Combination therapy for cancer with oncolytic virus and checkpoint inhibitor: A mathematical model

Adaptive Immunity Determines the Cancer Treatment Outcome of Oncolytic Virus and Anti-PD-1

The immune checkpoint inhibitor, anti-programmed death protein-1 (anti-PD-1), enhances adaptive immunity to kill tumor cells, and the oncolytic virus (OV) triggers innate immunity to clear the infected tumor cells. We create a mathematical model to investigate how the interaction between adaptive and innate immunities under OV and anti-PD-1 affects tumor reduction. For different immunity strength, we create the corresponding virtual baseline patients and cohort patients to decipher the major factors determining the treatment outcome. Global sensitivity analysis indicates that adaptive immunity has more control on the treatment outcome than innate immunity, and whether anti-PD-1 cancels out the OV treatment efficacy depends on the OV dosage and the balance between clearance of infected tumor cells and OV by T cells. The optimal OV infection rate and dosage suggest that OV treatment is more sensitive to adaptive immunity than innate immunity. Our model prediction also indicates that tumor reduction is more sensitive to anti-PD-1 efficacy as adaptive immunity becomes stronger, and anti-PD-1 trends to cancel out the OV treatment efficacy as innate immunity becomes stronger. Based on these results, the recommended treatment protocol for patients with different immunity strength can be determined.

CAR T-cell and oncolytic virus dynamics and determinants of combination therapy success for glioblastoma

Glioblastoma is a highly aggressive and treatment-resistant primary brain cancer. While chimeric antigen receptor (CAR) T-cell therapy has demonstrated promising results in targeting these tumors, it has not yet been curative. An innovative approach to improve CAR T-cell efficacy is to combine them with other immune modulating therapies. In this study, we investigate in vitro combination of IL-13Rα2 targeted CAR T-cells with an oncolytic virus (OV) and study the complex interplay between tumor cells, CAR T-cells, and OV dynamics with a novel mathematical model. We fit the model to data collected from experiments with each therapy individually and in combination to reveal determinants of therapy synergy and improved efficacy. Our analysis reveals that the virus bursting size is a critical parameter in determining the net tumor infection rate and overall combination treatment efficacy. Moreover, the model predicts that administering the oncolytic virus simultaneously with, or prior to, CAR T-cells could maximize therapeutic efficacy.

Mesenchymal stem cell origin contributes to the antitumor effect of oncolytic virus carriers

Oncolytic virotherapy shows promise as a cancer treatment approach; however, its systemic application is hindered by antibody neutralization. This issue can be overcome by using mesenchymal stem cells (MSCs) as carrier cells for oncolytic viruses (OVs). However, it remains elusive whether MSC source influences the antitumor effect. Here, we demonstrate that their source affects the migration ability and oncolytic activity of OV-loaded MSCs. Among human MSCs derived from different tissues, bone marrow-derived MSCs (BMMSCs) showed a high migration ability toward cancer cells in two- and three-dimensional MSC-cancer cell co-culture models. Comprehensive gene expression and Gene Ontology-based functional analyses suggested that genes involved in cell migration and cytokine response influence the cancer-specific tropism of BMMSCs. Furthermore, MSC origin affected the susceptibility to OVs, including cytotoxicity resistance and OV release from MSCs. MSC-mediated OV delivery significantly increased the viral spread and antitumor activity compared with delivery by OVs alone, and OV-loaded BMMSCs demonstrated the most potent antitumor effect among OV-loaded MSCs. Our results offer promising insights into cancer gene therapy with carrier cells and can help with the selection of an appropriate MSC source for MSC-based OV therapy.

Spatiotemporal spread of oncolytic virus in a heterogeneous cell population

Oncolytic (cancer-killing) virus treatment is a promising new therapy for cancer, with many viruses currently being tested for their ability to eradicate tumors. One of the major stumbling blocks to the development of this treatment modality has been preventing spread of the virus to non-cancerous cells. Our recent ability to manipulate RNA and DNA now allows for the possibility of creating designer viruses specifically targeted to cancer cells, thereby significantly reducing unwanted side effects in patients. In this study, we use a partial differential equation model to determine the characteristics of a virus needed to contain spread of an oncolytic virus within a spherical tumor and prevent it from spreading to non-cancerous cells outside the tumor. We find that oncolytic viruses that have different infection rates or different cell death rates in cancer and non-cancerous cells can be made to stay within the tumor. We find that there is a minimum difference in infection rates or cell death rates that will contain the virus and that this threshold value depends on the growth rate of the cancer. Identification of these types of thresholds can help researchers develop safer strains of oncolytic viruses allowing further development of this promising treatment.

