\r\n\tThis book aims to explore the issues around the rheology of polymers, with an emphasis on biopolymers as well as the modification of polymers using reactive extrusion.
",isbn:null,printIsbn:"979-953-307-X-X",pdfIsbn:null,doi:null,price:0,priceEur:0,priceUsd:0,slug:null,numberOfPages:0,isOpenForSubmission:!1,hash:"5bc21841d2b87388ad498bc09910944b",bookSignature:"Dr. Casparus Johannes Verbeek and Dr. Velram Mohan",publishedDate:null,coverURL:"https://cdn.intechopen.com/books/images_new/8880.jpg",keywords:"Extrusion, Injection Moulding, Thermoplastics, Natural Polymers, Biomass, Polymer Modification, Polymer Blends, Compatibilization, Processing Challenges, Reactive Compounding, Screw Design, Process Design",numberOfDownloads:null,numberOfWosCitations:0,numberOfCrossrefCitations:0,numberOfDimensionsCitations:0,numberOfTotalCitations:0,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"September 6th 2019",dateEndSecondStepPublish:"September 27th 2019",dateEndThirdStepPublish:"November 26th 2019",dateEndFourthStepPublish:"February 14th 2020",dateEndFifthStepPublish:"April 14th 2020",remainingDaysToSecondStep:"a year",secondStepPassed:!0,currentStepOfPublishingProcess:5,editedByType:null,kuFlag:!1,biosketch:null,coeditorOneBiosketch:null,coeditorTwoBiosketch:null,coeditorThreeBiosketch:null,coeditorFourBiosketch:null,coeditorFiveBiosketch:null,editors:[{id:"102391",title:"Dr.",name:"Casparus",middleName:"Johannes",surname:"Verbeek",slug:"casparus-verbeek",fullName:"Casparus Verbeek",profilePictureURL:"https://mts.intechopen.com/storage/users/102391/images/system/102391.jpeg",biography:"Dr Verbeek is a Chemical Engineer, currently an associate professor at the School of Engineering at the University of Waikato and is also the R&D manager for Aduro Biopolymers. He has 20 years experience in waste and by-product valorisation with an emphasis on renewable materials and biological products. Since his tertiary studies, Johan’s knowledge in the engineering field of sustainable products has led to a number of innovative developments in the engineering industry. 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\n
1. Introduction
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When injured, skeletal muscle regenerates by activation and proliferation of its own stem cells: muscle satellite cells. Therefore, muscle satellite cells were expected to be a cell source for cell therapy for devastating muscular dystrophies. However, clinical trials in the 1990s were unsuccessful [1], possibly because myoblasts that had been expanded in vitro lost the high ability to fuse with the host’s injured myofibers, indicating that improvement of muscle function requires a large quantity of myogenic progenitors with regenerative potential. Human embryonic stem cells (hESCs) and human-induced pluripotent stem cells (hiPSCs) [2] have almost unlimited proliferative potential and the ability to differentiate into the skeletal muscle lineage (reviewed in [3, 4]). Therefore, they are a promising source of new cells for cell therapy of muscle diseases such as muscular dystrophy (DMD). They are also useful for biological and physiological studies of human skeletal muscle.
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Disease-specific hiPS cells are generated from patients’ somatic cells (usually blood cells or skin fibroblasts) with almost the same efficiency and quality as cells from healthy donors [5]. Therefore, disease-specific-induced pluripotent stem (iPS) cells are being widely used to study the molecular mechanisms of these diseases and to screen potential drugs. As a method to directly derive skeletal muscle cells from hPSCs, MyoD-mediated reprogramming was established and is widely used. MyoD induces muscle cells in a relatively short period with high efficiency. In this chapter, we review the literature on derivation of skeletal muscle from human PSCs and discuss the next steps toward clinical applications. In the last part, we review the recent reports on successful disease modeling in vitro using patient iPS cells and discuss future directions.
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1.1. Muscle stem cells
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Muscle satellite cells were first identified by electron microscopy as a mononuclear cell between myofibers and the basal lamina and named by Mauro in 1961 [6]. Later, muscle satellite cells were shown to be skeletal muscle-specific stem cells in postnatal muscle [7]. Muscle satellite cells are activated upon muscle injury, proliferate as myoblasts, and fuse with each other or with regenerating myofibers to repair damaged muscle [8]. In 1989, Partridge et al. reported successful recovery of dystrophin expression in dystrophin-deficient mdx mice after direct injection of wild-type myoblasts [9]. Based on this finding, myoblast transfer therapy was performed on DMD patients in several hospitals. Unfortunately, the clinical trials failed to recover the muscle function of these patients. The majority of injected cells seemed to be lost within 48 h [1]. The results were unexpected at that time because endogenous muscle satellite cells themselves have high regenerative activity in situ and repair damaged muscle quickly. Later, researchers started to search for multipotent stem cells, which can be delivered systemically, engraft in muscle, and differentiate into myofibers. One of these cells is the mesoangioblalst, which showed an amazing ability to recover dystrophin expression in the muscles of dystrophic dogs after intra-arterial injection [10]. Mesenshymal stem/progenitor cells (MSC/MPC) are also expected to be a tool for regenerative medicine. They themselves do not differentiate into myofibers, but support muscle regeneration by paracrine effects [11]. The history of direct reprogramming in the muscle field is long, starting with the discovery of MyoD by Weintraub and his colleagues [12, 13]. MyoD powerfully converts non-muscle cells to skeletal muscle cells, but it is difficult to induce Pax7+ myogenic progenitors using MyoD alone. Recently Ito et al. reported that a combination of transcription factors (Pax3, Mef2b, and Pitx1 or Pax7, Mef2b, and Pitx1 for embryonic fibroblasts, and Pax7, Mef2b plus MyoD for adult fibroblasts) successfully induced transplantable myogenic progenitors from mouse fibroblasts [14]. Whether the same set of reprogramming factors can induce myogenic progenitors from human fibroblasts remains to be seen. Human iPS cells are relative newcomers in the muscle stem cell field. hiPSCs are pluripotent stem cells with almost equivalent properties to human ES cells, but can be derived from somatic cells such as skin fibroblasts [2]. Successful derivation of muscle cells from hiPS cells opened a new era of regenerative medicine for muscular dystrophies (Figure 1).
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Figure 1.
History of research on muscle stem cells and cell therapy for muscular dystrophies [2, 6, 10, 15, 16, 17, 18].
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Muscle satellite cells were identified and named by Mauro in 1961 [6]. Direct reprogramming was reported for the first time in the skeletal muscle field in 1987 [15], but MyoD alone cannot induce myogenic progenitors. After a surprising report of BM-derived myogenic cells by Ferrari in 1998 [16], researchers looked for multipotent stem cells that can be delivered via the circulation. MSCs are modulators of muscle regeneration and widely used in regenerative medicine. Human iPS cells are a relative newcomer in the muscle stem cell field.
