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Publications


Journal Articles

  1. T. Stiehl, W. Wang, C. Lutz, A. Marciniak-Czochra, "Mathematical modeling provides evidence for niche competition in human AML and serves as a tool to improve risk stratification" , Cancer Res, 2020. PUBMED
    Abstract

    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 hematopoietic stem cell 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 LSC exert on HSC 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 ALDH-rare AML patients 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.

    Details

    • Model: Quantitative and refined version of the stem cell niche model introduced in Wang et al. Haematologica 2017. The model assumes that leukemic stem cells (LSC) and hematopoietic stem cells (HSC) compete for spaces in a joined stem cell niche. Offspring of LSC arising from division can dislodge HSC from the niche and vice versa. Dislodged stem cells and stem cells not conquering a niche space differentiate. The model of the stem cell niche is coupled to dynamics of progenitor cells, precursor cells, mature cells and leukemic blasts. Cell properties are regulated by a feedback signal.
    • Conclusions: Competition in the stem cell niche is a key determinant of AML disease progression. Out-competition of HSC from the stem cell niche is governed by two parameters, i.e., (i) LSC proliferation rate and (ii) HSC dislodgement probability. The HSC dislodgement probability corresponds to the probability with which a LSC invades the niche by dislodging an HSC. In ALDH-rare AML these parameters can be estimated by combining the mathematical model with measurements of blasts and HSC counts at diagnosis. The estimated parameters allow to refine the risk-stratification and are independent predictors of overall and disease free survival. Using this approach a prognostically significant subdivision of the intermediate risk group is achieved.


  2. F. Klawe*, T. Stiehl*, P. Bastian, C. Gaillochet, JU. Lohmann, A. Marciniak-Czochra, "Mathematical modeling of plant cell fate transitions controlled by hormonal signals", PLoS Comput Biol, 16(7):e1007523, 2020. * shared first authorship Preprint PUBMED Software
    Abstract

    Coordination of fate transition and cell division is crucial to maintain the plant architecture and to achieve efficient production of plant organs. In this paper, we analysed the stem cell dynamics at the shoot apical meristem (SAM) that is one of the plant stem cells locations. We designed a mathematical model to elucidate the impact of {hormonal} signaling on the fate transition rates between different zones corresponding to slowly dividing stem cells and fast dividing transit amplifying cells. The model is based on a simplified two-dimensional disc geometry of the SAM and accounts for a continuous displacement towards the periphery of cells produced in the central zone. Coupling growth and hormonal signaling results in a nonlinear system of reaction-diffusion equations on a growing domain with the growth velocity depending on the model components. The model is tested by simulating perturbations in the level of key transcription factors that maintain SAM homeostasis . The model provides new insights on how the transcription factor HECATE is integrated in the regulatory network that governs stem cell differentiation.

    Details

    • Model: The model describes production, degradation and diffusion of key plant hormones (WUS, CLV3, CK, HEC) in the shoot apical meristem (SAM) of Arabidopsis thaliana. The SAM is approximated by a two-dimensional disc. The so-called organizing center which is responsible for the production of the stem cell inducing transcription factor WUS is modelled as a concentric circular source term. Cell division and differentiation depend on the concentrations of the hormones. The model is given by a nonlinear system of reaction-diffusion equations on a growing circular domain with the growth rate depending on the model components.
    • Conclusions: The model allows to reproduce a range of gain- and loss-of function experiments and provides new insights on how the transcription factor HECATE is integrated in the regulatory network governing stem cell differentiation. Simulations suggest that the experimentally observed expansion of the stem cell population during HEC over-expression requires both a direct and a CK-mediated effect of HEC on the organizing center.


  3. Y. Han, J. Franzen, T. Stiehl, M. Gobs, CC. Kuo, M. Nikolic, J. Hapala, BE. Koop, K. Strathmann, S. Ritz‐Timme, W. Wagner. "New Targeted Approaches for Epigenetic Age Predictions" BMC Biol , 18(1):71, 2020. Preprint PUBMED
    Abstract

    Aging causes epigenetic modifications, which are utilized as a biomarker for the aging process. While genome-wide DNA methylation profiles enable robust age-predictors by integration of many age-associated CG dinucleotides (CpGs), there are various alternative approaches for targeted measurements at specific CpGs that better support standardized and cost-effective high-throughput analysis. In this study, we utilized 4,650 Illumina BeadChip datasets of blood to select the best suited CpG sites for targeted analysis. DNA methylation analysis at these sites with either pyrosequencing or droplet digital PCR (ddPCR) revealed a high correlation with chronological age. In comparison, bisulfite barcoded amplicon sequencing (BBA-seq) gave slightly lower precision at individual CpGs. However, BBA-seq data revealed that the correlation of methylation levels with age at neighboring CpG sites follows a bell-shaped curve, often accompanied by a CTCF binding site at the peak. We demonstrate that within individual BBA-seq reads the DNA methylation at neighboring CpGs is not coherently modified but reveals a stochastic pattern. Based on this, we have developed an alternative model for epigenetic age predictions based on the binary sequel of methylated and non-methylated sites in individual reads, which reflects heterogeneity in epigenetic aging within a sample. Thus, the stochastic evolution of age-associated DNA methylation patterns, which seems to resemble epigenetic drift, enables epigenetic clocks for individual DNA strands.


