The age incidence of chronic myeloid leukemia can be explained by a one-mutation model

Accumulation of Oncogenic Mutations During Progression from Healthy Tissue to Cancer

Cancers are typically fueled by sequential accumulation of driver mutations in a previously healthy cell. Some of these mutations, such as inactivation of the first copy of a tumor suppressor gene, can be neutral, and some, like those resulting in activation of oncogenes, may provide cells with a selective growth advantage. We study a multi-type branching process that starts with healthy tissue in homeostasis and models accumulation of neutral and advantageous mutations on the way to cancer. We provide results regarding the sizes of premalignant populations and the waiting times to the first cell with a particular combination of mutations, including the waiting time to malignancy. Finally, we apply our results to two specific biological settings: initiation of colorectal cancer and age incidence of chronic myeloid leukemia. Our model allows for any order of neutral and advantageous mutations and can be applied to other evolutionary settings.

Minimal Requirements for Cancer Initiation: A Comparative Consideration of Three Prototypes of Human Leukemia

Even if its completed form is complex, cancer originates from one or two events that happened to a single cell. A simplified model can play a role in understanding how cancer initiates at the beginning. The pathophysiology of leukemia has been studied in the most detailed manner among all human cancers. In this review, based on milestone papers and the latest research developments in hematology, acute promyelocytic leukemia (APL), chronic myeloid leukemia (CML), and acute myeloid leukemia (AML) with RUNX1-RUNX1T1 are selected to consider minimal requirements for cancer initiation. A one-hit model can be applied to the initiation of APL and CML whereas a two-hit model is more suitable to the initiation of AML with RUNX1-RUNX1T1 and other AMLs. Even in cancer cells with multiple genetic abnormalities, there must be a few mutant genes critical for the mutant clone to survive and proliferate. Such genes should be identified and characterized in each case in order to develop individualized target therapy.

A mathematical model for cancer risk and accumulation of mutations caused by replication errors and external factors

Replication errors influence mutations, and thus, lifetime cancer risk can be explained by the number of stem-cell divisions. Additionally, mutagens also affect cancer risk, for instance, high-dose radiation exposure increases lifetime cancer risk. However, the influence of low-dose radiation exposure is still unclear because this influence, if any, is very slight. We can assess the minimal influence of the mutagen by virtually comparing the states with and without mutagen using a mathematical model. Here, we constructed a mathematical model to assess the influence of replication errors and mutagens on cancer risk. In our model, replication errors occur with a certain probability during cell division. Mutagens cause mutations at a constant rate. Cell division is arrested when the number of cells reaches the capacity of the cell pool. When the number of cells decreases because of cell death or other reasons, cells resume division. It was assumed that the mutations of cancer driver genes occur stochastically with each mutation and that cancer occurs when the number of cancer driver gene mutations exceeds a certain threshold. We approximated the number of mutations caused by errors and mutagens. Then, we examined whether cancer registry data on cancer risk can be explained only through replication errors. Although the risk of leukemia was not fitted to the model, the risks of esophageal, liver, thyroid, pancreatic, colon, breast, and prostate cancers were explained only by replication errors. Even if the risk was explained by replication errors, the estimated parameters did not always agree with previously reported values. For example, the estimated number of cancer driver genes in lung cancer was larger than the previously reported values. This discrepancy can be partly resolved by assuming the influence of mutagen. First, the influence of mutagens was analyzed using various parameters. The model predicted that the influence of mutagens will appear earlier, when the turnover rate of the tissue is higher and fewer mutations of cancer driver genes were necessary for carcinogenesis. Next, the parameters of lung cancer were re-estimated assuming the influence of mutagens. The estimated parameters were closer to the previously reported values. than when considering only replication errors. Although it may be useful to explain cancer risk by replication errors, it would be biologically more plausible to consider mutagens in cancers in which the effects of mutagens are apparent.

The Erlang distribution approximates the age distribution of incidence of childhood and young adulthood cancers

Background

It is widely believed that cancers develop upon acquiring a particular number of (epi) mutations in driver genes, but the law governing the kinetics of this process is not known. We have previously shown that the age distribution of incidence for the 20 most prevalent cancers of old age is best approximated by the Erlang probability distribution. The Erlang distribution describes the probability of several successive random events occurring by the given time according to the Poisson process, which allows an estimate for the number of critical driver events.

Methods

Here we employ a computational grid search method to find global parameter optima for five probability distributions on the CDC WONDER dataset of the age distribution of childhood and young adulthood cancer incidence.

Results

We show that the Erlang distribution is the only classical probability distribution we found that can adequately model the age distribution of incidence for all studied childhood and young adulthood cancers, in addition to cancers of old age.

Conclusions

This suggests that the Poisson process governs driver accumulation at any age and that the Erlang distribution can be used to determine the number of driver events for any cancer type. The Poisson process implies the fundamentally random timing of driver events and their constant average rate. As waiting times for the occurrence of the required number of driver events are counted in decades, and most cells do not live this long, it suggests that driver mutations accumulate silently in the longest-living dividing cells in the body—the stem cells.

Enhanced risk of cancer in companion animals as a response to the longevity

Cancer is caused by the lifetime accumulation of multiple somatic deformations of the genome and epigenome. At a very low rate, mistakes occur during genomic replication (e.g., mutations or modified epigenetic marks). Long-lived species, such as elephants, are suggested to have evolved mechanisms to slow down the cancer progression. Recently, the life span of companion dogs has increased considerably than before, owing to the improvement of their environment, which has led to an increase in the fraction of companion dogs developing cancer. These findings suggest that short-term responses of cancer risk to longevity differ from long-term responses. In this study, to clarify the situation, we used a simple multi-step model for cancer. The rates of events leading to malignant cancer are assumed to be proportional to those of genomic replication error. Perfect removal of replication error requires a large cost, resulting in the evolution of a positive rate of genomic replication error. The analysis of the model revealed: that, when the environment suddenly becomes benign, the relative importance of cancer enhances, although the age-dependent cancer risk remains unchanged. However, in the long run, the genomic error rate evolves to become smaller and mitigates the cancer risk.

Motion, fixation probability and the choice of an evolutionary process

Seemingly minor details of mathematical and computational models of evolution are known to change the effect of population structure on the outcome of evolutionary processes. For example, birth-death dynamics often result in amplification of selection, while death-birth processes have been associated with suppression. In many biological populations the interaction structure is not static. Instead, members of the population are in motion and can interact with different individuals at different times. In this work we study populations embedded in a flowing medium; the interaction network is then time dependent. We use computer simulations to investigate how this dynamic structure affects the success of invading mutants, and compare these effects for different coupled birth and death processes. Specifically, we show how the speed of the motion impacts the fixation probability of an invading mutant. Flows of different speeds interpolate between evolutionary dynamics on fixed heterogeneous graphs and well-stirred populations; this allows us to systematically compare against known results for static structured populations. We find that motion has an active role in amplifying or suppressing selection by fragmenting and reconnecting the interaction graph. While increasing flow speeds suppress selection for most evolutionary models, we identify characteristic responses to flow for the different update rules we test. In particular we find that selection can be maximally enhanced or suppressed at intermediate flow speeds.