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2. Myogenic induction by overexpression of myogenic transcription factors
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MyoD: Weintraub and colleagues showed that overexpression of MyoD, a muscle-specific basic helix-loop-helix transcription factor, converted non-myogenic cells to muscle cells [13]. In 2014, Abujarour et al. reported efficient conversion of hiPSCs into muscle cells using a lentiviral vector-mediated doxycycline (DOX)-inducible MyoD overexpression system [19]. Sakurai and his colleagues used a PiggyBac transposon system to overexpress DOX-inducible MyoD in hiPSCs [20]. Importantly, the induced myotubes contracted on electrical stimulation [20]. MyoD induces skeletal muscle cells in a short period with high efficiency, but it cannot induce PAX7(+) myogenic progenitors. MyoD-induced skeletal muscle is now widely used for in vitro modeling of inherited muscle diseases.
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Darabi et al. [21] reported derivation of engraftable muscle progenitors from hiPSCs by using a lentiviral vector encoding DOX-inducible PAX7. PAX7 expression was induced transiently in differentiating cells in a monolayer culture after a 7-day embryoid body (EB) culture [21]. Pax7-expressing GFP-positive cells purified by fluorescence-activated cell sorting (FACS) were then transplanted into the skeletal muscle of immune-deficient dystrophin-deficient mice, NSG-mdx4Cv, and improved the muscle function of the mice. Whether myogenic cells induced by overexpression of Pax7 are suitable for cell transplantation therapy remains to be determined because transgenes have a risk of tumor formation. As far as the integration sites of the expression units in the genome and the expression of PAX7 are strictly regulated, myogenic progenitors expanded by PAX7 successfully regenerated damaged muscle of patients [22].
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3. Stepwise induction of skeletal muscle by mimicking development
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The majority of stepwise muscle induction protocols recently reported for human ESCs/iPSCs utilize a GSK3b inhibitor in common, myogenic growth factors (HGF, IGF-1, bFGF, EGF, etc.), and a serum-free medium (Table 1; [3]). For example, Chal et al. treated hiPS cells with CHIR-99021, which activates Wnt signaling, and LDN-193189, which prevents hiPSCs from differentiation into lateral mesoderm and induces differentiation into paraxial mesoderm. Treatment with these molecules of hESC cultures induced myogenin(+) myogenic cells with 25–30% efficiencies [34, 36, 39].
EB culture and sphere culture are often used to induce muscle progenitor cells (Table 1). Hosoyama et al. reported that hESCs/hiPSCs cultured as floating cell aggregates (termed EZ spheres) in a medium developed for neural stem cells supplemented with bFGF and EGF efficiently differentiated into myogenic cells. After a 6-week floating culture, 40–50% of cells expressed PAX7, MyoD or myogenin [32]. Because dissociation of sphere cells into single cells during the induction process drastically reduces myogenic activity, direct cell-cell interaction might be essential for commitment of hPSCs to the skeletal muscle lineage.
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4. Mimicking the muscle microenvironment
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4.1. Importance of the extra-cellular matrix for myogenesis
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The extra-cellular matrix (ECM) is an interactive environment having, apart from its simple role as a mechanical support or physical barrier, a role in signaling and providing a niche for the stem cell [40].
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Collagens, laminins, fibronectin, or Matrigel have been used for in vitro studies in order to mimic the ECM of muscle cells in 2D or 3D culture systems because ECM is indispensable for skeletal muscle development [41]. Interestingly, native ECM obtained by decellularization of skeletal muscle stimulated muscle differentiation and a more rapid cell organization compared to single matrix glycoprotein culture [42], indicating again that ECM has functions in myogenesis. The use of a 3D fibrin-based hydrogel culture after production of myogenic cells with transient overexpression of Pax7 was recently reported to generate functional biomimetic skeletal muscle tissues from hiPSC-derived paraxial mesoderm cells for the first time [43].
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The stiffness of the microenvironment has also been reported to regulate differentiation of myogenic cells [44, 45]. More precisely, in an in vitro context, 12 kPa stiffness was shown to give optimal results for muscle stem cells, compared to the harsh 106 kPa stiffness of a regular polystyrene plastic culture dish [45]. The impact of stiffness can be partially explained by the activation of pathways such as N-RAP, FAK, or PKC [44].
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Some studies showed improvement of myoblast migration and differentiation through MMP-1 treatment [46], migration with MMP-13 [47], and fusion through MMP-7 overexpression [48], suggesting the importance of remodeling of the ECM for migration and differentiation of myogenic cells even in vitro.
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4.2. Co-culture, exosomes, and miRNA
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The interaction between myogenic cells and non-myogenic cells in muscle tissue may influence myogenesis either by interacting directly or by secretion of paracrine factors (Figure 2). Motor neurons were used to form neuro-muscular junctions [49] and further adapted to a 3D culture system [50]. The presence of motor neurons had positive effects on myotube maturation [50]. Co-culture with mesenchymal stem cells (MSCs) significantly enhanced the proliferation of muscle cells [51]. Co-culture of fibroblasts with myoblasts improved the alignment of the formed myotubes, but reduced differentiation [52]. Another paper, however, reported that the myoblasts formed longer, thicker myotubes with a mature phenotype in the presence of fibroblast-conditioning media, compared with control media [53].
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Figure 2.
Summary of environmental inputs that promote differentiation of muscle cells.
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Exosomes are major tools of cross talk between cells throughout the body and miRNAs are one of the elements they transport. Some miRNAs, such as miR-206, have been identified as promoters of skeletal muscle development and differentiation [54]. Therefore, miRNA-mediated induction of skeletal muscle from human iPSCs is a topic of great interest.
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4.3. Differentiation of skeletal muscle cells through stimulation
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Electrical: Another aspect of the muscle cell environment is the stimulation they are subjected to during the final steps of myogenesis. Exercise has been shown to have a great impact on muscle growth and differentiation in mice [55], and when electrically stimulated in vitro, C2C12 cells, a mouse myogenic cell line, showed similar responses to those of exercised skeletal muscle in vivo [56]. In the last couple of years, studies showed improvement of cardiac muscle differentiation of hiPSC by using electrical stimulation [57, 58].
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Mechanical: Mechanical or stretch-relaxation stimulation has been shown to promote muscle growth and alignment in an electrical stimulus-independent manner [59]. Stretch-relaxation cycles have been shown to promote differentiation, muscle growth, fibers alignment, and overall organization [59, 60, 61]. Whether mechanical stimulation improves muscle induction from human iPS cells and their maturation remains to be determined even though results using cardiomyocytes are encouraging [58].
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By mimicking the muscle microenvironment, it might be possible to increase the overall quantity, quality, and functionality of skeletal muscle cells produced from hiPSC.
