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Mahasa KJ, Ouifki R, de Pillis L, Eladdadi A. A Role of Effector CD 8 + T Cells Against Circulating Tumor Cells Cloaked with Platelets: Insights from a Mathematical Model. Bull Math Biol 2024; 86:89. [PMID: 38884815 DOI: 10.1007/s11538-024-01323-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/18/2024] [Accepted: 05/31/2024] [Indexed: 06/18/2024]
Abstract
Cancer metastasis accounts for a majority of cancer-related deaths worldwide. Metastasis occurs when the primary tumor sheds cells into the blood and lymphatic circulation, thereby becoming circulating tumor cells (CTCs) that transverse through the circulatory system, extravasate the circulation and establish a secondary distant tumor. Accumulating evidence suggests that circulating effector CD 8 + T cells are able to recognize and attack arrested or extravasating CTCs, but this important antitumoral effect remains largely undefined. Recent studies highlighted the supporting role of activated platelets in CTCs's extravasation from the bloodstream, contributing to metastatic progression. In this work, a simple mathematical model describes how the primary tumor, CTCs, activated platelets and effector CD 8 + T cells participate in metastasis. The stability analysis reveals that for early dissemination of CTCs, effector CD 8 + T cells can present or keep secondary metastatic tumor burden at low equilibrium state. In contrast, for late dissemination of CTCs, effector CD 8 + T cells are unlikely to inhibit secondary tumor growth. Moreover, global sensitivity analysis demonstrates that the rate of the primary tumor growth, intravascular CTC proliferation, as well as the CD 8 + T cell proliferation, strongly affects the number of the secondary tumor cells. Additionally, model simulations indicate that an increase in CTC proliferation greatly contributes to tumor metastasis. Our simulations further illustrate that the higher the number of activated platelets on CTCs, the higher the probability of secondary tumor establishment. Intriguingly, from a mathematical immunology perspective, our simulations indicate that if the rate of effector CD 8 + T cell proliferation is high, then the secondary tumor formation can be considerably delayed, providing a window for adjuvant tumor control strategies. Collectively, our results suggest that the earlier the effector CD 8 + T cell response is enhanced the higher is the probability of preventing or delaying secondary tumor metastases.
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Affiliation(s)
- Khaphetsi Joseph Mahasa
- Department of Mathematics and Computer Science, National University of Lesotho, Roma, Maseru, Lesotho.
| | - Rachid Ouifki
- Department of Mathematics and Applied Mathematics, Mafikeng Campus, North-West University, Private Bag X2046, Mmabatho, 2735, South Africa
| | | | - Amina Eladdadi
- Division of Mathematical Sciences, The National Science Foundation, Alexandria, VA, USA
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2
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Wang B, Li W, Zhao J, Trisovic N. Longtime evolution and stationary response of a stochastic tumor-immune system with resting T cells. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2024; 21:2813-2834. [PMID: 38454708 DOI: 10.3934/mbe.2024125] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/09/2024]
Abstract
In this paper, we take the resting T cells into account and interpret the progression and regression of tumors by a predator-prey like tumor-immune system. First, we construct an appropriate Lyapunov function to prove the existence and uniqueness of the global positive solution to the system. Then, by utilizing the stochastic comparison theorem, we prove the moment boundedness of tumor cells and two types of T cells. Furthermore, we analyze the impact of stochastic perturbations on the extinction and persistence of tumor cells and obtain the stationary probability density of the tumor cells in the persistent state. The results indicate that when the noise intensity of tumor perturbation is low, tumor cells remain in a persistent state. As this intensity gradually increases, the population of tumors moves towards a lower level, and the stochastic bifurcation phenomena occurs. When it reaches a certain threshold, instead the number of tumor cells eventually enter into an extinct state, and further increasing of the noise intensity will accelerate this process.
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Affiliation(s)
- Bingshuo Wang
- School of Mathematics and Statistics, Xidian University, Xi'an 710071, China
| | - Wei Li
- School of Mathematics and Statistics, Xidian University, Xi'an 710071, China
| | - Junfeng Zhao
- School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an 710071, China
| | - Natasa Trisovic
- Faculty of Mechanical Engineering, Department of Mechanics, University of Belgrade, Belgrade 11000, Serbia
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3
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Luque LM, Carlevaro CM, Llamoza Torres CJ, Lomba E. Physics-based tissue simulator to model multicellular systems: A study of liver regeneration and hepatocellular carcinoma recurrence. PLoS Comput Biol 2023; 19:e1010920. [PMID: 36877741 PMCID: PMC10019748 DOI: 10.1371/journal.pcbi.1010920] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/01/2022] [Revised: 03/16/2023] [Accepted: 02/03/2023] [Indexed: 03/07/2023] Open
Abstract
We present a multiagent-based model that captures the interactions between different types of cells with their microenvironment, and enables the analysis of the emergent global behavior during tissue regeneration and tumor development. Using this model, we are able to reproduce the temporal dynamics of regular healthy cells and cancer cells, as well as the evolution of their three-dimensional spatial distributions. By tuning the system with the characteristics of the individual patients, our model reproduces a variety of spatial patterns of tissue regeneration and tumor growth, resembling those found in clinical imaging or biopsies. In order to calibrate and validate our model we study the process of liver regeneration after surgical hepatectomy in different degrees. In the clinical context, our model is able to predict the recurrence of a hepatocellular carcinoma after a 70% partial hepatectomy. The outcomes of our simulations are in agreement with experimental and clinical observations. By fitting the model parameters to specific patient factors, it might well become a useful platform for hypotheses testing in treatments protocols.
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Affiliation(s)
- Luciana Melina Luque
- Instituto de Física de Líquidos y Sistemas Biológicos - CONICET. La Plata, Argentina
- * E-mail: (LML); (CMC)
| | - Carlos Manuel Carlevaro
- Instituto de Física de Líquidos y Sistemas Biológicos - CONICET. La Plata, Argentina
- Departamento de Ingeniería Mecánica, Universidad Tecnológica Nacional, Facultad Regional La Plata, La Plata, Argentina
- * E-mail: (LML); (CMC)
| | | | - Enrique Lomba
- Instituto de Química Física Rocasolano - CSIC. Madrid, España
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4
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Modeling tumour heterogeneity of PD-L1 expression in tumour progression and adaptive therapy. J Math Biol 2023; 86:38. [PMID: 36695961 DOI: 10.1007/s00285-023-01872-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/18/2022] [Revised: 12/06/2022] [Accepted: 01/09/2023] [Indexed: 01/26/2023]
Abstract
Although PD-1/PD-L1 inhibitors show potent and durable anti-tumour effects in some refractory tumours, the response rate in overall patients is unsatisfactory, which in part due to the inherent heterogeneity of PD-L1. In order to establish an approach for predicting and estimating the dynamic alternation of PD-L1 heterogeneity during cancer progression and treatment, this study establishes a comprehensive modelling and computational framework based on a mathematical model of cancer cell evolution in the tumour-immune microenvironment, and in combination with epigenetic data and overall survival data of clinical patients from The Cancer Genome Atlas. Through PD-L1 heterogeneous virtual patients obtained by the computational framework, we explore the adaptive therapy of administering anti-PD-L1 according to the dynamic of PD-L1 state among cancer cells. Our results show that in contrast to the continuous maximum tolerated dose treatment, adaptive therapy is more effective for PD-L1 positive patients, in that it prolongs the survival of patients by administration of drugs at lower dosage.
