Multiple mutant clones in blood rarely coexist

Interplay of mutations, alternate mechanisms, and treatment breaks in leukaemia: Understanding and implications studied with stochastic models

Bcr-Abl1 kinase domain mutations are the most prevalent cause of treatment resistance in chronic myeloid leukaemia (CML). Alternate resistance pathways nevertheless exist, and cell line experiments show certain patterns in the gain, and loss, of some of these alternate adaptations. These adaptations have clinical consequences when the tumour develops mechanisms that are beneficial to its growth under treatment, but slow down its growth when not treated. The results of temporarily halting treatment in CML have not been widely discussed in the clinic and there is no robust theoretical model that could suggest when such a pause in therapy can be tolerated. We constructed a dynamic model of how mechanisms such as Bcr-Abl1 overexpression and drug transporter upregulation evolve to produce resistance in cell lines, and investigate its behaviour subject to different treatment schedules, in particular when the treatment is paused ('drug holiday'). Our study results suggest that the presence of additional resistance mechanisms creates an environment which favours mutations that are either preexisting or occur late during treatment. Importantly, the results suggest the existence of tumour drug addiction, where cancer cells become dependent on the drug for (optimal) survival, which could be exploited through a treatment holiday. All simulation code is available at https://github.com/Sandalmoth/dual-adaptation.

Effect of dedifferentiation on noise propagation in cellular hierarchy

Many fast renewing tissues have a hierarchical structure. Tissue-specific stem cells are at the root of this cellular hierarchy, which give rive to a whole range of specialized cells via cellular differentiation. However, increasing evidence shows that the hierarchical structure can be broken due to cellular dedifferentiation in which cells at differentiated stages can revert to the stem cell stage. Dedifferentiation has significant impacts on many aspects of hierarchical tissues. Here we investigate the effect of dedifferentiation on noise propagation by developing a stochastic model composed of different cell types. The moment equations are derived, via which we systematically investigate how the noise in the cell number is changed by dedifferentiation. Our results suggest that dedifferentiation have different effects on the noises in the numbers of stem cells and nonstem cells. Specifically, the noise in the number of stem cells is significantly reduced by increasing dedifferentiation probability. Due to the dual effect of dedifferentiation on nonstem cells, however, more complex changes could happen to the noise in the number of nonstem cells by increasing dedifferentiation probability. Furthermore, it is found that even though dedifferentiation could turn part of the noise propagation process into a noise-amplifying step, it is very unlikely to turn the entire process into a noise-amplifying cascade.

Stochastic modelling of tyrosine kinase inhibitor rotation therapy in chronic myeloid leukaemia

Background

Resistance towards targeted cancer treatments caused by single nucleotide variations is a major issue in many malignancies. Currently, there are a number of available drugs for chronic myeloid leukaemia (CML), which are overcome by different sets of mutations. The main aim of this study was to explore if it can be possible to exploit this and create a treatment protocol that outperforms each drug on its own.

Methods

We present a computer program to test different treatment protocols against CML, based on available resistance mutation growth data. The evolution of a relatively stable pool of cancer stem cells is modelled as a stochastic process, with the growth of cells expressing a tumourigenic protein (here, Abl1) and any emerging mutants determined principally by the drugs used in the therapy.

Results

There can be some benefit to Bosutinib-Ponatinib rotation therapy even if the mutation status is unknown, whereas Imatinib-Nilotinib rotation is unlikely to improve the outcomes. Furthermore, an interplay between growth inhibition and selection effects generates a non-linear relationship between drug doses and the risk of developing resistance.

Conclusions

Drug rotation therapy might be able to delay the onset of resistance in CML patients without costly ongoing observation of mutation status. Moreover, the simulations give credence to the suggestion that lower drug concentrations may achieve better results following major molecular response in CML.

Electronic supplementary material

The online version of this article (10.1186/s12885-019-5690-5) contains supplementary material, which is available to authorized users.