  4. L. Harris, P. Rigo, T. Stiehl, Z. Gaber, S. H. L. Austin, M. del Mar Masdeu, A. Edwards, N. Urban, A. Marciniak-Czochra, F. Guillemot. "Progressive changes in hippocampal stem cell properties ensure lifelong neurogenesis", submitted. Preprint
    Abstract

    Neural stem cell numbers fall rapidly in the hippocampus of juvenile mice but stabilise during adulthood, ensuring lifelong hippocampal neurogenesis. We show that this reduction in stem cell depletion rate is the result of multiple coordinated changes in stem cell behaviour. In particular, while active neural stem cells divide only once or twice before differentiating rapidly in juveniles, they increasingly return to a resting state of shallow quiescence and progress through additional self-renewing divisions in adulthood. Single-cell transcriptomic, mathematical modelling and label-retention analyses indicate that resting cells have a higher activation rate and greater contribution to neurogenesis than dormant cells, which have not left quiescence. These progressive changes in stem cell behaviour result from reduced expression of the pro-activation protein ASCL1 due to increased post-translational degradation. These mechanisms help reconcile current contradictory models of hippocampal NSC dynamics and may contribute to the different rates of decline of hippocampal neurogenesis in mammalian species including humans.

    Details

    • Model: Extended version of the neural stem cell (NSC) model introduced by Ziebell et al. (Development 2018) and Kalamakis et al (Cell, 2019). The novel feature is the subdivision of quiescent NSC into dormant and resting NSC. Quiescent NSC are referred to as dormant if they have never been activated since establishment of the NSC niche at postnatal day 14, quiescent cells that have been activated since postnatal day 14 are referred to as resting cells. The model describes the age-related change of active, dormant and resting NSC numbers.
    • Conclusions: The activation rate of resting NSC is significantly higher compared to the activation rate of dormant NSC. The activation rates of both cell types decline with age.


  5. S. Chulian, A. Martínez-Rubio, A. Marciniak-Czochra, T. Stiehl, C. Blazquez Goni, JFR. Gutierrez, MR. Orellana, AC. Robleda, VM. Perez-Garcia, M. Rosa. "Dynamical properties of feedback signalling in B lymphopoiesis: A mathematical modelling approach", submitted. Preprint
    Abstract

    Haematopoiesis is the process of generation of blood cells. Lymphopoiesis generates lymphocytes, the cells in charge of the adaptive immune response. Disruptions of this process are associated with diseases like leukaemia, which is especially incident in children. The characteristics of self-regulation of this process make them suitable for a mathematical study. In this paper we develop mathematical models of lymphopoiesis using currently available data. We do this by drawing inspiration from existing structured models of cell lineage development and integrating them with paediatric bone marrow data, with special focus on regulatory mechanisms. A formal analysis of the models is carried out, giving steady states and their stability conditions. We use this analysis to obtain biologically relevant regions of the parameter space and to understand the dynamical behaviour of B-cell renovation. Finally, we use numerical simulations to obtain further insight into the influence of proliferation and maturation rates on the reconstitution of the cells in the B line. We conclude that a model including feedback regulation of cell proliferation represents a biologically plausible depiction for B-cell reconstitution in bone marrow. Research into haematological disorders could benefit from a precise dynamical description of B lymphopoiesis.


  6. G. Kalamakis, D. Brune, S. Ravichandran, J. Bolz, W. Fan, F. Ziebell, T. Stiehl, F. Catala-Martinez, J. Kupke, S. Zhao, E. Llorens-Bobadilla, K. Bauer, S. Limpert, B. Berger, U. Christen, P. Schmezer, J.P. Mallm, B. Berninger, S. Anders, A. Del Sol, A. Marciniak-Czochra, and A. Martin-Villalba. "Quiescence Modulates Stem Cell Maintenance and Regenerative Capacity in the Aging Brain", Cell, 176(6):1407-1419.e14, 2019. PUBMED
    Abstract

    The function of somatic stem cells declines with age. Understanding the molecular underpinnings of this decline is key to counteract age-related disease. Here, we report a dramatic drop in the neural stem cells (NSCs) number in the aging murine brain. We find that this smaller stem cell reservoir is protected from full depletion by an increase in quiescence that makes old NSCs more resistant to regenerate the injured brain. Once activated, however, young and old NSCs show similar proliferation and differentiation capacity. Single-cell transcriptomics of NSCs indicate that aging changes NSCs minimally. In the aging brain, niche-derived inflammatory signals and the Wnt antagonist sFRP5 induce quiescence. Indeed, intervention to neutralize them increases activation of old NSCs during homeostasis and following injury. Our study identifies quiescence as a key feature of old NSCs imposed by the niche and uncovers ways to activate NSCs to repair the aging brain.

    Details

    • Model: Adaptation of multi-compartment model from Ziebell et al. Development 2018.
    • Conclusions: Age-related changes of neural stem cell numbers and their activity can be explained by an age-dependent down-regulation of the activation rate from quiescence. Reduced activation prevents depletion of the stem cell pool.


