Mathematical Model of Granulocytopoiesis and Chronic Myelogenous Leukemia1

[CANCER RESEARCH 51. 2084-2091. April 15. 1991] Mathematical Model of Granulocytopoiesis and Chronic Myelogenous Leukemia1

A. S. Fokas,2 J. B. Keller, and B. D. Clarkson

Department of Mathematics and Computer Science and Institute of Nonlinear Studies, Clarkson University, Potsdam, New York 13699-5815 [A. S. F.J; Department of Mathematics, Stanford University, Stanford, California 94305 [J. B. K.]; and Department of Medicine, Memorial Sloan-Kettering Cancer Center, New York, New York 10021 [B. D. C.J

ABSTRACT by maturing without further dividing. In Fig. 2, the route via cell division is represented by the upper line, and that via We present a mathematical model of granulocytopoiesis that depends maturation is represented by the lower line. For each cell type, on certain physiologically meaningful parameters. By choosing different values of these parameters, the model describes both the normal process there is a specific number n of stages, a certain time that a cell and that in chronic myelogenous leukemia ((Ml,). The model fits all the remains in each stage, and a number/ which is the fraction of available experimental data tested. Furthermore, it shows how the CML cells that continues dividing as opposed to maturing without cells can ultimately outnumber the normal cells and how this process can further dividing. In Fig. 2, myeloblasts pass through 3 stages be very slow. The model provides a quantitative approach to the relation (nb = 3), promyelocytes go through 2 stages (/ip= 2), myelocytes ship between proliferation and maturation and resolves the apparent go through one stage (/im = 1), and cells of subsequent types contradiction between decreased proliferation and increased production, have one stage each, which involve maturing but no dividing. by assuming that a greater fraction of CML cells is produced by division The subscripts b, p, and m refer to myeloblasts, promyelocytes, rather than by maturation. The model should be helpful in designing and myelocytes, respectively. experiments to better define the abnormalities of proliferation and mat The data indicate that the /is and/or the/s are slightly greater uration in CML and in seeking to define the specific alterations in the cell regulatory networks resulting from the production of the chimeric for CML cells than for normal cells. We fit all the data for p2jQbor-.biprotejn characteristic of CML. CML by taking greater/s but by keeping the ns the same for both CML and normal cells. This is in accord with the claim of Strife et al. (7, 8) that CML involves discordant maturation INTRODUCTION rather than uncontrolled proliferation. The model for the proliferative cells and its consequences is Granulocytopoiesis, the production of white blood cells, oc presented in "Materials and Methods." It involves 8 parame curs in the bone marrow where cells evolve through a sequence ters, /ib, /ip, nm,/b, /p, /m, q, and T, where q denotes the rate at of cell types beginning with committed stem cells (see Fig. 1). which myeloblasts are produced by stem cells and T is the time Quantitative data have been obtained on various aspects of this a cell spends in each stage. The experimental data are then process, such as the number of cells of each type, the time they described under "Results," and it is shown that the model fits remain of that type, the time they spend in mitosis, the time the data when the parameters in it are given appropriate values. they spend in DNA synthesis, etc. Both normal subjects and We also present a model for the committed stem cells somewhat those with CML' have been studied. Recently, supplementary similar to others discussed in the literature (see for example data have been obtained on the growth of granulocytes in vitro Refs. 9 and 10). It hypothesizes that a stem cell differs from an (1), and progress has been made in identifying the pluripotent ordinary cell in having the ability to gain proliferative advantage stem cell (2, 3). by resting for a sufficiently long time. This hypothesis distin To organize and correlate the current data, as well as those guishes stem cells from ordinary cells, and gives physiological forthcoming from new experimental procedures, we have de meaning to the notion of "recycling" of cells used in previous vised a mathematical model of granulocytopoiesis. It describes models. The same model, but with different parameter values, both the normal process and that in CML, with different is assumed to apply in CML. It shows how the CML cells can parameter values for the 2 cases. The model is formulated in ultimately outnumber the normal cells, and how this process terms of physiologically meaningful measurable quantities. It can be very slow. is more complete than previous models (4-6), and although it incorporates many simplifications, it is reasonably compatible with available data, insofar as we have been able to resolve MATERIALS AND METHODS inconsistencies and input missing values in the data. As a Formulation of the Model. A list of the symbols used in formulating consequence, the model can provide quantitative information the model is shown in Table 1. about granulocytopoiesis and it can be used to make predictions. In granulocytopoiesis, a cell passes through a succession of stages The model deals with the number of cells of the 7 types before it reaches the bloodstream. Stem cells produce myeloblasts in indicated in Fig. 1, but primarily with those of the 3 proliferative Stage I at the rate q cells per unit time per kilogram of body weight. A fraction/, of these cells is active. After a time 7",,the active cells divide typesâ€”the myeloblasts, promyelocytes, and myelocytes. It is assumed that cells of each of these 3 types go through a number remaining myeloblasts but in Stage II, while the remaining cells enter of stages either by dividing a certain number of times, or else Stage II by maturing. We assume for simplicity that this also happens in time T\. Received 10/29/90; accepted 2/5/91. These processes of dividing and maturing continue as is indicated in The costs of publication of this article were defrayed in part by the payment Fig. 2. At each division, a fraction of the daughter cells remains active of page charges. This article must therefore be hereby marked advertisement in and the others become inactive. After a certain number nb of divisions accordance with 18 U.S.C. Section 1734 solely to indicate this fact. ' A. S. F. and J. B. K. were partially supported by the Office of Naval Research, or equivalent maturation, the myeloblasts become promyelocytes. After the National Science Foundation, and the Air Force Office of Scientific Research. np more divisions or equivalent maturation, the promyelocytes become B. D. C. was partially supported by the Rudin Foundation, the United Leukemia myelocytes and after nmadditional divisions or equivalent maturation, Fund, and Grant CA20194 from the NIH. 2To whom requests for reprints should be addressed. the myelocytes become metamyelocytes. Then the metamyelocytes ma 3The abbreviations used are: CML, chronic myelogenous leukemia; MI, mi- ture to become bands that mature into segmented granulocytes before totic index; TM, mitotic time; LI, labeling index. entering the bloodstream. 2084

