The impact of CD34+ cell dose on engraftment after SCTs: personalized estimates based on mathematical modeling

A 7-Day Decitabine-Included Conditioning Regimen Accelerated Donor Hematopoietic Engraftment while Reduced the Occurrence of Mucositis without Interfering with Prognosis

INTRODUCTION

Allogeneic hematopoietic stem cell transplantation (allo-HSCT) is the standard and curative treatment strategy for patients with hematologic malignancies. Recently, decitabine-included regimens have been investigated by several studies including ours, which may prevent relapse of primary malignant diseases.

METHODS

This study was to retrospectively evaluate a 7-day decitabine-included regimen with reduced dose of idarubicin for patients with hematologic malignancies who underwent allo-HSCT.

RESULTS

A total of 84 patients were enrolled, including 24 cases in 7-day and 60 cases in 5-day decitabine groups, respectively. Patients conditioned with 7-day decitabine regimen showed accelerated neutrophil (12.05 ± 1.97 vs. 13.86 ± 3.15; u = 9.309, p < 0.001) and platelet (16.32 ± 6.27 vs. 21.37 ± 8.57; u = 8.887, p < 0.001) engraftment compared with those treated with 5-day decitabine regimen. Patients in the 7-day decitabine group showed a significantly lower incidence rate of total (50.00% [12/24] versus 78.33% [47/60]; χ2 = 6.583, p = 0.010) and grade III or above (4.17% [1/24] vs. 31.67% [19/60]; χ2 = 7.147, p = 0.008) oral mucositis compared to those in the 5-day decitabine group. However, the occurrence of other major complications post-allo-HSCT and outcomes of patients in these two groups were comparable.

CONCLUSION

These results demonstrate that this 7-day decitabine-contained new conditioning regimen seems to be feasible and safe for patients with myeloid neoplasms who receive allo-HSCT, and a large-scale prospective study is needed to confirm the findings of this study.

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.

Comparison of cell state models derived from single-cell RNA sequencing data: graph versus multi-dimensional space

Single-cell sequencing technologies have revolutionized molecular and cellular biology and stimulated the development of computational tools to analyze the data generated from these technology platforms. However, despite the recent explosion of computational analysis tools, relatively few mathematical models have been developed to utilize these data. Here we compare and contrast two cell state geometries for building mathematical models of cell state-transitions with single-cell RNA-sequencing data with hematopoeisis as a model system; (i) by using partial differential equations on a graph representing intermediate cell states between known cell types, and (ii) by using the equations on a multi-dimensional continuous cell state-space. As an application of our approach, we demonstrate how the calibrated models may be used to mathematically perturb normal hematopoeisis to simulate, predict, and study the emergence of novel cell states during the pathogenesis of acute myeloid leukemia. We particularly focus on comparing the strength and weakness of the graph model and multi-dimensional model.

R4 RGS proteins suppress engraftment of human hematopoietic stem/progenitor cells by modulating SDF-1/CXCR4 signaling

Specific R4 RGS members are expressed in human HSPCs and regulated by the SDF-1/CXCR4 axis.

RGS1/13/16 suppress HSPC engraftment, SDF-1 signaling, and key effectors of stem cell trafficking/maintenance.

Homing and engraftment of hematopoietic stem/progenitor cells (HSPCs) into the bone marrow (BM) microenvironment are tightly regulated by the chemokine stromal cell–derived factor-1 (SDF-1) and its G-protein–coupled receptor C-X-C motif chemokine receptor 4 (CXCR4), which on engagement with G-protein subunits, trigger downstream migratory signals. Regulators of G-protein signaling (RGS) are GTPase-accelerating protein of the Gα subunit and R4 subfamily members have been implicated in SDF-1–directed trafficking of mature hematopoietic cells, yet their expression and influence on HSPCs remain mostly unknown. Here, we demonstrated that human CD34⁺ cells expressed multiple R4 RGS genes, of which RGS1, RGS2, RGS13, and RGS16 were significantly upregulated by SDF-1 in a CXCR4-dependent fashion. Forced overexpression of RGS1, RGS13, or RGS16 in CD34⁺ cells not only inhibited SDF-1–directed migration, calcium mobilization, and phosphorylation of AKT, ERK, and STAT3 in vitro, but also markedly reduced BM engraftment in transplanted NOD/SCID mice. Genome-wide microarray analysis of RGS-overexpressing CD34⁺ cells detected downregulation of multiple effectors with established roles in stem cell trafficking/maintenance. Convincingly, gain-of-function of selected effectors or ex vivo priming with their ligands significantly enhanced HSPC engraftment. We also constructed an evidence-based network illustrating the overlapping mechanisms of RGS1, RGS13, and RGS16 downstream of SDF-1/CXCR4 and Gα_i. This model shows that these RGS members mediate compromised kinase signaling and negative regulation of stem cell functions, complement activation, proteolysis, and cell migration. Collectively, this study uncovers an essential inhibitory role of specific R4 RGS proteins in stem cell engraftment, which could potentially be exploited to develop improved clinical HSPC transplantation protocols.

