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      Piecewise differentiation of the fractional order CAR-T cells-SARS-2 virus model

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          Abstract

          The pandemic caused by the SARS-CoV2 virus has prompted research into new therapeutic solutions that can be used to treat the CoVid-19 syndrome. As part of this research, immunotherapy, first developed against cancer, is offering new therapeutic horizons also against viral infections. CAR technology, with the production of CAR-T cells (adoptive immunotherapy), has shown applicability in the field of HIV viral infections through second generation CAR-T cells implemented with the “CD4CAR” system with a viral fusion inhibitor. In addition, to avoid the immunoescape of the virus, bi- or trispecific CAR receptors have been developed. Our research group hypothesizes the use of this immunotherapy system against SARS-CoV2, admitting the appropriate adjustments concerning the target-epitope and a possible remodeling of the nuclease related to the action of this virus. For a more in-depth analysis of this hypothesis, a mathematical model has been developed which, starting from the fractional derivative Caputo, creates a system of equations that describes the interactions between CAR-T cells, memory cells, and cells infected with SARS-CoV2. Through an analysis of the existence and non-negativity of the solutions, the hypothesis is stabilized; then is further demonstrated through the use of the piece-wise derivative and the consequent application of the formula of Newton polynomial interpolation.

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          A versatile system for rapid multiplex genome-edited CAR T cell generation

          Jiangtao Ren, Xuhua Zhang, Xiaojun Liu … (2017)
          The therapeutic potential of CRISPR system has already been demonstrated in many instances and begun to overlap with the rapidly expanding field of cancer immunotherapy, especially on the production of genetically modified T cell receptor or chimeric antigen receptor (CAR) T cells. Efficient genomic disruption of multiple gene loci to generate universal donor cells, as well as potent effector T cells resistant to multiple inhibitory pathways such as PD-1 and CTLA4 is an attractive strategy for cell therapy. In this study, we accomplished rapid and efficient multiplex genomic editing, and re-directing T cells with antigen specific CAR via a one-shot CRISPR protocol by incorporation of multiple gRNAs in a CAR lentiviral vector. High efficient double knockout of endogenous TCR and HLA class I could be easily achieved to generate allogeneic universal CAR T cells. We also generated Fas-resistant universal CAR T cells by triple gene disruption. Simultaneous gene editing of four gene loci using the one-shot CRISPR protocol to generate allogeneic universal T cells deficient of both PD1 and CTLA-4 was also attempted.
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            Redirection of regulatory T cells with predetermined specificity for the treatment of experimental colitis in mice.

            Tova Waks, Zelig Eshhar, Eran Elinav (2008)
            Treatment with ex vivo expanded regulatory T cells (Tregs) is regarded as a promising therapeutic approach in inflammatory bowel disease but is hampered by impaired Treg accumulation and function at inflammatory sites. We aim to study whether antigen-specific redirected Tregs can overcome these limitations. We developed transgenic mice whose T cells, including Tregs, express chimeric receptor (CR) made of antibody variable region as recognition unit and T-cell stimulatory and costimulatory domains to activate specifically in response to the predetermined model antigen 2,4,6-trinitrophenol (TNP). TNP-specific CR-bearing Tregs were potently and specifically activated by exogenous TNP and suppressed effector T cells in the absence of costimulatory B7-CD28 interaction. TNP-specific transgenic (Tg) mice were resistant to 2,4,6-trinitrobenzene sulphonic acid (TNBS) colitis but not to other hapten-mediated colitis. Adoptive transfer of CR-bearing Tregs to wild-type mice with TNBS colitis was associated with significant amelioration of colitis and improved survival. Although TNP-specific CR-bearing Tregs did not suppress oxazolone colitis, they cured it after addition of traces of TNBS to oxazolone-inflamed colons, demonstrating a "bystander" effect. In vivo imaging of adoptively transferred CR-bearing Tregs demonstrated that they preferentially migrate to TNBS-induced colonic mucosal lesions within hours of induction of colitis. Tregs can be redirected with specificity distinct from that of pathogenic lymphocytes, accumulate at colonic inflammatory lesions, and suppress effector T cells in a specific, nonmajor histocompatibility complex-restricted, and noncostimulatory-dependent manner, resulting in significant amelioration of colitis. Hopefully, this approach will lead to a novel therapy for inflammatory bowel disease, as well as other inflammatory diseases.
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              Supraphysiologic control over HIV-1 replication mediated by CD8 T cells expressing a re-engineered CD4-based chimeric antigen receptor