  7. T. Lorenzi, A. Marciniak-Czochra, T. Stiehl, "A structured population model of clonal selection in acute leukemias with multiple maturation stages", J Math Biol. 79(5):1587-1621, 2019. PUBMED
    Abstract

    Recent progress in genetic techniques has shed light on the complex co-evolution of malignant cell clones in leukemias. However, several aspects of clonal selection still remain unclear. In this paper, we present a multi-compartmental continuously structured population model of selection dynamics in acute leukemias, which consists of a system of coupled integro-differential equations. Our model can be analysed in a more efficient way than classical models formulated in terms of ordinary differential equations. Exploiting the analytical tractability of this model, we investigate how clonal selection is shaped by the self-renewal fraction and the proliferation rate of leukemic cells at different maturation stages. We integrate analytical results with numerical solutions of a calibrated version of the model based on real patient data. In summary, our mathematical results formalise the biological notion that clonal selection is driven by the self-renewal fraction of leukemic stem cells and the clones that possess the highest value of this parameter are ultimately selected. Moreover, we demonstrate that the self-renewal fraction and the proliferation rate of non-stem cells do not have a substantial impact on clonal selection. Taken together, our results indicate that interclonal variability in the self-renewal fraction of leukemic stem cells provides the necessary substrate for clonal selection to act upon.

    Details

    • Model: Continuous three-compartment version of the model from J. Royal Society Interface 11: 20140079, 2014. The model is given as a system of integro-differential equations. Self-renewal of all mitotic cell types is regulated by a feedback-mechanism that depends on the total number of mature cells and blasts.
    • New aspects: Three healthy and leukemic differentiation stages, continuous trait structure (infinite number of clones)
    • Conclusion: Only clones with maximal stem cell self-renewal survive for long times. Coexistence is only possible if multiple clones have the same stem cell self-renewal. Stem cell proliferation rate, progenitor proliferation rate and progenitor self-renewal impact on transient dynamics but have no impact on long term survival of a clone.


  8. T. Stiehl, A. Marciniak-Czochra, “How to characterize stem cells? Contributions from mathematical modeling.", Current stem cell reports, 5 (2): 57–65, 2019. (Review)" Journal
    Abstract

    Purpose of Review
    Adult stem cells play a key role in tissue regeneration and cancer. To translate findings from stem cell biology into clinics, we require a quantitative characterization of stem cell dynamics in vivo. This review explores how mathematical models can help to characterize stem cell behavior in health and disease.

    Recent Findings
    Mathematical models significantly contribute to quantification of stem cell traits such as proliferation, self-renewal, and quiescence. They provide insights into the role of systemic and micro-environmental feedback loops during regeneration and cancer. Computer simulations allow linking stem cell properties to tumor composition, clinical course, and drug response. Therefore, models are helpful in personalizing treatments and predicting patient survival.

    Summary
    Mathematical models coupled with tools of parameter estimation and model selection provide quantitative insights into stem cell properties and their regulation. They help to understand experimentally inaccessible processes occurring in regeneration, aging, and cancer.

    Details

    Review article summarizing how mathematical models can contribute to understand stem cell dynamics.


  9. F. Knauer, T. Stiehl, A. Marciniak-Czochra. Oscillations in a white blood cell production model with multiple differentiation stages, J. Math Biol. 80(3):575-600, 2020. PUBMED
    Abstract

    In this work we prove occurrence of a super-critical Hopf bifurcation in a model of white blood cell formation structured by three maturation stages. We provide an explicit analytical expression for the bifurcation point depending on model parameters. The Hopf bifurcation is a unique feature of the multi-compartment structure as it does not exist in the corresponding two-compartment model. It appears for a parameter set different from the parameters identified for healthy hematopoiesis and requires changes in at least two cell properties. Model analysis allows identifying a range of biologically plausible parameter sets that can explain persistent oscillations of white blood cell counts observed in some hematopoietic diseases. Relating the identified parameter sets to recent experimental and clinical findings provides insights into the pathological mechanisms leading to oscillating blood cell counts.

    Details

    • Model: Three-compartment model of blood cell production from Stem Cells and Development, 2009
    • Conclusions: Unlike the two-compartment version of the model the three-compartment version exhibits a Hopf-Bifurcation. Diseases with persistent oscillations of white blood cell counts can originate from perturbations of different parameters including proliferation, self-renewal and death of stem and progenitor cells.


  10. R. Stace, T. Stiehl, A. Marciniak-Czochra, T. Lorenzi, "Discrete and continuum phenotype- structured models for the evolution of cancer cell populations under chemotherapy.", Math. Mod. Natural Phenomena15:14, 2020.
    Abstract

    We present a stochastic individual-based model for the phenotypic evolution of cancer cellpopulations under chemotherapy. In particular, we consider the case of combination cancer therapywhereby a chemotherapeutic agent is administered as the primary treatment and an epigenetic drugis used as an adjuvant treatment. The cell population is structured by the expression level of a genethat controls cell proliferation and chemoresistance. In order to obtain an analytical description of evo-lutionary dynamics, we formally derive a deterministic continuum counterpart of this discrete model,which is given by a nonlocal parabolic equation for the cell population density function. Integratingcomputational simulations of the individual-based model with analysis of the corresponding continuummodel, we perform a complete exploration of the model parameter space. We show that harsher envi-ronmental conditions and higher probabilities of spontaneous epimutation can lead to more effectivechemotherapy, and we demonstrate the existence of an inverse relationship between the efficacy of theepigenetic drug and the probability of spontaneous epimutation. Taken together, the outcomes of themodel provide theoretical ground for the development of anticancer protocols that use lower concen-trations of chemotherapeutic agents in combination with epigenetic drugs capable of promoting there-expression of epigenetically regulated genes.


  11. T. Stiehl, A. D. Ho, A. Marciniak-Czochra, "Mathematical modeling of the impact of cytokine response of acute myeloid leukemia cells on patient prognosis", Scientific Reports 8:2809, 2018. PUBMED
    Abstract

    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.