BONE MARROW 1CommittedStem

Fig. 1. Conventional scheme of granulo- â€”1CellMyelo- Â»blast1Promyelo-â€” *cyteProliferatiâ€” *cyte_lMelamyelo-â€” Segcyte1 â€”Â» band â€”* Death cytopoiesis.

veMyelo- Non-Proliferative Marginal Pool

where aÂ«=2(1 -JÃœGtÃ¶~ l]/(2/ - I) and/Â¡=/b,/2 =/p, and/3 =/m Let Q denote the flux per kilogram of body weight from myelocytes to metamyelocytes and let /Vb,Â¿Vp,andNm denote the total number of myeloblasts, promyelocytes, and myelocytes per kilogram of body weight, respectively. Then: 14 " + AC- 0 = IÃŽ+MJ-),iÂ«=./myeloblast to a value near zero for a last-stage myelocyte. How locytes, respectively ever, for simplicity we assume thatyj is piecewise constant with values 7"m(h): Mitotic time T, (h): DNA synthesis time /b,/p, and/m for the relevant types. B (kg"1): Total blood granulocytes Equations 2.1 and 2.2 admit steady-state solutions for A, and MÂ¡.Let X(h"1): In 2/half-life of a granulocyte superscripts b, p, and m denote the myeloblasts, promyelocytes, and myelocytes, respectively, i.e.. A] = A, for 1 râ€”,â€” - ,â€”+â€”, i

Downloaded from cancerres.aacrjournals.org on September 28, 2021. © 1991 American Association for Cancer Research. GRANULOCYTOPOIESIS AND CML greater than 4 x 104/(mm)\ (LI)b for CML cells is slightly larger than one-half of the normal value. The labeling index for myelocytes seems to be independent of the white blood cell count and is approximately equal to the value for normal cells (23). The DNA synthesis time of CML myeloblasts is similar to that of normal myeloblasts (24). Using these data for mye Fig. 3. Elaboration of one compartment of granulocytopoiesis. loblasts and myelocytes, we find the GCMLSgiven in Table 2, where the value of (GCML)Pwas interpolated from the values of (LI)b = 0.46, (LI)P = 0.38, and (LI)m = 0.19. The DNA synthesis (GCML)I,andof (GcMÃœm.Thetotal number of blood granulocytes time. T*,,is the time spent in DNA synthesis; values both in and the half-life of granulocytes are also influenced by the white blood cell count. The half-life in CML is 5 to 10 times longer vivo and in vitro range from 13 to 16 h (16). The total number of myelocytes per kilogram of body weight, Nm, is 26 x 108/kg than for normal granulocytes (25) and B is increased by 10 to (18). 100 times (26). The estimated value of Q given in Table 2 is calculated as It is well-established that there is traffic of immature CML follows. The total number of blood granulocytes B equals the cells between bone marrow, spleen, and peripheral blood. The sum of circulating and marginal granulocytes, i.e., B = (3.1 x cytokinetics of cells in bone marrow and spleen are similar (20). 10s + 3.9 x 10s) = 7 x IO8(19). At steady state, Q = \B, where The immature CML cells in the periphery have the striking X= In 2/(half-life of a granulocyte); given that the half-life of a feature that, although they synthesize DNA, they divide ex granulocyte is 7 h (19), it follows that Q = 0.103, hence Q = 0.103 x 7 x IO8. Let G denote the ratio TJIA = TJMl; it tremely rarely. In what follows, we will consider a functional follows from the model that these ratios are equal. The esti pool of proliferative cells. This pool contains the immature mated values of the Gs given in Table 2 are computed as follows: cells existing in bone marrow, spleen, and blood. For the Assuming that (Ts)b = 14, (7"5)p= (7"s)m= 15, and the values of cytokinetic data of this pool, we will use the relevant data in Lis given above, we find Gb = 30, Gp = 40, and Gm= 79. Using bone marrow, since it contains the majority of the typical CML these Gs and the Mis given above, we find (7"m)b= 0.75, (7*m)p immature cells. Using the typical values XCML/A= 0.25 and = 0.56, and (Tm)m= 0.79. The only discrepancy is with respect BCML/B = 50, we find QCML= 12.5ÃŸ. to promyelocytes. Indeed judging from the low mitotic index One of the most important developments in recent years is we would expect a (LI)P around 0.28. Thus, a better value for the discovery of growth factors that allow investigators to Gpis 47. We point out that the data on promyelocytes appearing culture and follow granulocytes in vitro. In a typical such study, in the literature are the most disparate as compared with those an aspirate of cells is obtained from the bone marrow, and after of myeloblasts and myelocytes. A reasonable option is to as sume the experimental values for myeloblasts and myelocytes it is appropriately treated, so that only certain types of cells and then extrapolate the value for the promyelocytes. This also survive, it is cloned and followed for a certain period of time. implies that Gp = 47 is preferable to Gp = 40. Usually both the number of colonies and the number of cells in The generation time 7"was computed by using 7*5= 0.757. It each colony are recorded at 3, 7, and 14 days. A number of is consistent with the values of 7"sgiven previously (20). A such studies for CML are reviewed by Strife and Clarkson (8), measured value of T of about 30 h can be inferred from the from which we extract the following data. Let a denote the cinematography experiments described previously (15). How number of colonies produced, divided by the number of cells ever, it is known that during cinematography, the light slows cloned. Then OCML/Â«=2.5, where OCMLand a refer to CML down the mitotic process. and normal, respectively. If only immature cells are cloned Experimental Data for CML Patients (mature promyelocytes and essentially all myelocytes are ex cluded), then Â«c-ML/ff=L The proliferative model presented Values for Nf/N\, and Nm/Np are given (21 ). The data regard here provides a convenient basis for discussing the culture data. ing labeling index are quite variable (see for example Refs. 20, Since only the active compartment produces colonies, it follows 22, and 23). It appears that if the white blood cell count is that a = A/N, where A is the total number of active cells, M is the total number of maturing cells, and N = A + M. Further Table 2 ExpÃ©rimentaldata more, A, N, and M are the values at steady state. Recall that G = 7VLI, thus G = TNIA = T/a. Assuming that the value of G Ap/vÂ»NmN,GtOPG.Aâ€žQa.NmTNormal2.4-3.53-4.530477926for the entire proliferative compartment is approximately the same for normal and CML cells, then the culture data and T = Ga imply that the generation time for CML cells is approxi mately twice the value ofthat for normal cells. This is consistent with older cytokinetic data (20). The culture data also indicate that the number of divisions in x10*72 the proliferative compartment is in the range of 5 to 10 (21). x10'0.02820CML2.15.555677990x10'39References(11-14,21)(11-14.21)(18.26)(19.26)(20) A Fit to the Model

