Role of symmetric and asymmetric division of stem cells in developing drug resistance

Targeting Cervical Cancer Stem Cells by Phytochemicals

Cervical cancer (CaCx) poses a significant global health challenge, ranking as the fourth most common cancer among women worldwide. Despite the emergence of advanced treatment strategies, recurrence remains a bottleneck in favorable treatment outcomes and contributes to poor prognosis. The chemo- or radio-therapy resistance coupled with frequent relapse of more aggressive tumors are some key components that contribute to CaCx-related mortality. The onset of therapy resistance and relapse are attributed to a small subset of, slow-proliferating Cancer Stem Cells (CSC). These CSCs possess the properties of tumorigenesis, self-renewal, and multi-lineage differentiation potential. Because of slow cycling, these cells maintain themselves in a semi-quiescent stage and protect themselves from different anti-proliferative anti-cancer drugs. Keeping in view recent advances in their phenotypic and functional characterization, the feasibility of targeting CSC and associated stem cell signaling bears a strong translational value. The presence of CSC has been reported in CaCx (CCSC) which remains a forefront area of research. However, we have yet to identify clinically useful leads that can target CCSC. There is compelling evidence that phytochemicals, because of their advantages over synthetic anticancer drugs, could emerge as potential therapeutic leads to target these CCSCs. The present article examined the potential of phytochemicals with reported anti-CSC properties and evaluated their future in preclinical and clinical applications against CaCx.

Opportunities in Cancer Therapies: Deciphering the Role of Cancer Stem Cells in Tumour Repopulation

Tumour repopulation during treatment is a well acknowledged yet still challenging aspect of cancer management. The latest research results show clear evidence towards the existence of cancer stem cells (CSCs) that are responsible for tumour repopulation, dissemination, and distant metastases in most solid cancers. Cancer stem cell quiescence and the loss of asymmetrical division are two powerful mechanisms behind repopulation. Another important aspect in the context of cancer stem cells is cell plasticity, which was shown to be triggered during fractionated radiotherapy, leading to cell dedifferentiation and thus reactivation of stem-like properties. Repopulation during treatment is not limited to radiotherapy, as there is clinical proof for repopulation mechanisms to be activated through other conventional treatment techniques, such as chemotherapy. The dynamic nature of stem-like cancer cells often elicits resistance to treatment by escaping drug-induced cell death. The aims of this scoping review are (1) to describe the main mechanisms used by cancer stem cells to initiate tumour repopulation during therapy; (2) to present clinical evidence for tumour repopulation during radio- and chemotherapy; (3) to illustrate current trends in the identification of CSCs using specific imaging techniques; and (4) to highlight novel technologies that show potential in the eradication of CSCs.

Regulating POLR3G by MicroRNA-26a-5p as a promising therapeutic target of lung cancer stemness and chemosensitivity

Cancer stem cells (CSCs) identified in lung cancer exhibit resistance to chemotherapy, radiotherapy, and targeted therapy. Therefore, a technology for controlling CSCs is needed to overcome such resistance to cancer therapy. Various evidences about the association between epithelial-mesenchymal transition related transcriptomic alteration and acquisition of CSC phenotype have been proposed recently. Down-regulated miR-26a-5p is closely related to mesenchymal-like lung cancer cell lines. These findings suggest that miR-26a-5p might be involved in lung cancer stemness. RNA polymerase III subunit G (POLR3G) was selected as a candidate target of miR-26a-5p related to cancer stemness. It was found that miR-26a-5p directly regulates the expression of POLR3G.Overexpression of miR-26a-5p induced a marked reduction of colony formation and sphere formation. Co-treatment of miR-26a-5p and paclitaxel decreased cell growth, suggesting that miR-26a-5p might play a role as a chemotherapy sensitizer. In the cancer genome atlas data, high miR-26a-5p and low POLR3G expression were also related to higher survival rate of patients with lung adenocarcinoma. These results suggest that miR-26a-5p can suppress lung cancer stemness and make cancer cell become sensitive to chemotherapy. This finding provides a novel insight into a potential lung cancer treatment by regulating stemness.

Therapeutic Effectiveness of Anticancer Agents Targeting Different Signaling Molecules Involved in Asymmetric Division of Cancer Stem Cell

Intra-tumoral heterogeneity is maintained by cancer stem cells (CSCs) with dysregulated self-renewal and asymmetric cell division (ACD). According to the cancer stem cell theory, by ACD a CSC can generate two daughter progenies with different fates such as one cancer stem cell and one differentiated cell. Therefore, this type of mitotic division supports vital process of the maintenance of CSC population. But this CSC pool reservation by ACD complicates the treatment of cancer patients, as CSCs give rise to aggressive clones which are prone to metastasis and drug-insensitivity. Hence, identification of therapeutic modalities which can target ACD of cancer stem cell is an intriguing part of cancer research. In this review, other than the discussion about the extrinsic inducers of ACD role of different proteins, miRNAs and lncRNAs in this type of cell division is also mentioned. Other than these, mode of action of the proven and potential drugs targeting ACD of CSC is also discussed here.

MATHEMATICAL CHARACTERIZATION OF HETEROGENEITY IN A CANCER STEM CELL DRIVEN TUMOR GROWTH MODEL WITH NONLINEAR SELF-RENEWAL

The detection, in a wide variety of cancer types, of a population of highly tumorigenic cells that exhibit self-renewal and multipotency, which are hallmarks of stem cells, has transformed the current view of tumor initiation, progression, and treatment. Here, we develop and analyze a mathematical model for tumor growth that is based on the current biological understanding of the processes that underlie cellular expansion under the hierarchical guidelines of the cancer stem cell (CSC) hypothesis. Important features of the model include (i) a nonlinear probability of CSC self-renewal that reflects the fact that this key type of stem cell division can be regulated by extrinsic and intrinsic chemical signaling as well as environmental (niche) constraints and (ii) an amplification factor that captures the transient amplifying divisions that are a defining characteristic of progenitor cells. We present a thorough mathematical analysis of the model and highlight the conditions required for tumors to evolve toward either bounded or exponential growth. Numerical simulations further illustrate the impact of the various parameters on the tumor growth rate and on the heterogeneous cellular composition, which varies during progression.

Asymmetric cell division promotes therapeutic resistance in glioblastoma stem cells

Asymmetric cell division (ACD) enables the maintenance of a stem cell population while simultaneously generating differentiated progeny. Cancer stem cells (CSCs) undergo multiple modes of cell division during tumor expansion and in response to therapy, yet the functional consequences of these division modes remain to be determined. Using a fluorescent reporter for cell surface receptor distribution during mitosis, we found that ACD generated a daughter cell with enhanced therapeutic resistance and increased coenrichment of EGFR and neurotrophin receptor (p75NTR) from a glioblastoma CSC. Stimulation of both receptors antagonized differentiation induction and promoted self-renewal capacity. p75NTR knockdown enhanced the therapeutic efficacy of EGFR inhibition, indicating that coinheritance of p75NTR and EGFR promotes resistance to EGFR inhibition through a redundant mechanism. These data demonstrate that ACD produces progeny with coenriched growth factor receptors, which contributes to the generation of a more therapeutically resistant CSC population.

