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

Background:  

One of the mechanisms that ensure cancer robustness is tumor heterogeneity, and its effects on tumor cells dynamics have to be taken into account when studying cancer progression. There is no unifying theoretical framework in mathematical modeling of carcinogenesis that would account for parametric heterogeneity.     

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.     

Parameterization of individual-based models: comparisons with deterministic mean-field models

The relating of deterministic, mean-field models into network models, where epidemic spread occurs between interconnected susceptible and infectious individuals or populations, requires careful consideration. Here, we discuss models that consider differently the manner in which contact rate and infectiousness change over time, with different algorithms suitable for different underlying processes. Though these models give coincidental results to the mean-field in the case of large, highly connected networks, the results when sparsely connected networks are considered may differ. Different subsets of the parameters from the mean-field epidemic (R(0), generation time, infectiousness, etc.) are preserved in each case. Despite these differences, simulated epidemics generated under some model architectures are insensitive to the average degree of contact amongst nodes, k. Model-based estimates of k may be model dependent, and must therefore be viewed with caution.     

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 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.     

Redirecting oncolytic viruses: Engineering opportunists to take control of the tumour microenvironment

The transformation of healthy cells to malignant often drives them to become inherently susceptible to viral infection as a trade-off to achieve uninhibited growth and immune escape. Enter oncolytic viruses (OVs), an exciting class of viruses that specifically infect cancer cells, leaving healthy tissue unharmed. Unfortunately, there is more to this story. Tumours are much more than a group of cancer cells, the surrounding tumour microenvironment (TME) comprises a collection of cells which influence and nourish the development and spread of the tumour. While initially quite promising, OV therapy has been met with a myriad of barriers due to the unwelcoming nature of the TME. Riddled with immunosuppressive factors and physical barriers, many tumours have proven impenetrable by OVs. Herein, we review the diverse array of approaches being used to target each component of the TME from enhancing entry into specific tumour types, breaking through the dense tumour stroma, eliminating cancer stem cells, and activating the immune system. We highlight the value of combination approaches which have led to complete successes in several in vivo models, some of which have entered clinical development.     

Mathematical modeling for antibody therapy in the setting of antigenic modulation

The in vivo efficacy of passive monoclonal antibody therapy is limited in certain systems by the process of antigenic modulation. We describe a compartmental model which addresses the kinetics of in vivo cell binding of murine monoclonal antibody T101, modulation of the T65 target antigen, serum levels of T101, and elimination of target cells. Observed data compare favorably to that predicted by the model. The model suggests that there is no rationale for administering T101 as a prolonged, continuous infusion for passive antibody therapy.     

Mathematical modeling of capillary formation and development in tumor angiogenesis: penetration into the stroma

