51
|
Karlgren M, Simoff I, Keiser M, Oswald S, Artursson P. CRISPR-Cas9: A New Addition to the Drug Metabolism and Disposition Tool Box. Drug Metab Dispos 2018; 46:1776-1786. [PMID: 30126863 DOI: 10.1124/dmd.118.082842] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2018] [Accepted: 08/03/2018] [Indexed: 02/06/2023] Open
Abstract
Clustered regularly interspaced short palindromic repeats (CRISPR)-CRISPR associated protein 9 (Cas9), i.e., CRISPR-Cas9, has been extensively used as a gene-editing technology during recent years. Unlike earlier technologies for gene editing or gene knockdown, such as zinc finger nucleases and RNA interference, CRISPR-Cas9 is comparably easy to use, affordable, and versatile. Recently, CRISPR-Cas9 has been applied in studies of drug absorption, distribution, metabolism, and excretion (ADME) and for ADME model generation. To date, about 50 papers have been published describing in vitro or in vivo CRISPR-Cas9 gene editing of ADME and ADME-related genes. Twenty of these papers describe gene editing of clinically relevant genes, such as ATP-binding cassette drug transporters and cytochrome P450 drug-metabolizing enzymes. With CRISPR-Cas9, the ADME tool box has been substantially expanded. This new technology allows us to develop better and more predictive in vitro and in vivo ADME models and map previously underexplored ADME genes and gene families. In this mini-review, we give an overview of the CRISPR-Cas9 technology and summarize recent applications of CRISPR-Cas9 within the ADME field. We also speculate about future applications of CRISPR-Cas9 in ADME research.
Collapse
Affiliation(s)
- M Karlgren
- Department of Pharmacy (M.Ka., P.A.), Uppsala University Drug Optimization and Pharmaceutical Profiling Platform, Department of Pharmacy (I.S.), and Science for Life Laboratory (P.A.), Uppsala University, Uppsala, Sweden; and Department of Clinical Pharmacology, Center of Drug Absorption and Transport, University Medicine of Greifswald, Germany (M.Ke., S.O.)
| | - I Simoff
- Department of Pharmacy (M.Ka., P.A.), Uppsala University Drug Optimization and Pharmaceutical Profiling Platform, Department of Pharmacy (I.S.), and Science for Life Laboratory (P.A.), Uppsala University, Uppsala, Sweden; and Department of Clinical Pharmacology, Center of Drug Absorption and Transport, University Medicine of Greifswald, Germany (M.Ke., S.O.)
| | - M Keiser
- Department of Pharmacy (M.Ka., P.A.), Uppsala University Drug Optimization and Pharmaceutical Profiling Platform, Department of Pharmacy (I.S.), and Science for Life Laboratory (P.A.), Uppsala University, Uppsala, Sweden; and Department of Clinical Pharmacology, Center of Drug Absorption and Transport, University Medicine of Greifswald, Germany (M.Ke., S.O.)
| | - S Oswald
- Department of Pharmacy (M.Ka., P.A.), Uppsala University Drug Optimization and Pharmaceutical Profiling Platform, Department of Pharmacy (I.S.), and Science for Life Laboratory (P.A.), Uppsala University, Uppsala, Sweden; and Department of Clinical Pharmacology, Center of Drug Absorption and Transport, University Medicine of Greifswald, Germany (M.Ke., S.O.)
| | - P Artursson
- Department of Pharmacy (M.Ka., P.A.), Uppsala University Drug Optimization and Pharmaceutical Profiling Platform, Department of Pharmacy (I.S.), and Science for Life Laboratory (P.A.), Uppsala University, Uppsala, Sweden; and Department of Clinical Pharmacology, Center of Drug Absorption and Transport, University Medicine of Greifswald, Germany (M.Ke., S.O.)
| |
Collapse
|
52
|
Ogaugwu CE, Agbo SO, Adekoya MA. CRISPR in Sub-Saharan Africa: Applications and Education. Trends Biotechnol 2018; 37:234-237. [PMID: 30100229 PMCID: PMC6378648 DOI: 10.1016/j.tibtech.2018.07.012] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/07/2018] [Revised: 07/18/2018] [Accepted: 07/18/2018] [Indexed: 01/12/2023]
Abstract
Clustered regularly interspaced short palindromic repeats (CRISPR) technology has enabled genetic engineering feats previously considered impracticable, offering great hopes for solutions to problems facing society. We consider it timely to highlight how CRISPR can benefit public health, medicine, and agriculture in sub-Saharan Africa (SSA) and offer recommendations for successful implementation.