Whether a mutation spreads in a population or not is one of the most important questions in biology. The evolution of cancer and antibiotic resistance, for example, are mediated by invading mutants. Recent work has shown that population structure can have important consequences for the outcome of evolution. For instance, a mutant can have a higher or a lower chance of invasion than in unstructured populations. These effects can depend on seemingly minor details of the evolutionary model, such as the order of birth and death events. Many biological populations are in motion, for example due to external stirring. Experimentally this is known to be important; the performance of mutants in E. coli populations, for example, depends on the rate of mixing. Here, we focus on simulations of populations in a flowing medium, and compare the success of a mutant for different flow speeds. We contrast different evolutionary models, and identify what features of the evolutionary model affect mutant success for different speeds of the flow. We find that the chance of mutant invasion can be at its highest (or lowest) at intermediate flow speeds, depending on the order in which birth and death events occur in the evolutionary process.

Multi-stage models for the failure of complex systems, cascading disasters, and the onset of disease

Complex systems can fail through different routes, often progressing through a series of (rate-limiting) steps and modified by environmental exposures. The onset of disease, cancer in particular, is no different. Multi-stage models provide a simple but very general mathematical framework for studying the failure of complex systems, or equivalently, the onset of disease. They include the Armitage-Doll multi-stage cancer model as a particular case, and have potential to provide new insights into how failures and disease, arise and progress. A method described by E.T. Jaynes is developed to provide an analytical solution for a large class of these models, and highlights connections between the convolution of Laplace transforms, sums of random variables, and Schwinger/Feynman parameterisations. Examples include: exact solutions to the Armitage-Doll model, the sum of Gamma-distributed variables with integer-valued shape parameters, a clonal-growth cancer model, and a model for cascading disasters. Applications and limitations of the approach are discussed in the context of recent cancer research. The model is sufficiently general to be used in many contexts, such as engineering, project management, disease progression, and disaster risk for example, allowing the estimation of failure rates in complex systems and projects. The intended result is a mathematical toolkit for applying multi-stage models to the study of failure rates in complex systems and to the onset of disease, cancer in particular.

A generalized theory of age-dependent carcinogenesis

The Multi-Stage Model of Carcinogenesis (MMC), developed in the 1950 s-70s, postulated carcinogenesis as a Darwinian somatic selection process. The cellular organization of tissues was then poorly understood, with almost nothing known about cancer drivers and stem cells. The MMC paradigm was later confirmed, and cancer incidence was explained as a function of mutation occurrence. However, the MMC has never been tested for its ability to account for the discrepancies in the number of driver mutations and the organization of the stem cell compartments underlying different cancers that still demonstrate nearly universal age-dependent incidence patterns. Here we demonstrate by Monte Carlo modeling the impact of key somatic evolutionary parameters on the MMC performance, revealing that two additional major mechanisms, aging-dependent somatic selection and life history-dependent evolution of species-specific tumor suppressor mechanisms, need to be incorporated into the MMC to make it capable of generalizing cancer incidence across tissues and species.

Editorial note

This article has been through an editorial process in which the authors decide how to respond to the issues raised during peer review. The Reviewing Editor's assessment is that all the issues have been addressed (see decision letter).

Bridging blood cancers and inflammation: The reduced Cancitis model

A novel mechanism-based model - the Cancitis model - describing the interaction of blood cancer and the inflammatory system is proposed, analyzed and validated. The immune response is divided into two components, one where the elimination rate of malignant stem cells is independent of the level of the blood cancer and one where the elimination rate depends on the level of the blood cancer. A dimensional analysis shows that the full 6-dimensional system of nonlinear ordinary differential equations may be reduced to a 2-dimensional system - the reduced Cancitis model - using Fenichel theory. The original 18 parameters appear in the reduced model in 8 groups of parameters. The reduced model is analyzed. Especially the steady states and their dependence on the exogenous inflammatory stimuli are analyzed. A semi-analytic investigation reveals the stability properties of the steady states. Finally, positivity of the system and the existence of an attracting trapping region in the positive octahedron guaranteeing global existence and uniqueness of solutions are proved. The possible topologies of the dynamical system are completely determined as having a Janus structure, where two qualitatively different topologies appear for different sets of parameters. To classify this Janus structure we propose a novel concept in blood cancer - a reproduction ratio R. It determines the topological structure depending on whether it is larger or smaller than a threshold value. Furthermore, it follows that inflammation, affected by the exogenous inflammatory stimulation, may determine the onset and development of blood cancers. The body may manage initial blood cancer as long as the self-renewal rate is not too high, but fails to manage it if an inflammation appears. Thus, inflammation may trigger and drive blood cancers. Finally, the mathematical analysis suggests novel treatment strategies and it is used to discuss the in silico effect of existing treatment, e.g. interferon-α or T-cell therapy, and the impact of malignant cells becoming resistant.

A Simple 3-Parameter Model for Cancer Incidences

We propose a simple 3-parameter model that provides very good fits for incidence curves of 18 common solid cancers even when variations due to different locations, races, or periods are taken into account. From a data perspective, we use model selection (Akaike information criterion) to show that this model, which is based on the Weibull distribution, outperforms other simple models like the Gamma distribution. From a modeling perspective, the Weibull distribution can be justified as modeling the accumulation of driver events, which establishes a link to stem cell division based cancer development models and a connection to a recursion formula for intrinsic cancer risk published by Wu et al. For the recursion formula a closed form solution is given, which will help to simplify future analyses. Additionally, we perform a sensitivity analysis for the parameters, showing that two of the three parameters can vary over several orders of magnitude. However, the shape parameter of the Weibull distribution, which corresponds to the number of driver mutations required for cancer onset, can be robustly estimated from epidemiological data.

