Addressing current challenges in cancer immunotherapy with mathematical and computational modelling

Dose optimization of an adjuvanted peptide-based personalized neoantigen melanoma vaccine

The advancements in next-generation sequencing have made it possible to effectively detect somatic mutations, which has led to the development of personalized neoantigen cancer vaccines that are tailored to the unique variants found in a patient's cancer. These vaccines can provide significant clinical benefit by leveraging the patient's immune response to eliminate malignant cells. However, determining the optimal vaccine dose for each patient is a challenge due to the heterogeneity of tumors. To address this challenge, we formulate a mathematical dose optimization problem based on a previous mathematical model that encompasses the immune response cascade produced by the vaccine in a patient. We propose an optimization approach to identify the optimal personalized vaccine doses, considering a fixed vaccination schedule, while simultaneously minimizing the overall number of tumor and activated T cells. To validate our approach, we perform in silico experiments on six real-world clinical trial patients with advanced melanoma. We compare the results of applying an optimal vaccine dose to those of a suboptimal dose (the dose used in the clinical trial and its deviations). Our simulations reveal that an optimal vaccine regimen of higher initial doses and lower final doses may lead to a reduction in tumor size for certain patients. Our mathematical dose optimization offers a promising approach to determining an optimal vaccine dose for each patient and improving clinical outcomes.

Improving the efficacy of peptide vaccines in cancer immunotherapy

Peptide vaccines have shown great potential in cancer immunotherapy by targeting tumor antigens and activating the patient's immune system to mount a specific response against cancer cells. However, the efficacy of peptide vaccines in inducing a sustained immune response and achieving clinical benefit remains a major challenge. In this review, we discuss the current status of peptide vaccines in cancer immunotherapy and strategies to improve their efficacy. We summarize the recent advancements in the development of peptide vaccines in pre-clinical and clinical settings, including the use of novel adjuvants, neoantigens, nano-delivery systems, and combination therapies. We also highlight the importance of personalized cancer vaccines, which consider the unique genetic and immunological profiles of individual patients. We also discuss the strategies to enhance the immunogenicity of peptide vaccines such as multivalent peptides, conjugated peptides, fusion proteins, and self-assembled peptides. Although, peptide vaccines alone are weak immunogens, combining peptide vaccines with other immunotherapeutic approaches and developing novel approaches such as personalized vaccines can be promising methods to significantly enhance their efficacy and improve the clinical outcomes for cancer patients.

BioNetGMMFit: estimating parameters of a BioNetGen model from time-stamped snapshots of single cells

Mechanistic models are commonly employed to describe signaling and gene regulatory kinetics in single cells and cell populations. Recent advances in single-cell technologies have produced multidimensional datasets where snapshots of copy numbers (or abundances) of a large number of proteins and mRNA are measured across time in single cells. The availability of such datasets presents an attractive scenario where mechanistic models are validated against experiments, and estimated model parameters enable quantitative predictions of signaling or gene regulatory kinetics. To empower the systems biology community to easily estimate parameters accurately from multidimensional single-cell data, we have merged a widely used rule-based modeling software package BioNetGen, which provides a user-friendly way to code for mechanistic models describing biochemical reactions, and the recently introduced CyGMM, that uses cell-to-cell differences to improve parameter estimation for such networks, into a single software package: BioNetGMMFit. BioNetGMMFit provides parameter estimates of the model, supplied by the user in the BioNetGen markup language (BNGL), which yield the best fit for the observed single-cell, time-stamped data of cellular components. Furthermore, for more precise estimates, our software generates confidence intervals around each model parameter. BioNetGMMFit is capable of fitting datasets of increasing cell population sizes for any mechanistic model specified in the BioNetGen markup language. By streamlining the process of developing mechanistic models for large single-cell datasets, BioNetGMMFit provides an easily-accessible modeling framework designed for scale and the broader biochemical signaling community.

Modelling the Tumour Microenvironment, but What Exactly Do We Mean by "Model"?

The Oxford English Dictionary includes 17 definitions for the word "model" as a noun and another 11 as a verb. Therefore, context is necessary to understand the meaning of the word model. For instance, "model railways" refer to replicas of railways and trains at a smaller scale and a "model student" refers to an exemplary individual. In some cases, a specific context, like cancer research, may not be sufficient to provide one specific meaning for model. Even if the context is narrowed, specifically, to research related to the tumour microenvironment, "model" can be understood in a wide variety of ways, from an animal model to a mathematical expression. This paper presents a review of different "models" of the tumour microenvironment, as grouped by different definitions of the word into four categories: model organisms, in vitro models, mathematical models and computational models. Then, the frequencies of different meanings of the word "model" related to the tumour microenvironment are measured from numbers of entries in the MEDLINE database of the United States National Library of Medicine at the National Institutes of Health. The frequencies of the main components of the microenvironment and the organ-related cancers modelled are also assessed quantitatively with specific keywords. Whilst animal models, particularly xenografts and mouse models, are the most commonly used "models", the number of these entries has been slowly decreasing. Mathematical models, as well as prognostic and risk models, follow in frequency, and these have been growing in use.

