Leukaemia stem cells: hit or miss?

Mathematical modelling identifies conditions for maintaining and escaping feedback control in the intestinal epithelium

The intestinal epithelium is one of the fastest renewing tissues in mammals. It shows a hierarchical organisation, where intestinal stem cells at the base of crypts give rise to rapidly dividing transit amplifying cells that in turn renew the pool of short-lived differentiated cells. Upon injury and stem-cell loss, cells can also de-differentiate. Tissue homeostasis requires a tightly regulated balance of differentiation and stem cell proliferation, and failure can lead to tissue extinction or to unbounded growth and cancerous lesions. Here, we present a two-compartment mathematical model of intestinal epithelium population dynamics that includes a known feedback inhibition of stem cell differentiation by differentiated cells. The model shows that feedback regulation stabilises the number of differentiated cells as these become invariant to changes in their apoptosis rate. Stability of the system is largely independent of feedback strength and shape, but specific thresholds exist which if bypassed cause unbounded growth. When dedifferentiation is added to the model, we find that the system can recover faster after certain external perturbations. However, dedifferentiation makes the system more prone to losing homeostasis. Taken together, our mathematical model shows how a feedback-controlled hierarchical tissue can maintain homeostasis and can be robust to many external perturbations.

Quantitative prediction of long-term molecular response in TKI-treated CML - Lessons from an imatinib versus dasatinib comparison

Longitudinal monitoring of BCR-ABL transcript levels in peripheral blood of CML patients treated with tyrosine kinase inhibitors (TKI) revealed a typical biphasic response. Although second generation TKIs like dasatinib proved more efficient in achieving molecular remission compared to first generation TKI imatinib, it is unclear how individual responses differ between the drugs and whether mechanisms of drug action can be deduced from the dynamic data. We use time courses from the DASISION trial to address statistical differences in the dynamic response between first line imatinib vs. dasatinib treatment cohorts and we analyze differences between the cohorts by fitting an established mathematical model of functional CML treatment to individual time courses. On average, dasatinib-treated patients show a steeper initial response, while the long-term response only marginally differed between the treatments. Supplementing each patient time course with a corresponding confidence region, we illustrate the consequences of the uncertainty estimate for the underlying mechanisms of CML remission. Our model suggests that the observed BCR-ABL dynamics may result from different, underlying stem cell dynamics. These results illustrate that the perception and description of CML treatment response as a dynamic process on the level of individual patients is a prerequisite for reliable patient-specific response predictions and treatment optimizations.

Reduced tyrosine kinase inhibitor dose is predicted to be as effective as standard dose in chronic myeloid leukemia: a simulation study based on phase III trial data

Continuing tyrosine kinase inhibitor (TKI)-mediated targeting of the BCR-ABL1 oncoprotein is the standard therapy for chronic myeloid leukemia (CML) and allows for a sustained disease control in the majority of patients. While therapy cessation for patients appeared as a safe option for about half of those patients with optimal response, no systematic assessment of long-term TKI dose de-escalation has been made. We use a mathematical model to analyze and consistently describe biphasic treatment responses from TKI-treated patients from two independent clinical phase III trials. Scale estimates reveal that drug efficiency determines the initial response while the long-term behavior is limited by the rare activation of leukemic stem cells. We use this mathematical framework to investigate the influence of different dosing regimens on the treatment outcome. We provide strong evidence to suggest that TKI dose de-escalation (at least 50%) does not lead to a reduction of long-term treatment efficiency for most patients, who have already achieved sustained remission, and maintains the secondary decline of BCR-ABL1 levels. We demonstrate that continuous BCR-ABL1 monitoring provides patient-specific predictions of an optimal reduced dose without decreasing the anti-leukemic effect on residual leukemic stem cells. Our results are consistent with the interim results of the DESTINY trial and provide clinically testable predictions. Our results suggest that dose-halving should be considered as a long-term treatment option for CML patients with good response under continuing maintenance therapy with TKIs. We emphasize the clinical potential of this approach to reduce treatment-related side-effects and treatment costs.

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.

Combined Population Dynamics and Entropy Modelling Supports Patient Stratification in Chronic Myeloid Leukemia

Modelling the parameters of multistep carcinogenesis is key for a better understanding of cancer progression, biomarker identification and the design of individualized therapies. Using chronic myeloid leukemia (CML) as a paradigm for hierarchical disease evolution we show that combined population dynamic modelling and CML patient biopsy genomic analysis enables patient stratification at unprecedented resolution. Linking CD34⁺ similarity as a disease progression marker to patient-derived gene expression entropy separated established CML progression stages and uncovered additional heterogeneity within disease stages. Importantly, our patient data informed model enables quantitative approximation of individual patients’ disease history within chronic phase (CP) and significantly separates “early” from “late” CP. Our findings provide a novel rationale for personalized and genome-informed disease progression risk assessment that is independent and complementary to conventional measures of CML disease burden and prognosis.

Therapy of chronic myeloid leukaemia can benefit from the activation of stem cells: simulation studies of different treatment combinations

Background:

Newly diagnosed patients with chronic myeloid leukaemia (CML) are currently treated with tyrosine kinase inhibitors (TKIs) such as imatinib, nilotinib or dasatinib. However, incomplete eradication of residual disease is a general problem of long-term TKI therapy. Activation of mouse haematopoietic stem cells by interferon-α (IFNα) stimulated the discussion of whether a combination treatment leads to accelerated eradication of the CML clone.