Evolutionary dynamics of paroxysmal nocturnal hemoglobinuria

Paroxysmal nocturnal hemoglobinuria (PNH) is an acquired clonal blood disorder characterized by hemolysis and a high risk of thrombosis, that is due to a deficiency in several cell surface proteins that prevent complement activation. Its origin has been traced to a somatic mutation in the PIG-A gene within hematopoietic stem cells (HSC). However, to date the question of how this mutant clone expands in size to contribute significantly to hematopoiesis remains under debate. One hypothesis posits the existence of a selective advantage of PIG-A mutated cells due to an immune mediated attack on normal HSC, but the evidence supporting this hypothesis is inconclusive. An alternative (and simpler) explanation attributes clonal expansion to neutral drift, in which case selection neither favours nor inhibits expansion of PIG-A mutated HSC. Here we examine the implications of the neutral drift model by numerically evolving a Markov chain for the probabilities of all possible outcomes, and investigate the possible occurrence and evolution, within this framework, of multiple independently arising clones within the HSC pool. Predictions of the model agree well with the known incidence of the disease and average age at diagnosis. Notwithstanding the slight difference in clonal expansion rates between our results and those reported in the literature, our model results lead to a relative stability of clone size when averaging multiple cases, in accord with what has been observed in human trials. The probability of a patient harbouring a second clone in the HSC pool was found to be extremely low (~10-8). Thus our results suggest that in clinical cases of PNH where two independent clones of mutant cells are observed, only one of those is likely to have originated in the HSC pool.

The mechanisms leading to expansion of HSC with mutations in the PIG-A gene that leads to the PNH phenotype remains unclear. Data so far suggests there is no intrinsic fitness advantage of the mutant cells compared to normal cells. Assuming neutral drift within the HSC compartment, we determined from first principles the incidence of the disease in a population, the average clone size in patients, the probability of clonal extinction, the likelihood of several separate clones coexisting in the HSC pool, and the expected expansion rate of a mutant clone. Our results are similar to what is observed in clinical practice. We also find that in such a model the probability of multiple PNH clones arising independently in the HSC pool is exceptionally small. This suggests that in clinical cases where more than one distinct clone is observed, all but one of the clones are likely to have emerged in cells that are downstream of the HSC population. We propose that PNH is perhaps the first disease where neutral drift alone may be responsible for clonal expansion leading to a clinical problem.

Complex role of space in the crossing of fitness valleys by asexual populations

The evolution of complex traits requires the accumulation of multiple mutations, which can be disadvantageous, neutral or advantageous relative to the wild-type. We study two spatial (two-dimensional) models of fitness valley crossing (the constant-population Moran process and the non-constant-population contact process), varying the number of loci involved and the degree of mixing. We find that spatial interactions accelerate the crossing of fitness valleys in the Moran process in the context of neutral and disadvantageous intermediate mutants because of the formation of mutant islands that increase the lifespan of mutant lineages. By contrast, in the contact process, spatial structure can accelerate or delay the emergence of the complex trait, and there can even be an optimal degree of mixing that maximizes the rate of evolution. For advantageous intermediate mutants, spatial interactions always delay the evolution of complex traits, in both the Moran and contact processes. The role of the mutant islands here is the opposite: instead of protecting, they constrict the growth of mutants. We conclude that the laws of population growth can be crucial for the effect of spatial interactions on the rate of evolution, and we relate the two processes explored here to different biological situations.

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.

On the dynamics of neutral mutations in a mathematical model for a homogeneous stem cell population

The theory of the clonal origin of cancer states that a tumour arises from one cell that acquires mutation(s) leading to the malignant phenotype. It is the current belief that many of these mutations give a fitness advantage to the mutant population allowing it to expand, eventually leading to disease. However, mutations that lead to such a clonal expansion need not give a fitness advantage and may in fact be neutral--or almost neutral--with respect to fitness. Such mutant clones can be eliminated or expand stochastically, leading to a malignant phenotype (disease). Mutations in haematopoietic stem cells give rise to diseases such as chronic myeloid leukaemia (CML) and paroxysmal nocturnal haemoglobinuria (PNH). Although neutral drift often leads to clonal extinction, disease is still possible, and in this case, it has important implications both for the incidence of disease and for therapy, as it may be more difficult to eliminate neutral mutations with therapy. We illustrate the consequences of such dynamics, using CML and PNH as examples. These considerations have implications for many other tumours as well.