In silico cancer immunotherapy trials uncover the consequences of therapy-specific response patterns for clinical trial design and outcome

Late-stage cancer immunotherapy trials often lead to unusual survival curve shapes, like delayed curve separation or a plateauing curve in the treatment arm. It is critical for trial success to anticipate such effects in advance and adjust the design accordingly. Here, we use in silico cancer immunotherapy trials - simulated trials based on three different mathematical models - to assemble virtual patient cohorts undergoing late-stage immunotherapy, chemotherapy, or combination therapies. We find that all three simulation models predict the distinctive survival curve shapes commonly associated with immunotherapies. Considering four aspects of clinical trial design - sample size, endpoint, randomization rate, and interim analyses - we demonstrate how, by simulating various possible scenarios, the robustness of trial design choices can be scrutinized, and possible pitfalls can be identified in advance. We provide readily usable, web-based implementations of our three trial simulation models to facilitate their use by biomedical researchers, doctors, and trialists.

Immune-checkpoint inhibitor therapy response evaluation using oncophysics-based mathematical models

The field of oncology has transformed with the advent of immunotherapies. The standard of care for multiple cancers now includes novel drugs that target key checkpoints that function to modulate immune responses, enabling the patient's immune system to elicit an effective anti-tumor response. While these immune-based approaches can have dramatic effects in terms of significantly reducing tumor burden and prolonging survival for patients, the therapeutic approach remains active only in a minority of patients and is often not durable. Multiple biological investigations have identified key markers that predict response to the most common form of immunotherapy-immune checkpoint inhibitors (ICI). These biomarkers help enrich patients for ICI but are not 100% predictive. Understanding the complex interactions of these biomarkers with other pathways and factors that lead to ICI resistance remains a major goal. Principles of oncophysics-the idea that cancer can be described as a multiscale physical aberration-have shown promise in recent years in terms of capturing the essence of the complexities of ICI interactions. Here, we review the biological knowledge of mechanisms of ICI action and how these are incorporated into modern oncophysics-based mathematical models. Building on the success of oncophysics-based mathematical models may help to discover new, rational methods to engineer immunotherapy for patients in the future. This article is categorized under: Therapeutic Approaches and Drug Discovery > Nanomedicine for Oncologic Disease.

Analysis of tumor-immune functional responses in a mathematical model of neoantigen cancer vaccines

Cancer neoantigen vaccines have emerged as a promising approach to stimulating the immune system to fight cancer. We propose a simple model including key elements of cancer-immune interactions and conduct a phase plane analysis to understand the immunological mechanisms of cancer neoantigen vaccines. Analytical results are obtained for two widely used functional forms that represent the killing rate of tumor cells by immune cells: the law of mass action (LMA) and the dePillis-Radunskaya Law (LPR). Using the LMA, our results reveal that a slowly growing tumor can escape the immune surveillance and that there is a unique periodic solution. The LPR offers richer dynamics, in which tumor elimination and uncontrolled tumor growth are both present. We show that tumor elimination requires sufficient number of initial activated T cells in relationship to the malignant cells, which lends support to using the neoantigen cancer vaccine as an adjuvant therapy after the primary tumor is surgically removed or treated using radiotherapy. We also derive a sufficient condition for uncontrolled tumor growth under the assumption of the LPR. The juxtaposition of analyses with these two different choices for the killing rate function highlights their importance on model behavior and biological implications, by which we hope to spur further theoretical and experimental work to understand mechanisms underlying different functional forms for the killing rate.

Mathematical modeling of cancer immunotherapy for personalized clinical translation

Encouraging advances are being made in cancer immunotherapy modeling, especially in the key areas of developing personalized treatment strategies based on individual patient parameters, predicting treatment outcomes and optimizing immunotherapy synergy when used in combination with other treatment approaches. Here we present a focused review of the most recent mathematical modeling work on cancer immunotherapy with a focus on clinical translatability. It can be seen that this field is transitioning from pure basic science to applications that can make impactful differences in patients' lives. We discuss how researchers are integrating experimental and clinical data to fully inform models so that they can be applied for clinical predictions, and present the challenges that remain to be overcome if widespread clinical adaptation is to be realized. Lastly, we discuss the most promising future applications and areas that are expected to be the focus of extensive upcoming modeling studies.

Protocol for mathematical prediction of patient response and survival to immune checkpoint inhibitor immunotherapy

This protocol describes the application of a mechanistic mathematical model of immune checkpoint inhibitor (ICI) immunotherapy to patient tumor imaging data for predicting solid tumor response and patient survival under ICI intervention. We describe steps for data collection and processing, data pipelines, and approaches to increase precision. The protocol is highly predictive as early as the first restaging after treatment start and can be used with standard-of-care imaging measures. For complete details on the use and execution of this protocol, please refer to Butner et al. (2020)¹ and Butner et al. (2021).².

Cancerous Tumor Controlled Treatment Using Search Heuristic (GA)-Based Sliding Mode and Synergetic Controller

Simple Summary

Cancer is basically a tough condition on a patient’s body where cell grows uncontrollably. Normal cells are affected, which destroys the health of the patient. The main problem in cancer is spreading from one part to another. Therefore, the mathematical modeling of cancerous tumors integrates to check overall stability. A novel approach is introduced such as Bernstein polynomial with combination of genetic algorithm, sliding mode controller, and synergetic control. The proposed solution has easily eliminated cancerous cells within five days using synergetic control. In addition, five cases are incorporated to evaluate error function. In addition, a brief comparative study is added to contrast the simulation results with theoretical modeling.

