Stem cell regulation and the development of blast crisis in chronic myeloid leukemia: Implications for the outcome of Imatinib treatment and discontinuation

Predictive nonlinear modeling of malignant myelopoiesis and tyrosine kinase inhibitor therapy

Chronic myeloid leukemia (CML) is a blood cancer characterized by dysregulated production of maturing myeloid cells driven by the product of the Philadelphia chromosome, the BCR-ABL1 tyrosine kinase. Tyrosine kinase inhibitors (TKIs) have proved effective in treating CML, but there is still a cohort of patients who do not respond to TKI therapy even in the absence of mutations in the BCR-ABL1 kinase domain that mediate drug resistance. To discover novel strategies to improve TKI therapy in CML, we developed a nonlinear mathematical model of CML hematopoiesis that incorporates feedback control and lineage branching. Cell-cell interactions were constrained using an automated model selection method together with previous observations and new in vivo data from a chimeric BCR-ABL1 transgenic mouse model of CML. The resulting quantitative model captures the dynamics of normal and CML cells at various stages of the disease and exhibits variable responses to TKI treatment, consistent with those of CML patients. The model predicts that an increase in the proportion of CML stem cells in the bone marrow would decrease the tendency of the disease to respond to TKI therapy, in concordance with clinical data and confirmed experimentally in mice. The model further suggests that, under our assumed similarities between normal and leukemic cells, a key predictor of refractory response to TKI treatment is an increased maximum probability of self-renewal of normal hematopoietic stem cells. We use these insights to develop a clinical prognostic criterion to predict the efficacy of TKI treatment and design strategies to improve treatment response. The model predicts that stimulating the differentiation of leukemic stem cells while applying TKI therapy can significantly improve treatment outcomes.

Growth dynamics of breast cancer stem cells: effects of self-feedback and EMT mechanisms

Breast cancer stem cells (BCSCs) with the ability to self-renew and differentiate have been identified in primary breast cancer tissues and cell lines. The BCSCs are often resistant to traditional radiation and/or chemotherapies. Previous studies have also shown that successful therapy must eradicate cancer stem cells. The purpose of this paper is to develop a mathematical model with self-feedback mechanism to illustrate the issues regarding the difficulties of absolutely eliminating a breast cancer. In addition, we introduce the mechanism of the epithelial-mesenchymal transition (EMT) to investigate the influence of EMT on the effects of breast cancer growth and treatment. Results indicate that the EMT mechanism facilitates the growth of breast cancer and makes breast cancer more difficult to be cured. Therefore, targeting the signals involved in EMT can halt tumor progression in breast cancer. Finally, we apply the experimental data to carry out numerical simulations and validate our theoretical conclusions.

An extended Moran process that captures the struggle for fitness

When a new type of individual appears in a stable population, the newcomer is typically not advantageous. Due to stochasticity, the new type can grow in numbers, but the newcomers can only become advantageous if they manage to change the environment in such a way that they increase their fitness. This dynamics is observed in several situations in which a relatively stable population is invaded by an alternative strategy, for instance the evolution of cooperation among bacteria, the invasion of cancer in a multicellular organism and the evolution of ideas that contradict social norms. These examples also show that, by generating different versions of itself, the new type increases the probability of winning the struggle for fitness. Our model captures the imposed cooperation whereby the first generation of newcomers dies while changing the environment such that the next generations become more advantageous.

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.

'Real-life' study of imatinib therapy in chronic phase-chronic myeloid leukemia: A novel retrospective observational longitudinal analysis

OBJECTIVES

Imatinib is a cornerstone of treatment of chronic myeloid leukemia. It remains unclear whether transient treatment discontinuation or dose changes affect outcome and this approach has not yet been approved for use outside clinical trials.

METHODS

We conducted a retrospective single-institution observational study to evaluate factors affecting response in 'real-life' clinical practice in 138 chronic myeloid leukemia patients in chronic phase treated with imatinib. We used a novel longitudinal data analytical model, with a generalized estimating equation model, to study BCR-ABL variation according to continuous standard dose, change in dose or discontinuation; BCR-ABL transcript levels were recorded. Treatment history was subdivided into time periods for which treatment was given at constant dosage (total 483 time periods). Molecular and cytogenetic complete response was observed after 154 (32%) and 358 (74%) time periods, respectively.

RESULTS

After adjusting for length of time period, no association between dose and cytogenetic complete response rate was observed. There was a significantly lower molecular complete response rate after time periods at a high imatinib dosage.

DISCUSSION

This statistical approach can identify individual patient variation in longitudinal data collected over time and suggests that changes in dose or discontinuation of therapy could be considered in patients with appropriate biological characteristics.

