Open access journal of the Ferrata-Storti Foundation, a non-profit organization
Decision Making and Problem Solving

A one-mutation mathematical model can explain the age incidence of acute myeloid leukemia with mutated nucleophosmin (NPM1)

Vol. 93 No. 8 (2008): August, 2008 https://doi.org/10.3324/haematol.13209

Abstract

Acute myeloid leukemia with mutated NPM1 gene and aberrant cytoplasmic expression of nucleophosmin (NPMc+ acute myeloid leukemia) shows distinctive biological and clinical features. Experimental evidence of the oncogenic potential of the nucleophosmin mutant is, however, still lacking, and it is unclear whether other genetic lesion(s), e.g. FLT3 internal tandem duplication, cooperate with NPM1 mutations in acute myeloid leukemia development. An analysis of age-specific incidence, together with mathematical modeling of acute myeloid leukemia epidemiology, can help to uncover the number of genetic events needed to cause leukemia. We collected data on age at diagnosis of acute myeloid leukemia patients from five European Centers in Germany, The Netherlands and Italy, and determined the age-specific incidence of AML with mutated NPM1 (a total of 1,444 cases) for each country. Linear regression of the curves representing age-specific rates of diagnosis per year showed similar slopes of about 4 on a double logarithmic scale. We then adapted a previously designed mathematical model of hematopoietic tumorigenesis to analyze the age incidence of acute myeloid leukemia with mutated NPM1 and found that a one-mutation model can explain the incidence curve of this leukemia entity. This model fits with the hypothesis that NPMc+ acute myeloid leukemia arises from an NPM1 mutation with haploinsufficiency of the wild-type NPM1 allele.

Introduction

The nucleophosmin (NPM1) gene, which encodes a nucleolar multifunctional protein, is frequently translocated or mutated in hematologic malignancies.1,2 Mutation of NPM11 is one of the most common genetic alterations in adult acute myeloid leukemia (AML), occurring in about one-third of patients and accounting for 50–60% of all AML cases with normal karyotype.3 Since NPM1 mutations were first discovered in AML in 2005,1 about 40 mutation variants have been identified.3 Despite molecular heterogeneity, all variants lead to common changes at the C-terminus of the NPM1 protein4 which cause an increased nuclear export of the nucleophosmin leukemic mutant and its aberrant accumulation in the cytoplasm of leukemic cells;4–6 hence the term NPMc+ (cytoplasmic-positive) AML.1,3 AML with mutated NPM1 shows distinctive biological and clinical features,3 including a unique gene expression profile,7,8 a distinct microRNA signature,9 frequent CD34-negativity (more than 95% of cases),1, 3 increased incidence of FLT3-ITD mutations (about 40% of cases),1 good response to induction therapy1 and a favorable prognosis (in the absence of FLT3-ITD).10–15 These findings strongly suggest that AML with mutated NPM1 represents a new disease entity. Experimental evidence of the oncogenic potential of the nucleophosmin mutant is, however, still lacking, and it is unclear whether other genetic lesion(s), such as FLT3-ITD, cooperate with NPM1 mutations in generating the leukemic phenotype. The multi-step theory of carcinogenesis was conceived after mathematical modeling demonstrated that the increasing cancer incidence with age can be explained by several stochastic events needed for tumorigenesis.16–19 A recently developed population genetics model20 was used to study the age specific incidence of chronic myeloid leukemia and found that the data are consistent with the hypothesis that the BCR-ABL fusion oncogene alone is sufficient to cause the chronic phase of the disease. Later on, Vickers demonstrated that the age of onset of polycythemia vera is in accordance with the assumption of a single rate-limiting mutation and a small number of stem cell divisions per year.21

To investigate the age-specific incidence of AML with mutated NPM1, we adapted the one-mutation model that was originally designed to describe chronic myeloid leukemia age distribution.20 The model fits the NPMc AML age-specific incidence curve assuming plausible parameter values, supporting the hypothesis that a single genetic event, the NPM1 mutation, is sufficient to cause leukemia. The role of NPM1 mutations in AML development is discussed in the light of these findings.