Recall that G = -^,T LI = ATâ€”â€¢=,,andN = M + A. Hence G/T n /v / 2086

Table 3 Afit to the model A steady-state solution of these equations exists only if/equals N, NÂ«, Q_ Q one-half, and then they yield: /â€ž /Â» Nâ€ž N, N, q At = kA-t; AÂ¡= 2>-'kA-t, j = 1, (3.3) nb= 3, Â«p=nm= 2 Normal 0.8 0.6 0.5 2.2 2.3 0.03 16 Active stem cells from any Stagey equals 0, 1, â€¢â€¢-,m (see CML 0.8 0.8 0.7 2.3 2.4 0.023 29.5 Fig. 4) could in principle go to a resting state and then recycle. HI,=-NormalCML= 5, n, = nm 30.80.80.70.80.60.72.84.02.93.80.0240.01775217 However, since this more complicated situation does not alter our conclusions in a significant way, we assume for simplicity that recycling happens only from the active stage denoted by 0 in Fig. 4. Since we are concerned with granulocytopoiesis, we have treated granulocytopoiesis progenitors as if they were the Å’ fundamental stem cells. Although this is a mathematical ideal ization, it is straightforward to incorporate the pluripotent stem Fig. 4. A mathematical model for stem cells. cell in our model: (a) The granulocytopoiesis progenitors pos sess the property of "sternness," but they also get an input from = 1 + MÂ¡A.Using the experimental values in Table 2 for G the pluripotent stem cells. Thus a term Â«<;^sshould be added and T",we find (^) = 0.5, (^) = 1.35, (^) = 2.95 for to Equation 3.la, where 0Sis the flux from the pluripotent stem cell compartment, and Â«(1isthe fraction of these cells commit ted to granulocytopoiesis. (Similarly, aE and Â«Tarethe fraction normal cells and ) =0.41, ) = 0.72, ) = 1.03 for of cells committed to erythropoiesis and thrombopoiesis, re \^/b \A]9 \A/m spectively, and a(; + Â«F+ Â«T= 1.) (b) The pluripotent stem CML cells. Equation 2.3 implies that Iâ€”I is a certain function cells should be described by equations identical to Equations V'Vb 3.1 and 3.2. of/b and Â«b.Similarly, [â€”J is a function of/,, nh,fp, and nâ€ž, Several stem cell multiplication mechanisms have been pro M1 posed in the literature. The most popular is the clonal succes and I â€”I is a function of/b, /ib, /P, wp, /m, and nm. In what sion mechanism, which suggests that normal hematopoiesis is \^/m maintained by sequential activation of different stem cell cones follows, we assume values for the /is and we use these functions (27-31). In this system, there is always a large resting stem cell to determine the /s. For example, if nb = 3, wp= Â«m=2, then reserve. An alternative system suggests that the entire stem cell /b = 0.8, /p = 0.6,/m = 0.5 for normal cells, and/b = 0.8,/p = pool contributes to maintaining hematopoiesis (32-34). The 0.8, fm = 0.7 for CML cells. We also use Equation 2.3 to stem cell models are not necessarily mutually exclusive; one or compute Wp/yVb,NJNf, Q/Nm, Q/q. These results for 2 sets of another system may predominate in different circumstances Â«sare given in Table 3. depending on the need for replacement or expansion of the We can also fit all the data by taking greater Â«sfor CML mature cell compartments or for replenishment of the stem cell cells than for normal cells. But we cannot fit all the data by compartment (35-39). Pluripotent stem cells can presumably keeping the/s the same for both CML and normal cells. commit to produce cells of multiple lineages or exclusively of Using the culture studies reviewed in References 8 and 21 one lineage via a stochastic mechanism (27, 40, 41). The model and more recent comparative data on the growth of normal and depicted in Fig. 4 incorporates both the views mentioned above. CML progenitor cells of different degrees of maturity in culture, Indeed, if T-, Â» T,,, most of the sem cells are resting for most we have also used the proliferative model to compare the of the time. At the same time, the stem cell pool is continuously behavior of the cells in vitro with the older cytokinetic data rejuvenated through the production of new cells. This model obtained in vivo. The culture data will be presented in detail in admits a steady-state solution even with zero external input. another publication, but it should be noted here that there is This is a consequence of the postulate that cells "recuperate" generally good agreement between the in vitro and in vivo data. after resting. The loop between Stages -I and 0 may be inter preted as a concrete physiological realization of recycling. Extension of the Model to Stem Cells Recall that q denotes the flux from stem cells to myeloblasts. Thus, q equals 2Am/T0 equals 2mA-,/T-,, i.e.: The model can be extended by including in it the stem cell 2-M-, =

