Optimal experimental design for mathematical models of haematopoiesis.

The haematopoietic system has a highly regulated and complex structure in which cells are organized to successfully create and maintain new blood cells. It is known that feedback regulation is crucial to tightly control this system, but the specific mechanisms by which control is exerted are not completely understood. In this work, we aim to uncover the underlying mechanisms in haematopoiesis by conducting perturbation experiments, where animal subjects are exposed to an external agent in order to observe the system response and evolution. We have developed a novel Bayesian hierarchical framework for optimal design of perturbation experiments and proper analysis of the data collected. We use a deterministic model that accounts for feedback and feedforward regulation on cell division rates and self-renewal probabilities. A significant obstacle is that the experimental data are not longitudinal, rather each data point corresponds to a different animal. We overcome this difficulty by modelling the unobserved cellular levels as latent variables. We then use principles of Bayesian experimental design to optimally distribute time points at which the haematopoietic cells are quantified. We evaluate our approach using synthetic and real experimental data and show that an optimal design can lead to better estimates of model parameters

Mathematical Modeling of Malignant Myelopoiesis: Optimal Experimental Design and Targeted Therapy

Chronic myeloid leukemia (CML) is a blood cancer in which there is dysregulation of maturing myeloid cells (granulocytes) driven by a chromosomal mutation which creates the fusion gene, BCR-ABL1. Although there has been much progress in the treatment of CML using tyrosine kinase inhibitors (TKI), there are still unmet clinical needs. For example, there is still a small cohort of patients who, for reasons that are still unknown, do not respond to TKI treatment. Further, a significant proportion of patients who appear to have a complete molecular remission while on TKIs experience a relapse of CML when TKI treatment is discontinued. Mathematical modeling of CML hematopoiesis can provide insight on these processes. Current mathematical models of CML are highly simplified (e.g., linear) and have been used to estimate treatment-related model parameters, but fail to describe the mechanisms that underlie primary resistance and treatment-free remission. Here, we explore how more physiologically accurate, data-driven mathematical models of CML hematopoiesis that incorporate feedback control and lineage branching can provide such insight. Although it is recognized that feedback plays a role in CML hematopoiesis, the interactions are poorly understood. In many cases, we don’t know which cell types are providing and receiving the feedback, what signals are used, and what aspects of proliferative cell behavior they influence (i.e. cell cycle speed, renewal probability, or progeny fate choice). Here, we propose to use mathematical modeling combined with data from single cell transcriptomics to help sort this out. We develop an automated method for model selection that integrates data gleaned from experiments and single cell RNA sequencing to select plausible classes of feedback models. We first apply this approach to normal hematopoiesis and identify models that have desired system properties, e.g., stable equilibria, and make predictions about system behavior upon perturbation. New experiments are presented that validate model predictions. We use a Bayesian utility theory approach to determine the optimal experimental design that allows for identification of model parameters with maximum precision. When extended to incorporate CML hematopoiesis, our initial assessment shows that feedback/branching models are more robust, have a better fit to alternative patterns of patient response than simple linear models, and suggest new treatment strategies

Predictive nonlinear modeling of malignant myelopoiesis and tyrosine kinase inhibitor therapy

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

Predictive nonlinear modeling of malignant myelopoiesis and tyrosine kinase inhibitor therapy

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