    Details

    • Model: Multi-compartment models of healthy and leukemic cells. Leukemic cell expansion can be cytokine-dependent or cytokine- independent.
    • New aspects: cytokine-independent leukemic cell expansion, increased cell death in case of marrow-overcrowding.
    • Conclusion: Patients can be assigned to groups that differ significantly with respect to overall survival, depending on whether the model of cytokine-dependent or cytokine-independent leukemic cell expansion fits to their clinical data. Cytokine-independent cell expansion is related to poor survival and early relapses. The models help to indentify leukemic cell properties that can explain unexpected responses to external cytokines such as blast crisis or remission without chemotherapy.


  12. A. Marciniak-Czochra, A. Mikelic, T. Stiehl, "Renormalization group second order approximation for singularly perturbed nonlinear ordinary differential equations", Math. Methods in Applied Sciences 41: 5691-5710, 2018. Journal
    Abstract

    We consider a 2 time scale nonlinear system of ordinary differential equations. The small parameter of the system is the ratio ϵ of the time scales. We search for an approximation involving only the slow time unknowns and valid uniformly for all times at order O(epsilon^2). A classical approach to study these problems is Tikhonov's singular perturbation theorem. We develop an approach leading to a higher order approximation using the renormalization group (RG) method. We apply it in 2 steps. In the first step, we show that the RG method allows for approximation of the fast time variables by their RG expansion taken at the slow time unknowns. Next, we study the slow time equations, where the fast time unknowns are replaced by their RG expansion. This allows to rigorously show the second order uniform error estimate. Our result is a higher order extension of Hoppensteadt's work on the Tikhonov singular perturbation theorem for infinite times. The proposed procedure is suitable for problems from applications, and it is computationally less demanding than the classical Vasil'eva‐O'Malley expansion. We apply the developed method to a mathematical model of stem cell dynamics.

    Details

    • New aspects: Development of a reduction approach for 2 time scale nonlinear systems of ordinary differential equations. The result is a higher order extension of the Tikhonov singular perturbation theorem for infinite intervals. It can be directly applied to the 2 compartment model of healthy hematopoiesis where cytokine concentrations are given by an additional ODE evolving on a fast time scale compared to cell division.
    • Conclusion: The two compartment version of the healthy hematopoiesis model from 2009 (Stem Cells and Development) can be rigorously obtained using a time scale separation (quasi steady state approximation). The accuracy of this reduction is of order epsilon, where epsilon is the relation between the different time scales. Using the framework of renormalization groups an approximation of order epsilon squared can be rigorously derived.


  13. T. Stiehl, A. Marciniak-Czochra, "Stem cell self-renewal in regeneration and cancer: Insights from mathematical modeling", Current Opinion in Systems Biology 5: 112-120, 2017. (Review) Journal
    Abstract

    Self-renewal is the process by which stem cells give rise to stem cells. Recent insights from experimental and theoretical models suggest that self-renewal not only influences the stem cell population but has a crucial impact on dynamics of non-stem cells. Efficient production of mature cells in tissue regeneration requires up-regulation of stem cell self-renewal. Increased self-renewal confers a competitive advantage on cancer cell clones by leading to aggressive expansion of both stem and non-stem cancer cells. Recent models suggest that self-renewal is the key parameter to understand clonal competition, selection and emergence of resistance in cancer cell populations.

    Details

    Review article summarizing the role of stem cell self-renewal in regeneration and cancer. Insights and hypotheses from mathematical modeling are collected and discussed in the context of recent experimental findings. Different systems including hematopoiesis and neurogenesis are considered.


  14. C. Gaillochet, T. Stiehl, C. Wenzl, JJ. Ripoll, LJ. Bailey-Steinitz, L. Li, A. Pfeiffer, A. Miotk, J. Hakenjos, J. Forner, MF. Yanofsky, A. Marciniak-Czochra, JU Lohmann, "Control of plant cell fate transitions by transcriptional and hormonal signals", eLife 6:e30135, 2017. PUBMED
    Abstract

    Plant meristems carry pools of continuously active stem cells, whose activity is controlled by developmental and environmental signals. After stem cell division, daughter cells that exit the stem cell domain acquire transit amplifying cell identity before they are incorporated into organs and differentiate. In this study, we used an integrated approach to elucidate the role of HECATE (HEC) genes in regulating developmental trajectories of shoot stem cells in Arabidopsis thaliana. Our work reveals that HEC function stabilizes cell fate in distinct zones of the shoot meristem thereby controlling the spatio-temporal dynamics of stem cell differentiation. Importantly, this activity is concomitant with the local modulation of cellular responses to cytokinin and auxin, two key phytohormones regulating cell behaviour. Mechanistically, we show that HEC factors transcriptionally control and physically interact with MONOPTEROS (MP), a key regulator of auxin signalling, and modulate the autocatalytic stabilization of auxin signalling output.

    Details

    • Model: Computational population model of the shoot apical meristem (SAM) in Arabidopsis thaliana. Time dynamics of stem cells, transit amplifying cells and primordia cells are investigated. The spatial relation of the different populations is modeled assuming a circular SAM geometry where stem cells are located in the central zone (CZ) and transit amplifying cells in the peripheral zone (PZ). The model is used to understand the role of HEC on cell fate transitions.
    • Conclusion: The combination of single cell live imaging data and mathematical modeling implies that transition rates from the CZ to the PZ and from the PZ to organ primordia are increased in the HEC loss of function phenotype compared to the wildtype. Furthermore the time between initation and separation of organ primordia is decreased. These changes allow to explain the counterintuitive finding that HEC loss of function meristems are smaller than wildtype meristems but produce more organs per unit of time.