Abstract

Cancerous tumor cells divide uncontrollably, which results in either tumor or harm to the immune system of the body. Due to the destructive effects of chemotherapy, optimal medications are needed. Therefore, possible treatment methods should be controlled to maintain the constant/continuous dose for affecting the spreading of cancerous tumor cells. Rapid growth of cells is classified into primary and secondary types. In giving a proper response, the immune system plays an important role. This is considered a natural process while fighting against tumors. In recent days, achieving a better method to treat tumors is the prime focus of researchers. Mathematical modeling of tumors uses combined immune, vaccine, and chemotherapies to check performance stability. In this research paper, mathematical modeling is utilized with reference to cancerous tumor growth, the immune system, and normal cells, which are directly affected by the process of chemotherapy. This paper presents novel techniques, which include Bernstein polynomial (BSP) with genetic algorithm (GA), sliding mode controller (SMC), and synergetic control (SC), for giving a possible solution to the cancerous tumor cells (CCs) model. Through GA, random population is generated to evaluate fitness. SMC is used for the continuous exponential dose of chemotherapy to reduce CCs in about forty-five days. In addition, error function consists of five cases that include normal cells (NCs), immune cells (ICs), CCs, and chemotherapy. Furthermore, the drug control process is explained in all the cases. In simulation results, utilizing SC has completely eliminated CCs in nearly five days. The proposed approach reduces CCs as early as possible.

Analysis of the Equilibrium Phase in Immune-Controlled Tumors Provides Hints for Designing Better Strategies for Cancer Treatment

When it comes to improving cancer therapies, one challenge is to identify key biological parameters that prevent immune escape and maintain an equilibrium state characterized by a stable subclinical tumor mass, controlled by the immune cells. Based on a space and size structured partial differential equation model, we developed numerical methods that allow us to predict the shape of the equilibrium at low cost, without running simulations of the initial-boundary value problem. In turn, the computation of the equilibrium state allowed us to apply global sensitivity analysis methods that assess which and how parameters influence the residual tumor mass. This analysis reveals that the elimination rate of tumor cells by immune cells far exceeds the influence of the other parameters on the equilibrium size of the tumor. Moreover, combining parameters that sustain and strengthen the antitumor immune response also proves more efficient at maintaining the tumor in a long-lasting equilibrium state. Applied to the biological parameters that define each type of cancer, such numerical investigations can provide hints for the design and optimization of cancer treatments.

Comprehensive Analysis of mTORC1 Signaling Pathway–Related Genes in the Prognosis of HNSCC and the Response to Chemotherapy and Immunotherapy

Objective: The mammalian target of the rapamycin complex 1 (mTORC1) signaling pathway has emerged as a crucial player in the oncogenesis and development of head and neck squamous cell carcinoma (HNSCC), however, to date, no relevant gene signature has been identified. Therefore, we aimed to construct a novel gene signature based on the mTORC1 pathway for predicting the outcomes of patients with HNSCC and their response to treatment.

Methods: The gene expression and clinical data were retrieved from The Cancer Genome Atlas (TCGA) and Gene Expression Omnibus (GEO) databases. The key prognostic genes associated with the mTORC1 pathway were screened by univariate Cox regression analyses. A prognostic signature was then established based on significant factors identified in the multivariate Cox regression analysis. The performance of the multigene signature was evaluated by the Kaplan–Meier (K–M) survival analysis and receiver operating characteristic (ROC) analysis. Based on the median risk score, patients were categorized into high- and low-risk groups. Subsequently, a hybrid prognostic nomogram was constructed and estimated by a calibration plot and decision curve analysis. Furthermore, immune cell infiltration and therapeutic responses were compared between the two risk groups. Finally, we measured the expression levels of seven genes by quantitative real-time polymerase chain reaction (qRT-PCR) and immunohistochemistry (IHC).

Results: The mTORC1 pathway–based signature was constructed using the seven identified genes (SEC11A, CYB5B, HPRT1, SLC2A3, SC5D, CORO1A, and PIK3R3). Patients in the high-risk group exhibited a lower overall survival (OS) rate than those in the low-risk group in both datasets. Through the univariate and multivariate Cox regression analyses, this gene signature was confirmed to be an independent prognostic risk factor for HNSCC. The constructed nomogram based on age, American Joint Committee on Cancer (AJCC) stage, and the risk score exhibited satisfactory performance in predicting the OS. In addition, immune cell infiltration and chemotherapeutic and immunotherapeutic responses differed significantly between the two risk groups. The expression levels of SEC11A and CYB5B were higher in HNSCC tissues than in normal tissues.

Conclusion: Our study established and verified an mTORC1 signaling pathway–related gene signature that could be used as a novel prognostic factor for HNSCC.

A combination therapy of oncolytic viruses and chimeric antigen receptor T cells: a mathematical model proof-of-concept

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.