Downloaded from cancerres.aacrjournals.org on September 28, 2021. © 1991 American Association for Cancer Research. GRANULOCYTOPOIESIS AND CML but perhaps with different parameters. As an example, assume (a) Bands are produced from metamyelocytes through matura OTCML=m, (7"_,)cML= T-\. Then for the 2 numerical examples tion, i.e., metamyelocytes mature but do not divide. Since discussed in Table 1, Equation 3.4 yields (A-Â¡)c\\i./A-i 6.8 and myelocytes are not that different from metamyelocytes, one 4.3, respectively. would expect from continuity that myelocytes are also capable The steady state described above characterizes granulocyto- of maturing, (b) If one assumes only 2 compartments, resting poiesis after the CML clone has dominated. In order to under and active, then it can be shown that G = T + (1 â€”f)a, where stand how a single defective cell leads to the domination of the a is the time a cell spends resting. It has been well established leukemic over the normal cells, one needs to study the transient experimentally that Gm > Gp > Gb. Thus, according to this state. This state is still characterized by Equation 3.1. To model, increasing time is spent in resting as cells evolve toward simplify the mathematics, we take the relevant parameters / myelocytes. But this is in conflict with the concept that myelo T-1, and T0, to be piecewise linear. We assume that when a cytes were dividing more times than myeloblasts (see the Cronk defective stem cell appears, then a process similar to what ite-Vincent model). Also it is difficult to justify why proliferative happens in early granulocytopoiesis takes place. Namely, the cells spend increasingly longer times resting. In our model, the fraction of defective stem cells recycling is higher, and their increasing Gs reflect the fact that an increasing fraction of cells resting period is shorter. In a certain time period T, A-\ grows is produced via maturation the closer they are to myelocytes. from 1 to (/l-i)cML>/changes from some value Flo Vi, and T-, That is, a greater fraction of myelocytes follows the road to changes from (7"0)cMLto(7"_i)CMuwhere (A-,)CML,(r0)CML,and maturation than myeloblasts. This is also consistent, using a (7"-i)(Mi. denote the steady-state values of To, 7"-,, and A-, for continuity argument, with our assumption that stem cells are CML stem cells. By choosing F to be close to Vi it is possible produced only via division, (c) There is direct experimental to make r quite long. This is consistent with the fact that CML support for the concept above: Boll and KÃ¼hn(15),during one cells could take a long time [on the order of several years (42- of their cinematography experiments, happened to find a pro 45)] to dominate. myelocyte at mitosis and followed its history. One of its daugh ter cells entered mitosis after 29.5 h and the other after 28 h. Discussion and Extension of the Model The mitosis lasted for about l h and each of them gave birth to Discussion of the Model. The simplest and best-known model 2 myelocytes. One of the 4 newly born myelocytes could not be of granulocytopoiesis is that of Cronkite and Vincent (4). It followed. One entered mitosis after 29.5 h and gave birth to 2 postulates that each myeloblast divides once to produce 2 metamyelocytes after 1 h. These 2 metamyelocytes became promyelocytes, each promyelocyte divides once to produce 2 bands after 7 h. The other 2 myelocytes matured to bands after myelocytes, and each myelocyte divides twice to produce 4 37 h. Although these cells could not clearly be assigned to either metamyelocytes. Rubinow's (5) model is similar with one im myelocytes or metamyelocytes, in the process of maturation portant difference: it postulates that a fraction of the cells they had to become metamyelocytes before maturing to bands. produced by division of cells of any type remain of that type, Thus at least 2 metamyelocytes were created, not through the while the rest become cells of the next type. Rubinow and process of division, but through the maturation of 2 myelocytes. Lebowitz (6) proposed a time-dependent model based on the The arguments above suggest that when a cell divides, a fraction concepts of maturity and aging. It assumes that the stem cell /divides again and a fraction 1 -/enters a maturation state. A and all the proliferative cell types form one compartment in cell in a maturation state has a probability g of entering the which cells are either resting or dividing. As they note, none of next maturation state and a probability 1 â€”g of entering a the preceding models matches the experimental data. (Detailed dividing state. The cinematographic data mentioned earlier numerical values are given in Ref. 6.) A stem cell model describ indicate that, at least for myelocytes, 0 granulopoiesis has been presented suitable experiment is performed [similar to the experiment of (9). This model has been used to simulate several mouse exper Boll and KÃ¼hn(15)but more complete], we assume for simplic iments including acute, chronic, and postchronic irradiation, ity that g equals 1. By choosing suitable/s, we can fit all the hypoxia, various anemias, and hypertransfusion. Several other experimental data with any values of gs between 0 and 1. stem cell models have been discussed in the literature (see for The advantage of our proliferative model as compared with example Ref. 10). previous models is that it is more flexible. In particular, the We postulate that a cell can exist in 1 of 3 states: it can be parameters/can be chosen so that a large number of divisions resting, active, or maturing. A new cell can be produced through is possible. Since myelocytes are "close" to metamyelocytes 2 processes, via division or via maturation. Furthermore, we which only mature but do not divide, and since the myeloblasts assume that a stem cell can gain some proliferative advantage are more immature than myelocytes, we expect /, > /m and nb after resting. Thus, the most general model should include 3 > HP> /im. Table 3 shows 2 numerical examples in which we states (resting, active, and maturing), and it should allow stem are able to fit all the experimental data satisfying these con cells to recycle. We expect that in the stem cell compartment straints. It is interesting that we can fit the leukemic data by the maturing component can be neglected, whereas in the allowing slightly greater values of/s, without having to postulate proliferative compartment the resting component can be ne larger numbers of divisions for CML than for normal cells. glected. Thus, we assume a resting and an active state in the We note that/can be interpreted as the probability that when stem cell compartment, and an active and a maturing state in a cell divides it will go on to divide again, and 1 â€”/ as the the proliferative compartments. probability that it will enter a maturation state. Since there are no experimental data available yet for stem Regarding the stem cells, we assume as it was mentioned cells, we have concentrated on the non-stem proliferative cells. earlier that the maturing component can be neglected. To Most data concern the steady state, so we have investigated simplify the situation even further, let us assume that there is mainly the steady state of our model. There are several argu only one resting compartment. Then a normal cell would satisfy ments supporting the concept that proliferative cells can be the model of Fig. 5. It is clear that this model cannot admit a produced via the 2 mechanisms of division and of maturation: steady-state solution unless there exists an external input. But 2088