Collapse
Affiliation(s)
- Christian E Ogaugwu
- Department of Microbiology and Molecular Genetics, University of California, Irvine, CA 92697-4500, USA; Department of Animal and Environmental Biology, Federal University Oye-Ekiti, 371010 Ekiti State, Nigeria; Laboratory website: http://sites.uci.edu/jameslab.
| | - Stanley O Agbo
- Department of Animal and Environmental Biology, Federal University Oye-Ekiti, 371010 Ekiti State, Nigeria
| | - Modinat A Adekoya
- Department of Plant Science and Biotechnology, Federal University Oye-Ekiti, 371010 Ekiti State, Nigeria
| |
Collapse
|
53
|
Tan ZY, Huang T, Ngeow J. 65 YEARS OF THE DOUBLE HELIX: The advancements of gene editing and potential application to hereditary cancer. Endocr Relat Cancer 2018; 25:T141-T158. [PMID: 29980644 DOI: 10.1530/erc-18-0039] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 05/08/2018] [Accepted: 05/10/2018] [Indexed: 12/26/2022]
Abstract
Hereditary cancer predisposition syndromes are associated with germline mutations that lead to increased vulnerability for an individual to develop cancers. Such germline mutations in tumour suppressor genes, oncogenes and genes encoding for proteins essential in DNA repair pathways and cell cycle control can cause overall chromosomal instability in the genome and increase risk in developing cancers. Gene correction of these germline mutations to restore normal protein functions is anticipated as a new therapeutic option. This can be achieved through disruption of gain-of-function pathogenic mutation, restoration of loss-of-function mutation, addition of a transgene essential for cell function and single nucleotide changes. Genome editing tools are applicable to precise gene correction. Development of genome editing tools comes in two waves. The first wave focuses on improving targeting specificity and editing efficiency of nucleases, and the second wave of gene editing draws on innovative engineering of fusion proteins combining deactivated nucleases and other enzymes that are able to create limitless functional molecular tools. This gene editing advancement is going to impact medicine, particularly in hereditary cancers. In this review, we discuss the application of gene editing as an early intervention and possible treatment for hereditary cancers, by highlighting a selection of highly penetrant cancer syndromes as examples of how this may be achieved in clinical practice.
Collapse
Affiliation(s)
- Zi Ying Tan
- Lee Kong Chian School of Medicine, Nanyang Technological University, Singapore
- Institute of Molecular and Cell Biology, Singapore
| | - Taosheng Huang
- Division of Human Genetics, Cincinnati Children's Hospital Medical Center, Cincinnati, Ohio, USA
| | - Joanne Ngeow
- Lee Kong Chian School of Medicine, Nanyang Technological University, Singapore
- Institute of Molecular and Cell Biology, Singapore
- Cancer Genetics Service, Division of Medical Oncology, National Cancer Centre Singapore, Singapore
- Oncology Academic Clinical Program, Duke-NUS Medical School Singapore, Singapore
| |
Collapse
|
54
|
Hijacking CRISPR-Cas for high-throughput bacterial metabolic engineering: advances and prospects. Curr Opin Biotechnol 2018; 50:146-157. [DOI: 10.1016/j.copbio.2018.01.002] [Citation(s) in RCA: 50] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2017] [Revised: 12/18/2017] [Accepted: 01/02/2018] [Indexed: 12/18/2022]
|
55
|
McLoughlin NM, Mueller C, Grossmann TN. The Therapeutic Potential of PTEN Modulation: Targeting Strategies from Gene to Protein. Cell Chem Biol 2018; 25:19-29. [DOI: 10.1016/j.chembiol.2017.10.009] [Citation(s) in RCA: 32] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/19/2017] [Revised: 10/05/2017] [Accepted: 10/23/2017] [Indexed: 01/04/2023]
|
56
|
Perez Rojo F, Nyman RKM, Johnson AAT, Navarro MP, Ryan MH, Erskine W, Kaur P. CRISPR-Cas systems: ushering in the new genome editing era. Bioengineered 2018; 9:214-221. [PMID: 29968520 PMCID: PMC6067892 DOI: 10.1080/21655979.2018.1470720] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/05/2018] [Accepted: 04/25/2018] [Indexed: 12/26/2022] Open