Stem cell regulation: Implications when differentiated cells regulate symmetric stem cell division

We use a mathematical model to show that if symmetric stem cell division is regulated by differentiated cells, then changes in the population dynamics of the differentiated cells can lead to changes in the population dynamics of the stem cells. More precisely, the relative fitness of the stem cells can be affected by modifying the death rate of the differentiated cells. This result is interesting because stem cells are less sensitive than differentiated cells to environmental factors, such as medical therapy. Our result implies that stem cells can be manipulated indirectly by medical treatments that target the differentiated cells.

Leukemia stem cells: the root of chronic myeloid leukemia

Chronic myeloid leukemia (CML) is a clonal myeloproliferative disorder characterized by a chromosome translocation that generates the Bcr-Abl oncogene encoding a constitutive kinase activity. Despite remarkable success in controlling CML at chronic phase by Bcr-Abl tyrosine kinase inhibitors (TKIs), a significant proportion of CML patients treated with TKIs develop drug resistance due to the inability of TKIs to kill leukemia stem cells (LSCs) that are responsible for initiation, drug resistance, and relapse of CML. Therefore, there is an urgent need for more potent and safer therapies against leukemia stem cells for curing CML. A number of LSC-associated targets and corresponding signaling pathways, including CaMKII-γ, a critical molecular switch for co-activating multiple LSC-associated signaling pathways, have been identified over the past decades and various small inhibitors targeting LSC are also under development. Increasing evidence shows that leukemia stem cells are the root of CML and targeting LSC may offer a curable treatment option for CML patients. This review summarizes the molecular biology of LSC and its-associated targets, and the potential clinical application in chronic myeloid leukemia.

Leukemia stem cells: the root of chronic myeloid leukemia

Chronic myeloid leukemia (CML) is a clonal myeloproliferative disorder characterized by a chromosome translocation that generates the Bcr-Abl oncogene encoding a constitutive kinase activity. Despite remarkable success in controlling CML at chronic phase by Bcr-Abl tyrosine kinase inhibitors (TKIs), a significant proportion of CML patients treated with TKIs develop drug resistance due to the inability of TKIs to kill leukemia stem cells (LSCs) that are responsible for initiation, drug resistance, and relapse of CML. Therefore, there is an urgent need for more potent and safer therapies against leukemia stem cells for curing CML. A number of LSC-associated targets and corresponding signaling pathways, including CaMKII-γ, a critical molecular switch for co-activating multiple LSC-associated signaling pathways, have been identified over the past decades and various small inhibitors targeting LSC are also under development. Increasing evidence shows that leukemia stem cells are the root of CML and targeting LSC may offer a curable treatment option for CML patients. This review summarizes the molecular biology of LSC and its-associated targets, and the potential clinical application in chronic myeloid leukemia.

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.

Quantitative modeling of chronic myeloid leukemia: insights from radiobiology

Mathematical models of chronic myeloid leukemia (CML) cell population dynamics are being developed to improve CML understanding and treatment. We review such models in light of relevant findings from radiobiology, emphasizing 3 points. First, the CML models almost all assert that the latency time, from CML initiation to diagnosis, is at most ∼10 years. Meanwhile, current radiobiologic estimates, based on Japanese atomic bomb survivor data, indicate a substantially higher maximum, suggesting longer-term relapses and extra resistance mutations. Second, different CML models assume different numbers, between 400 and 10(6), of normal HSCs. Radiobiologic estimates favor values>10(6) for the number of normal cells (often assumed to be the HSCs) that are at risk for a CML-initiating BCR-ABL translocation. Moreover, there is some evidence for an HSC dead-band hypothesis, consistent with HSC numbers being very different across different healthy adults. Third, radiobiologists have found that sporadic (background, age-driven) chromosome translocation incidence increases with age during adulthood. BCR-ABL translocation incidence increasing with age would provide a hitherto underanalyzed contribution to observed background adult-onset CML incidence acceleration with age, and would cast some doubt on stage-number inferences from multistage carcinogenesis models in general.

