An error catastrophe in cancer?

A comparison between the evolution of cancer cell populations and RNA viruses reveals a number of remarkable similarities. Both display high levels of plasticity and adaptability as a consequence of high degrees of genetic variation. It has been suggested that, as it occurs with RNA viruses, there is a threshold in the levels of genetic instability affordable by cancer cells in order to be able to overcome selection barriers (Trends Genet. 15 (1999) M57). Here we explore this concept by means of a simple mathematical model. It is shown that an error threshold exists in this model, which investigates both competition between cancer cell populations and its impact on overall tumor growth dynamics. Once the threshold is reached, the highly unstable tumor cell populations, which were sustaining malignant growth, become unable to maintain their genetic information, which in turn triggers a slowed down overall tumor growth regime.     

A partial differential equation model and its reduction to an ordinary differential equation model for prostate tumor growth under intermittent hormone therapy

Hormonal therapy with androgen suppression is a common treatment for advanced prostate tumors. The emergence of androgen-independent cells, however, leads to a tumor relapse under a condition of long-term androgen deprivation. Clinical trials suggest that intermittent androgen suppression (IAS) with alternating on- and off-treatment periods can delay the relapse when compared with continuous androgen suppression (CAS). In this paper, we propose a mathematical model for prostate tumor growth under IAS therapy. The model elucidates initial hormone sensitivity, an eventual relapse of a tumor under CAS therapy, and a delay of a relapse under IAS therapy, which are due to the coexistence of androgen-dependent cells, androgen-independent cells resulting from reversible changes by adaptation, and androgen-independent cells resulting from irreversible changes by genetic mutations. The model is formulated as a free boundary problem of partial differential equations that describe the evolution of populations of the abovementioned three types of cells during on-treatment periods and off-treatment periods. Moreover, the model can be transformed into a piecewise linear ordinary differential equation model by introducing three new volume variables, and the study of the resulting model may help to devise optimal IAS schedules.     

Tumor bioenergetics: An emerging avenue for cancer metabolism targeted therapy

Cell proliferation is a delicately regulated process that couples growth signals and metabolic demands to produce daughter cells. Interestingly, the proliferation of tumor cells immensely depends on glycolysis, the Warburg effect, to ensure a sufficient amount of metabolic flux and bioenergetics for macromolecule synthesis and cell division. This unique metabolic derangement ould provide an opportunity for developing cancer therapeutic strategy, particularly when other diverse anti-cancer treatments have been proved ineffective in achieving durable response, largely due to the emergence of resistance. Recent advances in deeper understanding of cancer metabolism usher in new horizons of the next generation strategy for cancer therapy. Here, we discuss the focused review of cancer energy metabolism, and the therapeutic exploitation of glycolysis and OXPHOS as a novel anti-cancer strategy, with particular emphasis on the promise of this approach, among other cancer metabolism targeted therapies that reveal unexpected complexity and context-dependent metabolic adaptability, complicating the development of effective strategies. [BMB Reports 2014; 47(3): 158-166]     

A delay differential equation model for tumor growth

We present a competition model of tumor growth that includes the immune system response and a cycle-phase-specific drug. The model considers three populations: Immune system, population of tumor cells during interphase and population of tumor during mitosis. Delay differential equations are used to model the system to take into account the phases of the cell cycle. We analyze the stability of the system and prove a theorem based on the argument principle to determine the stability of a fixed point and show that the stability may depend on the delay. We show theoretically and through numerical simulations that periodic solutions may arise through Hopf Bifurcations.Send offprint requests to:Minaya Villasana     

Expression level and glycan dynamics determine the net effects of TIMP-1 on cancer progression