Stochastic stem cell models with mutation: A comparison of asymmetric and symmetric divisions

In order to fulfill cell proliferation and differentiation through cellular hierarchy, stem cells can undergo either asymmetric or symmetric divisions. Recent studies pay special attention to the effect of different modes of stem cell division on the lifetime risk of cancer, and report that symmetric division is more beneficial to delay the onset of cancer. The fate uncertainty of symmetric division is considered to be the reason for the cancer-delaying effect. In this paper we compare asymmetric and symmetric divisions of stem cells via studying stochastic stem cell models with mutation. Specially, by using rigorous mathematical analysis we find that both the asymmetric and symmetric models show the same statistical average, but the symmetric model shows higher fluctuation than the asymmetric model. We further show that the difference between the two models would be more remarkable for lower mutation rates. Our work quantifies the uncertainty of cell division and highlights the significance of stochasticity for distinguishing between different modes of stem cell division.

TNF-α inhibitor reduces drug-resistance to anti-PD-1: A mathematical model

Drug resistance is a primary obstacle in cancer treatment. In many patients who at first respond well to treatment, relapse occurs later on. Various mechanisms have been explored to explain drug resistance in specific cancers and for specific drugs. In this paper, we consider resistance to anti-PD-1, a drug that enhances the activity of anti-cancer T cells. Based on results in experimental melanoma, it is shown, by a mathematical model, that resistances to anti-PD-1 can be significantly reduced by combining it with anti-TNF-α. The model is used to simulate the efficacy of the combined therapy with different range of doses, different initial tumor volume, and different schedules. In particular, it is shown that under a course of treatment with 3-week cycles where each drug is injected in the first day of either week 1 or week 2, injecting anti-TNF-α one week after anti-PD-1 is the most effective schedule in reducing tumor volume.

A SOX2 Reporter System Identifies Gastric Cancer Stem-Like Cells Sensitive to Monensin

Gastric cancer remains a serious health burden with few therapeutic options. Therefore, the recognition of cancer stem cells (CSCs) as seeds of the tumorigenic process makes them a prime therapeutic target. Knowing that the transcription factors SOX2 and OCT4 promote stemness, our approach was to isolate stem-like cells in human gastric cancer cell lines using a traceable reporter system based on SOX2/OCT4 activity (SORE6-GFP). Cells transduced with the SORE6-GFP reporter system were sorted into SORE6+ and SORE6- cell populations, and their biological behavior characterized. SORE6+ cells were enriched for SOX2 and exhibited CSC features, including a greater ability to proliferate and form gastrospheres in non-adherent conditions, a larger in vivo tumor initiating capability, and increased resistance to 5-fluorouracil (5-FU) treatment. The overexpression and knockdown of SOX2 revealed a crucial role of SOX2 in cell proliferation and drug resistance. By combining the reporter system with a high-throughput screening of pharmacologically active small molecules we identified monensin, an ionophore antibiotic, displaying selective toxicity to SORE6+ cells. The ability of SORE6-GFP reporter system to recognize cancer stem-like cells facilitates our understanding of gastric CSC biology and serves as a platform for the identification of powerful therapeutics for targeting gastric CSCs.

Revisiting the tumorigenesis timeline with a data-driven generative model

Recently, investigators have shown that only a few driver gene mutational events appear to be needed for cancer to occur. However, the reason that some mutational events precede others in the same cancer and the explanation for tissue-specific differences in this timing, remain mysterious. We here combine mathematical modeling with epidemiologic studies and sequencing data to address these questions. We suggest that the first driver event in cancers generally occurred at early ages and provide estimates for the fitness of different types of drivers during tumor evolution, showing how they vary with the tissue of origin.

Cancer is driven by the sequential accumulation of genetic and epigenetic changes in oncogenes and tumor suppressor genes. The timing of these events is not well understood. Moreover, it is currently unknown why the same driver gene change appears as an early event in some cancer types and as a later event, or not at all, in others. These questions have become even more topical with the recent progress brought by genome-wide sequencing studies of cancer. Focusing on mutational events, we provide a mathematical model of the full process of tumor evolution that includes different types of fitness advantages for driver genes and carrying-capacity considerations. The model is able to recapitulate a substantial proportion of the observed cancer incidence in several cancer types (colorectal, pancreatic, and leukemia) and inherited conditions (Lynch and familial adenomatous polyposis), by changing only 2 tissue-specific parameters: the number of stem cells in a tissue and its cell division frequency. The model sheds light on the evolutionary dynamics of cancer by suggesting a generalized early onset of tumorigenesis followed by slow mutational waves, in contrast to previous conclusions. Formulas and estimates are provided for the fitness increases induced by driver mutations, often much larger than previously described, and highly tissue dependent. Our results suggest a mechanistic explanation for why the selective fitness advantage introduced by specific driver genes is tissue dependent.

Engineered 3D Model of Cancer Stem Cell Enrichment and Chemoresistance

Intraperitoneal dissemination of ovarian cancers is preceded by the development of chemoresistant tumors with malignant ascites. Despite the high levels of chemoresistance and relapse observed in ovarian cancers, there are no in vitro models to understand the development of chemoresistance in situ. Method: We describe a highly integrated approach to establish an in vitro model of chemoresistance and stemness in ovarian cancer, using the 3D hanging drop spheroid platform. The model was established by serially passaging non-adherent spheroids. At each passage, the effectiveness of the model was evaluated via measures of proliferation, response to treatment with cisplatin and a novel ALDH1A inhibitor. Concomitantly, the expression and tumor initiating capacity of cancer stem-like cells (CSCs) was analyzed. RNA-seq was used to establish gene signatures associated with the evolution of tumorigenicity, and chemoresistance. Lastly, a mathematical model was developed to predict the emergence of CSCs during serial passaging of ovarian cancer spheroids. Results: Our serial passage model demonstrated increased cellular proliferation, enriched CSCs, and emergence of a platinum resistant phenotype. In vivo tumor xenograft assays indicated that later passage spheroids were significantly more tumorigenic with higher CSCs, compared to early passage spheroids. RNA-seq revealed several gene signatures supporting the emergence of CSCs, chemoresistance, and malignant phenotypes, with links to poor clinical prognosis. Our mathematical model predicted the emergence of CSC populations within serially passaged spheroids, concurring with experimentally observed data. Conclusion: Our integrated approach illustrates the utility of the serial passage spheroid model for examining the emergence and development of chemoresistance in ovarian cancer in a controllable and reproducible format.