Dynamics of mutant cells in hierarchical organized tissues

Most tissues in multicellular organisms are maintained by continuous cell renewal processes. However, high turnover of many cells implies a large number of error-prone cell divisions. Hierarchical organized tissue structures with stem cell driven cell differentiation provide one way to prevent the accumulation of mutations, because only few stem cells are long lived. We investigate the deterministic dynamics of cells in such a hierarchical multi compartment model, where each compartment represents a certain stage of cell differentiation. The dynamics of the interacting system is described by ordinary differential equations coupled across compartments. We present analytical solutions for these equations, calculate the corresponding extinction times and compare our results to individual based stochastic simulations. Our general compartment structure can be applied to different tissues, as for example hematopoiesis, the epidermis, or colonic crypts. The solutions provide a description of the average time development of stem cell and non stem cell driven mutants and can be used to illustrate general and specific features of the dynamics of mutant cells in such hierarchically structured populations. We illustrate one possible application of this approach by discussing the origin and dynamics of PIG-A mutant clones that are found in the bloodstream of virtually every healthy adult human. From this it is apparent, that not only the occurrence of a mutant but also the compartment of origin is of importance.

We investigate the average stem cell driven dynamics of cell counts in an abstract multi compartment model. Within this framework one can represent different tissue structures, as for example hematopoiesis, the skin or the colonic crypt. Our analysis is based on an individual cell model in which cells can differentiate, reproduce or die. We give closed solutions to the corresponding system of coupled differential equations, that describe the average dynamics of all cell types. There are three cases of interest: (i) Mutations at the stem cell level, (ii) Mutations in downstream compartments associated with more mature, non stem cell types, (iii) Mutations in downstream compartments with cells acquiring stem cell like properties. The average dynamics shows for (i) and (iii) an increase of mutants towards an equilibrium, in case (ii) the average mutant cell count goes through a maximum, but mutants die out in the long run. We calculate the corresponding extinction times for every compartment. We discuss applications to hematopoietic diseases such as, PIG-A mutant cells or the classic oncogene BCR-ABL. Although the abstract model is a simplified sketch of cell differentiation, it is capable of describing many aspects of a wide variety of such tissues and associated diseases.

Stochastic dynamics and the evolution of mutations in stem cells

Stem cells are the target of mutations that can lead to life threatening diseases. However, stem cell populations tend to be small and therefore clonal expansion of mutant cells is highly sensitive to stochastic fluctuations. The evolutionary dynamics of mutations in these cells is discussed, taking into consideration the impact of such mutations on the reproductive fitness of cells. We show how stochastic effects can explain clinical observations, including extinction of acquired clonal stem cell disorders.

Evolutionary dynamics of two related malignant plasma cell lines

Cancer is the consequence of sequential acquisition of mutations within somatic cells. Mutations alter the relative reproductive fitness of cells, enabling the population to evolve in time as a consequence of selection. Cancer therapy itself can select for or against specific subclones. Given the large population of tumor cells, subclones inevitably emerge and their fate will depend on the evolutionary dynamics that define the interactions between such clones. Using a combination of in vitro studies and mathematical modeling, we describe the dynamic behavior of two cell lines isolated from the same patient at different time points of disease progression and show how the two clones relate to one another. We provide evidence that the two clones coexisted at the time of initial presentation. The dominant clone presented with biopsy proven cardiac AL amyloidosis. Initial therapy selected for the second clone that expanded leading to a change in the diagnosis to multiple myeloma. The evolutionary dynamics relating the two cell lines are discussed and a hypothesis is generated in regard to the mechanism of one of the phenotypic characteristics that is shared by these two cell lines.

Somatic mutations and the hierarchy of hematopoiesis

Clonal disease is often regarded as almost synonymous with cancer. However, it is becoming increasingly clear that our bodies harbor numerous mutant clones that are not tumors, and mostly give rise to no disease at all. Here we discuss three somatic mutations arising within the hematopoietic system: BCR-ABL, characteristic of chronic myeloid leukemia; mutations of the PIG-A gene, characteristic of paroxysmal nocturnal hemoglobinuria; the V617F mutation in the JAK2 gene, characteristic of myeloproliferative diseases. The population frequencies of these three blood disorders fit well with a hierarchical model of hematopoiesis. The fate of any mutant clone will depend on the target cell and on the fitness advantage, if any, that the mutation confers on the cell. In general, we can expect that only a mutation in a hematopoietic stem cell will give long-term disease; the same mutation taking place in a cell located more downstream may produce just a ripple in the hematopoietic ocean.