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5. Purification of myogenic cells
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Most published protocols for muscle induction from human iPS cells generate a heterogenous cell population, including myogenic cells, undifferentiated cells, and non-myogenic cells. Non-myogenic cells are in many cases of neuronal lineage. Undifferentiated cells proliferate actively and form tumors in the host muscle. Therefore, purification of myogenic progenitors is an important step for clinical use. Purification of myogenic cells would also facilitate the study of molecular pathogenesis and drug screening. To enrich myogenic cells by FACS, several iPS cell lines where the expression cassette of fluorescent proteins are inserted in the locus of myogenic regulators such as PAX7 [62] or Myf5 [63]. Combinations of myogenic cell-specific surface markers to enrich myogenic cells are also reported, for example, CD56 and CD82 [64], or CXCR4 (CD184) and C-MET [31]. We identified CD271 (NGFR) as a myogenic marker (submitted). M-cadherin antibody is also useful when the cells are dissociated into single cells by non-enzymatic treatment. Recently, Hicks et al. [38] identified ERBB3 (HER3) as a cell surface marker that enriches transplantable hiPSC-derived myogenic cells. To exclude neurogenic cells, CD57(HNK-1) is useful [31].
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6. Myogenic progenitors for cell therapy
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Cell source: Although cell therapy is a promising therapeutic approach to DMD and other muscular dystrophies, myoblast transfer therapy (MTT) in the early 90s failed to improve muscle function of DMD patients, possibly due to expansion of satellite cells in vitro. It was proposed that expansion of myoblasts in culture dishes reduced the regenerative activity of the injected cells. Incomplete immune suppression was also suggested as a cause of unsuccessful transplantation [1]. Because human iPSCs are highly proliferative, it might be possible to derive engraftable myogenic progenitors from hiPSCs on a large scale. iPSC-based cell therapy also allows the use of the patient’s own cells (autologous cell transplantation) to avoid an immune response against engrafted cells. However, it takes a long time and is expensive to custom-make iPSCs from each patient and correct the disease-causing gene mutation. To solve this problem, HLA-homozygous donor-iPSC stocks are now being prepared (e.g., https://www.cira.kyoto-u.ac.jp/e/research/stock.html). It is expected that HLA-matched cells will greatly lower the risk of rejection. In addition, the safety of the cells in an iPS cell bank can be carefully examined in advance.
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Tumorigenicity: A major concern of the use of hiPSCs for cell therapy is the tumorigenicity of hiPSC-derived cells. Tumor-forming cells could be roughly divided into two categories: residual undifferentiated cells and transformed cells. For undifferentiated iPS cells, purification of the differentiated cells with lineage-specific markers and elimination of undifferentiated cells using iPS markers would be effective. To avoid transformed cells, integration of the transgenes used for reprogramming into the genome should be carefully ruled out. Checking the integrity of the whole genome of parental iPS cells using genome-wide sequencing might be necessary. Prolonged culture of iPS cells should be avoided because long-term culture causes genomic abnormalities. Some groups propose, as a final line of defense, the use of a specific hiPSC line containing a HSV-tk gene [65] or an inducible Caspase-9 gene as a suicide gene, which would allow eradication of hiPSC-derived tumors in vivo after transplantation [66, 67, 68, 69].
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Quality control: For clinical use, (1) stable induction of myogenic progenitors in large quantity, (2) reduction of culture period and cost, and (3) establishment of a reliable system to monitor the quality and safety of the cells are all required. The monitoring system is especially important, because the cells change their properties during culture and it is difficult to keep the myogenic potential of the FACS-sorted cells high during culture.
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7. Disease modeling in vitro using patient-derived iPSCs
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During the past decades, researchers have generated numerous mouse models, such as knock-out mice to analyze the pathogenesis of muscle diseases. However, mouse models often fail to reproduce the phenotypes of patients. For example, dystrophic mdx mice, which carry a DMD-type mutation in the dystrophin gene, exhibit much milder dystrophic phenotypes than DMD patients. It also has happened that drugs proven to be effective in a mouse model have much less effect in human patients. This is why human iPS cells are expected to become a tool for disease modeling.
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These days, iPSCs from many kinds of muscular diseases have been established. For example, Abujarour et al. generated iPSC lines from patients with DMD or Becker muscular dystrophies (BMD) [19]. Shoji et al. established DMD-iPSCs and reported abnormal calcium ion influx in DMD myotubes. Importantly, dystrophin expression was restored to DMD myotubes by an exon-skipping technique, and the calcium ion overflow was suppressed [70]. Choi et al. [71] reported that DMD-iPS cells showed aberrant expression of inflammation or immune-response genes and collagen genes, increased BMP/TGFβ signaling, and reduced fusion competence. Tanaka et al. [20] established iPSC lines from patients with Miyoshi myopathy. Patient-iPSC-derived myotubes showed defective membrane repair, and the authors rescued the phenotype by expression of full-length DYSFERLIN. Snider et al. [72] showed the expression of full length DUX4 in embryoid bodies from iPSCs with facioscapulohumeral dystrophy (FSHD). Caron et al. reported that FSHD1 myotubes were thinner, and the genes involved in cell cycle control, oxidative stress response, and cell adhesion were differentially regulated [37]. Du et al. and Ueki et al. [73, 74] reported that the CTG-CAG triplet repeats were expanded by passaging iPSCs derived from myotonic dystrophy type1 (DM1) patients. Yoshida et al. [75] generated iPSCs from a patient with infantile-onset Pompe disease that showed lysosomal glycogen accumulation, which was dose-dependently rescued by rhGAA.
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These successful in vitro disease modelings using patient-iPSCs are encouraging and would be useful for screening new drugs. Because hiPSCs have unlimited proliferative potential, one can perform experiments repeatedly and screen potential drugs extensively even if it is a rare disease. It should be, however, also recognized that skeletal muscle cells derived from hPSCs are much more immature in gene expression, morphology, and function than real myofibers in the body. Therefore, to what extent patient-derived iPSCs can reproduce a disease phenotype in vitro is important. In addition, there are variations in differentiation propensity among hiPS cell lines [76], and it is important to confirm the reproducibility of the results. Patient-iPS cells whose mutated genes were corrected by genome-editing technique [77] would serve as good controls and help to validate the findings.
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8. Conclusion
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Skeletal muscle can be induced from hPSCs by direct reprogramming or a stepwise differentiation method. Disease modeling using patient-derived iPSCs is now widely used to elucidate disease mechanisms and to screen for drugs. For successful disease modeling, it is important to induce mature myofibers. For cell-based therapy, the protocols for induction of myogenic progenitors from hiPS cells and their purification have been almost completely established. However, to eliminate the risk of tumor formation by engrafted cells, more study is needed.
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Acknowledgments
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This study is supported by (1) Research Funds for “Development of cell transplantation methods for refractory muscle diseases” (Projects for Technological Development) and “Research on refractory musculoskeletal diseases using disease-specific induced pluripotent stem (iPS) cells” from the Research Center Network for Realization of Regenerative Medicine, Japan Science and Technology Agency (JST), and Japan Agency for Medical Research and Development (AMED), (2) Grants-in-aid for Scientific Research (C) (16 K08725, 24590497) from the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan and (3) Intramural Research Grants (24-9, 25-5, 27-7, and 28-6) for Neurological and Psychiatric Disorders of NCNP.