The purpose of this paper is to present a mathematical model for the tumor vascularization theory of tumor growth proposed by Judah Folkman in the early 1970s and subsequently established experimentally by him and his coworkers [Ausprunk, D. H. and J. Folkman (1977) Migration and proliferation of endothelial cells in performed and newly formed blood vessels during tumor angiogenesis, Microvasc Res., 14, 53–65; Brem, S., B. A. Preis, ScD. Langer, B. A. Brem and J. Folkman (1997) Inhibition of neovascularization by an extract derived from vitreous Am. J. Opthalmol., 84, 323–328; Folkman, J. (1976) The vascularization of tumors, Sci. Am., 234, 58–64; Gimbrone, M. A. Jr, R. S. Cotran, S. B. Leapman and J. Folkman (1974) Tumor growth and neovascularization: an experimental model using the rabbit cornea, J. Nat. Cancer Inst., 52, 413–419]. In the simplest version of this model, an avascular tumor secretes a tumor growth factor (TGF) which is transported across an extracellular matrix (ECM) to a neighboring vasculature where it stimulates endothelial cells to produce a protease that acts as a catalyst to degrade the fibronectin of the capillary wall and the ECM. The endothelial cells then move up the TGF gradient back to the tumor, proliferating and forming a new capillary network. In the model presented here, we include two mechanisms for the action of angiostatin. In the first mechanism, substantiated experimentally, the angiostatin acts as a protease inhibitor. A second mechanism for the production of protease inhibitor from angiostatin by endothelial cells is proposed to be of Michaelis-Menten type. Mathematically, this mechanism includes the former as a subcase. Our model is different from other attempts to model the process of tumor angiogenesis in that it focuses (1) on the biochemistry of the process at the level of the cell; (2) the movement of the cells is based on the theory of reinforced random walks; (3) standard transport equations for the diffusion of molecular species in porous media. One consequence of our numerical simulations is that we obtain very good computational agreement with the time of the onset of vascularization and the rate of capillary tip growth observed in rabbit cornea experiments [Ausprunk, D. H. and J. Folkman (1977) Migration and proliferation of endothelial cells in performed and newly formed blood vessels during tumor angiogenesis, Microvasc Res., 14, 73–65; Brem, S., B. A. Preis, ScD. Langer, B. A. Brem and J. Folkman (1997) Inhibition of neovascularization by an extract derived from vitreous Am. J. Opthalmol., 84, 323–328; Folkman, J. (1976) The vascularization of tumors, Sci. Am., 234, 58–64; Gimbrone, M. A. Jr, R. S. Cotran, S. B. Leapman and J. Folkman (1974) Tumor growth and neovascularization: An experimental model using the rabbit cornea, J. Nat. Cancer Inst., 52, 413–419]. Furthermore, our numerical experiments agree with the observation that the tip of a growing capillary accelerates as it approaches the tumor [Folkman, J. (1976) The vascularization of tumors, Sci. Am., 234, 58–64]. An erratum to this article is available at .     

Stochastic models of tumor growth and the probability of elimination by cytotoxic cells

The probability of tumor extinction due to the action of cytotoxic cell populations is investigated by several one dimensional stochastic models of the population growth and elimination processes of a tumor. The several models are made necessary by the nonlinearity of the processes and the different parameter ranges explored. The deterministic form of the model is where γ₀, k′₆ and k ₁ are positive constants. The parameter of most import is which determines the stability of the T = 0 equilibrium. With an initial tumor size of one, a (linear) branching process is used to estimate the extinction probability. However, in the case λ = 0 when the linearization of the deterministic model gives no information (T = 0 is actually unstable) the branching model is unsatisfactory. This makes necessary the utilization of a density-dependent branching process to approximate the population. Through scaling a diffusion limit is reached which enables one to again compute the probability of extinction. For populations away from one a sequence of density-dependent jump Markov processes are approximated by a sequence of diffusion processes. In limiting cases, the estimates of extinction correspond to that computed from the original branching process. Table 1 summarizes the results.     

Mathematical modeling of multi-drugs therapy: a challenge for determining the optimal combinations of antiviral drugs

In the current era of antiviral drug therapy, combining multiple drugs is a primary approach for improving antiviral effects, reducing the doses of individual drugs, relieving the side effects of strong antiviral drugs, and preventing the emergence of drug-resistant viruses. Although a variety of new drugs have been developed for HIV, HCV and influenza virus, the optimal combinations of multiple drugs are incompletely understood. To optimize the benefits of multi-drugs combinations, we must investigate the interactions between the combined drugs and their target viruses. Mathematical models of viral infection dynamics provide an ideal tool for this purpose. Additionally, whether drug combinations computed by these models are synergistic can be assessed by two prominent drug combination theories, Loewe additivity and Bliss independence. By combining the mathematical modeling of virus dynamics with drug combination theories, we could show the principles by which drug combinations yield a synergistic effect. Here, we describe the theoretical aspects of multi-drugs therapy and discuss their application to antiviral research.     