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.

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.

A Mathematical Model of the Transition from Normal Hematopoiesis to the Chronic and Accelerated-Acute Stages in Myeloid Leukemia

A mathematical model given by a two-dimensional differential system is introduced in order to understand the transition process from the normal hematopoiesis to the chronic and accelerated-acute stages in chronic myeloid leukemia. A previous model of Dingli and Michor is refined by introducing a new parameter in order to differentiate the bone marrow microenvironment sensitivities of normal and mutant stem cells. In the light of the new parameter, the system now has three distinct equilibria corresponding to the normal hematopoietic state, to the chronic state, and to the accelerated-acute phase of the disease. A characterization of the three hematopoietic states is obtained based on the stability analysis. Numerical simulations are included to illustrate the theoretical results.

Stability analysis of a state-dependent delay differential equation for cell maturation: analytical and numerical methods

We consider a mathematical model describing the maturation process of stem cells up to fully mature cells. The model is formulated as a differential equation with state-dependent delay, where maturity is described as a continuous variable. The maturation rate of cells may be regulated by the amount of mature cells and, moreover, it may depend on cell maturity: we investigate how the stability of equilibria is affected by the choice of the maturation rate. We show that the principle of linearised stability holds for this model, and develop some analytical methods for the investigation of characteristic equations for fixed delays. For a general maturation rate we resort to numerical methods and we extend the pseudospectral discretisation technique to approximate the state-dependent delay equation with a system of ordinary differential equations. This is the first application of the technique to nonlinear state-dependent delay equations, and currently the only method available for studying the stability of equilibria by means of established software packages for bifurcation analysis. The numerical method is validated on some cases when the maturation rate is independent of maturity and the model can be reformulated as a fixed-delay equation via a suitable time transformation. We exploit the analytical and numerical methods to investigate the stability boundary in parameter planes. Our study shows some drastic qualitative changes in the stability boundary under assumptions on the model parameters, which may have important biological implications.

Mutation, drift and selection in single-driver hematologic malignancy: Example of secondary myelodysplastic syndrome following treatment of inherited neutropenia

Cancer development is driven by series of events involving mutations, which may become fixed in a tumor via genetic drift and selection. This process usually includes a limited number of driver (advantageous) mutations and a greater number of passenger (neutral or mildly deleterious) mutations. We focus on a real-world leukemia model evolving on the background of a germline mutation. Severe congenital neutropenia (SCN) evolves to secondary myelodysplastic syndrome (sMDS) and/or secondary acute myeloid leukemia (sAML) in 30–40%. The majority of SCN cases are due to a germline ELANE mutation. Acquired mutations in CSF3R occur in >70% sMDS/sAML associated with SCN. Hypotheses underlying our model are: an ELANE mutation causes SCN; CSF3R mutations occur spontaneously at a low rate; in fetal life, hematopoietic stem and progenitor cells expands quickly, resulting in a high probability of several tens to several hundreds of cells with CSF3R truncation mutations; therapeutic granulocyte colony-stimulating factor (G-CSF) administration early in life exerts a strong selective pressure, providing mutants with a growth advantage. Applying population genetics theory, we propose a novel two-phase model of disease development from SCN to sMDS. In Phase 1, hematopoietic tissues expand and produce tens to hundreds of stem cells with the CSF3R truncation mutation. Phase 2 occurs postnatally through adult stages with bone marrow production of granulocyte precursors and positive selection of mutants due to chronic G-CSF therapy to reverse the severe neutropenia. We predict the existence of the pool of cells with the mutated truncated receptor before G-CSF treatment begins. The model does not require increase in mutation rate under G-CSF treatment and agrees with age distribution of sMDS onset and clinical sequencing data.