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Conflict of interest
The authors declare that they have no conflicts of interest.
Notes/Thanks/Other declarations
We thank Ms. Motoko Shimizu for supporting our research.
\n',keywords:"muscular dystrophy, myoblasts, skeletal muscle, pluripotent stem cells, iPSC, Pax7, MyoD, myogenic differentiation, cell therapy, disease modeling",chapterPDFUrl:"https://cdn.intechopen.com/pdfs/61400.pdf",chapterXML:"https://mts.intechopen.com/source/xml/61400.xml",downloadPdfUrl:"/chapter/pdf-download/61400",previewPdfUrl:"/chapter/pdf-preview/61400",totalDownloads:660,totalViews:341,totalCrossrefCites:0,totalDimensionsCites:0,hasAltmetrics:0,dateSubmitted:"December 4th 2017",dateReviewed:"April 16th 2018",datePrePublished:"November 5th 2018",datePublished:"October 10th 2018",dateFinished:null,readingETA:"0",abstract:"Human pluripotent stem cells (hPSCs) proliferate in vitro for long periods without losing pluripotency and can be induced to differentiate into various cell types including skeletal muscle cells (SMCs). Human embryonic stem cells (hESCs) are generated from a preimplantation-stage embryo. Human-induced pluripotent stem cells (hiPSCs) are derived from somatic cells of both healthy donors and patients with muscle diseases of any age using reprogramming factors. Currently, there are two kinds of protocols to induce skeletal muscle from hPSCs. One type utilizes overexpression of a potent myogenic master regulator, MyoD, to directly induce skeletal muscle. Stepwise induction of skeletal muscle has also been reported by many research groups, but hiPSC-based cell therapy for muscular dystrophy is still experimental. On the other hand, hiPSCs derived from patients with muscle disease are widely used for disease modeling in vitro. Here, we review the recent literature on derivation of skeletal muscle from human pluripotent stem cells and discuss their application.",reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/61400",risUrl:"/chapter/ris/61400",book:{slug:"muscle-cell-and-tissue-current-status-of-research-field"},signatures:"Ken’ichiro Nogami, Matthias Blanc, Fusako Takemura, Shin’ichi\nTakeda and Yuko Miyagoe-Suzuki",authors:[{id:"36800",title:"Dr.",name:"Shin",middleName:null,surname:"Takeda",fullName:"Shin Takeda",slug:"shin-takeda",email:"takeda@ncnp.go.jp",position:null,institution:null},{id:"84160",title:"Dr.",name:"Yuko",middleName:null,surname:"Miyagoe-Suzuki",fullName:"Yuko Miyagoe-Suzuki",slug:"yuko-miyagoe-suzuki",email:"miyagoe@ncnp.go.jp",position:null,institution:{name:"National Institute of Neurosciences & Hospital",institutionURL:null,country:{name:"Bangladesh"}}},{id:"238337",title:"MSc.",name:"Fusako",middleName:null,surname:"Sakai-Takemura",fullName:"Fusako Sakai-Takemura",slug:"fusako-sakai-takemura",email:"takemura@ncnp.go.jp",position:null,institution:null},{id:"238340",title:"BSc.",name:"Kenichiro",middleName:null,surname:"Nogami",fullName:"Kenichiro Nogami",slug:"kenichiro-nogami",email:"kenichironogami@ncnp.go.jp",position:null,institution:null},{id:"253503",title:"MSc.",name:"Matthias",middleName:null,surname:"Blanc",fullName:"Matthias Blanc",slug:"matthias-blanc",email:"matthias@ncnp.go.jp",position:null,institution:null}],sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_1_2",title:"1.1. Muscle stem cells",level:"2"},{id:"sec_3",title:"2. Myogenic induction by overexpression of myogenic transcription factors",level:"1"},{id:"sec_4",title:"3. Stepwise induction of skeletal muscle by mimicking development",level:"1"},{id:"sec_5",title:"4. Mimicking the muscle microenvironment",level:"1"},{id:"sec_5_2",title:"4.1. Importance of the extra-cellular matrix for myogenesis",level:"2"},{id:"sec_6_2",title:"4.2. Co-culture, exosomes, and miRNA",level:"2"},{id:"sec_7_2",title:"4.3. Differentiation of skeletal muscle cells through stimulation",level:"2"},{id:"sec_9",title:"5. Purification of myogenic cells",level:"1"},{id:"sec_10",title:"6. Myogenic progenitors for cell therapy",level:"1"},{id:"sec_11",title:"7. Disease modeling in vitro using patient-derived iPSCs",level:"1"},{id:"sec_12",title:"8. Conclusion",level:"1"},{id:"sec_13",title:"Acknowledgments",level:"1"},{id:"sec_16",title:"Conflict of interest",level:"1"},{id:"sec_16",title:"Notes/Thanks/Other declarations",level:"1"}],chapterReferences:[{id:"B1",body:'Mouly V, Aamiri A, Périé S, Mamchaoui K, Barani A, Bigot A, Bouazza B, François V, Furling D, Jacquemin V, Negroni E, Riederer I, Vignaud A, St Guily JL, Butler-Browne GS. Myoblast transfer therapy: Is there any light at the end of the tunnel? Acta Myologica. 2005;24:128-133\n'},{id:"B2",body:'Takahashi K, Tanabe K, Ohnuki M, Narita M, Ichisaka T, et al. Induction of pluripotent stem cells from adult human fibroblasts by defined factors. Cell. 2007;131:861-872\n'},{id:"B3",body:'Kodaka Y, Rabu G, Asakura A. Skeletal muscle cell induction from pluripotent stem cells. Stem Cells International. 2017;2017:1376151. DOI: 10.1155/2017/1376151\n'},{id:"B4",body:'Miyagoe-Suzuki Y, Takeda S. 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Department of Molecular Therapy, National Institute of Neuroscience, National Center of Neurology and Psychiatry, Tokyo, Japan
Department of Molecular Therapy, National Institute of Neuroscience, National Center of Neurology and Psychiatry, Tokyo, Japan
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\n
1. Introduction
\n
Carbon nanoribbons (CNRs) are strips of graphene whose edges symmetry, width and cut orientation give them specific electronic properties. These carbon nanostructures have attracted the attention in both experimental and theoretical fields because of their peculiar properties, which have been studied widely in the last decade as a function of topology, width, as well as doping. [1, 2, 3, 4, 5] Depending the chain-type along the periodic direction, carbon nanoribbons are commonly classified either armchair carbon nanoribbons (ACNR) when these grow through dimer chains, or zigzag carbon nanoribbons (ZCNR) if those have zigzag type chains along the periodic direction. Figure 1 shows a pristine ACNR and ZCNR respectively, their distances between their C – C edged lengths are 13.44 and 24.19 Å respectively, although there could be named referring their length and width (MxN), in such case, both CNRs shown in Figure 1 are 12x2 size.