Effect of resveratrol on drug resistance in colon cancer chemotherapy

To investigate the effects of resveratrol on the drug resistance of 5-FU in the colon cancer chemotherapy, an MTT assay was used to detect the effects of 5-FU and resveratrol combined with 5-FU on the proliferation of the LoVo and SW480 cell lines. Flow cytometry was used to detect the effect of 5-FU combined with resveratrol on the survival rate of the LoVo and SW480 cells. A western blot was used to detect the expression levels of the proteins associated with colon cancer. After flow sorting, the percentage of the SW480 and the LoVo cell line CD133+ was 97.5% and 95.8%, respectively. The cells cultured in vitro showed more rapid cell proliferation and differentiation. The MTT assay showed that as compared with the survival rate of the blank group LoVo and CD133+ LoVo cells, the survival rate of the cells containing the 5-FU group was lower (P < 0.05). When 5-FU was used in combination with different concentrations of resveratrol, the abovementioned phenomenon was more prominent. The sorted colon cancer cells have dry stem cells, and the sorted CD133+ cells are more resistant to drugs; the combination of resveratrol and 5-FU has the best effect on the colon cancer cells. Preliminary studies on the mechanism of action of the drug show that a combination of 5-FU and resveratrol regulates apoptosis in CD133+ colon cancer stem cells by regulating the BAX gene; however, more complex mechanisms may also be involved.

Mathematical modeling of bone marrow - peripheral blood dynamics in the disease state based on current emerging paradigms, part II

The cancer stem cell hypothesis has gained currency in recent times but concerns remain about its scientific foundations because of significant gaps that exist between research findings and comprehensive knowledge about cancer stem cells (CSCs). In this light, a mathematical model that considers hematopoietic dynamics in the diseased state of the bone marrow and peripheral blood is proposed and used to address findings about CSCs. The ensuing model, resulting from a modification and refinement of a recent model, develops out of the position that mathematical models of CSC development, that are few at this time, are needed to provide insightful underpinnings for biomedical findings about CSCs as the CSC idea gains traction. Accordingly, the mathematical challenges brought on by the model that mirror general challenges in dealing with nonlinear phenomena are discussed and placed in context. The proposed model describes the logical occurrence of discrete time delays, that by themselves present mathematical challenges, in the evolving cell populations under consideration. Under the challenging circumstances, the steady state properties of the model system of delay differential equations are obtained, analyzed, and the resulting mathematical predictions arising therefrom are interpreted and placed within the framework of findings regarding CSCs. Simulations of the model are carried out by considering various parameter scenarios that reflect different experimental situations involving disease evolution in human hosts. Model analyses and simulations suggest that the emergence of the cancer stem cell population alongside other malignant cells engenders higher dimensions of complexity in the evolution of malignancy in the bone marrow and peripheral blood at the expense of healthy hematopoietic development. The model predicts the evolution of an aberrant environment in which the malignant population particularly in the bone marrow shows tendencies of reaching an uncontrollable equilibrium state. Essentially, the model shows that a structural relationship exists between CSCs and non-stem malignant cells that confers on CSCs the role of temporally enhancing and stimulating the expansion of non-stem malignant cells while also benefitting from increases in their own population and these CSCs may be the main protagonists that drive the ultimate evolution of the uncontrollable equilibrium state of such malignant cells and these may have implications for treatment.

Oncogenic activation of PI3K induces progenitor cell differentiation to suppress epidermal growth

Oncogenic lesions are surprisingly common in morphologically and functionally normal human skin, however, the cellular and molecular mechanisms that suppress their cancer-driving potential to maintain tissue homeostasis are unknown. By employing assays for direct and quantitative assessment of cell fate choices in vivo, we show that oncogenic activation of PI3K/AKT, the most commonly activated oncogenic pathway in cancer, promotes differentiation and cell-cycle exit of epidermal progenitors. As a result, oncogenic PI3K/AKT activated epidermis exhibits growth disadvantage even though its cells are more proliferative. To uncover the underlying mechanism behind oncogene-induced differentiation, we conduct a series of genetic screens in vivo, and identify an AKT substrate SH3RF1 as a specific promoter of epidermal differentiation that has no effect on proliferation. Our study provides evidence for a direct, cell autonomous mechanism that can suppresses progenitor cell renewal and block clonal expansion of epidermal cells bearing a common and activating mutation in Pik3ca.

Exploring immuno-regulatory mechanisms in the tumor microenvironment: Model and design of protocols for cancer remission

The tumor microenvironment comprising of the immune cells and cytokines acts as the ‘soil’ that nourishes a developing tumor. Lack of a comprehensive study of the interactions of this tumor microenvironment with the heterogeneous sub-population of tumor cells that arise from the differentiation of Cancer Stem Cells (CSC), i.e. the ‘seed’, has limited our understanding of the development of drug resistance and treatment failures in Cancer. Based on this seed and soil hypothesis, for the very first time, we have captured the concept of CSC differentiation and tumor-immune interaction into a generic model that has been validated with known experimental data. Using this model we report that as the CSC differentiation shifts from symmetric to asymmetric pattern, resistant cancer cells start accumulating in the tumor that makes it refractory to therapeutic interventions. Model analyses unveiled the presence of feedback loops that establish the dual role of M2 macrophages in regulating tumor proliferation. The study further revealed oscillations in the tumor sub-populations in the presence of T_H1 derived IFN-γ that eliminates CSC; and the role of IL10 feedback in the regulation of T_H1/T_H2 ratio. These analyses expose important observations that are indicative of Cancer prognosis. Further, the model has been used for testing known treatment protocols to explore the reasons of failure of conventional treatment strategies and propose an improvised protocol that shows promising results in suppressing the proliferation of all the cellular sub-populations of the tumor and restoring a healthy T_H1/T_H2 ratio that assures better Cancer remission.

Role of the Interplay Between the Internal and External Conditions in Invasive Behavior of Tumors

Tumor growth, which plays a central role in cancer evolution, depends on both the internal features of the cells, such as their ability for unlimited duplication, and the external conditions, e.g., supply of nutrients, as well as the dynamic interactions between the two. A stem cell theory of cancer has recently been developed that suggests the existence of a subpopulation of self-renewing tumor cells to be responsible for tumorigenesis, and is able to initiate metastatic spreading. The question of abundance of the cancer stem cells (CSCs) and its relation to tumor malignancy has, however, remained an unsolved problem and has been a subject of recent debates. In this paper we propose a novel model beyond the standard stochastic models of tumor development, in order to explore the effect of the density of the CSCs and oxygen on the tumor's invasive behavior. The model identifies natural selection as the underlying process for complex morphology of tumors, which has been observed experimentally, and indicates that their invasive behavior depends on both the number of the CSCs and the oxygen density in the microenvironment. The interplay between the external and internal conditions may pave the way for a new cancer therapy.

Control of cell fraction and population recovery during tissue regeneration in stem cell lineages

Multicellular tissues are continually turning over, and homeostasis is maintained through regulated proliferation and differentiation of stem cells and progenitors. Following tissue injury, a dramatic increase in cell proliferation is commonly observed, resulting in rapid restoration of tissue size. This regulation is thought to occur via multiple feedback loops acting on cell self-renewal or differentiation. Models of ordinary differential equations have been widely used to study the cell lineage system. Prior modeling studies have suggested that loss of homeostasis and initiation of tumorigenesis can be contributed to the loss of control of these processes, and the rate of symmetric versus asymmetric division of the stem cells may also be altered. While most of the previous works focused on analysis of stability, existence and uniqueness of steady states of multistage cell lineage models, in this work we attempt to understand the cell lineage model from a different perspective. We compare three variants of hierarchical stem cell lineage tissue models with different combinations of negative feedbacks and use sensitivity analysis to examine the possible strategies for the cells to achieve certain performance objectives. Our results suggest that multiple negative feedback loops must be present in the stem cell lineage to keep the fractions of stem cells to differentiated cells in the total population as robust as possible to variations in cell division parameters, and to minimize the time for tissue recovery in a non-oscillatory manner.