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Wang Q, Dong Z, Lou F, Yin Y, Zhang J, Wen H, Lu T, Wang Y. Phenylboronic ester-modified polymeric nanoparticles for promoting TRP2 peptide antigen delivery in cancer immunotherapy. Drug Deliv 2022; 29:2029-2043. [PMID: 35766157 PMCID: PMC9248950 DOI: 10.1080/10717544.2022.2086941] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/17/2022] [Revised: 05/25/2022] [Accepted: 05/30/2022] [Indexed: 11/25/2022] Open
Abstract
The tremendous development of peptide-based cancer vaccine has attracted incremental interest as a powerful approach in cancer management, prevention and treatment. As successful as tumor vaccine has been, major challenges associated with achieving efficient immune response against cancer are (1) drainage to and retention in lymph nodes; (2) uptake by dendritic cells (DCs); (3) activation of DCs. In order to overcome these barriers, here we construct PBE-modified TRP2 nanovaccine, which comprises TRP2 peptide tumor antigen and diblock copolymer PEG-b-PAsp grafted with phenylboronic ester (PBE). We confirmed that this TRP2 nanovaccine can be effectively trapped into lymph node, uptake by dendritic cells and induce DC maturation, relying on increased negative charge, ROS response and pH response. Consistently, this vehicle loaded with TRP2 peptide could boost the strongest T cell immune response against melanoma in vivo and potentiate antitumor efficacy both in tumor prevention and tumor treatment without any exogenous adjuvant. Furthermore, the TRP2 nanovaccine can suppress the tumor growth and prolong animal survival time, which may result from its synergistic effect of inhibiting tumor immunosuppression and increasing cytotoxic lymphocyte (CTL) response. Hence this type of PBE-modified nanovaccine would be widely used as a simple, safe and robust platform to deliver other antigen in cancer immunotherapy.
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Affiliation(s)
- Qiyan Wang
- Key Laboratory of Biomedical Functional Materials, School of Sciences, China Pharmaceutical University, Nanjing, Jiangsu, China
- Center for Cutaneous Biology and Immunology Research, Department of Dermatology, Henry Ford Health System, Detroit, Michigan, USA
- Immunology Research program, Henry Ford Cancer Institute, Henry Ford Health System, Detroit, Michigan, USA
| | - Zhipeng Dong
- Key Laboratory of Biomedical Functional Materials, School of Sciences, China Pharmaceutical University, Nanjing, Jiangsu, China
| | - Fangning Lou
- Key Laboratory of Biomedical Functional Materials, School of Sciences, China Pharmaceutical University, Nanjing, Jiangsu, China
| | - Yunxue Yin
- Key Laboratory of Biomedical Functional Materials, School of Sciences, China Pharmaceutical University, Nanjing, Jiangsu, China
| | - Jiahao Zhang
- Key Laboratory of Biomedical Functional Materials, School of Sciences, China Pharmaceutical University, Nanjing, Jiangsu, China
| | - Hanning Wen
- Key Laboratory of Biomedical Functional Materials, School of Sciences, China Pharmaceutical University, Nanjing, Jiangsu, China
| | - Tao Lu
- Key Laboratory of Biomedical Functional Materials, School of Sciences, China Pharmaceutical University, Nanjing, Jiangsu, China
| | - Yue Wang
- Key Laboratory of Biomedical Functional Materials, School of Sciences, China Pharmaceutical University, Nanjing, Jiangsu, China
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Kariya Y, Honma M, Tokuda K, Konagaya A, Suzuki H. Utility of constraints reflecting system stability on analyses for biological models. PLoS Comput Biol 2022; 18:e1010441. [PMID: 36084151 PMCID: PMC9491612 DOI: 10.1371/journal.pcbi.1010441] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/04/2021] [Revised: 09/21/2022] [Accepted: 07/26/2022] [Indexed: 12/03/2022] Open
Abstract
Simulating complex biological models consisting of multiple ordinary differential equations can aid in the prediction of the pharmacological/biological responses; however, they are often hampered by the availability of reliable kinetic parameters. In the present study, we aimed to discover the properties of behaviors without determining an optimal combination of kinetic parameter values (parameter set). The key idea was to collect as many parameter sets as possible. Given that many systems are biologically stable and resilient (BSR), we focused on the dynamics around the steady state and formulated objective functions for BSR by partial linear approximation of the focused region. Using the objective functions and modified global cluster Newton method, we developed an algorithm for a thorough exploration of the allowable parameter space for biological systems (TEAPS). We first applied TEAPS to the NF-κB signaling model. This system shows a damped oscillation after stimulation and seems to fit the BSR constraint. By applying TEAPS, we found several directions in parameter space which stringently determines the BSR property. In such directions, the experimentally fitted parameter values were included in the range of the obtained parameter sets. The arachidonic acid metabolic pathway model was used as a model related to pharmacological responses. The pharmacological effects of nonsteroidal anti-inflammatory drugs were simulated using the parameter sets obtained by TEAPS. The structural properties of the system were partly extracted by analyzing the distribution of the obtained parameter sets. In addition, the simulations showed inter-drug differences in prostacyclin to thromboxane A2 ratio such that aspirin treatment tends to increase the ratio, while rofecoxib treatment tends to decrease it. These trends are comparable to the clinical observations. These results on real biological models suggest that the parameter sets satisfying the BSR condition can help in finding biologically plausible parameter sets and understanding the properties of biological systems. We propose a new method to analyze the properties of biological dynamic models, which we named TEAPS (Thorough Exploration of Allowable Parameter Space). TEAPS can thoroughly determine combinations of parameter values for ordinary differential equations with which an initial state in a certain range converges to a particular fixed point. This stable and resilient behavior is a characteristic shared with many biological systems, including metabolic systems and intracellular signaling systems. Therefore, this thorough search outlined the possible parameter space as biological systems for target models, which helps to understand the system constraints when the target systems behave dynamically. The obtained parameter space can be used as an initial space for parameter tuning. For models that include a large number of parameters, the parameter space to be searched in the parameter tuning process is too large; therefore, narrowing down the space by TEAPS potentially contributes to the analysis of the dynamics of complicated biological models. Thus, our approach can partly overcome the current problem in parameter tuning and can advance the computational dynamic analyses of biological systems.
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Affiliation(s)
- Yoshiaki Kariya
- Department of Pharmacy, The University of Tokyo Hospital, Faculty of Medicine, The University of Tokyo, Bunkyo-ku, Tokyo, Japan
| | - Masashi Honma
- Department of Pharmacy, The University of Tokyo Hospital, Faculty of Medicine, The University of Tokyo, Bunkyo-ku, Tokyo, Japan
- * E-mail:
| | - Keita Tokuda
- Department of Computer Science, University of Tsukuba, Tsukuba, Ibaraki, Japan
| | - Akihiko Konagaya
- Molecular Robotics Research Institute, Limited, Kyowa Create Dai-ichi, Minato-ku, Tokyo, Japan
| | - Hiroshi Suzuki
- Department of Pharmacy, The University of Tokyo Hospital, Faculty of Medicine, The University of Tokyo, Bunkyo-ku, Tokyo, Japan
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Abstract
The literature suggests that effective defence against tumour cells requires contributions from both Natural Killer (NK) cells and CD8+ T cells. NK cells are spontaneously active against infected target cells, whereas CD8+ T cells take some times to activate cell called as cell-specific targeting, to kill the virus. The interaction between NK cells and tumour cells has produced the other CD8+ T cell, called tumour-specific CD8+ T cells. We illustrate the tumour–immune interaction through mathematical modelling by considering the cell cycle. The interaction of the cells is described by a system of delay differential equations, and the delay, τ represent time taken for tumour cell reside interphase. The stability analysis and the bifurcation behaviour of the system are analysed. We established the stability of the model by analysing the characteristic equation to produce a stability region. The stability region is split into two regions, tumour decay and tumour growth. By applying the Routh–Hurwitz Criteria, the analysis of the trivial and interior equilibrium point of the model provides conditions for stability and is illustrated in the stability map. Numerical simulation is carried out to show oscillations through Hopf Bifurcation, and stability switching is found for the delay system. The result also showed that the interaction of NK cells with tumour cells could suppress tumour cells since it can increase the population of CD8+ T cells. This concluded that the inclusion of delay and immune responses (NK-CD8+ T cells) into consideration gives us a deep insight into the tumour growth and helps us understand how their interactions contribute to kill tumour cells.