Tissue inhibitor of metalloproteinases (TIMPs; TIMP-1, -2, -3 and -4) are endogenous inhibitor for matrix metalloproteinases (MMPs) that are responsible for remodeling the extracellular matrix (ECM) and involved in migration, invasion and metastasis of tumor cells. Unlike under normal conditions, the imbalance between MMPs and TIMPs is associated with various diseased states. Among TIMPs, TIMP-1, a 184-residue protein, is the only N-linked glycoprotein with glycosylation sites at N30 and N78. The structural analysis of the catalytic domain of human stromelysin-1 (MMP-3) and human TIMP-1 suggests new possibilities of the role of TIMP-1 glycan moieties as a tuner for the proteolytic activities by MMPs. Because the TIMP-1 glycosylation participate in the interaction, aberrant glycosylation of TIMP-1 presumably affects the interaction, thereby leading to pathogenic dysfunction in cancer cells. TIMP-1 has not only the cell proliferation activities but also anti-oncogenic properties. Cancer cells appear to utilize these bilateral aspects of TIMP-1 for cancer progression; an elevated TIMP-1 level exerts to cancer development via MMP-independent pathway during the early phase of tumor formation, whereas it is the aberrant glycosylation of TIMP-1 that overcome the high anti-proteolytic burden. The aberrant glycosylation of TIMP-1 can thus be used as staging and/or prognostic biomarker in colon cancer. [BMB Reports 2012; 45(11): 623-628]     

Somatic selection for and against cancer

In multicellular organisms, cells cooperate within a well-defined developmental program. Cancer is a breakdown of such cooperation: cells mutate to phenotypes of uncoordinated proliferation. We study basic principles of the architecture of solid tissues that influence the rate of cancer initiation. In particular, we explore how somatic selection acts to prevent or to promote cancer. Cells with mutations in oncogenes or tumor suppressor genes often have increased proliferation rates. Somatic selection increases their abundance and thus enhances the risk of cancer. Many potentially harmful mutations, however, increase the probability of triggering apoptosis and, hence, initially lead to cells with reduced net proliferation rates. Such cells are eliminated by somatic selection, which therefore also works to reduce the risk of cancer. We show that a tissue organization into small compartments avoids the rapid spread of mutations in oncogenes and tumor suppressor genes, but promotes genetic instability. In small compartments, genetic instability, which confers a selective disadvantage for the cell, can spread by random drift. If both deleterious and advantageous mutations participate in tumor initiation, then we find an intermediate optimum for the compartment size.     

A stochastic carcinogenesis model incorporating multiple types of genomic instability fitted to colon cancer data

A generalization of the two-mutation stochastic carcinogenesis model of Moolgavkar, Venzon and Knudson and certain models constructed by Little [Little, M.P. (1995). Are two mutations sufficient to cause cancer? Some generalizations of the two-mutation model of carcinogenesis of Moolgavkar, Venzon, and Knudson, and of the multistage model of Armitage and Doll. Biometrics 51, 1278-1291] and Little and Wright [Little, M.P., Wright, E.G. (2003). A stochastic carcinogenesis model incorporating genomic instability fitted to colon cancer data. Math. Biosci. 183, 111-134] is developed; the model incorporates multiple types of progressive genomic instability and an arbitrary number of mutational stages. The model is fitted to US Caucasian colon cancer incidence data. On the basis of the comparison of fits to the population-based data, there is little evidence to support the hypothesis that the model with more than one type of genomic instability fits better than models with a single type of genomic instability. Given the good fit of the model to this large dataset, it is unlikely that further information on presence of genomic instability or of types of genomic instability can be extracted from age-incidence data by extensions of this model.     

The stochastic model of non-equilibrium mutagen-induced alterations of DNA: implication to genetic instability in cancer