Engineered in vitro tumor models for cell-based immunotherapy

Tumor immunotherapy is rapidly evolving as one of the major pillars of cancer treatment. Cell-based immunotherapies, which utilize patient's own immune cells to eliminate cancer cells, have shown great promise in treating a range of malignancies, especially those of hematopoietic origins. However, their performance on a broader spectrum of solid tumor types still fall short of expectations in the clinical stage despite promising preclinical assessments. In this review, we briefly introduce cell-based immunotherapies and the inhibitory mechanisms in tumor microenvironments that may have contributed to this discrepancy. Specifically, a major obstacle to the clinical translation of cell-based immunotherapies is in the lack of preclinical models that can accurately assess the efficacies and mechanisms of these therapies in a (patho-)physiologically relevant manner. Lately, tissue engineering and organ-on-a-chip tools and microphysiological models have allowed for more faithful recapitulation of the tumor microenvironments, by incorporating crucial tumor tissue features such as cellular phenotypes, tissue architecture, extracellular matrix, physical parameters, and their dynamic interactions. This review summarizes the existing engineered tumor models with a focus on tumor immunology and cell-based immunotherapy. We also discuss some key considerations for the future development of engineered tumor models for immunotherapeutics. STATEMENT OF SIGNIFICANCE: Cell-based immunotherapies have shown great promise in treating hematological malignancies and some epithelial tumors. However, their performance on a broader spectrum of solid tumor types still fall short of expectations. Major obstacles include the inhibitory mechanisms in tumor microenvironments (TME) and the lack of preclinical models that can accurately assess the efficacies and mechanisms of cellular therapies in a (patho-)physiologically relevant manner. In this review, we introduce recent progress in tissue engineering and microphysiological models for more faithful recapitulation of TME for cell-based immunotherapies, and some key considerations for the future development of engineered tumor models. This overview will provide a better understanding on the role of engineered models in accelerating immunotherapeutic discoveries and clinical translations.

Multiscale modeling in disease

Multiscale computational modeling aims to connect the complex networks of effects at different length and/or time scales. For example, these networks often include intracellular molecular signaling, crosstalk, and other interactions between neighboring cell populations, and higher levels of emergent phenomena across different regions of tissues and among collections of tissues or organs interacting with each other in the whole body. Recent applications of multiscale modeling across intracellular, cellular, and/or tissue levels are highlighted here. These models incorporated the roles of biochemical and biomechanical modulation in processes that are implicated in the mechanisms of several diseases including fibrosis, joint and bone diseases, respiratory infectious diseases, and cancers.

Biologically-Based Mathematical Modeling of Tumor Vasculature and Angiogenesis via Time-Resolved Imaging Data

Tumor-associated vasculature is responsible for the delivery of nutrients, removal of waste, and allowing growth beyond 2-3 mm3. Additionally, the vascular network, which is changing in both space and time, fundamentally influences tumor response to both systemic and radiation therapy. Thus, a robust understanding of vascular dynamics is necessary to accurately predict tumor growth, as well as establish optimal treatment protocols to achieve optimal tumor control. Such a goal requires the intimate integration of both theory and experiment. Quantitative and time-resolved imaging methods have emerged as technologies able to visualize and characterize tumor vascular properties before and during therapy at the tissue and cell scale. Parallel to, but separate from those developments, mathematical modeling techniques have been developed to enable in silico investigations into theoretical tumor and vascular dynamics. In particular, recent efforts have sought to integrate both theory and experiment to enable data-driven mathematical modeling. Such mathematical models are calibrated by data obtained from individual tumor-vascular systems to predict future vascular growth, delivery of systemic agents, and response to radiotherapy. In this review, we discuss experimental techniques for visualizing and quantifying vascular dynamics including magnetic resonance imaging, microfluidic devices, and confocal microscopy. We then focus on the integration of these experimental measures with biologically based mathematical models to generate testable predictions.

CARTmath-A Mathematical Model of CAR-T Immunotherapy in Preclinical Studies of Hematological Cancers

Immunotherapy has gained great momentum with chimeric antigen receptor T cell (CAR-T) therapy, in which patient's T lymphocytes are genetically manipulated to recognize tumor-specific antigens, increasing tumor elimination efficiency. In recent years, CAR-T cell immunotherapy for hematological malignancies achieved a great response rate in patients and is a very promising therapy for several other malignancies. Each new CAR design requires a preclinical proof-of-concept experiment using immunodeficient mouse models. The absence of a functional immune system in these mice makes them simple and suitable for use as mathematical models. In this work, we develop a three-population mathematical model to describe tumor response to CAR-T cell immunotherapy in immunodeficient mouse models, encompassing interactions between a non-solid tumor and CAR-T cells (effector and long-term memory). We account for several phenomena, such as tumor-induced immunosuppression, memory pool formation, and conversion of memory into effector CAR-T cells in the presence of new tumor cells. Individual donor and tumor specificities are considered uncertainties in the model parameters. Our model is able to reproduce several CAR-T cell immunotherapy scenarios, with different CAR receptors and tumor targets reported in the literature. We found that therapy effectiveness mostly depends on specific parameters such as the differentiation of effector to memory CAR-T cells, CAR-T cytotoxic capacity, tumor growth rate, and tumor-induced immunosuppression. In summary, our model can contribute to reducing and optimizing the number of in vivo experiments with in silico tests to select specific scenarios that could be tested in experimental research. Such an in silico laboratory is an easy-to-run open-source simulator, built on a Shiny R-based platform called CARTmath. It contains the results of this manuscript as examples and documentation. The developed model together with the CARTmath platform have potential use in assessing different CAR-T cell immunotherapy protocols and its associated efficacy, becoming an accessory for in silico trials.

Modelling treatment-response rates

The time course of tumour responses to immunotherapies can be mathematically predicted on the basis of tumour-growth rates, the rates of immune activation and of tumour–immune-cell interactions, and the efficacy of immune-mediated tumour killing.

A caution for oncologists: chemotherapy can cause chaotic dynamics

BACKGROUND AND OBJECTIVE

The effect of chemotherapy in cancer models is mostly handled by using a separate equation for chemotherapeutic agent. In this study, we do not consider a separate equation for drug but rather introduce its effect in terms of a parameter m representing the fraction of tumor cells killed by chemotherapeutic drug module. The main objective of this study is to provide conditions on model parameters which when fulfilled the grave consequences of cancer can be avoided. This study also shows that chemotherapy at times can produce unexpected results.

