Cell division patterns in acute myeloid leukemia stem-like cells determine clinical course: a model to predict patient survival

Mathematical modelling of stem and progenitor cell dynamics during ruxolitinib treatment of patients with myeloproliferative neoplasms

Introduction

The Philadelphia chromosome-negative myeloproliferative neoplasms are a group of slowly progressing haematological malignancies primarily characterised by an overproduction of myeloid blood cells. Patients are treated with various drugs, including the JAK1/2 inhibitor ruxolitinib. Mathematical modelling can help propose and test hypotheses of how the treatment works.

Materials and methods

We present an extension of the Cancitis model, which describes the development of myeloproliferative neoplasms and their interactions with inflammation, that explicitly models progenitor cells and can account for treatment with ruxolitinib through effects on the malignant stem cell response to cytokine signalling and the death rate of malignant progenitor cells. The model has been fitted to individual patients' data for the JAK2 V617F variant allele frequency from the COMFORT-II and RESPONSE studies for patients who had substantial reductions (20 percentage points or 90% of the baseline value) in their JAK2 V617F variant allele frequency (n = 24 in total).

Results

The model fits very well to the patient data with an average root mean square error of 0.0249 (2.49%) when allowing ruxolitinib treatment to affect both malignant stem and progenitor cells. This average root mean square error is much lower than if allowing ruxolitinib treatment to affect only malignant stem or only malignant progenitor cells (average root mean square errors of 0.138 (13.8%) and 0.0874 (8.74%), respectively).

Discussion

Systematic simulation studies and fitting of the model to the patient data suggest that an initial reduction of the malignant cell burden followed by a monotonic increase can be recapitulated by the model assuming that ruxolitinib affects only the death rate of malignant progenitor cells. For patients exhibiting a long-term reduction of the malignant cells, the model predicts that ruxolitinib also affects stem cell parameters, such as the malignant stem cells' response to cytokine signalling.

Sox13 and M2-like leukemia-associated macrophages contribute to endogenous IL-34 caused accelerated progression of acute myeloid leukemia

Interleukin 34 (IL-34) mainly plays physiologic and pathologic roles through the sophisticated multi-ligand signaling system, macrophage colony-stimulating factor (M-CSF, CSF-1)/IL-34-CSF-1R axis, which exhibits functional redundancy, tissue-restriction and diversity. This axis is vital for the survival, differentiation and function of monocytic lineage cells and plays pathologic roles in a broad range of diseases. However, the role of IL-34 in leukemia has not been established. Here MLL-AF9 induced mouse acute myeloid leukemia (AML) model overexpressing IL-34 (MA9-IL-34) was used to explore its role in AML. MA9-IL-34 mice exhibited accelerated disease progression and short survival time with significant subcutaneous infiltration of AML cells. MA9-IL-34 cells showed increased proliferation. In vitro colony forming assays and limiting dilution transplantation experiments demonstrated that MA9-IL-34 cells had elevated leukemia stem cell (LSC) levels. Gene expression microarray analysis revealed a panel of differential expressed genes including Sex-determining region Y (SRY)-box 13 (Sox13). Furthermore, a positive correlation between the expressions of IL-34 and Sox13 was detected human datasets. Knockdown of Sox13 rescued the enhanced proliferation, high LSC level and subcutaneous infiltration in MA9-IL-34 cells. Moreover, more leukemia-associated macrophages (LAMs) were detected in MA9-IL-34 microenvironment. Additionally, those LAMs showed M2-like phenotype since they expressed high level of M2-associated genes and had attenuated phagocytic potential, suggesting that LAMs should also contribute to IL-34 caused adverse phenotypes. Therefore, our findings uncover the intrinsic and microenvironmental mechanisms of IL-34 in AML and broadens the knowledge of M-CSF/IL-34-CSF-1R axis in malignancies.

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.

Understanding Hematopoietic Stem Cell Dynamics—Insights from Mathematical Modelling

Purpose of review

Hematopoietic stem cells (HSCs) drive blood-cell production (hematopoiesis). Out-competition of HSCs by malignant cells occurs in many hematologic malignancies like acute myeloid leukemia (AML). Through mathematical modelling, HSC dynamics and their impact on healthy blood cell formation can be studied, using mathematical analysis and computer simulations. We review important work within this field and discuss mathematical modelling as a tool for attaining biological insight.

Recent findings

Various mechanism-based models of HSC dynamics have been proposed in recent years. Key properties of such models agree with observations and medical knowledge and suggest relations between stem cell properties, e.g., rates of division and the temporal evolution of the HSC population. This has made it possible to study how HSC properties shape clinically relevant processes, including engraftment following an HSC transplantation and the response to different treatment.

Summary

Understanding how properties of HSCs affect hematopoiesis is important for efficient treatment of diseases. Mathematical modelling can contribute significantly to these efforts.

An integrative systems biology approach to overcome venetoclax resistance in acute myeloid leukemia

The over-expression of the Bcl-2 protein is a common feature of many solid cancers and hematological malignancies, and it is typically associated with poor prognosis and resistance to chemotherapy. Bcl-2-specific inhibitors, such as venetoclax, have recently been approved for the treatment of chronic lymphocytic leukemia and small lymphocytic lymphoma, and they are showing promise in clinical trials as a targeted therapy for patients with relapsed or refractory acute myeloid leukemia (AML). However, successful treatment of AML with Bcl-2-specific inhibitors is often followed by the rapid development of drug resistance. An emerging paradigm for overcoming drug resistance in cancer treatment is through the targeting of mitochondrial energetics and metabolism. In AML in particular, it was recently observed that inhibition of mitochondrial translation via administration of the antibiotic tedizolid significantly affects mitochondrial bioenergetics, activating the integrated stress response (ISR) and subsequently sensitizing drug-resistant AML cells to venetoclax. Here we develop an integrative systems biology approach to acquire a deeper understanding of the molecular mechanisms behind this process, and in particular, of the specific role of the ISR in the commitment of cells to apoptosis. Our multi-scale mathematical model couples the ISR to the intrinsic apoptosis pathway in venetoclax-resistant AML cells, includes the metabolic effects of treatment, and integrates RNA, protein level, and cellular viability data. Using the mathematical model, we identify the dominant mechanisms by which ISR activation helps to overcome venetoclax resistance, and we study the temporal sequencing of combination treatment to determine the most efficient and robust combination treatment protocol.

In this work, we develop a multi-scale systems biology approach to study the mechanisms by which the integrated stress response (ISR) activation helps to overcome venetoclax resistance in acute myeloid leukemia (AML). The multi-scale model enables the integration of RNA-level, protein-level, and cellular viability and proliferation data. The model developed in this work can predict several important features of the resistant AML cell lines that are consistent with experimental data. Further, our integrative systems biology approach led to the determination of the optimal combination treatment protocol.

