and neonatal mice with perinatal exposure to Zika virus (ZIKV), regardless of apparent abnormal brain structure. Thus, special attention should be paid to all children born to ZIKV infected mothers for screening of abnormal behaviors and sensory function during childhood.

Let G = ( V , E ) be an n -vertex graph, where V = { v 0 , v 1 , … , v n − 1 } . The augmented Zagreb index ( A Z I ) of G is defined as A Z I ( G ) = ∑ v i v j ∈ E [ d i d j / ( d i + d j − 2 ) ] 3 , where d i is the degree of v i . Let T n d be the set of all trees on n vertices with given diameter d . In this paper, we determine the tree with maximum A Z I among T n d when n ≥ 3 2 ( d − 1 ) + 381 . Our result partially resolve a problem given in [12].

Zika virus (ZIKV) has evolved into a global health threat because of its causal link to congenital Zika syndrome. Different case reports indicate that ZIKV infection of pregnant women may cause a spectrum of abnormalities in children. Here we evaluated a large cohort of children with perinatal exposure to ZIKV and identified a spectrum of neurodevelopmental abnormalities in the group. In addition, we show that infection of the mouse neonatal brain by a contemporary ZIKV strain instead of an Asian ancestral strain can cause microcephaly and various abnormal neurological functions. These include defects in social interaction and depression, impaired learning and memory, in addition to severe motor defects, which are present in adult mice as well as in our cohort of children. Importantly, although mouse brains infected later after birth do not have apparent abnormal brain structure, those mice still show significant impairments of visual cortical functions, circuit organization and experience-dependent plasticity. Thus, our study suggests that special attention should be paid to all children born to ZIKV infected mothers for screening of abnormal behaviors and sensory function during childhood. Funding Statement: This work was supported by the Strategic Priority Research Program and Innovation Program of the Chinese Academy of Sciences (No. XDB32020100, QYZDJ-SSW-SMC007), the National Natural Science Foundation of China (NSFC) (31730108, 31430037, U170220023, 81772176, 31670883, 91542201, 81590765, and 31500145), Beijing Municipal Science & Technology Commission (Z181100001518001), the Interdisciplinary Research Funds of Beijing Normal University, the CAMS Initiative Innovative Medicine (No. 2016-I2M-1-005), Major Project for "Significant New Drugs Innovation and Development" (2015ZX09102023), NIH R01 AI140718, AI069120, AI056154 and AI078389 502 grants, MOST (China, 2016YFD0500304). C.L. was supported by the PUMC Youth Fund (No. 3332016125). Declaration of Interests: The authors confirm that there are no known conflicts of interest associated with this publication. Ethics Approval Statement: The experimental procedures on mice were performed under biosafety level 2 (BSL-2) at Beijing Institute of Microbiology and Epidemiology with Institutional Biosafety Committee approval. The mouse care and experimentation were approved by the Animal Care and Use Committees of the Institutional Animal Care and Use Committee at Institute of Genetics and Developmental Biology (IGDB), Chinese Academy of Sciences, Beijing Institute of Microbiology and Epidemiology and the State Key Laboratory of Cognitive Neuroscience & Learning at Beijing Normal University. For the infant cohort, the study protocol was approved by the institutional review boards at Fundacao Oswaldo Cruz (Fiocruz) and the University of California, Los Angeles. All mothers provided written informed consent for themselves and for their children.