Aberrantly activated Cox-2 and Wnt signaling interact to maintain cancer stem cells in glioblastoma

Glioblastoma recurrence after aggressive therapy typically occurs within six months, and patients inevitably succumb to their disease. Tumor recurrence is driven by a subpopulation of cancer stem cells in glioblastoma (glioblastoma stem-like cells, GSCs), which exhibit resistance to cytotoxic therapies, compared to their non-stem-cell counterparts. Here, we show that the Cox-2 and Wnt signaling pathways are aberrantly activated in GSCs and interact to maintain the cancer stem cell identity. Cox-2 stimulates GSC self-renewal and proliferation through prostaglandin E2 (PGE2), which in turn activates the Wnt signaling pathway. Wnt signaling underlies PGE2-induced GSC self-renewal and independently directs GSC self-renewal and proliferation. Inhibition of PGE2 enhances the effect of temozolomide on GSCs, but affords only a modest survival advantage in a xenograft model in the setting of COX-independent Wnt activation. Our findings uncover an aberrant positive feedback interaction between the Cox-2/PGE2 and Wnt pathways that mediates the stem-like state in glioblastoma.

Photobiomodulation of breast and cervical cancer stem cells using low-intensity laser irradiation

Breast and cervical cancers are dangerous threats with regard to the health of women. The two malignancies have reached the highest record in terms of cancer-related deaths among women worldwide. Despite the use of novel strategies with the aim to treat and cure advanced stages of cancer, post-therapeutic relapse believed to be caused by cancer stem cells is one of the challenges encountered during tumor therapy. Therefore, further attention should be paid to cancer stem cells when developing novel anti-tumor therapeutic approaches. Low-intensity laser irradiation is a form of phototherapy making use of visible light in the wavelength range of 630-905 nm. Low-intensity laser irradiation has shown remarkable results in a wide range of medical applications due to its biphasic dose and wavelength effect at a cellular level. Overall, this article focuses on the cellular responses of healthy and cancer cells after treatment with low-intensity laser irradiation alone or in combination with a photosensitizer as photodynamic therapy and the influence that various wavelengths and fluencies could have on the therapeutic outcome. Attention will be paid to the biomodulative effect of low-intensity laser irradiation on cancer stem cells.

Dynamical models of mutated chronic myelogenous leukemia cells for a post-imatinib treatment scenario: Response to dasatinib or nilotinib therapy

Targeted inhibition of the oncogenic BCR-ABL1 fusion protein using the ABL1 tyrosine kinase inhibitor imatinib has become standard therapy for chronic myelogenous leukemia (CML), with most patients reaching total and durable remission. However, a significant fraction of patients develop resistance, commonly due to mutated ABL1 kinase domains. This motivated development of second-generation drugs with broadened or altered protein kinase selectivity profiles, including dasatinib and nilotinib. Imatinib-resistant patients undergoing treatment with second-line drugs typically develop resistance to them, but dynamic and clonal properties of this response differ. Shared, however, is the observation of clonal competition, reflected in patterns of successive dominance of individual clones. We present three deterministic mathematical models to study the origins of clinically observed dynamics. Each model is a system of coupled first-order differential equations, considering populations of three mutated active stem cell strains and three associated pools of differentiated cells; two models allow for activation of quiescent stem cells. Each approach is distinguished by the way proliferation rates of the primary stem cell reservoir are modulated. Previous studies have concentrated on simulating the response of wild-type leukemic cells to imatinib administration; our focus is on modelling the time dependence of imatinib-resistant clones upon subsequent exposure to dasatinib or nilotinib. Performance of the three computational schemes to reproduce selected CML patient profiles is assessed. While some simple cases can be approximated by a basic design that does not invoke quiescence, others are more complex and require involvement of non-cycling stem cells for reproduction. We implement a new feedback mechanism for regulation of coupling between cycling and non-cycling stem cell reservoirs that depends on total cell populations. A bifurcation landscape analysis is also performed for solutions to the basic ansatz. Computational models reproducing patient data illustrate potential dynamic mechanisms that may guide optimization of therapy of drug resistant CML.

Analysis of temozolomide resistance in low-grade gliomas using a mechanistic mathematical model

Understanding how tumors develop resistance to chemotherapy is a major issue in oncology. When treated with temozolomide (TMZ), an oral alkylating chemotherapy drug, most low-grade gliomas (LGG) show an initial volume decrease but this effect is rarely long lasting. In addition, it has been suggested that TMZ may drive tumor progression in a subset of patients as a result of acquired resistance. Using longitudinal tumor size measurements from 121 patients, the aim of this study was to develop a semi-mechanistic mathematical model to determine whether resistance of LGG to TMZ was more likely to result from primary and/or from chemotherapy-induced acquired resistance that may contribute to tumor progression. We applied the model to a series of patients treated upfront with TMZ (n = 109) or PCV (procarbazine, CCNU, vincristine) chemotherapy (n = 12) and used a population mixture approach to classify patients according to the mechanism of resistance most likely to explain individual tumor growth dynamics. Our modeling results predicted acquired resistance in 51% of LGG treated with TMZ. In agreement with the different biological effects of nitrosoureas, none of the patients treated with PCV were classified in the acquired resistance group. Consistent with the mutational analysis of recurrent LGG, analysis of growth dynamics using mathematical modeling suggested that in a subset of patients, TMZ might paradoxically contribute to tumor progression as a result of chemotherapy-induced resistance. Identification of patients at risk of developing acquired resistance is warranted to better define the role of TMZ in LGG.

The role of cell location and spatial gradients in the evolutionary dynamics of colon and intestinal crypts

BACKGROUND

Colon and intestinal crypts serve as an important model system for adult stem cell proliferation and differentiation. We develop a spatial stochastic model to study the rate of somatic evolution in a normal crypt, focusing on the production of two-hit mutants that inactivate a tumor suppressor gene. We investigate the effect of cell division pattern along the crypt on mutant production, assuming that the division rate of each cell depends on its location.

RESULTS

We find that higher probability of division at the bottom of the crypt, where the stem cells are located, leads to a higher rate of double-hit mutant production. The optimal case for delaying mutations occurs when most of the cell divisions happen at the top of the crypt. We further consider an optimization problem where the "evolutionary" penalty for double-hit mutant generation is complemented with a "functional" penalty that assures that fully differentiated cells at the top of the crypt cannot divide.

CONCLUSION

The trade-off between the two types of objectives leads to the selection of an intermediate division pattern, where the cells in the middle of the crypt divide with the highest rate. This matches the pattern of cell divisions obtained experimentally in murine crypts.

REVIEWERS

This article was reviewed by David Axelrod (nominated by an Editorial Board member, Marek Kimmel), Yang Kuang and Anna Marciniak-Czochra. For the full reviews, please go to the Reviewers' comments section.