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ZHANG ZHIBO, LI SHENG, SI PENG, LI XUEFANG, HE XIONGXIONG. A TUMOR-IMMUNE MODEL WITH MIXED IMMUNOTHERAPY AND CHEMOTHERAPY: QUALITATIVE ANALYSIS AND OPTIMAL CONTROL. J BIOL SYST 2022. [DOI: 10.1142/s0218339022500127] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
We develop a mathematical model of tumor-immune interactions, including six populations (tumor cells, CD8[Formula: see text]T cells, natural killer (NK) cells, dendritic cells, helper T cells, cytokine interleukin-12 (IL-12)) and three potential treatments (chemotherapy, Tumor-infiltrating lymphocyte (TIL) therapy and IL-12 therapy). We characterize the dynamics of our model without treatment through stability and sensitivity analysis, which provides a broad understanding of the long-term qualitative behavior. To find the best combination of the chemo-immunotherapy regimens to eliminate tumors, we formulate an optimal control problem with path constraints of total drug dose and solve it numerically with the optimal control software Pyomo. We also simulate the scenarios of traditional treatment protocols as a comparison and find that our optimal treatment strategies have a better therapeutic effect. In addition, numerical simulation results show that IL-12 therapy is a good adjunctive therapy and has a high potential for inhibiting a large tumor in combination with other therapy. In most cases, combination therapy is more effective than a single treatment.
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Affiliation(s)
- ZHIBO ZHANG
- College of Information Engineering, Zhejiang University of Technology, Hangzhou 310023, P. R. China
| | - SHENG LI
- College of Information Engineering, Zhejiang University of Technology, Hangzhou 310023, P. R. China
| | - PENG SI
- College of Information Engineering, Zhejiang University of Technology, Hangzhou 310023, P. R. China
| | - XUEFANG LI
- School of Intelligent Systems, Engineering Sun Yat-Sen University, Guangzhou 510275, P. R. China
| | - XIONGXIONG HE
- College of Information Engineering, Zhejiang University of Technology, Hangzhou 310023, P. R. China
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Dai X, Li J, Chen Y, Ostrikov KK. When Onco-Immunotherapy Meets Cold Atmospheric Plasma: Implications on CAR-T Therapies. Front Oncol 2022; 12:837995. [PMID: 35280746 PMCID: PMC8905244 DOI: 10.3389/fonc.2022.837995] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/22/2021] [Accepted: 01/31/2022] [Indexed: 12/03/2022] Open
Abstract
T cells engineered with chimeric antigen receptors (CAR) have demonstrated its widespread efficacy as a targeted immunotherapeutic modality. Yet, concerns on its specificity, efficacy and generalization prevented it from being established into a first-line approach against cancers. By reviewing challenges limiting its clinical application, ongoing efforts trying to resolve them, and opportunities that emerging oncotherapeutic modalities may bring to temper these challenges, we conclude that careful CAR design should be done to avoid the off-tumor effect, enhance the efficacy of solid tumor treatment, improve product comparability, and resolve problems such as differential efficacies of co-stimulatory molecules, cytokine storm, tumor lysis syndrome, myelosuppression and severe hepatotoxicity. As a promising solution, we propose potential synergies between CAR-T therapies and cold atmospheric plasma, an emerging onco-therapeutic strategy relying on reactive species, towards improved therapeutic efficacies and enhanced safety that deserve extensive investigations.
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Affiliation(s)
- Xiaofeng Dai
- Wuxi School of Medicine, Jiangnan University, Wuxi, China.,CAPsoul Biotechnology Company, Ltd, Beijing, China
| | - Jitian Li
- Henan Luoyang Orthopedic Hospital (Henan Provincial Orthopedic Hospital)/Henan Provincial Orthopedic Institute, Zhengzhou, China
| | - Yiming Chen
- Wuxi School of Medicine, Jiangnan University, Wuxi, China
| | - Kostya Ken Ostrikov
- School of Chemistry and Physics and Centre for Biomedical Technologies, Queensland University of Technology, Brisbane, QLD, Australia
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Mahasa KJ, Ouifki R, Eladdadi A, Pillis LD. A combination therapy of oncolytic viruses and chimeric antigen receptor T cells: a mathematical model proof-of-concept. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2022; 19:4429-4457. [PMID: 35430822 DOI: 10.3934/mbe.2022205] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
Combining chimeric antigen receptor T (CAR-T) cells with oncolytic viruses (OVs) has recently emerged as a promising treatment approach in preclinical studies that aim to alleviate some of the barriers faced by CAR-T cell therapy. In this study, we address by means of mathematical modeling the main question of whether a single dose or multiple sequential doses of CAR-T cells during the OVs therapy can have a synergetic effect on tumor reduction. To that end, we propose an ordinary differential equations-based model with virus-induced synergism to investigate potential effects of different regimes that could result in efficacious combination therapy against tumor cell populations. Model simulations show that, while the treatment with a single dose of CAR-T cells is inadequate to eliminate all tumor cells, combining the same dose with a single dose of OVs can successfully eliminate the tumor in the absence of virus-induced synergism. However, in the presence of virus-induced synergism, the same combination therapy fails to eliminate the tumor. Furthermore, it is shown that if the intensity of virus-induced synergy and/or virus oncolytic potency is high, then the induced CAR-T cell response can inhibit virus oncolysis. Additionally, the simulations show a more robust synergistic effect on tumor cell reduction when OVs and CAR-T cells are administered simultaneously compared to the combination treatment where CAR-T cells are administered first or after OV injection. Our findings suggest that the combination therapy of CAR-T cells and OVs seems unlikely to be effective if the virus-induced synergistic effects are included when genetically engineering oncolytic viral vectors.
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Affiliation(s)
- Khaphetsi Joseph Mahasa
- Department of Mathematics and Computer Science, National University of Lesotho, Roma 180, Maseru, Lesotho
| | - Rachid Ouifki
- Department of Mathematics and Applied Mathematics, North-West University, Mafikeng campus, Private Bag X2046, Mmabatho 2735, South Africa
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Delay induced interaction of humoral- and cell-mediated immune responses with cancer. Theory Biosci 2022; 141:27-40. [DOI: 10.1007/s12064-022-00364-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/05/2021] [Accepted: 01/22/2022] [Indexed: 11/25/2022]
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Shafiekhani S, Jafari A, Jafarzadeh L, Sadeghi V, Gheibi N. Predicting efficacy of 5-fluorouracil therapy via a mathematical model with fuzzy uncertain parameters. JOURNAL OF MEDICAL SIGNALS & SENSORS 2022; 12:202-218. [PMID: 36120402 PMCID: PMC9480509 DOI: 10.4103/jmss.jmss_92_21] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2021] [Revised: 11/12/2021] [Accepted: 01/21/2022] [Indexed: 11/08/2022]
Abstract
Background: Due to imprecise/missing data used for parameterization of ordinary differential equations (ODEs), model parameters are uncertain. Uncertainty of parameters has hindered the application of ODEs that require accurate parameters. Methods: We extended an available ODE model of tumor-immune system interactions via fuzzy logic to illustrate the fuzzification procedure of an ODE model. The fuzzy ODE (FODE) model assigns a fuzzy number to the parameters, to capture parametric uncertainty. We used the FODE model to predict tumor and immune cell dynamics and to assess the efficacy of 5-fluorouracil (5-FU) chemotherapy. Result: FODE model investigates how parametric uncertainty affects the uncertainty band of cell dynamics in the presence and absence of 5-FU treatment. In silico experiments revealed that the frequent 5-FU injection created a beneficial tumor microenvironment that exerted detrimental effects on tumor cells by enhancing the infiltration of CD8+ T cells, and natural killer cells, and decreasing that of myeloid-derived suppressor cells. The global sensitivity analysis was proved model robustness against random perturbation to parameters. Conclusion: ODE models with fuzzy uncertain kinetic parameters cope with insufficient/imprecise experimental data in the field of mathematical oncology and can predict cell dynamics uncertainty band.
