Mathematical modeling of tumor therapy with oncolytic viruses: Regimes with complete tumor elimination within the framework of deterministic models

Background  

Oncolytic viruses that specifically target tumor cells are promising anti-cancer therapeutic agents. The interaction between an oncolytic virus and tumor cells is amenable to mathematical modeling using adaptations of techniques employed previously for modeling other types of virus-cell interaction.     

溶瘤病毒调控肿瘤微环境及联合治疗的研究进展

溶瘤病毒是一类天然的或经改造后获得具有靶向杀伤癌细胞能力的病毒,除了能特异性杀伤肿瘤细胞外,经改造后的溶瘤病毒对肿瘤微环境的调控作用也会影响其最终疗效.通过调控肿瘤微环境中肿瘤细胞抗原的表达、免疫抑制状态、肿瘤相关成纤维细胞及肿瘤血管新生等,溶瘤病毒为肿瘤的治疗提供了更为系统的治疗策略;联合免疫检查点抑制剂的使用能使两者获得协同和互补的功效,进一步提升了肿瘤全面和有效的治疗.本文将对溶瘤病毒对肿瘤微环境调控作用及联合治疗的研究进展进行综述.     

Impact of tumor microenvironment on oncolytic viral therapy

Interactions between tumor cells and their microenvironment have been shown to play a very significant role in the initiation, progression, and invasiveness of cancer. These tumor–stromal interactions are capable of altering the delivery and effectiveness of therapeutics into the tumor and are also known to influence future resistance and re-growth after treatment. Here we review recent advances in the understanding of the tumor microenvironment and its response to oncolytic viral therapy. The multifaceted environmental response to viral therapy can influence viral infection, replication, and propagation within the tumor. Recent studies have unveiled the complicated temporal changes in the tumor vasculature post-oncolytic virus (OV) treatment, and their impact on tumor biology. Similarly, the secreted extracellular matrix in solid tumors can affect both infection and spread of the therapeutic virus. Together, these complex changes in the tumor microenvironment also modulate the activation of the innate antiviral host immune response, leading to quick and efficient viral clearance. In order to combat these detrimental responses, viruses have been combined with pharmacological adjuvants and “armed” with therapeutic genes in order to suppress the pernicious environmental conditions following therapy. In this review we will discuss the impact of the tumor environment on viral therapy and examine some of the recent literature investigating methods of modulating this environment to enhance oncolysis.     

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.     

Targeting human glioblastoma cells: comparison of nine viruses with oncolytic potential

Brain tumors classified as glioblastomas have proven refractory to treatment and generally result in death within a year of diagnosis. We used seven in vitro tests and one in vivo trial to compare the efficacy of nine different viruses for targeting human glioblastoma. Green fluorescent protein (GFP)-expressing vesicular stomatitis (VSV), Sindbis virus, pseudorabies virus (PRV), adeno-associated virus (AAV), and minute virus of mice i-strain (MVMi) and MVMp all infected glioblastoma cells. Mouse and human cytomegalovirus, and simian virus 40 showed only low levels of infection or GFP expression. VSV and Sindbis virus showed strong cytolytic actions and high rates of replication and spread, leading to an elimination of glioblastoma. PRV and both MVM strains generated more modest lytic effects and replication capacity. VSV showed a similar oncolytic profile on U-87 MG and M059J glioblastoma. In contrast, Sindbis virus showed strong preference for U-87 MG, whereas MVMi and MVMp preferred M059J. Sindbis virus and both MVM strains showed highly tumor-selective actions in glioblastoma plus fibroblast coculture. VSV and Sindbis virus were serially passaged on glioblastoma cells; we isolated a variant, VSV-rp30, that had increased selectivity and lytic capacity in glioblastoma cells. VSV and Sindbis virus were very effective at replicating, spreading within, and selectively killing human glioblastoma in an in vivo mouse model, whereas PRV and AAV remained at the injection site with minimal spread. Together, these data suggest that four (VSV, Sindbis virus, MVMi, and MVMp) of the nine viruses studied merit further analysis for potential therapeutic actions on glioblastoma.     