Genetic alterations such as point mutations, chromosomal rearrangements, modification of DNA methylation and chromosome aberrations accumulate during the lifetime of an organism. They can be caused by intrinsic errors in the DNA replication and repair as well as by external factors such as exposure to mutagenic substances or radiation. The main purpose of the present work is to begin an exploration of the stochastic nature of non-equilibrium DNA alteration caused by events such as tautomeric shifts. This is done by modeling the genetic DNA code chain as a sequence of DNA-bit values ('1' for normal bases and '-1' for abnormal bases). We observe the number of DNA-bit changes resulting from the random point mutation process which, in the model, is being induced by a stochastic Brownian mutagen (BM) as it diffuses through the DNA-bit systems. Using both an analytical and Monte Carlo (MC) simulation techniques, we observe the local and global number of DNA-bit changes. It is found that in 1D, the local DNA-bit density behaves like 1/t, the global total number of the switched (abnormal) DNA-bit increases as t. The probability distribution P(b, 0, t) of b(0, t) is log-normal. It is also found that when the number of mutagens is increased, the number of the total abnormal DNA-bits does not grow linearly with the number of mutagens. All analytic results are in good agreement with the simulation results.     

Weak convergence of a sequence of stochastic difference equations to a stochastic ordinary differential equation

We consider a sequence of discrete parameter stochastic processes defined by solutions to stochastic difference equations. A condition is given that this sequence converges weakly to a continuous parameter process defined by solutions to a stochastic ordinary differential equation. Applying this result, two limit theorems related to population biology are proved. Random parameters in stochastic difference equations are autocorrelated stationary Gaussian processes in the first case. They are jump-type Markov processes in the second case. We discuss a problem of continuous time approximations for discrete time models in random environments.     

Comparison of adjuvant activity of N- and C-terminal domain of gp96 in a Her2-positive breast cancer model

It has been frequently reported that gp96 acts as a strong biologic adjuvant. Some studies have even investigated adjuvant activity of the gp96 C- or N-terminal domain. The controversy surrounding adjuvant activity of gp96 terminal domains prompted us to compare adjuvant activity of gp96 C- or N-terminal domain toward Her2/neu, as DNA vaccine in a Her2/neu-positive breast cancer model. To do so, mice were immunized with DNA vaccine consisting of transmembrane and extracellular domain (TM + ECD) of rat Her2/neu alone or fused to N- or C-terminal domain of gp96. Treatment with Her2/neu fused to N-terminal domain of gp96 resulted in tumor progression, compared to the groups vaccinated with pCT/Her2 or pHer2. Immunological examination revealed that treatment with Her2/neu fused to N-terminal domain of gp96 led to significantly lower survival rates, higher interferon-γ secretion, and induced infiltration of CD4⁺/CD8⁺ cells to the tumor site. However, it could not induce cytotoxic T lymphocyte activity, did not decrease regulatory T cell percentage at the tumor site, and eventually led to tumor progression. Our results reveal that gp96 N-terminal domain does not have adjuvant activity toward Her2/neu. It is also proposed that adjuvant activity and the resultant immune response of gp96 terminal domains may be directed by the antigen applied.     

Up-regulation of miR-21 mediates resistance to trastuzumab therapy for breast cancer

Trastuzumab resistance emerges to be a major issue in anti-human epidermal growth factor receptor 2 (HER2) therapy for breast cancers. Here, we demonstrated that miR-21 expression was up-regulated and its function was elevated in HER2(+) BT474, SKBR3, and MDA-MB-453 breast cancer cells that are induced to acquire trastuzumab resistance by long-term exposure to the antibody, whereas protein expression of the PTEN gene, a miR-21 target, was reduced. Blocking the action of miR-21 with antisense oligonucleotides re-sensitized the resistant cells to the therapeutic activities of trastuzumab by inducing growth arrest, proliferation inhibition, and G(1)-S cell cycle checking in the presence of the antibody. Ectopic expression of miR-21 in HER2(+) breast cancer cells confers resistance to trastuzumab. Rescuing PTEN expression with a p3XFLAG-PTEN-mut construct with deleted miR-21 targeting sequence at its 3' UTR restored the growth inhibition of trastuzumab in the resistant cells by inducing PTEN activation and AKT inhibition. In vivo, administering miR-21 antisense oligonucleotides restored trastuzumab sensitivity in the resistant breast cancer xenografts by inducing PTEN expression, whereas injection of miR-21 mimics conferred trastuzumab resistant in the sensitive breast tumors via PTEN silence. Up-regulatin of miR-21 in tumor biopsies obtained from patients receiving pre-operative trastuzumab therapy was associated with poor trastuzumab response. Therefore, miR-21 overexpression contributes to trastuzumab resistance in HER2(+) breast cancers and antagonizing miR-21 demonstrates therapeutic potential by sensitizing the malignancy to anti-HER2 treatment.     