Abstract
In recent years there has been great progress with the implementation and utilization of Clustered Regularly Interspaced Palindromic Repeats (CRISPR) and CRISPR-associated protein (Cas) systems in the world of genetic engineering. Many forms of CRISPR-Cas9 have been developed as genome editing tools and techniques and, most recently, several non-genome editing CRISPR-Cas systems have emerged. Most of the CRISPR-Cas systems have been classified as either Class I or Class II and are further divided among several subtypes within each class. Research teams and companies are currently in dispute over patents for these CRISPR-Cas systems as numerous powerful applications are concurrently under development. This mini review summarizes the appearance of CRISPR-Cas systems with a focus on the predominant CRISPR-Cas9 system as well as the classifications and subtypes for CRISPR-Cas. Non-genome editing uses of CRISPR-Cas are also highlighted and a brief overview of the commercialization of CRISPR is provided.
Collapse
Affiliation(s)
- Fernando Perez Rojo
- Centre for Plant Genetics and Breeding, School of Agriculture and Environment, The University of Western Australia, Crawley, WA, Australia
| | - Rikard Karl Martin Nyman
- Centre for Plant Genetics and Breeding, School of Agriculture and Environment, The University of Western Australia, Crawley, WA, Australia
| | | | - Maria Pazos Navarro
- Centre for Plant Genetics and Breeding, School of Agriculture and Environment, The University of Western Australia, Crawley, WA, Australia
- Institute of Agriculture, The University of Western Australia, Crawley, WA, Australia
| | - Megan Helen Ryan
- Institute of Agriculture, The University of Western Australia, Crawley, WA, Australia
- School of Agriculture and Environment, The University of Western Australia, Crawley, WA, Australia
| | - William Erskine
- Centre for Plant Genetics and Breeding, School of Agriculture and Environment, The University of Western Australia, Crawley, WA, Australia
- Institute of Agriculture, The University of Western Australia, Crawley, WA, Australia
| | - Parwinder Kaur
- Centre for Plant Genetics and Breeding, School of Agriculture and Environment, The University of Western Australia, Crawley, WA, Australia
- Institute of Agriculture, The University of Western Australia, Crawley, WA, Australia
- Telethon Kids Institute, Subiaco, WA, Australia
| |
Collapse
|
57
|
Mougiakos I, Mohanraju P, Bosma EF, Vrouwe V, Finger Bou M, Naduthodi MIS, Gussak A, Brinkman RBL, van Kranenburg R, van der Oost J. Characterizing a thermostable Cas9 for bacterial genome editing and silencing. Nat Commun 2017; 8:1647. [PMID: 29162801 PMCID: PMC5698299 DOI: 10.1038/s41467-017-01591-4] [Citation(s) in RCA: 93] [Impact Index Per Article: 13.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2017] [Accepted: 10/03/2017] [Indexed: 01/05/2023] Open
Abstract
CRISPR-Cas9-based genome engineering tools have revolutionized fundamental research and biotechnological exploitation of both eukaryotes and prokaryotes. However, the mesophilic nature of the established Cas9 systems does not allow for applications that require enhanced stability, including engineering at elevated temperatures. Here we identify and characterize ThermoCas9 from the thermophilic bacterium Geobacillus thermodenitrificans T12. We show that in vitro ThermoCas9 is active between 20 and 70 °C, has stringent PAM-preference at lower temperatures, tolerates fewer spacer-protospacer mismatches than SpCas9 and its activity at elevated temperatures depends on the sgRNA-structure. We develop ThermoCas9-based engineering tools for gene deletion and transcriptional silencing at 55 °C in Bacillus smithii and for gene deletion at 37 °C in Pseudomonas putida. Altogether, our findings provide fundamental insights into a thermophilic CRISPR-Cas family member and establish a Cas9-based bacterial genome editing and silencing tool with a broad temperature range.
