Oncolytic potency and reduced virus tumor-specificity in oncolytic virotherapy. A mathematical modelling approach

Oscillations in a Spatial Oncolytic Virus Model

Virotherapy treatment is a new and promising target therapy that selectively attacks cancer cells without harming normal cells. Mathematical models of oncolytic viruses have shown predator-prey like oscillatory patterns as result of an underlying Hopf bifurcation. In a spatial context, these oscillations can lead to different spatio-temporal phenomena such as hollow-ring patterns, target patterns, and dispersed patterns. In this paper we continue the systematic analysis of these spatial oscillations and discuss their relevance in the clinical context. We consider a bifurcation analysis of a spatially explicit reaction-diffusion model to find the above mentioned spatio-temporal virus infection patterns. The desired pattern for tumor eradication is the hollow ring pattern and we find exact conditions for its occurrence. Moreover, we derive the minimal speed of travelling invasion waves for the cancer and for the oncolytic virus. Our numerical simulations in 2-D reveal complex spatial interactions of the virus infection and a new phenomenon of a periodic peak splitting. An effect that we cannot explain with our current methods.

The role of immune cells in resistance to oncolytic viral therapy

Resistance to treatment poses a major challenge for cancer therapy, and oncoviral treatment encounters the issue of viral resistance as well. In this investigation, we introduce deterministic differential equation models to explore the effect of resistance on oncolytic viral therapy. Specifically, we classify tumor cells into resistant, sensitive, or infected with respect to oncolytic viruses for our analysis. Immune cells can eliminate both tumor cells and viruses. Our research shows that the introduction of immune cells into the tumor-virus interaction prevents all tumor cells from becoming resistant in the absence of conversion from resistance to sensitivity, given that the proliferation rate of immune cells exceeds their death rate. The inclusion of immune cells leads to an additional virus-free equilibrium when the immune cell recruitment rate is sufficiently high. The total tumor burden at this virus-free equilibrium is smaller than that at the virus-free and immune-free equilibrium. Therefore, immune cells are capable of reducing the tumor load under the condition of sufficient immune strength. Numerical investigations reveal that the virus transmission rate and parameters related to the immune response significantly impact treatment outcomes. However, monotherapy alone is insufficient for eradicating tumor cells, necessitating the implementation of additional therapies. Further numerical simulation shows that combination therapy with chimeric antigen receptor (CAR T-cell) therapy can enhance the success of treatment.

Assessment of Clinical Response to V937 Oncolytic Virus After Intravenous or Intratumoral Administration Using Physiologically-Based Modeling

Oncolytic viruses (OVs) represent a potential therapeutic strategy in cancer treatment. However, there is currently a lack of comprehensive quantitative models characterizing clinical OV kinetics and distribution to the tumor. In this work, we present a mechanistic modeling framework for V937 OV, after intratumoral (i.t.) or intravascular (i.v.) administration in patients with cancer. A minimal physiologically-based pharmacokinetic model was built to characterize biodistribution of OVs in humans. Viral dynamics was incorporated at the i.t. cellular level and linked to tumor response, enabling the characterization of a direct OV killing triggered by the death of infected tumor cells and an indirect killing induced by the immune response. The model provided an adequate description of changes in V937 mRNA levels and tumor size obtained from phase I/II clinical trials after V937 administration. The model showed prominent role of viral clearance from systemic circulation and infectivity in addition to known tumor aggressiveness on clinical response. After i.v. administration, i.t. exposure of V937 was predicted to be several orders of magnitude lower compared with i.t. administration. These differences could be overcome if there is high virus infectivity and/or replication. Unfortunately, the latter process could not be identified at the current clinical setting. This work provides insights on selecting optimal OV considering replication rate and infectivity.

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.