  15. W. Wang, T. Stiehl, S. Raffel, V. T. Hoang, I. Hoffmann, L. Poisa-Beiro, B. R. Saeed, R. Blume, L. Manta, V. Eckstein, T. Bochtler, P. Wuchter, M. Essers, A. Jauch, A. Trumpp, A. Marciniak- Czochra, A. D. Ho, C. Lutz, "Reduced hematopoietic stem cell frequency predicts outcome in acute myeloid leukemia", Haematologica 102: 1567-1577, 2017. PUBMED
    Abstract

    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.

    Details

    • Model: Multi-compartment model of healthy and leukemic cells with replicative senescence of non-stem cells and detailed description of the stem cell niche.
    • New aspects: competition of healthy and leukemic stem cells in the bone marrow niche.
    • Conclusion: Clinical data show that the number of healthy hematopoietic stem cells (HSC, CD34+CD38-ALDH+) decreases before relapse of the leukemia. Mathematical models imply that this observation can only be explained by competition of healthy and leukemic stem cells inside the bone marrow niche. High affinity of leukemic stem cells to the niche leads to low HSC numbers at the time of relapse. Clinical data imply that this is linked to a poor prognosis.


  16. T. Stiehl, C. Lutz, A. Marciniak-Czochra, "Emergence of heterogeneity in acute leukemias", Biology Direct 11: 51, 2016. PUBMED
    Abstract

    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.

    Details

    • Model: Multi-clonal model of hematopoietic and leukemic cells with random mutations.
    • New aspects: Random mutations, tracking of clonal hierarchies and comparison to data
    • Conclusions: Self-renewal of leukemic clones increases with increasing depth of the clonal hierarchy, proliferation does not change significantly. The emergence of deep clonal hierarchies is facilitated by cooperativity of different mutations. The structure of the clonal hierarchy may serve as a marker for patient prognosis.


  17. T. Stiehl, N. Baran, A. D. Ho, A. Marciniak-Czochra, "Cell division patterns in acute myeloid leukemia stem-like cells determine clinical course: a model to predict patient survival", Cancer Research 75: 940-949, 2015. PUBMED
    Abstract

    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.

    Details

    • Model: Multi-compartmental model of hematopoietic and leukemic cells.
    • New aspects: Model based estimation of leukemic cell parameters.
    • Conclusion: Self-renewal and proliferation of leukemic progenitor cells have little impact on the course of the disease. Model based estimation of surrogate leukemic stem cell parameters allows to define prognostic subgroups. Self-renewal and/or proliferation of leukemic stem cells increase between relapses.


  18. T. Walenda*, T. Stiehl*, H. Braun, J. Fröbel, A. D. Ho, T. Schroeder, T. Goecke, U. Germing, A. Marciniak-Czochra, W. Wagner, "Feedback Signals in Myelodysplastic Syndromes: Increased Self-Renewal of the Malignant Clone Suppresses Normal Hematopoiesis", PLoS Comp. Biol. 10: e1003599, 2014. * shared first authorship PUBMED
    Abstract

    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.

    Details

    • Model: Multi-compartment model of hematopoietic and dysplastic cells. Feedback regulation of self-renewal depending on the number of primitive cell types residing in the stem cell niche. Feedback regulation of proliferation depending on the number of mature cells.
    • New aspects: Regulation of self-renewal in dependence of the primitive cell types (normal and dysplastic) residing in the stem cell niche.
    • Conclusion: MDS disease dynamics might be explained by down-regulation of self-renewal signals in the presence of dysplastic cells. Increased self-renewal of the most primitive malignant cell clone is a prerequisite for disease development.


  19. T. Stiehl, N. Baran, A. D. Ho, A. Marciniak-Czochra, "Clonal selection and therapy resistance in acute leukemias: Mathematical modelling explains different proliferation patterns at diagnosis and relapse", J. Royal Society Interface 11: 20140079, 2014. PUBMED
    Abstract

    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.

    Details

    • Model: Multi-compartmental model of hematopoietic cells and multiple leukemic clones.
    • New aspects: Extension of the previous models to take into account multiple leukemic clones. Cells compete for growth factors and bone marrow space.
    • Conclusion: Leukemic cells at dignosis are characterized by high self-renewal and high proliferation rate. At relapse self-renewal is high and proliferation rate is low. Experimentally observed clonal heterogeneity can be explained by selection in absence of additional mutations between diagnosis and relapse.

  20. T. Stiehl, A. D. Ho, A. Marciniak-Czochra, "The impact of CD34+ cell dose on engraftment after Stem Cell Transplantations: personalized estimates based on mathematical modeling", Bone Marrow Transplantation 49: 30-37, 2014. PUBMED
    Abstract

    It is known that the number of transplanted cells has a significant impact on the outcome after SCT. We identify issues that cannot be addressed by conventional analysis of clinical trials and ask whether it is possible to develop a refined analysis to conclude about the outcome of individual patients given clinical trial results. To accomplish this, we propose an interdisciplinary approach based on mathematical modeling. We devise and calibrate a mathematical model of short-term reconstitution and simulate treatment of large patient groups with random interindividual variation. Relating model simulations to clinical data allows quantifying the effect of transplant size on reconstitution time in the terms of patient populations and individual patients. The model confirms the existence of lower bounds on cell dose necessary for secure and efficient reconstitution but suggests that for some patient subpopulations higher thresholds might be appropriate. Simulations demonstrate that relative time gain because of increased cell dose is an 'interpersonally stable' parameter, in other words that slowly engrafting patients profit more from transplant enlargements than average cases. We propose a simple mathematical formula to approximate the effect of changes of transplant size on reconstitution time.