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Figure 1.
Optimized structure of bare (a) ACNR and (b) ZCNR of size 12x2.
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Through different experimental techniques, it is possible to obtain carbon nanoribbons. [6, 7, 8] However, these techniques have not succeeded in controlling the edges shape of carbon nanoribbons. For example, Cai et al. [9] have proposed a chemical technique which is able to synthesize narrow nanoribbons having symmetric edges, so that, it is possible to obtain experimentally carbon nanoribbons with perfect edges and specific topology. To date, succeeding methods to obtain CNRs come from two different strategies, namely, top-down, which refers to break down large performed carbon-base structures, i. e., CNTs and multiwall CNTs (MWCNTs) and bottom-up, i. e., using several chemical reactions to tailor building-blocks into a complex structure. Table 1 shows a comparative chart representing synthetic strategies to obtain CNRs, employed characterization techniques, advantages and disadvantages.
Surface assisted polymerization followed by dehydrogenation in an ultra-high vacuum environment
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Defined edge type and narrow widths, potential techniques for scale-up
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Depends on the precursor’s nature, which defines the ribbon’s dimension
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\n\n
Table 1.
Comparative chart of synthetic methods to obtain nanoribbons and their advantages or disadvantages.
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Because of their finite dimension, at nanoscale, CNRs have peculiar properties associated to their electronic states close the edges, playing an important role on the reactivity. [17, 18, 19, 20, 21, 22] Several theoretical models, e. g., tight binding, all electron techniques, density functional theory (DFT), etc., have been applied to explore the electronic properties, magnetic states or band structure of carbon nanoribbons. [1, 5, 23] Some of them, have focused on the zigzag topology because they intrinsically have dangling bonds at the edges. This behavior provides active sites for chemical reactions. Moreover, ZCNRs have peculiar properties, e.g., theoretical calculations have shown that ZCNRs have localized electrons largely on the edge C atoms close to the Fermi level. [4, 22] This large contribution of electronic states forms two-fold degenerate flat band at Fermi level, such that, the ground state has spin coupling of each edge ferromagnetic whereas between edges antiferromagnetic. Despite zigzag edges of synthesized carbon nanoribbons have been observed, [8] there is not direct experimental evidence about the magnetic states of ZCNRs. It was theoretically suggested that magnetism of ZCNR could be destroyed substituting defects or vacancies directly on carbon edges. [24]
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On the other hand, all hydrogen-passivated ACNRs are semiconducting [22]. However, ACNRs are expected to reach the graphene limit of zero band gap for sufficiently large widths. [25]
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Concerning these fascinating properties, CNRs may fit for promising technological applications, mainly if the presence of donor or acceptor impurities bring specific reactive properties. [26, 27] So that, this chapter is proposed as a guidance to help the readers to apply conceptual density functional theory to calculate helpful intrinsic properties, e. g., energetic, electronic and reactivity of one-dimension nanomaterial’s, such as, carbon nanoribbons in order to predict or tune their properties; particularly when they are substitutional doped.
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2. Structural and energetic properties
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To give insights about the structural stability of nanostructures, firstly, it is suggested to evaluate if the proposal unit cell may array forming a stable crystalline state. Usually, a structural analysis is carried out computing the cohesive energy per atoms o per unit cell. The cohesive energy (EC) is the energy required to disassemble a molecular system into its constituent parts. From a physical point of view, a bound (stable) system has a positive value of EC, which represents the energy gained during the formation of the bound state. To calculate the EC of ACNRs, it is necessary to obtain the optimized energy of the unit cell being aware of the well converged energy with respect to the k-points and the cutoff energy for the planewave basis set, evaluating the impact of the exchange-correlation functional used and its ability to accurately describe both the atom and bulk phase.
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Although EC is a reference to know the stability of bulk materials, it differs from a nanoparticle. [28, 29, 30] At nanoscale, size effects on the cohesive energy of nanoparticles has been demonstrated, which decreases with decreasing the particle size. [31] However, slight differences of EC are found when nuclei radii of constituent are similar, which do difficult to analyze or find a trend, e. g., the effect of the relative position of dopants along the NRs. For example, Table 2 shows the calculated values of EC of armchair carbon nanoribbons (ACNR) doped with boron atoms in randomly (ACNR-R) and forming one B nanoisland (ACNR-I) arrangements compared with those pristine ACNRS of size 16x2, 20x2, 16x2 and 20x4 respectively. [32] The arrangement of the nanoisland (ACNR-I) explained in this section is shown in part (a) of Figure 1 numbering from 1 to 6 the C atoms are substituted for impurities. Note that, B doping slightly reduces the cohesive energy of ACNRs compared with the pristine ones with similar EC values mainly found in the largest B-ACNRs. However, at lower doping concentrations, i. e. in the case of the largest ACNR (20x4) very close values of EC are obtained which makes difficult to observe a trend.
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MxN
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Pristine
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ACNR -R
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ACNR-I
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\n\n\n
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16x2
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7.224 (0.003)
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6.992 (−0.272)
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7.003 (−0.291)
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20x2
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7.338 (0.002)
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7.143 (−0.224)
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7.158 (−0.239)
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16x4
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7.225 (0.003)
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7.112 (−0.142)
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7.116 (−0.147)
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20x4
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7.338 (0.002)
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7.249 (−0.119)
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7.250 (−0.130)
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Table 2.
Cohesive per atom (Gibbs free) energy in eV of pristine and B-doped ACNRs of randomly (ANCR-R) and forming a B-nanoisland (ACNR-I) [32].
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Because of these CNRs has 3 different chemical species, EC does not provide a suitable way to evaluate the relative stability. Table 2 also shows in brackets the calculated values of the Gibbs free formation energy to take into account the chemical composition of ACNRs. The relative thermodynamic stability that is considered to evaluate the relative stability of multicomponent systems. This approach has been used in binary and tertiary phase thermodynamics and nanostructures other than NRs. [25, 33, 34] it can be calculated by using the following expression:
where \n\nE\n\nx\n\n\n is the binding energy per atom of the B-ACNR for the example shown in Table 1, \n\n\nx\ni\n\n\n corresponds to the molar fraction of the conformant components (H, N, B, C) which satisfies \n\n\n∑\n\n\nx\ni\n\n=\n1\n\n, where \n\n\nx\ni\n\n=\n\n\nn\ni\n\n\nn\nT\n\n\n\n, being \n\n\nn\ni\n\n\nthe number of atoms of specie i in the unit cell and \n\n\nn\nT\n\n\nthe total number of atoms conforming the unit cell. The chemical potential (\n\n\nμ\ni\n\n\n) can be approximate as the binding energy per atom of the singlet ground state of the H2, the triplet ground state of the B2 molecule and the cohesive energy per atom of the graphene sheet respectively. Note that positive values of \n\nδ\nG\n\n represent a metastable structure with respect to the conforming constituents, whereas negative values of \n\nδ\nG\n\n refer to stable structures in accordance with their constituents. As we can observe in Table 2, \n\nδ\nG\n\n suggests that the arrangement of B-nanoisland leads to stabilize energetically the pristine carbon nanoribbons more than the randomly cases.