Accurate prediction of the age incidence of chronic myeloid leukemia with an improved two-mutation mathematical model

Chronic myeloid leukemia (CML) is a malignant clonal disorder whose hallmark is a reciprocal translocation between chromosomes 9 and 22 occurring in 95% of affected patients. This translocation causes the expression of a deregulated BCR/ABL fusion oncogene and, interestingly, is detectable in healthy individuals. Based on this information we assumed that the sole presence of the BCR/ABL transcript represents a necessary but not sufficient event for the clonal expansion of CML precursors. We developed a mathematical model introducing a probability that any normal cell undergoes a first aberration, and a probability that a cell that experienced a first mutation undergoes a second mutation as well. Two variants are proposed and analyzed: in the first the probability of the first mutation is supposed to be age independent and in the second, it depends on the hemopoietic cell turnover and mass. The model parameters have been estimated by regression from the observed CML incidence curves. Our models offer a significantly improved version of existing one-step and two-steps models, as they integrate key clinical and biological data reported in the literature and accurately fit the observed incidence. Our models also estimate the increased radiation-associated mutation rate at a younger age in atomic bomb survivors. Although this work focuses on CML, the modelling approach can be applied to all types of leukemia and lymphoma.

Mathematical modelling as a proof of concept for MPNs as a human inflammation model for cancer development

The chronic Philadelphia-negative myeloproliferative neoplasms (MPNs) are acquired stem cell neoplasms which ultimately may transform to acute myelogenous leukemia. Most recently, chronic inflammation has been described as an important factor for the development and progression of MPNs in the biological continuum from early cancer stage to the advanced myelofibrosis stage, the MPNs being described as "A Human Inflammation Model for Cancer Development". This novel concept has been built upon clinical, experimental, genomic, immunological and not least epidemiological studies. Only a few studies have described the development of MPNs by mathematical models, and none have addressed the role of inflammation for clonal evolution and disease progression. Herein, we aim at using mathematical modelling to substantiate the concept of chronic inflammation as an important trigger and driver of MPNs.The basics of the model describe the proliferation from stem cells to mature cells including mutations of healthy stem cells to become malignant stem cells. We include a simple inflammatory coupling coping with cell death and affecting the basic model beneath. First, we describe the system without feedbacks or regulatory interactions. Next, we introduce inflammatory feedback into the system. Finally, we include other feedbacks and regulatory interactions forming the inflammatory-MPN model. Using mathematical modeling, we add further proof to the concept that chronic inflammation may be both a trigger of clonal evolution and an important driving force for MPN disease progression. Our findings support intervention at the earliest stage of cancer development to target the malignant clone and dampen concomitant inflammation.

Evolutionary Dynamics of Chronic Myeloid Leukemia Progression: the Progression-Inhibitory Effect of Imatinib

The t(9;22) translocation that causes chronic myeloid leukemia (CML) drives both transformation and the progression process that eventually results in the disease changing to acute leukemia. Constitutively activated Bcr-Abl signaling in CML creates high levels of reactive oxygen species (ROS) that produce 8-oxo-guanine in DNA; this is mutagenic and causes chronic phase (CP) progression to blast phase (BP). We modeled three types of mutations involved in this progression: mutations that result in myeloid progenitor cells proliferating independently of external growth factors; mutations causing failure of myeloid progenitor cells to differentiate; and mutations that enable these cells to survive independently of attachment to marrow stroma. We further modeled tyrosine kinase inhibitors (TKI) as restoring myeloid cell apoptosis and preventing ROS-driven mutagenesis, and mutations that cause TKI resistance. We suggest that the unusually low rate of resistance to TKI arises because these drugs deplete ROS, which in turn decrease mutation rates.

Management of Elderly Patients with Newly Diagnosed Chronic Myeloid Leukemia in the Accelerated or Blastic Phase

In the elderly population, the accelerated and blastic phases of chronic myeloid leukemia (CML) are difficult to treat, not just because of the higher chance of acquired mutations than in younger individuals, but because of additional associated co-morbidities. Tyrosine kinase inhibitors are well-established in the treatment of the chronic phase of CML, and their use in advanced phases is ever-increasing. Elderly patients who are still eligible candidates for transplant can undergo reduced-intensity transplants from related or unrelated donors after reverting to chronic phase. Post-transplantation, these patients require adequate monitoring and therapy to prevent relapses. Newer modalities of treatment or interventions are urgently required in this complex group of patients.

Smoking: additional burden on aging and death

Tobacco smoking is a major cause of lung cancer. It has been suggested that there is an approximately linear dose–response relationship between the number of cigarettes smoked per day and clinical outcome such as lung cancer mortality. It has also been proposed that there is a greater increase in mortality at high doses when the dose is represented by the duration of the smoking habit rather than the number of cigarettes. The multistep carcinogenesis theory indicates that a greater increase in mortality rate at high doses is possible, as is the case between aging and cancer, even though each dose–response relationship between a carcinogenic factor and a carcinogenic step forward is linear. The high incidence of lung cancer after long-term smoking and the decreased relative risk after smoking cessation suggests a similarity between the effects of smoking and aging. Prediction of lung cancer risk in former smokers by simple integration of smoking effects with aging demonstrated a good correlation with that estimated from the relative risk of the period of smoking cessation. In contrast to the smoking period, there appears to be a linear relationship between smoking strength and cancer risk. This might arise if the dose–response relationship between smoking strength and each carcinogenic step is less than linear, or the effects become saturated with a large dose of daily smoking. Such a dose–response relationship could lead to relatively large clinical effects, such as cardiovascular mortality, by low-dose tobacco smoke exposure, e.g., second-hand smoking. Consideration of the dose–response of each effect is important to evaluate the risk arising from each carcinogenic factor.

Toward an evolutionary model of cancer: Considering the mechanisms that govern the fate of somatic mutations

Our understanding of cancer has greatly advanced since Nordling [Nordling CO (1953) Br J Cancer 7(1):68-72] and Armitage and Doll [Armitage P, Doll R (1954) Br J Cancer 8(1):1-12] put forth the multistage model of carcinogenesis. However, a number of observations remain poorly understood from the standpoint of this paradigm in its contemporary state. These observations include the similar age-dependent exponential rise in incidence of cancers originating from stem/progenitor pools differing drastically in size, age-dependent cell division profiles, and compartmentalization. This common incidence pattern is characteristic of cancers requiring different numbers of oncogenic mutations, and it scales to very divergent life spans of mammalian species. Also, bigger mammals with larger underlying stem cell pools are not proportionally more prone to cancer, an observation known as Peto's paradox. Here, we present a number of factors beyond the occurrence of oncogenic mutations that are unaccounted for in the current model of cancer development but should have significant impacts on cancer incidence. Furthermore, we propose a revision of the current understanding for how oncogenic and other functional somatic mutations affect cellular fitness. We present evidence, substantiated by evolutionary theory, demonstrating that fitness is a dynamic environment-dependent property of a phenotype and that oncogenic mutations should have vastly different fitness effects on somatic cells dependent on the tissue microenvironment in an age-dependent manner. Combined, this evidence provides a firm basis for understanding the age-dependent incidence of cancers as driven by age-altered systemic processes regulated above the cell level.