Methods:

We base our simulation approach on a mathematical model describing human CML as a competition phenomenon between normal and malignant cells. We amend this model to incorporate the description of IFNα activity and simulate different scenarios for potential treatment combinations.

Results:

We demonstrate that the overall sensitivity of CML stem cells to IFNα activation is a crucial determinant for the benefit of a potential combination therapy. We furthermore show that pulsed IFNα together with continuous TKI administration is the most promising strategy for a combination treatment in which the therapeutic benefit prevails adverse side effects.

Conclusion:

Our modelling approach is a highly beneficial tool to quantitatively address the competition between normal and leukaemic haematopoiesis in treated CML patients. We derive testable predictions for different experimental settings that are suggested before the clinical implementation of the combination treatment.

Abcg2 overexpression represents a novel mechanism for acquired resistance to the multi-kinase inhibitor Danusertib in BCR-ABL-positive cells in vitro

The success of Imatinib (IM) therapy in chronic myeloid leukemia (CML) is compromised by the development of IM resistance and by a limited IM effect on hematopoietic stem cells. Danusertib (formerly PHA-739358) is a potent pan-aurora and ABL kinase inhibitor with activity against known BCR-ABL mutations, including T315I. Here, the individual contribution of both signaling pathways to the therapeutic effect of Danusertib as well as mechanisms underlying the development of resistance and, as a consequence, strategies to overcome resistance to Danusertib were investigated. Starting at low concentrations, a dose-dependent inhibition of BCR-ABL activity was observed, whereas inhibition of aurora kinase activity required higher concentrations, pointing to a therapeutic window between the two effects. Interestingly, the emergence of resistant clones during Danusertib exposure in vitro occurred considerably less frequently than with comparable concentrations of IM. In addition, Danusertib-resistant clones had no mutations in BCR-ABL or aurora kinase domains and remained IM-sensitive. Overexpression of Abcg2 efflux transporter was identified and functionally validated as the predominant mechanism of acquired Danusertib resistance in vitro. Finally, the combined treatment with IM and Danusertib significantly reduced the emergence of drug resistance in vitro, raising hope that this drug combination may also achieve more durable disease control in vivo.

Immunotherapy of chronic myeloid leukemia: present state and future prospects

In spite of the considerable successes that have been achieved in the treatment of chronic myeloid leukemia (CML), cure for the disease can only be obtained by the present means in a rather small minority of patients. During the past decade, considerable progress has been made in the understanding of the immunology of CML, which has raised hopes that this disease may be curable by supplementing the current targeted chemotherapy with immunotherapeutic approaches. More than ten small-scale clinical trials have been carried out with experimental vaccines predominantly based on the p210bcr-abl fusion protein. Their results suggested beneficial effects in some patients. Recent data obtained in human patients as well as in animal models indicate that the p210bcr-abl protein does not carry the immunodominant epitope(s). These observations, combined with the recognition of an ever increasing number of other immunogenic proteins in CML cells, strongly support the concept that gene-modified, cell-based vaccines containing the full spectrum of tumor antigens might be the most effective immunotherapeutic approach. Recently created mathematical models have provided important leads for the timing of the combination of targeted drug therapy with vaccine administration. A strategy of how targeted drug therapy might be combined with vaccination is outlined.

A stochastic model for cancer stem cell origin in metastatic colon cancer

Human cancers have been found to include transformed stem cells that may drive cancer progression to metastasis. Here, we report that metastatic colon cancer contains clonally derived tumor cells with all of the critical properties expected of stem cells, including self-renewal and the ability to differentiate into mature colon cells. Additionally, when injected into mice, these cells initiated tumors that closely resemble human cancer. Karyotype analyses of parental and clonally derived tumor cells expressed many consistent (clonal) along with unique chromosomal aberrations, suggesting the presence of chromosomal instability in the cancer stem cells. Thus, this new model for cancer origin and metastatic progression includes features of both the hierarchical model for cancerous stem cells and the stochastic model, driven by the observation of chromosomal instability.

Pathogenesis, treatment effects, and resistance dynamics in chronic myeloid leukemia--insights from mathematical model analyses

Mathematical models and simulation studies are powerful tools to investigate dynamic properties of complex systems. Specifically, they can be used to test alternative hypotheses on underlying biological mechanisms for their consistency with real data and therefore to effectively guide the design of new experimental strategies or clinical trials. In this study, we present an overview of recently published mathematical approaches applied to the description of chronic myeloid leukemia (CML). We discuss three different fields relevant to clinical issues: the pathogenesis of the malignancy, the treatment effects of the tyrosine kinase inhibitor imatinib, and the process of acquired treatment resistance highlighting both the differences and the consistencies in the proposed hypotheses and the resulting conclusions. The mathematical models presented agree that CML can adequately be described as a clonal competition between normal and leukemic stem cells for a common resource. Furthermore, a certain therapeutic effect of imatinib on leukemic stem cells turned out to be necessary to consistently explain clinical data on the long-term response of CML patients under imatinib treatment. However, the approaches described cannot resolve the question whether or not this effect is sufficient to ultimately eradicate malignant stem cells. A number of different hypotheses have been proposed concerning the initiation and the dynamics of treatment-resistant malignant stem cell clones. The theoretical results clearly indicate that further experimental effort with the particular focus on the quantitative monitoring of resistant clones will be required to definitely distinguish between these hypotheses.