The ecology in the hematopoietic stem cell niche determines the clinical outcome in chronic myeloid leukemia

Dynamically adjusted cell fate decisions and resilience to mutant invasion during steady-state hematopoiesis revealed by an experimentally parameterized mathematical model

A major next step in hematopoietic stem cell (HSC) biology is to enhance our quantitative understanding of cellular and evolutionary dynamics involved in undisturbed hematopoiesis. Mathematical models have been and continue to be key in this respect, and are most powerful when parameterized experimentally and containing sufficient biological complexity. In this paper, we use data from label propagation experiments in mice to parameterize a mathematical model of hematopoiesis that includes homeostatic control mechanisms as well as clonal evolution. We find that nonlinear feedback control can drastically change the interpretation of kinetic estimates at homeostasis. This suggests that short-term HSC and multipotent progenitors can dynamically adjust to sustain themselves temporarily in the absence of long-term HSCs, even if they differentiate more often than they self-renew in undisturbed homeostasis. Additionally, the presence of feedback control in the model renders the system resilient against mutant invasion. Invasion barriers, however, can be overcome by a combination of age-related changes in stem cell differentiation and evolutionary niche construction dynamics based on a mutant-associated inflammatory environment. This helps us understand the evolution of e.g., TET2 or DNMT3A mutants, and how to potentially reduce mutant burden.

Mathematical modelling, selection and hierarchical inference to determine the minimal dose in IFNα therapy against myeloproliferative neoplasms

Myeloproliferative neoplasms (MPN) are blood cancers that appear after acquiring a driver mutation in a hematopoietic stem cell. These hematological malignancies result in the overproduction of mature blood cells and, if not treated, induce a risk of cardiovascular events and thrombosis. Pegylated IFN$\alpha $ is commonly used to treat MPN, but no clear guidelines exist concerning the dose prescribed to patients. We applied a model selection procedure and ran a hierarchical Bayesian inference method to decipher how dose variations impact the response to the therapy. We inferred that IFN$\alpha $ acts on mutated stem cells by inducing their differentiation into progenitor cells; the higher the dose, the higher the effect. We found that the treatment can induce long-term remission when a sufficient (patient-dependent) dose is reached. We determined this minimal dose for individuals in a cohort of patients and estimated the most suitable starting dose to give to a new patient to increase the chances of being cured.

The importance of host physical niches for the stability of gut microbiome composition

Gut bacteria are prevalent throughout the Metazoa and form complex microbial communities associated with food breakdown, nutrient provision and disease prevention. How hosts acquire and maintain a consistent bacterial flora remains mysterious even in the best-studied animals, including humans, mice, fishes, squid, bugs, worms and flies. This essay visits the evidence that hosts have co-evolved relationships with specific bacteria and that some of these relationships are supported by specialized physical niches that select, sequester and maintain microbial symbionts. Genetics approaches could uncover the mechanisms for recruiting and maintaining the stable and consistent members of the microbiome. This article is part of the theme issue 'Sculpting the microbiome: how host factors determine and respond to microbial colonization'.

Computational modeling reveals key factors driving treatment-free remission in chronic myeloid leukemia patients

Patients with chronic myeloid leukemia (CML) who receive tyrosine kinase inhibitors (TKIs) have been known to achieve treatment-free remission (TFR) upon discontinuing treatment. However, the underlying mechanisms of this phenomenon remain incompletely understood. This study aims to elucidate the mechanism of TFR in CML patients, focusing on the feedback interaction between leukemia stem cells and the bone marrow microenvironment. We have developed a mathematical model to explore the interplay between leukemia stem cells and the bone marrow microenvironment, allowing for the simulation of CML progression dynamics. Our proposed model reveals a dichotomous response following TKI discontinuation, with two distinct patient groups emerging: one prone to early molecular relapse and the other capable of achieving long-term TFR after treatment cessation. This finding aligns with clinical observations and underscores the essential role of feedback interaction between leukemic cells and the tumor microenvironment in sustaining TFR. Notably, we have shown that the ratio of leukemia cells in peripheral blood (PBLC) and the tumor microenvironment (TME) index can be a valuable predictive tool for identifying patients likely to achieve TFR after discontinuing treatment. This study provides fresh insights into the mechanism of TFR in CML patients and underscores the significance of microenvironmental control in achieving TFR.