Normal neural development is essential for the formation of neuronal networks and brain function. Cutaneous T cell lymphoma-associated antigen 5 (cTAGE5)/meningioma expressed antigen 6 (MEA6) plays a critical role in the secretion of proteins. However, its roles in the transport of nonsecretory cellular components and in brain development remain unknown. Here, we show that cTAGE5/MEA6 is important for brain development and function. Conditional knockout of cTAGE5/MEA6 in the brain leads to severe defects in neural development, including deficits in dendrite outgrowth and branching, spine formation and maintenance, astrocyte activation, and abnormal behaviors. We reveal that loss of cTAGE5/MEA6 affects the interaction between the coat protein complex II (COPII) components, SAR1 and SEC23, leading to persistent activation of SAR1 and defects in COPII vesicle formation and transport from the endoplasmic reticulum to the Golgi, as well as disturbed trafficking of membrane components in neurons. These defects affect not only the transport of materials required for the development of dendrites and spines but also the signaling pathways required for neuronal development. Because mutations in cTAGE5/MEA6 have been found in patients with Fahr’s disease, our study potentially also provides insight into the pathogenesis of this disorder.

Xyloglucan endotransglycosylase (XET) catalyses the transglycosylation of xyloglucan, the major hemicellulose polymer, which has been thought to mediate the cross-linking of cellulose microfibrils in cellular walls and proposed to be involved in the control of cell wall relaxation. To understand the relationship between litchi fruit cracking and gene expression patterns, three XET genes from litchi fruit were identified and then examined for their expression profiles in pericarp and aril tissues at different development stages, using a cracking-resistant cultivar, 'Huaizhi', and a cracking-susceptible cultivar, 'Nuomici'. Three full-length cDNAs of 1267, 1095 and 1156 bp encoding XETs, named LcXET1, LcXET2 and LcXET3, respectively, were isolated from expanding fruit using RT-PCR and RACE-PCR (rapid amplification of cDNA ends) methods. Northern blotting analysis showed that LcXET1 mRNA accumulation occurred much earlier in aril tissues at 59 days after anthesis (DAA) than in pericarp tissues at 73 DAA in 'Nuomici'. However, it appeared at almost the same time (66 DAA) in pericarp and aril tissues in 'Huaizhi', which suggested that differential accumulation of LcXET1 in pericarp and aril tissues in 'Nuomici' and 'Huaizhi' was closely associated with fruit cracking. LcXET2 mRNA accumulation could be detected in pericarp and aril tissues throughout fruit development but exhibited a differential accumulation pattern between pericarp and aril tissues. In the aril of 'Nuomici', intensive signal bands were detectable at 59-73 DAA in rapidly expanding fruits of 'Nuomici' but only weak bands could be found in the pericarp tissues. In contrast, moderate signal bands were detectable both in pericarp and aril tissues of 'Huaizhi' fruits. Furthermore, LcXET3 showed constitutive expression in both pericarp and aril tissues of developing 'Nuomici' and 'Huaizhi' litchi fruit. In addition, differential expression patterns of three XETs genes were observed in different tissues of litchi, with only LcXET1 being fruit-specific. To further address the role of LcXET in fruit cracking, alpha-naphthalene acetic acid (NAA) was used to treat 'Nuomoci' to reduce fruit cracking. Enhanced LcXET1 mRNA accumulation appeared in pericarp while LcXET2 and LcXET3 mRNA accumulation enhanced in aril tissues in the NAA-treated fruits. Thus, LcXET1 is more likely to play a role in reducing litchi fruit cracking than LcXET2 and LcXET3.

Litchi fruit were treated with 10 mL/L ethylene (C2H4), 0.1% cobalt chloride (CoCl2) and 1 mL/L 1-methylcyclopropene, respectively, packed individually in closed but vented containers, and then stored at ambient temperature (28–33°C). The effects of these treatments on the browning, energy metabolism and disease incidence of the fruit were investigated. Treatment with C2H4 enhanced the activities of polyphenol oxidase and phenylalanine ammonia-lyase. Ethylene also increased the accumulation of ADP and AMP, but decreased energy charge in fruit peel. Cobalt chloride treatment had an inhibitory effect on increases of peroxidase activity, ATP : ADP ratio, energy charge and ATP, ADP and AMP. Browning index was reduced by 8.4 and 10.4% and disease index was reduced by 10.7 and 12.7% in CoCl2 and 1-methylcyclopropene-treated fruit, respectively, suggesting a relationship between energy metabolism, browning and disease index.