Design and Methods

Patients

National registry-based AML incidence data with details of NPM1 mutation status are not available. Therefore, we collected data sets at five major European Institutions involved in the diagnosis and treatment of AML patients: (i) the Laboratory of Cytogenetic and Molecular Diagnostics, University Hospital Ulm, representing the German-Austrian AML study Group (AMLSG); (ii) the Laboratory of Hemopathology, Institute of Hematology, University of Perugia, representing the Gruppo Italiano Malattie Ematologiche dell’ Adulto (GIMEMA); (iii) the Laboratory for Molecular Diagnostics, University Hospital Carl Gustav Carus, Dresden, Germany, representing the Deutsche Studieninitiative Leukämie (DSIL); (iv) the Munich Leukemia Laboratory (MLL), Munich, Germany; and (v) the Department of Hematology, Erasmus University Medical Center, Rotterdam, The Netherlands.

A total of 1,444 AML patients (age range: 20–59; median 47) carrying a mutated NPM1 gene were included in this study (n=476 from AMLSG; n=354 from GIMEMA; n=251 from DSIL; n=223 from MLL; and n=140 from The Netherlands). Exclusion criteria were: i) patients under 20 years of age because few cases were available, due to the low frequency of NPM1 mutations in this age group22; and ii) patients over 59 years of age who are often treated in local hospitals. Consequently, those patients referred to major institutions for diagnosis and treatment may not be representative of the population of AML patients in this age group.

Information on FLT3 status was available in 1,386/1,444 AML patients with mutated NPM1 (96%). FLT3-ITD was detected in 553/1,386 cases (40%). For analysis, the 1,444 NPM1-mutated AML patients were stratified in 5-year age classes.

For this study, we assume that the mutational event needed to develop NPMc AML occurs independently of local exposure to environmental leukemogenic factors and that the age specific rates of NPM1-mutated AML patients 20–59 years in age reflect those of the general population in the three European countries included in the study.

Modeling age specific incidence

The mathematical model by Michor et al.20 was adapted to analyze the AML incidence data. Our model is based on the following considerations: (i) we consider a population of N hematopoietic stem cells. Initially, all cells are wild type and proliferate according to a stochastic process known as the Moran model:23 every τ days, a cell is chosen at random proportional to fitness to divide; its offspring replaces another randomly chosen cell. The population size is strictly constant; (ii) a wild-type cell gives rise to a mutated cell at rate u per cell division. A mutated cell has a relative growth rate (fitness) of r. If r=1, the mutation is neutral as compared to wild type cells; if r<1, the mutant is disadvantageous, and if r>1, the mutant has a proliferation advantage over the wild type cell. We assume that an NPM1 mutation confers a fitness advantage to the cell, r>1; (iii) Our model adheres to standard Moran process until a surviving mutant cell appears; thereafter, clonal growth is initiated that continues until the mutated cell population reaches population size N̄. Unlike the model designed by Michor et al.,20 which assumes a constant population size of N cells, our model allows the mutant clone to expand until a maximal size, N̄. This change is intended to account for the marked expansion of the initial cell compartment which is peculiar to AML; (iv) the AML detection rate is proportional to the number of mutated cells present; if there are Nm mutated cells, the rate of diagnosis is q Nm. From assumptions (i) and (ii) it follows that the waiting time for the first successful (=surviving) mutation has a negative exponential distribution, b=Nu (1-1/r). Let a be the time since the occurrence of the first surviving mutation. Then assumption (3) states that the number of mutated cells, Nm, grows according to

where c=(r-1)/τ and Nm (0)=1/(1-1/r). To account for the significant expansion of the mutated clone, we assume N̄>>N. Finally, if (q) is the proportionality constant between the rate of detection and the number of mutated cells (assumption iv), then the probability of diagnosis20 at time t is given by