FitMultiCell: simulating and parameterizing computational models of multi-scale and multi-cellular processes

MOTIVATION

Biological tissues are dynamic and highly organized. Multi-scale models are helpful tools to analyse and understand the processes determining tissue dynamics. These models usually depend on parameters that need to be inferred from experimental data to achieve a quantitative understanding, to predict the response to perturbations, and to evaluate competing hypotheses. However, even advanced inference approaches such as approximate Bayesian computation (ABC) are difficult to apply due to the computational complexity of the simulation of multi-scale models. Thus, there is a need for a scalable pipeline for modeling, simulating, and parameterizing multi-scale models of multi-cellular processes.

RESULTS

Here, we present FitMultiCell, a computationally efficient and user-friendly open-source pipeline that can handle the full workflow of modeling, simulating, and parameterizing for multi-scale models of multi-cellular processes. The pipeline is modular and integrates the modeling and simulation tool Morpheus and the statistical inference tool pyABC. The easy integration of high-performance infrastructure allows to scale to computationally expensive problems. The introduction of a novel standard for the formulation of parameter inference problems for multi-scale models additionally ensures reproducibility and reusability. By applying the pipeline to multiple biological problems, we demonstrate its broad applicability, which will benefit in particular image-based systems biology.

AVAILABILITY AND IMPLEMENTATION

FitMultiCell is available open-source at https://gitlab.com/fitmulticell/fit.

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.

Open problems in mathematical biology

Biology is data-rich, and it is equally rich in concepts and hypotheses. Part of trying to understand biological processes and systems is therefore to confront our ideas and hypotheses with data using statistical methods to determine the extent to which our hypotheses agree with reality. But doing so in a systematic way is becoming increasingly challenging as our hypotheses become more detailed, and our data becomes more complex. Mathematical methods are therefore gaining in importance across the life- and biomedical sciences. Mathematical models allow us to test our understanding, make testable predictions about future behaviour, and gain insights into how we can control the behaviour of biological systems. It has been argued that mathematical methods can be of great benefit to biologists to make sense of data. But mathematics and mathematicians are set to benefit equally from considering the often bewildering complexity inherent to living systems. Here we present a small selection of open problems and challenges in mathematical biology. We have chosen these open problems because they are of both biological and mathematical interest.

Changing our view of the Schistosoma granuloma to an ecological standpoint

Schistosomiasis, a neglected parasitic tropical disease that has plagued humans for centuries, remains a major public health burden. A primary challenge to understanding schistosomiasis is deciphering the most remarkable pathological feature of this disease, the granuloma - a highly dynamic and self-organized structure formed by both host and parasite components. Granulomas are considered a remarkable example of how parasites evolved with their hosts to establish complex and intimate associations. However, much remains unclear regarding life within the granuloma, and strategies to restrain its development are still lacking. Here we explore current information on the hepatic Schistosoma mansoni granuloma in the light of Ecology and propose that this intricate structure acts as a real ecosystem. The schistosomal granuloma is formed by cells (biotic component), protein scaffolds, fibres, and chemical compounds (abiotic components) with inputs/outputs of energy and matter, as complex as in classical ecosystems. We review the distinct cell populations ('species') within the granuloma and examine how they integrate with each other and interact with their microenvironment to form a multifaceted cell community in different space-time frames. The colonization of the hepatic tissue to form granulomas is explained from the point of view of an ecological succession whereby a community is able to modify its physical environment, creating conditions and resources for ecosystem construction. Remarkably, the granuloma represents a dynamic evolutionary system that undergoes progressive changes in the 'species' that compose its community over time. In line with ecological concepts, we examine the granuloma not only as a place where a community of cells is settled (spatial niche or habitat) but also as a site in which the functional activities of these combined populations occur in an orchestrated way in response to microenvironmental gradients such as cytokines and egg antigens. Finally, we assert how the levels of organization of cellular components in a granuloma as conventionally defined by Cell Biology can fit perfectly into a hierarchical structure of biological systems as defined by Ecology. By rethinking the granuloma as an integrating and evolving ecosystem, we draw attention to the inner workings of this structure that are central to the understanding of schistosomiasis and could guide its future treatment.