Local asymptotic stability of a system of integro-differential equations describing clonal evolution of a self-renewing cell population under mutation

In this paper we consider a system of non-linear integro-differential equations (IDEs) describing evolution of a clonally heterogeneous population of malignant white blood cells (leukemic cells) undergoing mutation and clonal selection. We prove existence and uniqueness of non-trivial steady states and study their asymptotic stability. The results are compared to those of the system without mutation. Existence of equilibria is proved by formulating the steady state problem as an eigenvalue problem and applying a version of the Krein-Rutmann theorem for Banach lattices. The stability at equilibrium is analysed using linearisation and the Weinstein-Aronszajn determinant which allows to conclude local asymptotic stability.

Predicting Time to Relapse in Acute Myeloid Leukemia through Stochastic Modeling of Minimal Residual Disease Based on Clonality Data

Event-free and overall survival remain poor for patients with acute myeloid leukemia. Chemoresistant clones contributing to relapse arise from minimal residual disease (MRD) or newly-acquired mutations. However, the dynamics of clones comprising MRD is poorly understood. We developed a predictive stochastic model, based on a multitype age-dependent Markov branching process, to describe how random events in MRD contribute to the heterogeneity in treatment response. We employed training and validation sets of patients who underwent whole genome sequencing and for whom mutant clone frequencies at diagnosis and relapse were available. The disease evolution and treatment outcome are subject to stochastic fluctuations. Estimates of malignant clone growth rates, obtained by model fitting, are consistent with published data. Using the estimates from the training set, we developed a function linking MRD and time of relapse, with MRD inferred from the model fits to clone frequencies and other data. An independent validation set confirmed our model. In a third data set, we fitted the model to data at diagnosis and remission and predicted the time to relapse. As a conclusion, given bone marrow genome at diagnosis and MRD at or past remission, the model can predict time to relapse, and help guide treatment decisions to mitigate relapse.

A systematic review of modeling and simulation approaches in designing targeted treatment technologies for Leukemia Cancer in low and middle income countries

Virtual experimentation is a widely used approach for predicting systems behaviour especially in situations where resources for physical experiments are very limited. For example, targeted treatment inside the human body is particularly challenging, and as such, modeling and simulation is utilised to aid planning before a specific treatment is administered. In such approaches, precise treatment, as it is the case in radiotherapy, is used to administer a maximum dose to the infected regions while minimizing the effect on normal tissue. Complicated cancers such as leukemia present even greater challenges due to their presentation in liquid form and not being localised in one area. As such, science has led to the development of targeted drug delivery, where the infected cells can be specifically targeted anywhere in the body. Despite the great prospects and advances of these modeling and simulation tools in the design and delivery of targeted drugs, their use by Low and Middle Income Countries (LMICs) researchers and clinicians is still very limited. This paper therefore reviews the modeling and simulation approaches for leukemia treatment using nanoparticles as an example for virtual experimentation. A systematic review from various databases was carried out for studies that involved cancer treatment approaches through modeling and simulation with emphasis to data collected from LMICs. Results indicated that whereas there is an increasing trend in the use of modeling and simulation approaches, their uptake in LMICs is still limited. According to the review data collected, there is a clear need to employ these tools as key approaches for the planning of targeted drug treatment approaches.

Computational Reconstruction of Clonal Hierarchies From Bulk Sequencing Data of Acute Myeloid Leukemia Samples

Acute myeloid leukemia is an aggressive cancer of the blood forming system. The malignant cell population is composed of multiple clones that evolve over time. Clonal data reflect the mechanisms governing treatment response and relapse. Single cell sequencing provides most direct insights into the clonal composition of the leukemic cells, however it is still not routinely available in clinical practice. In this work we develop a computational algorithm that allows identifying all clonal hierarchies that are compatible with bulk variant allele frequencies measured in a patient sample. The clonal hierarchies represent descendance relations between the different clones and reveal the order in which mutations have been acquired. The proposed computational approach is tested using single cell sequencing data that allow comparing the outcome of the algorithm with the true structure of the clonal hierarchy. We investigate which problems occur during reconstruction of clonal hierarchies from bulk sequencing data. Our results suggest that in many cases only a small number of possible hierarchies fits the bulk data. This implies that bulk sequencing data can be used to obtain insights in clonal evolution.

Effective Drug Concentration and Selectivity Depends on Fraction of Primitive Cells

Poor efficiency of chemotherapeutics in the eradication of Cancer Stem Cells (CSCs) has been driving the search for more active and specific compounds. In this work, we show how cell density-dependent stage culture profiles can be used in drug development workflows to achieve more robust drug activity (IC₅₀ and EC₅₀) results. Using flow cytometry and light microscopy, we characterized the cytological stage profiles of the HL-60-, A-549-, and HEK-293-derived sublines with a focus on their primitive cell content. We then used a range of cytotoxic substances—C-123, bortezomib, idarubicin, C-1305, doxorubicin, DMSO, and ethanol—to highlight typical density-related issues accompanying drug activity determination. We also showed that drug EC₅₀ and selectivity indices normalized to primitive cell content are more accurate activity measurements. We tested our approach by calculating the corrected selectivity index of a novel chemotherapeutic candidate, C-123. Overall, our study highlights the usefulness of accounting for primitive cell fractions in the assessment of drug efficiency.

Understanding the influence of substrate when growing tumorspheres

Background

Cancer stem cells are important for the development of many solid tumors. These cells receive promoting and inhibitory signals that depend on the nature of their environment (their niche) and determine cell dynamics. Mechanical stresses are crucial to the initiation and interpretation of these signals.

Methods

A two-population mathematical model of tumorsphere growth is used to interpret the results of a series of experiments recently carried out in Tianjin, China, and extract information about the intraspecific and interspecific interactions between cancer stem cell and differentiated cancer cell populations.

Results

The model allows us to reconstruct the time evolution of the cancer stem cell fraction, which was not directly measured. We find that, in the presence of stem cell growth factors, the interspecific cooperation between cancer stem cells and differentiated cancer cells induces a positive feedback loop that determines growth, independently of substrate hardness. In a frustrated attempt to reconstitute the stem cell niche, the number of cancer stem cells increases continuously with a reproduction rate that is enhanced by a hard substrate. For growth on soft agar, intraspecific interactions are always inhibitory, but on hard agar the interactions between stem cells are collaborative while those between differentiated cells are strongly inhibitory. Evidence also suggests that a hard substrate brings about a large fraction of asymmetric stem cell divisions. In the absence of stem cell growth factors, the barrier to differentiation is broken and overall growth is faster, even if the stem cell number is conserved.

Conclusions

Our interpretation of the experimental results validates the centrality of the concept of stem cell niche when tumor growth is fueled by cancer stem cells. Niche memory is found to be responsible for the characteristic population dynamics observed in tumorspheres. The model also shows why substratum stiffness has a deep influence on the behavior of cancer stem cells, stiffer substrates leading to a larger proportion of asymmetric doublings. A specific condition for the growth of the cancer stem cell number is also obtained

Supplementary Information

The online version contains supplementary material available at (10.1186/s12885-021-07918-1).