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3. Electronic properties of nanoribbons
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The electronic properties of nanoribbons can be inferred from the band structure and total and local density of states (DOS and LDOS) respectively. For the case of NRs, these calculations are relatively simple because they are computed sampling the Brillouin zone only in one direction, i. e., the grown direction from 0 to gamma point. We recommend to use a denser grid than the case of the total energy calculations, including a Gaussian smearing (of width 0.01 eV) to improve the convergence of the integrals of the energy levels for the band structure calculations, for DOS calculations, to use the tetrahedron method with Blöchl corrections. [35, 36]
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Pristine CNRs with hydrogen passivated armchair edges passivated are direct bandgap semiconducting, which decreases as their width increases. The edges of ACNRs play an important role on their electronic properties and reactivity because of quantum confinement gaps, which can be characterized by \n\n\nΔ\n\nN\na\n\n\n~\n\nw\na\n\n−\n1\n\n\n\n. [19, 23, 37]
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In order to evaluate the electronic nature of nanoribbons, firstly, spin-polarized and non-spin polarized solutions of the Kohn-Sham equations must be taken into account to evaluate possible magnetic configurations, as found in zigzag carbon nanoribbons, [38] that implies the magnetic state is the most stable. For armchair ribbons, the non-magnetic state is always the most stable [22] even for ACNRs doped with boron atoms, [32] so that, for simplicity, we consider the armchair topology as a case of study.
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The electronic behavior of ACNRs can be tuned for the influence of substitutional dopants. To illustrate this fact, we think about a unit cell containing one pristine CNR with even number of electrons of valence. If we replace only one carbon atom (with 4 valence electrons) for B (3 valence electrons) or N (5 valence electrons) such change gives one unit cell with odd number of valence electrons, in such cases is necessary to search for spin polarized solutions of the Kohn Sham equation, i. e, to evaluate if there are significant differences with respect to the non-spin polarized solution.
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\nFigure 2 presents the band structure, total density of states and local density of states of dopants (shown in line red) of the 12x2 ACNR pristine, B-doped and N-doped substituting two dopants on positions 3 and 4 using the numbering shown in Figure 1. Note that, the pristine ACNR is a semiconducting in agreement with the literature [22] and the positive doping caused for the B moves the Fermi level (EF) to lower energies meanwhile the negative doping related with the N moves the EF to higher energies with respect to the pristine one. In both cases, the closest energy bands to EF are partially unoccupied and occupied respectively giving rise to metallic behavior in both cases.
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Figure 2.
Band structure and DOS of (a) pristine, (b) B-doped and (c) N-doped ACNRs of size 12x2.
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4. Reactivity of nanoribbons
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In order to explore the reactivity of 1D nanomaterial’s, such as nanoribbons, it is mandatory to use appropriate reactivity descriptor. However, there is not a well stablish criteria to accomplish this task without prior knowing of an adsorption mechanism or experimental evidence, particularly for doped nanoribbons.
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This is why, it is suggested the employment of two reactivity descriptors that are able to cover covalent and non-covalent interactions. The first one is the electrostatic potential, defined as:
Where \n\n\nZ\nA\n\n\n and \n\n\nR\nA\n\n\n are the atomic number of nucleus A and its position respectively, \n\n\n\n\nR\nA\n\n−\nr\n\n\n\n is its distance from the point \n\nr\n\n and \n\nρ\n\n\nr\n′\n\n\n\n is the electron density in each volume element. This descriptor provides the response of electron density when a positive unit charge is approaching, which is commonly plotted in a color scheme. Because of the electrostatic potential \n\nV\n\nr\n\n\n, is a local property, it has one value for each \n\nr\n\n point in the space surrounding a molecule or unit cell, so that, depending the nature of the ions (for instance positive or negative nature), the electrostatic potential will depend on the radial distance \n\nr\n\n from the nucleus. Commonly is followed that the contour of the electrostatic potential is plotted on the isovalue of the molecular electron density, for example, see the Bader’s suggestion. [39] Be aware that, the chosen outer electron density contour depends on the Van der Waals radii of involving ions, which should reflect the molecular properties we want to observe, e. g., lone pairs, strained bonds, conjugated π systems, etc.
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To illustrate, Figure 3 shows the electrostatic potential of pristine, B-doped and N-doped carbon nanoribbons of size 12x2 plotted on the electron density surface of value 0.001 au, computed by using the generalized gradient approximation (GGA) in the form proposed by Perdew et al. for exchange-correlation functional. Figure 3 was built in the software VESTA [40] plotting the charge file and then, adding the cube file containing the local potential. The color scheme used in Figure 3 represents in blue, regions where a positive charge may repel each other, unlike in red, it represents regions where a positive charge, ion or chemical group can interact.
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Figure 3.
Molecular electrostatic potential of the nanoribbons (a) pristine (b) B-doped and (c) N-doped of size 12x2.
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We can observe from Figure 3a that, hydrogens are weak positive meanwhile the delocalized charge is distributed along the carbon atoms, particularly found in the edged carbons, which is in agreement with the DOS of pristine ACNRs. The lacking of π electrons of the boron atoms is particularly observed in Figure 3b, which influences over their neighbor carbon atoms finding localized charge in such region. On the other hand, the N doping influences over the edges with more negative electrostatic potential than the pristine carbon nanoribbon.
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The second reactivity descriptor is the Fukui or frontier functions (Ffs), helpful chemical reactivity descriptors for process controlled by electron transfer. Ffs were introduced for the first time by Parr and Yang, [41], which is convinced from the area of research so-called conceptual Density Functional Theory given by Geerlings in a comprehensive way. [42] Fukui functions play an important role linking the Molecular Orbital Theory with the HSAB principle, [43] they are defined as the change of the electronic density with respect to number of electrons (N), considering the nuclei position fixed, i.e. constant external potential v(\n\nr\n\n):
Where \n\n\nρ\n\nv\n,\nN\n+\n1\n\n\n\nr\n\n\n, \n\n\nρ\n\nv\n,\nN\n\n\n\nr\n\n\n, and \n\n\nρ\n\nv\n,\nN\n−\n1\n\n\n\nr\n\n\n, are the electronic densities of the system with N + 1, N, and N–1 electrons, respectively, all with the ground state geometry of the N electron system. Expressions 4–6 concern the Fukui function for: nucleophilic attack, the chemical change where a molecule gains an electron; electrophilic attack, when a molecule loses charge; and for free radical attacks. [44]
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Although, the finite difference approximation to the Fukui functions works for a specific set of configurations whilst for others is worthless to implement (i.e., full configuration interaction), [45] in most cases they are considered a reliable descriptor to indicate how the electron (incoming or outcoming) is redistributed in regions of the molecules. [46] Chemical reactivity is based on the assumption that, when molecules A and B interact in order to form a product AB, occurs a molecular densities-perturbation. [47] As the electronic density contains all sort of information, the chemical reactivity has to be reflected within its sensitivity to infinitesimal electron changes at constant external potential \n\nv\n\nr\n\n\n. Calculation of the frontier orbitals (HOMO or LUMO) are unambiguously defined. Within the frozen orbital approximation, [48] Ffs can be written in terms of the Kohn-Sham orbitals as follows:
In molecules, the relaxation term is usually very small for the discrete nature of Kohn Sham orbitals. So that, if Eqs. 7 and 8 neglect the second-order variations in the electron density, Ffs may approximate to the electron densities of its frontier orbitals.