We compared the predictions of equation (1) with the direct computer simulation of the stochastic process. The simulation is performed by first determining the time at which the first surviving mutated cell arises in a population of N wild type cells; this time follows a negative exponential distribution with mean 1/b. Once such a cell has emerged, the branching process of clonal expansion is simulated by choosing a cell for reproduction or for death at random at each time step. The probability that the number of wild type cells, N, increases by one is given by

where Γ = (1+d)N + (r+d)Nm. Here d denotes the death rate of both wild type and mutated cells. The probability that the number of mutated cells, Nm, increases by one is given by

The probabilities that the numbers of wild type and mutated cells decrease by one are respectively given by

A patient is diagnosed at rate qNm and is entered into the incidence data base of his age class. Online Supplementary Figure 1 shows the fit of equation (1) and system (2). Under particular circumstances, i.e. when the waiting time for the first successful mutation is long and clonal expansion occurs fast and reaches large cell numbers, the incidence data can be a kinked curve. A more detailed mathematical investigation of such situations is forthcoming (Michor F. et al., in preparation) but will not be discussed here since the experimentally determined incidence data is a straight line on a doubly logarithmic plot.

Finally, we compared equation (1) with the experimental data, which allowed us to quantify AML-specific parameters.

Statistical analysis

The χ test (α<0.05) was used to assess independence of the age distribution of cases by center of diagnosis. The likelihood ratio test, comparing a Poisson regression model including age, country, and age x country interaction terms with the nested model without the interaction term was performed to evaluate dependence of age specific NPM1-mutated AML rates on the country.

Results

Age specific rates of acute myeloid leukemia with mutated NPM1 are similar in different countries

First, we determined whether age specific incidence curves of AML with NPM1 mutations were comparable in Italy, Germany and The Netherlands. The AML cases registered by each center do not provide a precise estimate of incidence, since the population that is referred to each study center for diagnosis cannot be identified. However, it is important to note that the slope of the incidence curve is needed for our purpose, not population-based incidence figures. Therefore, population data from the U.S. Census Bureau website (http://www.census.gov/ipc/www/idb, accessed on February 12, 2008) were used to obtain demographic data (person-years) for each country. In each country the number of AML cases was stratified into age classes. The cases in each age class were divided by the total population in that age class, which provided the age specific rate of diagnoses per year per million inhabitants.

Chi-square testing of the age distribution of cases on center of diagnosis was not significant (p=0.48) indicating that, although absolute incidence levels vary because they reflect the percentage of the general population that is covered by participating centers, number of cases by age class does not differ among study centers (Table 1). The likelihood ratio test comparing the Poisson model which includes a country x age class interaction with the simpler model without the interaction term (Online Supplementary Table 1) was non-significant (p=0.85). Together, these findings provide evidence that AML data from the three countries are comparable. In particular, AML incidence curves analyzed via linear regression all showed a slope of about 4 on a log-log scale (Figure 1).

The one-mutation model fits the incidence curve of acute myeloid leukemia with mutated NPM1

We next adapted the one-mutation mathematical model that was originally designed to describe chronic myeloid leukemia epidemiology20 to investigate age specific incidence data in AML with NPM1 mutations. The model provided adequate data fitting and generated slopes similar to real age specific incidence curves from patients (Figure 2) from Germany, The Netherlands, and Italy. The corresponding χ and p values for the three countries were 0.02027 (p=0.9899), 0.00862 (p=0.9956), and 0.15275 (p=0.9264). The fitting procedure provided estimates of the parameters in each country (Table 2) generating numbers that are biologically plausible (see below).