cause faulty programming of the genes whose expression is â€¢Â»onecessary for controlling the normal orderly sequence of prolif eration, differentiation, and maturation of hematopoietic cells, and that the consequence of this misregulation is asynchronous Resting development of the nucleus and cytoplasm (8,21). It was further Fig. 5. A mathematical model for dividing and resting cells. proposed that the lag in nuclear maturation produces the fol lowing 3 effects in CML cells: (a) They manifest the kinetic changes mentioned earlier as well as various dysplastic, bio -o2 â€¢Â»o chemical, and functional abnormalities; indeed a number of Dividing O investigators have emphasized that many if not all of the biochemical and functional abnormalities of CML granulocytes, including impaired adhesiveness and phagocytic and bac Resting teriocidal activities, are related to the degree of nuclear matu ration (59-61). (b) They have decreased proliferative activity Fig. 6. A mathematical model for dividing and resting stem cells. and live longer, (c) They perform 1 or 2 more divisions in the process of maturation than do comparable normal cells. The then how can the stem cells reproduce themselves? We have increased longevity and the additional divisions are used to proposed the following concrete physiological mechanism. explain the increased CML cellularity. The "discordant maturation" hypothesis described earlier (8, Consider a stem cell at the resting Stage I. We postulate that, 21) for CML is similar to the "blocked ontogeny" theory for as a result of resting for a sufficiently long time, when this cell becomes active it moves to Stage 0 as opposed to Stage I, i.e., experimental hepatomas (62, 63), and similar theories have a stem cell satisfies the model of Fig. 6. In other words, as a been suggested for other tumors (64-66). Therefore, models result of resting, a stem cell gains some proliferative advantage. used to elucidate the relationship between maturation and pro Although it could divide m times without resting, it can now liferation for CML cells should also be useful for analyzing a divide m + 1 times. The longer the resting period, the fewer variety of other neoplasms. The model for the proliferative divisions a stem cell undergoes, therefore lessening its exposure component of granulopoiesis presented here provides a quan to the risks of genetic errors that might occur during DNA titative approach to the relationship between proliferation and replication or mitosis. A long resting period also allows the cell maturation. It resolves the apparent contradiction between de ample opportunity to repair any DNA damage it may have creased proliferation and increased production, by assuming incurred previously. that a greater fraction of CML cells is produced by division Biological Implications. CML is among the best understood than by maturation. It suggests specific experiments to define of human neoplasms (21). In the great majority of CML pa better the relative roles of proliferation and maturation. It also tients, there exists a translocation of the distal segment of the implies that in trying to uncover the specific abnormalities in transduction pathways resulting from the production of p210bcr~ long arm of chromosome 22 to the distal portion of the long arm of chromosome 9 (46-48). This results in the transposition abl,the specific biological consequences of altered tyrosine phos of the c-ab\ oncogene to a specific region (ber) on chromosome phorylation must be clearly understood. For example, if one 22 and in the production of a novel chimeric phosphoprotein assumes that simple unregulated cell proliferation instead of p2jQbtr-aw(49_52). This chimeric protein is qualitatively differ discordant maturation is the end result of aberrant phosphor ent than the protein products of the ber and abl genes in normal ylation (21), experiments trying to correlate the molecular and cells, and has altered protein tyrosine kinase activity. It is likely biological abnormalities may be improperly designed. The that the t(9;22) translocation is the primary causative genetic model presented here should aid in designing specific experi lesion in CML and that the p210bcr~ablgene product is respon ments to better define the relative roles of proliferation and sible for inducing subtle distortion of critical regulatory mes maturation and the abnormalities occurring in CML. In seeking sages in the signal transduction pathways (8, 21). The trans- to define the specific alterations in the regulatory networks duction regulatory networks are highly complex and as yet resulting from the production of p21 OlXT~abl,itwould be advis incompletely understood (53). The protein tyrosine kinases that able to concentrate on how a cell committed to differentiation phosphorylate proteins exclusively on the hydroxyl group of along a particular linkage makes the decision whether to con tyrosine have key roles in signal transduction and regulation of tinue proliferating in a given maturation compartment or else cell growth and differentiation. There is increasing evidence to proceed directly to the next stage of maturation without that aberrant tyrosine phosphorylation is a common mechanism further division. The time-dependent solution of the model of malignant transformation; many of the known oncoproteins discussed here should also be of interest in analyzing the effect that act outside the nucleus are protein tyrosine kinases (54). It of hematopoietic growth factors on granulocytopoiesis and the is suspected that mutations that convert normal protein kinase competition between regenerating normal and leukemic cells genes into oncogenic genes somehow interfere with negative after bone marrow transplantation. An analysis of the time- regulatory domains, thus allowing the kinases to escape from dependent model should provide a better understanding of the their normal regulation and act constitutively to phosphorylate mechanisms of regulation of granulopoiesis by hematopoietic their substrates. Whereas there is as yet very little information growth factors (67-72), and it should aid in defining the optimal about what specific proteins in the regulatory networks may be dosage and temporal intervention of stimulatory factors. Allo- abnormally phosphorylated by oncoproteins with increased ty geneic bone marrow transplantation is the only consistently rosine kinase activity (21), the transforming potency of p210bcr~ curative treatment for CML. Transplantation is performed after abland other bcr-abl oncogene products appear to be correlated lethal marrow ablative doses of irradiation and/or cytotoxic with their kinase activities (55-58). It has been proposed that drugs have been given to try to cure the leukemia (73). When the aberrant phosphorylation of key regulatory proteins may successful, all leukemic progenitor cells are eradicated and 2089