METHODS

Linearization method to study the stability of model equilibria.

RESULTS

The results obtained in this study are governed by the trichotomy law on the number 1-a₁₂-d₁, where a₁₂ represents the negative effect on the growth of cancer cells due to their competition with host cells for resources and d₁ is rate of annihilation of cancer cells due to chemotherapy. It is seen that in case of under-dose drug module when d₁<1-a₁₂, the complete eradication of cancer is not possible. When d₁=1-a₁₂, the model suggests occurrence of chaotic dynamics. When the drug dose is properly adjusted so that d₁>1-a₁₂, the complete eradication of cancer is guaranteed.

CONCLUSION

The results of the model of this paper given for the post vascular stages of tumor suggest criteria to select a particular drug module (a single drug or a combination of drugs) that the chemotherapy procedure should adapt to eradicate cancer. This study injects a note of caution for oncologists that chemotherapy as cancer treatment can also cause chaotic dynamics in certain situations. This study also presents a plausible explanation to the question why sometimes a tumor grows in the body and then gets cured without any medical intervention.

Dual-Target CAR-Ts with On- and Off-Tumour Activity May Override Immune Suppression in Solid Cancers: A Mathematical Proof of Concept

Simple Summary

(CAR)-T cell-based therapies have achieved substantial success against different haematological malignancies. However, results for solid tumours have been limited up to now, in part due to the fact that the immunosuppressive tumour microenvironment inactivates CAR-T cell clones. In this paper we study mathematically the competition of CAR-T and tumour cells, taking into account their immunosuppressive capacity. Using computer simulations, we show that the use of large numbers of CAR-T cells targetting the solid tumour antigens could overcome the immunosuppressive potential of cancer. To achieve such high levels of CAR-T cells we propose, and study in silico, the manufacture and injection of CAR-T cells targetting two antigens: CD19 and a tumour-associated antigen. This strategy lead in our simulations to the expansion of the CAR-T cells injected and the production of a massive army of CAR-T cells targetting the solid tumour, and potentially overcoming its immune suppression capabilities. Thus, our proposed strategy could provide a way to develop successful CAR-T cell therapies against solid tumours.

Abstract

Chimeric antigen receptor (CAR)-T cell-based therapies have achieved substantial success against B-cell malignancies, which has led to a growing scientific and clinical interest in extending their use to solid cancers. However, results for solid tumours have been limited up to now, in part due to the immunosuppressive tumour microenvironment, which is able to inactivate CAR-T cell clones. In this paper we put forward a mathematical model describing the competition of CAR-T and tumour cells, taking into account their immunosuppressive capacity. Using the mathematical model, we show that the use of large numbers of CAR-T cells targetting the solid tumour antigens could overcome the immunosuppressive potential of cancer. To achieve such high levels of CAR-T cells we propose, and study computationally, the manufacture and injection of CAR-T cells targetting two antigens: CD19 and a tumour-associated antigen. We study in silico the resulting dynamics of the disease after the injection of this product and find that the expansion of the CAR-T cell population in the blood and lymphopoietic organs could lead to the massive production of an army of CAR-T cells targetting the solid tumour, and potentially overcoming its immune suppression capabilities. This strategy could benefit from the combination with PD-1 inhibitors and low tumour loads. Our computational results provide theoretical support for the treatment of different types of solid tumours using T cells engineered with combination treatments of dual CARs with on- and off-tumour activity and anti-PD-1 drugs after completion of classical cytoreductive treatments.

A mathematical model for the quantification of a patient's sensitivity to checkpoint inhibitors and long-term tumour burden

A large proportion of patients with cancer are unresponsive to treatment with immune checkpoint blockade and other immunotherapies. Here, we report a mathematical model of the time-course of tumour responses to immune-checkpoint inhibitors. The model takes into account intrinsic tumour-growth rates, the rates of immune activation and of tumour–immune-cell interactions, and the efficacy of immune-mediated tumour killing. For 124 patients, four cancer types and two immunotherapy agents, the model reliably described the immune responses and final tumour burden across all different cancers and drug combinations examined. In validation cohorts from four clinical trials of checkpoint inhibitors (with a total of 177 patients), the model accurately stratified the patients according to reduced or increased long-term tumour burden. We also provide model-derived quantitative measures of treatment sensitivity for specific drug–cancer combinations. The model can be used to predict responses to therapy and to quantify specific drug–cancer sensitivities in individual patients.

Computational modelling of modern cancer immunotherapy

Modern cancer immunotherapy has revolutionised oncology and carries the potential to radically change the approach to cancer treatment. However, numerous questions remain to be answered to understand immunotherapy response better and further improve the benefit for future cancer patients. Computational models are promising tools that can contribute to accelerated immunotherapy research by providing new clues and hypotheses that could be tested in future trials, based on preceding simulations in addition to the empirical rationale. In this topical review, we briefly summarise the history of cancer immunotherapy, including computational modelling of traditional cancer immunotherapy, and comprehensively review computational models of modern cancer immunotherapy, such as immune checkpoint inhibitors (as monotherapy and combination treatment), co-stimulatory agonistic antibodies, bispecific antibodies, and chimeric antigen receptor T cells. The modelling approaches are classified into one of the following categories: data-driven top-down vs mechanistic bottom-up, simplistic vs detailed, continuous vs discrete, and hybrid. Several common modelling approaches are summarised, such as pharmacokinetic/pharmacodynamic models, Lotka-Volterra models, evolutionary game theory models, quantitative systems pharmacology models, spatio-temporal models, agent-based models, and logic-based models. Pros and cons of each modelling approach are critically discussed, particularly with the focus on the potential for successful translation into immuno-oncology research and routine clinical practice. Specific attention is paid to calibration and validation of each model, which is a necessary prerequisite for any successful model, and at the same time, one of the main obstacles. Lastly, we provide guidelines and suggestions for the future development of the field.