Cancer develops by multistep acquisition of mutations in a progenitor cell and its daughter cells. Severe congenital neutropenia (SCN) manifests itself through an inability to produce enough granulocytes to prevent infections. SCN commonly results from a germline ELANE mutation. Large doses of the blood growth factor granulocyte colony-stimulating factor (G-CSF) rescue granulocyte production. However, SCN frequently transforms to a myeloid malignancy, commonly associated with a somatic mutation in CSF3R, the gene encoding the G-CSF Receptor. We built a mathematical model of evolution for CSF3R mutation starting with bone marrow expansion at the fetal development stage and continuing with postnatal competition between normal and malignant bone marrow cells. We employ tools of probability theory such as multitype branching processes and Moran models modified to account for expansion of hematopoiesis during human development. With realistic coefficients, we obtain agreement with the age range at which malignancy arises in patients. In addition, our model predicts the existence of a pool of cells with mutated CSF3R before G-CSF treatment begins. Our findings may be clinically applied to intervene more effectively and selectively in SCN patients.

Modeling large fluctuations of thousands of clones during hematopoiesis: The role of stem cell self-renewal and bursty progenitor dynamics in rhesus macaque

In a recent clone-tracking experiment, millions of uniquely tagged hematopoietic stem cells (HSCs) and progenitor cells were autologously transplanted into rhesus macaques and peripheral blood containing thousands of tags were sampled and sequenced over 14 years to quantify the abundance of hundreds to thousands of tags or “clones.” Two major puzzles of the data have been observed: consistent differences and massive temporal fluctuations of clone populations. The large sample-to-sample variability can lead clones to occasionally go “extinct” but “resurrect” themselves in subsequent samples. Although heterogeneity in HSC differentiation rates, potentially due to tagging, and random sampling of the animals’ blood and cellular demographic stochasticity might be invoked to explain these features, we show that random sampling cannot explain the magnitude of the temporal fluctuations. Moreover, we show through simpler neutral mechanistic and statistical models of hematopoiesis of tagged cells that a broad distribution in clone sizes can arise from stochastic HSC self-renewal instead of tag-induced heterogeneity. The very large clone population fluctuations that often lead to extinctions and resurrections can be naturally explained by a generation-limited proliferation constraint on the progenitor cells. This constraint leads to bursty cell population dynamics underlying the large temporal fluctuations. We analyzed experimental clone abundance data using a new statistic that counts clonal disappearances and provided least-squares estimates of two key model parameters in our model, the total HSC differentiation rate and the maximum number of progenitor-cell divisions.

Hematopoiesis of virally tagged cells in rhesus macaques is analyzed in the context of a mechanistic and statistical model. We find that the clone size distribution and the temporal variability in the abundance of each clone (viral tag) in peripheral blood are consistent with (i) stochastic HSC self-renewal during bone marrow repair, (ii) clonal aging that restricts the number of generations of progenitor cells, and (iii) infrequent and small-size samples. By fitting data, we infer two key parameters that control the level of fluctuations of clone sizes in our model: the total HSC differentiation rate and the maximum proliferation capacity of progenitor cells. Our analysis provides insight into the mechanisms of hematopoiesis and a framework to guide future multiclone barcoding/lineage tracking measurements.

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.

Clonal dominance and transplantation dynamics in hematopoietic stem cell compartments

Hematopoietic stem cells in mammals are known to reside mostly in the bone marrow, but also transitively passage in small numbers in the blood. Experimental findings have suggested that they exist in a dynamic equilibrium, continuously migrating between these two compartments. Here we construct an individual-based mathematical model of this process, which is parametrised using existing empirical findings from mice. This approach allows us to quantify the amount of migration between the bone marrow niches and the peripheral blood. We use this model to investigate clonal hematopoiesis, which is a significant risk factor for hematologic cancers. We also analyse the engraftment of donor stem cells into non-conditioned and conditioned hosts, quantifying the impact of different treatment scenarios. The simplicity of the model permits a thorough mathematical analysis, providing deeper insights into the dynamics of both the model and of the real-world system. We predict the time taken for mutant clones to expand within a host, as well as chimerism levels that can be expected following transplantation therapy, and the probability that a preconditioned host is reconstituted by donor cells.

Clonal hematopoiesis—where mature myeloid cells in the blood deriving from a single stem cell are over-represented—is a major risk factor for overt hematologic malignancies. To quantify how likely this phenomena is, we combine existing observations with a novel stochastic model and extensive mathematical analysis. This approach allows us to observe the hidden dynamics of the hematopoietic system. We conclude that for a clone to be detectable within the lifetime of a mouse, it requires a selective advantage. I.e. the clonal expansion cannot be explained by neutral drift alone. Furthermore, we use our model to describe the dynamics of hematopoiesis after stem cell transplantation. In agreement with earlier findings, we observe that niche-space saturation decreases engraftment efficiency. We further discuss the implications of our findings for human hematopoiesis where the quantity and role of stem cells is frequently debated.