Downloaded from cancerres.aacrjournals.org on September 28, 2021. © 1991 American Association for Cancer Research. GRANULOCYTOPOIESIS AND CML hematopoietic reconstruction occurs as a result of sustained 20. Ogawa, M., Fried. J.. Sakai, Y., Strife, A., and Clarkson, B. D. Studies of cellular proliferation in human leukemia. VI. The proliferative activity, proliferation of normal stem cells from the marrow graft (74- generation time, and emergence time of neutrophilic granulocytes in chronic 77). In some instances, it appears that it is possible to achieve granulocytic leukemia. Cancer (Phila.). 25: 1031-1049, 1970. 21. Clarkson, B. D., and Strife, A. Discordant maturation in chronic myelogen hematopoietic regeneration from only a few donor stem cells ous leukemia. In: A. Deisseroth and R. B. Arlinghaus (eds.). Chronic Mye or possibly even a single stem cell (76) as was previously logenous Leukemiaâ€”Molecular Approaches to Research and Therapy, pp. demonstrated in mice (29-31). In unsuccessful cases, the donor 3-90. New York: Marcel Dekker. Inc.. 1990. 22. Stryckmans, P. A. Current concepts in chronic myelogenous leukemia. marrow fails to engraft or is later rejected, or if any leukemic Semin. Hematol., //: 101-127, 1974. stem cells have survived the ablative treatment, they may regen 23. Stryckmans, P.. Debusscher, L.. and Socquet, M. Regulation of bone marrow erate and cause a recurrence of the disease. Bone marrow myeloblast proliferation in chronic myeloid leukemia. Cancer Res., 36:3034- 3038, 1976. transplantation provides a unique opportunity to study regen 24. Vincent, P. C., Cronkite, E. P., Greenberg. M. L.. Kirsten, C., Schiffer. L. erating normal hematopoietic progenitors as well as the com M., and Stryckmans, P. A. Leukocyte kinetics in chronic myeloid leukemia: I. DNA synthesis time in blood and marrow myelocytes. Blood. 33: 843- petition between repopulating normal and leukemic progenitors 850. 1969. (75, 77). When CML cells do reappear after transplantation, 25. Athens. J. W.. Raab, S. O.. Haab, O. P.. Boggs. D. R.. Ashenbrucker, H., they often proliferate more slowly, and it is much easier to Cartwright. G. E., and Wintrobe. M. M. Leukokinetic studies. X. Blood granulocyte kinetics in chronic myelocytic leukemia. J. Clin. Invest., 44: control the recurrent disease with antiproliferative drugs such 765-777. 1965. as hydroxyurea than was the case prior to transplantation (74- 26. Galbraith. P. R., and Abu-Zahra, H. T. Granulopoiesis in chronic granulo 77). Several possible theories have been proposed to explain cytic leukaemia. Br. J. Haematol., 22: 135-143, 1972. 27. Kay, H. E. M. How many cell generations? Lancet, //: 418-419, 1965. the altered biological properties of the residual CML cells after Micklem. H. S.. Burton, D. I., Ansell, J. D.. and Gray. R. A. Clonal transplantation (21), and we are planning additional experi organization of murine hematopoiesis: studies with an x-linked enzyme marker. In: S. A. Killman. E. I. Cronkite, C. N. Berat-Muller (eds.), Hae- ments to try to determine which theory is correct. We are also mopoietic Stem Cells, pp. 138-149. Copenhagen: Munksgaards. 1983. conducting additional experiments comparing the proliferation 29. Dick, J. E.. Magli, M. C., and Huszar. D. Introduction of a selectable gene into primitive stem cells capable of long-term reconstitution of the hemopoi- and maturation kinetics of normal and CML progenitors in etic system of W/Wv mice. Cell, 42: 71-79. 1985. culture systems before and after treatment and their response 30. Lemischka. 1.R.. Raulet, D. H., and Mulligan. R. C. Developmental potential to various regulatory factors. The time-dependent model should and dynamic behavior of hematopoietic stem cells. Cell, 45: 917-927, 1986. 31. Capel, B., Hawley, R., Covarrubias, L.. Hawley. T.. and Mintz, B. Clonal provide a useful framework to discuss and analyze such studies, contributions of small numbers of retrovirally marked hematopoietic stem especially those pertinent to granulopoiesis. cells engrafted in unirradiated neonatal W/Wv mice. Dev. Biol., 86: 4564- 4568. 1989. 32. Siminovitch, L., Till, J. E., and McCulloch, E. A. Decline in colony-forming REFERENCES ability of marrow cells subjected to serial transplantation into irradiated mice. J. Cell. Comp. Physiol.. 64: 23-32, 1964. Buescher. E. S., Ailing, D. W.. and Fallin, J. I. Use of an x-linked human 1. Metcalf. D.. Moore, M. A. S., Sheriden. J. W., and Spitzer. G. Responsive 33. ness of human granulocyte leukemic cells to colony stimulating factor. Blood. neutrophil marker to estimate timing of lyonization and site of the dividing Â«â€¢847-859.1979. stem cell pool. J. Clin. Invest., 76: 1581-1584, 1986. 2. Jones, R. J.. Wagner, J. E., Celano, P., Zicha, M. S., and Sharkis, S. J. 34. Harrison, D. E., Lerner, C., and Hoppe, P. C. Large numbers of primitive Separation of pluripotent haematopoietic stem cells from spleen colony- stem cells are active simultaneously in aggregated embryo chimeric mice. Blood, 69: 773-777, 1987. forming cells. Nature (Lond.). 347: 188-189. 1990. 