Study of dose-dependent combination immunotherapy using engineered T cells and IL-2 in cervical cancer

Adoptive T cell based immunotherapy is gaining significant traction in cancer treatment. Despite its limited efficacy so far in treating solid tumors compared to hematologic cancers, recent advances in T cell engineering render this treatment increasingly more successful in solid tumors, demonstrating its broader therapeutic potential. In this paper we develop a mathematical model to study the efficacy of engineered T cell receptor (TCR) T cell therapy targeting the E7 antigen in cervical cancer cell lines. We consider a dynamical system that follows the population of cancer cells, TCR T cells, and IL-2 treatment concentration. We demonstrate that there exists a TCR T cell dosage window for a successful cancer elimination that can be expressed in terms of the initial tumor size. We obtain the TCR T cell dose for two cervical cancer cell lines: 4050 and CaSki. Finally, a combination therapy of TCR T cell and IL-2 treatment is studied. We show that certain treatment protocols can improve therapy responses in the 4050 cell line, but not in the CaSki cell line.

The emergence of new trends in clinical laboratory diagnosis

Diagnostic processes typically rely on traditional and laborious methods, that are prone to human error, resulting in frequent misdiagnosis of diseases. Computational approaches are being increasingly used for more precise diagnosis of the clinical pathology, diagnosis of genetic and microbial diseases, and analysis of clinical chemistry data. These approaches are progressively used for improving the reliability of testing, resulting in reduced diagnostic errors. Artificial intelligence (AI)-based computational approaches mostly rely on training sets obtained from patient data stored in clinical databases. However, the use of AI is associated with several ethical issues, including patient privacy and data ownership. The capacity of AI-based mathematical models to interpret complex clinical data frequently leads to data bias and reporting of erroneous results based on patient data. In order to improve the reliability of computational approaches in clinical diagnostics, strategies to reduce data bias and analyzing real-life patient data need to be further refined.

A mixed therapy minimal model: Some strategies for eradication or minimization of cancer

BACKGROUND AND OBJECTIVE

In most of the cancer therapeutic models separate equations for consumption of drugs are used, we however use parameters m and s to see the effect of chemotherapy and immunotherapy respectively. The main objective of this theoretical study is to develop strategies for eradication or minimization of cancer.

METHODS

Linearization method to study the local stability of model equilibria.

RESULTS

The results obtained in this study provide thresholds on m-fraction of cancer cells killed by chemotherapy and s-fraction of immune cells stimulated by immunotherapy.

CONCLUSION

The model considered relates to immune-cancer-normal cell interactions in post vascularization process. The study aims to develop strategies for complete eradication or minimization of cancer in terms of model parameters. This paper presents a minimal immuno-chemotherapeutic cancer model by describing interacting dynamics of cancer, immune and normal cells in a system of three ordinary differential equations. The source of the immune cells is considered outside the sytem given by a constant influx rate, s. The minimality of the model lies in not considering a separate equation for the dynamics of the drug but its overall killing effect on the cancer cells represented by a parameter, m. Thus the parameter m relates to chemotherapy and s to immunotherapy. The analysis of the model yields thresholds on these parameters for therapeutic strategies which guarantee either eradication or minimization of cancer from a patient's body.

Integrative Approaches to Cancer Immunotherapy

Cancer immunotherapy aims to arm patients with cancer-fighting immunity. Many new cancer-specific immunotherapeutic drugs have gained approval in the past several years, demonstrating immunotherapy's efficacy and promise as an anticancer modality. Despite these successes, several outstanding questions remain for cancer immunotherapy, including how to make immunotherapy more efficacious in a broader range of cancer types and patients, and how to predict which patients will respond or not respond to therapy. We present a case for integrative systems approaches that will answer these questions. This involves applying mechanistic and statistical modeling, establishing consistent and widely adopted experimental tools to generate systems-level data, and creating sustained mechanisms of support. If implemented, these approaches will lead to major advances in cancer treatment.

Systems biology of ferroptosis: A modeling approach

Ferroptosis is a recently discovered form of iron-dependent regulated cell death (RCD) that occurs via peroxidation of phospholipids containing polyunsaturated fatty acid (PUFA) moieties. Activating this form of cell death is an emerging strategy in cancer treatment. Because multiple pathways and molecular species contribute to the ferroptotic process, predicting which tumors will be sensitive to ferroptosis is a challenge. We thus develop a mathematical model of several critical pathways to ferroptosis in order to perform a systems-level analysis of the process. We show that sensitivity to ferroptosis depends on the activity of multiple upstream cascades, including PUFA incorporation into the phospholipid membrane, and the balance between levels of pro-oxidant factors (reactive oxygen species, lipoxogynases) and antioxidant factors (GPX4). We perform a systems-level analysis of ferroptosis sensitivity as an outcome of five input variables (ACSL4, SCD1, ferroportin, transferrin receptor, and p53) and organize the resulting simulations into 'high' and 'low' ferroptosis sensitivity groups. We make a novel prediction corresponding to the combinatorial requirements of ferroptosis sensitivity to SCD1 and ACSL4 activity. To validate our prediction, we model the ferroptotic response of an ovarian cancer stem cell line following single- and double-knockdown of SCD1 and ACSL4. We find that the experimental outcomes are consistent with our simulated predictions. This work suggests that a systems-level approach is beneficial for understanding the complex combined effects of ferroptotic input, and in predicting cancer susceptibility to ferroptosis.