Computational modeling of stem and progenitor cell kinetics identifies plausible hematopoietic lineage hierarchies

Classically, hematopoietic stem cell (HSC) differentiation is assumed to occur via progenitor compartments of decreasing plasticity and increasing maturity in a specific, hierarchical manner. The classical hierarchy has been challenged in the past by alternative differentiation pathways. We abstracted experimental evidence into 10 differentiation hierarchies, each comprising 7 cell type compartments. By fitting ordinary differential equation models with realistic waiting time distributions to time-resolved data of differentiating HSCs from 10 healthy human donors, we identified plausible lineage hierarchies and rejected others. We found that, for most donors, the classical model of hematopoiesis is preferred. Surprisingly, multipotent lymphoid progenitor differentiation into granulocyte-monocyte progenitors is plausible in 90% of samples. An in silico analysis confirmed that, even for strong noise, the classical model can be identified robustly. Our computational approach infers differentiation hierarchies in a personalized fashion and can be used to gain insights into kinetic alterations of diseased hematopoiesis.

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We assembled 10 lineage hierarchy models of human hematopoiesis

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Multiparameter immunophenotyping determines HSC differentiation for 10 healthy donors

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ODE fitting and model selection allows to identify plausible hierarchies

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A simulation study confirms robustness of model selection for different noise levels

Importance of Stability Analysis When Using Nonlinear Semimechanistic Models to Describe Drug-Induced Hematotoxicity

Stability analysis, often overlooked in pharmacometrics, is essential to explore dynamical systems. The model developed by Friberg et al.¹ to describe drug‐induced hematotoxicity is widely used to support decisions across drug development, and parameter values are often identified from observed blood counts. We use stability analysis to study the parametric dependence of stable and unstable solutions of several Friberg‐type models and highlight the risks associated with system instability in the context of nonlinear mixed effects modeling. We emphasize the consequences of unstable solutions on prediction performance by demonstrating nonbiological system behaviors in a real case study of drug‐induced thrombocytopenia. Ultimately, we provide simple criteria for identifying parameters associated with stable solutions of Friberg‐type models. For instance, in the original Friberg model, we find that stability depends only on the parameter that governs the feedback from peripheral cells to progenitors and provide the exact range of values that results in stable solutions.

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

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

Designing combination therapies using multiple optimal controls

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

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.

Mapping and targeting of the leukemic microenvironment

Numerous studies support a role of the microenvironment in maintenance of the leukemic clone, as well as in treatment resistance. It is clear that disruption of the normal bone marrow microenvironment is sufficient to promote leukemic transformation and survival in both a cell autonomous and non-cell autonomous manner. In this review, we provide a snapshot of the various cell types shown to contribute to the leukemic microenvironment as well as treatment resistance. Several of these studies suggest that leukemic blasts occupy specific cellular and biochemical "niches." Effective dissection of critical leukemic niche components using single-cell approaches has allowed a more precise and extensive characterization of complexity that underpins both the healthy and malignant bone marrow microenvironment. Knowledge gained from these observations can have an important impact in the development of microenvironment-directed targeted approaches aimed at mitigating disease relapse.

Optimal control of acute myeloid leukaemia

Acute myeloid leukaemia (AML) is a blood cancer affecting haematopoietic stem cells. AML is routinely treated with chemotherapy, and so it is of great interest to develop optimal chemotherapy treatment strategies. In this work, we incorporate an immune response into a stem cell model of AML, since we find that previous models lacking an immune response are inappropriate for deriving optimal control strategies. Using optimal control theory, we produce continuous controls and bang-bang controls, corresponding to a range of objectives and parameter choices. Through example calculations, we provide a practical approach to applying optimal control using Pontryagin's Maximum Principle. In particular, we describe and explore factors that have a profound influence on numerical convergence. We find that the convergence behaviour is sensitive to the method of control updating, the nature of the control, and to the relative weighting of terms in the objective function. All codes we use to implement optimal control are made available.