Stochastic modeling indicates that aging and somatic evolution in the hematopoetic system are driven by non-cell-autonomous processes

Age-dependent tissue decline and increased cancer incidence are widely accepted to be rate-limited by the accumulation of somatic mutations over time. Current models of carcinogenesis are dominated by the assumption that oncogenic mutations have defined advantageous fitness effects on recipient stem and progenitor cells, promoting and rate-limiting somatic evolution. However, this assumption is markedly discrepant with evolutionary theory, whereby fitness is a dynamic property of a phenotype imposed upon and widely modulated by environment. We computationally modeled dynamic microenvironment-dependent fitness alterations in hematopoietic stem cells (HSC) within the Sprengel-Liebig system known to govern evolution at the population level. Our model for the first time integrates real data on age-dependent dynamics of HSC division rates, pool size, and accumulation of genetic changes and demonstrates that somatic evolution is not rate-limited by the occurrence of mutations, but instead results from aged microenvironment-driven alterations in the selective/fitness value of previously accumulated genetic changes. Our results are also consistent with evolutionary models of aging and thus oppose both somatic mutation-centric paradigms of carcinogenesis and tissue functional decline. In total, we demonstrate that aging directly promotes HSC fitness decline and somatic evolution via non-cell-autonomous mechanisms.

The functional interplay between the t(9;22)-associated fusion proteins BCR/ABL and ABL/BCR in Philadelphia chromosome-positive acute lymphatic leukemia

The hallmark of Philadelphia chromosome positive (Ph⁺) leukemia is the BCR/ABL kinase, which is successfully targeted by selective ATP competitors. However, inhibition of BCR/ABL alone is unable to eradicate Ph⁺ leukemia. The t(9;22) is a reciprocal translocation which encodes not only for the der22 (Philadelphia chromosome) related BCR/ABL, but also for der9 related ABL/BCR fusion proteins, which can be detected in 65% of patients with chronic myeloid leukemia (CML) and 100% of patients with Ph⁺ acute lymphatic leukemia (ALL). ABL/BCRs are oncogenes able to influence the lineage commitment of hematopoietic progenitors. Aim of this study was to further disclose the role of p96^ABL/BCR for the pathogenesis of Ph⁺ ALL. The co-expression of p96^ABL/BCR enhanced the kinase activity and as a consequence, the transformation potential of p185^BCR/ABL. Targeting p96^ABL/BCR by RNAi inhibited growth of Ph⁺ ALL cell lines and Ph⁺ ALL patient-derived long-term cultures (PD-LTCs). Our in vitro and in vivo stem cell studies further revealed a functional hierarchy of p96^ABL/BCR and p185^BCR/ABL in hematopoietic stem cells. Co-expression of p96^ABL/BCR abolished the capacity of p185^BCR/ABL to induce a CML-like disease and led to the induction of ALL. Taken together our here presented data reveal an important role of p96^ABL/BCR for the pathogenesis of Ph⁺ ALL.

The t(9;22) is a reciprocal translocation, which causes chronic myeloid leukemia (CML) and a subset of high risk acute lymphatic leukemia (ALL). The derivative chromosome 22 is the so called Philadelphia chromosome (Ph) which encodes the BCR/ABL kinase. Targeting BCR/ABL by selective ATP competitors, such as imatinib or nilotinib, is a well validated therapeutic concept, but unable to definitively eradicate the disease. Little is known about the role of the fusion protein encoded by the reciprocal derivative chromosome 9, the ABL/BCR. In models of Ph⁺ ALL we show that the functional interplay between ABL/BCR and BCR/ABL not only increases the transformation potential of BCR/ABL but is also indispensable for the growth and survival of Ph⁺ ALL leukemic cells. The presence of ABL/BCR changed the phenotype of the leukemia most likely due to its capacity to influence the stem cell population as shown by our in vivo data. Taken together our here presented data reveal an important role of p96^ABL/BCR for the pathogenesis of Ph⁺ ALL.

Etiology and treatment of hematological neoplasms: stochastic mathematical models

Leukemias are driven by stemlike cancer cells (SLCC), whose initiation, growth, response to treatment, and posttreatment behavior are often "stochastic", i.e., differ substantially even among very similar patients for reasons not observable with present techniques. We review the probabilistic mathematical methods used to analyze stochastics and give two specific examples. The first example concerns a treatment protocol, e.g., for acute myeloid leukemia (AML), where intermittent cytotoxic drug dosing (e.g., once each weekday) is used with intent to cure. We argue mathematically that, if independent SLCC are growing stochastically during prolonged treatment, then, other things being equal, front-loading doses are more effective for tumor eradication than back loading. We also argue that the interacting SLCC dynamics during treatment is often best modeled by considering SLCC in microenvironmental niches, with SLCC-SLCC interactions occurring only among SLCC within the same niche, and we present a stochastic dynamics formalism, involving "Poissonization," applicable in such situations. Interactions at a distance due to partial control of total cell numbers are also considered. The second half of this chapter concerns chromosomal aberrations, lesions known to cause some leukemias. A specific example is the induction of a Philadelphia chromosome by ionizing radiation, subsequent development of chronic myeloid leukemia (CML), CML treatment, and treatment outcome. This time evolution involves a coordinated sequence of > 10 steps, each stochastic in its own way, at the subatomic, molecular, macromolecular, cellular, tissue, and population scales, with corresponding time scales ranging from picoseconds to decades. We discuss models of these steps and progress in integrating models across scales.

Multifocality and recurrence risk: a quantitative model of field cancerization

Primary tumors often emerge within genetically altered fields of premalignant cells that appear histologically normal but have a high chance of progression to malignancy. Clinical observations have suggested that these premalignant fields pose high risks for emergence of recurrent tumors if left behind after surgical removal of the primary tumor. In this work, we develop a spatio-temporal stochastic model of epithelial carcinogenesis, combining cellular dynamics with a general framework for multi-stage genetic progression to cancer. Using the model, we investigate how various properties of the premalignant fields depend on microscopic cellular properties of the tissue. In particular, we provide analytic results for the size-distribution of the histologically undetectable premalignant fields at the time of diagnosis, and investigate how the extent and the geometry of these fields depend upon key groups of parameters associated with the tissue and genetic pathways. We also derive analytical results for the relative risks of local vs. distant secondary tumors for different parameter regimes, a critical aspect for the optimal choice of post-operative therapy in carcinoma patients. This study contributes to a growing literature seeking to obtain a quantitative understanding of the spatial dynamics in cancer initiation.