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Investigating Optimal Chemotherapy Options for Osteosarcoma Patients through a Mathematical Model. Cells 2021; 10:cells10082009. [PMID: 34440778 PMCID: PMC8394778 DOI: 10.3390/cells10082009] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/07/2021] [Revised: 08/03/2021] [Accepted: 08/04/2021] [Indexed: 12/22/2022] Open
Abstract
Simple Summary Osteosarcoma is a rare type of cancer with poor prognoses. However, to the best of our knowledge, there are no mathematical models that study the impact of chemotherapy treatments on the osteosarcoma microenvironment. In this study, we developed a data driven mathematical model to analyze the dynamics of the important players in three groups of osteosarcoma tumors with distinct immune patterns in the presence of the most common chemotherapy drugs. The results indicate that the treatments’ start times and optimal dosages depend on the unique growth rate of the tumor, which implies the necessity of personalized medicine. Furthermore, the developed model can be extended by others to build models that can recommend individual-specific optimal dosages. Abstract Since all tumors are unique, they may respond differently to the same treatments. Therefore, it is necessary to study their characteristics individually to find their best treatment options. We built a mathematical model for the interactions between the most common chemotherapy drugs and the osteosarcoma microenvironments of three clusters of tumors with unique immune profiles. We then investigated the effects of chemotherapy with different treatment regimens and various treatment start times on the behaviors of immune and cancer cells in each cluster. Saliently, we suggest the optimal drug dosages for the tumors in each cluster. The results show that abundances of dendritic cells and HMGB1 increase when drugs are given and decrease when drugs are absent. Populations of helper T cells, cytotoxic cells, and IFN-γ grow, and populations of cancer cells and other immune cells shrink during treatment. According to the model, the MAP regimen does a good job at killing cancer, and is more effective than doxorubicin and cisplatin combined or methotrexate alone. The results also indicate that it is important to consider the tumor’s unique growth rate when deciding the treatment details, as fast growing tumors need early treatment start times and high dosages.
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Sancho-Araiz A, Mangas-Sanjuan V, Trocóniz IF. The Role of Mathematical Models in Immuno-Oncology: Challenges and Future Perspectives. Pharmaceutics 2021; 13:pharmaceutics13071016. [PMID: 34371708 PMCID: PMC8309057 DOI: 10.3390/pharmaceutics13071016] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2021] [Revised: 06/24/2021] [Accepted: 06/29/2021] [Indexed: 12/12/2022] Open
Abstract
Immuno-oncology (IO) focuses on the ability of the immune system to detect and eliminate cancer cells. Since the approval of the first immune checkpoint inhibitor, immunotherapies have become a major player in oncology treatment and, in 2021, represented the highest number of approved drugs in the field. In spite of this, there is still a fraction of patients that do not respond to these therapies and develop resistance mechanisms. In this sense, mathematical models offer an opportunity to identify predictive biomarkers, optimal dosing schedules and rational combinations to maximize clinical response. This work aims to outline the main therapeutic targets in IO and to provide a description of the different mathematical approaches (top-down, middle-out, and bottom-up) integrating the cancer immunity cycle with immunotherapeutic agents in clinical scenarios. Among the different strategies, middle-out models, which combine both theoretical and evidence-based description of tumor growth and immunological cell-type dynamics, represent an optimal framework to evaluate new IO strategies.
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Affiliation(s)
- Aymara Sancho-Araiz
- Department of Pharmaceutical Technology and Chemistry, School of Pharmacy and Nutrition, University of Navarra, 31009 Pamplona, Spain; (A.S.-A.); (I.F.T.)
- Navarra Institute for Health Research (IdiSNA), 31009 Pamplona, Spain
| | - Victor Mangas-Sanjuan
- Department of Pharmacy and Pharmaceutical Technology and Parasitology, University of Valencia, 46100 Valencia, Spain
- Interuniversity Research Institute for Molecular Recognition and Technological Development, 46100 Valencia, Spain
- Correspondence: ; Tel.: +34-96354-3351
| | - Iñaki F. Trocóniz
- Department of Pharmaceutical Technology and Chemistry, School of Pharmacy and Nutrition, University of Navarra, 31009 Pamplona, Spain; (A.S.-A.); (I.F.T.)
- Navarra Institute for Health Research (IdiSNA), 31009 Pamplona, Spain
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15
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Senekal NS, Mahasa KJ, Eladdadi A, de Pillis L, Ouifki R. Natural Killer Cells Recruitment in Oncolytic Virotherapy: A Mathematical Model. Bull Math Biol 2021; 83:75. [PMID: 34008149 DOI: 10.1007/s11538-021-00903-6] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/07/2020] [Accepted: 04/20/2021] [Indexed: 01/17/2023]
Abstract
In this paper, we investigate how natural killer (NK) cell recruitment to the tumor microenvironment (TME) affects oncolytic virotherapy. NK cells play a major role against viral infections. They are, however, known to induce early viral clearance of oncolytic viruses, which hinders the overall efficacy of oncolytic virotherapy. Here, we formulate and analyze a simple mathematical model of the dynamics of the tumor, OV and NK cells using currently available preclinical information. The aim of this study is to characterize conditions under which the synergistic balance between OV-induced NK responses and required viral cytopathicity may or may not result in a successful treatment. In this study, we found that NK cell recruitment to the TME must take place neither too early nor too late in the course of OV infection so that treatment will be successful. NK cell responses are most influential at either early (partly because of rapid response of NK cells to viral infections or antigens) or later (partly because of antitumoral ability of NK cells) stages of oncolytic virotherapy. The model also predicts that: (a) an NK cell response augments oncolytic virotherapy only if viral cytopathicity is weak; (b) the recruitment of NK cells modulates tumor growth; and (c) the depletion of activated NK cells within the TME enhances the probability of tumor escape in oncolytic virotherapy. Taken together, our model results demonstrate that OV infection is crucial, not just to cytoreduce tumor burden, but also to induce the stronger NK cell response necessary to achieve complete or at least partial tumor remission. Furthermore, our modeling framework supports combination therapies involving NK cells and OV which are currently used in oncolytic immunovirotherapy to treat several cancer types.
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Affiliation(s)
- Noma Susan Senekal
- Department of Mathematics and Computer Science, National University of Lesotho, Roma, Maseru, Lesotho.
| | - Khaphetsi Joseph Mahasa
- Department of Mathematics and Computer Science, National University of Lesotho, Roma, Maseru, Lesotho
| | | | | | - Rachid Ouifki
- Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria, South Africa
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16
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Le T, Su S, Kirshtein A, Shahriyari L. Data-Driven Mathematical Model of Osteosarcoma. Cancers (Basel) 2021; 13:cancers13102367. [PMID: 34068946 PMCID: PMC8156666 DOI: 10.3390/cancers13102367] [Citation(s) in RCA: 20] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/16/2021] [Revised: 05/10/2021] [Accepted: 05/10/2021] [Indexed: 12/22/2022] Open
Abstract
As the immune system has a significant role in tumor progression, in this paper, we develop a data-driven mathematical model to study the interactions between immune cells and the osteosarcoma microenvironment. Osteosarcoma tumors are divided into three clusters based on their relative abundance of immune cells as estimated from their gene expression profiles. We then analyze the tumor progression and effects of the immune system on cancer growth in each cluster. Cluster 3, which had approximately the same number of naive and M2 macrophages, had the slowest tumor growth, and cluster 2, with the highest population of naive macrophages, had the highest cancer population at the steady states. We also found that the fastest growth of cancer occurred when the anti-tumor immune cells and cytokines, including dendritic cells, helper T cells, cytotoxic cells, and IFN-γ, switched from increasing to decreasing, while the dynamics of regulatory T cells switched from decreasing to increasing. Importantly, the most impactful immune parameters on the number of cancer and total cells were the activation and decay rates of the macrophages and regulatory T cells for all clusters. This work presents the first osteosarcoma progression model, which can be later extended to investigate the effectiveness of various osteosarcoma treatments.
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Affiliation(s)
- Trang Le
- Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA 01003, USA; (T.L.); (S.S.)
| | - Sumeyye Su
- Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA 01003, USA; (T.L.); (S.S.)
| | - Arkadz Kirshtein
- Department of Mathematics, Tufts University, Medford, MA 02155, USA;
| | - Leili Shahriyari
- Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA 01003, USA; (T.L.); (S.S.)