Training improves inhibitory control in water rescue dogs

Inhibitory control is a collection of several processes that are aimed to refrain from any impulsive response in the subject during inappropriate situations. Evidence suggests that in dogs, the inhibitory control is affected by domestication process, but also experiences during ontogeny could be an important driver in acquiring inhibitory control. The aim of the study was to compare the performance of highly trained dogs (i.e., water rescue dogs) and pet dogs in the A-not-B task. In this procedure, the animals have to inhibit their urge of going to a previous reinforced place. The results showed that the trained dogs committed fewer errors in the task than the pet dogs suggesting a better inhibitory control. This result could indicate that inhibitory control is a flexible ability affected by ontogenetic processes such as the training experience.

Understanding Hematological Toxicities Using Mathematical Modeling

Balancing antitumor efficacy with toxicity is a significant challenge, and drug-induced myelosuppression is a common dose-limiting toxicity of cancer treatments. Mathematical modeling has proven to be a powerful ally in this field, scaling results from animal models to humans, and designing optimized treatment regimens. Here we outline existing mathematical approaches for studying bone marrow toxicity, identify gaps in current understanding, and make future recommendations to advance this vital field of safety research further.

Feedback regulation in a stem cell model with acute myeloid leukaemia

Background

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

Results

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

Conclusions

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

Chemokines as a Conductor of Bone Marrow Microenvironment in Chronic Myeloid Leukemia

All blood lineage cells are generated from hematopoietic stem cells (HSCs), which reside in bone marrow after birth. HSCs self-renew, proliferate, and differentiate into mature progeny under the control of local microenvironments including hematopoietic niche, which can deliver regulatory signals in the form of bound or secreted molecules and from physical cues such as oxygen tension and shear stress. Among these mediators, accumulating evidence indicates the potential involvement of several chemokines, particularly CXCL12, in the interaction between HSCs and bone marrow microenvironments. Fusion between breakpoint cluster region (BCR) and Abelson murine leukemia viral oncogene homolog (ABL)-1 gene gives rise to BCR-ABL protein with a constitutive tyrosine kinase activity and transforms HSCs and/or hematopoietic progenitor cells (HPCs) into disease-propagating leukemia stem cells (LSCs) in chronic myeloid leukemia (CML). LSCs can self-renew, proliferate, and differentiate under the influence of the signals delivered by bone marrow microenvironments including niche, as HSCs can. Thus, the interaction with bone marrow microenvironments is indispensable for the initiation, maintenance, and progression of CML. Moreover, the crosstalk between LSCs and bone marrow microenvironments can contribute to some instances of therapeutic resistance. Furthermore, evidence is accumulating to indicate the important roles of bone marrow microenvironment-derived chemokines. Hence, we will herein discuss the roles of chemokines in CML with a focus on bone marrow microenvironments.

CBP/Catenin antagonists: Targeting LSCs' Achilles heel

Cancer stem cells (CSCs), including leukemia stem cells (LSCs), exhibit self-renewal capacity and differentiation potential and have the capacity to maintain or renew and propagate a tumor/leukemia. The initial isolation of CSCs/LSCs was in adult myelogenous leukemia, although more recently, the existence of CSCs in a wide variety of other cancers has been reported. CSCs, in general, and LSCs, specifically with respect to this review, are responsible for initiation of disease, therapeutic resistance and ultimately disease relapse. One key focus in cancer research over the past decade has been the development of therapies that safely eliminate the LSC/CSC population. One major obstacle to this goal is the identification of key mechanisms that distinguish LSCs from normal endogenous hematopoietic stem cells. An additional daunting feature that has recently come to light with advances in next-generation sequencing and single-cell sequencing is the heterogeneity within leukemias/tumors, with multiple combinations of mutations, gain and loss of function of genes, and so on being capable of driving disease, even within the CSC/LSC population. The focus of this review/perspective is on our work in identifying and validating, in both chronic myelogenous leukemia and acute lymphoblastic leukemia, a safe and efficacious mechanism to target an evolutionarily conserved signaling nexus, which constitutes a common "Achilles heel" for LSCs/CSCs, using small molecule-specific CBP/catenin antagonists.