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On the other hand, referring to periodic systems, it is difficult to identify one frontier state because of the continuous character of the Blöch states, which makes difficult to compute the Fukui functions in DFT of the solid state. Although there is scarcely literature on this topic, a very useful reference for the numerical calculation of the condensed Ffs in periodic boundary conditions within the DFT applied to oxide bulk and surfaces is found here. [49]
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One qualitative way to obtain Ffs for delocalized periodic systems, such as, the carbon nanoribbons is to extract its electron density and evaluate it by using the Eq. (7) and (8) respectively. From the electronic structure of these nanomaterials we can observe that only one occupied electronic band contributes below and above the Fermi level.
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\nFigure 3 depicts the Ffs evaluated for electrophilic attacks respectively for B-doped and N-doped armchair carbon nanoribbons of size 12x2 with doping made on positions 3 and 4 using the numbering shown in Figure 1.
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We observe from Figure 4 that the B atoms contributes to form regions where an electrophilic attack can occur on the doped nanoribbons, i. e. larges values of \n\n\nf\n−\n\n\n mean regions where the ACNR will lose charge to stabilize it in a chemical change.
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Figure 4.
Fukui functions for nucleophilic attack of (a) B-doped and (b) N-doped ACNRs of size 12x2.
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The electrostatic potential and the Fukui functions provide information on the local selectivity for donor-acceptor interactions. In here, the electrostatic potential describes the long-range non-covalent interactions. [50] The evaluation of the incoming charge distribution on nanoribbons states that “The Fukui function is strong while regions of a molecule are chemically softer than the regions where the Fukui function is weak. By invoking the hard and soft acid and bases (HSAB) principle [51] in a local sense, it is possible to establish the behavior of the different sites as function of hard or soft reagents (adsorbates)”. [32, 52, 53, 54] Figure 4 shows the Fukui functions for electrophilic attack, calculated by using Eq. (8), we observe the contribution of doping particularly on the neighboring carbon atoms. Indeed, from parts (b) and (c) of Figure 2 is observed the electronic states of dopants contributing near the Fermi level.
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\n
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5. Conclusions
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In this chapter is presented how the energetic, electronic and reactivity of can be calculated for 1D nanomaterial’s, such as, carbon nanoribbons. Although the carbon nanoribbons are used as case of study, this methodology can be applied for other kind of chemical compositions, in our experience we have explore the reactivity and stability of doped boron nitride at nanoscale. It is worthy to mention that, the evaluation of Fukui functions in periodic boundary conditions is limited in the usual computational approaches, so that, we suggest to support and compare such analysis with others e. g., charge analysis, global reactivity descriptors depending the nature of the involving chemical species.
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\n
Acknowledgments
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PNS thanks to CONACYT for grant number 252239 and Cátedras CONACYT for Research Fellow.
\n
Conflict of interest
The authors declare no conflict of interest.
\n',keywords:"DFT, band structure, DOS, MEP",chapterPDFUrl:"https://cdn.intechopen.com/pdfs/74229.pdf",chapterXML:"https://mts.intechopen.com/source/xml/74229.xml",downloadPdfUrl:"/chapter/pdf-download/74229",previewPdfUrl:"/chapter/pdf-preview/74229",totalDownloads:85,totalViews:0,totalCrossrefCites:0,dateSubmitted:"August 10th 2020",dateReviewed:"October 19th 2020",datePrePublished:"December 3rd 2020",datePublished:null,dateFinished:"November 27th 2020",readingETA:"0",abstract:"It has been demonstrated that matter at low dimensionality exhibits novel properties, which could be used in promising applications. An effort to understand their behavior is being through the application of computational methods providing strategies to study structures, which present greater experimental challenges. It is proven that thin and narrow carbon-based nanostructures, such as, nanoribbons show promising tunable electronic properties, particularly when they are substitutionally functionalized. This chapter is proposed as a guidance to help the readers to apply conceptual density functional theory to calculate helpful intrinsic properties, e. g., energetic, electronic and reactivity of one-dimension nanomaterial’s, such as, carbon nanoribbons. As a case of study, it is discussed the effect of boron atoms on the properties of pristine carbon nanoribbons concerning the main aspect and considerations must take into account in their computational calculations.",reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/74229",risUrl:"/chapter/ris/74229",signatures:"Pedro Navarro-Santos, Rafael Herrera-Bucio, Judit Aviña-Verduzco and Jose Luis Rivera",book:{id:"10469",title:"Nanofibers",subtitle:null,fullTitle:"Nanofibers",slug:null,publishedDate:null,bookSignature:"Dr. Brajesh Kumar",coverURL:"https://cdn.intechopen.com/books/images_new/10469.jpg",licenceType:"CC BY 3.0",editedByType:null,editors:[{id:"176093",title:"Dr.",name:"Brajesh",middleName:null,surname:"Kumar",slug:"brajesh-kumar",fullName:"Brajesh Kumar"}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"}},authors:null,sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_2",title:"2. Structural and energetic properties",level:"1"},{id:"sec_3",title:"3. Electronic properties of nanoribbons",level:"1"},{id:"sec_4",title:"4. Reactivity of nanoribbons",level:"1"},{id:"sec_5",title:"5. Conclusions",level:"1"},{id:"sec_6",title:"Acknowledgments",level:"1"},{id:"sec_9",title:"Conflict of interest",level:"1"}],chapterReferences:[{id:"B1",body:'\nNakada K, Fujita M, Dresselhaus G, Dresselhaus MS. Edge state in graphene ribbons: Nanometer size effect and edge shape dependence. Phys Rev B. 1996;54(24):17954-17961\n'},{id:"B2",body:'\nMartins TB, Miwa RH, da Silva AJR, Fazzio A. Electronic and Transport Properties of Boron-Doped Graphene Nanoribbons. Phys Rev Lett. 2007;98(19):196803.