Determining the control networks regulating stem cell lineages in colonic crypts

The question of stem cell control is at the center of our understanding of tissue functioning, both in healthy and cancerous conditions. It is well accepted that cellular fate decisions (such as divisions, differentiation, apoptosis) are orchestrated by a network of regulatory signals emitted by different cell populations in the lineage and the surrounding tissue. The exact regulatory network that governs stem cell lineages in a given tissue is usually unknown. Here we propose an algorithm to identify a set of candidate control networks that are compatible with (a) measured means and variances of cell populations in different compartments, (b) qualitative information on cell population dynamics, such as the existence of local controls and oscillatory reaction of the system to population size perturbations, and (c) statistics of correlations between cell numbers in different compartments. Using the example of human colon crypts, where lineages are comprised of stem cells, transit amplifying cells, and differentiated cells, we start with a theoretically known set of 32 smallest control networks compatible with tissue stability. Utilizing near-equilibrium stochastic calculus of stem cells developed earlier, we apply a series of tests, where we compare the networks' expected behavior with the observations. This allows us to exclude most of the networks, until only three, very similar, candidate networks remain, which are most compatible with the measurements. This work demonstrates how theoretical analysis of control networks combined with only static biological data can shed light onto the inner workings of stem cell lineages, in the absence of direct experimental assessment of regulatory signaling mechanisms. The resulting candidate networks are dominated by negative control loops and possess the following properties: (1) stem cell division decisions are negatively controlled by the stem cell population, (2) stem cell differentiation decisions are negatively controlled by the transit amplifying cell population.

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.

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.

Mass concentration in a nonlocal model of clonal selection

Self-renewal is a constitutive property of stem cells. Testing the cancer stem cell hypothesis requires investigation of the impact of self-renewal on cancer expansion. To better understand this impact, we propose a mathematical model describing the dynamics of a continuum of cell clones structured by the self-renewal potential. The model is an extension of the finite multi-compartment models of interactions between normal and cancer cells in acute leukemias. It takes a form of a system of integro-differential equations with a nonlinear and nonlocal coupling which describes regulatory feedback loops of cell proliferation and differentiation. We show that this coupling leads to mass concentration in points corresponding to the maxima of the self-renewal potential and the solutions of the model tend asymptotically to Dirac measures multiplied by positive constants. Furthermore, using a Lyapunov function constructed for the finite dimensional counterpart of the model, we prove that the total mass of the solution converges to a globally stable equilibrium. Additionally, we show stability of the model in the space of positive Radon measures equipped with the flat metric (bounded Lipschitz distance). Analytical results are illustrated by numerical simulations.

The evolution of T-cell depletion in haploidentical stem-cell transplantation

T-cell depletion (TCD) can prevent the onset of graft-versus-host disease (GvHD) in animal models of bone marrow transplantation; this manipulation enabled the successful application in the 1980s of T-cell depleted bone marrow (BM) for the treatment of babies with severe combined immune deficiency (SCID). However, in leukaemia patients, implementation of T-cell depletion has been more difficult, especially due to high rate of graft-rejection, leukaemia relapse and delayed immune reconstitution. These hurdles were gradually overcome by modifying the cell composition of the graft, and by reducing the toxicities associated with conditioning protocols. Although no 'gold standard' TCD method exists, T-cell depletion in its modern forms could offer clinical benefit, even for patients with a matched sibling donor.

The overshoot and phenotypic equilibrium in characterizing cancer dynamics of reversible phenotypic plasticity

The paradigm of phenotypic plasticity indicates reversible relations of different cancer cell phenotypes, which extends the cellular hierarchy proposed by the classical cancer stem cell (CSC) theory. Since it is still questionable if the phenotypic plasticity is a crucial improvement to the hierarchical model or just a minor extension to it, it is worthwhile to explore the dynamic behavior characterizing the reversible phenotypic plasticity. In this study we compare the hierarchical model and the reversible model in predicting the cell-state dynamics observed in biological experiments. Our results show that the hierarchical model shows significant disadvantages over the reversible model in describing both long-term stability (phenotypic equilibrium) and short-term transient dynamics (overshoot) in cancer cell populations. In a very specific case in which the total growth of population due to each cell type is identical, the hierarchical model predicts neither phenotypic equilibrium nor overshoot, whereas the reversible model succeeds in predicting both of them. Even though the performance of the hierarchical model can be improved by relaxing the specific assumption, its prediction to the phenotypic equilibrium strongly depends on a precondition that may be unrealistic in biological experiments. Moreover, it still does not show as rich dynamics as the reversible model in capturing the overshoots of both CSCs and non-CSCs. By comparison, it is more likely for the reversible model to correctly predict the stability of the phenotypic mixture and various types of overshoot behavior.