Mathematical modelling of the hematopoietic stem cell-niche system: Clonal dominance based on stem cell fitness

Human blood cell production is maintained by hematopoietic stem cells (HSC) which give rise to all types of mature blood cells. Experimental observation of HSC in their physiologic bone-marrow microenvironment, the so-called stem cell niche, is challenging. Therefore, the details of HSC dynamics and the cellular interactions in the stem cell niche remain elusive. Mutations that lead to a competitive advantage are the cause of clinical challenges when treating HSC-derived malignancies such as acute myeloid leukemia or the myeloproliferative neoplasms (MPNs). To investigate the significance of the interaction between the HSC and the stem cell niche in these malignancies, we propose and analyse a mechanism-based mathematical model of HSC dynamics within the bone-marrow microenvironment. The model is based on the central hypothesis that HSC self-renewal depends on the niche. In the model, the interaction of HSC with specific niches located in the bone marrow are key to the indefinite HSC renewal necessary for long-term maintenance of blood cell production. We formulate a general model of n distinct clones that differ with respect to cell properties. We identify an attractive trapping region and compute and classify all steady states. A concept of HSC fitness naturally arises from the model analysis. HSC fitness is found to determine the asymptotic behaviour of the model, as the HSC clone with the highest fitness is related to the unique locally stable steady state. Based on biological assumptions about HSC, we propose two reduced models of different complexity. A thorough mathematical analysis reveals that both reduced models have the same asymptotic behaviour as the full model. We compare the simpler of the two models, a logistic equation of the disease burden, to clinical data of MPN-patients. The reduced model is found to agree well with data and suggests a simple interpretation and possible prediction of patient prognosis. The proposed mathematical model and the reduced forms have the potential to provide insights into the regulation of HSC dynamics and blood cell formation, and ultimately for future advances in treatment of hematologic malignancies.

The ecology of cancer differentiation therapy

A promising, yet still under development approach to cancer treatment is based on the idea of differentiation therapy (DTH). Most tumours are characterized by poorly differentiated cell populations exhibiting a marked loss of traits associated to communication and tissue homeostasis. DTH has been suggested as an alternative (or complement) to cytotoxic-based approaches, and has proven successful in some specific types of cancer such as acute promyelocytic leukemia (APL). While novel drugs favouring the activation of differentiation therapies are being tested, several open problems emerge in relation to its effectiveness on solid tumors. Here we present a mathematical framework to DTH based on a well-known ecological model used to describe habitat loss. The models presented here account for some of the observed clinical and in vitro outcomes of DTH, providing relevant insight into potential therapy design. Furthermore, the same ecological approach is tested in a hierarchical model that accounts for cancer stem cells, highlighting the role of niche specificity in CSC therapy resistance. We show that the lessons learnt from metapopulation ecology can help guide future developments and potential difficulties of DTH.

Using mathematical models to improve risk-scoring in acute myeloid leukemia

Acute myeloid leukemia (AML) is an aggressive cancer of the blood forming (hematopoietic) system. Due to the high patient variability of disease dynamics, risk-scoring is an important part of its clinical management. AML is characterized by impaired blood cell formation and the accumulation of so-called leukemic blasts in the bone marrow of patients. Recently, it has been proposed to use counts of blood-producing (hematopoietic) stem cells (HSCs) as a biomarker for patient prognosis. In this work, we use a non-linear mathematical model to provide mechanistic evidence for the suitability of HSC counts as a prognostic marker. Using model analysis and computer simulations, we compare different risk-scores involving HSC quantification. We propose and validate a simple approach to improve risk prediction based on HSC and blast counts measured at the time of diagnosis.

Differential response to cytotoxic therapy explains treatment dynamics of acute myeloid leukaemia patients: insights from a mathematical modelling approach

Disease response and durability of remission are very heterogeneous in patients with acute myeloid leukaemia (AML). There is increasing evidence that the individual risk of early relapse can be predicted based on the initial treatment response. However, it is unclear how such a correlation is linked to functional aspects of AML progression and treatment. We suggest a mathematical model in which leukaemia-initiating cells and normal/healthy haematopoietic stem and progenitor cells reversibly change between an active state characterized by proliferation and chemosensitivity and a quiescent state, in which the cells do not divide, but are also insensitive to chemotherapy. Applying this model to 275 molecular time courses of nucleophosmin 1-mutated patients, we conclude that the differential chemosensitivity of the leukaemia-initiating cells together with the cells' intrinsic proliferative capacity is sufficient to reproduce both, early relapse as well as long-lasting remission. We can, furthermore, show that the model parameters associated with individual chemosensitivity and proliferative advantage of the leukaemic cells are closely linked to the patients' time to relapse, while a reliable prediction based on early response only is not possible based on the currently available data. Although we demonstrate with our approach, that the complete response data is sufficient to quantify the aggressiveness of the disease, further investigations are necessary to study how an intensive early sampling strategy may prospectively improve risk assessment and help to optimize individual treatments.

Mathematical Modeling of MPNs Offers Understanding and Decision Support for Personalized Treatment

(1) Background: myeloproliferative neoplasms (MPNs) are slowly developing hematological cancers characterized by few driver mutations, with JAK2V617F being the most prevalent. (2) Methods: using mechanism-based mathematical modeling (MM) of hematopoietic stem cells, mutated hematopoietic stem cells, differentiated blood cells, and immune response along with longitudinal data from the randomized Danish DALIAH trial, we investigate the effect of the treatment of MPNs with interferon-α2 on disease progression. (3) Results: At the population level, the JAK2V617F allele burden is halved every 25 months. At the individual level, MM describes and predicts the JAK2V617F kinetics and leukocyte- and thrombocyte counts over time. The model estimates the patient-specific treatment duration, relapse time, and threshold dose for achieving a good response to treatment. (4) Conclusions: MM in concert with clinical data is an important supplement to understand and predict the disease progression and impact of interventions at the individual level.

Survival outcomes and clinical benefit in patients with acute myeloid leukemia treated with glasdegib and low-dose cytarabine according to response to therapy

Background

The phase 2 BRIGHT AML 1003 trial evaluated efficacy and safety of glasdegib + low-dose cytarabine (LDAC) in patients with acute myeloid leukemia ineligible for intensive chemotherapy. The multicenter, open-label study randomized patients to receive glasdegib + LDAC (n = 78) or LDAC alone (n = 38). The rate of complete remission (CR) was 19.2% in the glasdegib + LDAC arm versus 2.6% in the LDAC arm (P = 0.015).

Methods

This post hoc analysis determines whether the clinical benefits of glasdegib are restricted to patients who achieve CR, or if they extend to those who do not achieve CR.