Effects of virus-induced immunogenic cues on oncolytic virotherapy

Oncolytic virotherapy is a promising form of cancer treatment that uses viruses to infect and kill cancer cells. In addition to their direct effects on cancer cells, the viruses stimulate various immune responses partly directed against the tumour. Efforts are made to genetically engineer oncolytic viruses to enhance their immunogenic potential. However, the interplay between tumour growth, viral infection, and immune responses is complex and not fully understood, leading to variable and sometimes counterintuitive therapeutic outcomes. Here, we employ a spatio-temporal model to shed more light on this interplay. We investigate systematically how the properties of virus-induced immunogenic signals (their half-life, rate of spread, and potential to promote T-cell-mediated cytotoxicity) affect the therapeutic outcome. Our simulations reveal that strong immunogenic signals, combined with faster diffusion rates, improve the spread of immune activation, leading to better tumour eradication. However, replicate simulations suggest that the outcome of virotherapy is more stochastic than generally appreciated. Our model shows that virus-induced immune responses can interfere with virotherapy, by targeting virus-infected cancer cells and/or by impeding viral spread. In the presence of immune responses, the mode of virus introduction is important, with systemic viral delivery throughout the tumour yielding the most favourable outcomes. The timing of virus introduction also plays a critical role; depending on the efficacy of the immune response, a later start of virotherapy can be advantageous. Overall, our results emphasise that the rational design of oncolytic viruses requires optimising virus-induced immunogenic signals and strategies that balance viral spread with immune activity for improved therapeutic success.

Disentangling Anti-Tumor Response of Immunotherapy Combinations: A Physiologically Based Framework for V937 Oncolytic Virus and Pembrolizumab

Immuno-oncology (IO) is a growing strategy in cancer treatment. Oncolytic viruses (OVs) can selectively infect cancer cells and lead to direct and/or immune-dependent tumor lysis. This approach represents an opportunity to potentiate the efficacy of immune checkpoint inhibitors (ICI), such as pembrolizumab. Currently, there is a lack of comprehensive quantitative models for the aforementioned scenarios. In this work, we developed a mechanistic framework describing viral kinetics, viral dynamics, and tumor response after intratumoral (i.t.) or intravenous (i.v.) administration of V937 alone or in combination with pembrolizumab. The model accounts for tumor shrinkage, in both injected and non-injected lesions, induced by: viral-infected tumor cell death and activated CD8 cells. OV-infected tumor cells enhanced the expansion of CD8 cells, whereas pembrolizumab inhibits their exhaustion by competing with PD-L1 in their binding to PD-1. Circulating viral levels and treatment effects on tumor volume were adequately characterized in all the different scenarios. This mechanistic-based model has been developed by combining top-down and bottom-up approaches and provides individual estimates of viral and ICI responses. The robustness of the model is reflected by the description of the tumor size time profiles in a variety of clinical scenarios. Additionally, this platform allows us to investigate not only the contribution of processes related to the viral kinetics and dynamics on tumor response, but also the influence of its interaction with an ICI. Additionally, the model can be used to explore different scenarios aiming to optimize treatment combinations and support clinical development.

Agent-Based Modeling of Virtual Tumors Reveals the Critical Influence of Microenvironmental Complexity on Immunotherapy Efficacy

Since the introduction of the first immune checkpoint inhibitor (ICI), immunotherapy has changed the landscape of molecular therapeutics for cancers. However, ICIs do not work equally well on all cancers and for all patients. There has been a growing interest in using mathematical and computational models to optimize clinical responses. Ordinary differential equations (ODEs) have been widely used for mechanistic modeling in immuno-oncology and immunotherapy. They allow rapid simulations of temporal changes in the cellular and molecular populations involved. Nonetheless, ODEs cannot describe the spatial structure in the tumor microenvironment or quantify the influence of spatially-dependent characteristics of tumor-immune dynamics. For these reasons, agent-based models (ABMs) have gained popularity because they can model more detailed phenotypic and spatial heterogeneity that better reflect the complexity seen in vivo. In the context of anti-PD-1 ICIs, we compare treatment outcomes simulated from an ODE model and an ABM to show the importance of including spatial components in computational models of cancer immunotherapy. We consider tumor cells of high and low antigenicity and two distinct cytotoxic T lymphocyte (CTL) killing mechanisms. The preferred mechanism differs based on the antigenicity of tumor cells. Our ABM reveals varied phenotypic shifts within the tumor and spatial organization of tumor and CTLs despite similarities in key immune parameters, initial simulation conditions, and early temporal trajectories of the cell populations.

Mathematical model of MMC chemotherapy for non-invasive bladder cancer treatment

Mitomycin-C (MMC) chemotherapy is a well-established anti-cancer treatment for non-muscle-invasive bladder cancer (NMIBC). However, despite comprehensive biological research, the complete mechanism of action and an ideal regimen of MMC have not been elucidated. In this study, we present a theoretical investigation of NMIBC growth and its treatment by continuous administration of MMC chemotherapy. Using temporal ordinary differential equations (ODEs) to describe cell populations and drug molecules, we formulated the first mathematical model of tumor-immune interactions in the treatment of MMC for NMIBC, based on biological sources. Several hypothetical scenarios for NMIBC under the assumption that tumor size correlates with cell count are presented, depicting the evolution of tumors classified as small, medium, and large. These scenarios align qualitatively with clinical observations of lower recurrence rates for tumor size ≤ 30[mm] with MMC treatment, demonstrating that cure appears up to a theoretical x[mm] tumor size threshold, given specific parameters within a feasible biological range. The unique use of mole units allows to introduce a new method for theoretical pre-treatment assessments by determining MMC drug doses required for a cure. In this way, our approach provides initial steps toward personalized MMC chemotherapy for NMIBC patients, offering the possibility of new insights and potentially holding the key to unlocking some of its mysteries.