Near Equilibrium Calculus of Stem Cells in Application to the Airway Epithelium Lineage

Homeostatic maintenance of tissues is orchestrated by well tuned networks of cellular signaling. Such networks regulate, in a stochastic manner, fates of all cells within the respective lineages. Processes such as symmetric and asymmetric divisions, differentiation, de-differentiation, and death have to be controlled in a dynamic fashion, such that the cell population is maintained at a stable equilibrium, has a sufficiently low level of stochastic variation, and is capable of responding efficiently to external damage. Cellular lineages in real tissues may consist of a number of different cell types, connected by hierarchical relationships, albeit not necessarily linear, and engaged in a number of different processes. Here we develop a general mathematical methodology for near equilibrium studies of arbitrarily complex hierarchical cell populations, under regulation by a control network. This methodology allows us to (1) determine stability properties of the network, (2) calculate the stochastic variance, and (3) predict how different control mechanisms affect stability and robustness of the system. We demonstrate the versatility of this tool by using the example of the airway epithelium lineage. Recent research shows that airway epithelium stem cells divide mostly asymmetrically, while the so-called secretory cells divide predominantly symmetrically. It further provides quantitative data on the recovery dynamics of the airway epithelium, which can include secretory cell de-differentiation. Using our new methodology, we demonstrate that while a number of regulatory networks can be compatible with the observed recovery behavior, the observed division patterns of cells are the most optimal from the viewpoint of homeostatic lineage stability and minimizing the variation of the cell population size. This not only explains the observed yet poorly understood features of airway tissue architecture, but also helps to deduce the information on the still largely hypothetical regulatory mechanisms governing tissue turnover, and lends insight into how different control loops influence the stability and variance properties of cell populations.

Tissue stability is the basic property of healthy organs, and yet the mechanisms governing the stable, long-term maintenance of cell numbers in tissues are poorly understood. While more and more signaling pathways are being discovered, for the most part it remains unknown how they are being put together by different cell types into complex, nonlinear, hierarchical control networks that, on the one hand, reliably maintain constant cell numbers, and on the other hand, quickly adjust to oversee the robust response to tissue damage. Theoretical approaches can fill the gap by being able to reconstruct the underlying control network, based on the observations about the aspects of cellular dynamics. We argue that while many hypothetical networks may be capable of basic cell lineage maintenance, some are much more efficient from the viewpoint of variance minimization. Thus, we developed a new methodology that can test various control networks for stability, variance, and robustness. In the example of the airway epithelium that we highlight, it turns out that the evolutionary selected, actual architecture coincides with the mathematically optimal solution that minimizes the fluctuations of cell numbers at homeostasis.

Actions of Estrogenic Endocrine Disrupting Chemicals on Human Prostate Stem/Progenitor Cells and Prostate Carcinogenesis

Substantial evidences from epidemiological and animal-based studies indicate that early exposure to endocrine disrupting chemicals (EDCs) during the developmental stage results in a variety of disorders including cancer. Previous studies have demonstrated that early estrogen exposure results in life-long reprogramming of the prostate gland that leads to an increased incidence of prostatic lesions with aging. We have recently documented that bisphenol A (BPA), one of the most studied EDCs with estrogenic activity has similar effects in increasing prostate carcinogenic potential, supporting the connection between EDCs exposure and prostate cancer risk. It is well accepted that stem cells play a crucial role in development and cancer. Accumulating evidence suggest that stem cells are regulated by extrinsic factors and may be the potential target of hormonal carcinogenesis. Estrogenic EDCs which interfere with normal hormonal signaling may perturb prostate stem cell fate by directly reprogramming stem cells or breaking down the stem cell niche. Transformation of stem cells into cancer stem cells may underlie cancer initiation accounting for cancer recurrence, which becomes a critical therapeutic target of cancer management. We therefore propose that estrogenic EDCs may influence the development and progression of prostate cancer through reprogramming and transforming the prostate stem and early stage progenitor cells. In this review, we summarize our current studies and have updated recent advances highlighting estrogenic EDCs on prostate carcinogenesis by possible targeting prostate stem/progenitor cells. Using novel stem cell assays we have demonstrated that human prostate stem/progenitor cells express estrogen receptors (ER) and are directly modulated by estrogenic EDCs. Moreover, employing anin vivohumanized chimeric prostate model, we further demonstrated that estrogenic EDCs initiate and promote prostatic carcinogenesis in an androgen-supported environment. These findings support our hypothesis that prostate stem/progenitor cells may be the direct targets of estrogenic EDCs as a consequence of developmental exposure which carry permanent reprogrammed epigenetic and oncogenic events and subsequently deposit into cancer initiation and progression in adulthood.

Modeling Tumor Clonal Evolution for Drug Combinations Design

Cancer is a clonal evolutionary process. This presents challenges for effective therapeutic intervention, given the constant selective pressure towards drug resistance. Mathematical modeling from population genetics, evolutionary dynamics, and engineering perspectives are being increasingly employed to study tumor progression, intratumoral heterogeneity, drug resistance, and rational drug scheduling and combinations design. In this review, we discuss promising opportunities these inter-disciplinary approaches hold for advances in cancer biology and treatment. We propose that quantitative modeling perspectives can complement emerging experimental technologies to facilitate enhanced understanding of disease progression and improved capabilities for therapeutic drug regimen designs.

The Role of Symmetric Stem Cell Divisions in Tissue Homeostasis

Successful maintenance of cellular lineages critically depends on the fate decision dynamics of stem cells (SCs) upon division. There are three possible strategies with respect to SC fate decision symmetry: (a) asymmetric mode, when each and every SC division produces one SC and one non-SC progeny; (b) symmetric mode, when 50% of all divisions produce two SCs and another 50%-two non-SC progeny; (c) mixed mode, when both the asymmetric and two types of symmetric SC divisions co-exist and are partitioned so that long-term net balance of the lineage output stays constant. Theoretically, either of these strategies can achieve lineage homeostasis. However, it remains unclear which strategy(s) are more advantageous and under what specific circumstances, and what minimal control mechanisms are required to operate them. Here we used stochastic modeling to analyze and quantify the ability of different types of divisions to maintain long-term lineage homeostasis, in the context of different control networks. Using the example of a two-component lineage, consisting of SCs and one type of non-SC progeny, we show that its tight homeostatic control is not necessarily associated with purely asymmetric divisions. Through stochastic analysis and simulations we show that asymmetric divisions can either stabilize or destabilize the lineage system, depending on the underlying control network. We further apply our computational model to biological observations in the context of a two-component lineage of mouse epidermis, where autonomous lineage control has been proposed and notable regional differences, in terms of symmetric division ratio, have been noted-higher in thickened epidermis of the paw skin as compared to ear and tail skin. By using our model we propose a possible explanation for the regional differences in epidermal lineage control strategies. We demonstrate how symmetric divisions can work to stabilize paw epidermis lineage, which experiences high level of micro-injuries and a lack of hair follicles as a back-up source of SCs.

