Mathematical models for immunology:current state of the art and future research directions

The advances in genetics and biochemistry that have taken place over the last 10 years led to significant advances in experimental and clinical immunology. In turn, this has led to the development of new mathematical models to investigate qualitatively and quantitatively various open questions in immunology. In this study we present a review of some research areas in mathematical immunology that evolved over the last 10 years. To this end, we take a step-by-step approach in discussing a range of models derived to study the dynamics of both the innate and immune responses at the molecular, cellular and tissue scales. To emphasise the use of mathematics in modelling in this area, we also review some of the mathematical tools used to investigate these models. Finally, we discuss some future trends in both experimental immunology and mathematical immunology for the upcoming years

Hopf Bifurcation and Stability of Periodic Solutions for Delay Differential Model of HIV Infection of CD4 +

This paper deals with stability and Hopf bifurcation analyses of a mathematical model of HIV infection of CD4+ T-cells. The model is based on a system of delay differential equations with logistic growth term and antiretroviral treatment with a discrete time delay, which plays a main role in changing the stability of each steady state. By fixing the time delay as a bifurcation parameter, we get a limit cycle bifurcation about the infected steady state. We study the effect of the time delay on the stability of the endemically infected equilibrium. We derive explicit formulae to determine the stability and direction of the limit cycles by using center manifold theory and normal form method. Numerical simulations are presented to illustrate the results

Translating simulation approaches for immunology

This thesis presents a novel set of guidelines to convert between simulation modelling approaches, namely, Ordinary differential Equations (ODEs), System Dynamics (SD) and Agent-based Modelling and Simulation (ABMS). In our literature review we identify a gap in establishing translation techniques between these approaches. We therefore focus our research in developing these techniques and assessing the impact of these conversions in the simulation outcomes. In particular, our interest lies in investigating our techniques applied to simulation problems for the immune system, as we wish to aid immunologists with the choice of the most appropriate approach for a certain problem. The aims of this thesis are therefore defined as: (1) with no explicit guidelines available from the literature, we want to develop, test and validate our own set of guidelines for converting between approaches: from ODE models to SD, from SD to ABMS and from ABMS to SD; and (2) we seek to discuss the merits of SD and ABMS for Immunology to assist researchers with the choice between both approaches. The assessment of the effectiveness of the conversion guidelines is achieved by using a case study approach involving six cases of established mathematical models describing immunological phenomena. These case studies are chosen by considering aspects such as the behaviour of the entities of the model (whether they are static or interact with other entities and whether they have spatial representation or not), the type of hypothesis to be tested, the empirical embeddedness of real data, population sizes, number of elements involved and the modelling effort. In order to conduct our conversion for the case studies, we first convert their original ODE model into an SD model, and then perform the translation from SD to ABMS. For the last three case studies, we also test the conversion guidelines from ABMS to SD. Evidence from the experiments reveal that for all cases it was possible to obtain equivalent approaches by using the conversion guidelines developed. However, outcome differences occur given the intrinsic characteristics of each simulation modelling paradigm. By observing these differences we could conclude that (1) SD is incapable of reflecting exactly the same variability as that obtained from the agent-based simulation, as it is a deterministic approach; (2) SD variables change continuously in time and therefore population numbers over time might be different from those obtained by the agent-based simulation; (3) as the number of different agents and behaviours increase, the corresponding SD becomes very intricate and difficult to develop and understand; (4) there are cases where it is preferable not to convert from ABMS to SD, as the agent-based model is easier to conceptualise and implement; (5) For other circumstances, ABMS outcomes are the same as those produced by the ODEs and SD, with the disadvantage to be more resource consuming in terms of computational memory and processing capacity; and (6) For some cases SD is less informative than ABMS, as it does not produce multiple scenarios or variations over the course of more than one run within the same parameters

Forecasting the action of CAR-T cells against SARS-corona virus-II infection with branching process