Multiscale modeling of tumor growth and angiogenesis: Evaluation of tumor-targeted therapy

The dynamics of tumor growth and associated events cover multiple time and spatial scales, generally including extracellular, cellular and intracellular modifications. The main goal of this study is to model the biological and physical behavior of tumor evolution in presence of normal healthy tissue, considering a variety of events involved in the process. These include hyper and hypoactivation of signaling pathways during tumor growth, vessels’ growth, intratumoral vascularization and competition of cancer cells with healthy host tissue. The work addresses two distinctive phases in tumor development—the avascular and vascular phases—and in each stage two cases are considered—with and without normal healthy cells. The tumor growth rate increases considerably as closed vessel loops (anastomoses) form around the tumor cells resulting from tumor induced vascularization. When taking into account the host tissue around the tumor, the results show that competition between normal cells and cancer cells leads to the formation of a hypoxic tumor core within a relatively short period of time. Moreover, a dense intratumoral vascular network is formed throughout the entire lesion as a sign of a high malignancy grade, which is consistent with reported experimental data for several types of solid carcinomas. In comparison with other mathematical models of tumor development, in this work we introduce a multiscale simulation that models the cellular interactions and cell behavior as a consequence of the activation of oncogenes and deactivation of gene signaling pathways within each cell. Simulating a therapy that blocks relevant signaling pathways results in the prevention of further tumor growth and leads to an expressive decrease in its size (82% in the simulation).     

Gene therapy for pancreatic cancer targeting the genomic alterations of tumor suppressor genes using replication-selective oncolytic adenovirus

In order to develop an effective therapeutic intervention for patients with pancreatic cancer, we examined the genetic alternations of pancreatic cancer. Based on these results, we are developing a new gene therapy targeting the genetic character of pancreatic cancer using mutant adenoviruses selectively replication-competent in tumor cells. Loss of heterozygosity (LOH) of 30% or more were observed on chromosome arms 17p (47%), 9p (45%), 18q (43%), 12q (34%), and 6q (30%). LOH of 12q, 17p, and 18q showed the significant association with poor prognosis. These data strongly suggest that mutation of the putative suppressor genes, TP53 and SMAD4 play significant roles in the disease progression. Based on this rationale, we are developing a new gene therapy targeting tumors without normal TP53 function. E1B-55kDa-deleted adenovirus (AxE1AdB) can selectively replicate in TP53-deficient human tumor cells but not cells with functional TP53. We evaluated the therapeutic effect of this AxE1AdB on pancreatic cancer without normal TP53 function. The growth of human pancreatic tumor in SCID mice model was markedly inhibited by the consecutive injection of AxE1AdB. Furthermore, AxE1AdB is not only the strong weapon but also useful carrier of genes possessing anti-tumor activities as a virus vector specific to tumors without normal TP53 function. It was reported that uracil phosphoribosyl transferase (UPRT) overcomes 5FU resistance. UPRT catalyzes the synthesis of 5-fluorouridine monophosphate (FUMP) from Uracil and phosphoribosylpyrophosphate (PRPP). The antitumor effect of 5FU is enhanced by augmenting 5-fluorodeoxyuridine monophosphate (FdUMP) converted from FUMP, which inhibits Thymidylate Synthetase (TS). The therapeutic advantage of restricted replication competent adenovirus that expresses UPRT (AxE1AdB-UPRT) was evaluatedin an intra-peritoneal disseminated tumor model. To study the anti-tumor effect of AxE1AdB-UPRT/5FU, mice with disseminated AsPC-1 tumors were administered the adenovirus, followed by the 5FU treatment. It was shown that the treatment with AxE1AdB-UPRT/5FU caused a dramatic reduction of the disseminated tumor burden without toxicity in normal tissues. These results revealed thatthe AxE1AdB-UPRT/5FU system is a promising tool for intraperitoneal disseminated pancreatic cancer.     

Multi-scale modeling of macrophage—T cell interactions within the tumor microenvironment

Within the tumor microenvironment, macrophages exist in an immunosuppressive state, preventing T cells from eliminating the tumor. Due to this, research is focusing on immunotherapies that specifically target macrophages in order to reduce their immunosuppressive capabilities and promote T cell function. In this study, we develop an agent-based model consisting of the interactions between macrophages, T cells, and tumor cells to determine how the immune response changes due to three macrophage-based immunotherapeutic strategies: macrophage depletion, recruitment inhibition, and macrophage reeducation. We find that reeducation, which converts the macrophages into an immune-promoting phenotype, is the most effective strategy and that the macrophage recruitment rate and tumor proliferation rate (tumor-specific properties) have large impacts on therapy efficacy. We also employ a novel method of using a neural network to reduce the computational complexity of an intracellular signaling mechanistic model.