35. Trainer, K. J.. Seshadri. R. S., and Morley, A. A. Residual marrow injury 3. Spangrude. G. J.. Heimfeld. S., and Weissman. I. L. Research articles: following cytotoxic drugs. Leuk. Res., 3: 205-210. 1979. purification and characterization of mouse hematopoietic stem cells. Science (Washington DC). 241: 58-62, 1988. 36. Ross, E. A. M., Anderson, N., and Micklem. H. S. Serial depletion and regeneration of the murine hematopoietic system. Implications for hemato 4. Cronkite. E. P., and Vincent. P. C. Granulocytopoiesis. Ser. Haematol.. 2: poietic organization and the study of cellular aging. J. Exp. Med.. 155: 432- 3-43, 1969. 444. 1982. 5. RubinoÂ», S. I. A simple model of a steady state differentiating cell system. J.Cell Biol.. 43: 32-39. 1969. 37. Harrison. D. E., and Astle, C. M. Loss of stem cell repopulating ability upon transplantation. Effects of donor age, cell number, and transplantation pro 6. Ruhinow, S. I., and Lebowitz, J. L. A mathematical model of neutrophil cedure. J. Exp. Med., 156: 1767-1779, 1982. production and control in normal man. J. Math. Biol.. /: 187-225, 1975. 38. MacMillan, J. R., and Wolf. N. S. Depletion of reserve in the hemopoietic 7. Strife, A., Lambek, C., Wisniewski, D., WÃ¤chter. M., Gulati, S. C., and system. II. Deadline in CFU-S self renewal capacity following prolonged cell Clarkson. B. D. Discordant maturation as the primary biological defect in cycling. Stem Cells, 2: 45-58, 1982. chronic myelogenous leukemia. Cancer Res., 48: 1035-1041, 1988. 39. Mauch, P., Rosenblatt. M., and Hellman, S. Permanent loss in stem cell self- 8. Strife, A., and Clarkson. B. Biology of chronic myelogenous leukemia: is renewal capacity following stress to the marrow. Blood. 72: 1193-1196, discordant maturation the primary defect? Semin. Hematol., 25: 1-19, 1988. 1988. 9. Wichmann, H. E., and Loeffler, M. Mathematical Modeling of Stem Cell 40. Leary, A. G., and Ogawa, M. Concise report: blast cell colony assay for Proliferation. Boca Raton. FL: CRC Press. 1985. umbilical cord blood and adult bone marrow progenitors. Blood, 69: 953- 10. Macken. C. A., and Perelson, A. S. Stem Cell Proliferation and Differentia 956, 1987. tion, A Multitype Branching Process Model. Lecture Notes in Biomathe- 41. Nakahata, T., Gross, A. J., and Ogawa, M. A stochastic model of self-renewal matics. Vol. 76. New York: Springer-Verlag, 1988. and commitment to differentiation of the primitive hemopoietic stem cells 11. Rondanelli. G. E.. Magliulo. E., Giraldi, A., and Cario, E. P. The chronology in culture. J. Cell Physiol.. 113: 455-458, 1982. of the mitotic cycle of human granulocytopoietic cells. Blood. 30: 557-568, 42. Kamada, N., and Uchino, H. Chronologic sequence in appearance of clinical 1967. and laboratory findings characteristic of chronic myelocytic leukemia. Blood, 12. Killman. S. A., Cronkite, E. P., Fliedner, T. M., and Bond. V. P. Mitotic 51: 843-850. 1978. indices of human bone marrow cells. I. Number and cytologie distribution of 43. Ichimaru. M.. and Ishimaru. T. Review of thirty years study of Hiroshima mitoses. Blood. 19: 743-750. 1962. and Nagasaki atomic bomb survivors: biological effects: leukemia and related 13. Wintrobe, M. M. Clinical Hematology, Ed. 6. Philadelphia: Lea & Febiger disorders. J. Radial. Res., (Suppl.) 89-96, 1975. Publishing Co., 1967. 44. Kamada, N.. and Tanaka. K. Cytogenetic studies of hematological disorders 14. Handbook of Biological Data of the National Academy of Sciences. Phila in atomic bomb survivors. In: T. Ishihara and M. S. Sasaki (eds.). Radiation- delphia: W. B. Saunders Company. 1956. induced Chromosome Damage in Man, pp. 455-474. New York: Alan R. 15. Boll. I., and KÃ¼hn,A. Granulocytopoiesis in human bone marrow culture Liss, Inc., 1983. studies by means of kinematography. Blood, 26: 449-470. 1965. 45. Tanaka, K., Takechi, M., Hong, J., Shigeta, C., Oguma, N.. Kamada, N., 16. Stryckmans, P.. Cronkite, E. P., Fache, F.. Fliedner. T. M., and Ramos. J. Takimoto, Y.. Kuramoto, A.. Dohy. H.. and Kyo, T. 9;22 translocation and Deoxyribonucleic acid synthesis time of erythropoietic and granulopoietic ber rearrangements in chronic myelocytic leukemia patients among atomic cells in human beings. Nature (Lond.), 211: 717-720. 1966. bomb survivors. J. Radial. Res., 30: 352-358, 1989. 17. Gavosto. F. Granulopoiesis and cell kinetics in CML. Cell Tissue Kinet., 7: 46. Nowell, P. C.. and Hungerford. D. A. Chromosome studies on normal and 151-163, 1974. leukemic human leukocytes. J. Nati. Cancer Inst.. 25: 85-109, 1960. 18. Donohue. D. M.. Reiff. R. H.. Hansen, M. L. Betson. Y., and Finch, C. A. 47. Rowley. J. D. A new consistent chromosomal abnormality in chronic mye Quantitative measurement of the erythrocytic and granulocytic cells of the logenous leukemia identified by quinacrine. fluorescence and Giemsa staining marrow and blood. J. Clin. Invest.. 37: 1571-1576. 1958. (Letter). Nature (Lond.). 243: 290-293. 1973. 19. Cartwright. G. E., Athens. J. W.. and Wintrobe. M. M. The kinetics of 48. Bernstein. R. Cytogenetics of chronic myelogenous leukemia. Semin. Hem granulopoiesis in normal man. Blood. 24: 780-803. 1964. atol.. 25: 20-34, 1988. 2090