Optimal strategies of oncolytic virus-bortezomib therapy via the apoptotic, necroptotic, and oncolysis signaling network

Bortezomib and oncolytic virotherapy are two emerging targeted cancer therapies. Bortezomib, a proteasome inhibitor, disrupts protein degradation in cells, leading to the accumulation of unfolded proteins that induce apoptosis. On the other hand, virotherapy uses genetically modified oncolytic viruses (OVs) to infect cancer cells, trigger cell lysis, and activate anti-tumor response. Despite progress in cancer treatment, identifying administration protocols for therapeutic agents remains a significant concern, aiming to strike a balance between efficacy, minimizing toxicity, and administrative costs. In this work, optimal control theory was employed to design a cost-effective and efficient co-administration protocols for bortezomib and OVs that could significantly diminish the population of cancer cells via the cell death program with the NF$ \kappa $B-BAX-RIP1 signaling network. Both linear and quadratic control strategies were explored to obtain practical treatment approaches by adapting necroptosis protocols to efficient cell death programs. Our findings demonstrated that a combination therapy commencing with the administration of OVs followed by bortezomib infusions yields an effective tumor-killing outcome. These results could provide valuable guidance for the development of clinical administration protocols in cancer treatment.

IL-27 in combination with anti-PD-1 can be anti-cancer or pro-cancer

Interleukin-27 (IL-27) is known to play opposing roles in immunology. The present paper considers, specifically, the role IL-27 plays in cancer immunotherapy when combined with immune checkpoint inhibitor anti-PD-1. We first develop a mathematical model for this combination therapy, by a system of Partial Differential Equations, and show agreement with experimental results in mice injected with melanoma cells. We then proceed to simulate tumor volume with IL-27 injection at a variable dose F and anti-PD-1 at a variable dose g. We show that in some range of "small" values of g, as f increases tumor volume decreases as long as fFc(g), where Fc(g) is a monotone increasing function of g. This demonstrates that IL-27 can be both anti-cancer and pro-cancer, depending on the ranges of both anti-PD-1 and IL-27.

Different mechanisms of CD200-CD200R induce diverse outcomes in cancer treatment

The CD200 is a cell membrane protein expressed by tumor cells, and its receptor CD200 receptor (CD200R) is expressed by immune cells including macrophages and dendritic cells. The formation of CD200-CD200R inhibits the cellular functions of the targeted immune cells, so CD200 is one type of the immune checkpoint and blockade CD200-CD200R formation is a potential cancer treatment. However, the CD200 blockade has opposite treatment outcomes in different types of cancers. For instance, the CD200R deficient mice have a higher tumor load than the wild type (WT) mice in melanoma suggesting that CD200-CD200R inhibits melanoma. On the other hand, the antibody anti-CD200 treatment in pancreatic ductal adenocarcinoma (PDAC) and head and neck squamous cell carcinoma (HNSCC) significantly reduces the tumor load indicating that CD200-CD200R promotes PDAC and HNSCC. In this work, we hypothesize that different mechanisms of CD200-CD200R in tumor microenvironment could be one of the reasons for the diverse treatment outcomes of CD200 blockade in different types of cancers. We create one Ordinary Differential Equations (ODEs) model for melanoma including the inhibition of CCL8 and regulatory T cells and the switching from M2 to M1 macrophages by CD200-CD200R to capture the tumor inhibition by CD200-CD200R. We also create another ODEs model for PDAC and HNSCC including the promotion of the polarization and suppressive activities of M2 macrophages by CD200-CD200R to generate the tumor promotion by CD200-CD200R. Furthermore, we use these two models to investigate the treatment efficacy of the combination treatment between the CD200-CD200R blockade and the other immune checkpoint inhibitor, anti-PD-1. Our result shows that different mechanisms of CD200-CD200R can induce different treatment outcomes in combination treatments, namely, only the CD200-CD200R blockade reduces tumor load in melanoma and only the anti-PD-1 and CD200 knockout decrease tumor load in PDAC and HNSCC. Moreover, in melanoma, the CD200-CD200R mainly utilizes the inhibitions on M1 macrophages and dendritic cells to inhibit tumor growth, instead of M2 macrophages.

Modeling of oncolytic viruses in a heterogeneous cell population to predict spread into non-cancerous cells

New cancer treatment modalities that limit patient discomfort need to be developed. One possible new therapy is the use of oncolytic (cancer-killing) viruses. It is only recently that our ability to manipulate viral genomes has allowed us to consider deliberately infecting cancer patients with viruses. One key consideration is to ensure that the virus exclusively targets cancer cells and does not harm nearby non-cancerous cells. Here, we use a mathematical model of viral infection to determine the characteristics a virus would need to have in order to eradicate a tumor, but leave non-cancerous cells untouched. We conclude that the virus must differ in its ability to infect the two different cell types, with the infection rate of non-cancerous cells needing to be less than one hundredth of the infection rate of cancer cells. Differences in viral production rate or infectious cell death rate alone are not sufficient to protect non-cancerous cells.