Robustness of differentiation cascades with symmetric stem cell division

Stem cells (SCs) perform the task of maintaining tissue homeostasis by both self-renewal and differentiation. While it has been argued that SCs divide asymmetrically, there is also evidence that SCs undergo symmetric division. Symmetric SC division has been speculated to be key for expanding cell numbers in development and regeneration after injury. However, it might lead to uncontrolled growth and malignancies such as cancer. In order to explore the role of symmetric SC division, we propose a mathematical model of the effect of symmetric SC division on the robustness of a population regulated by a serial differentiation cascade and we show that this may lead to extinction of such population. We examine how the extinction likelihood depends on defining characteristics of the population such as the number of intermediate cell compartments. We show that longer differentiation cascades are more prone to extinction than systems with less intermediate compartments. Furthermore, we have analysed the possibility of mixed symmetric and asymmetric cell division against invasions by mutant invaders in order to find optimal architecture. Our results show that more robust populations are those with unfrequent symmetric behaviour.

Effect of dedifferentiation on time to mutation acquisition in stem cell-driven cancers

Accumulating evidence suggests that many tumors have a hierarchical organization, with the bulk of the tumor composed of relatively differentiated short-lived progenitor cells that are maintained by a small population of undifferentiated long-lived cancer stem cells. It is unclear, however, whether cancer stem cells originate from normal stem cells or from dedifferentiated progenitor cells. To address this, we mathematically modeled the effect of dedifferentiation on carcinogenesis. We considered a hybrid stochastic-deterministic model of mutation accumulation in both stem cells and progenitors, including dedifferentiation of progenitor cells to a stem cell-like state. We performed exact computer simulations of the emergence of tumor subpopulations with two mutations, and we derived semi-analytical estimates for the waiting time distribution to fixation. Our results suggest that dedifferentiation may play an important role in carcinogenesis, depending on how stem cell homeostasis is maintained. If the stem cell population size is held strictly constant (due to all divisions being asymmetric), we found that dedifferentiation acts like a positive selective force in the stem cell population and thus speeds carcinogenesis. If the stem cell population size is allowed to vary stochastically with density-dependent reproduction rates (allowing both symmetric and asymmetric divisions), we found that dedifferentiation beyond a critical threshold leads to exponential growth of the stem cell population. Thus, dedifferentiation may play a crucial role, the common modeling assumption of constant stem cell population size may not be adequate, and further progress in understanding carcinogenesis demands a more detailed mechanistic understanding of stem cell homeostasis.

Recent evidence suggests that, like many normal tissues, many cancers are maintained by a small population of immortal stem cells that divide indefinitely to produce many differentiated cells. Cancer stem cells may come directly from mutation of normal stem cells, but this route demands high mutation rates, because there are few normal stem cells. There are, however, many differentiated cells, and mutations can cause such cells to “dedifferentiate” into a stem-like state. We used mathematical modeling to study the effects of dedifferentiation on the time to cancer onset. We found that the effect of dedifferentiation depends critically on how stem cell numbers are controlled by the body. If homeostasis is very tight (due to all divisions being asymmetric), then dedifferentiation has little effect, but if homeostatic control is looser (allowing both symmetric and asymmetric divisions), then dedifferentiation can dramatically hasten cancer onset and lead to exponential growth of the cancer stem cell population. Our results suggest that dedifferentiation may be a very important factor in cancer and that more study of dedifferentiation and stem cell control is necessary to understand and prevent cancer onset.

A specific PTPRC/CD45 phosphorylation event governed by stem cell chemokine CXCL12 regulates primitive hematopoietic cell motility

CXCL12 governs cellular motility, a process deregulated by hematopoietic stem cell oncogenes such as p210-BCR-ABL. A phosphoproteomics approach to the analysis of a hematopoietic progenitor cell line treated with CXCL12 and the Rac 1 and 2 inhibitor NSC23766 has been employed to objectively discover novel mechanisms for regulation of stem cells in normal and malignant hematopoiesis. The proteomic data sets identified new aspects of CXCL12-mediated signaling and novel features of stem cell regulation. We also identified a novel phosphorylation event in hematopoietic progenitor cells that correlated with motile response and governed by the chemotactic factor CXCL12. The novel phosphorylation site on PTPRC/CD45; a protein tyrosine phosphatase, was validated by raising an antibody to the site and also using a mass spectrometry absolute quantification strategy. Site directed mutagenesis and inhibitor studies demonstrated that this single phosphorylation site governs hematopoietic progenitor cell and lymphoid cell motility, lies downstream from Rac proteins and potentiates Src signaling. We have also demonstrated that PTPRC/CD45 is down-regulated in leukemogenic tyrosine kinase expressing cells. The use of discovery proteomics has enabled further understanding of the regulation of PTPRC/CD45 and its important role in cellular motility in progenitor cells.

Inter-cellular signaling network reveals a mechanistic transition in tumor microenvironment

We conducted inter-cellular cytokine correlation and network analysis based upon a stochastic population dynamics model that comprises five cell types and fifteen signaling molecules inter-connected through a large number of cell-cell communication pathways. We observed that the signaling molecules are tightly correlated even at very early stages (e.g. the first month) of human glioma, but such correlation rapidly diminishes when tumor grows to a size that can be clinically detected. Further analysis suggests that paracrine is shown to be the dominant force during tumor initiation and priming, while autocrine supersedes it and supports a robust tumor expansion. In correspondence, the cytokine correlation network evolves through an increasing to decreasing complexity. This study indicates a possible mechanistic transition from the microenvironment-controlled, paracrine-based regulatory mechanism to self-sustained rapid progression to fetal malignancy. It also reveals key nodes that are responsible for such transition and can be potentially harnessed for the design of new anti-cancer therapies.

How animal models of leukaemias have already benefited patients

The relative genetic simplicity of leukaemias, the development of which likely relies on a limited number of initiating events has made them ideal for disease modelling, particularly in the mouse. Animal models provide incomparable insights into the mechanisms of leukaemia development and allow exploration of the molecular pillars of disease maintenance, an aspect often biased in cell lines or ex vivo systems. Several of these models, which faithfully recapitulate the characteristics of the human disease, have been used for pre-clinical purposes and have been instrumental in predicting therapy response in patients. We plea for a wider use of genetically defined animal models in the design of clinical trials, with a particular focus on reassessment of existing cancer or non-cancer drugs, alone or in combination.