- Correspondence:
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17
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Modeling the effect of immunotherapies on human castration-resistant prostate cancer. J Theor Biol 2020; 509:110500. [PMID: 32980372 DOI: 10.1016/j.jtbi.2020.110500] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/24/2020] [Revised: 07/28/2020] [Accepted: 09/17/2020] [Indexed: 12/31/2022]
Abstract
In this paper we analyze the potential effect of immunotherapies on castration-resistant form of human Prostate Cancer (PCa). In particular, we examine the potential effect of the dendritic vaccine sipuleucel-T, the only currently available immunotherapy option for advanced PCa, and of ipilimumab, a drug targeting the Cytotoxic T-Lymphocyte Antigen 4 (CTLA4), exposed on the CTLs membrane, currently under Phase II clinical trial. The model, building on the one by Rutter and Kuang, includes different types of immune cells and interactions and is parameterized on available data. Our results show that the vaccine has only a very limited effect on PCa, while repeated treatments with ipilimumab appear potentially capable of controlling and even eradicating an androgen-independent prostate cancer. From a mathematical analysis of a simplified model, it seems likely that, under continuous administration of ipilimumab, the system lies in a bistable situation where both the no-tumor equilibrium and the high-tumor equilibrium are attractive. The schedule of periodic treatments could then determine the outcome, and mathematical models could help determine an optimal schedule.
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Griffiths JI, Wallet P, Pflieger LT, Stenehjem D, Liu X, Cosgrove PA, Leggett NA, McQuerry JA, Shrestha G, Rossetti M, Sunga G, Moos PJ, Adler FR, Chang JT, Sharma S, Bild AH. Circulating immune cell phenotype dynamics reflect the strength of tumor-immune cell interactions in patients during immunotherapy. Proc Natl Acad Sci U S A 2020; 117:16072-16082. [PMID: 32571915 PMCID: PMC7355015 DOI: 10.1073/pnas.1918937117] [Citation(s) in RCA: 54] [Impact Index Per Article: 13.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
Abstract
The extent to which immune cell phenotypes in the peripheral blood reflect within-tumor immune activity prior to and early in cancer therapy is unclear. To address this question, we studied the population dynamics of tumor and immune cells, and immune phenotypic changes, using clinical tumor and immune cell measurements and single-cell genomic analyses. These samples were serially obtained from a cohort of advanced gastrointestinal cancer patients enrolled in a trial with chemotherapy and immunotherapy. Using an ecological population model, fitted to clinical tumor burden and immune cell abundance data from each patient, we find evidence of a strong tumor-circulating immune cell interaction in responder patients but not in those patients that progress on treatment. Upon initiation of therapy, immune cell abundance increased rapidly in responsive patients, and once the peak level is reached tumor burden decreases, similar to models of predator-prey interactions; these dynamic patterns were absent in nonresponder patients. To interrogate phenotype dynamics of circulating immune cells, we performed single-cell RNA sequencing at serial time points during treatment. These data show that peripheral immune cell phenotypes were linked to the increased strength of patients' tumor-immune cell interaction, including increased cytotoxic differentiation and strong activation of interferon signaling in peripheral T cells in responder patients. Joint modeling of clinical and genomic data highlights the interactions between tumor and immune cell populations and reveals how variation in patient responsiveness can be explained by differences in peripheral immune cell signaling and differentiation soon after the initiation of immunotherapy.
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Affiliation(s)
- Jason I Griffiths
- Department of Medical Oncology & Therapeutics Research, City of Hope National Medical Center, Duarte, CA 91010
- Department of Mathematics, University of Utah, Salt Lake City, UT 84112
| | - Pierre Wallet
- Department of Medical Oncology & Therapeutics Research, City of Hope National Medical Center, Duarte, CA 91010
| | - Lance T Pflieger
- Department of Medical Oncology & Therapeutics Research, City of Hope National Medical Center, Duarte, CA 91010
| | - David Stenehjem
- College of Pharmacy, University of Minnesota, Duluth, MN 55812
| | - Xuan Liu
- Department of Integrative Biology and Pharmacology, School of Medicine, School of Biomedical Informatics, The University of Texas Health Science Center at Houston, Houston, TX 77030
| | - Patrick A Cosgrove
- Department of Medical Oncology & Therapeutics Research, City of Hope National Medical Center, Duarte, CA 91010
| | - Neena A Leggett
- Department of Integrative Biology and Pharmacology, School of Medicine, School of Biomedical Informatics, The University of Texas Health Science Center at Houston, Houston, TX 77030
| | - Jasmine A McQuerry
- Department of Medical Oncology & Therapeutics Research, City of Hope National Medical Center, Duarte, CA 91010
- Department of Oncological Sciences, School of Medicine, University of Utah, Salt Lake City, UT 84112
- Department of Pharmacology and Toxicology, College of Pharmacy, University of Utah, Salt Lake City, UT 84112
| | - Gajendra Shrestha
- Department of Pharmacology and Toxicology, College of Pharmacy, University of Utah, Salt Lake City, UT 84112
| | - Maura Rossetti
- Department of Pathology and Laboratory Medicine, David Geffen School of Medicine, Los Angeles, CA 90095
| | - Gemalene Sunga
- Department of Pathology and Laboratory Medicine, David Geffen School of Medicine, Los Angeles, CA 90095
| | - Philip J Moos
- Department of Pharmacology and Toxicology, College of Pharmacy, University of Utah, Salt Lake City, UT 84112
| | - Frederick R Adler
- Department of Mathematics, University of Utah, Salt Lake City, UT 84112
| | - Jeffrey T Chang
- Department of Integrative Biology and Pharmacology, School of Medicine, School of Biomedical Informatics, The University of Texas Health Science Center at Houston, Houston, TX 77030
| | - Sunil Sharma
- Translational Oncology Research & Drug Discovery, Translational Genomics Research Institute, Phoenix, AZ 85004
| | - Andrea H Bild
- Department of Medical Oncology & Therapeutics Research, City of Hope National Medical Center, Duarte, CA 91010;
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Makaryan SZ, Finley SD. Enhancing network activation in natural killer cells: predictions from in silico modeling. Integr Biol (Camb) 2020; 12:109-121. [PMID: 32409824 PMCID: PMC7480959 DOI: 10.1093/intbio/zyaa008] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/20/2019] [Revised: 03/28/2020] [Accepted: 03/30/2020] [Indexed: 01/08/2023]
Abstract
Natural killer (NK) cells are part of the innate immune system and are capable of killing diseased cells. As a result, NK cells are being used for adoptive cell therapies for cancer patients. The activation of NK cell stimulatory receptors leads to a cascade of intracellular phosphorylation reactions, which activates key signaling species that facilitate the secretion of cytolytic molecules required for cell killing. Strategies that maximize the activation of such intracellular species can increase the likelihood of NK cell killing upon contact with a cancer cell and thereby improve efficacy of NK cell-based therapies. However, due to the complexity of intracellular signaling, it is difficult to deduce a priori which strategies can enhance species activation. Therefore, we constructed a mechanistic model of the CD16, 2B4 and NKG2D signaling pathways in NK cells to simulate strategies that enhance signaling. The model predictions were fit to published data and validated with a separate dataset. Model simulations demonstrate strong network activation when the CD16 pathway is stimulated. The magnitude of species activation is most sensitive to the receptor's initial concentration and the rate at which the receptor is activated. Co-stimulation of CD16 and NKG2D in silico required fewer ligands to achieve half-maximal activation than other combinations, suggesting co-stimulating these pathways is most effective in activating the species. We applied the model to predict the effects of perturbing the signaling network and found two strategies that can potently enhance network activation. When the availability of ligands is low, it is more influential to engineer NK cell receptors that are resistant to proteolytic cleavage. In contrast, for high ligand concentrations, inhibiting phosphatase activity leads to sustained species activation. The work presented here establishes a framework for understanding the complex, nonlinear aspects of NK cell signaling and provides detailed strategies for enhancing NK cell activation.