Second tyrosine kinase inhibitor discontinuation attempt in patients with chronic myeloid leukemia

BACKGROUND

Several studies have demonstrated that approximately one-half of patients with chronic myeloid leukemia (CML) who receive treatment with tyrosine kinase inhibitors (TKIs) and achieve and maintain a deep molecular response (DMR) are able to successfully discontinue therapy. In patients who have a molecular relapse, a DMR is rapidly regained upon treatment re-initiation.

METHODS

The authors report the results from RE-STIM, a French observational, multicenter study that evaluated treatment-free remission (TFR) in 70 patients who re-attempted TKI discontinuation after a first unsuccessful attempt. After the second TKI discontinuation attempt, the trigger for treatment re-introduction was the loss of a major molecular response in all patients.

RESULTS

The median follow-up was 38.3 months (range, 4.7-117 months), and 45 patients (64.3%) lost a major molecular response after a median time off therapy of 5.3 months (range, 2-42 months). TFR rates at 12, 24, and 36 months were 48% (95% confidence interval [CI], 37.6%-61.5%), 42% (95% CI, 31.5%-55.4%), and 35% (95% CI, 24.4%-49.4%), respectively. No progression toward advanced-phase CML occurred, and no efficacy issue was observed upon TKI re-introduction. In univariate analysis, the speed of molecular relapse after the first TKI discontinuation attempt was the only factor significantly associated with outcome. The TFR rate at 24 months was 72% (95% CI, 48.8%-100%) in patients who remained in DMR within the first 3 months after the first TKI discontinuation and 36% (95% CI, 25.8%-51.3%) for others.

CONCLUSIONS

This study is the first to demonstrate that a second TKI discontinuation attempt is safe and that a first failed attempt at discontinuing TKI does not preclude a second successful attempt. Cancer 2017;123:4403-10. © 2017 American Cancer Society.

Chronic Myeloid Leukemia in the Era of Tyrosine Kinase Inhibitors: An Evolving Paradigm of Molecularly Targeted Therapy

Chronic myeloid leukemia (CML) is a myeloproliferative neoplasm, characterized by the unrestrained expansion of pluripotent hematopoietic stem cells. CML was the first malignancy in which a unique chromosomal abnormality was identified and a pathophysiologic association was suggested. The hallmark of CML is a reciprocal chromosomal translocation between the long arms of chromosomes 9 and 22, t(9; 22)(q34; q11), creating a derivative 9q+ and a shortened 22q-. The latter, known as the Philadelphia (Ph) chromosome, harbors the breakpoint cluster region-abelson (BCR-ABL) fusion gene, encoding the constitutively active BCR-ABL tyrosine kinase that is necessary and sufficient for initiating CML. The successful implementation of tyrosine kinase inhibitors (TKIs) for the treatment of CML remains a flagship for molecularly targeted therapy in cancer. TKIs have changed the clinical course of CML; however, some patients nonetheless demonstrate primary or secondary resistance to such therapy and require an alternative therapeutic strategy. Therefore, the assessment of early response to treatment with TKIs has become an important tool in the clinical monitoring of CML patients. Although mutations in the BCR-ABL have proven to be the most prominent mechanism of resistance to TKIs, other mechanisms-either rendering the leukemic cells still dependent on BCR-ABL activity or supporting oncogenic properties of the leukemic cells independent of BCR-ABL signaling-have been identified. This article provides an overview of the current understanding of CML pathogenesis; recommendations for diagnostic tools, treatment strategies, and management guidelines; and highlights the BCR-ABL-dependent and -independent mechanisms that contribute to the development of resistance to TKIs.