The effect of one additional driver mutation on tumor progression

Tumor growth is caused by the acquisition of driver mutations, which enhance the net reproductive rate of cells. Driver mutations may increase cell division, reduce cell death, or allow cells to overcome density-limiting effects. We study the dynamics of tumor growth as one additional driver mutation is acquired. Our models are based on two-type branching processes that terminate in either tumor disappearance or tumor detection. In our first model, both cell types grow exponentially, with a faster rate for cells carrying the additional driver. We find that the additional driver mutation does not affect the survival probability of the lesion, but can substantially reduce the time to reach the detectable size if the lesion is slow growing. In our second model, cells lacking the additional driver cannot exceed a fixed carrying capacity, due to density limitations. In this case, the time to detection depends strongly on this carrying capacity. Our model provides a quantitative framework for studying tumor dynamics during different stages of progression. We observe that early, small lesions need additional drivers, while late stage metastases are only marginally affected by them. These results help to explain why additional driver mutations are typically not detected in fast-growing metastases.

Clinical and Hematological Features of 335 Patients of Chronic Myelogenous Leukemia Diagnosed at Single Centre in Northern Pakistan

There are no studies regarding analysis of clinical and haematological features of chronic myelogenous leukemia (CML) from Pakistan. This study analyzes the data of patients suffering from CML, reporting to a major referral Institute in Northern Pakistan in the past 6 years and 3 months. CML constitutes approximately 80% of all myeloproliferative disorders, with a peak incidence between 21-50 years of age, and a male:female ratio of 2:1. Anaemia and massive splenomegaly were the main clinical features found in 92% and 47% patients respectively. There was significant correlation between anaemia and WBC counts with degree of splenomegaly. Three percent of all CML patients presented as de novo accelerated phase, and another 3% presented as blast crises without any previous history of chronic phase. The ratio of myeloid and lymphoid blast crisis was 2:1. Median duration of chronic phase in patients on hydroxyurea treatment was 6 years. Thirty six percent of patients in chronic phase of CML belonged to intermediate and high risk according to Sokal and Hasford scoring systems. In contrast to the Caucasian populations where the peak incidence of the disease is in 6th to 7th decade, CML occurs in Pakistan in a much younger population, with a broad peak between 21-50 years of age. Patients present in fairly advanced disease because of poor access to health care facilities, due to non-affordability and lack of health insurance coverage.

Analyzing transformation of myelodysplastic syndrome to secondary acute myeloid leukemia using a large patient database

One-third of patients with myelodysplastic syndrome (MDS) progress to secondary acute myeloid leukemia (sAML), with its concomitant poor prognosis. Recently, multiple mutations have been identified in association with MDS-to-sAMLtransition, but it is still unclear whether all these mutations are necessary for transformation. If multiple independent mutations are required for the transformation, sAML risk should increase with time from MDS diagnosis. In contrast, if a single critical biological event determines sAML transformation; its risk should be constant in time elapsing from MDS diagnosis. To elucidate this question, we studied a database of 1079 patients with MDS. We classified patients according to the International Prognostic Scoring System (IPSS), using either the French-American-British (FAB) or the World Health Organization (WHO) criteria, and statistically analyzed the resulting transformation risk curves of each group. The risk of transformation after MDS diagnosis remained constant in time within three out of four risk groups, and in all four risk groups, when patients were classified according to FAB or to the WHO-determined criteria, respectively. Further subdivision by blast percentage or cytogenetics had no influence on this result. Our analysis suggests that a single random biological event leads to transformation to sAML, thus calling for the exclusion of time since MDS diagnosis from the clinical decision-making process.

Quantitative modeling of chronic myeloid leukemia: insights from radiobiology

Mathematical models of chronic myeloid leukemia (CML) cell population dynamics are being developed to improve CML understanding and treatment. We review such models in light of relevant findings from radiobiology, emphasizing 3 points. First, the CML models almost all assert that the latency time, from CML initiation to diagnosis, is at most ∼10 years. Meanwhile, current radiobiologic estimates, based on Japanese atomic bomb survivor data, indicate a substantially higher maximum, suggesting longer-term relapses and extra resistance mutations. Second, different CML models assume different numbers, between 400 and 10(6), of normal HSCs. Radiobiologic estimates favor values>10(6) for the number of normal cells (often assumed to be the HSCs) that are at risk for a CML-initiating BCR-ABL translocation. Moreover, there is some evidence for an HSC dead-band hypothesis, consistent with HSC numbers being very different across different healthy adults. Third, radiobiologists have found that sporadic (background, age-driven) chromosome translocation incidence increases with age during adulthood. BCR-ABL translocation incidence increasing with age would provide a hitherto underanalyzed contribution to observed background adult-onset CML incidence acceleration with age, and would cast some doubt on stage-number inferences from multistage carcinogenesis models in general.

Expression of testis-specific genes, TEX101 and ODF4, in chronic myeloid leukemia and evaluation of TEX101 immunogenicity

BACKGROUND AND OBJECTIVES

Cancer-testis (CT) antigens are a group of antigens with a restricted expression in normal tissues, except testis, and they have aberrant expression in different tumors. This pattern of expression has made them promising targets for immunotherapy and cancer detection. Our aim was to find new members of this group that might be useful as markers in the detection of cancer and immunotherapy.

DESIGN AND SETTING

A descriptive study conducted in referral centers of Tehran University of Medical Science from January 2008 to January 2009.

PATIENTS AND METHODS

We analyzed the expression of two testis-specific genes named ODF4 (outer dense fiber of sperm tails 4) and TEX101 (testis expressed 101) in 20 chronic myeloid leukemia (CML) and 20 normal samples by reverse transcription-polymerase chain reaction and sequencing. Immunogenicity of TEX101 was evaluated by means of enzyme-linked immunosorbent assay.

RESULTS

These two genes were expressed in 30% of CML patients but not in any of the healthy donors. Humoral response against TEX101 was not detected in any samples.

CONCLUSIONS

TEX101 and ODF4 are CT genes useful for detection of CML. Unlike many CT genes, overexpression of TEX101 was not shown to induce immunologic responses in these samples. According to the previous studies, overexpression of TEX101 leads to suppression of cancer invasion and metastasis; thus, the induction of the expression of TEX101 in cancer by epigenetic mechanisms may be a treatment strategy.