Stem cell niche dynamics: from homeostasis to carcinogenesis

The stem cell microenvironment is involved in regulating the fate of the stem cell with respect to self-renewal, quiescence, and differentiation. Mathematical models are helpful in understanding how key pathways regulate the dynamics of stem cell maintenance and homeostasis. This tight regulation and maintenance of stem cell number is thought to break down during carcinogenesis. As a result, the stem cell niche has become a novel target of cancer therapeutics. Developing a quantitative understanding of the regulatory pathways that guide stem cell behavior will be vital to understanding how these systems change under conditions of stress, inflammation, and cancer initiation. Predictions from mathematical modeling can be used as a clinical tool to guide therapy design. We present a survey of mathematical models used to study stem cell population dynamics and stem cell niche regulation, both in the hematopoietic system and other tissues. Highlighting the quantitative aspects of stem cell biology, we describe compelling questions that can be addressed with modeling. Finally, we discuss experimental systems, most notably Drosophila, that can best be used to validate mathematical predictions.

A multicellular basis for the origination of blast crisis in chronic myeloid leukemia

Chronic myeloid leukemia (CML) is characterized by a specific chromosome translocation, and its pathobiology is considered comparatively well understood. Thus, quantitative analysis of CML and its progression to blast crisis may help elucidate general mechanisms of carcinogenesis and cancer progression. Hitherto, it has been widely postulated that CML blast crisis originates mainly via cell-autonomous mechanisms such as secondary mutations or genomic instability. However, recent results suggest that carcinogenic transformation may be an inherently multicellular event, in departure from the classic unicellular paradigm. We investigate this possibility in the case of blast crisis origination in CML. A quantitative, mechanistic cell population dynamics model was employed. This model used recent data on imatinib-treated CML; it also used earlier clinical data, not previously incorporated into current mathematical CML/imatinib models. With the pre-imatinib data, which include results on many more blast crises, we obtained evidence that the driving mechanism for blast crisis origination is a cooperation between specific cell types. Assuming leukemic-normal interactions resulted in a statistically significant improvement over assuming either cell-autonomous mechanisms or interactions between leukemic cells. This conclusion was robust with regard to changes in the model's adjustable parameters. Application of the results to patients treated with imatinib suggests that imatinib may act not only on malignant blast precursors, but also, to a limited degree, on the malignant blasts themselves.

Cancer biomarker discovery: the entropic hallmark

Background

It is a commonly accepted belief that cancer cells modify their transcriptional state during the progression of the disease. We propose that the progression of cancer cells towards malignant phenotypes can be efficiently tracked using high-throughput technologies that follow the gradual changes observed in the gene expression profiles by employing Shannon's mathematical theory of communication. Methods based on Information Theory can then quantify the divergence of cancer cells' transcriptional profiles from those of normally appearing cells of the originating tissues. The relevance of the proposed methods can be evaluated using microarray datasets available in the public domain but the method is in principle applicable to other high-throughput methods.

Methodology/Principal Findings

Using melanoma and prostate cancer datasets we illustrate how it is possible to employ Shannon Entropy and the Jensen-Shannon divergence to trace the transcriptional changes progression of the disease. We establish how the variations of these two measures correlate with established biomarkers of cancer progression. The Information Theory measures allow us to identify novel biomarkers for both progressive and relatively more sudden transcriptional changes leading to malignant phenotypes. At the same time, the methodology was able to validate a large number of genes and processes that seem to be implicated in the progression of melanoma and prostate cancer.

Conclusions/Significance

We thus present a quantitative guiding rule, a new unifying hallmark of cancer: the cancer cell's transcriptome changes lead to measurable observed transitions of Normalized Shannon Entropy values (as measured by high-througput technologies). At the same time, tumor cells increment their divergence from the normal tissue profile increasing their disorder via creation of states that we might not directly measure. This unifying hallmark allows, via the the Jensen-Shannon divergence, to identify the arrow of time of the processes from the gene expression profiles, and helps to map the phenotypical and molecular hallmarks of specific cancer subtypes. The deep mathematical basis of the approach allows us to suggest that this principle is, hopefully, of general applicability for other diseases.

Differential destruction of stem cells: implications for targeted cancer stem cell therapy

Cancer stem cells represent a novel therapeutic target. The major challenge in targeting leukemic stem cells (LSC) is finding therapies that largely spare normal hematopoietic stem cells (HSC) while eradicating quiescent LSCs. We present a mathematical model to predict how selective a therapy must be to ensure that enough HSCs survive when LSCs have been eradicated. Stem cell population size is modeled as a birth-death process. This permits comparison of LSC and HSC eradication times under therapy and calculation of the number of HSCs at the time of LSC eradication for varied initial population sizes and stem cell death rates. We further investigate the effects of LSC quiescence and resistance mutations on our predictions. From a clinical point of view, our models suggest criteria by which cancer stem cell therapy safety can be assessed. We anticipate that in conjunction with experimental observation of cancer stem cell killing rates, our results will be useful in screening targeted therapies for both hematologic and solid tumor malignancies.