The CAR-T cells are the genetically engineered T cells, designed to work specifically for the virus antigens (or other antigens, such as tumour specific antigens). The CAR-T cells work as the living drug and thus provides an adoptive immunotherapy strategy. The novel corona virus treatment and control designs are still under clinical trials. One of such techniques is the injection of CAR-T cells to fight against the COVID-19 infection. In this manuscript, the hypothesis is based on the CAR-T cells, that are suitably engineered towards SARS-2 viral antigen, by the N protein. The N protein binds to the SARS-2 viral RNA and is found in abundance in this virus, thus for the engineered cell research, this protein sequence is chosen as a potential target. The use of the sub-population of T-reg cells is also outlined. Mathematical modeling of such complex line of action can help to understand the dynamics. The modeling approach is inspired from the probabilistic rules, including the branching process, the Moran process and kinetic models. The Moran processes are well recognized in the fields of artificial intelligence and data science. The model depicts the infectious axis “virus—CAR-T cells—memory cells”. The theoretical analysis provides a positive therapeutic action; the delay in viral production may have a significant impact on the early stages of infection. Although it is necessary to carefully evaluate the possible side effects of therapy. This work introduces the possibility of hypothesizing an antiviral use by CAR-T cells

Applying antibodies inside cells: Principles and recent advances in neurobiology, virology and oncology

To interfere with cell function, many scientists rely on methods that target DNA or RNA due to the ease with which they can be applied. Proteins are usually the final executors of function but are targeted only indirectly by these methods. Recent advances in targeted degradation of proteins based on proteolysis-targeting chimaeras (PROTACs), ubiquibodies, deGradFP (degrade Green Fluorescent Protein) and other approaches have demonstrated the potential of interfering directly at the protein level for research and therapy. Proteins can be targeted directly and very specifically by antibodies, but using antibodies inside cells has so far been considered to be challenging. However, it is possible to deliver antibodies or other proteins into the cytosol using standard laboratory equipment. Physical methods such as electroporation have been demonstrated to be efficient and validated thoroughly over time. The expression of intracellular antibodies (intrabodies) inside cells is another way to interfere with intracellular targets at the protein level. Methodological strategies to target the inside of cells with antibodies, including delivered antibodies and expressed antibodies, as well as applications in the research areas of neurobiology, viral infections and oncology, are reviewed here. Antibodies have already been used to interfere with a wide range of intracellular targets. Disease-related targets included proteins associated with neurodegenerative diseases such as Parkinson's disease (α-synuclein), Alzheimer's disease (amyloid-β) or Huntington's disease (mutant huntingtin [mHtt]). The applications of intrabodies in the context of viral infections include targeting proteins associated with HIV (e.g. HIV1-TAT, Rev, Vif, gp41, gp120, gp160) and different oncoviruses such as human papillomavirus (HPV), hepatitis B virus (HBV), hepatitis C virus (HCV) and Epstein-Barr virus, and they have been used to interfere with various targets related to different processes in cancer, including oncogenic pathways, proliferation, cell cycle, apoptosis, metastasis, angiogenesis or neo-antigens (e.g. p53, human epidermal growth factor receptor-2 [HER2], signal transducer and activator of transcription 3 [STAT3], RAS-related RHO-GTPase B (RHOB), cortactin, vascular endothelial growth factor receptor 2 [VEGFR2], Ras, Bcr-Abl). Interfering at the protein level allows questions to be addressed that may remain unanswered using alternative methods. This review addresses why direct targeting of proteins allows unique insights, what is currently feasible in vitro, and how this relates to potential therapeutic applications