Mathematical modeling of viral infection dynamics in spherical organs

A general mathematical model of viral infections inside a spherical organ is presented. Transported quantities are used to represent external cells or viral particles that penetrate the organ surface to either promote or combat the infection. A diffusion mechanism is considered for the migration of transported quantities to the organ inner tissue. Cases that include the effect of penetration, diffusion and proliferation of immune system cells, the generation of latently infected cells and the delivery of antiviral treatment are analyzed. Different antiviral mechanisms are modeled in the context of spatial variation. Equilibrium conditions are also calculated to determine the radial profile after the infection progresses and antiviral therapy is delivered for a long period of time. The dynamic and equilibrium solutions obtained in this paper provide insight into the temporal and spatial evolution of viral infections.     

Mathematical modeling and analysis of meningococcal meningitis transmission dynamics

Meningococcal meningitis(MCM)is one of the serious public health threats in the tropical and sub-tropical regions.In this paper,we propose an epidemic model to study the transmission dynamics of MCM with high-and low-risk susceptible populations.The model considers two different groups of susceptible individuals depending on the availability of medical resources(MR,including hospitals,health workers,etc.),which varies the infection risk.We find that the model exhibits the phenomenon of backward bifurcation(BB),which increases the difficulty of MCM control since the dynamics are not merely relying on the basic reproduction number,TZo.This study explores the effects of MR on the MCM epidemics by mathematical analysis and shows the existence of BB on MCM disease.Our findings suggest that providing adequate MR in a community is crucial in mitigating MCM incidences and deaths,especially,in the MCM endemic regions.     

Mathematical modeling of pulmonary tuberculosis therapy: Insights from a prototype model with rifampin

There is a critical need for improved and shorter tuberculosis (TB) treatment. Current in vitro models of TB, while valuable, are poor predictors of the antibacterial effect of drugs in vivo. Mathematical models may be useful to overcome the limitations of traditional approaches in TB research. The objective of this study was to set up a prototype mathematical model of TB treatment by rifampin, based on pharmacokinetic, pharmacodynamic and disease submodels.The full mathematical model can simulate the time-course of tuberculous disease from the first day of infection to the last day of therapy. Therapeutic simulations were performed with the full model to study the antibacterial effect of various dosage regimens of rifampin in lungs.The model reproduced some qualitative and quantitative properties of the bactericidal activity of rifampin observed in clinical data. The kill curves simulated with the model showed a typical biphasic decline in the number of extracellular bacteria consistent with observations in TB patients. Simulations performed with more simple pharmacokinetic/pharmacodynamic models indicated a possible role of a protected intracellular bacterial compartment in such a biphasic decline.This modeling effort strongly suggests that current dosage regimens of RIF may be further optimized. In addition, it suggests a new hypothesis for bacterial persistence during TB treatment.     

The impact of population dynamics on Y-chromosome microsatellite polymorphism. Mathematical modeling

In this article, we use mathematical modeling to study the impact of population dynamics on Y-chromosome STR-polymorphism accumulation in two independently evolving populations, namely, on the changes in genetic distance between the populations. Comparative analysis using two definitions of genetic distance—(δμ)² and ASD—shows that, in contrast to (δμ)², ASD is almost linearly dependent on time (except for sparse stationary populations, where deviations are observed). When the population numbers undergo oscillations, ASD proves to be smaller than that for stationary populations.     

The impact of population dynamics on Y-chromosome microsatellite Polymorphism. Mathematical modeling

In this article, we use mathematical modeling to study the impact of population dynamics on Y-chromosome STR-polymorphism accumulation in two independently evolving populations, namely, on the changes in genetic distance among the populations. Using two definitions of the genetic distance: (deltamu)2 and ASD, we carry out comparative research on the genetic distance changes and show that in contrast to (deltamu)2, ASD is characterized by a near-linear dependence on time. As the populations undergo oscillations, ASD is shown to be smaller than that in stationary populations. The linear dependence of ASD on time is shown to break down in relatively scanty stationary populations.     