Dynamical models of mutated chronic myelogenous leukemia cells for a post-imatinib treatment scenario: Response to dasatinib or nilotinib therapy

Targeted inhibition of the oncogenic BCR-ABL1 fusion protein using the ABL1 tyrosine kinase inhibitor imatinib has become standard therapy for chronic myelogenous leukemia (CML), with most patients reaching total and durable remission. However, a significant fraction of patients develop resistance, commonly due to mutated ABL1 kinase domains. This motivated development of second-generation drugs with broadened or altered protein kinase selectivity profiles, including dasatinib and nilotinib. Imatinib-resistant patients undergoing treatment with second-line drugs typically develop resistance to them, but dynamic and clonal properties of this response differ. Shared, however, is the observation of clonal competition, reflected in patterns of successive dominance of individual clones. We present three deterministic mathematical models to study the origins of clinically observed dynamics. Each model is a system of coupled first-order differential equations, considering populations of three mutated active stem cell strains and three associated pools of differentiated cells; two models allow for activation of quiescent stem cells. Each approach is distinguished by the way proliferation rates of the primary stem cell reservoir are modulated. Previous studies have concentrated on simulating the response of wild-type leukemic cells to imatinib administration; our focus is on modelling the time dependence of imatinib-resistant clones upon subsequent exposure to dasatinib or nilotinib. Performance of the three computational schemes to reproduce selected CML patient profiles is assessed. While some simple cases can be approximated by a basic design that does not invoke quiescence, others are more complex and require involvement of non-cycling stem cells for reproduction. We implement a new feedback mechanism for regulation of coupling between cycling and non-cycling stem cell reservoirs that depends on total cell populations. A bifurcation landscape analysis is also performed for solutions to the basic ansatz. Computational models reproducing patient data illustrate potential dynamic mechanisms that may guide optimization of therapy of drug resistant CML.

The proportion of cancer-related entries in PubMed has increased considerably; is cancer truly "The Emperor of All Maladies"?

In this work, the public database of biomedical literature PubMed was mined using queries with combinations of keywords and year restrictions. It was found that the proportion of Cancer-related entries per year in PubMed has risen from around 6% in 1950 to more than 16% in 2016. This increase is not shared by other conditions such as AIDS, Malaria, Tuberculosis, Diabetes, Cardiovascular, Stroke and Infection some of which have, on the contrary, decreased as a proportion of the total entries per year. Organ-related queries were performed to analyse the variation of some specific cancers. A series of queries related to incidence, funding, and relationship with DNA, Computing and Mathematics, were performed to test correlation between the keywords, with the hope of elucidating the cause behind the rise of Cancer in PubMed. Interestingly, the proportion of Cancer-related entries that contain “DNA”, “Computational” or “Mathematical” have increased, which suggests that the impact of these scientific advances on Cancer has been stronger than in other conditions. It is important to highlight that the results obtained with the data mining approach here presented are limited to the presence or absence of the keywords on a single, yet extensive, database. Therefore, results should be observed with caution. All the data used for this work is publicly available through PubMed and the UK’s Office for National Statistics. All queries and figures were generated with the software platform Matlab and the files are available as supplementary material.

Identifying niche-mediated regulatory factors of stem cell phenotypic state: a systems biology approach

Understanding how the cellular niche controls the stem cell phenotype is often hampered due to the complexity of variegated niche composition, its dynamics, and nonlinear stem cell–niche interactions. Here, we propose a systems biology view that considers stem cell–niche interactions as a many‐body problem amenable to simplification by the concept of mean field approximation. This enables approximation of the niche effect on stem cells as a constant field that induces sustained activation/inhibition of specific stem cell signaling pathways in all stem cells within heterogeneous populations exhibiting the same phenotype (niche determinants). This view offers a new basis for the development of single cell‐based computational approaches for identifying niche determinants, which has potential applications in regenerative medicine and tissue engineering.