Chimeric antigen receptor for treatment of T-cell malignancies and HIV-1 cure

Chimeric Antigen Receptors (CARs) T cell therapy has achieved great success in the treatment of B-cell malignancies by targeting B-cell specific antigen CD19. However, a similar approach targeting the CD4 molecule for T cell lymphoma has thus far been unrealised. CD4, a cell surface glycoprotein, is highly expressed in the majority of mature T-cell malignancies, and absent in hematopoietic stem cells. Anti-CD4 monoclonal antibodies have been widely assessed for T-cell leukaemia/lymphoma treatment, but yielded limited efficacy, suggesting more potent therapies targeting CD4 are required. Here T cells were transduced with a third-generation CAR specifically targeting CD4 molecule (CART4) via a two-step retroviral system, incorporating with truncated epidermal growth factor receptor (tEGFR) as tracking marker and inducible caspase-9 (iC9) as safety switch. CART4 transduced T cells showed remarkable cytotoxicity against CD4+ T cells in vitro. Those CART4 cells effectively eliminated CD4+ T tumour cell line and primary tumour cells from patients with adult T-cell leukaemia/lymphoma (ATLL) and cutaneous T-cell lymphoma (CTCL). In a xenograft model bearing T cell leukaemia cell line, CART4 cells efficiently suppressed tumour progression and prolonged mouse survival, suggesting that CART4 T cells could be a promising strategy for T-cell malignancy. Besides, as CD4 as serves the primary receptor for HIV-1 entry, it was hypothesised that the anti-CD4 CAR could be applied for HIV eradication. By in vitro co-culture assays, CART4 cells effectively eliminated target cells, including CD4+ T cells, dendritic cells (DCs), and macrophages. In vivo test utilizing A humanized mouse model of HIV treatment demonstrated that CART4 cells were superior at expanding upon antigen stimulation, eliminating target cells, and controlling HIV rebound after antiretroviral therapy (ART) interruption. Together, these results support the therapeutic potential of CART4 in patients with T-cell malignancies and HIV-1 infection, respectively.Open Acces

Potential role of MAIT cells in cancer immunotherapy and viral infection

Mucosa-associated invariant T (MAIT) cells are an unconventional T cell subset with specialized antimicrobial functions. In humans, MAIT cells are characterized by their effector memory phenotype, rapid cytolytic capacity, and tissue-homing properties. Given their natural enrichment in the liver and mucosal barrier tissues, this thesis aimed to explore the potential of redirecting MAIT cells for hepatitis virus-related liver cancer immunotherapy using MHC class-I restricted T cell receptors (TCRs). Additionally, we sought to explore the role of MAIT cells in the context of another front-line immune tissue, the female genital mucosa, in human immunodeficiency virus type 1 (HIV-1) infection. In paper I, a MAIT cell expansion methodology was developed to generate clinically relevant quantities of human MAIT cells for immunotherapies. The MAIT cell expansion protocol was highly reproducible and resulted in MAIT cell cultures with an activated phenotype, enhanced cytolytic potential, and improved tissue homing capacity. These features make them particularly suitable for solid tumour-targeting. We tested this hypothesis in paper II, by engineering expanded MAIT cells to express a TCR with specificity for hepatitis B virus (HBV). Using 2D and 3D hepatoma cell models of HBV-related hepatocellular carcinoma, we compared the antiviral, cytotoxic, and tumour homing properties of the TCR-redirected MAIT cells with those of conventional T cells currently being used in the clinic. We demonstrated that the MAIT cells not only acquired a distinct polyfunctional antigen-specific profile in response to HBV, but also retained their antimicrobial properties, and readily migrated towards the tumor targets in a 3D microfluidic model. In paper III, we investigated the phenotype of MAIT cells in women living with chronic HIV-1 infection. We initially confirmed that circulating MAIT cells were activated and numerically depleted in the blood. However, MAIT cells were preserved in the cervical mucosa. The TRAV1-2-TRAJ20 MAIT TCR transcript was highly expressed in the ectocervix and was significantly upregulated in the HIV-1 infected women relative to uninfected controls. This indicates that MAIT cells may be poised to recognize stimuli unique to that environment, and that HIV-1 infection may shape the MAIT cell population in the female genital tract. In summary, the research covered by this thesis demonstrates the potential role of MAIT cells in the context of virus-related cancer immunotherapy and barrier tissue infiltration. Taken together, these findings illuminate new avenues of research in MAIT cell biology in human health and disease