Multiple colonies of cancer involved in mutual suppression with the immune system

We study the effects of the immune system on multiple cancer colonies. When cancer cells proliferate, cytotoxic T lymphocytes (CTLs) reactive to the cancer-specific antigens are activated, suppressing the growth of cancer colonies. The immune reaction activated by a large cancer colony may suppress and eliminate smaller colonies. However, cancer cells mitigate immune reactions by slowing down the activation of CTLs in dendritic cells with regulatory T cells and by inactivating CTLs attacking cancer cells with immune checkpoints. If cancer cells strongly suppress the immune reaction, the system may become bistable, where both the cancer-dominated and immunity-dominated states are locally stable. We study several models differing in the distance between colonies and the migration speeds of CTLs and regulatory T cells. We examine how the domains of attraction for multiple equilibria change with parameters. Nonlinear cancer-immunity dynamics may produce a sharp transition from a state with a small number of colonies and strong immunity to one with many colonies and weak immunity, resulting in the rapid emergence of many cancer colonies in the same organ or metastatic sites.

Mathematical Modeling of Oncolytic Virus Therapy Reveals Role of the Immune Response

Oncolytic adenoviruses (OAds) present a promising path for cancer treatment due to their selectivity in infecting and lysing tumor cells and their ability to stimulate the immune response. In this study, we use an ordinary differential equation (ODE) model of tumor growth inhibited by oncolytic virus activity to parameterize previous research on the effect of genetically re-engineered OAds in A549 lung cancer tumors in murine models. We find that the data are best fit by a model that accounts for an immune response, and that the immune response provides a mechanism for elimination of the tumor. We also find that parameter estimates for the most effective OAds share characteristics, most notably a high infection rate and low viral clearance rate, that might be potential reasons for these viruses' efficacy in delaying tumor growth. Further studies observing E1A and P19 recombined viruses in different tumor environments may further illuminate the extent of the effects of these genetic modifications.

Cancer therapy with immune checkpoint inhibitor and CSF-1 blockade: A mathematical model

Immune checkpoint inhibitors (ICIs) introduced in recent years have revolutionized the treatment of many metastatic cancers. However, data suggest that treatment has benefits only in a limited percentage of patients, and that this is due to immune suppression of the tumor microenvironment (TME). Anti-tumor inflammatory macrophages (M1), which are attracted to the TME, are converted by tumor secreted cytokines, such as CSF-1, to pro-tumor anti-inflammatory macrophages (M2), or tumor associated macrophages (TAMs), which block the anti-tumor T cells. In the present paper we develop a mathematical model that represents the interactions among the immune cells and cancer in terms of differential equations. The model can be used to assess treatments of combination therapy of anti-PD-1 with anti-CSF-1. Examples are given in comparing the efficacy among different strategies for anti-CSF-1 dosing in a setup of clinical trials.

Dynamic analysis of an age structure model for oncolytic virus therapy

Cancer is recognized as one of the serious diseases threatening human health. Oncolytic therapy is a safe and effective new cancer treatment method. Considering the limited ability of uninfected tumor cells to infect and the age of infected tumor cells have a significant effect on oncolytic therapy, an age-structured model of oncolytic therapy involving Holling-Ⅱ functional response is proposed to investigate the theoretical significance of oncolytic therapy. First, the existence and uniqueness of the solution is obtained. Furthermore, the stability of the system is confirmed. Then, the local stability and global stability of infection-free homeostasis are studied. The uniform persistence and local stability of the infected state are studied. The global stability of the infected state is proved by constructing the Lyapunov function. Finally, the theoretical results are verified by numerical simulation. The results show that when the tumor cells are at the appropriate age, injection of the right amount of oncolytic virus can achieve the purpose of tumor treatment.

Optimal timing of steroid initiation in response to CTLA-4 antibody in metastatic cancer: A mathematical model

Immune checkpoint inhibitors, introduced in recent years, have revolutionized the treatment of many cancers. However, the toxicity associated with this therapy may cause severe adverse events. In the case of advanced lung cancer or metastatic melanoma, a significant number (10%) of patients treated with CTLA-4 inhibitor incur damage to the pituitary gland. In order to reduce the risk of hypophysitis and other severe adverse events, steroids may be combined with CTLA-4 inhibitor; they reduce toxicity, but they also diminish the anti-cancer effect of the immunotherapy. This trade-off between tumor reduction and the risk of severe adverse events poses the following question: What is the optimal time to initiate treatment with steroid. We address this question with a mathematical model from which we can also evaluate the comparative benefits of each schedule of steroid administration. In particular, we conclude that treatment with steroid should not begin too early, but also not very late, after immunotherapy began; more precisely, it should start as soon as tumor volume, under the effect of CTLA-4 inhibitor alone, begins to decrease. We can also compare the benefits of short term treatment of steroid at high doses to a longer term treatment with lower doses.