Reproductive fitness advantage of BCR-ABL expressing leukemia cells

Mutations in oncogenes and tumor suppressor genes confer a fitness advantage to cells that can lead to cancer. The tumor phenotype normally results from the interaction of many mutant genes making it difficult to estimate the fitness advantage provided by any oncogene, except when tumors depend on one oncogene only. We utilize a model of chronic myeloid leukemia (CML), to quantitate the fitness advantage conferred by expression of BCR-ABL in hematopoietic cells from in vivo patient data. We show that BCR-ABL expression provides a high fitness advantage, which explains why this single mutation drives the chronic phase of CML.

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.

Cancer phenotype as the outcome of an evolutionary game between normal and malignant cells

BACKGROUND

There is variability in the cancer phenotype across individuals: two patients with the same tumour may experience different disease life histories, resulting from genetic variation within the tumour and from the interaction between tumour and host. Until now, phenotypic variability has precluded a clear-cut identification of the fundamental characteristics of a given tumour type.

METHODS

Using multiple myeloma as an example, we apply the principles of evolutionary game theory to determine the fundamental characteristics that define the phenotypic variability of a tumour.

RESULTS

Tumour dynamics is determined by the frequency-dependent fitness of different cell populations, resulting from the benefits and costs accrued by each cell type in the presence of others. Our study shows how the phenotypic variability in multiple myeloma bone disease can be understood through the theoretical approach of a game that allows the identification of key genotypic features in a tumour and provides a natural explanation for phenotypic variability. This analysis also illustrates how complex biochemical signals can be translated into cell fitness that determines disease dynamics.

CONCLUSION

The present paradigm is general and extends well beyond multiple myeloma, and even to non-neoplastic disorders. Furthermore, it provides a new perspective in dealing with cancer eradication. Instead of trying to kill all cancer cells, therapies should aim at reducing the fitness of malignant cells compared with normal cells, allowing natural selection to eradicate the tumour.

The allometry of chronic myeloid leukemia

Chronic myeloid leukemia (CML) is an acquired neoplastic hematopoietic stem cell (HSC) disorder characterized by the expression of the BCR-ABL oncoprotein. This gene product is necessary and sufficient to explain the chronic phase of CML. The only known cause of CML is radiation exposure leading to a mutation of at least one HSC, although the vast majority of patients with CML do not have a history of radiation exposure. Nonetheless, in humans, significant radiation exposure (after exposure to atomic bomb fallout) leads to disease diagnosis in 3-5 years. In murine models, disease dynamics are much faster and CML is fatal over the span of a few months. Our objective is to develop a model that accounts for CML across all mammals. In the following, we combine a model of CML dynamics in humans with allometric scaling of hematopoiesis across mammals to illustrate the natural history of chronic phase CML in various mammals. We show how a single cell can lead to a fatal illness in mice and humans but a higher burden of CML stem cells is necessary to induce disease in larger mammals such as elephants. The different dynamics of the disease is rationalized in terms of mammalian mass. Our work illustrates the relevance of animal models to understand human disease and highlights the importance of considering the re-scaling of the dynamics that accrues to the same biological process when planning experiments involving different species.

Neutral evolution in paroxysmal nocturnal hemoglobinuria

Paroxysmal nocturnal hemoglobinuria is an acquired hematopoietic stem cell (HSC) disorder characterized by the partial or complete deficiency of glycosyl-phosphatidylinositol (GPI)-linked membrane proteins, which leads to intravascular hemolysis. A loss of function mutation in the PIG-A gene, required for GPI biosynthesis, explains how the deficiency of many membrane proteins can result from a single genetic event. However, to date the mechanism of expansion of the GPI(-) clone has not been fully understood. Two hypotheses have been proposed: A selective advantage of GPI(-) cells because of a second mutation or a conditional growth advantage of GPI(-) cells in the presence of an immune attack on normal (GPI(+)) HSCs. Here, we explore a third possibility, whereby the PNH clone does not have a selective advantage. Simulations in a large virtual population accurately reproduce the known incidence of the disease; and the fit is optimized when the number of stem cells is decreased, reflecting a component of bone marrow failure in PNH. The model also accounts for the occurrence of spontaneous cure in PNH, consequent on clonal extinction. Thus, a clonal advantage may not be always necessary to explain clonal expansion in PNH.