Computational models of melanoma

Genes, proteins, or cells influence each other and consequently create patterns, which can be increasingly better observed by experimental biology and medicine. Thereby, descriptive methods of statistics and bioinformatics sharpen and structure our perception. However, additionally considering the interconnectivity between biological elements promises a deeper and more coherent understanding of melanoma. For instance, integrative network-based tools and well-grounded inductive in silico research reveal disease mechanisms, stratify patients, and support treatment individualization. This review gives an overview of different modeling techniques beyond statistics, shows how different strategies align with the respective medical biology, and identifies possible areas of new computational melanoma research.

Modeling immune cell behavior across scales in cancer

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

Modeling and Analyzing Stem-Cell Therapy toward Cancer: Evolutionary Game Theory Perspective

BACKGROUND

Immunotherapy is a recently developed method of cancer therapy, aiming to strengthen a patient's immune system in different ways to fight cancer. One of these ways is to add stem cells into the patient's body.

METHODS

The study was conducted in Kermanshah, western Iran, 2016-2017. We first modeled the interaction between cancerous and healthy cells using the concept of evolutionary game theory. System dynamics were analyzed employing replicator equations and control theory notions. We categorized the system into separate cases based on the value of the parameters. For cases in which the system converged to undesired equilibrium points, "stem-cell injection" was employed as a therapeutic suggestion. The effect of stem cells on the model was considered by reforming the replicator equations as well as adding some new parameters to the system.

RESULTS

By adjusting stem cell-related parameters, the system converged to desired equilibrium points, i.e., points with no or a scanty level of cancerous cells. In addition to the theoretical analysis, our simulation results suggested solutions were effective in eliminating cancerous cells.

CONCLUSION

This model could be applicable to different types of cancer, so we did not restrict it to a specific type of cancer. In fact, we were seeking a flexible mathematical framework that could cover different types of cancer by adjusting the system parameters.

Oncolytic adenovirus programmed by synthetic gene circuit for cancer immunotherapy

Improving efficacy of oncolytic virotherapy remains challenging due to difficulty increasing specificity and immune responses against cancer and limited understanding of its population dynamics. Here, we construct programmable and modular synthetic gene circuits to control adenoviral replication and release of immune effectors selectively in hepatocellular carcinoma cells in response to multiple promoter and microRNA inputs. By performing mouse model experiments and computational simulations, we find that replicable adenovirus has a superior tumor-killing efficacy than non-replicable adenovirus. We observe a synergistic effect on promoting local lymphocyte cytotoxicity and systematic vaccination in immunocompetent mouse models by combining tumor lysis and secretion of immunomodulators. Furthermore, our computational simulations show that oncolytic virus which encodes immunomodulators can exert a more robust therapeutic efficacy than combinatorial treatment with oncolytic virus and immune effector. Our results provide an effective strategy to engineer oncolytic adenovirus, which may lead to innovative immunotherapies for a variety of cancers.

It is difficult to improve the efficacy of oncolytic virotherapy due to immune system responses and limited understanding of population dynamics. Here the authors use synthetic biology gene circuits to control adenoviral replication and release of immunomodulators in hepatocellular carcinoma cells.

Learning-accelerated discovery of immune-tumour interactions

We present an integrated framework for enabling dynamic exploration of design spaces for cancer immunotherapies with detailed dynamical simulation models on high-performance computing resources. Our framework combines PhysiCell, an open source agent-based simulation platform for cancer and other multicellular systems, and EMEWS, an open source platform for extreme-scale model exploration. We build an agent-based model of immunosurveillance against heterogeneous tumours, which includes spatial dynamics of stochastic tumour-immune contact interactions. We implement active learning and genetic algorithms using high-performance computing workflows to adaptively sample the model parameter space and iteratively discover optimal cancer regression regions within biological and clinical constraints.

Review on biofabrication and applications of heterogeneous tumor models

Resolving the origin and development of tumor heterogeneity has proven to be a crucial challenge in cancer research. In vitro tumor models have been widely used for both scientific and clinical research. Currently, tumor models based on 2D cell culture, animal models, and 3D cell-laden constructs are widely used. Heterogeneous tumor models, which consist of more than one cell type and mimic cell-cell as well as cell-matrix interactions, are attracting increasing attention. Heterogeneous tumor models can serve as pathological models to study the microenvironment and tumor development such as tumorigenesis, invasiveness, and malignancy. They also provide disease models for drug screening and personalized therapy. In this review, the current techniques, models, and oncological applications regarding 3D heterogeneous tumor models are summarized and discussed.

A mathematical model of combined CD8 T cell costimulation by 4-1BB (CD137) and OX40 (CD134) receptors

Combined agonist stimulation of the TNFR costimulatory receptors 4-1BB (CD137) and OX40(CD134) has been shown to generate supereffector CD8 T cells that clonally expand to greater levels, survive longer, and produce a greater quantity of cytokines compared to T cells stimulated with an agonist of either costimulatory receptor individually. In order to understand the mechanisms for this effect, we have created a mathematical model for the activation of the CD8 T cell intracellular signaling network by mono- or dual-costimulation. We show that supereffector status is generated via downstream interacting pathways that are activated upon engagement of both receptors, and in silico simulations of the model are supported by published experimental results. The model can thus be used to identify critical molecular targets of T cell dual-costimulation in the context of cancer immunotherapy.