Systems Analysis of the Dynamic Inflammatory Response to Tissue Damage Reveals Spatiotemporal Properties of the Wound Attractant Gradient

In the acute inflammatory phase following tissue damage, cells of the innate immune system are rapidly recruited to sites of injury by pro-inflammatory mediators released at the wound site. Although advances in live imaging allow us to directly visualize this process in vivo, the precise identity and properties of the primary immune damage attractants remain unclear, as it is currently impossible to directly observe and accurately measure these signals in tissues. Here, we demonstrate that detailed information about the attractant signals can be extracted directly from the in vivo behavior of the responding immune cells. By applying inference-based computational approaches to analyze the in vivo dynamics of the Drosophila inflammatory response, we gain new detailed insight into the spatiotemporal properties of the attractant gradient. In particular, we show that the wound attractant is released by wound margin cells, rather than by the wounded tissue per se, and that it diffuses away from this source at rates far slower than those of previously implicated signals such as H₂O₂ and ATP, ruling out these fast mediators as the primary chemoattractant. We then predict, and experimentally test, how competing attractant signals might interact in space and time to regulate multi-step cell navigation in the complex environment of a healing wound, revealing a period of receptor desensitization after initial exposure to the damage attractant. Extending our analysis to model much larger wounds, we uncover a dynamic behavioral change in the responding immune cells in vivo that is prognostic of whether a wound will subsequently heal or not.

Video Abstract

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Computational modeling of in vivo inflammatory response to tissue damage is applied

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The model infers novel spatiotemporal properties of the wound attractant gradient

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Wound signal is released from the wound edge for 30 min and diffuses at 200 μm²/min

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Modeling two competing wounds reveals a period of immune cell desensitization

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

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

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

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

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

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

A Personalized Framework for Dynamic Modeling of Disease Trajectories in Chronic Lymphocytic Leukemia

Chronic lymphocytic leukemia (CLL) is the most common peripheral blood and bone marrow cancer in the developed world. This manuscript proposes mathematical model equations representing the disease dynamics of B-cell CLL. We interconnect delay differential cell cycle models in each of the tumor-involved disease centers using physiologically relevant cell migration. We further introduce five hypothetical case studies representing CLL heterogeneity commonly seen in clinical practice and demonstrate how the proposed CLL model framework may capture disease pathophysiology across patient types. We conclude by exploring the capacity of the proposed temporally- and spatially distributed model to capture the heterogeneity of CLL disease progression. By using global sensitivity analysis, the critical parameters influencing disease trajectory over space and time are: 1) the initial number of CLL cells in peripheral blood, the number of involved lymph nodes, the presence and degree of splenomegaly; 2) the migratory fraction of nonproliferating as well as proliferating CLL cells from bone marrow into blood and of proliferating CLL cells from blood into lymph nodes; and 3) the parameters inducing nonproliferative cells to proliferate. The proposed model offers a practical platform that may be explored in future personalized patient protocols once validated.

Mathematical and Statistical Techniques for Systems Medicine: The Wnt Signaling Pathway as a Case Study

The last decade has seen an explosion in models that describe phenomena in systems medicine. Such models are especially useful for studying signaling pathways, such as the Wnt pathway. In this chapter we use the Wnt pathway to showcase current mathematical and statistical techniques that enable modelers to gain insight into (models of) gene regulation and generate testable predictions. We introduce a range of modeling frameworks, but focus on ordinary differential equation (ODE) models since they remain the most widely used approach in systems biology and medicine and continue to offer great potential. We present methods for the analysis of a single model, comprising applications of standard dynamical systems approaches such as nondimensionalization, steady state, asymptotic and sensitivity analysis, and more recent statistical and algebraic approaches to compare models with data. We present parameter estimation and model comparison techniques, focusing on Bayesian analysis and coplanarity via algebraic geometry. Our intention is that this (non-exhaustive) review may serve as a useful starting point for the analysis of models in systems medicine.