Evolutionary dynamics of chronic myeloid leukemia

Cancer is an evolutionary process that arises due to mutations and expands through the selection of clones with higher reproductive success that will outcompete their peers. Most tumors require many mutations to explain the cancer phenotype, making it difficult to identify the gene(s) that confer the reproductive fitness to the clone. Moreover, the impact of any oncogene is context dependent: it can increase the fitness of particular stages of cell differentiation but not other stages. In addition, the fitness advantage of an oncogene is not irreversible: sometimes it can be reversed with targeted therapy, for example. The understanding of these dynamical processes and their consequences may be greatly simplified when addressed from an evolutionary perspective. Using the dynamics of chronic myeloid leukemia-perhaps the best understood human neoplasm-as an example, we show how three fundamental evolutionary behaviors provide insights into the dynamics of this disease: (1) BCR-ABL does not affect the reproductive success of any cell within the stem cell pool (resulting therefore in neutral drift), (2) BCR-ABL expression gives a fitness (selective) advantage to progenitor cells, and (3) imatinib therapy reduces the fitness of progenitor cells expressing the oncogene (selective disadvantage) and consequently leads to significant reductions in disease burden. These three different evolutionary dynamics scenarios based on the interpretation of mutation and gene expression as potentially leading to a fitness imbalance of cell populations clearly explain the course of the disease, providing as such a better grasp of cancer dynamics and the role of related therapies.

Stochastic dynamics of cancer initiation

Most human cancer types result from the accumulation of multiple genetic and epigenetic alterations in a single cell. Once the first change (or changes) have arisen, tumorigenesis is initiated and the subsequent emergence of additional alterations drives progression to more aggressive and ultimately invasive phenotypes. Elucidation of the dynamics of cancer initiation is of importance for an understanding of tumor evolution and cancer incidence data. In this paper, we develop a novel mathematical framework to study the processes of cancer initiation. Cells at risk of accumulating oncogenic mutations are organized into small compartments of cells and proliferate according to a stochastic process. During each cell division, an (epi)genetic alteration may arise which leads to a random fitness change, drawn from a probability distribution. Cancer is initiated when a cell gains a fitness sufficiently high to escape from the homeostatic mechanisms of the cell compartment. To investigate cancer initiation during a human lifetime, a 'race' between this fitness process and the aging process of the patient is considered; the latter is modeled as a second stochastic Markov process in an aging dimension. This model allows us to investigate the dynamics of cancer initiation and its dependence on the mutational fitness distribution. Our framework also provides a methodology to assess the effects of different life expectancy distributions on lifetime cancer incidence. We apply this methodology to colorectal tumorigenesis while considering life expectancy data of the US population to inform the dynamics of the aging process. We study how the probability of cancer initiation prior to death, the time until cancer initiation, and the mutational profile of the cancer-initiating cell depends on the shape of the mutational fitness distribution and life expectancy of the population.

Tyrosine kinase inhibitor therapy can cure chronic myeloid leukemia without hitting leukemic stem cells

BACKGROUND

Tyrosine kinase inhibitors, such as imatinib, are not considered curative for chronic myeloid leukemia--regardless of the significant reduction of disease burden during treatment--since they do not affect the leukemic stem cells. However, the stochastic nature of hematopoiesis and recent clinical observations suggest that this view must be revisited.

DESIGN AND METHODS

We studied the natural history of a large cohort of virtual patients with chronic myeloid leukemia under tyrosine kinase inhibitor therapy using a computational model of hematopoiesis and chronic myeloid leukemia that takes into account stochastic dynamics within the hematopoietic stem and early progenitor cell pool.

RESULTS

We found that in the overwhelming majority of patients the leukemic stem cell population undergoes extinction before disease diagnosis. Hence leukemic progenitors, susceptible to tyrosine kinase inhibitor attack, are the natural target for chronic myeloid leukemia treatment. Response dynamics predicted by the model closely match data from clinical trials. We further predicted that early diagnosis together with administration of tyrosine kinase inhibitor opens the path to eradication of chronic myeloid leukemia, leading to the wash out of the aberrant progenitor cells, ameliorating the patient's condition while lowering the risk of blast transformation and drug resistance.

CONCLUSIONS

Tyrosine kinase inhibitor therapy can cure chronic myeloid leukemia, although it may have to be prolonged. The depth of response increases with time in the vast majority of patients. These results illustrate the importance of stochastic effects on the dynamics of acquired hematopoietic stem cell disorders and have direct relevance for other hematopoietic stem cell-derived diseases.

Reciprocal t(9;22) ABL/BCR fusion proteins: leukemogenic potential and effects on B cell commitment

Background

t(9;22) is a balanced translocation, and the chromosome 22 breakpoints (Philadelphia chromosome – Ph⁺) determine formation of different fusion genes that are associated with either Ph⁺ acute lymphatic leukemia (Ph⁺ ALL) or chronic myeloid leukemia (CML). The “minor” breakpoint in Ph⁺ ALL encodes p185^BCR/ABL from der22 and p96^ABL/BCR from der9. The “major” breakpoint in CML encodes p210^BCR/ABL and p40^ABL/BCR. Herein, we investigated the leukemogenic potential of the der9-associated p96^ABL/BCR and p40^ABL/BCR fusion proteins and their roles in the lineage commitment of hematopoietic stem cells in comparison to BCR/ABL.

Methodology

All t(9;22) derived proteins were retrovirally expressed in murine hematopoietic stem cells (SL cells) and human umbilical cord blood cells (UCBC). Stem cell potential was determined by replating efficiency, colony forming - spleen and competitive repopulating assays. The leukemic potential of the ABL/BCR fusion proteins was assessed by in a transduction/transplantation model. Effects on the lineage commitment and differentiation were investigated by culturing the cells under conditions driving either myeloid or lymphoid commitment. Expression of key factors of the B-cell differentiation and components of the preB-cell receptor were determined by qRT-PCR.

Principal Findings

Both p96^ABL/BCR and p40^ABL/BCR increased proliferation of early progenitors and the short term stem cell capacity of SL-cells and exhibited own leukemogenic potential. Interestingly, BCR/ABL gave origin exclusively to a myeloid phenotype independently from the culture conditions whereas p96^ABL/BCR and to a minor extent p40^ABL/BCR forced the B-cell commitment of SL-cells and UCBC.

Conclusions/Significance

Our here presented data establish the reciprocal ABL/BCR fusion proteins as second oncogenes encoded by the t(9;22) in addition to BCR/ABL and suggest that ABL/BCR contribute to the determination of the leukemic phenotype through their influence on the lineage commitment.

