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发表于 2009-3-5 00:55 |只看该作者 |倒序浏览 |打印

作者：Franziska Michor作者单位：Society of Fellows, Harvard University, Cambridge, Massachusetts, USA, and Dana Farber Cancer Institute, Boston, Massachusetts, USA 5 H! w" D- k1 ~9 M5 ?/ @- ?, _
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      【摘要】' }. z- d/ `4 ~  h
   Chronic myeloid leukemia (CML) progresses through three distinct clinical stages: chronic phase, accelerated phase, and blast crisis. The progression to accelerated phase and blast crisis is driven by activation of oncogenes, inactivation of tumor suppressor genes, and/or amplification of the BCR-ABL fusion gene, which causes the chronic phase of the disease. The cell of origin of blast crisis is a subject of speculation. Here, I develop a simple mathematical model of CML blast crisis to investigate whether blasts arise from leukemic stem cells or more differentiated leukemic cells. I use data of patients treated with imatinib and previous agents to estimate the effects of therapy on the rate of progression. Imatinib reduces the progression rate 10-fold as compared with previous (ineffective) therapies. If blasts were produced by leukemic stem cells, there would be no difference in the rate of progression between patients treated with imatinib and previous therapies, because imatinib seems to be incapable of depleting leukemic stem cells. Imatinib does, however, deplete leukemic progenitors. Therefore, CML blasts are likely to arise from leukemic progenitors.
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Disclosure of potential conflicts of interest is found at the end of this article.
      【关键词】 Chronic myeloid leukemia Hematopoietic stem cells Hematopoietic progenitor cells Differentiation$ L. S# n7 m" e9 ]$ m
   INTRODUCTION
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Chronic myeloid leukemia (CML) is associated with the Philadelphia (Ph) chromosome, a t(9;22) translocation producing the BCR-ABL fusion gene .

The cell of origin of CML has been the subject of much discussion .! s: V; F% k  v* G5 o+ I2 g

Progression to blast crisis is driven by additional genetic and/or epigenetic events such as duplication of the Ph chromosome, trisomy 8, and mutations or deletions in tumor suppressor genes like p16 and p53 . Hence, the experimental evidence remains inconclusive and invites theoretical investigations.

It is important to identify the cell population that is responsible for driving the progression of chronic phase CML to blast crisis. Knowledge of the cell type and mutations responsible for disease progression might suggest new treatment strategies for accelerated phase and blast crisis patients and help us understand the natural history of CML. In this paper, I design a simple mathematical model of CML progression and investigate the cell of origin and the dynamics of blast crisis.4 ]) I3 g7 V& d% N7 ~2 L

MATERIALS AND METHODS

Denote the abundance of leukemic stem cells and leukemic progenitors by y0 and y1, respectively. Leukemic stem cells grow at rate r and die at rate d0 per day. Leukemic progenitors are produced by leukemic stem cells at rate a and die at rate d1 per day. The leukemic stem cell population is described by y0 = (r ¨C d0)y0 and the leukemic progenitor population by y1 = ay0 ¨C d1y1, where x = dx / dt. With the initial conditions y0(0) = 1 and y1(0) = 0, the numbers of leukemic stem cells and progenitors at time t are given by1 y1 y- E  o. S$ {* @
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and
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1

This model assumes exponential expansion of leukemic stem cells and neglects density dependence effects within the bone marrow for mathematical simplicity. A model considering density effects is the topic of another paper .8 V7 D! `) M/ P* B, `! o

Blasts can arise either from leukemic stem cells or from leukemic progenitors. Denote the abundance of blasts at time t by z(t) and their rate of production per cell division by µ. If blasts arise from leukemic stem cells, then their abundance at time t is given by
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2

If blasts arise from leukemic progenitors, then their abundance is given by' e( {( K' @; W( z" c1 \8 L

3

where s = r ¨C d0 d1. The probability of blast crisis at time t is given by  u% Z% p+ L1 L: E( M

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RESULTS
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This model allows us to study the dynamics of blast crisis CML and to test the hypothesis that blasts arise from leukemic progenitors. A detailed quantitative analysis of the in vivo kinetics of chronic phase CML demonstrates that imatinib leads to an exponential decline of leukemic progenitors . Their abundance decreases at a rate of 0.8% per day, which corresponds to an average lifespan of 125 days during therapy., |# L* ~$ K: k2 k
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Leukemic stem cells, however, do not seem to be depleted during imatinib therapy. This conclusion is drawn from the relapse dynamics of patients who discontinue therapy. Despite being treated with imatinib for up to 3 years, the leukemic cell counts in those patients rise within weeks after stopping therapy to levels at or beyond pretreatment baseline .2 Z! u& v& n) g
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The observed probability of progression to blast crisis is 1%¨C2% per year for patients on imatinib therapy and 10%¨C20% per year for patients on previous therapies such as -interferon plus cytarabine (Table 1) . For the purpose of the analysis, I regard previous therapies as ineffective and compare the probabilities of progression to blast crisis with and without imatinib treatment, respectively, at 1%¨C2% and 10%¨C20% per year. Hence, imatinib reduces the probability of blast crisis 10-fold." b/ H( p7 r4 t! g( ~