Mathematical modeling for the combination treatment of IFN- γ and anti-PD-1 in cancer immunotherapy

When the immune-checkpoint programmed death-1 (PD-1) binds to its ligand programmed death ligand 1 (PD-L1) to form the complex PD-1-PD-L1, this complex inactivates immune cells resulting in cell apoptosis, downregulation of immune reaction, and tumor evasion. The antibody, anti-PD-1 or anti-PD-L1, blocks the PD-1-PD-L1 complex formation to restore the functions of T cells. Combination of anti-PD-1 with other treatment shows promising in different types of cancer treatments. Interferon-gamma (IFN-γ) plays an important role in immune responses. It is mainly regarded as a pro-inflammatory cytokine that promotes the proliferation of CD8⁺ T cell and cytotoxic T cell, enhances the activation of Th1 cells and CD8⁺ T cells, and enhances tumor elimination. However, recent studies have been discovering many anti-inflammatory functions of IFN-γ, such as promotion of the PD-L1 expression, T cell apoptosis, and tumor metastasis, as well as inhibition of the immune recognition and the killing rates by T cells. In this work, we construct a mathematical model incorporating pro-inflammatory and anti-inflammatory functions of IFN-γ to capture tumor growth under anti-PD-1 treatment in the wild type and IFN-γ null mutant melanoma. Our simulation results qualitatively fit experimental data that IFN-γ null mutant with anti-PD-1 obtains the highest tumor reduction comparing to IFN-γ null mutant without anti-PD-1 and wild type tumor with anti-PD-1 therapy. Moreover, our synergy analysis indicates that, in the combination treatment, the tumor volume decreases as either the dosage of anti-PD-1 increases or the IFN-γ production efficiency decreases. Thus, the combination of anti-PD-1 and IFN-γ blockade improves the tumor reduction comparing to the monotherapy of anti-PD-1 or the monotherapy of IFN-γ blockade. We also find a threshold curve of the minimal dosage of anti-PD-1 corresponding to the IFN-γ production efficiency to ensure the tumor reduction under the presence of IFN-γ.

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.

Interlocked feedback loops balance the adaptive immune response

Adaptive immune responses can be activated by harmful stimuli. Upon activation, a cascade of biochemical events ensues the proliferation and the differentiation of T cells, which can remove the stimuli and undergo cell death to maintain immune cell homeostasis. However, normal immune processes can be disrupted by certain dysregulations, leading to pathological responses, such as cytokine storms and immune escape. In this paper, a qualitative mathematical model, composed of key feedback loops within the immune system, was developed to study the dynamics of various response behaviors. First, simulation results of the model well reproduce the results of several immune response processes, particularly pathological immune responses. Next, we demonstrated how the interaction of positive and negative feedback loops leads to irreversible bistable, reversible bistable and monostable, which characterize different immune response processes: cytokine storm, normal immune response, immune escape. The stability analyses suggest that the switch-like behavior is the basis of rapid activation of the immune system, and a balance between positive and negative regulation loops is necessary to prevent pathological responses. Furthermore, we have shown how the treatment moves the system back to a healthy state from the pathological immune response. The bistable mechanism that revealed in this work is helpful to understand the dynamics of different immune response processes.

Combination therapy for mCRPC with immune checkpoint inhibitors, ADT and vaccine: A mathematical model

Metastatic castration resistant prostate cancer (mCRPC) is commonly treated by androgen deprivation therapy (ADT) in combination with chemotherapy. Immune therapy by checkpoint inhibitors, has become a powerful new tool in the treatment of melanoma and lung cancer, and it is currently being used in clinical trials in other cancers, including mCRPC. However, so far, clinical trials with PD-1 and CTLA-4 inhibitors have been disappointing. In the present paper we develop a mathematical model to assess the efficacy of any combination of ADT with cancer vaccine, PD-1 inhibitor, and CTLA-4 inhibitor. The model is represented by a system of partial differential equations (PDEs) for cells, cytokines and drugs whose density/concentration evolves in time within the tumor. Efficacy of treatment is determined by the reduction in tumor volume at the endpoint of treatment. In mice experiments with ADT and various combinations of PD-1 and CTLA-4 inhibitors, tumor volume at day 30 was always larger than the initial tumor. Our model, however, shows that we can decrease tumor volume with large enough dose; for example, with 10 fold increase in the dose of anti-PD-1, initial tumor volume will decrease by 60%. Although the treatment with ADT in combination with PD-1 inhibitor or CTLA-4 inhibitor has been disappointing in clinical trials, our simulations suggest that, disregarding negative effects, combinations of ADT with checkpoint inhibitors can be effective in reducing tumor volume if larger doses are used. This points to the need for determining the optimal combination and amounts of dose for individual patients.

Uses of Bacteriophages as Bacterial Control Tools and Environmental Safety Indicators

Bacteriophages are bacterial-specific viruses and the most abundant biological form on Earth. Each bacterial species possesses one or multiple bacteriophages and the specificity of infection makes them a promising alternative for bacterial control and environmental safety, as a biotechnological tool against pathogenic bacteria, including those resistant to antibiotics. This application can be either directly into foods and food-related environments as biocontrol agents of biofilm formation. In addition, bacteriophages are used for microbial source-tracking and as fecal indicators. The present review will focus on the uses of bacteriophages like bacterial control tools, environmental safety indicators as well as on their contribution to bacterial control in human, animal, and environmental health.

