Predictive nonlinear modeling of malignant myelopoiesis and tyrosine kinase inhibitor therapy

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

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  1. eLife assessment

    This is an important study that investigates the impact of tyrosine kinase inhibitors (TKIs) in chronic myeloid leukemia. Through a combination of pre-clinical in vivo measurements, clinical data, and computational modeling, the authors present solid evidence regarding the heterogeneous effects of TKIs in patients and how the response to treatment may be improved. With the assumptions about differences between normal and leukemic cells addressed, this study would be of interest to those working in the fields of mathematical oncology and cancer biology.

  2. Reviewer #1 (Public Review):

    This work introduces a new computational model of healthy blood cell formation and chronic myeloid leukemia (CML). By combining data from the literature, animal experiments and patients the authors aim to develop a detailed description of the regulatory mechanisms governing healthy blood cell formation and CML therapy response. The model is used to derive hypotheses explaining why some patients respond to tyrosine kinase inhibitors (TKI) better than others. Based on the model simulations the authors seek predictors of TKI efficacy and for concepts to improve CML therapy.


    (1) The authors start from all possible ordinary differential equation models which describe positive and negative regulations of proliferation rates and self-renewal/differentiation probabilities. The models account for hematopoietic stem cells, multipotent progenitors, terminally differentiated myeloid cells, and terminally differentiated lymphoid cells. Using an automated approach referred to as design space analysis (DSA) the authors exclude models with unfeasible qualitative dynamics. Using data from mouse experiments the authors exclude all regulatory configurations except one. This systematic approach combining model analysis and data from various sources is clearly a strength of the work.

    (2) The authors consider a large number of parameter sets that are in line with physiological steady-state cell counts and realistic responses to system perturbations. Thus the authors can potentially account for inter-patient differences.

    (3) The model predictions are compared to experimental and published data. The proposed predictors of TKI efficacy are tested on retrospective patient data.


    (1) In my opinion the sub-model of leukemic cells requires a more solid justification. The authors assume that the configuration of regulatory loops and most key parameters are identical for normal and leukemic cells. The only difference the proposed model accounts for is that leukemic cells exhibit a weaker response to the feedback signal acting on stem cell self-renewal. The weaker response of leukemic stem cells is justified by data from the literature supporting differential responses to CCL3. However, the authors propose no justification for the assumption that all other parameters, such as proliferation rates or maximal self-renewal probabilities, are identical or have minor impacts.

    (2) The authors come to the conclusion that "a key predictor of refractory response to TKI treatment is an increased probability of self-renewal of normal hematopoietic stem cells" (Abstract). This conclusion is, in my opinion, not fully supported by the model as it is. In the model, it is assumed that normal and leukemic stem cells have the same maximal self-renewal probability. Only the regulation of self-renewal by feedback signals is different. The parameter which is a predictor in the presented analysis (p_{0,max}) is the maximal self-renewal probability of both normal AND leukemic stem cells. Therefore, the conclusion that normal stem cell self-renewal is a predictor of TKI response is, in my opinion, questionable. If I understand the analysis correctly, the authors show the following: Under the assumptions that the maximal self-renewal probability of normal and leukemic stem cells is identical and that the feedback inhibition of self-renewal is weaker in leukemic stem cells compared to normal stem cells, the maximal self-renewal probability of the two stem cell populations is a predictor of TKI response. Notably, if the value of maximal self-renewal probability is increased, the self-renewal probability of leukemic and normal stem cells increases simultaneously at all time points. Therefore, I find it difficult to argue that normal stem cell self-renewal [as opposed to leukemic stem cell self-renewal] is the relevant quantity.

    (3) The simulation of differentiation therapy is interesting, however, due to a lack of knowledge in the field, the specific impacts of such therapy on normal versus leukemic cell differentiation have to be rather hypothetical.

    (4) The used patient cohort is very small (n = 21).

    The proposed model of the regulations governing blood cell formation is a valuable contribution to the fields of computational modeling and experimental hematology. The derived predictors of TKI efficacy are potentially useful.

  3. Reviewer #2 (Public Review):

    The authors want to capture the dynamics of CML therapy with TKI and understand why some patients fail to respond to therapy (primary resistance). They develop a mathematical model of hematopoiesis that includes stem cells, progenitor cells, and mature cells linked through feedback mechanisms. They explore parameter space using sophisticated algorithms to reduce this parameter space and the potential models to one final model and then apply it to chronic myeloid leukemia in the chronic phase under therapy with a tyrosine kinase inhibitor. The novelty in the model is the feedback mechanism introduced and the concomitant animal model data to understand the parameters.

    The model is tractable and yet captures important physiologic aspects of hematopoiesis that have not been explored previously in CML. The animal data to validate it is also quite important. Finally, the application of the model to clinical data illustrates its applicability to real clinical scenarios and provides interesting insights.

    One concern is whether the short-term transplantation experiments truly reflect the steady state of hematopoiesis and how CML develops in humans.

    It is possible that the model can be applied to other hematologic conditions such as myeloproliferative disorders since one would expect the dynamics and interactions to be similar.

  4. Reviewer #3 (Public Review):

    Rodriguez et al. develop a nonlinear ordinary differential equation model of hematopoiesis under normal and chronic myeloid leukaemia (CML) conditions, incorporating feedback control, lineage branching, and signaling between normal and CML cells. Design space analysis is used to identify viable models of cell-cell signalling interaction. Data from mouse models are used to refine the set of cell-cell interactions considered viable, resulting in a novel feedback-feedforward model. Through this framework, the response to tyrosine kinase inhibitor (TKI) therapy is analysed. Model behaviour is qualitatively consistent with experimental data from mouse models, and clinical data. In particular, the model demonstrates varying responses to tyrosine kinase inhibitor therapy across a range of parameter sets consistent with "normal" hematopoietic cell counts; and predicts that a relatively high proportion of leukemic hematopoietic stem cells is a contributor to (though does not guarantee) primary tyrosine kinase inhibitor resistance, consistent with experimental and clinical data.

    Mathematical modelling in the work is validated using both experimental and clinical data.

    The approach to model selection and identification of reasonable parameter regions is interesting and appealing, particularly in the context of modelling processes such as CML which can exhibit significant heterogeneity between patients.

    I expect that this work will be useful to the community, as the approach employed in this work could be readily adapted to study other similar problems (for example, different conditions or treatments), provided that suitable experimental and/or clinical data are collected or available.

    The work is supported by extensive supplementary material, clearly documenting in detail the techniques involved and assumptions made.

    Clinical data from CML patients treated with TKI therapy is limited (n=21).

    As acknowledged by the authors, there are some physiological aspects that may be important that are not modelled; including stem cell-niche interactions in the bone marrow microenvironment, and interactions with immune cells.