Translating simulation approaches for immunology

This thesis presents a novel set of guidelines to convert between simulation modelling approaches, namely, Ordinary differential Equations (ODEs), System Dynamics (SD) and Agent-based Modelling and Simulation (ABMS). In our literature review we identify a gap in establishing translation techniques between these approaches. We therefore focus our research in developing these techniques and assessing the impact of these conversions in the simulation outcomes. In particular, our interest lies in investigating our techniques applied to simulation problems for the immune system, as we wish to aid immunologists with the choice of the most appropriate approach for a certain problem. The aims of this thesis are therefore defined as: (1) with no explicit guidelines available from the literature, we want to develop, test and validate our own set of guidelines for converting between approaches: from ODE models to SD, from SD to ABMS and from ABMS to SD; and (2) we seek to discuss the merits of SD and ABMS for Immunology to assist researchers with the choice between both approaches. The assessment of the effectiveness of the conversion guidelines is achieved by using a case study approach involving six cases of established mathematical models describing immunological phenomena. These case studies are chosen by considering aspects such as the behaviour of the entities of the model (whether they are static or interact with other entities and whether they have spatial representation or not), the type of hypothesis to be tested, the empirical embeddedness of real data, population sizes, number of elements involved and the modelling effort. In order to conduct our conversion for the case studies, we first convert their original ODE model into an SD model, and then perform the translation from SD to ABMS. For the last three case studies, we also test the conversion guidelines from ABMS to SD. Evidence from the experiments reveal that for all cases it was possible to obtain equivalent approaches by using the conversion guidelines developed. However, outcome differences occur given the intrinsic characteristics of each simulation modelling paradigm. By observing these differences we could conclude that (1) SD is incapable of reflecting exactly the same variability as that obtained from the agent-based simulation, as it is a deterministic approach; (2) SD variables change continuously in time and therefore population numbers over time might be different from those obtained by the agent-based simulation; (3) as the number of different agents and behaviours increase, the corresponding SD becomes very intricate and difficult to develop and understand; (4) there are cases where it is preferable not to convert from ABMS to SD, as the agent-based model is easier to conceptualise and implement; (5) For other circumstances, ABMS outcomes are the same as those produced by the ODEs and SD, with the disadvantage to be more resource consuming in terms of computational memory and processing capacity; and (6) For some cases SD is less informative than ABMS, as it does not produce multiple scenarios or variations over the course of more than one run within the same parameters

Novel codynamics of the HIV-1/HTLV-Ⅰ model involving humoral immune response and cellular outbreak: A new approach to probability density functions and fractional operators

Both human immunodeficiency virus type 1 (HIV-1) and human T-lymphotropic virus type Ⅰ (HTLV-Ⅰ) are retroviruses that afflict CD4 T cells. In this article, the codynamics of within-host HIV-1 and HTLV-Ⅰ are presented via piecewise fractional differential equations by employing a stochastic system with an influential strategy for biological research. It is demonstrated that the scheme is mathematically and biologically feasible by illustrating that the framework has positive and bounded global findings. The necessary requirements are deduced, ensuring the virus's extinction. In addition, the structure is evaluated for the occurrence of an ergodic stationary distribution and sufficient requirements are developed. A deterministic-stochastic mechanism for simulation studies is constructed and executed in MATLAB to reveal the model's long-term behavior. Utilizing rigorous analysis, we predict that the aforesaid model is an improvement of the existing virus-to-cell and cell-to-cell interactions by investigating an assortment of behaviour patterns that include cross-over to unpredictability processes. Besides that, the piecewise differential formulations, which can be consolidated with integer-order, Caputo, Caputo-Fabrizio, Atangana-Baleanu and stochastic processes, have been declared to be exciting opportunities for researchers in a spectrum of disciplines by enabling them to incorporate distinctive features in various temporal intervals. As a result, by applying these formulations to difficult problems, researchers can achieve improved consequences in reporting realities with white noise. White noise in fractional HIV-1/HTLV-Ⅰ codynamics plays an extremely important function in preventing the proliferation of an outbreak when the proposed flow is constant and disease extermination is directly proportional to the magnitude of the white noise