Collapse
Affiliation(s)
- Ioannis Mougiakos
- Laboratory of Microbiology, Wageningen University, Stippeneng 4, 6708 WE, Wageningen, The Netherlands
| | - Prarthana Mohanraju
- Laboratory of Microbiology, Wageningen University, Stippeneng 4, 6708 WE, Wageningen, The Netherlands
| | - Elleke F Bosma
- Laboratory of Microbiology, Wageningen University, Stippeneng 4, 6708 WE, Wageningen, The Netherlands
- The Novo Nordisk Foundation Center for Biosustainability, Technical University of Denmark, Kemitorvet B220, 2800 Kgs, Lyngby, Denmark
| | - Valentijn Vrouwe
- Laboratory of Microbiology, Wageningen University, Stippeneng 4, 6708 WE, Wageningen, The Netherlands
| | - Max Finger Bou
- Laboratory of Microbiology, Wageningen University, Stippeneng 4, 6708 WE, Wageningen, The Netherlands
| | - Mihris I S Naduthodi
- Laboratory of Microbiology, Wageningen University, Stippeneng 4, 6708 WE, Wageningen, The Netherlands
| | - Alex Gussak
- Laboratory of Microbiology, Wageningen University, Stippeneng 4, 6708 WE, Wageningen, The Netherlands
| | | | - Richard van Kranenburg
- Laboratory of Microbiology, Wageningen University, Stippeneng 4, 6708 WE, Wageningen, The Netherlands
- Corbion, Arkelsedijk 46, 4206 AC, Gorinchem, The Netherlands
| | - John van der Oost
- Laboratory of Microbiology, Wageningen University, Stippeneng 4, 6708 WE, Wageningen, The Netherlands.
| |
Collapse
|
58
|
Cancer induction and suppression with transcriptional control and epigenome editing technologies. J Hum Genet 2017; 63:187-194. [PMID: 29215091 DOI: 10.1038/s10038-017-0377-8] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/23/2017] [Revised: 09/27/2017] [Accepted: 10/10/2017] [Indexed: 12/22/2022]
Abstract
Cancer epigenetics is one of the most important research subjects in dissecting cancer mechanisms and therapeutic targets because the emergence and malignant transformation of various cancers are caused by unnatural expression of cancer-related genes attributed to their epigenetic errors. The original concept of cancer epigenetics basically stands on the analysis of the epigenetic status in naturally occurring cancer cells; however, the rapidly emerging technology called epigenome editing would change this situation drastically. Epigenome editing, the most promising derivative technology of genome editing, can modify the epigenetic states at the pre-defined genomic locus using the programmable effectors, consisting of various epigenetic factors combined with site-specific DNA-binding domains. This technology can be utilized in a reversible manner; i.e., cancer modeling can be achieved by introducing aberrant epigenetic marks in normal cells, and cancer suppression can be achieved by correcting the epigenetic errors in cancer cells. In this review, we summarize the basics of epigenome editing and cancer epigenetics, followed by the current examples of cancer induction and suppression with the transcriptional control and epigenome editing technologies.