    Details

    • Model: Realistic model of granulocytopoiesis after stem cell transplantation, 8 maturation stages, non-linear feedback regulation of self-renewal, proliferation and death.
    • New aspects: Calibration of model parameters based on literature and clinical data. Development of a formula to estimate relative reduction of reconstitution time in case of increased dose of transplanted cells.
    • Conclusion: Patients at risk for slow engraftment could benefit from cell doses that are larger than the standard transplants used in clinical practice.


  21. T. Stiehl, A. D. Ho, A. Marciniak-Czochra, "Assessing hematopoietic (stem-) cell behavior during regenerative pressure", Adv Exp Med Biol 844: 347-67, 2014. PUBMED
    Abstract

    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.

    Details

    • Model: Calibrated model of granulocytopoiesis with 8 compartments and feedback-regulation of self-renewal, proliferation and death.
    • New aspects: Investigation of reasons for delayed engraftment after stem cell transplantation.
    • Conclusion: Reduced self-renewal or increased cell death in the post-transplant period lead to delayed engraftment, which cannot be rescued by increased transplant dose. Reduced proliferation or pre-homing cell death lead to delayed engraftment that can be rescued by increased transplant dose.


  22. F. Clement, P. Michel, D. Monniaux, T. Stiehl, "Coupled Somatic Cell Kinetics and Germ Cell Growth: Multiscale Model-Based Insight on Ovarian Follicular Development", SIAM Multiscale Model. Simul. 11: 719-746, 2013. Journal
    Abstract

    The development of ovarian follicles is a unique instance of a morphogenesis processstill occurring during adult life and resulting from the interactions between somatic and germ cells.In mammals, the initiation of follicular development from the pool of resting follicles is characterizedby an increase in the oocyte size concomitant with the surrounding somatic cells proliferating to buildan avascular tissue called granulosa. We present a stochastic individual-based model describing thefirst stages of follicular development, where the cell population is structured with respect to age (pro-gression within the cell cycle) and space (radial distance from the oocyte). The model accounts forthe molecular dialogue existing between the oocyte and granulosa cells. Three dynamically interact-ing scales are considered in the model: (i) a microscopic, local scale corresponding to an individualcell embedded in its immediate environment, (ii) a mesoscopic, semilocal scale corresponding toanatomical or functional areas of follicles, and (iii) a macroscopic, global scale corresponding to themorphology of the follicle. Numerical simulations are performed to reproduce the three-dimensionalmorphogenesis of follicles and to follow simultaneously the detailed spatial distribution of individualgranulosa cells, their organization as concentric layers or functional cell clones, and the increase inthe follicle size. Detailed quantitative simulation results are provided in the ovine species, in whichwell-characterized genetic mutations lead to a variety of phenotypic follicle morphogenesis. Themodel can help to explain pathological situations of imbalance between oocyte growth and follicularcell proliferation.

    Details

    • Model: Stochastic individual-based model of the first stages of follicular development. Structured cell population with respect to age and space. Molecular feedback between the oocyte and granulosa cells.
    • Conclusions: Secretion of oocyte growth factors by granulosa cells and the cell cycle duration of granulosa cells are important determinants of follicle morphogenesis. The model can reproduce follicle phenotypes of wild type sheep and important mutants.


  23. T. Stiehl, A. Marciniak-Czochra, "Mathematical modelling of leukemogenesis and cancer stem cell dynamics", Math. Mod. Natural Phenomena 7: 166-202, 2012. Journal
    Abstract

    The cancer stem cell hypothesis has evolved to one of the most important paradigms in biomedical research. During recent years evidence has been accumulating for the existence of stem cell-like populations in different cancers, especially in leukemias. In the current work we propose a mathematical model of cancer stem cell dynamics in leukemias. We apply the model to compare cellular properties of leukemic stem cells to those of their benign counterparts. Using linear stability analysis we derive conditions necessary and sufficient for expansion of malignant cell clones, based on fundamental cellular properties. This approach reveals different scenarios of cancer initiation and provides qualitative hints to possible treatment strategies.

    Details

    • Model: Multi-compartmental model of hematopoietic and leukemic cells. Cells interact by non-linear feedback signaling. Leukemic and hematopoietic cells compete for the same signals.
    • New aspects: Extension of the hematopoiesis model to leukemias. Rigorous characterization of the differences between hematopoietic and leukemic stem cells in terms of self-renewal, proliferation and death. Linear stability analysis with consideration of dynamics in case of zero-eigenvalues.
    • Conclusion: If self-renewal of leukemic cells is high enough, leukemias can emerge, even if leukemic cells proliferate slower than hematopoietic cells. Besides, enhanced proliferation or reduced apoptosis are scenarios leading to leukemia.