Mathematical modeling reveals differential effects of erythropoietin on proliferation and lineage commitment of human hematopoietic progenitors in early erythroid culture

Erythropoietin is essential for the production of mature erythroid cells, promoting both proliferation and survival. Whether erythropoietin and other cytokines can influence lineage commitment of hematopoietic stem and progenitor cells is of significant interest. To study lineage restriction of the common myeloid progenitor to the megakaryocyte/erythroid progenitor of peripheral blood CD34(+) cells, we have shown that the cell surface protein CD36 identifies the earliest lineage restricted megakaryocyte/erythroid progenitor. Using this marker and carboxyfluorescein succinimidyl ester to track cell divisions in vitro, we have developed a mathematical model that accurately predicts population dynamics of erythroid culture. Parameters derived from the modeling of cultures without added erythropoietin indicate that the rate of lineage restriction is not affected by erythropoietin. By contrast, megakaryocyte/erythroid progenitor proliferation is sensitive to erythropoietin from the time that CD36 first appears at the cell surface. These results shed new light on the role of erythropoietin in erythropoiesis and provide a powerful tool for further study of hematopoietic progenitor lineage restriction and erythropoiesis.

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

Acute myeloid leukemia (AML) is a heterogeneous disease in which a variety of distinct genetic alterations might occur. Recent attempts to identify the leukemia stem-like cells (LSC) have also indicated heterogeneity of these cells. On the basis of mathematical modeling and computer simulations, we have provided evidence that proliferation and self-renewal rates of the LSC population have greater impact on the course of disease than proliferation and self-renewal rates of leukemia blast populations, that is, leukemia progenitor cells. The modeling approach has enabled us to estimate the LSC properties of 31 individuals with relapsed AML and to link them to patient survival. On the basis of the estimated LSC properties, the patients can be divided into two prognostic groups that differ significantly with respect to overall survival after first relapse. The results suggest that high LSC self-renewal and proliferation rates are indicators of poor prognosis. Nevertheless, high LSC self-renewal rate may partially compensate for slow LSC proliferation and vice versa. Thus, model-based interpretation of clinical data allows estimation of prognostic factors that cannot be measured directly. This may have clinical implications for designing treatment strategies.

Mathematical Modelling as a Tool to Understand Cell Self-renewal and Differentiation

Mathematical modeling is a powerful technique to address key questions and paradigms in a variety of complex biological systems and can provide quantitative insights into cell kinetics, fate determination and development of cell populations. The chapter is devoted to a review of modeling of the dynamics of stem cell-initiated systems using mathematical methods of ordinary differential equations. Some basic concepts and tools for cell population dynamics are summarized and presented as a gentle introduction to non-mathematicians. The models take into account different plausible mechanisms regulating homeostasis. Two mathematical frameworks are proposed reflecting, respectively, a discrete (punctuated by division events) and a continuous character of transitions between differentiation stages. Advantages and constraints of the mathematical approaches are presented on examples of models of blood systems and compared to patients data on healthy hematopoiesis.

Feedback signals in myelodysplastic syndromes: increased self-renewal of the malignant clone suppresses normal hematopoiesis