Analysis of stochastic stem cell models with control

Understanding the dynamics of stem cell lineages is of central importance both for healthy and cancerous tissues. We study stochastic population dynamics of stem cells and differentiated cells, where cell decisions, such as proliferation vs. differentiation decisions, or division and death decisions, are under regulation from surrounding cells. The goal is to understand how different types of control mechanisms affect the means and variances of cell numbers. We use the assumption of weak dependencies of the regulatory functions (the controls) on the cell populations near the equilibrium to formulate moment equations. We then study three different methods of closure, showing that they all lead to the same results for the highest order terms in the expressions for the moments. We derive simple explicit expressions for the means and the variances of stem cell and differentiated cell numbers. It turns out that the variance is expressed as an algebraic function of partial derivatives of the controls with respect to the population sizes at the equilibrium. We demonstrate that these findings are consistent with the results previously obtained in the context of particular systems, and also present two novel examples with negative and positive control of division and differentiation decisions. This methodology is formulated without any specific assumptions on the functional form of the controls, and thus can be used for any biological system.

Mechanical model of geometric cell and topological algorithm for cell dynamics from single-cell to formation of monolayered tissues with pattern

Geometric and mechanical properties of individual cells and interactions among neighboring cells are the basis of formation of tissue patterns. Understanding the complex interplay of cells is essential for gaining insight into embryogenesis, tissue development, and other emerging behavior. Here we describe a cell model and an efficient geometric algorithm for studying the dynamic process of tissue formation in 2D (e.g. epithelial tissues). Our approach improves upon previous methods by incorporating properties of individual cells as well as detailed description of the dynamic growth process, with all topological changes accounted for. Cell size, shape, and division plane orientation are modeled realistically. In addition, cell birth, cell growth, cell shrinkage, cell death, cell division, cell collision, and cell rearrangements are now fully accounted for. Different models of cell-cell interactions, such as lateral inhibition during the process of growth, can be studied in detail. Cellular pattern formation for monolayered tissues from arbitrary initial conditions, including that of a single cell, can also be studied in detail. Computational efficiency is achieved through the employment of a special data structure that ensures access to neighboring cells in constant time, without additional space requirement. We have successfully generated tissues consisting of more than 20,000 cells starting from 2 cells within 1 hour. We show that our model can be used to study embryogenesis, tissue fusion, and cell apoptosis. We give detailed study of the classical developmental process of bristle formation on the epidermis of D. melanogaster and the fundamental problem of homeostatic size control in epithelial tissues. Simulation results reveal significant roles of solubility of secreted factors in both the bristle formation and the homeostatic control of tissue size. Our method can be used to study broad problems in monolayered tissue formation. Our software is publicly available.

Drug resistance

Drug resistance is a fundamental problem in the treatment of cancer since cancer that becomes resistant to the available drugs may leave the patient with no therapeutic alternatives. In this chapter, we consider the dynamics of drug resistance in blood cancer and the related issue of the dynamics of cancer stem cells. After describing the main types of chemotherapeutic agents available for cancer treatment, we review the different mechanisms of drug resistance development. Various mathematical models of drug resistance found in the literature are then reviewed. Given the well-known hierarchy of the hematopoietic system, it is critical to focus on those cells that have the ability to self-renew, since these will be the only cells able to induce long-term drug resistance. Thus, a recent mathematical model taking into account the complex dynamics of the leukemic stem-like cells is described. The chapter closes with a few applications of this model to chronic myeloid leukemia.

Modeling drug resistance in a conjoint normal-tumor setting

Background

In this paper, we modify our previously developed conjoint tumor-normal cell model in order to make a distinction between tumor cells that are responsive to chemotherapy and those that may show resistance.

Results

Using this newly developed core model, the evolution of three cell types: normal, tumor, and drug-resistant tumor cells, is studied through a series of numerical simulations. In addition, we illustrate critical factors that cause different dynamical patterns for normal and tumor cells. Among these factors are the co-dependency of the normal and tumor cells, the cells’ response mechanism to a single or multiple chemotherapeutic treatment, the drug administration sequence, and the treatment starting time.

Conclusion

The results provide us with a deeper understanding of the possible evolution of normal, drug-responsive, and drug-resistant tumor cells during the cancer progression, which may contribute to improving the therapeutic strategies.

Only three driver gene mutations are required for the development of lung and colorectal cancers

Cancer arises through the sequential accumulation of mutations in oncogenes and tumor suppressor genes. However, how many such mutations are required for a normal human cell to progress to an advanced cancer? The best estimates for this number have been provided by mathematical models based on the relation between age and incidence. For example, the classic studies of Nordling [Nordling CO (1953) Br J Cancer 7(1):68-72] and Armitage and Doll [Armitage P, Doll R (1954) Br J Cancer 8(1):1-12] suggest that six or seven sequential mutations are required. Here, we describe a different approach to derive this estimate that combines conventional epidemiologic studies with genome-wide sequencing data: incidence data for different groups of patients with the same cancer type were compared with respect to their somatic mutation rates. In two well-documented cancer types (lung and colon adenocarcinomas), we find that only three sequential mutations are required to develop cancer. This conclusion deepens our understanding of the process of carcinogenesis and has important implications for the design of future cancer genome-sequencing efforts.

A study on stability and medical implications for a complex delay model for CML with cell competition and treatment

We study a mathematical model describing the dynamics of leukemic and normal cell populations (stem-like and differentiated) in chronic myeloid leukemia (CML). This model is a system of four delay differential equations incorporating three types of cell division. The competition between normal and leukemic stem cell populations for the common microenvironment is taken into consideration. The stability of one steady state is investigated. The results are discussed via their medical interpretation.

Etiology and treatment of hematological neoplasms: stochastic mathematical models

Leukemias are driven by stemlike cancer cells (SLCC), whose initiation, growth, response to treatment, and posttreatment behavior are often "stochastic", i.e., differ substantially even among very similar patients for reasons not observable with present techniques. We review the probabilistic mathematical methods used to analyze stochastics and give two specific examples. The first example concerns a treatment protocol, e.g., for acute myeloid leukemia (AML), where intermittent cytotoxic drug dosing (e.g., once each weekday) is used with intent to cure. We argue mathematically that, if independent SLCC are growing stochastically during prolonged treatment, then, other things being equal, front-loading doses are more effective for tumor eradication than back loading. We also argue that the interacting SLCC dynamics during treatment is often best modeled by considering SLCC in microenvironmental niches, with SLCC-SLCC interactions occurring only among SLCC within the same niche, and we present a stochastic dynamics formalism, involving "Poissonization," applicable in such situations. Interactions at a distance due to partial control of total cell numbers are also considered. The second half of this chapter concerns chromosomal aberrations, lesions known to cause some leukemias. A specific example is the induction of a Philadelphia chromosome by ionizing radiation, subsequent development of chronic myeloid leukemia (CML), CML treatment, and treatment outcome. This time evolution involves a coordinated sequence of > 10 steps, each stochastic in its own way, at the subatomic, molecular, macromolecular, cellular, tissue, and population scales, with corresponding time scales ranging from picoseconds to decades. We discuss models of these steps and progress in integrating models across scales.