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Affiliation(s)
- Sahak Z. Makaryan
- Department of Biomedical Engineering, University of Southern California, Los Angeles, CA, USA
| | - Stacey D. Finley
- Department of Biomedical Engineering, Mork Family Department of Chemical Engineering and Materials Science, and Department of Biological Sciences, University of Southern California, Los Angeles, CA, USA
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20
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Makaryan SZ, Cess CG, Finley SD. Modeling immune cell behavior across scales in cancer. WILEY INTERDISCIPLINARY REVIEWS-SYSTEMS BIOLOGY AND MEDICINE 2020; 12:e1484. [PMID: 32129950 PMCID: PMC7317398 DOI: 10.1002/wsbm.1484] [Citation(s) in RCA: 20] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/09/2019] [Revised: 01/07/2020] [Accepted: 02/04/2020] [Indexed: 12/17/2022]
Abstract
Detailed, mechanistic models of immune cell behavior across multiple scales in the context of cancer provide clinically relevant insights needed to understand existing immunotherapies and develop more optimal treatment strategies. We highlight mechanistic models of immune cells and their ability to become activated and promote tumor cell killing. These models capture various aspects of immune cells: (a) single‐cell behavior by predicting the dynamics of intracellular signaling networks in individual immune cells, (b) multicellular interactions between tumor and immune cells, and (c) multiscale dynamics across space and different levels of biological organization. Computational modeling is shown to provide detailed quantitative insight into immune cell behavior and immunotherapeutic strategies. However, there are gaps in the literature, and we suggest areas where additional modeling efforts should be focused to more prominently impact our understanding of the complexities of the immune system in the context of cancer. This article is categorized under:Biological Mechanisms > Cell Signaling Models of Systems Properties and Processes > Mechanistic Models Models of Systems Properties and Processes > Cellular Models
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Affiliation(s)
- Sahak Z Makaryan
- Department of Biomedical Engineering, University of Southern California, Los Angeles, California, USA
| | - Colin G Cess
- Department of Biomedical Engineering, University of Southern California, Los Angeles, California, USA
| | - Stacey D Finley
- Department of Biomedical Engineering, Mork Family Department of Chemical Engineering and Materials Science, Department of Biological Sciences, University of Southern California, Los Angeles, California, USA
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21
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Makhlouf AM, El-Shennawy L, Elkaranshawy HA. Mathematical Modelling for the Role of CD4 +T Cells in Tumor-Immune Interactions. COMPUTATIONAL AND MATHEMATICAL METHODS IN MEDICINE 2020; 2020:7187602. [PMID: 32148558 PMCID: PMC7049850 DOI: 10.1155/2020/7187602] [Citation(s) in RCA: 21] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/04/2019] [Revised: 12/17/2019] [Accepted: 01/20/2020] [Indexed: 12/27/2022]
Abstract
Mathematical modelling has been used to study tumor-immune cell interaction. Some models were proposed to examine the effect of circulating lymphocytes, natural killer cells, and CD8+T cells, but they neglected the role of CD4+T cells. Other models were constructed to study the role of CD4+T cells but did not consider the role of other immune cells. In this study, we propose a mathematical model, in the form of a system of nonlinear ordinary differential equations, that predicts the interaction between tumor cells and natural killer cells, CD4+T cells, CD8+T cells, and circulating lymphocytes with or without immunotherapy and/or chemotherapy. This system is stiff, and the Runge-Kutta method failed to solve it. Consequently, the "Adams predictor-corrector" method is used. The results reveal that the patient's immune system can overcome small tumors; however, if the tumor is large, adoptive therapy with CD4+T cells can be an alternative to both CD8+T cell therapy and cytokines in some cases. Moreover, CD4+T cell therapy could replace chemotherapy depending upon tumor size. Even if a combination of chemotherapy and immunotherapy is necessary, using CD4+T cell therapy can better reduce the dose of the associated chemotherapy compared to using combined CD8+T cells and cytokine therapy. Stability analysis is performed for the studied patients. It has been found that all equilibrium points are unstable, and a condition for preventing tumor recurrence after treatment has been deduced. Finally, a bifurcation analysis is performed to study the effect of varying system parameters on the stability, and bifurcation points are specified. New equilibrium points are created or demolished at some bifurcation points, and stability is changed at some others. Hence, for systems turning to be stable, tumors can be eradicated without the possibility of recurrence. The proposed mathematical model provides a valuable tool for designing patients' treatment intervention strategies.
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Affiliation(s)
- Ahmed M. Makhlouf
- Department of Engineering Mathematics and Physics, Faculty of Engineering, Alexandria University, Alexandria, Egypt
| | - Lamiaa El-Shennawy
- Institute of Graduate Studies and Research, Alexandria University, Alexandria, Egypt
| | - Hesham A. Elkaranshawy
- Department of Engineering Mathematics and Physics, Faculty of Engineering, Alexandria University, Alexandria, Egypt
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22
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Wang Q, Wang Z, Wu Y, Klinke DJ. An in silico exploration of combining Interleukin-12 with Oxaliplatin to treat liver-metastatic colorectal cancer. BMC Cancer 2020; 20:26. [PMID: 31914948 PMCID: PMC6950805 DOI: 10.1186/s12885-019-6500-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2019] [Accepted: 12/24/2019] [Indexed: 11/10/2022] Open
Abstract
Background Combining anti-cancer therapies with orthogonal modes of action, such as direct cytotoxicity and immunostimulatory, hold promise for expanding clinical benefit to patients with metastatic disease. For instance, a chemotherapy agent Oxaliplatin (OXP) in combination with Interleukin-12 (IL-12) can eliminate pre-existing liver metastatic colorectal cancer and protect from relapse in a murine model. However, the underlying dynamics associated with the targeted biology and the combinatorial space consisting of possible dosage and timing of each therapy present challenges for optimizing treatment regimens. To address some of these challenges, we developed a predictive simulation platform for optimizing dose and timing of the combination therapy involving Mifepristone-induced IL-12 and chemotherapy agent OXP. Methods A multi-scale mathematical model comprised of impulsive ordinary differential equations was developed to describe the interaction between the immune system and tumor cells in response to the combined IL-12 and OXP therapy. An ensemble of model parameters were calibrated to published experimental data using a genetic algorithm and used to represent three different phenotypes: responders, partial-responders, and non-responders. Results The multi-scale model captures tumor growth patterns of the three phenotypic responses observed in mice in response to the combination therapy against a tumor re-challenge and was used to explore the impacts of changing the dose and timing of the mixed immune-chemotherapy on tumor growth subjected to a tumor re-challenge in mice. An increased ratio of CD8 + T effectors to regulatory T cells during and after treatment was key to improve tumor control in the responder cohort. Sensitivity analysis indicates that combined OXP and IL-12 therapy worked more efficiently in responders by increased priming of T cells, enhanced CD8 + T cell-mediated killing, and functional inhibition of regulatory T cells. In a virtual cohort that mimics non-responders and partial-responders, simulations show that an increased dose of OXP alone would improve the response. In addition, enhanced IL-12 expression alone or an increased number of treatment cycles of the mixed immune-chemotherapy can barely improve tumor control for non-responders and partial responders. Conclusions Overall, this study illustrates how mechanistic models can be used for in silico screening of the optimal therapeutic dose and timing in combined cancer treatment strategies.
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Affiliation(s)
- Qing Wang
- Department of Computer Sciences, Mathematics, and Engineering, Shepherd University, Shepherdstown, 25443, WV, USA
| | - Zhijun Wang
- Department of Computer Sciences, Mathematics, and Engineering, Shepherd University, Shepherdstown, 25443, WV, USA
| | - Yan Wu
- Department of Mathematical Sciences, Georgia Southern University, Statesboro, 30458, GA, USA
| | - David J Klinke
- Department of Chemical and Biomedical Engineering and WVU Cancer Institute, West Virginia University, Morgantown, 25606, WV, USA. .,Department of Microbiology, Immunology, & Cell Biology, West Virginia University, Morgantown, 25606, WV, USA.