The initial hematopoietic stem cell (HSC) compartment was quantified as 1.03×10–1.14×10. This fits with experimental findings24 suggesting that, although humans require more blood cells per lifetime than mice (because of their larger size and longer life expectancy), the total number of human HSCs is equivalent to the total number of HSCs in mice, which has been shown to be of about 11,400±5,400.24

The maximum number of mutated cells generated by the model was about N̄ =10. This number is consistent with the high tumor burden observed in leukemia patients, if one assumes that, under physiological conditions, the amount of human nucleated marrow cells per kg body weight has been calculated to be approximately 2.1×10 (1.5×10 in a subject of 70 kg).25 The relative fitness of mutated cells spanned the range 1.38–1.61. The mean cell generation time (i.e. the time needed for a cell to divide), was between 2.67 and three days, which concurs with early experimental findings26 and with clinical data.3 In the NPM1-mutated AML case, the rate of cancer detection per mutated cell was found to be in the range of 7.77×10–1.58×10 days. This implies that the total rate of detection (qN) is in the range of 0.26–1.78, which is higher than previous estimates in chronic myeloid leukemia.20 Leukemic clones are initiated by single NPM1 mutations occurring at rates ranging from 2.43×10 to 4.86×10 days per cell division. Taken together, these estimates imply that for a single individual the waiting time for the appearance of a surviving mutation is on average 1/(Nu(1–1/r)), which is about 5532, 9940 and 8779 days for Germany, The Netherlands and Italy respectively.

Table 1.Cumulative incidence of the NPM1-mutated acute myeloid leukemia in Germany (DE), the Netherlands (NL) and Italy (IT).*

Figure 1.Incidence data for the NPMc+ acute myeloid leukemia in Germany (DE), The Netherlands (NL) and Italy (IT). Linear regression shows a slope of about 4 on a doubly logarithmic scale.

Figure 2.The incidence data can be fit to the one-mutation model assuming plausible parameter values for Germany (A), The Netherlands (B) and Italy (C). χ2 and corresponding p-values reported as labels in the corresponding figures show the quality of the fit.

Table 2.Parameters of the one-mutation model for all NPM1 mutated acute myeloid leukemias.

FLT3 gene status does not influence the age specific incidence of acute myeloid leukemia with mutated NPM1

Internal tandem duplication (ITD) at the FLT3 gene locus has been implicated as a cooperating genetic alteration in various AML subtypes.27,28 Since FLT3-ITD frequently associates with NPM1 mutations1 and appears to abrogate the favorable prognostic effect of NPM1 mutations in AML1,15,29 we determined whether the age incidence of NPM1-mutated AMLs with FLT3-ITD differs from cases with wild-type FLT3. No significant difference emerged in the slopes of FLT3-ITD-positive and -negative AML with mutated NPM1 (Figure 3). The quality of fit with the model-generated data was adequate and similar to the quality of fit for all AMLs with NPM1 mutations (Figure 4). The one-mutation model parameters for fitting FLT3-ITD positive and FLT3-ITD negative AML with mutated NPM1 are reported in Table 3. The slopes of the three groups (NPM1 mutated, NPM1 mutated/FLT3-ITD, NPM1-mutated/FLT3 wild-type) are not significantly different according to the Mann-Witney U test (p>0.05) (Online Supplementary Table 2).

Discussion

In this study, we adapted a one-mutation mathematical model that was originally designed to describe chronic myeloid leukemia epidemiology20 to investigate the age specific incidence data in AML with mutated NPM1. The model fits the NPMc AML age specific incidence curve for plausible parameter choices, supporting the hypothesis that a single genetic event, the NPM1 mutation, is sufficient to cause this type of leukemia. However, evidence derived from in vitro functional studies and experimental models are required to confirm or refute this hypothesis.

Our findings add to the body of evidence that NPM1 mutation is a founder genetic lesion in NPMc AML: i) cytoplasmic mutated nucleophosmin is specific for AML1, 30, 31 and clinically shows close association with AML of de novo origin1,32–34; ii) all NPM1 mutations generate changes at the C-terminus of nucleophosmin protein which appear to maximise nuclear export of NPM leukemic mutants,3,35–37 pointing to cytoplasmic dislocation of the mutants as the central event for leukemogenesis; iii) NPM1 mutations are mutually exclusive with other recurrent genetic abnormalities,1,38 with the exception of rare cases in which both NPM1 and CEPBA (or FLT3-ITD) mutations are found;15 iv) they are stable during the course of the disease39,40 as the same type of NPM1 mutation is consistently detected at relapse in medullary and extramedullary sites;40 and v) quantitative real-time PCR shows that NPM1 mutations disappear at complete remission.41,42

Figure 3.Incidence data for the NPMc+ acute myeloid leukemia bearing FLT3-ITD (A) or FLT3 wild-type for Germany (DE), The Netherlands (NL) and Italy (IT) (B).