Strategies for the treatment of breast cancer: from classical drugs to mathematical models

Breast cancer is one of the most common cancers and generally affects women. It is a heterogeneous disease that presents different entities, different biological characteristics, and differentiated clinical behaviors. With this in mind, this literature review had as its main objective to analyze the path taken from the simple use of classical drugs to the application of mathematical models, which through the many ongoing studies, have been considered as one of the reliable strategies, explaining the reasons why chemotherapy is not always successful. Besides, the most commonly mentioned strategies are immunotherapy, which includes techniques and therapies such as the use of antibodies, cytokines, antitumor vaccines, oncolytic and genomic viruses, among others, and nanoparticles, including metallic, magnetic, polymeric, liposome, dendrimer, micelle, and others, as well as drug reuse, which is a process by which new therapeutic indications are found for existing and approved drugs. The most commonly used pharmacological categories are cardiac, antiparasitic, anthelmintic, antiviral, antibiotic, and others. For the efficient development of reused drugs, there must be a process of exchange of purposes, methods, and information already available, and for their better understanding, computational mathematical models are then used, of which the methods of blind search or screening, based on the target, knowledge, signature, pathway or network and the mechanism to which it is directed, stand out. To conclude it should be noted that these different strategies can be applied alone or in combination with each other always to improve breast cancer treatment.

Natural Killer Cells Recruitment in Oncolytic Virotherapy: A Mathematical Model

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.

Dynamical systems analysis as an additional tool to inform treatment outcomes: The case study of a quantitative systems pharmacology model of immuno-oncology

Quantitative systems pharmacology (QSP) proved to be a powerful tool to elucidate the underlying pathophysiological complexity that is intensified by the biological variability and overlapped by the level of sophistication of drug dosing regimens. Therapies combining immunotherapy with more traditional therapeutic approaches, including chemotherapy and radiation, are increasingly being used. These combinations are purposed to amplify the immune response against the tumor cells and modulate the suppressive tumor microenvironment (TME). In order to get the best performance from these combinatorial approaches and derive rational regimen strategies, a better understanding of the interaction of the tumor with the host immune system is needed. The objective of the current work is to provide new insights into the dynamics of immune-mediated TME and immune-oncology treatment. As a case study, we will use a recent QSP model by Kosinsky et al. [J. Immunother. Cancer 6, 17 (2018)] that aimed to reproduce the dynamics of interaction between tumor and immune system upon administration of radiation therapy and immunotherapy. Adopting a dynamical systems approach, we here investigate the qualitative behavior of the representative components of this QSP model around its key parameters. The ability of T cells to infiltrate tumor tissue, originally identified as responsible for individual therapeutic inter-variability [Y. Kosinsky et al., J. Immunother. Cancer 6, 17 (2018)], is shown here to be a saddle-node bifurcation point for which the dynamical system oscillates between two states: tumor-free or maximum tumor volume. By performing a bifurcation analysis of the physiological system, we identified equilibrium points and assessed their nature. We then used the traditional concept of basin of attraction to assess the performance of therapy. We showed that considering the therapy as input to the dynamical system translates into the changes of the trajectory shapes of the solutions when approaching equilibrium points and thus providing information on the issue of therapy.

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.

The role of viral infectivity in oncolytic virotherapy outcomes: A mathematical study

A model capturing the dynamics between virus and tumour cells in the context of oncolytic virotherapy is presented and analysed. The ability of the virus to be internalised by uninfected cells is described by an infectivity parameter, which is inferred from available experimental data. The parameter is also able to describe the effects of changes in the tumour environment that affect viral uptake from tumour cells. Results show that when a virus is inoculated inside a growing tumour, strategies for enhancing infectivity do not lead to a complete eradication of the tumour. Within typical times of experiments and treatments, we observe the onset of oscillations, which always prevent a full destruction of the tumour mass. These findings are in good agreement with available laboratory results. Further analysis shows why a fully successful therapy cannot exist for the proposed model and that care must be taken when designing and engineering viral vectors with enhanced features. In particular, bifurcation analysis reveals that creating longer lasting virus particles or using strategies for reducing infected cell lifespan can cause unexpected and unwanted surges in the overall tumour load over time. Our findings suggest that virotherapy alone seems unlikely to be effective in clinical settings unless adjuvant strategies are included.

A mathematical model of the multiple sclerosis plaque

Multiple sclerosis is an autoimmune disease that affects white matter in the central nervous system. It is one of the primary causes of neurological disability among young people. Its characteristic pathological lesion is called a plaque, a zone of inflammatory activity and tissue destruction that expands radially outward by destroying the myelin and oligodendrocytes of white matter. The present paper develops a mathematical model of the multiple sclerosis plaques. Although these plaques do not provide reliable information of the clinical disability in MS, they are nevertheless useful as a primary outcome measure of Phase II trials. The model consists of a system of partial differential equations in a simplified geometry of the lesion, consisting of three domains: perivascular space, demyelinated plaque, and white matter. The model describes the activity of various pro- and anti-inflammatory cells and cytokines in the plaque, and quantifies their effect on plaque growth. We show that volume growth of plaques are in qualitative agreement with reported clinical studies of several currently used drugs. We then use the model to explore treatments with combinations of such drugs, and with experimental drugs. We finally consider the benefits of early vs. delayed treatment.