Results

In patients who did not achieve CR, the addition of glasdegib to LDAC improved overall survival (OS) versus LDAC alone (hazard ratio = 0.63 [95% confidence interval, 0.41–0.98]; P = 0.0182; median OS, 5.0 vs 4.1 months). Additionally, more patients receiving glasdegib + LDAC achieved durable recovery of absolute neutrophil count (≥ 1000/μl, 45.6% vs 35.5%), hemoglobin (≥ 9 g/dl, 54.4% vs 38.7%), and platelets (≥ 100,000/μl, 29.8% vs 9.7%). Transfusion independence was achieved by 15.0% and 2.9% of patients receiving glasdegib + LDAC and LDAC alone, respectively.

Conclusions

Collectively, these data suggest that there are clinical benefits with glasdegib in the absence of CR.

Trial registration

ClinicalTrials.gov NCT01546038 (March 7, 2012)

Mathematical Modeling Provides Evidence for Niche Competition in Human AML and Serves as a Tool to Improve Risk Stratification

Acute myeloid leukemia (AML) is a stem cell-driven malignant disease. There is evidence that leukemic stem cells (LSC) interact with stem cell niches and outcompete hematopoietic stem cells (HSC). The impact of this interaction on the clinical course of the disease remains poorly understood. We developed and validated a mathematical model of stem cell competition in the human HSC niche. Model simulations predicted how processes in the stem cell niche affect the speed of disease progression. Combining the mathematical model with data of individual patients, we quantified the selective pressure LSCs exert on HSCs and demonstrated the model's prognostic significance. A novel model-based risk-stratification approach allowed extraction of prognostic information from counts of healthy and malignant cells at the time of diagnosis. This model's feasibility was demonstrable based on a cohort of patients with ALDH-rare AML and shows that the model-based risk stratification is an independent predictor of disease-free and overall survival. This proof-of-concept study shows how model-based interpretation of patient data can improve prognostic scoring and contribute to personalized medicine. SIGNIFICANCE: Combining a novel mathematical model of the human hematopoietic stem cell niche with individual patient data enables quantification of properties of leukemic stem cells and improves risk stratification in acute myeloid leukemia.

Global dynamics of healthy and cancer cells competing in the hematopoietic system

Stem cells in the bone marrow differentiate to ultimately become mature, functioning blood cells through a tightly regulated process (hematopoiesis) including a stem cell niche interaction and feedback through the immune system. Mutations in a hematopoietic stem cell can create a cancer stem cell leading to a less controlled production of malfunctioning cells in the hematopoietic system. This was mathematically modelled by Andersen et al. (2017) including the dynamic variables: healthy and cancer stem cells and mature cells, dead cells and an immune system response. Here, we apply a quasi steady state approximation to this model to construct a two dimensional model with four algebraic equations denoted the simple cancitis model. The two dynamic variables are the clinically available quantities JAK2V617F allele burden and the number of white blood cells. The simple cancitis model represents the original model very well. Complete phase space analysis of the simple cancitis model is performed, including proving the existence and location of globally attracting steady states. Hence, parameter values from compartments of stem cells, mature cells and immune cells are directly linked to disease and treatment prognosis, showing the crucial importance of early intervention. The simple cancitis model allows for a complete analysis of the long term evolution of trajectories. In particular, the value of the self renewal of the hematopoietic stem cells divided by the self renewal of the cancer stem cells is found to be an important diagnostic marker and perturbing this parameter value at intervention allows the model to reproduce clinical data. Treatment at low cancer cell numbers allows returning to healthy blood production while the same intervention at a later disease stage can lead to eradication of healthy blood producing cells. Assuming the total number of white blood cells is constant in the early cancer phase while the allele burden increases, a one dimensional model is suggested and explicitly solved, including parameters from all original compartments. The solution explicitly shows that exogenous inflammation promotes blood cancer when cancer stem cells reproduce more efficiently than hematopoietic stem cells.

Designing combination therapies using multiple optimal controls

Strategic management of populations of interacting biological species routinely requires interventions combining multiple treatments or therapies. This is important in key research areas such as ecology, epidemiology, wound healing and oncology. Despite the well developed theory and techniques for determining single optimal controls, there is limited practical guidance supporting implementation of combination therapies. In this work we use optimal control theory to calculate optimal strategies for applying combination therapies to a model of acute myeloid leukaemia. We present a versatile framework to systematically explore the trade-offs that arise in designing combination therapy protocols using optimal control. We consider various combinations of continuous and bang-bang (discrete) controls, and we investigate how the control dynamics interact and respond to changes in the weighting and form of the pay-off characterising optimality. We demonstrate that the optimal controls respond non-linearly to treatment strength and control parameters, due to the interactions between species. We discuss challenges in appropriately characterising optimality in a multiple control setting and provide practical guidance for applying multiple optimal controls. Code used in this work to implement multiple optimal controls is available on GitHub.

Mathematical modeling reveals the factors involved in the phenomena of cancer stem cells stabilization

Cancer Stem Cells (CSC), a subset of cancer cells resembling normal stem cells with self-renewal and asymmetric division capabilities, are present at various but low proportions in many tumors and are thought to be responsible for tumor relapses following conventional cancer therapies. In vitro, most intriguingly, isolated CSCs rapidly regenerate the original population of stem and non-stem cells (non-CSCs) as shown by various investigators. This phenomenon still remains to be explained. We propose a mathematical model of cancer cell population dynamics, based on the main parameters of cell population growth, including the proliferation rates, the rates of cell death and the frequency of symmetric and asymmetric cell divisions both in CSCs and non-CSCs sub-populations, and taking into account the stabilization phenomenon. The analysis of the model allows determination of time-varying corridors of probabilities for different cell fates, given the particular dynamics of cancer cells populations; and determination of a cell-cell communication factors influencing these time-varying probabilities of cell behavior (division, transition) scenarios. Though the results of the model have to be experimentally confirmed, we can anticipate the development of several fundamental and practical applications based on the theoretical results of the model.

Clonal hematopoiesis of indeterminate potential and its impact on patient trajectories after stem cell transplantation

Clonal hematopoiesis of indeterminate potential (CHIP) is a recently identified process where older patients accumulate distinct subclones defined by recurring somatic mutations in hematopoietic stem cells. CHIP's implications for stem cell transplantation have been harder to identify due to the high degree of mutational heterogeneity that is present within the genetically distinct subclones. In order to gain a better understanding of CHIP and the impact of clonal dynamics on transplantation outcomes, we created a mathematical model of clonal competition dynamics. Our analyses highlight the importance of understanding competition intensity between healthy and mutant clones. Importantly, we highlight the risk that CHIP poses in leading to dominance of precancerous mutant clones and the risk of donor derived leukemia. Furthermore, we estimate the degree of competition intensity and bone marrow niche decline in mice during aging by using our modeling framework. Together, our work highlights the importance of better characterizing the ecological and clonal composition in hematopoietic donor populations at the time of stem cell transplantation.