A computational model for radiation-induced cellular transformation to in vitro irradiation of cells by acute doses of X-rays

This research incorporates new biological concepts to improve the predictive ability of a state-vector model with respect to dose-response data on in vitro oncogenic transformation, including mechanisms of DNA damage, DNA repair, cell death, cell proliferation and intercellular communication. Experimentally recognized biological processes, including background transformation, compensatory proliferation and bystander cell-killing effect were formulated mathematically and included as model parameters. These were then adjusted with an optimization method to reproduce in vitro transformation frequency data from C3H10T1/2 mouse cells exposed to acute doses of X-rays. A plateau observed in the data at low doses is reproduced well and a dose-dependent increase above 1Gy is predicted almost precisely. Extension of the model predictions to the dose range 0-100mGy indicates that transformation frequencies are practically constant over this low dose region. Results suggest a protective, rather than detrimental, bystander cell-killing effect. Further analysis of model sensitivity to this bystander parameter, though, revealed uncertainties with respect to its biological plausibility in the model.     

Up-regulation of Bcl-2 is required for the progression of prostate cancer cells from an androgen-dependent to an androgen-independent growth stage

Bcl-2 is an anti-apoptotic oncoprotein and its protein levels are inversely correlated with prognosis in many cancers.However, the role of Bcl-2 in the progression of prostate cancer is not clear. Here we report that Bcl-2 is required for theprogression of LNCaP prostate cancer cells from an androgen-dependent to an androgen-independent growth stage. ThemRNA and protein levels of Bcl-2 are significantly increased in androgen-independent prostate cancer cells. shRNA-medi-ated gene silencing of Bcl-2 in androgen-independent prostate cancer cells promotes UV-induced apoptosis and suppressesthe growth of prostate tumors in vivo. Growing androgen-dependent cells under androgen-deprivation conditions resultsin formation of androgen-independent colonies; and the transition from androgen-dependent to androgen-independentgrowth is blocked by ectopic expression of the Bcl-2 antagonist Bax or Bcl-2 shRNA. Thus, our results demonstratethat Bcl-2 is not only critical for the survival of androgen-independent prostate cancer cells, but is also required for theprogression of prostate cancer cells from an androgen-dependent to an androgen-independent growth stage.     

A predictive model for the selective accumulation of chemicals in tumor cells

Cationic lipophilic dyes can accumulate in mitochondria, and especially in mitochondria of tumor cells. We investigated the chemical properties and the processes allowing selective uptake into tumor cells using the Fick–Nernst–Planck equation. The model simulates uptake into cytoplasm and mitochondria and is valid for neutral molecules and ions, and thus also for weak electrolytes. The differential equation system was analytically solved for the steady-state and the dynamic case. The parameterization was for a generic human cell, with a 60 mV more negative potential at the inner mitochondrial membrane of generic tumor cells. The chemical input data were the lipophilicity (logK_OW), the acid/base dissociation constant (pK_a) and the electric charge (z). Accumulation in mitochondria occurred for polar acids with pK_a between 5 and 9 owing to the ion trap, and for lipophilic bases with pK_a>11 or permanent cations owing to electrical attraction. Selective accumulation in tumor cells was found for monovalent cations or strong bases with logK_OW of the cation between –2 and 2, with the optimum near 0. The results are in agreement with experimental results for rhodamine 123, a series of cationic triarylmethane dyes, F16 and MKT-077, an anticancer drug targeting tumor mitochondria.     