  24. A. Schellenberg, T. Stiehl, P. Horn, S. Joussen, N. Pallua, A. D. Ho, W. Wagner, "Population dynamics of mesenchymal stromal cells during culture expansion", Cytotherapy 14: 401-411, 2012. PUBMED
    Abstract

    BACKGROUND AIMS:
    Mesenchymal stromal cells (MSC) are heterogeneous and only a subset possesses multipotent differentiation potential. It has been proven that long-term culture has functional implications for MSC. However, little is known how the composition of subpopulation changes during culture expansion.

    METHODS:
    We addressed the heterogeneity of MSC using limiting-dilution assays at subsequent passages. In addition, we used a cellular automaton model to simulate population dynamics under the assumption of mixed numbers of remaining cell divisions until replicative senescence. The composition of cells with adipogenic or osteogenic differentiation potential during expansion was also determined at subsequent passages.

    RESULTS:
    Not every cell was capable of colony formation upon passaging. Notably, the number of fibroblastoid colony-forming units (CFU-f) decreased continuously, with a rapid decay within early passages. Therefore the CFU-f frequency might be used as an indicator of the population doublings remaining before entering the senescent state. Predictions of the cellular automaton model suited the experimental data best if most cells were already close to their replicative limit by the time of culture initiation. Analysis of differentiated clones revealed that subsets with very high levels of adipogenic or osteogenic differentiation capacity were only observed at early passages.

    CONCLUSIONS:
    These data support the notion of heterogeneity in MSC, and also with regard to replicative senescence. The composition of subpopulations changes during culture expansion and clonogenic subsets, especially those with the highest differentiation capacity, decrease already at early passages.

    Details

    • Model: 2D discrete square-lattice cellular automaton for simulation of mesenchymal stromal cell cultures under various passaging and plating conditions.
    • Assumptions: limited number of cell divisions, contact inhibition, migration. At culture initiation cells are heterogeneous with respect to the number of performed divisions.
    • Conclusion: Predictions of the cellular automaton model reproduce the experimental data if most cells are close to their replicative limit by the time of culture initiation.


  25. T. Stiehl, A. Marciniak-Czochra, "Characterization of stem cells using mathematical models of multistage cell lineages", Math. Comput. Model 53: 1505-1517, 2011. Journal
    Abstract

    Stem cells dynamics is an important field of research with promising clinical impacts. Due to the revolutionary new technologies of biological data collection, an enormous amount of information on specific factors and genes responsible for cell differentiation is available. However, the mechanisms controlling stem cell self-renewal, maintenance and differentiation are still poorly understood and there exists no general characterization of stem cells based on observable cell properties. We address these problems with the help of mathematical models. Stem cells are described as the cell type that is most responsive to certain environmental signals. This results in a dynamic characterization of stemness that depends on environmental conditions and is not necessarily linked to a unique cell population.

    Details

    • Model: Multi-compartmental model of hematopoietic and leukemic cells. Cells interact by non-linear feedback signaling. Leukemic and hematopoietic cells compete for the same signals.
    • New aspects: Extension of the hematopoiesis model to leukemias. Rigorous characterization of the differences between hematopoietic and leukemic stem cells in terms of self-renewal, proliferation and death. Linear stability analysis with consideration of dynamics in case of zero-eigenvalues.
    • Conclusion: If self-renewal of leukemic cells is high enough, leukemias can emerge, even if leukemic cells proliferate slower than hematopoietic cells. Besides, enhanced proliferation or reduced apoptosis are scenarios leading to leukemia.


  26. D. Cholewa*, T. Stiehl*, G. Bokermann, S. Joussen, C. Koch, T. Walenda, N. Pallua, A. Marciniak-Czochra, C. V. Suschek, W. Wagner, "Expansion of Adipose Mesenchymal Stromal Cells is Affected by Human Platelet Lysate and Plating Density", Cell Transplantation 20: 1409-22, 2011. * shared first authorship PUBMED
    Abstract

    The composition of mesenchymal stromal cells (MSCs) changes in the course of in vitro culture expansion. Little is known how these cell preparations are influenced by culture media, plating density, or passaging. In this study, we have isolated MSCs from human adipose tissue in culture medium supplemented with either fetal calf serum (FCS) or human platelet lysate (HPL). In addition, culture expansion was simultaneously performed at plating densities of 10 or 10,000 cells/cm(2). The use of FCS resulted in larger cells, whereas HPL significantly enhanced proliferation. Notably, HPL also facilitated expansion for more population doublings than FCS (43 ± 3 vs. 22 ± 4 population doubling; p less than 0.001), while plating density did not have a significant effect on long-term growth curves. To gain further insight into population dynamics, we conceived a cellular automaton model to simulate expansion of MSCS. It is based on the assumptions that the number of cell divisions is limited and that due to contact inhibition proliferation occurs only at the rim of colonies. The model predicts that low plating densities result in more heterogeneity with regard to cell division history, and favor subpopulations of higher migratory activity. In summary, HPL is a suitable serum supplement for isolation of MSC from adipose tissue and facilitates more population doublings than FCS. Cellular automaton computer simulations provided additional insights into how complex population dynamics during long-term expansion are affected by plating density and migration.

    Details

    • Model: 2D discrete square-lattice cellular automaton for simulation of mesenchymal stromal cell cultures under various passaging and plating conditions.
    • Assumptions: limited number of cell divisions, contact inhibition, different migratory phenotypes.
    • Conclusion: Low plating densities in mesenchymal stromal cell cultures result in more heterogeneity with regard to cell division history and favor subpopulations of higher migratory activity.