Exploring the Interactions of Oncolytic Viral Therapy and Immunotherapy of Anti-CTLA-4 for Malignant Melanoma Mice Model

Oncolytic ability to direct target and lyse tumor cells makes oncolytic virus therapy (OVT) a promising approach to treating cancer. Despite its therapeutic potential to stimulate anti-tumor immune responses, it also has immunosuppressive effects. The efficacy of OVTs as monotherapies can be enhanced by appropriate adjuvant therapy such as anti-CTLA-4. In this paper, we propose a mathematical model to explore the interactions of combined therapy of oncolytic viruses and a checkpoint inhibitor, anti-CTLA-4. The model incorporates both the susceptible and infected tumor populations, natural killer cell population, virus population, tumor-specific immune populations, virus-specific immune populations, tumor suppressive cytokine IFN-g, and the effect of immune checkpoint inhibitor CTLA-4. In particular, we distinguish the tumor-specific immune abilities of CD8⁺ T, NK cells, and CD4⁺ T cells and describe the destructive ability of cytokine on tumor cells as well as the inhibitory capacity of CTLA-4 on various components. Our model is validated through the experimental results. We also investigate various dosing strategies to improve treatment outcomes. Our study reveals that tumor killing rate by cytokines, cytokine decay rate, and tumor growth rate play important roles on both the OVT monotherapy and the combination therapy. Moreover, parameters related to CD8⁺ T cell killing have a large impact on treatment outcomes with OVT alone, whereas parameters associated with IFN-g strongly influence treatment responses for the combined therapy. We also found that virus killing by NK cells may halt the desired spread of OVs and enhance the probability of tumor escape during the treatment. Our study reveals that it is the activation of host anti-tumor immune system responses rather than its direct destruction of the tumor cells plays a major biological function of the combined therapy.

Oncolytic viral kinetics mechanistic modeling of Talimogene Laherparepvec (T-VEC) a first-in-class oncolytic viral therapy in patients with advanced melanoma

Talimogene Laherparepvec (T-VEC) is a first-in-class oncolytic virotherapy approved for the treatment of unresectable melanoma recurrent after initial surgery. Biodistribution data from a phase II study was used to develop a viral kinetic mechanistic model describing the interaction between cytokines such as granulocyte-macrophage colony-stimulating factor (GM-CSF), the immune system, and T-VEC treatment. Our analysis found that (1) the viral infection rate has a great influence on T-VEC treatment efficacy; (2) an increase in T-VEC dose of 10² plaque-forming units/ml 21 days and beyond after the initial dose of T-VEC resulted in an ~12% increase in response; and (3) at the systemic level, the ratio of resting innate immune cells to the death rate of innate immune impact T-VEC treatment efficacy. This analysis clarifies under which condition the immune system either assists in eliminating tumor cells or inhibits T-VEC treatment efficacy, which is critical to both efficiently design future oncolytic agents and understand cancer development.

Modelling the spatial dynamics of oncolytic virotherapy in the presence of virus-resistant tumour cells

Oncolytic virotherapy is a promising form of cancer treatment that uses native or genetically engineered viruses to target, infect and kill cancer cells. Unfortunately, this form of therapy is not effective in a substantial proportion of cancer patients, partly due to the occurrence of infection-resistant tumour cells. To shed new light on the mechanisms underlying therapeutic failure and to discover strategies that improve therapeutic efficacy we designed a cell-based model of viral infection. The model allows us to investigate the dynamics of infection-sensitive and infection-resistant cells in tumour tissue in presence of the virus. To reflect the importance of the spatial configuration of the tumour on the efficacy of virotherapy, we compare three variants of the model: two 2D models of a monolayer of tumour cells and a 3D model. In all model variants, we systematically investigate how the therapeutic outcome is affected by the properties of the virus (e.g. the rate of viral spread), the tumour (e.g. production rate of resistant cells, cost of resistance), the healthy stromal cells (e.g. degree of resistance to the virus) and the timing of treatment. We find that various therapeutic outcomes are possible when resistant cancer cells arise at low frequency in the tumour. These outcomes depend in an intricate but predictable way on the death rate of infected cells, where faster death leads to rapid virus clearance and cancer persistence. Our simulations reveal three different causes of therapy failure: rapid clearance of the virus, rapid selection of resistant cancer cells, and a low rate of viral spread due to the presence of infection-resistant healthy cells. Our models suggest that improved therapeutic efficacy can be achieved by sensitizing healthy stromal cells to infection, although this remedy has to be weighed against the toxicity induced in the healthy tissue.