Collapse
|
59
|
Millette K, Georgia S. Gene Editing and Human Pluripotent Stem Cells: Tools for Advancing Diabetes Disease Modeling and Beta-Cell Development. Curr Diab Rep 2017; 17:116. [PMID: 28980194 DOI: 10.1007/s11892-017-0947-3] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 12/26/2022]
Abstract
PURPOSE OF REVIEW This review will focus on the multiple approaches to gene editing and address the potential use of genetically modified human pluripotent stem cell-derived beta cells (SC-β) as a tool to study human beta-cell development and model their function in diabetes. We will explore how new variations of CRISPR/Cas9 gene editing may accelerate our understanding of beta-cell developmental biology, elucidate novel mechanisms that establish and regulate beta-cell function, and assist in pioneering new therapeutic modalities for treating diabetes. RECENT FINDINGS Improvements in CRISPR/Cas9 target specificity and homology-directed recombination continue to advance its use in engineering stem cells to model and potentially treat disease. We will review how CRISPR/Cas9 gene editing is informing our understanding of beta-cell development and expanding the therapeutic possibilities for treating diabetes and other diseases. Here we focus on the emerging use of gene editing technology, specifically CRISPR/Cas9, as a means of manipulating human gene expression to gain novel insights into the roles of key factors in beta-cell development and function. Taken together, the combined use of SC-β cells and CRISPR/Cas9 gene editing will shed new light on human beta-cell development and function and accelerate our progress towards developing new therapies for patients with diabetes.
Collapse
Affiliation(s)
- Katelyn Millette
- Center for Endocrinology, Diabetes and Metabolism, Department of Pediatrics, Children's Hospital Los Angeles, Los Angeles, CA, USA
| | - Senta Georgia
- Center for Endocrinology, Diabetes and Metabolism, Department of Pediatrics, Children's Hospital Los Angeles, Los Angeles, CA, USA.
- Departments of Pediatrics and Stem Cell Biology and Regenerative Medicine, Keck School of Medicine, University of Southern California, Los Angeles, CA, USA.
- Developmental Biology and Regenerative Medicine Program, Saban Research Institute of Children's Hospital Los Angeles, Los Angeles, CA, USA.
| |
Collapse
|
60
|
White MK, Kaminski R, Young WB, Roehm PC, Khalili K. CRISPR Editing Technology in Biological and Biomedical Investigation. J Cell Biochem 2017; 118:3586-3594. [PMID: 28460414 DOI: 10.1002/jcb.26099] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/26/2017] [Accepted: 04/27/2017] [Indexed: 01/01/2023]
Abstract
The CRISPR or clustered regularly interspaced short palindromic repeats system is currently the most advanced approach to genome editing and is notable for providing an unprecedented degree of specificity, effectiveness, and versatility in genetic manipulation. CRISPR evolved as a prokaryotic immune system to provide an acquired immunity and resistance to foreign genetic elements such as bacteriophages. It has recently been developed into a tool for the specific targeting of nucleotide sequences within complex eukaryotic genomes for the purpose of genetic manipulation. The power of CRISPR lies in its simplicity and ease of use, its flexibility to be targeted to any given nucleotide sequence by the choice of an easily synthesized guide RNA, and its ready ability to continue to undergo technical improvements. Applications for CRISPR are numerous including creation of novel transgenic cell animals for research, high-throughput screening of gene function, potential clinical gene therapy, and nongene-editing approaches such as modulating gene activity and fluorescent tagging. In this prospect article, we will describe the salient features of the CRISPR system with an emphasis on important drawbacks and considerations with respect to eliminating off-target events and obtaining efficient CRISPR delivery. We will discuss recent technical developments to the system and we will illustrate some of the most recent applications with an emphasis on approaches to eliminate human viruses including HIV-1, JCV and HSV-1 and prospects for the future. J. Cell. Biochem. 118: 3586-3594, 2017. © 2017 Wiley Periodicals, Inc.