\n'},{id:"B3",body:'\nJiang D-e, Sumpter BG, Dai S. Unique chemical reactivity of a graphene nanoribbon’s zigzag edge. J Chem Phys. 2007;126(13):-.\n'},{id:"B4",body:'\nYu SS, Zheng WT, Wen QB, Jiang Q. 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Nano Lett. 2006;6(12):2748-54.\n'},{id:"B26",body:'\nNovoselov KS, Geim AK, Morozov SV, Jiang D, Zhang Y, Dubonos SV, et al. Electric Field Effect in Atomically Thin Carbon Films. Science. 2004;306(5696):666-9.\n'},{id:"B27",body:'\nZhang Y, Tan Y-W, Stormer HL, Kim P. Experimental observation of the quantum Hall effect and Berry\'s phase in graphene. Nature. 2005;438(7065):201-4.\n'},{id:"B28",body:'\nJiang Q, Aya N, Shi FG. Nanotube size-dependent melting of single crystals in carbon nanotubes. Appl Phys A. 1997;64(6):627-9.\n'},{id:"B29",body:'\nDavid TB, Lereah Y, Deutscher G, Kofman R, Cheyssac P. Solid-liquid transition in ultra-fine lead particles. Philos Mag A. 1995;71(5):1135-43.\n'},{id:"B30",body:'\nLamber R, Wetjen S, Jaeger NI. Size dependence of the lattice parameter of small palladium particles. Phys Rev B. 1995;51(16):10968-71.\n'},{id:"B31",body:'\nQi WH, Wang MP. Size effect on the cohesive energy of nanoparticle. J Mater Sci Lett. 2002;21(22):1743-5.\n'},{id:"B32",body:'\nNavarro-Santos P, Ricardo-Chávez JL, Reyes-Reyes M, Rivera JL, López-Sandoval R. Tuning the electronic properties of armchair carbon nanoribbons by a selective boron doping. J Phys: Condens Matter. 2010;22(50):505302.\n'},{id:"B33",body:'\nDumitrică T, Hua M, Yakobson BI. Endohedral silicon nanotubes as thinnest silicide wires. Phys Rev B. 2004;70(24):241303.\n'},{id:"B34",body:'\nKan E-j, Li Z, Yang J, Hou JG. Half-Metallicity in Edge-Modified Zigzag Graphene Nanoribbons. J Am Chem Soc. 2008;130(13):4224-5.\n'},{id:"B35",body:'\nKresse G, Joubert D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys Rev B. 1999;59(3):1758-75.\n'},{id:"B36",body:'\nBlöchl PE. Projector augmented-wave method. Phys Rev B. 1994;50(24):17953-79.\n'},{id:"B37",body:'\nAbanin DA, Lee PA, Levitov LS. Spin-Filtered Edge States and Quantum Hall Effect in Graphene. Phys Rev Lett. 2006;96(17):176803.\n'},{id:"B38",body:'\nMagda GZ, Jin X, Hagymási I, Vancsó P, Osváth Z, Nemes-Incze P, et al. Room-temperature magnetic order on zigzag edges of narrow graphene nanoribbons. Nature. 2014;514(7524):608-11.\n'},{id:"B39",body:'\nBader RFW, Carroll MT, Cheeseman JR, Chang C. Properties of atoms in molecules: atomic volumes. J Am Chem Soc. 1987;109(26):7968-79.\n'},{id:"B40",body:'\nMomma K, Izumi F. VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data. J Appl Crystallogr. 2011;44(6):1272-6.\n'},{id:"B41",body:'\nYang W, Parr RG. Hardness, softness, and the fukui function in the electronic theory of metals and catalysis. 1985;82(20):6723-6.\n'},{id:"B42",body:'\nGeerlings P, De Proft F, Langenaeker W. Conceptual Density Functional Theory. Chem Rev. 2003;103(5):1793-874.\n'},{id:"B43",body:'\nLi Y, Evans JNS. The Fukui Function: A Key Concept Linking Frontier Molecular Orbital Theory and the Hard-Soft-Acid-Base Principle. J Am Chem Soc. 1995;117(29):7756-9.\n'},{id:"B44",body:'\nYang W, Mortier WJ. The use of global and local molecular parameters for the analysis of the gas-phase basicity of amines. J Am Chem Soc. 1986;108(19):5708-11.\n'},{id:"B45",body:'\nAyers PW, De Proft F, Borgoo A, Geerlings P. Computing Fukui functions without differentiating with respect to electron number. I. Fundamentals. J Chem Phys. 2007;126(22):224107.\n'},{id:"B46",body:'\nChermette H, Boulet P, Stefan P. Reviews of Modern Quantum Chemistry: A Celebration of the Contributions of Robert G. Parr Parr. Singapore: World Scientific; 2002.\n'},{id:"B47",body:'\nL. GJ. Structure and Bonding. Berlin: Springer-Verlag; 1993. 268 p.\n'},{id:"B48",body:'\nAyers PW, Yang W, Bartolotti LJ. Chemical Reactivity Theory: A Density Functional View: CRC Press; 2009. 610 p.\n'},{id:"B49",body:'\nCerón ML, Gomez T, Calatayud M, Cárdenas C. Computing the Fukui Function in Solid-State Chemistry: Application to Alkaline Earth Oxides Bulk and Surfaces. The Journal of Physical Chemistry A. 2020;124(14):2826-33.\n'},{id:"B50",body:'\nPolitzer P, Murray JS, Peralta-Inga Z. Molecular surface electrostatic potentials in relation to noncovalent interactions in biological systems. Int J Quantum Chem. 2001;85(6):676-84.\n'},{id:"B51",body:'\nPearson RG. Hard and Soft Acids and Bases. J Am Chem Soc. 1963;85(22):3533-9.\n'},{id:"B52",body:'\nMorales-Palacios FG, Navarro-Santos P, Beiza-Granados L, Rivera JL, García-Gutiérrez HA, Herrera-Bucio R. Conjugate addition between syringol and a captodative olefin catalyzed by BF3. 2019;32(12):e4011.\n'},{id:"B53",body:'\nRivera JL, Navarro-Santos P, Guerra-Gonzalez R, Lima E. Interaction of Refractory Dibenzothiophenes and Polymerizable Structures. International Journal of Polymer Science. 2014;2014:11.\n'},{id:"B54",body:'\nRivera JL, Navarro-Santos P, Hernandez-Gonzalez L, Guerra-Gonzalez R. Reactivity of Alkyldibenzothiophenes Using Theoretical Descriptors. J Chem. 2014;2014:8\n'}],footnotes:[],contributors:[{corresp:"yes",contributorFullName:"Pedro Navarro-Santos",address:"pnavarrosa@conacyt.mx",affiliation:'
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OASPA
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STM
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COPE
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Creative Commons
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Crossref
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Altmetric and Dimensions from Digital Science
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CLOCKSS
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iThenticate
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Enago
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Amazon
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DHL
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