Identifying and characterising the impact of excitability in a mathematical model of tumour-immune interactions

We study a five-compartment mathematical model originally proposed by Kuznetsov et al. (1994) to investigate the effect of nonlinear interactions between tumour and immune cells in the tumour microenvironment, whereby immune cells may induce tumour cell death, and tumour cells may inactivate immune cells. Exploiting a separation of timescales in the model, we use the method of matched asymptotics to derive a new two-dimensional, long-timescale, approximation of the full model, which differs from the quasi-steady-state approximation introduced by Kuznetsov et al. (1994), but is validated against numerical solutions of the full model. Through a phase-plane analysis, we show that our reduced model is excitable, a feature not traditionally associated with tumour-immune dynamics. Through a systematic parameter sensitivity analysis, we demonstrate that excitability generates complex bifurcating dynamics in the model. These are consistent with a variety of clinically observed phenomena, and suggest that excitability may underpin tumour-immune interactions. The model exhibits the three stages of immunoediting - elimination, equilibrium, and escape, via stable steady states with different tumour cell concentrations. Such heterogeneity in tumour cell numbers can stem from variability in initial conditions and/or model parameters that control the properties of the immune system and its response to the tumour. We identify different biophysical parameter targets that could be manipulated with immunotherapy in order to control tumour size, and we find that preferred strategies may differ between patients depending on the strength of their immune systems, as determined by patient-specific values of associated model parameters.

TNF-α inhibitor reduces drug-resistance to anti-PD-1: A mathematical model

Drug resistance is a primary obstacle in cancer treatment. In many patients who at first respond well to treatment, relapse occurs later on. Various mechanisms have been explored to explain drug resistance in specific cancers and for specific drugs. In this paper, we consider resistance to anti-PD-1, a drug that enhances the activity of anti-cancer T cells. Based on results in experimental melanoma, it is shown, by a mathematical model, that resistances to anti-PD-1 can be significantly reduced by combining it with anti-TNF-α. The model is used to simulate the efficacy of the combined therapy with different range of doses, different initial tumor volume, and different schedules. In particular, it is shown that under a course of treatment with 3-week cycles where each drug is injected in the first day of either week 1 or week 2, injecting anti-TNF-α one week after anti-PD-1 is the most effective schedule in reducing tumor volume.

Analysis of a mathematical model of rheumatoid arthritis

Rheumatoid arthritis is an autoimmune disease characterized by inflammation in the synovial fluid within the synovial joint connecting two contiguous bony surfaces. The inflammation diffuses into the cartilage adjacent to each of the bony surfaces, resulting in their gradual destruction. The interface between the cartilage and the synovial fluid is an evolving free boundary. In this paper we consider a two-phase free boundary problem based on a simplified model of rheumatoid arthritis. We prove global existence and uniqueness of a solution, and derive properties of the free boundary. In particular it is proved that the free boundary increases in time, and the cartilage shrinks to zero as [Formula: see text], even under treatment by a drug. It is also shown in the reduced one-phased problem, with cartilage alone, that a larger prescribed inflammation function leads to a faster destruction of the cartilage.

Mathematical Modeling of Oncolytic Virotherapy

Mathematical modeling in biology has a long history as it allows the analysis and simulation of complex dynamic biological systems at little cost. A mathematical model trained on experimental or clinical data can be used to generate and evaluate hypotheses, to ask "what if" questions, and to perform in silico experiments to guide future experimentation and validation. Such models may help identify and provide insights into the mechanisms that drive changes in dynamic systems. While a mathematical model may never replace actual experiments, it can synergize with experiments to save time and resources by identifying experimental conditions that are unlikely to yield favorable outcomes, and by using optimization principles to identify experiments that are most likely to be successful. Over the past decade, numerous models have also been developed for oncolytic virotherapy, ranging from merely theoretic frameworks to fully integrated studies that utilize experimental data to generate actionable hypotheses. Here we describe how to develop such models for specific oncolytic virotherapy experimental setups, and which questions can and cannot be answered using integrated mathematical oncology.

Kinetics of Oncolytic Reovirus T3D Replication and Growth Pattern in Mesenchymal Stem Cells

Objective

Currently, application of oncolytic-virus in cancer treatment of clinical trials are growing. Oncolytic-reovirus is an attractive anti-cancer therapeutic agent for clinical testing. Many studies used mesenchymal stem cells (MSCs) as a carrier cell to enhance the delivery and quality of treatment with oncolytic-virotherapy. But, biosynthetic capacity and behavior of cells in response to viral infections are different. The infecting process of reoviruses takes from two-hours to one-week, depends on host cell and the duration of different stages of virus replication cycle. The latter includes the binding of virus particle, entry, uncoating, assembly and release of progeny-viruses. We evaluated the timing and infection cycle of reovirus type-3 strain Dearing (T3D), using one-step replication experiment by molecular and conventional methods in MSCs and L929 cell as control.

Materials and Methods

In this experimental study, L929 and adipose-derived MSCs were infected with different multiplicities of infection (MOI) of reovirus T3D. At different time points, the quantity of progeny viruses has been measured using virus titration assay and quantitative real-time polymerase chain reaction (qRT-PCR) to investigate the ability of these cells to support the reovirus replication. One-step growth cycle were examined by 50% cell culture infectious dose (CCID₅₀) and qRT-PCR.