Future of cancer immunotherapy using plant virus-based nanoparticles

Immunotherapy potentiates a patient’s immune response against some forms of cancer, including malignant tumors. In this Special Report, we have summarized the use of nanoparticles that have been designed for use in cancer immunotherapy with particular emphasis on plant viruses. Plant virus-based nanoparticles are an ideal choice for therapeutic applications, as these nanoparticles are not only capable of targeting the desired cells but also of being safely delivered to the body without posing any threat of infection. Plant viruses can be taken up by tumor cells and can be functionalized as drug delivery vehicles. This Special Report describes how the future of cancer immunotherapy could be a success through the merger of computer-based technology using plant-virus nanoparticles.

The nonpathogenic nature of plant viral nanoparticles makes them an ideal choice for therapeutic applications such as cancer. Understanding the molecular mechanisms behind the immune response to cancer has facilitated the use of nanotechnology as an effective cancer therapy. Biologically active self-replicating plant virus particles can be introduced to the bloodstream of the human body and used as effective drug delivery vehicles. This Special Report describes how a combination of computer-based technology and plant-virus nanoparticles can assist in cancer immunotherapy.

Pharmacodynamic Drug-Drug Interactions

Pharmacodynamic drug-drug interactions (DDIs) occur when the pharmacological effect of one drug is altered by that of another drug in a combination regimen. DDIs often are classified as synergistic, additive, or antagonistic in nature, albeit these terms are frequently misused. Within a complex pathophysiological system, the mechanism of interaction may occur at the same target or through alternate pathways. Quantitative evaluation of pharmacodynamic DDIs by employing modeling and simulation approaches is needed to identify and optimize safe and effective combination therapy regimens. This review investigates the opportunities and challenges in pharmacodynamic DDI studies and highlights examples of quantitative methods for evaluating pharmacodynamic DDIs, with a particular emphasis on the use of mechanism-based modeling and simulation in DDI studies. Advancements in both experimental and computational techniques will enable the application of better, model-informed assessments of pharmacodynamic DDIs in drug discovery, development, and therapeutics.

Multiscale Agent-Based and Hybrid Modeling of the Tumor Immune Microenvironment

Multiscale systems biology and systems pharmacology are powerful methodologies that are playing increasingly important roles in understanding the fundamental mechanisms of biological phenomena and in clinical applications. In this review, we summarize the state of the art in the applications of agent-based models (ABM) and hybrid modeling to the tumor immune microenvironment and cancer immune response, including immunotherapy. Heterogeneity is a hallmark of cancer; tumor heterogeneity at the molecular, cellular, and tissue scales is a major determinant of metastasis, drug resistance, and low response rate to molecular targeted therapies and immunotherapies. Agent-based modeling is an effective methodology to obtain and understand quantitative characteristics of these processes and to propose clinical solutions aimed at overcoming the current obstacles in cancer treatment. We review models focusing on intra-tumor heterogeneity, particularly on interactions between cancer cells and stromal cells, including immune cells, the role of tumor-associated vasculature in the immune response, immune-related tumor mechanobiology, and cancer immunotherapy. We discuss the role of digital pathology in parameterizing and validating spatial computational models and potential applications to therapeutics.

A structural methodology for modeling immune-tumor interactions including pro- and anti-tumor factors for clinical applications

The immune system turns out to have both stimulatory and inhibitory factors influencing on tumor growth. In recent years, the pro-tumor role of immunity factors such as regulatory T cells and TGF-β cytokines has specially been considered in mathematical modeling of tumor-immune interactions. This paper presents a novel structural methodology for reviewing these models and classifies them into five subgroups on the basis of immune factors included. By using our experimental data due to immunotherapy experimentation in mice, these five modeling groups are evaluated and scored. The results show that a model with a small number of variables and coefficients performs efficiently in predicting the tumor-immune system interactions. Though immunology theorems suggest to employ a larger number of variables and coefficients, more complicated models are here shown to be inefficient due to redundant parallel pathways. So, these models are trapped in local minima and restricted in prediction capability. This paper investigates the mathematical models that were previously developed and proposes variables and pathways that are essential for modeling tumor-immune. Using these variables and pathways, a minimal structure for modeling tumor-immune interactions is proposed for future studies.

Chaos synchronization and Nelder-Mead search for parameter estimation in nonlinear pharmacological systems: Estimating tumor antigenicity in a model of immunotherapy

In mathematical pharmacology, models are constructed to confer a robust method for optimizing treatment. The predictive capability of pharmacological models depends heavily on the ability to track the system and to accurately determine parameters with reference to the sensitivity in projected outcomes. To closely track chaotic systems, one may choose to apply chaos synchronization. An advantageous byproduct of this methodology is the ability to quantify model parameters. In this paper, we illustrate the use of chaos synchronization combined with Nelder-Mead search to estimate parameters of the well-known Kirschner-Panetta model of IL-2 immunotherapy from noisy data. Chaos synchronization with Nelder-Mead search is shown to provide more accurate and reliable estimates than Nelder-Mead search based on an extended least squares (ELS) objective function. Our results underline the strength of this approach to parameter estimation and provide a broader framework of parameter identification for nonlinear models in pharmacology.