A stochastic carcinogenesis model incorporating genomic instability fitted to colon cancer data

A generalization of the two-mutation stochastic carcinogenesis model of Moolgavkar, Venzon and Knudson and certain models constructed by Little is developed; the model incorporates progressive genomic instability and an arbitrary number of mutational stages. This model is shown to have the property that, at least in the case when the parameters of the model are eventually constant, the excess relative and absolute cancer rates following changes in any of the parameters will eventually tend to zero. It is also shown that when the parameters governing the processes of cell division, death, or additional mutation (whether of the normal sort or that resulting in genomic destabilization) at the penultimate stage are subject to perturbations, there are relatively large fluctuations in the hazard function for the model, which start almost as soon as the parameters are changed. The model is fitted to US Caucasian colon cancer incidence data. A model with five stages and two levels of genomic destabilization fits the data well. Comparison with patterns of excess risk in the Japanese atomic bomb survivor colon cancer incidence data indicate that radiation might act on early mutation rates in the model; a major role for radiation in initiating genomic destabilization is less likely.     

An epigenomic approach to identifying differential overlapping and cis-acting lncRNAs in cisplatin-resistant cancer cells

Long noncoding RNAs (lncRNAs) are critical regulators of cell biology whose alteration can lead to the development of diseases such as cancer. The potential role of lncRNAs and their epigenetic regulation in response to platinum treatment are largely unknown. We analyzed four paired cisplatin-sensitive/resistant non-small cell lung cancer and ovarian cancer cell lines. The epigenetic landscape of overlapping and cis-acting lncRNAs was determined by combining human microarray data on 30,586 lncRNAs and 20,109 protein coding mRNAs with whole-genome bisulfite sequencing. Selected candidate lncRNAs were further characterized by PCR, gene-ontology analysis, and targeted bisulfite sequencing. Differential expression in response to therapy was observed more frequently in cis-acting than in overlapping lncRNAs (78% vs. 22%, fold change ≥1.5), while significantly altered methylation profiles were more commonly associated with overlapping lncRNAs (29% vs. 8%; P value <0.001). Moreover, overlapping lncRNAs contain more CpG islands (CGIs) (25% vs. 17%) and the majority of CGI-containing overlapping lncRNAs share these CGIs with their associated coding genes (84%). The differences in expression between sensitive and resistant cell lines were replicated in 87% of the selected candidates (P<0.05), while our bioinformatics approach identifying differential methylation was confirmed in all of the selected lncRNAs (100%). Five lncRNAs under epigenetic regulation appear to be involved in cisplatin resistance (AC091814.2, AC141928.1, RP11-65J3.1-002, BX641110, and AF198444). These novel findings provide new insights into epigenetic mechanisms and acquired resistance to cisplatin that highlight specific lncRNAs, some with unknown function, that may signal strategies in epigenetic therapies.     

An immunotherapy approach with dendritic cells genetically modified to express the tumor-associated antigen,HER2

Dendritic cells (DC), genetically modified to express ovalbumin by the retroviral vector GCDNsap, can elicit stronger anti-tumor immunity than those loaded with the peptides. To assess the clinical feasibility of the strategy, such DC were prepared by differentiation of hematopoietic progenitor cells transduced with the human epidermal growth factor receptor 2 (HER2). When inoculated in mice, the DC primed both HER2-specific cytotoxic T lymphocytes and type 1 T helper lymphocytes, resulting in production of HER2-specific antibody. Of importance is that the antibody mediated antibody-dependent cellular cytotoxicity and opsonization. The potent anti-tumor effects were also confirmed by results of experiments using HER2-transgenic mice. Inoculation of HER2-transduced DC resulted in longer disease-free survival of treated mice that showed significant reduction of primary and metastatic tumors. Interestingly, footpad inoculation resulted in stronger anti-tumor effects compared to subcutaneous administration and induced higher levels of the HER2-specific antibody, suggesting that an important role of humoral immunity in anti-tumor effects for malignancies with membrane-type tumor-associated antigens (TAA). Taken together, vaccination of the TAA-transduced DC may represent a promising form of therapy for breast cancers expressing HER2.