In-silico comparison of two induction regimens (7 + 3 vs 7 + 3 plus additional bone marrow evaluation) in acute myeloid leukemia treatment

BACKGROUND

Clinical integration of systems biology approaches is gaining in importance in the course of digital revolution in modern medicine. We present our results of the analysis of an extended mathematical model describing abnormal human hematopoiesis. The model is able to describe the course of an acute myeloid leukemia including its treatment. In first-line treatment of acute myeloid leukemia, the induction chemotherapy aims for a rapid leukemic cell reduction. We consider combinations of cytarabine and anthracycline-like chemotherapy. Both substances are widely used as standard treatment to achieve first remission. In particular, we compare two scenarios: a single-induction course with 7 days cytarabine and 3 day of anthracycline-like treatment (7 + 3) with a 7 + 3 course and a bone marrow evaluation that leads, in case of insufficient leukemic cell reduction, to the provision of a second chemotherapy course. Three scenarios, based on the leukemias growth kinetics (slow, intermediate, fast), were analyzed. We simulated different intensity combinations for both therapy schemata (7 + 3 and 7 + 3 + evaluation).

RESULTS

Our model shows that within the 7 + 3 regimen a wider range of intensity combinations result in a complete remission (CR), compared to 7 + 3 + evaluation (fast: 64.3% vs 46.4%; intermediate: 63.7% vs 46.7%; slow: 0% vs 0%). Additionally, the number of simulations resulting in a prolonged CR was higher within the standard regimen (fast: 59.8% vs 40.1%; intermediate: 48.6% vs 31.0%; slow: 0% vs 0%). On the contrary, the 7 + 3 + evaluation regimen allows CR and prolonged CR by lower chemotherapy intensities compared to 7 + 3. Leukemic pace has a strong impact on treatment response and especially on specific effective doses. As a result, faster leukemias are characterized by superior treatment outcomes and can be treated effectively with lower treatment intensities.

CONCLUSIONS

We could show that 7 + 3 treatment has considerable more chemotherapy combinations leading to a first CR. However, the 7 + 3 + evaluation regimen leads to CR for lower therapy intensity and presumably less side effects. An additional evaluation can be considered beneficial to control therapy success, especially in low dose settings. The treatment success is dependent on leukemia growth dynamics. The determination of leukemic pace should be a relevant part of a personalized medicine.

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.

Bridging blood cancers and inflammation: The reduced Cancitis model

A novel mechanism-based model - the Cancitis model - describing the interaction of blood cancer and the inflammatory system is proposed, analyzed and validated. The immune response is divided into two components, one where the elimination rate of malignant stem cells is independent of the level of the blood cancer and one where the elimination rate depends on the level of the blood cancer. A dimensional analysis shows that the full 6-dimensional system of nonlinear ordinary differential equations may be reduced to a 2-dimensional system - the reduced Cancitis model - using Fenichel theory. The original 18 parameters appear in the reduced model in 8 groups of parameters. The reduced model is analyzed. Especially the steady states and their dependence on the exogenous inflammatory stimuli are analyzed. A semi-analytic investigation reveals the stability properties of the steady states. Finally, positivity of the system and the existence of an attracting trapping region in the positive octahedron guaranteeing global existence and uniqueness of solutions are proved. The possible topologies of the dynamical system are completely determined as having a Janus structure, where two qualitatively different topologies appear for different sets of parameters. To classify this Janus structure we propose a novel concept in blood cancer - a reproduction ratio R. It determines the topological structure depending on whether it is larger or smaller than a threshold value. Furthermore, it follows that inflammation, affected by the exogenous inflammatory stimulation, may determine the onset and development of blood cancers. The body may manage initial blood cancer as long as the self-renewal rate is not too high, but fails to manage it if an inflammation appears. Thus, inflammation may trigger and drive blood cancers. Finally, the mathematical analysis suggests novel treatment strategies and it is used to discuss the in silico effect of existing treatment, e.g. interferon-α or T-cell therapy, and the impact of malignant cells becoming resistant.

Global stability analysis and optimal control therapy of blood cell production process (hematopoiesis) in acute myeloid leukemia

In this paper we analyze the global stability of a coupled model for Acute Myeloid Leukemia and propose a therapy approach based on an optimal control strategy. Firstly, based on the positivity of the model, stability of trivial solutions for healthy and cancerous cell subsystems is assessed. To this end we use new Lyapunov functionals and take into account the interconnection between cell populations. Secondly, stability conditions for healthy situation in interconnected model are established by using Nyquist criterion. And thirdly, we design an optimal control based therapy that aims to eradicate cancerous cells and minimize the side effects of the treatment on healthy ones. After showing the existence of an optimal control, this one is determined by using Pontriagyn's principal. We assess the effect of interconnection between healthy and cancerous cells on their dynamics and on the stability conditions for different cases. The behavior of the system in open loop and with application of the optimal control therapy is illustrated by simulation and results are biologically explained and motivated.

Dual Targeting of Aurora Kinases with AMG 900 Exhibits Potent Preclinical Activity Against Acute Myeloid Leukemia with Distinct Post-Mitotic Outcomes

Aurora kinase A and B have essential and non-overlapping roles in mitosis, with elevated expression in a subset of human cancers, including acute myeloid leukemia (AML). In this study, pan-aurora kinase inhibitor (AKI) AMG 900 distinguishes itself as an anti-leukemic agent that is more uniformly potent against a panel of AML cell lines than are isoform-selective AKIs and classic AML drugs. AMG 900 inhibited AML cell growth by inducing polyploidization and/or apoptosis. AMG 900 and aurora-B-selective inhibitor AZD1152-hQPA showed comparable cellular effects on AML lines that do not harbor a FLT3-ITD mutation. AMG 900 was active against P-glycoprotein-expressing AML cells resistant to AZD1152-hQPA and was effective at inducing expression of megakaryocyte-lineage markers (CD41, CD42) on human CHRF-288-11 cells and mouse Jak2 V617F cells. In MOLM-13 cells, inhibition of p-histone H3 by AMG 900 was associated with polyploidy, extra centrosomes, accumulation of p53 protein, apoptosis, and cleavage of Bcl-2 protein. Co-administration of cytarabine (Ara-C) with AMG 900 potentiated cell killing in a subset of AML lines, with evidence of attenuated polyploidization. AMG 900 inhibited the proliferation of primary human bone marrow cells in culture, with a better proliferation recovery profile relative to classic antimitotic drug docetaxel. In vivo, AMG 900 significantly reduced tumor burden in a systemic MOLM-13 xenograft model where we demonstrate the utility of 3'-deoxy-3'-18F-fluorothymidine [18F]FLT positron emission tomographic (PET)-CT imaging to measure the antiproliferative effects of AMG 900 in skeletal tissues in mice.