Myelodysplastic syndromes (MDS) are triggered by an aberrant hematopoietic stem cell (HSC). It is, however, unclear how this clone interferes with physiologic blood formation. In this study, we followed the hypothesis that the MDS clone impinges on feedback signals for self-renewal and differentiation and thereby suppresses normal hematopoiesis. Based on the theory that the MDS clone affects feedback signals for self-renewal and differentiation and hence suppresses normal hematopoiesis, we have developed a mathematical model to simulate different modifications in MDS-initiating cells and systemic feedback signals during disease development. These simulations revealed that the disease initiating cells must have higher self-renewal rates than normal HSCs to outcompete normal hematopoiesis. We assumed that self-renewal is the default pathway of stem and progenitor cells which is down-regulated by an increasing number of primitive cells in the bone marrow niche – including the premature MDS cells. Furthermore, the proliferative signal is up-regulated by cytopenia. Overall, our model is compatible with clinically observed MDS development, even though a single mutation scenario is unlikely for real disease progression which is usually associated with complex clonal hierarchy. For experimental validation of systemic feedback signals, we analyzed the impact of MDS patient derived serum on hematopoietic progenitor cells in vitro: in fact, MDS serum slightly increased proliferation, whereas maintenance of primitive phenotype was reduced. However, MDS serum did not significantly affect colony forming unit (CFU) frequencies indicating that regulation of self-renewal may involve local signals from the niche. Taken together, we suggest that initial mutations in MDS particularly favor aberrant high self-renewal rates. Accumulation of primitive MDS cells in the bone marrow then interferes with feedback signals for normal hematopoiesis – which then results in cytopenia.

Myelodysplastic syndromes are diseases which are characterized by ineffective blood formation. There is accumulating evidence that they are caused by an aberrant hematopoietic stem cell. However, it is yet unclear how this malignant clone suppresses normal hematopoiesis. To this end, we generated mathematical models under the assumption that feedback signals regulate self-renewal and proliferation of normal and diseased stem cells. The simulations demonstrate that the malignant cells must have particularly higher self-renewal rates than normal stem cells – rather than higher proliferation rates. On the other hand, down-regulation of self-renewal by the increasing number of malignant cells in the bone marrow niche can explain impairment of normal blood formation. In fact, we show that serum of patients with myelodysplastic syndrome, as compared to serum of healthy donors, stimulates proliferation and moderately impacts on maintenance of hematopoietic stem and progenitor cells in vitro. Thus, aberrant high self-renewal rates of the malignant clone seem to initiate disease development; suppression of normal blood formation is then caused by a rebound effect of feedback signals which down-regulate self-renewal of normal stem and progenitor cells as well.

Clonal selection and therapy resistance in acute leukaemias: mathematical modelling explains different proliferation patterns at diagnosis and relapse

Recent experimental evidence suggests that acute myeloid leukaemias may originate from multiple clones of malignant cells. Nevertheless, it is not known how the observed clones may differ with respect to cell properties, such as proliferation and self-renewal. There are scarcely any data on how these cell properties change due to chemotherapy and relapse. We propose a new mathematical model to investigate the impact of cell properties on the multi-clonal composition of leukaemias. Model results imply that enhanced self-renewal may be a key mechanism in the clonal selection process. Simulations suggest that fast proliferating and highly self-renewing cells dominate at primary diagnosis, while relapse following therapy-induced remission is triggered mostly by highly self-renewing but slowly proliferating cells. Comparison of simulation results to patient data demonstrates that the proposed model is consistent with clinically observed dynamics based on a clonal selection process.

Stochasticity and determinism in models of hematopoiesis

This chapter represents a novel view of modeling in hematopoiesis, synthesizing both deterministic and stochastic approaches. Whereas the stochastic models work in situations where chance dominates, for example when the number of cells is small, or under random mutations, the deterministic models are more important for large-scale, normal hematopoiesis. New types of models are on the horizon. These models attempt to account for distributed environments such as hematopoietic niches and their impact on dynamics. Mixed effects of such structures and chance events are largely unknown and constitute both a challenge and promise for modeling. Our discussion is presented under the separate headings of deterministic and stochastic modeling; however, the connections between both are frequently mentioned. Four case studies are included to elucidate important examples. We also include a primer of deterministic and stochastic dynamics for the reader's use.

Assessing hematopoietic (stem-) cell behavior during regenerative pressure

Hematopoiesis is a complex and strongly regulated process. In case of regenerative pressure, efficient recovery of blood cell counts is crucial for survival of an individual. We propose a quantitative mathematical model of white blood cell formation based on the following cell parameters: (1) proliferation rate, (2) self-renewal, and (3) cell death. Simulating this model we assess the change of these parameters under regenerative pressure. The proposed model allows to quantitatively describe the impact of these cell parameters on engraftment time after stem cell transplantation. Results indicate that enhanced self-renewal during the posttransplant period is crucial for efficient regeneration of blood cell counts while constant or reduced self-renewal leads to delayed recovery or graft failure. Increased cell death in the posttransplant period has a similar impact. In contrast, reduced proliferation or pre-homing cell death causes only mild delays in blood cell recovery which can be compensated sufficiently by increasing the dose of transplanted cells.