Mathematical modeling of tumor therapy with oncolytic viruses: effects of parametric heterogeneity on cell dynamics

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.

A physiologically based pharmacokinetic model for V937 oncolytic virus in mice

Introduction: Oncolytic viruses (OVs) represent a novel therapeutic strategy in oncology due to their capability to selectively infect and replicate in cancer cells, triggering a direct and/or immune-induced tumor lysis. However, the mechanisms governing OV pharmacokinetics are still poorly understood. This work aims to develop a physiologically based pharmacokinetic model of the novel OV, V937, in non-tumor-bearing mice to get a quantitative understanding of its elimination and tissue uptake processes. Materials and methods: Model development was performed using data obtained from 60 mice. Viral levels were quantified from eight tissues after a single intravenous V937 dose. An external dataset was used for model validation. This test set included multiple-dose experiments with different routes of administration. V937 distribution in each organ was described using a physiological structure based on mouse-specific organ blood flows and volumes. Analyses were performed using the non-linear mixed-effects approach with NONMEM 7.4. Results: Viral levels showed a drop from 108 to 105 copies/µg RNA at day 1 in blood, reflected in a high estimate of total clearance (18.2 mL/h). A well-stirred model provided an adequate description for all organs except the muscle and heart, where a saturable uptake process improved data description. The highest numbers of viral copies were observed in the brain, lymph node, kidney, liver, lung, and spleen on the first day after injection. On the other hand, the maximum amount of viral copies in the heart, muscle, and pancreas occurred 3 days after administration. Conclusion: To the best of our knowledge, this is the first physiologically based pharmacokinetic model developed to characterize OV biodistribution, representing a relevant source of quantitative knowledge regarding the in vivo behavior of OVs. This model can be further expanded by adding a tumor compartment, where OVs could replicate.

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.

Modelling heterogeneity in viral-tumour dynamics: The effects of gene-attenuation on viral characteristics

The use of viruses as a cancer treatment is becoming increasingly more robust; however, there is still a long way to go before a completely successful treatment is formulated. One major challenge in the field is to select which virus, out of a burgeoning number of oncolytic viruses and engineered derivatives, can maximise both treatment spread and anticancer cytotoxicity. To assist in solving this problem, an in-depth understanding of the virus-tumour interaction is crucial. In this article, we present a novel integro-differential system with distributed delays embodying the dynamics of an oncolytic adenovirus with a fixed population of tumour cells in vitro, allowing for heterogeneity to exist in the virus and cell populations. The parameters of the model are optimised in a hierarchical manner, the purpose of which is not to obtain a perfect representation of the data. Instead, we place our parameter values in the correct region of the parameter space. Due to the sparse nature of the data it is not possible to obtain the parameter values with any certainty, but rather we demonstrate the suitability of the model. Using our model we quantify how modifications to the viral genome alter the viral characteristics, specifically how the attenuation of the E1B 19 and E1B 55 gene affect the system performance, and identify the dominant processes altered by the mutations. From our analysis, we conclude that the deletion of the E1B 55 gene significantly reduces the replication rate of the virus in comparison to the deletion of the E1B 19 gene. We also found that the deletion of both the E1B 19 and E1B 55 genes resulted in a long delay in the average replication start time of the virus. This leads us to propose the use of E1B 19 gene-attenuated adenovirus for cancer therapy, as opposed to E1B 55 gene-attenuated adenoviruses.

Mathematical and Computational Modeling for Tumor Virotherapy with Mediated Immunity

We propose a new mathematical modeling framework based on partial differential equations to study tumor virotherapy with mediated immunity. The model incorporates both innate and adaptive immune responses and represents the complex interaction among tumor cells, oncolytic viruses, and immune systems on a domain with a moving boundary. Using carefully designed computational methods, we conduct extensive numerical simulation to the model. The results allow us to examine tumor development under a wide range of settings and provide insight into several important aspects of the virotherapy, including the dependence of the efficacy on a few key parameters and the delay in the adaptive immunity. Our findings also suggest possible ways to improve the virotherapy for tumor treatment.