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23
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Sigal D, Przedborski M, Sivaloganathan D, Kohandel M. Mathematical modelling of cancer stem cell-targeted immunotherapy. Math Biosci 2019; 318:108269. [DOI: 10.1016/j.mbs.2019.108269] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/15/2019] [Revised: 09/17/2019] [Accepted: 10/05/2019] [Indexed: 12/15/2022]
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Khazen R, Müller S, Lafouresse F, Valitutti S, Cussat-Blanc S. Sequential adjustment of cytotoxic T lymphocyte densities improves efficacy in controlling tumor growth. Sci Rep 2019; 9:12308. [PMID: 31444380 PMCID: PMC6707257 DOI: 10.1038/s41598-019-48711-2] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/23/2019] [Accepted: 08/09/2019] [Indexed: 12/30/2022] Open
Abstract
Understanding the human cytotoxic T lymphocyte (CTL) biology is crucial to develop novel strategies aiming at maximizing their lytic capacity against cancer cells. Here we introduce an agent-based model, calibrated on population-scale experimental data that allows quantifying human CTL per capita killing. Our model highlights higher individual CTL killing capacity at lower CTL densities and fits experimental data of human melanoma cell killing. The model allows extending the analysis over prolonged time frames, difficult to investigate experimentally, and reveals that initial high CTL densities hamper efficacy to control melanoma growth. Computational analysis forecasts that sequential addition of fresh CTL cohorts improves tumor growth control. In vivo experimental data, obtained in a mouse melanoma model, confirm this prediction. Taken together, our results unveil the impact that sequential adjustment of cellular densities has on enhancing CTL efficacy over long-term confrontation with tumor cells. In perspective, they can be instrumental to refine CTL-based therapeutic strategies aiming at controlling tumor growth.
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Affiliation(s)
- Roxana Khazen
- Centre de Recherches en Cancérologie de Toulouse (CRCT), UMR 1037 INSERM/ Université Toulouse III Paul Sabatier, «Equipe labellisée Ligue Nationale contre le cancer 2018», INSERM, Toulouse, France.,INSERM U1223, Dynamics of Immune Responses Unit, Institut Pasteur, 75015, Paris, France
| | - Sabina Müller
- Centre de Recherches en Cancérologie de Toulouse (CRCT), UMR 1037 INSERM/ Université Toulouse III Paul Sabatier, «Equipe labellisée Ligue Nationale contre le cancer 2018», INSERM, Toulouse, France
| | - Fanny Lafouresse
- Centre de Recherches en Cancérologie de Toulouse (CRCT), UMR 1037 INSERM/ Université Toulouse III Paul Sabatier, «Equipe labellisée Ligue Nationale contre le cancer 2018», INSERM, Toulouse, France
| | - Salvatore Valitutti
- Centre de Recherches en Cancérologie de Toulouse (CRCT), UMR 1037 INSERM/ Université Toulouse III Paul Sabatier, «Equipe labellisée Ligue Nationale contre le cancer 2018», INSERM, Toulouse, France. .,Department of Pathology, Institut Universitaire du Cancer-Oncopole de Toulouse, 31059, Toulouse, France.
| | - Sylvain Cussat-Blanc
- Institute of Advanced Technologies in Living Sciences, CNRS - USR3505, Toulouse, France.,University of Toulouse, Institute of Research in Informatics of Toulouse, CNRS - UMR5505, Toulouse, France
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Baleanu D, Jajarmi A, Sajjadi SS, Mozyrska D. A new fractional model and optimal control of a tumor-immune surveillance with non-singular derivative operator. CHAOS (WOODBURY, N.Y.) 2019; 29:083127. [PMID: 31472488 DOI: 10.1063/1.5096159] [Citation(s) in RCA: 33] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/03/2023]
Abstract
In this paper, we present a new fractional-order mathematical model for a tumor-immune surveillance mechanism. We analyze the interactions between various tumor cell populations and immune system via a system of fractional differential equations (FDEs). An efficient numerical procedure is suggested to solve these FDEs by considering singular and nonsingular derivative operators. An optimal control strategy for investigating the effect of chemotherapy treatment on the proposed fractional model is also provided. Simulation results show that the new presented model based on the fractional operator with Mittag-Leffler kernel represents various asymptomatic behaviors that tracks the real data more accurately than the other fractional- and integer-order models. Numerical simulations also verify the efficiency of the proposed optimal control strategy and show that the growth of the naive tumor cell population is successfully declined.
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Affiliation(s)
- D Baleanu
- Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, 06530 Ankara, Turkey
| | - A Jajarmi
- Department of Electrical Engineering, University of Bojnord, P.O. Box 94531-1339, Bojnord, Iran
| | - S S Sajjadi
- Department of Electrical and Computer Engineering, Hakim Sabzevari University, Sabzevar, Iran
| | - D Mozyrska
- Faculty of Computer Science, Białystok University of Technology, Wiejska 45A, Białystok, Poland
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26
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Sun X, Hu B. Mathematical modeling and computational prediction of cancer drug resistance. Brief Bioinform 2019; 19:1382-1399. [PMID: 28981626 PMCID: PMC6402530 DOI: 10.1093/bib/bbx065] [Citation(s) in RCA: 59] [Impact Index Per Article: 11.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2017] [Indexed: 12/23/2022] Open
Abstract
Diverse forms of resistance to anticancer drugs can lead to the failure of chemotherapy. Drug resistance is one of the most intractable issues for successfully treating cancer in current clinical practice. Effective clinical approaches that could counter drug resistance by restoring the sensitivity of tumors to the targeted agents are urgently needed. As numerous experimental results on resistance mechanisms have been obtained and a mass of high-throughput data has been accumulated, mathematical modeling and computational predictions using systematic and quantitative approaches have become increasingly important, as they can potentially provide deeper insights into resistance mechanisms, generate novel hypotheses or suggest promising treatment strategies for future testing. In this review, we first briefly summarize the current progress of experimentally revealed resistance mechanisms of targeted therapy, including genetic mechanisms, epigenetic mechanisms, posttranslational mechanisms, cellular mechanisms, microenvironmental mechanisms and pharmacokinetic mechanisms. Subsequently, we list several currently available databases and Web-based tools related to drug sensitivity and resistance. Then, we focus primarily on introducing some state-of-the-art computational methods used in drug resistance studies, including mechanism-based mathematical modeling approaches (e.g. molecular dynamics simulation, kinetic model of molecular networks, ordinary differential equation model of cellular dynamics, stochastic model, partial differential equation model, agent-based model, pharmacokinetic–pharmacodynamic model, etc.) and data-driven prediction methods (e.g. omics data-based conventional screening approach for node biomarkers, static network approach for edge biomarkers and module biomarkers, dynamic network approach for dynamic network biomarkers and dynamic module network biomarkers, etc.). Finally, we discuss several further questions and future directions for the use of computational methods for studying drug resistance, including inferring drug-induced signaling networks, multiscale modeling, drug combinations and precision medicine.
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Affiliation(s)
- Xiaoqiang Sun
- Zhong-shan School of Medicine, Sun Yat-Sen University
| | - Bin Hu
- School of Information Science and Engineering, Lanzhou University
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27
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Stiehl T, Marciniak-Czochra A. How to Characterize Stem Cells? Contributions from Mathematical Modeling. CURRENT STEM CELL REPORTS 2019. [DOI: 10.1007/s40778-019-00155-0] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
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28
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Mahlbacher GE, Reihmer KC, Frieboes HB. Mathematical modeling of tumor-immune cell interactions. J Theor Biol 2019; 469:47-60. [PMID: 30836073 DOI: 10.1016/j.jtbi.2019.03.002] [Citation(s) in RCA: 58] [Impact Index Per Article: 11.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/14/2018] [Revised: 02/14/2019] [Accepted: 03/01/2019] [Indexed: 12/22/2022]
Abstract
The anti-tumor activity of the immune system is increasingly recognized as critical for the mounting of a prolonged and effective response to cancer growth and invasion, and for preventing recurrence following resection or treatment. As the knowledge of tumor-immune cell interactions has advanced, experimental investigation has been complemented by mathematical modeling with the goal to quantify and predict these interactions. This succinct review offers an overview of recent tumor-immune continuum modeling approaches, highlighting spatial models. The focus is on work published in the past decade, incorporating one or more immune cell types and evaluating immune cell effects on tumor progression. Due to their relevance to cancer, the following immune cells and their combinations are described: macrophages, Cytotoxic T Lymphocytes, Natural Killer cells, dendritic cells, T regulatory cells, and CD4+ T helper cells. Although important insight has been gained from a mathematical modeling perspective, the development of models incorporating patient-specific data remains an important goal yet to be realized for potential clinical benefit.