Chronic myeloid leukemia: advances in understanding disease biology and mechanisms of resistance to tyrosine kinase inhibitors

The successful implementation of tyrosine kinase inhibitors (TKIs) for the treatment of chronic myeloid leukemia (CML) remains a flagship for molecularly targeted therapy in cancer. This focused review highlights critical elements of the underlying biology of CML and provides a summary of the molecular mechanisms that lead to TKI resistance: BCR-ABL1 mutation-based resistance and therapy escape through alternative pathway activation despite inhibition of BCR-ABL1 tyrosine kinase activity. We direct attention to the most current manifestations of these issues, including emergence of pan-TKI-resistant BCR-ABL1 compound mutants, new strategies for identification and therapeutic targeting of alternative pathways, and the exciting, controversial topic of cessation of TKI therapy leading to durable treatment-free remissions for a subset of patients. Further gains in our understanding of the biology of Philadelphia chromosome-positive (Ph-positive) leukemia and mechanisms of resistance to BCR-ABL1 TKIs will benefit patients and also provide a blueprint for similar discovery in other cancers.

Parameter-free methods distinguish Wnt pathway models and guide design of experiments

The canonical Wnt signaling pathway, mediated by β-catenin, is crucially involved in development, adult stem cell tissue maintenance, and a host of diseases including cancer. We analyze existing mathematical models of Wnt and compare them to a new Wnt signaling model that targets spatial localization; our aim is to distinguish between the models and distill biological insight from them. Using Bayesian methods we infer parameters for each model from mammalian Wnt signaling data and find that all models can fit this time course. We appeal to algebraic methods (concepts from chemical reaction network theory and matroid theory) to analyze the models without recourse to specific parameter values. These approaches provide insight into aspects of Wnt regulation: the new model, via control of shuttling and degradation parameters, permits multiple stable steady states corresponding to stem-like vs. committed cell states in the differentiation hierarchy. Our analysis also identifies groups of variables that should be measured to fully characterize and discriminate between competing models, and thus serves as a guide for performing minimal experiments for model comparison.

The inherent metastasis of leukaemia and its exploitation by sonodynamic therapy

Nearly all cancers are linked by the inexorable phenotype of metastasis as malignant growths have the capability to spread from their place of origin to distant sites throughout the body. While different cancers may have various propensities to migrate towards specific locations, they are all linked by this unifying principal. Unlike most neoplasms, leukaemia has inherent cell motility as leukocytes are required to move throughout the vascular system, suggesting that no mutations are required for anchorage independent growth. As such, it seems likely that leukaemias are inherently metastatic, endowed with the deadliest phenotype of cancer simply due to cell of origin. This article presents the biology of metastasis development and how leukaemia cells are inherently provided these phenotypic characteristics. It is then proposed how clinicians may be able to exploit the motility of leukaemia and metastatic emboli of other cancer types through an approach known as sonodynamic therapy (SDT), a treatment modality that combines chemotherapeutic agents with ultrasound to preferentially damage malignant cells. As experimental evidence has indicated, SDT is a promising therapeutic approach in need of clinical testing for further validation.

Epithelial-Mesenchymal Transition in Metastatic Cancer Cell Populations Affects Tumor Dormancy in a Simple Mathematical Model

Signaling from the c-Met receptor tyrosine kinase is associated with progression and metastasis of epithelial tumors. c-Met, the receptor for hepatocyte growth factor, triggers epithelial-mesenchymal transition (EMT) of cultured cells, which is thought to drive migration of tumor cells and confer on them critical stem cell properties. Here, we employ mathematical modeling to better understand how EMT affects population dynamics in metastatic tumors. We find that without intervention, micrometastatic tumors reach a steady-state population. While the rates of proliferation, senescence and death only have subtle effects on the steady state, changes in the frequency of EMT dramatically alter population dynamics towards exponential growth. We also find that therapies targeting cell proliferation or cell death are markedly more successful when combined with one that prevents EMT, though such therapies do little when used alone. Stochastic modeling reveals the probability of tumor recurrence from small numbers of residual differentiated tumor cells. EMT events in metastatic tumors provide a plausible mechanism by which clinically detectable tumors can arise from dormant micrometastatic tumors. Modeling the dynamics of this process demonstrates the benefit of a treatment that eradicates tumor cells and reduces the rate of EMT simultaneously.