Lentivirus-mediated p21/Waf-1 short hairpin RNA enhances the cytotoxic effects and replicative potential of a bladder cancer-specific oncolytic adenovirus in vitro

Our previous work confirmed that the bladder cancer-specific oncolytic adenovirus Ad/PSCAE/UPII/E1A could selectively replicate in bladder cancer cells, thus causing specific tumor cell lysis. The replicative potential is a crucial factor in determining the therapeutic efficacy of oncolytic adenoviruses. However, viral replication is attenuated by the low-activity promoter that we used, thus compromising viral cytotoxicity. In this study, we investigated the effect of the cell cycle-dependent kinase inhibitor p21/Waf-1 on an adenovirus. We used lentivirus-mediated short hairpin RNA to knock down p21/Waf-1 in two bladder cancer cell lines EJ and 5637. The p21/Waf-1 knockdown not only induced stronger cytopathic effects but also augmented apoptosis, which was closely associated with the enhancement of Fas and the subsequent significant activation of caspase-3. A replicative assay showed that p21/Waf-1 knockdown increased the viral particle production. Western blot analysis confirmed that p21/Waf-1 knockdown upregulated the expression of androgen receptor (AR) and two adenovirus replication indicators E1A and hexon. A luciferase activity assay indicated higher transcriptional activity of the uroplakin II (UPII) promoter in the p21/Waf-1 knockdown cells, and one possible mechanism could be that the increased expression of AR induced the UPII promoter through the AR-binding sites of the prostate stem cell antigen enhancer. These findings indicating that p21/Waf-1 knockdown could enhance cell killing and viral replication have significant implications for the development of bladder cancer-specific oncolytic adenovirus therapies.

Computational modeling approaches to the dynamics of oncolytic viruses

Replicating oncolytic viruses represent a promising treatment approach against cancer, specifically targeting the tumor cells. Significant progress has been made through experimental and clinical studies. Besides these approaches, however, mathematical models can be useful when analyzing the dynamics of virus spread through tumors, because the interactions between a growing tumor and a replicating virus are complex and nonlinear, making them difficult to understand by experimentation alone. Mathematical models have provided significant biological insight into the field of virus dynamics, and similar approaches can be adopted to study oncolytic viruses. The review discusses this approach and highlights some of the challenges that need to be overcome in order to build mathematical and computation models that are clinically predictive. WIREs Syst Biol Med 2016, 8:242-252. doi: 10.1002/wsbm.1332 For further resources related to this article, please visit the WIREs website.

A mathematical approach to virus therapy of glioblastomas

BACKGROUND

It is widely believed that the treatment of glioblastomas (GBM) could benefit from oncolytic virus therapy. Clinical research has shown that Vesicular Stomatitis Virus (VSV) has strong oncolytic properties. In addition, mathematical models of virus treatment of tumors have been developed in recent years. Some experiments in vitro and in vivo have been done and shown promising results, but have been never compared quantitatively with mathematical models. We use in vitro data of this virus applied to glioblastoma.

RESULTS

We describe three increasingly realistic mathematical models for the VSV-GBM in vitro experiment with progressive incorporation of time-delay effects. For the virus dynamics, we obtain results consistent with the in vitro experimental speed data only when applying the more complex and comprehensive model, with time-delay effects both in the reactive and diffusive terms. The tumor speed is given by the minimum of a very simple function that nonetheless yields results within the experimental measured range.

CONCLUSIONS

We have improved a previous model with new ideas and carefully incorporated concepts from experimental results. We have shown that the delay time τ is the crucial parameter in this kind of models. We have demonstrated that our new model can satisfactorily predict the front speed for the lytic action of oncolytic VSV on glioblastoma observed in vitro. We provide a basis that can be applied in the near future to realistically simulate in vivo virus treatments of several cancers.

Basic stage structure measure valued evolutionary game model

The ideas and techniques developed in [12,3] are extended to a basic stage structured model. Each strategy consists of two stages: a Juvenile (L for larvae), and Adult (A). A general model of this basic stage structure is formulated as a dynamical system on the state space of finite signed measures. Nonnegativity, well-posedness and uniform eventual boundedness are established under biologically natural conditions on the rates. Similar to [12] we also have the unifying of discrete and continuous systems and the containment of the classic nonlinearities.