The major finding in the present study is that the one-mutation mathematical model can explain the age specific incidence in NPMc AML. This hypothesis is in contrast to current concepts in AML development which, like other human cancers, is believed to be a consequence of more than one oncogenic hit.43 Indeed, several animal models of AML clearly point to leukemogenesis as a multi-step process.43 Moreover, in vitro findings that the NPM1 leukemic mutant specifically cooperates with the E1A adenovirus to transform primary MEFs in soft agar44 suggest that NPM1 mutations need to act in close concert with other oncogenic hits. In MEF cells, this mutual cooperation involves the NPM1 mutant inhibiting the E1A-elicited p19(Arf) induction and E1A overcoming NPM1 mutant-induced cellular senescence.44 Furthermore, an activating mutation of the FLT3 gene (FLT3-ITD) leading to an internal tandem duplication of the juxtamembrane portion of FLT3, a receptor which plays an important role in controlling proliferation and/or survival of hematopoietic progenitors, has been implicated as a cooperating genetic alteration in various AML subtypes.27,28 Since FLT3-ITD has been detected in about 40% of AML with mutated NPM1,1 it has been suggested that it may play an important role also in this leukemia subtype.

Figure 4.Fitting the incidence data with the one-mutation model (A) leads to plausible parameter values in all cases (NPMc+ acute myeloid leukemia with FLT3-ITD or FLT3 wild-type) for all three countries (Germany, The Netherlands (B) and Italy (C)). χ2 and corresponding p-values reported as labels in the corresponding figures show the quality of the fit.

Table 3.Parameters of the one-mutation model for the NPM1-mutated/FLT3-ITD and NPM1-mutated/FLT3 wild-type (wt) subsets.

The findings of this paper suggest that the role of FLT3-ITD as a cooperative mutation in the pathogenesis of NPMc AML should be interpreted with caution. In fact, no difference can be detected between the slopes of the age specific incidence of FLT3-ITD-positive and -negative NPMc AML, supporting the view that NPMc AML is a homogeneous group irrespective of the FLT3 mutational status. This is consistent with the observation that the unique gene expression profile of AML with mutated NPM1, i.e. upregulation of HOX genes and downregulation of CD34,7,8 does not appear to be significantly influenced by the FLT3 gene status. This is also in keeping with the clinical observation that FLT3-ITD can appear or disappear in NPM1-mutated AML patients during the course of the disease.39 Moreover, in oncogenic cooperation tests, the NPM1 leukemic mutant and FLT3-ITD did not cooperate to transform mouse embryonic fibroblasts (MEFs).44 Hypothetically, FLT3-ITD may not be necessary for the development of AML but rather provide a selective advantage for leukemic cells that already harbor the NPM1 mutation. Unfortunately, there is as yet no experimental mouse model to prove or disprove this hypothesis. However, this interpretation would at least fit with the clinical observation that FLT3-ITD appears to abrogate the favorable prognostic impact of NPM1 mutations,29 suggesting that it may play a role at later stages of NPMc AML, leading to a more aggressive AML phenotype.