Development of Molecular Mechanisms and Their Application on Oncolytic Newcastle Disease Virus in Cancer Therapy

Cancer is caused by the destruction or mutation of cellular genetic materials induced by environmental or genetic factors. It is defined by uncontrolled cell proliferation and abnormality of the apoptotic pathways. The majority of human malignancies are characterized by distant metastasis and dissemination. Currently, the most common means of cancer treatment include surgery, radiotherapy, and chemotherapy, which usually damage healthy cells and cause toxicity in patients. Targeted therapy is an effective tumor treatment method with few side effects. At present, some targeted therapeutic drugs have achieved encouraging results in clinical studies, but finding an effective solution to improve the targeting and delivery efficiency of these drugs remains a challenge. In recent years, oncolytic viruses (OVs) have been used to direct the tumor-targeted therapy or immunotherapy. Newcastle disease virus (NDV) is a solid oncolytic agent capable of directly killing tumor cells and increasing tumor antigen exposure. Simultaneously, NDV can trigger the proliferation of tumor-specific immune cells and thus improve the therapeutic efficacy of NDV in cancer. Based on NDV’s inherent oncolytic activity and the stimulation of antitumor immune responses, the combination of NDV and other tumor therapy approaches can improve the antitumor efficacy while reducing drug toxicity, indicating a broad application potential. We discussed the biological properties of NDV, the antitumor molecular mechanisms of oncolytic NDV, and its application in the field of tumor therapy in this review. Furthermore, we presented new insights into the challenges that NDV will confront and suggestions for increasing NDV’s therapeutic efficacy in cancer.

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.

Bistability in a model of tumor-immune system interactions with an oncolytic viral therapy

A mathematical model of tumor-immune system interactions with an oncolytic virus therapy for which the immune system plays a twofold role against cancer cells is derived. The immune cells can kill cancer cells but can also eliminate viruses from the therapy. In addition, immune cells can either be stimulated to proliferate or be impaired to reduce their growth by tumor cells. It is shown that if the tumor killing rate by immune cells is above a critical value, the tumor can be eradicated for all sizes, where the critical killing rate depends on whether the immune system is immunosuppressive or proliferative. For a reduced tumor killing rate with an immunosuppressive immune system, that bistability exists in a large parameter space follows from our numerical bifurcation study. Depending on the tumor size, the tumor can either be eradicated or be reduced to a size less than its carrying capacity. However, reducing the viral killing rate by immune cells always increases the effectiveness of the viral therapy. This reduction may be achieved by manipulating certain genes of viruses via genetic engineering or by chemical modification of viral coat proteins to avoid detection by the immune cells.

An Agent-Based Model of Combination Oncolytic Viral Therapy and Anti-PD-1 Immunotherapy Reveals the Importance of Spatial Location When Treating Glioblastoma

Simple Summary

A combination of oncolytic viral therapy and immunotherapy provides an alternative option to the standard of care for treating the lethal brain tumor glioblastoma (GBM). Although this combination therapy shows promise, there are many unknown questions regarding how the tumor landscape and spatial dosing strategies impact the effectiveness of the treatment. Our study aims to shed light on these questions using a novel spatially explicit computational model of GBM response to treatment. Our results suggest that oncolytic viral dosing in the location of highest tumor cell density leads to substantial tumor size reduction over viral dosing in the center of the tumor. These results can help to inform future clinical trials and more effective treatment strategies for oncolytic viral therapy in GBM patients.

Abstract

Oncolytic viral therapies and immunotherapies are of growing clinical interest due to their selectivity for tumor cells over healthy cells and their immunostimulatory properties. These treatment modalities provide promising alternatives to the standard of care, particularly for cancers with poor prognoses, such as the lethal brain tumor glioblastoma (GBM). However, uncertainty remains regarding optimal dosing strategies, including how the spatial location of viral doses impacts therapeutic efficacy and tumor landscape characteristics that are most conducive to producing an effective immune response. We develop a three-dimensional agent-based model (ABM) of GBM undergoing treatment with a combination of an oncolytic Herpes Simplex Virus and an anti-PD-1 immunotherapy. We use a mechanistic approach to model the interactions between distinct populations of immune cells, incorporating both innate and adaptive immune responses to oncolytic viral therapy and including a mechanism of adaptive immune suppression via the PD-1/PD-L1 checkpoint pathway. We utilize the spatially explicit nature of the ABM to determine optimal viral dosing in both the temporal and spatial contexts. After proposing an adaptive viral dosing strategy that chooses to dose sites at the location of highest tumor cell density, we find that, in most cases, this adaptive strategy produces a more effective treatment outcome than repeatedly dosing in the center of the tumor.