Control exponential growth of tumor cells with slow spread of oncolytic virus

Great attention has been paid to cancer therapy by means of oncolytic viruses, but the fast virus-spread, which eliminates all tumor cells, cannot be applied to solid tumors. As slow virus-spread is applied, solid tumors are expected to be controlled but complicated dynamical behaviors appear. In this paper we investigate bifurcations of equilibria in the oncolytic virus dynamics model with exponential growth of tumor cells and slow virus-spread. We find conditions of parameters for saddle-node bifurcation, Hopf bifurcation and Bogdanov-Takens bifurcation. Those conditions give thresholds for slow virus-spread to control the population of tumor cells within an appropriate range.

Complex spatial dynamics of oncolytic viruses in vitro: mathematical and experimental approaches

Oncolytic viruses replicate selectively in tumor cells and can serve as targeted treatment agents. While promising results have been observed in clinical trials, consistent success of therapy remains elusive. The dynamics of virus spread through tumor cell populations has been studied both experimentally and computationally. However, a basic understanding of the principles underlying virus spread in spatially structured target cell populations has yet to be obtained. This paper studies such dynamics, using a newly constructed recombinant adenovirus type-5 (Ad5) that expresses enhanced jellyfish green fluorescent protein (EGFP), AdEGFPuci, and grows on human 293 embryonic kidney epithelial cells, allowing us to track cell numbers and spatial patterns over time. The cells are arranged in a two-dimensional setting and allow virus spread to occur only to target cells within the local neighborhood. Despite the simplicity of the setup, complex dynamics are observed. Experiments gave rise to three spatial patterns that we call "hollow ring structure", "filled ring structure", and "disperse pattern". An agent-based, stochastic computational model is used to simulate and interpret the experiments. The model can reproduce the experimentally observed patterns, and identifies key parameters that determine which pattern of virus growth arises. The model is further used to study the long-term outcome of the dynamics for the different growth patterns, and to investigate conditions under which the virus population eliminates the target cells. We find that both the filled ring structure and disperse pattern of initial expansion are indicative of treatment failure, where target cells persist in the long run. The hollow ring structure is associated with either target cell extinction or low-level persistence, both of which can be viewed as treatment success. Interestingly, it is found that equilibrium properties of ordinary differential equations describing the dynamics in local neighborhoods in the agent-based model can predict the outcome of the spatial virus-cell dynamics, which has important practical implications. This analysis provides a first step towards understanding spatial oncolytic virus dynamics, upon which more detailed investigations and further complexity can be built.

Dynamics of melanoma tumor therapy with vesicular stomatitis virus: explaining the variability in outcomes using mathematical modeling

Tumor selective, replication competent viruses are being tested for cancer gene therapy. This approach introduces a new therapeutic paradigm due to potential replication of the therapeutic agent and induction of a tumor-specific immune response. However, the experimental outcomes are quite variable, even when studies utilize highly inbred strains of mice and the same cell line and virus. Recognizing that virotherapy is an exercise in population dynamics, we utilize mathematical modeling to understand the variable outcomes observed when B16ova malignant melanoma tumors are treated with vesicular stomatitis virus in syngeneic, fully immunocompetent mice. We show how variability in the initial tumor size and the actual amount of virus delivered to the tumor have critical roles on the outcome of therapy. Virotherapy works best when tumors are small, and a robust innate immune response can lead to superior tumor control. Strategies that reduce tumor burden without suppressing the immune response and methods that maximize the amount of virus delivered to the tumor should optimize tumor control in this model system.

RNA interference-mediated knockdown of p21(WAF1) enhances anti-tumor cell activity of oncolytic adenoviruses

The ability of oncolytic adenoviruses to replicate in and lyse cancer cells offers a potential therapeutic approach. However, selectivity and efficacy of adenovirus replication need to be improved. In this study, we present that loss of p21^WAF1 promotes adenovirus replication and more effective cell killing. To test our hypothesis, we took HCT116 colon cancer cell lines carrying deletions of either p21^WAF1 or p53, and infected these cell lines with wild-type adenovirus (WtD) or the oncolytic adenoviruses, ONYX-015 and Delta-24. We found that WtD, ONYX-015 and Delta-24 induced stronger cytopathic effects in HCT116 p21−/− cells compared with HCT116-WT cells. This was accompanied by increased virus production. siRNA-mediated knockdown of p21^WAF1, and similarly of p27^KIP1, in HCT116-WT cells also enhanced replication of and cell killing by these viruses. Furthermore, we found that TE7, an esophageal carcinoma cell line, also showed a strong cell-killing effect and virus production when p21^WAF1 expression was suppressed by RNA interference before adenoviruses infection. Also, H1299 and DU-145 cells transfected with p21^WAF1 siRNA showed higher virus production after ONYX-015 and Delta-24 infections. These observations suggest that p21^WAF1 plays a role in mediating replication of oncolytic viruses with potential implications for adenoviral therapy of cancer.