Results

The growth curve of reovirus in cells shows that MOI: 1 might be optimal for virus production compared to higher and lower MOIs. The maximum quantity of virus production using MOI: 1 was achieved at 48-hours post-infection. The infectious virus titer became stationary at 72-hours post-infection and then gradually decreased. The virus cytopathic effect was obvious in MSCs and this cells were susceptible to reovirus infection and support the virus replication.

Conclusion

Our data highlights the timing schedule for reovirus replication, kinetics models and burst size. Further investigation is recommended to better understanding of the challenges and opportunities, for using MSCs loaded with reovirus in cancer-therapy.

Targeting Negative and Positive Immune Checkpoints with Monoclonal Antibodies in Therapy of Cancer

The immune checkpoints are regulatory molecules that maintain immune homeostasis in physiological conditions. By sending T cells a series of co-stimulatory or co-inhibitory signals via receptors, immune checkpoints can both protect healthy tissues from adaptive immune response and activate lymphocytes to remove pathogens effectively. However, due to their mode of action, suppressive immune checkpoints may serve as unwanted protection for cancer cells. To restore the functioning of the immune system and make the patient’s immune cells able to recognize and destroy tumors, monoclonal antibodies are broadly used in cancer immunotherapy to block the suppressive or to stimulate the positive immune checkpoints. In this review, we aim to present the current state of application of monoclonal antibodies in clinics, used either as single agents or in a combined treatment. We discuss the limitations of these therapies and possible problem-solving with combined treatment approaches involving both non-biological and biological agents. We also highlight the most promising strategies based on the use of monoclonal or bispecific antibodies targeted on immune checkpoints other than currently implemented in clinics.

Spatial Model for Oncolytic Virotherapy with Lytic Cycle Delay

We formulate a mathematical model of functional partial differential equations for oncolytic virotherapy which incorporates virus diffusivity, tumor cell diffusion, and the viral lytic cycle based on a basic oncolytic virus dynamics model. We conduct a detailed analysis for the dynamics of the model and carry out numerical simulations to demonstrate our analytic results. Particularly, we establish the positive invariant domain for the [Formula: see text] limit set of the system and show that the model has three spatially homogenous equilibriums solutions. We prove that the spatially uniform virus-free steady state is globally asymptotically stable for any viral lytic period delay and diffusion coefficients of tumor cells and viruses when the viral burst size is smaller than a critical value. We obtain the conditions, for example the ratio of virus diffusion coefficient to that of tumor cells is greater than a value and the viral lytic cycle, is greater than a critical value, under which the spatially uniform positive steady state is locally asymptotically stable. We also obtain conditions under which the system undergoes Hopf bifurcations, and stable periodic solutions occur. We point out medical implications of our results which are difficult to obtain from models without combining diffusive properties of viruses and tumor cells with viral lytic cycles.

Modeling Pancreatic Cancer Dynamics with Immunotherapy

We develop a mathematical model of pancreatic cancer that includes pancreatic cancer cells, pancreatic stellate cells, effector cells and tumor-promoting and tumor-suppressing cytokines to investigate the effects of immunotherapies on patient survival. The model is first validated using the survival data of two clinical trials. Local sensitivity analysis of the parameters indicates there exists a critical activation rate of pro-tumor cytokines beyond which the cancer can be eradicated if four adoptive transfers of immune cells are applied. Optimal control theory is explored as a potential tool for searching the best adoptive cellular immunotherapies. Combined immunotherapies between adoptive ex vivo expanded immune cells and TGF-[Formula: see text] inhibition by siRNA treatments are investigated. This study concludes that mono-immunotherapy is unlikely to control the pancreatic cancer and combined immunotherapies between anti-TGF-[Formula: see text] and adoptive transfers of immune cells can prolong patient survival. We show through numerical explorations that how these two types of immunotherapies are scheduled is important to survival. Applying TGF-[Formula: see text] inhibition first followed by adoptive immune cell transfers can yield better survival outcomes.

The viral approach to breast cancer immunotherapy

Despite years of intensive research, breast cancer remains the leading cause of death in women worldwide. New technologies including oncolytic virus therapies, virus, and phage display are among the most powerful and advanced methods that have emerged in recent years with potential applications in cancer prevention and treatment. Oncolytic virus therapy is an interesting strategy for cancer treatment. Presently, a number of viruses from different virus families are under laboratory and clinical investigation as oncolytic therapeutics. Oncolytic viruses (OVs) have been shown to be able to induce and initiate a systemic antitumor immune response. The possibility of application of a multimodal therapy using a combination of the OV therapy with immune checkpoint inhibitors and cancer antigen vaccination holds a great promise in the future of cancer immunotherapy. Display of immunologic peptides on bacterial viruses (bacteriophages) is also increasingly being considered as a new and strong cancer vaccine delivery strategy. In phage display immunotherapy, a peptide or protein antigen is presented by genetic fusions to the phage coat proteins, and the phage construct formulation acts as a protective or preventive vaccine against cancer. In our laboratory, we have recently tested a few peptides (E75, AE37, and GP2) derived from HER2/neu proto-oncogene as vaccine delivery modalities for the treatment of TUBO breast cancer xenograft tumors of BALB/c mice. Here, in this paper, we discuss the latest advancements in the applications of OVs and bacterial viruses display systems as new and advanced modalities in cancer immune therapeutics.