Age-structure model for oncolytic virotherapy

A non-local delay differential system was developed by age-infected consideration to understand the interaction between tumor cells and oncolytic virus. The critical threshold value [Formula: see text] was obtained that dominates the dynamical behaviors of our model. By strongly [Formula: see text]-persistent and Comparison theorem, the global stability and uniformly strongly persistent were investigated. Our global sensitivity analyses indicate that [Formula: see text] is most sensitive to virus clearance rate [Formula: see text] while is least sensitive to viral life cycle [Formula: see text]. Finally, our model was used to fit with experimental data which indicates that viral life cycle [Formula: see text] plays a key role in data fitting. And the trained model shows perfect prediction in the testing data set with the coefficient of determination [Formula: see text].

Computation of the conditions for anti-angiogenesis and gene therapy synergistic effects: Sensitivity analysis and robustness of target solutions

Both anti-angiogenesis and gene therapy involve complex processes depending on non-point parameters belonging to a space of values. To successfully overcome the challenges involved in their therapeutic approaches, there is a need to analyze the sensitivity of these parameters. In this paper, a new mathematical model that combines immune system stimulations, inflammatory processes associated with tumor development, and gene therapy aimed at enhancing the efficacy of both treatments are explored. Using the global sensitivity methods of Sobol and Morris, the most important parameters are estimated. Estimation of the sensitivity variance revealed a strong interdependence between the parameters. Also, determinations of the conditions for effective therapy lead to a target of reducing the cancer cell numbers by at least 50%. This opened the way for delimiting the parameter spaces making it possible to reach the treatment target in addition to enhancing the estimation of the minimum time of remission. The combination of therapies and sensitivity analysis have demonstrated the robustness of therapy success.

Mechanistic Modeling of a Novel Oncolytic Virus, V937, to Describe Viral Kinetic and Dynamic Processes Following Intratumoral and Intravenous Administration

V937 is an investigational novel oncolytic non-genetically modified Kuykendall strain of Coxsackievirus A21 which is in clinical development for the treatment of advanced solid tumor malignancies. V937 infects and lyses tumor cells expressing the intercellular adhesion molecule I (ICAM-I) receptor. We integrated in vitro and in vivo data from six different preclinical studies to build a mechanistic model that allowed a quantitative analysis of the biological processes of V937 viral kinetics and dynamics, viral distribution to tumor, and anti-tumor response elicited by V937 in human xenograft models in immunodeficient mice following intratumoral and intravenous administration. Estimates of viral infection and replication which were calculated from in vitro experiments were successfully used to describe the tumor response in vivo under various experimental conditions. Despite the predicted high clearance rate of V937 in systemic circulation (t_1/2 = 4.3 min), high viral replication was observed in immunodeficient mice which resulted in tumor shrinkage with both intratumoral and intravenous administration. The described framework represents a step towards the quantitative characterization of viral distribution, replication, and oncolytic effect of a novel oncolytic virus following intratumoral and intravenous administrations in the absence of an immune response. This model may further be expanded to integrate the role of the immune system on viral and tumor dynamics to support the clinical development of oncolytic viruses.

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.

A mathematical model of viral oncology as an immuno-oncology instigator

We develop and analyse a mathematical model of tumour-immune interaction that explicitly incorporates heterogeneity in tumour cell cycle duration by using a distributed delay differential equation. We derive a necessary and sufficient condition for local stability of the cancer-free equilibrium in which the amount of tumour-immune interaction completely characterizes disease progression. Consistent with the immunoediting hypothesis, we show that decreasing tumour-immune interaction leads to tumour expansion. Finally, by simulating the mathematical model, we show that the strength of tumour-immune interaction determines the long-term success or failure of viral therapy.