              Rachel S. Leibman, Max Richardson, Christoph Ellebrecht … (2017)
              HIV is adept at avoiding naturally generated T cell responses; therefore, there is a need to develop HIV-specific T cells with greater potency for use in HIV cure strategies. Starting with a CD4-based chimeric antigen receptor (CAR) that was previously used without toxicity in clinical trials, we optimized the vector backbone, promoter, HIV targeting moiety, and transmembrane and signaling domains to determine which components augmented the ability of T cells to control HIV replication. This re-engineered CAR was at least 50-fold more potent in vitro at controlling HIV replication than the original CD4 CAR, or a TCR-based approach, and substantially better than broadly neutralizing antibody-based CARs. A humanized mouse model of HIV infection demonstrated that T cells expressing optimized CARs were superior at expanding in response to antigen, protecting CD4 T cells from infection, and reducing viral loads compared to T cells expressing the original, clinical trial CAR. Moreover, in a humanized mouse model of HIV treatment, CD4 CAR T cells containing the 4-1BB costimulatory domain controlled HIV spread after ART removal better than analogous CAR T cells containing the CD28 costimulatory domain. Together, these data indicate that potent HIV-specific T cells can be generated using improved CAR design and that CAR T cells could be important components of an HIV cure strategy.
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                Author and article information

                Journal
                Journal ID (nlm-ta): Results Phys
                Journal ID (iso-abbrev): Results Phys
                Title: Results in Physics
                Publisher: The Author(s). Published by Elsevier B.V.
                ISSN (Electronic): 2211-3797
                Publication date PMC-release: 24 December 2021
                Publication date (Electronic): 24 December 2021
                Electronic Location Identifier: 105046
                Affiliations
                [a ]Department of Mathematics, Comsats University Islamabad, Lahore 54000, Pakistan
                [b ]Institute of Systems Security and Control, College of Computer Science and Technology, Xi’an University of Science and Technology, Xi’an 710054, China
                [c ]Biology and Biomechanics division - Centro Studi Attività Motorie via di Tiglio 94, loc. Arancio 55100 Lucca, Italy
                [d ]Department of Mathematics and Statistics, Faculty of Science, Taif University, Taif, Saudi Arabia
                Author notes
                [* ]Corresponding author.
                Article
                Publisher Item ID: S2211-3797(21)01035-4 Publisher ID: 105046
                DOI: 10.1016/j.rinp.2021.105046
                PMC ID: 8702298
                PubMed ID: 34976709
                SO-VID: d45bac87-8069-4738-9ead-6c1435bd41bd
                Copyright © © 2021 The Author(s)
                License:

                Since January 2020 Elsevier has created a COVID-19 resource centre with free information in English and Mandarin on the novel coronavirus COVID-19. The COVID-19 resource centre is hosted on Elsevier Connect, the company's public news and information website. Elsevier hereby grants permission to make all its COVID-19-related research that is available on the COVID-19 resource centre - including this research content - immediately available in PubMed Central and other publicly funded repositories, such as the WHO COVID database with rights for unrestricted research re-use and analyses in any form or by any means with acknowledgement of the original source. These permissions are granted for free by Elsevier for as long as the COVID-19 resource centre remains active.

                History
                Date received : 10 October 2021
                Date revision received : 15 November 2021
                Date accepted : 20 November 2021
                Categories
                Subject: Article

                Keywords: piecewise approach,dynamical analysis,car-t cells,sars-2
                Data availability:
                Keywords: piecewise approach, dynamical analysis, car-t cells, sars-2

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