Study of cohabitation and interconnection effects on normal and leukaemic stem cells dynamics in acute myeloid leukaemia

On the basis of recent studies, understanding the intimate relationship between normal and leukaemic stem cells is very important in leukaemia treatment. The authors' aim in this work is to clarify and assess the effect of coexistence and interconnection phenomenon on the healthy and cancerous stem cell dynamics. To this end, they perform the analysis of two time-delayed stem cell models in acute myeloid leukaemia. The first model is based on decoupled healthy and cancerous stem cell populations (i.e. there is no interaction between cell dynamics) and the second model includes interconnection between both population's dynamics. By using the positivity of both systems, they build new linear functions that permit to derive global stability conditions for each model. Moreover, knowing that most common types of haematological diseases are characterised by the existence of oscillations, they give conditions for the existence of a limit cycle (oscillations) in a particularly interesting healthy situation based on Poincare-Bendixson theorem. The obtained results are simulated and interpreted to be significant in understanding the effect of interconnection and would lead to an improvement in leukaemia treatment.

A stochastic model of myeloid cell lineages in hematopoiesis and pathway mutations in acute myeloid leukemia

A model for hematopoiesis is presented that explicitly includes the erythrocyte, granulocyte, and thrombocyte lineages and their common precursors. A small number of stem cells proliferate and differentiate through different compartments to produce the vast number of blood cells needed every day. Growth factors regulate the proliferation of cells dependent on the current demand. We provide a steady state analysis of the model and rough parameter estimates. Furthermore, we extend the model to include mutations that alter the replicative capacity of cells and introduce differentiation blocks. With these mutations the model develops signs of acute myeloid leukemia.

Synthesis and biological evaluation of dithiocarbamate esters of parthenolide as potential anti-acute myelogenous leukaemia agents

A series of dithiocarbamate esters of parthenolide (PTL) was designed, synthesised, and evaluated for their anti- acute myelogenous leukaemia (AML) activities. The most promising compound 7l showed greatly improved potency against AML progenitor cell line KG1a with IC₅₀ value of 0.7 μM, and the efficacy was 8.7-folds comparing to that of PTL (IC₅₀ = 6.1 μM). Compound 7l induced apoptosis of total primary human AML cells and leukaemia stem cell (LSCs) of primary AML cells while sparing normal cells. Furthermore, 7l suppressed the colony formation of primary human leukaemia cells. Moreover, compound 12, the salt form of 7l, prolonged the lifespan of mice in two patient-derived xenograft models and had no observable toxicity. The preliminary molecular mechanism study revealed that 7l-mediated apoptosis is associated with mitogen-activated protein kinase signal pathway. On the basis of these investigations, we propose that 12 might be a promising drug candidate for ultimate discovery of anti-LSCs drug.

Feedback regulation in a stem cell model with acute myeloid leukaemia

Background

The haematopoietic lineages with leukaemia lineages are considered in this paper. In particular, we mainly consider that haematopoietic lineages are tightly controlled by negative feedback inhibition of end-product. Actually, leukemia has been found 100 years ago. Up to now, the exact mechanism is still unknown, and many factors are thought to be associated with the pathogenesis of leukemia. Nevertheless, it is very necessary to continue the profound study of the pathogenesis of leukemia. Here, we propose a new mathematical model which include some negative feedback inhibition from the terminally differentiated cells of haematopoietic lineages to the haematopoietic stem cells and haematopoietic progenitor cells in order to describe the regulatory mechanisms mentioned above by a set of ordinary differential equations. Afterwards, we carried out detailed dynamical bifurcation analysis of the model, and obtained some meaningful results.

Results

In this work, we mainly perform the analysis of the mathematic model by bifurcation theory and numerical simulations. We have not only incorporated some new negative feedback mechanisms to the existing model, but also constructed our own model by using the modeling method of stem cell theory with probability method. Through a series of qualitative analysis and numerical simulations, we obtain that the weak negative feedback for differentiation probability is conducive to the cure of leukemia. However, with the strengthening of negative feedback, leukemia will be more difficult to be cured, and even induce death. In contrast, strong negative feedback for differentiation rate of progenitor cells can promote healthy haematopoiesis and suppress leukaemia.

Conclusions

These results demonstrate that healthy progenitor cells are bestowed a competitive advantage over leukaemia stem cells. Weak g₁, g₂, and h₁ enable the system stays in the healthy state. However, strong h₂ can promote healthy haematopoiesis and suppress leukaemia.

Integrated Pharmacokinetic/Pharmacodynamic Model of a Bispecific CD3xCD123 DART Molecule in Nonhuman Primates: Evaluation of Activity and Impact of Immunogenicity

Purpose: Flotetuzumab (MGD006 or S80880) is a bispecific molecule that recognizes CD3 and CD123 membrane proteins, redirecting T cells to kill CD123-expressing cells for the treatment of acute myeloid leukemia. In this study, we developed a mathematical model to characterize MGD006 exposure-response relationships and to assess the impact of its immunogenicity in cynomolgus monkeys.Experimental Design: Thirty-two animals received multiple escalating doses (100-300-600-1,000 ng/kg/day) via intravenous infusion continuously 4 days a week. The model reflects sequential binding of MGD006 to CD3 and CD123 receptors. Formation of the MGD006/CD3 complex was connected to total T cells undergoing trafficking, whereas the formation of the trimolecular complex results in T-cell activation and clonal expansion. Activated T cells were used to drive the peripheral depletion of CD123-positive cells. Anti-drug antibody development was linked to MGD006 disposition as an elimination pathway. Model validation was tested by predicting the activity of MGD006 in eight monkeys receiving continuous 7-day infusions.Results: MGD006 disposition and total T-cell and CD123-positive cell profiles were well characterized. Anti-drug antibody development led to the suppression of T-cell trafficking but did not systematically abolish CD123-positive cell depletion. Target cell depletion could persist after drug elimination owing to the self-proliferation of activated T cells generated during the first cycles. The model was externally validated with the 7-day infusion dosing schedule.Conclusions: A translational model was developed for MGD006 that features T-cell activation and expansion as a key driver of pharmacologic activity and provides a mechanistic quantitative platform to inform dosing strategies in ongoing clinical studies. Clin Cancer Res; 24(11); 2631-41. ©2018 AACR.

Mathematical modeling of the impact of cytokine response of acute myeloid leukemia cells on patient prognosis

Acute myeloid leukemia (AML) is a heterogeneous disease. One reason for the heterogeneity may originate from inter-individual differences in the responses of leukemic cells to endogenous cytokines. On the basis of mathematical modeling, computer simulations and patient data, we have provided evidence that cytokine-independent leukemic cell proliferation may be linked to early relapses and poor overall survival. Depending whether the model of cytokine-dependent or cytokine-independent leukemic cell proliferation fits to the clinical data, patients can be assigned to two groups that differ significantly with respect to overall survival. The modeling approach further enables us to identify parameter constellations that can explain unexpected responses of some patients to external cytokines such as blast crisis or remission without chemotherapy.