Decreasing the Susceptibility of Malignant Cells to Infection Does Not Impact the Overall Efficacy of Myxoma Virus-Based Oncolytic Virotherapy

Oncolytic virotherapy relies on the induction of anti-tumor immune responses to achieve therapeutic efficacy. The factors that influence the induction of these responses, however, are not well understood. To begin to address this lack of knowledge, we asked how decreasing the susceptibility of malignant cells to direct viral infection would impact the induction of immune responses and therapeutic efficacy caused by oncolytic myxoma virus treatment. To accomplish this, we used CRISPR-Cas9 genome editing to remove the essential sulfation enzyme N-deacetylase/N-sulfotransferase-1 from B16/F10 murine melanoma cells. This eliminates the negative cell surface charges associated with glycosaminoglycan sulfation, which reduces a cell’s susceptibility to infection with the myxoma virus by ∼3- to 10-fold. With the use of these cells as a model of reduced susceptibility to oncolytic infection, our data demonstrate that 3- to 10-fold reductions in in vivo infection do not hinder the ability of the oncolytic myxoma virus to induce anti-tumor immunity and do not lower the overall efficacy of localized treatment. Additionally, our data show that in mice bearing multiple distinct tumor masses, the choice to treat a less-susceptible tumor mass does not reduce the overall therapeutic impact against either the injected or noninjected lesion. Taken together, these data suggest that minor changes in the susceptibility of malignant cells to direct oncolytic infection do not necessarily influence the overall outcomes of treatment.

Optimising Hydrogel Release Profiles for Viro-Immunotherapy Using Oncolytic Adenovirus Expressing IL-12 and GM-CSF with Immature Dendritic Cells

Sustained-release delivery systems, such as hydrogels, significantly improve cancer therapies by extending the treatment efficacy and avoiding excess wash-out. Combined virotherapy and immunotherapy (viro-immunotherapy) is naturally improved by these sustained-release systems, as it relies on the continual stimulation of the antitumour immune response. In this article, we consider a previously developed viro-immunotherapy treatment where oncolytic viruses that are genetically engineered to infect and lyse cancer cells are loaded onto hydrogels with immature dendritic cells (DCs). The time-dependent release of virus and immune cells results in a prolonged cancer cell killing from both the virus and activated immune cells. Although effective, a major challenge is optimising the release profile of the virus and immature DCs from the gel so as to obtain a minimum tumour size. Using a system of ordinary differential equations calibrated to experimental results, we undertake a novel numerical investigation of different gel-release profiles to determine the optimal release profile for this viro-immunotherapy. Using a data-calibrated mathematical model, we show that if the virus is released rapidly within the first few days and the DCs are released for two weeks, the tumour burden can be significantly decreased. We then find the true optimal gel-release kinetics using a genetic algorithm and suggest that complex profiles present unnecessary risk and that a simple linear-release model is optimal. In this work, insight is provided into a fundamental problem in the growing field of sustained-delivery systems using mathematical modelling and analysis.

Modeling Oncolytic Viral Therapy, Immune Checkpoint Inhibition, and the Complex Dynamics of Innate and Adaptive Immunity in Glioblastoma Treatment

Oncolytic viruses are of growing interest to cancer researchers and clinicians, due to their selectivity for tumor cells over healthy cells and their immunostimulatory properties. The immune response to an oncolytic virus plays a critical role in treatment efficacy. However, uncertainty remains regarding the circumstances under which the immune system either assists in eliminating tumor cells or inhibits treatment via rapid viral clearance, leading to the cessation of the immune response. In this work, we develop an ordinary differential equation model of treatment for a lethal brain tumor, glioblastoma, using an oncolytic Herpes Simplex Virus. We use a mechanistic approach to model the interactions between distinct populations of immune cells, incorporating both innate and adaptive immune responses to oncolytic viral therapy (OVT), and including a mechanism of adaptive immune suppression via the PD-1/PD-L1 checkpoint pathway. We focus on the tradeoff between viral clearance by innate immune cells and the innate immune cell-mediated recruitment of antiviral and antitumor adaptive immune cells. Our model suggests that when a tumor is treated with OVT alone, the innate immune cells' ability to clear the virus quickly after administration has a much larger impact on the treatment outcome than the adaptive immune cells' antitumor activity. Even in a highly antigenic tumor with a strong innate immune response, the faster recruitment of antitumor adaptive immune cells is not sufficient to offset the rapid viral clearance. This motivates our subsequent incorporation of an immunotherapy that inhibits the PD-1/PD-L1 checkpoint pathway by blocking PD-1, which we combine with OVT within the model. The combination therapy is most effective for a highly antigenic tumor or for intermediate levels of innate immune localization. Extreme levels of innate immune cell activity either clear the virus too quickly or fail to activate a sufficiently strong adaptive response, yielding ineffective combination therapy of GBM. Hence, we show that the innate and adaptive immune interactions significantly influence treatment response and that combining OVT with an immune checkpoint inhibitor expands the range of immune conditions that allow for tumor size reduction or clearance.