The effects of spatial heterogeneity in population dynamics

The dynamics of a population inhabiting a heterogeneous environment are modelled by a diffusive logistic equation with spatially varying growth rate. The overall suitability of an environment is characterized by the principal eigenvalue of the corresponding linearized equation. The dependence of the eigenvalue on the spatial arrangement of regions of favorable and unfavorable habitat and on boundary conditions is analyzed in a number of cases.Research supported by National Science Foundation grant #DMS 88-02346     

Mast cell heterogeneity: effects of neuroenteric peptides on histamine release

Recent reports suggesting that the actions of certain neuroenteric peptides may be mediated in part by the secretion of histamine and other mast cell contents could have important implications for gastrointestinal motility and secretion. However, evidence for a mast cell-hormonal interaction is based on studies using peritoneal or cutaneous mast cells. Because intestinal mucosal mast cells (MMC) differ functionally from peritoneal mast cells (PMC), we compared the effects of several neurotransmitters and intestinal hormones on histamine secretion from two mast cell types in the rat. MMC hyperplasia was induced in rats by infection with the nematode Nippostrongylus brasiliensis, and MMC were isolated from the small intestine by collagenase digestion. Substance P, somatostatin, vasoactive intestinal polypeptide (VIP), neurotensin, and bradykinin had a potent secretagogue effect on (10(-7) to 10(-4)M) PMC which was temperature-, energy-, and calcium-dependent. In contrast to PMC, MMC released significant amounts of histamine only when challenged with substance P. Acetylcholine, bombesin, motilin, and pentagastrin had no secretory effect on either PMC or MMC. The differences between PMC and MMC in responsiveness to peptides could not be attributed to the MMC isolation procedure because PMC treated similarly or mixed with MMC suspensions retained their responsiveness to these stimuli. Our results extend the concept of neurocrine control of mast cell function, but indicate that mast cells from different sites have distinct profiles of responsiveness to regulatory peptides.     

肠道病毒溶瘤作用的研究进展

溶瘤病毒(oncolytic virus,OV)是一类能选择性地在肿瘤细胞中复制并且能够溶解肿瘤细胞,对正常组织细胞无损伤的自然状态或基因改造过的病毒。肠道病毒(enterovirus)是一类单股正链RNA病毒,包括脊髓灰质炎病毒(Poliovirus, PV)、柯萨奇病毒和埃可病毒等。研究证实多种肠道病毒具有溶瘤作用,如已在拉脱维亚等国上市的RIGVIR~?(埃可病毒7型,Echovirus 7, ECHO7),已进入Ⅱ期临床试验的柯萨奇病毒A组21型(Coxsackievirus A21, CVA21),以及处于临床前研究阶段的柯萨奇病毒B组3型(Coxsackievirus B3, CVB3)及PV等。现就有关肠道病毒的溶瘤作用作一概述。     

Mathematical and computation modeling of self-organizing sarcomere with chaotic dynamics of the order parameter

The results of constructing a nonlinear model of sarcomere contraction are summarized. A strange attractor has been obtained, which is related to the randomness of the dynamics of the order parameter during sarcomere deformation. A hypothesis is proposed that upon fixation of the actin filaments in the sarcomere the myosin system undergoes nonlinear oscillations with dissipation, which leads to elevation of solution temperature. The increase in temperature has been determined for pulsations of the inertial range. Normalized power spectra of the pulsations of the order parameter have been constructed for the model by Fourier transform. The thermodynamics of sarcomere contraction is considered.     

Synergistic induction of tumor cell death by combining cisplatin with an oncolytic adenovirus carrying TRAIL

Chemoresistance and side effects are considered as the major obstacles in cisplatin-based chemotherapy of various human malignant tumors. Conjugation with cancer-specific apoptotic stimuli TRAIL or typical viro-agent ONYX-015 has been extensively investigated to enhance the antitumor activity of cisplatin. In this study, we presented a novel chemo-gene-virotherapeutic strategy to further improve the toxic effects in cancer cells and reduce the damage in normal cells. Here, an oncolytic adenoviral vector (ZD55), with a deletion of E1B 55-kDa gene, was employed to express the therapeutic TRAIL gene by constructing a recombinant virus ZD55-TRAIL. Exogenous gene delivery efficacy was determined by both in vitro and in vivo experiments and enhanced cytotoxicity of combined treatment of ZD55-TRAIL with cisplatin was evaluated in several cancer cell lines. Moreover, negative effects on normal cells have been tested in both L-02 and MRC-5 cell lines by MTT assay and apoptotic cell staining. According to our observation, combination of ZD55-TRAIL with cisplatin exhibited an apparent synergistic cytotoxicity in cancer cells, yet significantly abolished the negative toxicity in normal cells by reducing the dosage. Thus, a novel chemo-gene-virotherapeutic strategy for cancer therapy was proposed.