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Affiliation(s)
| | - Kara C Reihmer
- Department of Bioengineering, University of Louisville, KY, USA
| | - Hermann B Frieboes
- Department of Bioengineering, University of Louisville, KY, USA; James Graham Brown Cancer Center, University of Louisville, KY, USA; Department of Pharmacology & Toxicology, University of Louisville, KY, USA.
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Gong C, Milberg O, Wang B, Vicini P, Narwal R, Roskos L, Popel AS. A computational multiscale agent-based model for simulating spatio-temporal tumour immune response to PD1 and PDL1 inhibition. J R Soc Interface 2018; 14:rsif.2017.0320. [PMID: 28931635 PMCID: PMC5636269 DOI: 10.1098/rsif.2017.0320] [Citation(s) in RCA: 93] [Impact Index Per Article: 15.5] [Reference Citation Analysis] [Abstract] [Key Words] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/23/2017] [Accepted: 08/30/2017] [Indexed: 12/11/2022] Open
Abstract
When the immune system responds to tumour development, patterns of immune infiltrates emerge, highlighted by the expression of immune checkpoint-related molecules such as PDL1 on the surface of cancer cells. Such spatial heterogeneity carries information on intrinsic characteristics of the tumour lesion for individual patients, and thus is a potential source for biomarkers for anti-tumour therapeutics. We developed a systems biology multiscale agent-based model to capture the interactions between immune cells and cancer cells, and analysed the emergent global behaviour during tumour development and immunotherapy. Using this model, we are able to reproduce temporal dynamics of cytotoxic T cells and cancer cells during tumour progression, as well as three-dimensional spatial distributions of these cells. By varying the characteristics of the neoantigen profile of individual patients, such as mutational burden and antigen strength, a spectrum of pretreatment spatial patterns of PDL1 expression is generated in our simulations, resembling immuno-architectures obtained via immunohistochemistry from patient biopsies. By correlating these spatial characteristics with in silico treatment results using immune checkpoint inhibitors, the model provides a framework for use to predict treatment/biomarker combinations in different cancer types based on cancer-specific experimental data.
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Affiliation(s)
- Chang Gong
- Department of Biomedical Engineering, Johns Hopkins University School of Medicine, Baltimore, MD 21205, USA
| | - Oleg Milberg
- Department of Biomedical Engineering, Johns Hopkins University School of Medicine, Baltimore, MD 21205, USA
| | | | | | | | | | - Aleksander S Popel
- Department of Biomedical Engineering, Johns Hopkins University School of Medicine, Baltimore, MD 21205, USA.,Department of Oncology, Sidney Kimmel Comprehensive Cancer Center, Johns Hopkins University School of Medicine, Baltimore, MD 21205, USA
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Malinzi J, Eladdadi A, Sibanda P. Modelling the spatiotemporal dynamics of chemovirotherapy cancer treatment. JOURNAL OF BIOLOGICAL DYNAMICS 2017; 11:244-274. [PMID: 28537127 DOI: 10.1080/17513758.2017.1328079] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Chemovirotherapy is a combination therapy with chemotherapy and oncolytic viruses. It is gaining more interest and attracting more attention in the clinical setting due to its effective therapy and potential synergistic interactions against cancer. In this paper, we develop and analyse a mathematical model in the form of parabolic non-linear partial differential equations to investigate the spatiotemporal dynamics of tumour cells under chemovirotherapy treatment. The proposed model consists of uninfected and infected tumour cells, a free virus, and a chemotherapeutic drug. The analysis of the model is carried out for both the temporal and spatiotemporal cases. Travelling wave solutions to the spatiotemporal model are used to determine the minimum wave speed of tumour invasion. A sensitivity analysis is performed on the model parameters to establish the key parameters that promote cancer remission during chemovirotherapy treatment. Model analysis of the temporal model suggests that virus burst size and virus infection rate determine the success of the virotherapy treatment, whereas travelling wave solutions to the spatiotemporal model show that tumour diffusivity and growth rate are critical during chemovirotherapy. Simulation results reveal that chemovirotherapy is more effective and a good alternative to either chemotherapy or virotherapy, which is in agreement with the recent experimental studies.
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Affiliation(s)
- Joseph Malinzi
- a Department of Mathematics and Applied Mathematics , University of Pretoria , Hatfield , South Africa
| | - Amina Eladdadi
- b Department of Mathematics , The College of Saint Rose , Albany , New York , USA
| | - Precious Sibanda
- c School of Mathematics, Statistics, and Computer Science , University of KwaZulu Natal , Scottsville , South Africa
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Jin W, Penington CJ, McCue SW, Simpson MJ. A computational modelling framework to quantify the effects of passaging cell lines. PLoS One 2017; 12:e0181941. [PMID: 28750084 PMCID: PMC5531485 DOI: 10.1371/journal.pone.0181941] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/18/2017] [Accepted: 07/10/2017] [Indexed: 11/28/2022] Open
Abstract
In vitro cell culture is routinely used to grow and supply a sufficiently large number of cells for various types of cell biology experiments. Previous experimental studies report that cell characteristics evolve as the passage number increases, and various cell lines can behave differently at high passage numbers. To provide insight into the putative mechanisms that might give rise to these differences, we perform in silico experiments using a random walk model to mimic the in vitro cell culture process. Our results show that it is possible for the average proliferation rate to either increase or decrease as the passaging process takes place, and this is due to a competition between the initial heterogeneity and the degree to which passaging damages the cells. We also simulate a suite of scratch assays with cells from near–homogeneous and heterogeneous cell lines, at both high and low passage numbers. Although it is common in the literature to report experimental results without disclosing the passage number, our results show that we obtain significantly different closure rates when performing in silico scratch assays using cells with different passage numbers. Therefore, we suggest that the passage number should always be reported to ensure that the experiment is as reproducible as possible. Furthermore, our modelling also suggests some avenues for further experimental examination that could be used to validate or refine our simulation results.
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Affiliation(s)
- Wang Jin
- School of Mathematical Sciences, Queensland University of Technology (QUT) Brisbane, Queensland 4000, Australia
| | - Catherine J. Penington
- School of Mathematical Sciences, Queensland University of Technology (QUT) Brisbane, Queensland 4000, Australia
| | - Scott W. McCue
- School of Mathematical Sciences, Queensland University of Technology (QUT) Brisbane, Queensland 4000, Australia
| | - Matthew J. Simpson
- School of Mathematical Sciences, Queensland University of Technology (QUT) Brisbane, Queensland 4000, Australia
- * E-mail:
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MiR-21 is required for anti-tumor immune response in mice: an implication for its bi-directional roles. Oncogene 2017; 36:4212-4223. [PMID: 28346427 DOI: 10.1038/onc.2017.62] [Citation(s) in RCA: 29] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2016] [Revised: 12/29/2016] [Accepted: 02/08/2017] [Indexed: 12/17/2022]
Abstract
Here we show that miR-21, a microRNA known for its oncogenic activity, is also essential for mediating immune responses against tumor. Knockout of miR-21 in mice slowed the proliferation of both CD4+ and CD8+ cells, reduced their cytokine production and accelerated the grafted tumor growth. Further investigations indicated that miR-21 could activate CD4+ and CD8+ T cells via the PTEN/Akt pathway in response to stimulations. Taken together, these data suggest the key functions of miR-21 in mediating anti-tumor immune response and thereby uncover a bi-directional role of this traditionally known 'oncomiR' in tumorigenesis. Our study may provide new insights for the design of cancer therapies targeting microRNAs, with an emphasis on the dynamic and possibly unexpected role of these molecules.
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