Mesenchymal stem cells used as carrier cells of oncolytic adenovirus results in enhanced oncolytic virotherapy

Mesenchymal stem cells (MSCs) loaded with oncolytic viruses are presently being investigated as a new modality of advanced/metastatic tumors treatment and enhancement of virotherapy. MSCs can, however, either promote or suppress tumor growth. To address the critical question of how MSCs loaded with oncolytic viruses affect virotherapy outcomes and tumor growth patterns in a tumor microenvironment, we developed and analyzed an integrated mathematical-experimental model. We used the model to describe both the growth dynamics in our experiments of firefly luciferase-expressing Hep3B tumor xenografts and the effects of the immune response during the MSCs-based virotherapy. We further employed it to explore the conceptual clinical feasibility, particularly, in evaluating the relative significance of potential immune promotive/suppressive mechanisms induced by MSCs loaded with oncolytic viruses. We were able to delineate conditions which may significantly contribute to the success or failure of MSC-based virotherapy as well as generate new hypotheses. In fact, one of the most impactful outcomes shown by this investigation, not inferred from the experiments alone, was the initially counter-intuitive fact that using tumor-promoting MSCs as carriers is not only helpful but necessary in achieving tumor control. Considering the fact that it is still currently a controversial debate whether MSCs exert a pro- or anti-tumor action, mathematical models such as this one help to quantitatively predict the consequences of using MSCs for delivering virotherapeutic agents in vivo. Taken together, our results show that MSC-mediated systemic delivery of oncolytic viruses is a promising strategy for achieving synergistic anti-tumor efficacy with improved safety profiles.

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.

Mathematical Models of Cancer: When to Predict Novel Therapies, and When Not to

The number of publications on mathematical modeling of cancer is growing at an exponential rate, according to PubMed records, provided by the US National Library of Medicine and the National Institutes of Health. Seminal papers have initiated and promoted mathematical modeling of cancer and have helped define the field of mathematical oncology (Norton and Simon in J Natl Cancer Inst 58:1735-1741, 1977; Norton in Can Res 48:7067-7071, 1988; Hahnfeldt et al. in Can Res 59:4770-4775, 1999; Anderson et al. in Comput Math Methods Med 2:129-154, 2000. https://doi.org/10.1080/10273660008833042 ; Michor et al. in Nature 435:1267-1270, 2005. https://doi.org/10.1038/nature03669 ; Anderson et al. in Cell 127:905-915, 2006. https://doi.org/10.1016/j.cell.2006.09.042 ; Benzekry et al. in PLoS Comput Biol 10:e1003800, 2014. https://doi.org/10.1371/journal.pcbi.1003800 ). Following the introduction of undergraduate and graduate programs in mathematical biology, we have begun to see curricula developing with specific and exclusive focus on mathematical oncology. In 2018, 218 articles on mathematical modeling of cancer were published in various journals, including not only traditional modeling journals like the Bulletin of Mathematical Biology and the Journal of Theoretical Biology, but also publications in renowned science, biology, and cancer journals with tremendous impact in the cancer field (Cell, Cancer Research, Clinical Cancer Research, Cancer Discovery, Scientific Reports, PNAS, PLoS Biology, Nature Communications, eLife, etc). This shows the breadth of cancer models that are being developed for multiple purposes. While some models are phenomenological in nature following a bottom-up approach, other models are more top-down data-driven. Here, we discuss the emerging trend in mathematical oncology publications to predict novel, optimal, sometimes even patient-specific treatments, and propose a convention when to use a model to predict novel treatments and, probably more importantly, when not to.