A Review of Mathematical Models for Leukemia and Lymphoma

Recently, there has been significant activity in the mathematical community, aimed at developing quantitative tools for studying leukemia and lymphoma. Mathematical models have been applied to evaluate existing therapies and to suggest novel therapies. This article reviews the recent contributions of mathematical modeling to leukemia and lymphoma research. These developments suggest that mathematical modeling has great potential in this field. Collaboration between mathematicians, clinicians, and experimentalists can significantly improve leukemia and lymphoma therapy.

Stochastic control of proliferation and differentiation in stem cell dynamics

In self-renewing tissues, cell lineages consisting of stem cell and classes of daughter cells are the basic units which are responsible for the correct functioning of the organ. Cell proliferation and differentiation in lineages is thought to be mediated by feedback signals. In the simplest case a lineage is comprised of stem cells and differentiated cells. We create a model where stem cell proliferation and differentiation are controlled by the size of cell populations by means of a negative feedback loop. This two-dimensional Markov process allows for an analytical solution for the mean numbers and variances of stem and daughter cells. The mean values and the amounts of variation in cell numbers can be tightly regulated by the parameters of the control loop.

The protective role of symmetric stem cell division on the accumulation of heritable damage

Stem cell divisions are either asymmetric—in which one daughter cell remains a stem cell and one does not—or symmetric, in which both daughter cells adopt the same fate, either stem or non-stem. Recent studies show that in many tissues operating under homeostatic conditions stem cell division patterns are strongly biased toward the symmetric outcome, raising the question of whether symmetry confers some benefit. Here, we show that symmetry, via extinction of damaged stem-cell clones, reduces the lifetime risk of accumulating phenotypically silent heritable damage (mutations or aberrant epigenetic changes) in individual stem cells. This effect is greatest in rapidly cycling tissues subject to accelerating rates of damage accumulation over time, a scenario that describes the progression of many cancers. A decrease in the rate of cellular damage accumulation may be an important factor favoring symmetric patterns of stem cell division.

Recently, highly symmetric patterns of stem cell division have been observed in a variety of adult mammalian somatic tissues. Here we identify conditions under which this behavior serves as a strategy to protect the organism against mutation accumulation. First, we find that a sufficient number of lifetime stem cell divisions must occur, potentially explaining why stem cell pools with the most symmetric divisions are rapidly cycling. Second, we find that late-occurring mutations must occur rapidly, a scenario known in cancer biology as genetic instability. These findings provide a potential explanation for the observation that cancer risks among large, long-lived organisms fail to rise as expected with lifespan and body size.

SOX2 is a cancer-specific regulator of tumour initiating potential in cutaneous squamous cell carcinoma

Although the principles that balance stem cell self-renewal and differentiation in normal tissue homeostasis are beginning to emerge, it is still unclear whether cancer cells with tumor initiating potential are similarly governed, or whether they have acquired distinct mechanisms to sustain self-renewal and long-term tumor growth. Here we show that the transcription factor Sox2, which is not expressed in normal skin epithelium and is dispensable for epidermal homeostasis, marks tumor initiating cells (TICs) in cutaneous squamous cell carcinomas (SCC). We demonstrate that Sox2 is required for SCC growth in mouse and human, where it enhances Nrp1/Vegf signaling to promote the expansion of TICs along the tumor-stroma interface. Our findings suggest that distinct transcriptional programs govern self-renewal and long-term growth of TICs and normal skin epithelial stem and progenitor cells. These programs present promising diagnostic markers and targets for cancer specific therapies.

The new concepts on overcoming drug resistance in lung cancer

Lung cancer is one of the most deadly diseases worldwide. The current first-line therapies include chemotherapy using epidermal growth factor receptor tyrosine kinase inhibitors and radiotherapies. With the current progress in identifying new molecular targets, acquired drug resistance stands as an obstacle for good prognosis. About half the patients receiving epidermal growth factor receptor-tyrosine kinase inhibitor treatments develop resistance. Although extensive studies have been applied to elucidate the underlying mechanisms, evidence is far from enough to establish a well-defined picture to correct resistance. In the review, we will discuss four different currently developed strategies that have the potential to overcome drug resistance in lung cancer therapies and facilitate prolonged anticancer effects of the first-line therapies.

A multicompartment mathematical model of cancer stem cell-driven tumor growth dynamics

Tumors are appreciated to be an intrinsically heterogeneous population of cells with varying proliferation capacities and tumorigenic potentials. As a central tenet of the so-called cancer stem cell hypothesis, most cancer cells have only a limited lifespan, and thus cannot initiate or reinitiate tumors. Longevity and clonogenicity are properties unique to the subpopulation of cancer stem cells. To understand the implications of the population structure suggested by this hypothesis--a hierarchy consisting of cancer stem cells and progeny non-stem cancer cells which experience a reduction in their remaining proliferation capacity per division--we set out to develop a mathematical model for the development of the aggregate population. We show that overall tumor progression rate during the exponential growth phase is identical to the growth rate of the cancer stem cell compartment. Tumors with identical stem cell proportions, however, can have different growth rates, dependent on the proliferation kinetics of all participating cell populations. Analysis of the model revealed that the proliferation potential of non-stem cancer cells is likely to be small to reproduce biologic observations. Furthermore, a single compartment of non-stem cancer cell population may adequately represent population growth dynamics only when the compartment proliferation rate is scaled with the generational hierarchy depth.

Mathematical models of the transitions between endocrine therapy responsive and resistant states in breast cancer

Endocrine therapy, targeting the oestrogen receptor pathway, is the most common treatment for oestrogen receptor-positive breast cancers. Unfortunately, these tumours frequently develop resistance to endocrine therapies. Among the strategies to treat resistant tumours are sequential treatment (in which second-line drugs are used to gain additional responses) and intermittent treatment (in which a 'drug holiday' is imposed between treatments). To gain a more rigorous understanding of the mechanisms underlying these strategies, we present a mathematical model that captures the transitions among three different, experimentally observed, oestrogen-sensitivity phenotypes in breast cancer (sensitive, hypersensitive and independent). To provide a global view of the transitions between these phenotypes, we compute the potential landscape associated with the model. We show how this oestrogen response landscape can be reshaped by population selection, which is a crucial force in promoting acquired resistance. Techniques from statistical physics are used to create a population-level state-transition model from the cellular-level model. We then illustrate how this population-level model can be used to analyse and optimize sequential and intermittent oestrogen-deprivation protocols for breast cancer. The approach used in this study is general and can also be applied to investigate treatment strategies for other types of cancer.

Effect of dedifferentiation on time to mutation acquisition in stem cell-driven cancers

Accumulating evidence suggests that many tumors have a hierarchical organization, with the bulk of the tumor composed of relatively differentiated short-lived progenitor cells that are maintained by a small population of undifferentiated long-lived cancer stem cells. It is unclear, however, whether cancer stem cells originate from normal stem cells or from dedifferentiated progenitor cells. To address this, we mathematically modeled the effect of dedifferentiation on carcinogenesis. We considered a hybrid stochastic-deterministic model of mutation accumulation in both stem cells and progenitors, including dedifferentiation of progenitor cells to a stem cell-like state. We performed exact computer simulations of the emergence of tumor subpopulations with two mutations, and we derived semi-analytical estimates for the waiting time distribution to fixation. Our results suggest that dedifferentiation may play an important role in carcinogenesis, depending on how stem cell homeostasis is maintained. If the stem cell population size is held strictly constant (due to all divisions being asymmetric), we found that dedifferentiation acts like a positive selective force in the stem cell population and thus speeds carcinogenesis. If the stem cell population size is allowed to vary stochastically with density-dependent reproduction rates (allowing both symmetric and asymmetric divisions), we found that dedifferentiation beyond a critical threshold leads to exponential growth of the stem cell population. Thus, dedifferentiation may play a crucial role, the common modeling assumption of constant stem cell population size may not be adequate, and further progress in understanding carcinogenesis demands a more detailed mechanistic understanding of stem cell homeostasis.