  27. A. Marciniak-Czochra, T. Stiehl, W. Wagner, "Modeling of replicative senescence in hematopoietic development", Aging 1: 723-732, 2009. PUBMED
    Abstract

    Hematopoietic stem cells (HSC) give rise to an enormous number of blood cells throughout our life. In contrast their number of cell divisions preceding senescence is limited underin vitro culture conditions. Here we consider the question whether HSC can rejuvenate indefinitely or if the number of cell divisions is restricted. We have developed a multi-compartmental model for hematopoietic differentiation based on ordinary differential equations. The model is based on the hypothesis that in each step of maturation, the percentage of self-renewal versus differentiation is regulated by a single external feedback mechanism. We simulate the model under the assumption that hematopoietic differentiation precedes the six steps of maturation and the cells ultimately cease to proliferate after 50 divisions. Our results demonstrate that it is conceivable to maintain hematopoiesis over a life-time if HSC have a slow division rate and a high self-renewal rate. With age, the feedback signal increases and this enhances self-renewal, which results in the increase of the number of stem and progenitor cells. This study demonstrates that replicative senescence is compatible with life-long hematopoiesis and that model predictions are in line with experimental observations. Thus, HSC might not divide indefinitely with potentially important clinical implications.

    Details

    • Model: Multi-compartmental model of hematopoiesis with senescence and nonlinear regulation of self-renewal. Cells stop to proliferate after 50 divisions.
    • New aspects: Senescence
    • Conclusion: Replicative senescence of hematopoietic stem cells is compatible with life-long blood formation.

  28. A. Marciniak-Czochra, T. Stiehl, A. D. Ho, W. Jäger, W. Wagner, "Modeling asymmetric cell division in hematopietic stem cells regulation of self-renewal is essential for efficient repopulation", Stem Cells Dev. 18: 377-385, 2009. PUBMED
    Abstract

    Hematopoietic stem cells (HSCs) are characterized by their ability of self-renewal to replenish the stem cell pool and differentiation to more mature cells. The subsequent stages of progenitor cells also share some of this dual ability. It is yet unknown whether external signals modulate proliferation rate or rather the fraction of self-renewal. We propose three multicompartment models, which rely on a single external feedback mechanism. In Model 1 the signal enhances proliferation, whereas the self-renewal rates in all compartments are fixed. In Model 2 the signal regulates the rate of self-renewal, whereas the proliferation rate is unchanged. In Model 3, the signal regulates both proliferation and self-renewal rates. This study demonstrates that a unique strictly positive stable steady state can only be achieved by regulation of the rate of self-renewal. Furthermore, it requires a lower number of effective cell doublings. In order to maintain the stem cell pool, the self-renewal ratio of the HSC has to be greater or =50% and it has to be higher than the self-renewal ratios of all downstream compartments. Interestingly, the equilibrium level of mature cells depends only on the parameters of self-renewal of HSC and it is independent of the parameters of dynamics of all upstream compartments. The model is compatible with the increase of leukocyte numbers following HSC transplantation. This study demonstrates that extrinsic regulation of the self-renewal rate of HSC is most essential in the process of hematopoiesis.

    Details

    • Model: Multi-compartmental model of hematopoiesis with nonlinear feedback regulation. Self-renewal and/or proliferation are regulated based on the number of mature cells.
    • Conclusion: Up-regulation of self-renewal in case of low mature cell counts is essential for recovery after bone marrow transplantation. Up-regulation of proliferation alone is not sufficient for recovery within a realistic time span.

Book Chapters

  1. A. Marciniak-Czochra, T. Stiehl, "Mathematical models of hematopoietic reconstitution after stem cell transplantation", in Model Based Parameter Estimation: Theory and Applications H. G. Bock, T. Carraro, W. Jäger, S. Körkel, R. Rannacher, J. P. Schlöder (Eds.), Contributions in Mathematical and Computational Sciences Volume 3, Springer, 2013.
    Abstract

    Transplantation of bone marrow stern cells is a widely used option to treat leukemias and other diseases. Nevertheless, this intervention is linked to life-threatening complications. Numerous clinical trials have been performed to evaluate various treatment options. Since there exist strong interindividual variations in patients' responses, results of clinical trials are hardly applicable to individual patients. In this paper a mathematical model of hematopoiesis introduced by us in (Marciniak-Czochra et al.: Stem Cells Dev. 8:377-85, 2009) is calibrated based on clinical data and applied to study several aspects of short term reconstitution after bone marrow transplantation. Parameter estimation is performed based on the data of time evolution of leukocyte counts after chemotherapy and bone marrow transplantation obtained for individual patients. The model allows to simulate various treatment options for large groups of individual patients, to compare the effects of the treatments on individual patients and to evaluate how the properties of the transplant and cytokine treatment affect the time of reconstitution.

    Details

    • Model: Model of granulocytopoiesis after stem cell transplantation with 8 maturation stages and feedback regulation of self-renewal. Feedback regulation is simplified compared to Bone Marrow Transplantation 49: 30-37.
    • New aspects: calibration of model parameters based on clinical data.
    • Conclusion: Clinically observed heterogeneity of patients' recovery from stem cell transplantation can be reproduced by the model and might originate from small interindividual differences of proliferation and self-renewal rates.

  2. J. Ottesen, T. Stiehl, M. Andersen, "Systems biology of blood cancer and immune surveillance", in E. Voit (Ed), Systems Medicine: Integrative, Qualitative and Computational Approaches, Elsevier, accepted.