Collapse
Affiliation(s)
- Martyn K White
- Center for Neurovirology and Comprehensive NeuroAIDS Center, Department of Neuroscience, Lewis Katz School of Medicine at Temple University, 3500 N. Broad Street, Philadelphia, Pennsylvania, 19140
| | - Rafal Kaminski
- Center for Neurovirology and Comprehensive NeuroAIDS Center, Department of Neuroscience, Lewis Katz School of Medicine at Temple University, 3500 N. Broad Street, Philadelphia, Pennsylvania, 19140
| | - Won-Bin Young
- Center for Neurovirology and Comprehensive NeuroAIDS Center, Department of Neuroscience, Lewis Katz School of Medicine at Temple University, 3500 N. Broad Street, Philadelphia, Pennsylvania, 19140
| | - Pamela C Roehm
- Center for Neurovirology and Comprehensive NeuroAIDS Center, Department of Neuroscience, Lewis Katz School of Medicine at Temple University, 3500 N. Broad Street, Philadelphia, Pennsylvania, 19140
| | - Kamel Khalili
- Center for Neurovirology and Comprehensive NeuroAIDS Center, Department of Neuroscience, Lewis Katz School of Medicine at Temple University, 3500 N. Broad Street, Philadelphia, Pennsylvania, 19140
| |
Collapse
|
61
|
Nakamae K, Nishimura Y, Takenaga M, Nakade S, Sakamoto N, Ide H, Sakuma T, Yamamoto T. Establishment of expanded and streamlined pipeline of PITCh knock-in - a web-based design tool for MMEJ-mediated gene knock-in, PITCh designer, and the variations of PITCh, PITCh-TG and PITCh-KIKO. Bioengineered 2017; 8:302-308. [PMID: 28453368 PMCID: PMC5470537 DOI: 10.1080/21655979.2017.1313645] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022] Open
Abstract
The emerging genome editing technology has enabled the creation of gene knock-in cells easily, efficiently, and rapidly, which has dramatically accelerated research in the field of mammalian functional genomics, including in humans. We recently developed a microhomology-mediated end-joining-based gene knock-in method, termed the PITCh system, and presented various examples of its application. Since the PITCh system only requires very short microhomologies (up to 40 bp) and single-guide RNA target sites on the donor vector, the targeting construct can be rapidly prepared compared with the conventional targeting vector for homologous recombination-based knock-in. Here, we established a streamlined pipeline to design and perform PITCh knock-in to further expand the availability of this method by creating web-based design software, PITCh designer (http://www.mls.sci.hiroshima-u.ac.jp/smg/PITChdesigner/index.html), as well as presenting an experimental example of versatile gene cassette knock-in. PITCh designer can automatically design not only the appropriate microhomologies but also the primers to construct locus-specific donor vectors for PITCh knock-in. By using our newly established pipeline, a reporter cell line for monitoring endogenous gene expression, and transgenesis (TG) or knock-in/knockout (KIKO) cell line can be produced systematically. Using these new variations of PITCh, an exogenous promoter-driven gene cassette expressing fluorescent protein gene and drug resistance gene can be integrated into a safe harbor or a specific gene locus to create transgenic reporter cells (PITCh-TG) or knockout cells with reporter knock-in (PITCh-KIKO), respectively.
Collapse
Affiliation(s)
- Kazuki Nakamae
- a Department of Mathematical and Life Sciences, Graduate School of Science , Hiroshima University , Hiroshima , Japan
| | - Yuki Nishimura
- a Department of Mathematical and Life Sciences, Graduate School of Science , Hiroshima University , Hiroshima , Japan
| | - Mitsumasa Takenaga
- a Department of Mathematical and Life Sciences, Graduate School of Science , Hiroshima University , Hiroshima , Japan
| | - Shota Nakade
- a Department of Mathematical and Life Sciences, Graduate School of Science , Hiroshima University , Hiroshima , Japan
| | - Naoaki Sakamoto
- a Department of Mathematical and Life Sciences, Graduate School of Science , Hiroshima University , Hiroshima , Japan
| | - Hiroshi Ide
- a Department of Mathematical and Life Sciences, Graduate School of Science , Hiroshima University , Hiroshima , Japan
| | - Tetsushi Sakuma
- a Department of Mathematical and Life Sciences, Graduate School of Science , Hiroshima University , Hiroshima , Japan
| | - Takashi Yamamoto
- a Department of Mathematical and Life Sciences, Graduate School of Science , Hiroshima University , Hiroshima , Japan
| |
Collapse
|