Table 1. Annual rate of failure on imatinib
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If blasts arise by mutation from the leukemic stem cell pool, then the probabilities of progression to blast crisis with and without imatinib should be the same, because imatinib does not seem to deplete leukemic stem cells. Treatment would not attenuate blast crisis if it did not change the abundance of the cells driving blast crisis. Figure 1 shows the probability of blast crisis at time t when blasts arise from stem cells (equations 2 and 4). The probability is the same with and without imatinib therapy, because imatinib is assumed not to change the behavior of leukemic stem cells.
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Figure 1. The figure shows the probability of progression to blast crisis over time when blasts arise by mutation from leukemic stem cells. Equations 2 and 4 are shown. The curve is the same for patients receiving imatinib therapy and for untreated patients, because imatinib cannot deplete leukemic stem cells. Parameter values are the growth rate of leukemic stem cells r = .008, the death rate of leukemic stem cells d0 = 0.003, and the rate at which blasts arise per cell division µ = 10¨C8. See the text for a discussion of the parameter values. Abbreviations: p, probability of progression to blast crisis; t, time.
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If blast crisis is driven by leukemic progenitors, however, then the probability of progression with imatinib treatment is expected to differ from the probability of progression without imatinib treatment, because imatinib does deplete leukemic progenitors. Figure 2 shows the probability of blast crisis at time t when blasts arise from progenitor cells (equations 3 and 4). The probability is much (10-fold) lower when the patient is treated with imatinib than when there is no treatment.

Figure 2. The figure shows the probability of progression to blast crisis over time when blasts arise by mutation from leukemic progenitors. Equations 3 and 4 are shown. The right curve shows the probability of blast crisis when the patient is treated with imatinib, and the left curve shows the probability of blast crisis when there is no treatment. The rate of progression with imatinib therapy is 10-fold lower than the rate of progression without imatinib therapy. Parameter values are the growth rate of leukemic stem cells r = .008, the death rate of leukemic stem cells d0 = 0.003, the death rate of leukemic progenitors d1 = 0.008, the rate at which blasts arise per cell division µ = 10¨C8, and the rate at which leukemic progenitors are produced by stem cells a = 0.1 (right curve) and a = 1 (left curve). Abbreviations: p, probability of progression to blast crisis; t, time.

Unfortunately, growth and death rates of leukemic stem cells have not been measured in vivo. However, the net proliferation rate can be inferred indirectly. The Philadelphia translocation might be the only genetic aberration needed to cause chronic phase CML ). In Figures 1 and 2, I chose r = 0.008 and d0 = 0.003 as a particular example. These rates are the same for imatinib-treated and untreated leukemia. The rate at which leukemic progenitors are produced from stem cells, a, depends on the presence of imatinib treatment. I assume a = 1 for an untreated patient and a = 0.1 for a treated patient.
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The probability of blast crisis depends on the mutation rate of producing blasts. If one single base change can transform a cell into a blast and this cell has a high probability of survival, then the rate at which blasts arise is µ = 10¨C8 (Figs. 1, 2) . Figure 3 shows how the probability of blast crisis depends on the parameter µ.

Figure 3. The figure shows the dependence of the probability of blast crisis on the rate at which blasts are produced from leukemic stem cells, µ. Equations 2 and 4 are shown. Parameter values are the growth rate of leukemic stem cells r = .008, the death rate of leukemic stem cells d0 = 0.003, and the rate at which blasts arise per cell division µ = 10¨C12 (right curve), µ = 10¨C11, ... µ = 10¨C6 (left curve). Abbreviations: p, probability of blast crisis; t, time.7 H6 G0 B3 W: c7 B
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DISCUSSION. [& E1 F+ l* K# T2 Z3 @
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In this paper, I design a mathematical model of CML progression and investigate which population of leukemic cells is responsible for driving blast crisis. Blasts can, in principle, arise by mutations occurring in leukemic stem cells or in leukemic progenitors. The mutations arising in stem cells could be activation of oncogenes, inactivation of tumor suppressor genes, and/or other genetic changes deregulating cellular growth, whereas the mutations occurring in progenitors could additionally include changes facilitating self-renewal. In the model, the evolutionary process of mutation is encapsulated in the parameter µ, which denotes the rate at which blasts arise. This parameter includes one or more mutations and also the probability that cells carrying such mutations survive to initiate blast crisis. The specific genetic changes needed to induce blast crisis are unknown, and their identification is an important goal in CML research.

Leukemic stem cells seem to be insensitive to imatinib therapy in vivo . Currently, the mechanism of insensitivity of leukemic stem cells to imatinib therapy is subject of speculation, and more experimental and theoretical studies must be undertaken to elucidate this phenomenon.5 W: [* K& {4 ^0 z

The probability of progression to blast crisis is 10-fold higher for patients who are not treated with imatinib than for patients receiving imatinib therapy. If imatinib does not significantly deplete leukemic stem cells, then blasts must arise from leukemic progenitors¡ªotherwise, the probabilities of progression with and without imatinib would be the same. There are two caveats to this conclusion. The first is that imatinib could be capable of reducing the elevated mutation rates brought about by the BCR-ABL oncogene. Indeed, a CML mouse model suggests that BCR-ABL leads to a two- to threefold increase in the point mutation rate, which can be reversed by imatinib therapy . Therefore, an explanation invoking decreased expansion of leukemic stem cells seems ungeneric. I conclude that CML blast crisis likely arises from leukemic progenitors., n, x# N- r, t5 O0 c4 I& V

DISCLOSURE OF POTENTIAL CONFLICTS OF INTEREST: T3 p0 z) @! K  e1 @# E

The author indicates no potential conflict of interest.
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