Mathematical modelling as a proof of concept for MPNs as a human inflammation model for cancer development

The chronic Philadelphia-negative myeloproliferative neoplasms (MPNs) are acquired stem cell neoplasms which ultimately may transform to acute myelogenous leukemia. Most recently, chronic inflammation has been described as an important factor for the development and progression of MPNs in the biological continuum from early cancer stage to the advanced myelofibrosis stage, the MPNs being described as "A Human Inflammation Model for Cancer Development". This novel concept has been built upon clinical, experimental, genomic, immunological and not least epidemiological studies. Only a few studies have described the development of MPNs by mathematical models, and none have addressed the role of inflammation for clonal evolution and disease progression. Herein, we aim at using mathematical modelling to substantiate the concept of chronic inflammation as an important trigger and driver of MPNs.The basics of the model describe the proliferation from stem cells to mature cells including mutations of healthy stem cells to become malignant stem cells. We include a simple inflammatory coupling coping with cell death and affecting the basic model beneath. First, we describe the system without feedbacks or regulatory interactions. Next, we introduce inflammatory feedback into the system. Finally, we include other feedbacks and regulatory interactions forming the inflammatory-MPN model. Using mathematical modeling, we add further proof to the concept that chronic inflammation may be both a trigger of clonal evolution and an important driving force for MPN disease progression. Our findings support intervention at the earliest stage of cancer development to target the malignant clone and dampen concomitant inflammation.

An Integrative multi-lineage model of variation in leukopoiesis and acute myelogenous leukemia

Background

Acute myelogenous leukemia (AML) progresses uniquely in each patient. However, patients are typically treated with the same types of chemotherapy, despite biological differences that lead to differential responses to treatment.

Results

Here we present a multi-lineage multi-compartment model of the hematopoietic system that captures patient-to-patient variation in both the concentration and rates of change of hematopoietic cell populations. By constraining the model against clinical hematopoietic cell recovery data derived from patients who have received induction chemotherapy, we identified trends for parameters that must be met by the model; for example, the mitosis rates and the probability of self-renewal of progenitor cells are inversely related. Within the data-consistent models, we found 22,796 parameter sets that meet chemotherapy response criteria. Simulations of these parameter sets display diverse dynamics in the cell populations. To identify large trends in these model outputs, we clustered the simulated cell population dynamics using k-means clustering and identified thirteen ‘representative patient’ dynamics. In each of these patient clusters, we simulated AML and found that clusters with the greatest mitotic capacity experience clinical cancer outcomes more likely to lead to shorter survival times. Conversely, other parameters, including lower death rates or mobilization rates, did not correlate with survival times.

Conclusions

Using the multi-lineage model of hematopoiesis, we have identified several key features that determine leukocyte homeostasis, including self-renewal probabilities and mitosis rates, but not mobilization rates. Other influential parameters that regulate AML model behavior are responses to cytokines/growth factors produced in peripheral blood that target the probability of self-renewal of neutrophil progenitors. Finally, our model predicts that the mitosis rate of cancer is the most predictive parameter for survival time, followed closely by parameters that affect the self-renewal of cancer stem cells; most current therapies target mitosis rate, but based on our results, we propose that additional therapeutic targeting of self-renewal of cancer stem cells will lead to even higher survival rates.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-017-0469-2) contains supplementary material, which is available to authorized users.

Reduced hematopoietic stem cell frequency predicts outcome in acute myeloid leukemia

In patients with acute myeloid leukemia and low percentages of aldehyde-dehydrogenase-positive cells, non-leukemic hematopoietic stem cells can be separated from leukemic cells. By relating hematopoietic stem cell frequencies to outcome we detected poor overall- and disease-free survival of patients with low hematopoietic stem cell frequencies. Serial analysis of matched diagnostic and follow-up samples further demonstrated that hematopoietic stem cells increased after chemotherapy in patients who achieved durable remissions. However, in patients who eventually relapsed, hematopoietic stem cell numbers decreased dramatically at the time of molecular relapse demonstrating that hematopoietic stem cell levels represent an indirect marker of minimal residual disease, which heralds leukemic relapse. Upon transplantation in immune-deficient mice cases with low percentages of hematopoietic stem cells of our cohort gave rise to leukemic or no engraftment, whereas cases with normal hematopoietic stem cell levels mostly resulted in multi-lineage engraftment. Based on our experimental data, we propose that leukemic stem cells have increased niche affinity in cases with low percentages of hematopoietic stem cells. To validate this hypothesis, we developed new mathematical models describing the dynamics of healthy and leukemic cells under different regulatory scenarios. These models suggest that the mechanism leading to decreases in hematopoietic stem cell frequencies before leukemic relapse must be based on expansion of leukemic stem cells with high niche affinity and the ability to dislodge hematopoietic stem cells. Thus, our data suggest that decreasing numbers of hematopoietic stem cells indicate leukemic stem cell persistence and the emergence of leukemic relapse.

Targeting acute myeloid leukemia stem cell signaling by natural products

Acute myeloid leukemia (AML) is the most commonly diagnosed leukemia in adults (25%) and comprises 15-20% in children. It is a genetically heterogeneous aggressive disease characterized by the accumulation of somatically acquired genetic changes, altering self-renewal, proliferation, and differentiation of hematopoietic progenitor cells, resulting in uncontrolled clonal proliferation of malignant progenitor myeloid cells in the bone marrow, peripheral blood, and occasionally in other body tissues. Treatment with modern chemotherapy regimen (cytarabine and daunorubicin) usually achieves high remission rates, still majority of patients are found to relapse, resulting in only 40-45% overall 5 year survival in young patients and less than 10% in the elderly AML patients. The leukemia stem cells (LSCs) are characterized by their unlimited self-renewal, repopulating potential and long residence in a quiescent state of G0/G1 phase. LSCs are considered to have a pivotal role in the relapse and refractory of AML. Therefore, new therapeutic strategies to target LSCs with limited toxicity towards the normal hematopoietic population is critical for the ultimate curing of AML. Ongoing research works with natural products like parthenolide (a natural plant extract derived compound) and its derivatives, that have the ability to target multiple pathways that regulate the self-renewal, growth and survival of LSCs point to ways for a possible complete remission in AML. In this review article, we will update and discuss various natural products that can target LSCs in AML.

Prognostic nomogram for previously untreated adult patients with acute myeloid leukemia

This study was designed to perform an acceptable prognostic nomogram for acute myeloid leukemia. The clinical data from 311 patients from our institution and 165 patients generated with Cancer Genome Atlas Research Network were reviewed. A prognostic nomogram was designed according to the Cox's proportional hazard model to predict overall survival (OS). To compare the capacity of the nomogram with that of the current prognostic system, the concordance index (C-index) was used to validate the accuracy as well as the calibration curve. The nomogram included 6 valuable variables: age, risk stratifications based on cytogenetic abnormalities, status of FLT3-ITD mutation, status of NPM1 mutation, expression of CD34, and expression of HLA-DR. The C-indexes were 0.71 and 0.68 in the primary and validation cohort respectively, which were superior to the predictive capacity of the current prognostic systems in both cohorts. The nomogram allowed both patients with acute myeloid leukemia and physicians to make prediction of OS individually prior to treatment.