On mathematical theory of selection: continuous time population dynamics

Mathematical theory of selection is developed within the frameworks of general models of inhomogeneous populations with continuous time. Methods that allow us to study the distribution dynamics under natural selection and to construct explicit solutions of the models are developed. All statistical characteristics of interest, such as the mean values of the fitness or any trait can be computed effectively, and the results depend in a crucial way on the initial distribution. The developed theory provides an effective method for solving selection systems; it reduces the initial complex model to a special system of ordinary differential equations (the escort system). Applications of the method to the Price equations are given; the solutions of some particular inhomogeneous Malthusian, Ricker and logistic-like models used but not solved in the literature are derived in explicit form.

On the spread of epidemics in a closed heterogeneous population

Heterogeneity is an important property of any population experiencing a disease. Here we apply general methods of the theory of heterogeneous populations to the simplest mathematical models in epidemiology. In particular, an SIR (susceptible-infective-removed) model is formulated and analyzed when susceptibility to or infectivity of a particular disease is distributed. It is shown that a heterogeneous model can be reduced to a homogeneous model with a nonlinear transmission function, which is given in explicit form. The widely used power transmission function is deduced from the model with distributed susceptibility and infectivity with the initial gamma-distribution of the disease parameters. Therefore, a mechanistic derivation of the phenomenological model, which is believed to mimic reality with high accuracy, is provided. The equation for the final size of an epidemic for an arbitrary initial distribution of susceptibility is found. The implications of population heterogeneity are discussed, in particular, it is pointed out that usual moment-closure methods can lead to erroneous conclusions if applied for the study of the long-term behavior of the models.

Potent oncolytic activity of human enteroviruses against human prostate cancer

BACKGROUND

Oncolytic virotherapy offers a unique treatment modality for prostate cancer, especially stages that are resistant to current therapies, with the additional benefit of preferentially targeting tumor cells amongst an environment of healthy tissue. Herein, the low pathogenic enteroviruses; Coxsackievirus A21 (CVA21), as well as a bio-selected variant of Coxsackievirus A21 (CVA21-DAFv) and Echovirus 1 (EV1) are evaluated as novel oncolytic agents against human prostate cancer.

METHODS

The surface expression of viral receptors required for enterovirus cell attachment/entry, including intercellular adhesion molecule-1 (ICAM-1), decay-accelerating factor (DAF) and integrin alpha(2)beta(1) on a number of human prostate cancer lines was assessed by flow cytometry. Susceptibility to viral oncolysis was determined via in vitro cell lysis assays performed on cell monolayers cultured in micro titer plates. The in vivo oncolytic efficacy of the enteroviruses was assessed using xenograft models in immune compromised SCID-mice following systemic challenge.

RESULTS

The majority of prostate cancer lines tested expressed surface ICAM-1 and/or DAF, or alpha(2)beta(1), facilitating significant degrees of oncolysis following in vitro viral challenge. Systemic delivery of each of the three viruses induced reduction of xenograft tumor burdens in vivo, and a therapeutic dose-response was demonstrated for escalating doses of EV1 in the LNCaP animal model.

CONCLUSION

Enteroviruses CVA21, CVA21-DAFv, and EV1 are potentially potent oncolytic agents against human prostate cancer.

Oncolytic viruses in cancer therapy

Oncolytic virotherapy is a promising form of gene therapy for cancer, employing nature’s own agents to find and destroy malignant cells. The purpose of this review is to provide an introduction to this very topical field of research and to point out some of the current observations, insights and ideas circulating in the literature. We have strived to acknowledge as many different oncolytic viruses as possible to give a broader picture of targeting cancer using viruses. Some of the newest additions to the panel of oncolytic viruses include the avian adenovirus, foamy virus, myxoma virus, yaba-like disease virus, echovirus type 1, bovine herpesvirus 4, Saimiri virus, feline panleukopenia virus, Sendai virus and the non-human coronaviruses. Although promising, virotherapy still faces many obstacles that need to be addressed, including the emergence of virus-resistant tumor cells.