Chandipura Virus Utilizes the Prosurvival Function of RelA NF-κB for Its Propagation

Chandipura virus (CHPV), a cytoplasmic RNA virus, has been implicated in several outbreaks of acute encephalitis in India. Despite the relevance of CHPV to human health, how the virus interacts with the host signaling machinery remains obscure. In response to viral infections, mammalian cells activate RelA/NF-κB heterodimers, which induce genes encoding interferon beta (IFN-β) and other immune mediators. Therefore, RelA is generally considered to be an antiviral transcription factor. However, RelA activates a wide spectrum of genes in physiological settings, and there is a paucity of direct genetic evidence substantiating antiviral RelA functions. Using mouse embryonic fibroblasts, we genetically dissected the role of RelA in CHPV pathogenesis. We found that CHPV indeed activated RelA and that RelA deficiency abrogated the expression of IFN-β in response to virus infections. Unexpectedly, infection of Rela ^-/- fibroblasts led to a decreased CHPV yield. Our investigation clarified that RelA-dependent synthesis of prosurvival factors restrained infection-inflicted cell death and that exacerbated cell death processes prevented multiplication of CHPV in RelA-deficient cells. Chikungunya virus, a cytopathic RNA virus associated also with epidemics, required RelA, and Japanese encephalitis virus, which produced relatively minor cytopathic effects in fibroblasts, circumvented the need of RelA for their propagation. In sum, we documented a proviral function of the pleiotropic factor RelA linked to its prosurvival properties. RelA promoted the growth of cytopathic RNA viruses by extending the life span of infected cells, which serve as the replicative niche of intracellular pathogens. We argue that our finding bears significance for understanding host-virus interactions and may have implications for antiviral therapeutic regimes.IMPORTANCE RelA/NF-κB participates in a wide spectrum of physiological processes, including shaping immune responses against invading pathogens. In virus-infected cells, RelA typically induces the expression of IFN-β, which restrains viral propagation in neighboring cells involving paracrine mechanisms. Our study suggested that RelA might also play a proviral role. A cell-autonomous RelA activity amplified the yield of Chandipura virus, a cytopathic RNA virus associated with human epidemics, by extending the life span of infected cells. Our finding necessitates a substantial revision of our understanding of host-virus interactions and indicates a dual role of NF-κB signaling during the course of RNA virus infections. Our study also bears significance for therapeutic regimes which alter NF-κB activities while alleviating the viral load.

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.

In silico simulation of a clinical trial with anti-CTLA-4 and anti-PD-L1 immunotherapies in metastatic breast cancer using a systems pharmacology model

The low response rate of immune checkpoint blockade in breast cancer has highlighted the need for predictive biomarkers to identify responders. While a number of clinical trials are ongoing, testing all possible combinations is not feasible. In this study, a quantitative systems pharmacology model is built to integrate immune-cancer cell interactions in patients with breast cancer, including central, peripheral, tumour-draining lymph node (TDLN) and tumour compartments. The model can describe the immune suppression and evasion in both TDLN and the tumour microenvironment due to checkpoint expression, and mimic the tumour response to checkpoint blockade therapy. We investigate the relationship between the tumour response to checkpoint blockade therapy and composite tumour burden, PD-L1 expression and antigen intensity, including their individual and combined effects on the immune system, using model-based simulations. The proposed model demonstrates the potential to make predictions of tumour response of individual patients given sufficient clinical measurements, and provides a platform that can be further adapted to other types of immunotherapy and their combination with molecular-targeted therapies. The patient predictions demonstrate how this systems pharmacology model can be used to individualize immunotherapy treatments. When appropriately validated, these approaches may contribute to optimization of breast cancer treatment.

Developing a Minimally Structured Mathematical Model of Cancer Treatment with Oncolytic Viruses and Dendritic Cell Injections

Mathematical models of biological systems must strike a balance between being sufficiently complex to capture important biological features, while being simple enough that they remain tractable through analysis or simulation. In this work, we rigorously explore how to balance these competing interests when modeling murine melanoma treatment with oncolytic viruses and dendritic cell injections. Previously, we developed a system of six ordinary differential equations containing fourteen parameters that well describes experimental data on the efficacy of these treatments. Here, we explore whether this previously developed model is the minimal model needed to accurately describe the data. Using a variety of techniques, including sensitivity analyses and a parameter sloppiness analysis, we find that our model can be reduced by one variable and three parameters and still give excellent fits to the data. We also argue that our model is not too simple to capture the dynamics of the data, and that the original and minimal models make similar predictions about the efficacy and robustness of protocols not considered in experiments. Reducing the model to its minimal form allows us to increase the tractability of the system in the face of parametric uncertainty.