Recent evidence suggests that, like many normal tissues, many cancers are maintained by a small population of immortal stem cells that divide indefinitely to produce many differentiated cells. Cancer stem cells may come directly from mutation of normal stem cells, but this route demands high mutation rates, because there are few normal stem cells. There are, however, many differentiated cells, and mutations can cause such cells to “dedifferentiate” into a stem-like state. We used mathematical modeling to study the effects of dedifferentiation on the time to cancer onset. We found that the effect of dedifferentiation depends critically on how stem cell numbers are controlled by the body. If homeostasis is very tight (due to all divisions being asymmetric), then dedifferentiation has little effect, but if homeostatic control is looser (allowing both symmetric and asymmetric divisions), then dedifferentiation can dramatically hasten cancer onset and lead to exponential growth of the cancer stem cell population. Our results suggest that dedifferentiation may be a very important factor in cancer and that more study of dedifferentiation and stem cell control is necessary to understand and prevent cancer onset.

Symmetric vs. asymmetric stem cell divisions: an adaptation against cancer?

Traditionally, it has been held that a central characteristic of stem cells is their ability to divide asymmetrically. Recent advances in inducible genetic labeling provided ample evidence that symmetric stem cell divisions play an important role in adult mammalian homeostasis. It is well understood that the two types of cell divisions differ in terms of the stem cells' flexibility to expand when needed. On the contrary, the implications of symmetric and asymmetric divisions for mutation accumulation are still poorly understood. In this paper we study a stochastic model of a renewing tissue, and address the optimization problem of tissue architecture in the context of mutant production. Specifically, we study the process of tumor suppressor gene inactivation which usually takes place as a consequence of two “hits”, and which is one of the most common patterns in carcinogenesis. We compare and contrast symmetric and asymmetric (and mixed) stem cell divisions, and focus on the rate at which double-hit mutants are generated. It turns out that symmetrically-dividing cells generate such mutants at a rate which is significantly lower than that of asymmetrically-dividing cells. This result holds whether single-hit (intermediate) mutants are disadvantageous, neutral, or advantageous. It is also independent on whether the carcinogenic double-hit mutants are produced only among the stem cells or also among more specialized cells. We argue that symmetric stem cell divisions in mammals could be an adaptation which helps delay the onset of cancers. We further investigate the question of the optimal fraction of stem cells in the tissue, and quantify the contribution of non-stem cells in mutant production. Our work provides a hypothesis to explain the observation that in mammalian cells, symmetric patterns of stem cell division seem to be very common.

A possible explanation for the variable frequencies of cancer stem cells in tumors

A controversy surrounds the frequency of cancer stem cells (CSCs) in solid tumors. Initial studies indicated that these cells had a frequency ranging from 0.0001 to 0.1% of the total cells. Recent studies have shown that this does not always seem to be the case. Some of these studies have indicated a frequency of [Formula: see text]. In this paper we propose a stochastic model that is able to capture this potential variability in the frequency of CSCs among the various type of tumors. Considerations regarding the heterogeneity of the tumor cells and its consequences are included. Possible effects on conventional treatments in clinical practice are also described. The model results suggest that traditional attempts to combat cancer cells with rapid cycling can be very stimulating for the cancer stem cell populations.

Why tyrosine kinase inhibitor resistance is common in advanced gastrointestinal stromal tumors

BACKGROUND

Most patients with advanced gastrointestinal stromal tumors (GIST) develop drug resistance to tyrosine kinase inhibitors (TKIs) within two years of starting therapy, whereas most chronic myeloid leukemia (CML) patients in chronic phase still exhibit disease control after a decade on therapy. This article aims to explain this divergence in long term outcomes.

METHODS AND RESULTS

By combining clinical and experimental observations with mathematical formulas we estimate that, in advanced GIST, the genetic changes responsible for resistance are generally already present at disease detection.

CONCLUSION

This result has relevant clinical implications by providing support for the exploration of combination therapies.

Evolutionary dynamics of cancer in response to targeted combination therapy

In solid tumors, targeted treatments can lead to dramatic regressions, but responses are often short-lived because resistant cancer cells arise. The major strategy proposed for overcoming resistance is combination therapy. We present a mathematical model describing the evolutionary dynamics of lesions in response to treatment. We first studied 20 melanoma patients receiving vemurafenib. We then applied our model to an independent set of pancreatic, colorectal, and melanoma cancer patients with metastatic disease. We find that dual therapy results in long-term disease control for most patients, if there are no single mutations that cause cross-resistance to both drugs; in patients with large disease burden, triple therapy is needed. We also find that simultaneous therapy with two drugs is much more effective than sequential therapy. Our results provide realistic expectations for the efficacy of new drug combinations and inform the design of trials for new cancer therapeutics.

DOI:http://dx.doi.org/10.7554/eLife.00747.001

As medicine becomes increasingly personalized, more and more emphasis is being placed on the development of therapies that target specific cancer-causing mutations. But while many of these drugs are effective in the short term, and do extend patient lives, tumors tend to evolve resistance to them within a few months.

The key problem is that large tumors are genetically diverse. This means that for any given treatment, there is likely to be a small population of cells within the tumor that is resistant to the effects of the drug. When the drug is given to a patient, these cells will survive and multiply and this will lead ultimately to treatment failure. Given that a single drug is therefore highly unlikely to eradicate a tumor, combinations of two or more drugs may offer a higher chance of cure. This approach has been effective in the treatment of HIV as well as certain forms of leukemia.

Here, Bozic et al. present a mathematical model designed to predict the effects of combination targeted therapies on tumors, based on the data obtained from 20 melanoma (skin cancer) patients. Their model revealed that if even 1 of the 6.6 billion base pairs of DNA present in a human diploid cell has undergone a mutation that confers resistance to each of two drugs, treatment with those drugs will not lead to sustained improvement for the majority of patients. This confirms the need to develop drugs that target distinct pathways.

The model also reveals that combination therapy with two drugs given simultaneously is far more effective than sequential therapy where the drugs are used one after the other. Indeed, the model of Bozic et al. indicates that sequential treatment offers no chance of a cure, even when there are no cross-resistance mutations present, whereas combination therapy offers some hope of a cure, even in the presence of cross-resistance mutations.

By emphasizing the need to develop drugs that target distinct pathways, and to administer them in combination rather than sequentially, the study by Bozic et al. offers valuable advice for drug development and the design of clinical trials, as well as for clinical practice.

DOI:http://dx.doi.org/10.7554/eLife.00747.002