49. Bartram, C. R., de Klein, A., Hagemeijer, A., van Agthoven, T., Geurts von 63. Potter, V. R. On the road to the blocked ontogeny theory. Adv. Oncol., 4: Kessel, A., Bootsma, D., Grosveld, G., Ferguson-Smith, M. A., Davies, T., 3-8, 1988. Stone, M., Heisterkamp, N., Stephenson, J. R., and Groffen, J. Translocation 64. Osgood, E. E. A unifying concept of the etiology of the leukemias, lympho- of c-abl oncogene correlates with the presence of a Philadelphia chromosome mas. and cancers. J. Nati. Cancer Inst., IS: 155-166, 1957. in chronic myelocytic leukaemia. Nature (Lond.), 306: 277-280. 1983. 65. Pierce, G. B., Nakane, P. K., and Mazurkiewicz, J. E. Natural history of 50. Groffen, J.. Stephenson, J. R., Heisterkamp, Nâ€žde Klein, A., Bartram, C. malignant stem cells. In: W. Nakahara, T. Ono, T. Sugimura. and H. Sugano R., and Grosveld, G. Philadelphia chromosomal breakpoints are clustered (eds.), pp. 453-469. Differentiation and Control of Malignancy of Tumor within a limited region, ber, on chromosome 22. Cell, 36: 93-99, 1984. Cells. Tokyo: University of Tokyo Press, 1974. 51. Hermans, A., Selleri. L., Gow, J., Wiedemann, L., and Grosveld, G. Molec 66. Lotem, J., and Sachs, L. Different blocks in the differentiation of myeloid ular analysis of the Philadelphia translocation in chronic myelogenous and leukemia cells. Proc. Nati. Acad. Sci. USA, 71: 3507-3511, 1974. acute lymphoblastic leukemia. Cancer Cells, 7: 21-26, 1989. 67. Metcalf, D. The granulocyte-macrophage colony-stimulating factors. Science 52. Clark, S. S., Najfeld, V., Dow, L., Champlin, R., Crist, W., and Witte, O. (Washington DC), 229:16-22, 1986. Molecular pathogenesis of bcr-aW oncogene expression in Ph+ leukemias. 68. Clark, S. C., and Kamen, R. The human hematopoietic colony-stimulating Cancer Cells, 7: 15-20, 1989. factors. Science (Washington DC), 236: 1229-1237, 1987. 53. Bourne, H. R., and DeFranco, A. L. Signal transduction and intracellular 69. Gill, G. N. Growth factors and their receptors. In: R. A. Weinberg (ed.), messengers. In: R. A. Weinberg (ed.), pp. 97-124. Oncogenes and the Oncogenes and the Molecular Origins of Cancer, pp. 67-96. Cold Spring Molecular Origins of Cancer. New York: Cold Spring Harbor Laboratory Harbor, NY: Cold Spring Harbor Laboratory Press, 1990. Press, 1989. 70. Leary, A. G., Hirai, Y., Kishimoto, T., Clark, S. C., and Ogawa, M. Survival 54. Hunter, T. Oncogene products in the cytoplasm: the protein kinases. In: R. of hemopoietic progenitors in the G0 period of the cell cycle does not require A. Weinberg (ed.), pp. 147-173. Oncogenes and the Molecular Origins of early hemopoietic regulators. Proc. Nati. Acad. Sci. USA, 86: 4535-4538, Cancer. New York: Cold Spring Harbor Laboratory Press, 1989. 1989. 55. Daley, G. Q., Van Etten, R. A., and Baltimore, D. Induction of chronic 71. Isfort, R. J., and Ihle, J. N. Multiple hematopoietic growth factors signal myelogenous leukemia in mice by the P210bcr-abl gene of the Philadelphia through tyrosine phosphorylation. Growth Factors, 2: 213-220, 1990. 72. Evans, J. P. M., Mire-Sluis, A. R., Hoffbrand, A. V., and Wickremasinghe, chromosome. Science (Washington DC), 247: 824-830, 1990. R. G. Binding of G-CSF, GM-CSF, tumor necrosis factor-alpha, and gamma- 56. Lugo, T. G., Pendergast, A-M., Muller, A. J., and Witte, O. N. Tyrosine interferon to cell surface receptors on human myeloid leukemia cells triggers kinase activity and transformation potency of bcr-aW oncogene products. rapid tyrosine and serine phosphorylation of a 75-Kd protein. Blood, 75:88- Science (Washington DC), 247: 1079-1082, 1990. 95, 1990. 57. Heisterkamp, N., Jenster, G., ten Hoeve, J., Zovich, D., Pattengale, P. K., 73. Thomas, E. D. Marrow transplantation for malignant diseases. J. Clin. and Groffen, J. Acute leukemia in bcr/aW transgenic mice. Nature (Lond.), Oncol., /: 517-531, 1983. ^4:251-253. 74. Thomas, E. D., Clift, R. A., and Fefer, A. Marrow transplantation for the 58. Elefanty, A. G., Hariharan, I. K., and Cory, S. bcr-abl, the hallmark of treatment of chronic myelogenous leukemia. Ann. Intern. Med., 104: 155- chronic myelogenous leukemia in man, induces multiple haemopoietic neo 163, 1986. plasms in mice. EMBO J., 9: 1069-1078. 75. Arthur, C. K., Apperley, J. F., Guo, A. P., Rassool, F., Gao, L. M., and 59. Pedersen, B. Annotation: functional and biochemical phenotype in relation Goldman, J. M. Cytogenetic events after bone marrow transplantation for to cellular age of differentiated neutrophils in chronic myeloid leukemia, lit. chronic myeloid leukemia in chronic phase. Blood, 71: 1179-1186, 1988. J. Haematol., 51: 339-344, 1982. 76. Turhan, A. G.. Humphries. R. K., Phillips, G. L., Eaves, A. C., and Eaves, 60. Brandt, L. Adhesiveness to glass and phagocytic activity of neutrophilic C. J. Clonal hematopoiesis demonstrated by X-linked DNA polymorphisms leukocytes in myeloproliferative diseases. Scand. J. Haematol., 2: 126-136, after allogeneic bone marrow transplantation. N. Engl. J. Med., 320: 1655- 1965. 1661, 1989. 61. Anklesaria, P. N., and Bhisey, A. N. Studies on electrophoretic mobility of 77. Offit, K., Burns, J. P., Cunningham, I.. Jhanwar, S. C., Black. P., Kernan, leucocytes and chronic myeloid leukemia patients. Ind. J. Exp. Biol., 23: N. A., O'Reilly, R. J., and Chaganti, R. S. K. Cytogenetic analysis of 609-612, 1985. chimerism and leukemia relapse in chronic myelogenous leukemia patients 62. Potter, V. R. Phenotypic diversity in experimental hepatomas: the concept after T cell-depleted bone marrow transplantation. Blood. 75: 1346-1355, of partially blocked ontogeny. Br. J. Cancer, 38: 1-23, 1978. 1990.

2091

A. S. Fokas, J. B. Keller and B. D. Clarkson

Cancer Res 1991;51:2084-2091.

Updated version Access the most recent version of this article at: http://cancerres.aacrjournals.org/content/51/8/2084

E-mail alerts Sign up to receive free email-alerts related to this article or journal.

Reprints and To order reprints of this article or to subscribe to the journal, contact the AACR Publications Subscriptions Department at [email protected].

Permissions To request permission to re-use all or part of this article, use this link http://cancerres.aacrjournals.org/content/51/8/2084. Click on "Request Permissions" which will take you to the Copyright Clearance Center's (CCC) Rightslink site.