Thus, how can we reconcile the results of our one-mutation mathematical model with current evidence that favor the hypothesis that AML is the result of more than one oncogenic hit43 ? One possible explanation is that NPMc AML arises from the concerted action of an NPM1 mutation and another leukemogenic event occurring at the same time. Since the NPM1 mutant has intrinsic oncogenic properties44 and in knock-out mice NPM haploinsufficiency results in a MDS-like syndrome45 and in overt leukemia,46 an attractive hypothesis would be that these alterations act together to cause NPMc AML.3,47 Indeed, NPM1 mutations are associated with haploinsufficiency of wild-type NPM in leukemic cells, since mutations are always monoallelic3 and lead to dislocation of functionally active wild-type NPM from the nucleoli to the cytoplasm through formation of heterodimers with the NPM1 leukemic mutant.4

However, other scenarios cannot be excluded with certainty only on the basis of the mathematical model. NPM1 and yet undiscovered mutation(s) may act synergistically such that their actions cannot be discerned when investigating incidence data. Moreover, even though NPM1 mutations may be sufficient to cause leukemia, secondary mutations (e.g. FLT3-ITD) could increase the fitness of leukemic cells and/or result in the development of more aggressive AML stages. Finally, it is still possible that cancer incidence data cannot be used to identify the number of genetic changes necessary to cause cancer. Therefore, further experimental studies are warranted to clarify the oncogenic role of NPM1 mutations and other putative cooperating genetic lesions in NPMc AML.

Acknowledgments

we would like to thank Prof. Yoh Iwasa for advice and Dr. Geraldine Boyd for her assistance in editing the manuscript.

Footnotes

  • Funding: this work was supported by A.I.R.C. (Associazione Italiana per la Ricerca sul Cancro); University of Foggia Research Grant, PRIN-MiUR; the BMBF-InnoRegio; the TP8 as well as the Josè-Carreras Leukemia Foundation; the Study Alliance Leukemia (SAL); the Competence Net “Acute and Chronic Leukemias”; and the Dutch Cancer Society “Koningin Wilhelmina Fonds”. FC and AC acknowledge partial support of the EC contract FP6-2004-IST-4, No.028069 (ImmunoGrid).
  • This paper contains Supplementary Material. AL, FC and AC contributed equally to this work.
  • The online version of this article contains a supplemental appendix.
  • Authorship and Disclosures AL and BF had the original idea, coordinated the whole project and wrote the paper; FC and AC adapted the one-mutation mathematical model to the study of AML with mutated NPM1 and helped write the manuscript. FS performed the statistical analyses on incident cases before fitting the one-mutation model; RFS collected molecular and clinical data from patients of the AMLSG study and helped write the manuscript; SA was involved in designing the GIMEMA study and collecting clinical data from patients; CT performed molecular analyses of patients from DSIL and helped write the manuscript; SS performed mutational analysis in patients from the Munich Leukemia Laboratory (MLL) and helped write the manuscript; PJMV carried out molecular studies on AML patients from The Netherlands and reviewed the manuscript; KD collected molecular and clinical data from patients of AMLSG study and helped write the manuscript; MFM recruited patients in the GIMEMA study and reviewed the manuscript; MS designed and coordinated the clinical study (DSIL); JK collected molecular and clinical data from patients of the AMLSG study; AG collected clinical data from patients of the AMLSG study and coordinated the clinical study (AMLSG); MPM and NB performed immunohistochemical studies on the GIMEMA patients; BL recruited patients from The Netherlands and reviewed the manuscript; TH coordinated the study of patients from the Munich Leukemia Laboratory (MLL) and helped write the manuscript; GE designed and coordinated the clinical study (DSIL); FM designed and coordinated the clinical study (GIMEMA); HD designed and coordinated the clinical study (AMLSG); FM carried out computational simulation studies and helped write the manuscript.
  • The authors reported no potential conflicts of interest.
  • Received April 9, 2008.
  • Accepted May 7, 2008.

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Vol. 93 No. 8 (2008): August, 2008 : Decision Making and Problem Solving
 
DOI
https://doi.org/10.3324/haematol.13209
Pubmed
18603563
 
Published
2008-08-01
Published By
Ferrata Storti Foundation, Pavia, Italy
Print ISSN
0390-6078
Online ISSN
1592-8721
 

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