Eradication of chronic myeloid leukemia stem cells: a novel mathematical model predicts no therapeutic benefit of adding G-CSF to imatinib

Imatinib mesylate induces complete cytogenetic responses in patients with chronic myeloid leukemia (CML), yet many patients have detectable BCR-ABL transcripts in peripheral blood even after prolonged therapy. Bone marrow studies have shown that this residual disease resides within the stem cell compartment. Quiescence of leukemic stem cells has been suggested as a mechanism conferring insensitivity to imatinib, and exposure to the Granulocyte-Colony Stimulating Factor (G-CSF), together with imatinib, has led to a significant reduction in leukemic stem cells in vitro. In this paper, we design a novel mathematical model of stem cell quiescence to investigate the treatment response to imatinib and G-CSF. We find that the addition of G-CSF to an imatinib treatment protocol leads to observable effects only if the majority of leukemic stem cells are quiescent; otherwise it does not modulate the leukemic cell burden. The latter scenario is in agreement with clinical findings in a pilot study administering imatinib continuously or intermittently, with or without G-CSF (GIMI trial). Furthermore, our model predicts that the addition of G-CSF leads to a higher risk of resistance since it increases the production of cycling leukemic stem cells. Although the pilot study did not include enough patients to draw any conclusion with statistical significance, there were more cases of progression in the experimental arms as compared to continuous imatinib. Our results suggest that the additional use of G-CSF may be detrimental to patients in the clinic.

Imatinib mesylate (Gleevec) is currently the standard treatment for chronic myeloid leukemia (CML) and elicits a large reduction in leukemic cell burden in most patients. However, strong evidence suggests that imatinib does not cure the disease; approximately 20% of patients relapse within three years, and discontinuation of imatinib therapy often leads to a rebound of the leukemic cell burden. Laboratory studies have suggested that there exists a subpopulation of “quiescent” leukemia cells (i.e., cells that do not divide) that may be insensitive to imatinib treatment. It has been postulated that the disease outcome may be improved by administering imatinib in conjunction with the Granulocyte-Colony Stimulating Factor (G-CSF), a growth factor which “wakes up” the quiescent stem cells and sensitizes them to imatinib. In this study, we design a novel mathematical model of stem cell quiescence to investigate the treatment response to imatinib and G-CSF. We find that adding G-CSF to an imatinib treatment protocol leads to observable effects only if the majority of leukemic stem cells are quiescent. Our model also predicts that adding G-CSF leads to a higher risk of resistance, since it increases the number of leukemic stem cell divisions and thus the probability of acquiring a resistance mutation.

Evolutionary theory of cancer

As Theodosius Dobzhansky famously noted in 1973, "Nothing in biology makes sense except in the light of evolution," and cancer is no exception to this rule. Our understanding of cancer initiation, progression, treatment, and resistance has advanced considerably by regarding cancer as the product of evolutionary processes. Here we review the literature of mathematical models of cancer evolution and provide a synthesis and discussion of the field.

New experimental and theoretical investigations of hematopoietic stem cells and chronic myeloid leukemia

We report on a focused workshop of The Leukemia and Lymphoma Society that was held at Goldsmiths, University of London in 2008. During this workshop we discussed new clinical and experimental data in chronic myeloid leukemia (CML) research, particularly focusing on the validity (or otherwise) of corresponding mathematical models and simulations. We were specifically interested in whether the models could shed light on any of the fundamental mechanisms underlying this disease. Moreover, we were aiming to form a new community of clinicians and modelers looking at this disease and to define a common language and theoretical framework within which collaboration could flourish. The workshop showed the role that models can play, not just in trying to fit to existing data or predicting what individual mechanisms or system behaviors might occur, but also in challenging the orthodoxy of the concept of a stem cell and concepts such as "differentiation" and "determination". For years the prevailing view of a stem cell has been an entity (object) with a fixed set of behaviors and with a pre-determined fate. New perspectives in modeling, coupled with the new data that are being accumulated in the genesis of CML and its treatment, questions these assumptions. We propose how we can reach a consensus about a functional view of stem cells in a more continuous and flexible way and how, within this context, we can investigate the significance of modeling results and how they might impact on our interpretation of experimental observations and the development of new clinical strategies. This paper reports on the workshop and the state-of-the-art models and data from experimental and clinical trials, and sets out a roadmap for more interdisciplinary collaboration between modelers, wet-lab experimentalists, and clinicians interested in CML. It is our strong belief that a more integrated and coherent interdisciplinary approach will further advance the treatment of CML in future years.

Characterization and quantification of clonal heterogeneity among hematopoietic stem cells: a model-based approach

Hematopoietic stem cells (HSCs) show pronounced heterogeneity in self-renewal and differentiation behavior, which is reflected in their repopulation kinetics. Here, a single-cell-based mathematical model of HSC organization is used to examine the basis of HSC heterogeneity. Our modeling results, which are based on the analysis of limiting dilution competitive repopulation experiments in mice, demonstrate that small quantitative but clonally fixed differences of cellular properties are necessary and sufficient to account for the observed functional heterogeneity. The model predicts, and experimental data validate, that competitive pressures will amplify small clonal differences into large changes in the number of differentiated progeny. We further predict that the repertoire of HSC clones will evolve over time. Last, our results suggest that larger differences in cellular properties have to be assumed to account for genetically determined differences in HSC behavior as observed in different inbred mice strains. The model provides comprehensive systemic and quantitative insights into the clonal heterogeneity among HSCs with potential applications in predicting the behavior of malignant and/or genetically modified cells.

Mathematical models of cancer stem cells

Human cancers are thought to be sustained in their growth by a pathologic counterpart of normal adult stem cells: cancer stem cells. This concept was first developed in human myeloid leukemias and is today being extended to solid tumors such as breast and brain cancers. A quantitative understanding of cancer stem cells requires a mathematical framework to describe the dynamics of cancer initiation and progression, the response to treatment, and the evolution of resistance. In this review, I use chronic myeloid leukemia as an example to discuss how mathematical and computational techniques have been used to gain insights into the biology of cancer stem cells.

Rac GTPases as key regulators of p210-BCR-ABL-dependent leukemogenesis

Chronic myelogenous leukemia (CML) is a malignant disease characterized by expression of p210-BCR-ABL, the product of the Philadelphia chromosome. Survival of CML patients has been significantly improved with the introduction of tyrosine kinase inhibitors that induce long-term hematologic remissions. However, mounting evidence indicates that the use of a single tyrosine kinase inhibitor does not cure this disease due to the persistence of p210-BCR-ABL at the molecular level or the acquired resistance in the stem cell compartment to individual inhibitors. We have recently shown in a murine model that deficiency of the Rho GTPases Rac1 and Rac2 significantly reduces p210-BCR-ABL-mediated proliferation in vitro and myeloproliferative disease in vivo, suggesting Rac as a potential therapeutic target in p210-BCR-ABL-induced disease. This target has been further validated using a first-generation Rac-specific small molecule inhibitor. In this review we describe the role of Rac GTPases in p210-BCR-ABL-induced leukemogenesis and explore the possibility of combinatorial therapies that include tyrosine kinase inhibitor(s) and Rac GTPase inhibitors in the treatment of CML.