Emergence of heterogeneity in acute leukemias

BACKGROUND

Leukemias are malignant proliferative disorders of the blood forming system. Sequencing studies demonstrate that the leukemic cell population consists of multiple clones. The genetic relationship between the different clones, referred to as the clonal hierarchy, shows high interindividual variability. So far, the source of this heterogeneity and its clinical relevance remain unknown. We propose a mathematical model to study the emergence and evolution of clonal heterogeneity in acute leukemias. The model allows linking properties of leukemic clones in terms of self-renewal and proliferation rates to the structure of the clonal hierarchy.

RESULTS

Computer simulations imply that the self-renewal potential of the first emerging leukemic clone has a major impact on the total number of leukemic clones and on the structure of their hierarchy. With increasing depth of the clonal hierarchy the self-renewal of leukemic clones increases, whereas the proliferation rates do not change significantly. The emergence of deep clonal hierarchies is a complex process that is facilitated by a cooperativity of different mutations.

CONCLUSION

Comparison of patient data and simulation results suggests that the self-renewal of leukemic clones increases with the emergence of clonal heterogeneity. The structure of the clonal hierarchy may serve as a marker for patient prognosis.

REVIEWERS

This article was reviewed by Marek Kimmel, Tommaso Lorenzi and Tomasz Lipniacki.

Tracking the evolution of cancer cell populations through the mathematical lens of phenotype-structured equations

Background

A thorough understanding of the ecological and evolutionary mechanisms that drive the phenotypic evolution of neoplastic cells is a timely and key challenge for the cancer research community. In this respect, mathematical modelling can complement experimental cancer research by offering alternative means of understanding the results of in vitro and in vivo experiments, and by allowing for a quick and easy exploration of a variety of biological scenarios through in silico studies.

Results

To elucidate the roles of phenotypic plasticity and selection pressures in tumour relapse, we present here a phenotype-structured model of evolutionary dynamics in a cancer cell population which is exposed to the action of a cytotoxic drug. The analytical tractability of our model allows us to investigate how the phenotype distribution, the level of phenotypic heterogeneity, and the size of the cell population are shaped by the strength of natural selection, the rate of random epimutations, the intensity of the competition for limited resources between cells, and the drug dose in use.

Conclusions

Our analytical results clarify the conditions for the successful adaptation of cancer cells faced with environmental changes. Furthermore, the results of our analyses demonstrate that the same cell population exposed to different concentrations of the same cytotoxic drug can take different evolutionary trajectories, which culminate in the selection of phenotypic variants characterised by different levels of drug tolerance. This suggests that the response of cancer cells to cytotoxic agents is more complex than a simple binary outcome, i.e., extinction of sensitive cells and selection of highly resistant cells. Also, our mathematical results formalise the idea that the use of cytotoxic agents at high doses can act as a double-edged sword by promoting the outgrowth of drug resistant cellular clones. Overall, our theoretical work offers a formal basis for the development of anti-cancer therapeutic protocols that go beyond the ‘maximum-tolerated-dose paradigm’, as they may be more effective than traditional protocols at keeping the size of cancer cell populations under control while avoiding the expansion of drug tolerant clones.

Reviewers

This article was reviewed by Angela Pisco, Sébastien Benzekry and Heiko Enderling.

Electronic supplementary material

The online version of this article (doi:10.1186/s13062-016-0143-4) contains supplementary material, which is available to authorized users.

Evidence that high-migration drug-surviving MOLT4 leukemia cells exhibit cancer stem cell-like properties

Leukemia represents a spectrum of hematological malignancies threatening human health. Resistance to treatments and metastasis of leukemia are the main causes of death in patients. Leukemia stem cells (LSCs) are the initiating cells of leukemia as well as the main source of drug resistance, invasion and metastasis. Consequently, eliminating LSCs is a prerequisite to eradicate leukemia. Preliminary studies in our laboratory have shown that chemokines and their related receptors play an important role in the drug resistance and metastasis of leukemic cells. In this study, we obtained high migration drug-surviving (short term) MOLT4 cells (hMDSCs-MOLT4) with treatment of doxorubicin (DOX) after Transwell assay. Then we detected stem cell-associated molecular markers on hMDSCs-MOLT4 cells and the parental MOLT4 cells by FCM, QPCR, western blotting, H&E staining and immunohisto-chemistry experimental techniques in vitro and in vivo. Moreover, we explored its impact on drug resistance and tumor formation. Then we found that compared with the parental MOLT4 cells, the mRNA expression levels of stem cell-related factors Sox2, Oct4, C-myc, Klf4, Nanog, Bmi-1, CXCR4 are increased in hMDSCs-MOLT4 cells, together with the protein expression levels of Sox2, Oct4, Klf4, Nanog, CXCR4 and CD34. Our results indicated that hMDSCs-MOLT4 cells exhibited strong drug resistance and certain cancer stem cell-like characteristics. It is the first indication that the targeting stemness factors such as Sox2, Oct4, Klf4, Nanog and CXCR4 may represent plausible options for eliminating T-ALL stem-like cells. The present findings shed light on the relationship between drug-tolerant leukemic cells and cancer stem cells.

Feedback mechanisms control coexistence in a stem cell model of acute myeloid leukaemia

Haematopoietic stem cell dynamics regulate healthy blood cell production and are disrupted during leukaemia. Competition models of cellular species help to elucidate stem cell dynamics in the bone marrow microenvironment (or niche), and to determine how these dynamics impact leukaemia progression. Here we develop two models that target acute myeloid leukaemia with particular focus on the mechanisms that control proliferation via feedback signalling. It is within regions of parameter space permissive of coexistence that the effects of competition are most subtle and the clinical outcome least certain. Steady state and linear stability analyses identify parameter regions that allow for coexistence to occur, and allow us to characterise behaviour near critical points. Where analytical expressions are no longer informative, we proceed statistically and sample parameter space over a coexistence region. We find that the rates of proliferation and differentiation of healthy progenitors exert key control over coexistence. We also show that inclusion of a regulatory feedback onto progenitor cells promotes healthy haematopoiesis at the expense of leukaemia, and that – somewhat paradoxically – within the coexistence region feedback increases the sensitivity of the system to dominance by one lineage over another.

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Models of competition between cell populations can describe the progression of acute myeloid leukaemia.

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We identify regions of coexistence in which leukaemia and healthy haematopoietic species can coexist in the niche.

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The dynamics of progenitor cells exert key control over species coexistence.

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The introduction of regulatory feedback can promote healthy haematopoiesis and suppress leukaemia.