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Furth, R. van

Meer, J.W.M. van der

Rytömaa, T.

Toivonen, H.

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RES: Journal of the Reticuloendothelial Society 34:227-234 (1983)
Kinetic Analysis of the Growth of Bone 
Marrow Mononuclear Phagocytes in 
Long-Term Cultures
R. van Furth, J.W.M. van der Meer, H. Toivonen, and T. Rytomaa
Department of Infectious Diseases, University Hospital, Leiden, The Netherlands 
(R.v.F., J.W.M. v.d.M.), and Institute of Radiation Protection, Helsinki, Finland (H. T., 
T.R.)
The present work concerns a mathematical analysis of the growth of mono­
blasts, promonocytes, and macrophages in long-term bone marrow cultures in 
the presence of conditioned medium. For this purpose, use was made of the 
normalized data of four experiments, each done in triplicate. The computer 
program was based on a concept of hypothetical subcompartments within 
each developmental stage. The growth parameters were then determined 
experimentally or by trial and error after a series of computer simulations.
The mathematical results are in close agreement with the numbers of mono­
blasts, promonocytes, and macrophages obtained by counts in 21-day-old 
bone marrow cultures. This approach provides a means to understand the 
kinetic behaviour of mononuclear phagocytes.
Key words: monoblasts, promonocytes, macrophages, kinetic analysis, bone-
marrow colonies
INTRODUCTION
Bone marrow cells proliferate in vitro when appropriate growth factors are 
added to the medium. Among other constituents of the medium, such growth factors 
determine which of the cell lines originating from the pluripotent stem cell will 
proliferate. For example, colony stimulating factor in fibroblasts or L-cell conditioned 
medium favours the growth of the mononuclear phagocyte and granulocytic cell 
lineages [2,4]. In a liquid culture system with a glass surface for the cells to adhere 
to, two kinds of colonies develop, one composed of mature granulocytes and their 
precursors and the other comprising macrophages, promonocytes and monoblasts [2 ]. 
Mixed colonies consisting of cells from both cell lines were never observed.
In a later study it proved possible to lengthen the initial culture time from 4 
days to about 2 1 days [7|. Cultures older than 9 days were found to consist entirely 
of  mononuclear phagocyte colonies. In these long-term cultures counts of  the total 
numbers of each type of cell were performed at various time-points. Since it is known
Received August 30, 1982.
Reprint requests: R. van Furth, Department o f  Infectious Diseases, Leiden, The Netherlands.
© 1983 Alan R. Liss, Inc
228 van Furth et al
that the sequence of development in vitro is monoblast, promonocyte, and macro­
phage [2], quantitative data allow a mathematical analysis of  the proliferation of 
mononuclear phagocytes in vitro. This had been done previously for 4-day cultures 
with a simple calculation [1]. The present study concerns a rigorous kinetic analysis 
of mononuclear phagocytes grown in vitro for 21 days.
MATERIALS AND METHODS
Bone Marrow Cultures
Bone marrow cells from SPF-Swiss mice were cultured in medium consisting 
of Dulbecco’s modified Eagle's medium containing 20% horse serum and 20% 
embryonic mouse fibroblast conditioned medium [colony stimulating factor (CSF-1)] 
in petri dishes provided with a glass coverslip [7]. The cultures were terminated after 
various periods of incubation.
For determination of the total number of mononuclear phagocytes during the 
first 4 days of culture, counts of these cells were performed on fixed coverslips; for 
counting at later time-points, the cells w'erc carefully removed from the coverslip by 
placing the petri dish on crushed ice before scraping with a rubber policeman. The 
cells were counted in a hcmocytometer. Next, for investigation of the cells remaining 
on the glass, the coverslips were fixed and stained. For calculation of the total number 
of cells in culture, a correction was made for the area of the petri dish surface not 
covered by the coverslip. Coverslips of duplicate cultures were rapidly dried in an 
airflow, fixed in absolute methanol, and stained with Giemsa stain. On these cover­
slips the distinction between granulocytic and mononuclear phagocyte colonies was 
made light microscopically. The cells of mononuclear phagocyte colonies were 
characterized as monoblasts, promonocytes, or macrophages as described elsewhere 
[2]. Monocytes cannot be identified in these colonies, because they stretch immedi­
ately after they are formed and then have a morphology indistinguishable from that 
of  macrophages [2].
RESULTS
Quantitative Data of Long-term Bone Marrow Cultures
Approximately 2.5 x 10' nucleated bone marrow cells/ml culture medium were 
incubated for a period of 21 days. To be able to apply quantitative data in a 
mathematical model permitting easy analysis, the data were normalized, the initial 
number of monoblasts being taken as one cell at time zero. An earlier study done in 
4-day bone marrow cultures had shown that each colony originates from one monob­
last [1,2]. Moreover, it was found that on day 4 there is one mononuclear phagocyte 
colony per 103 nucleated bone marrow cells plated [1,7]. The normalized data are 
presented in Table 1.
Model of Mononuclear Phagocyte Proliferation In Vitro
The developmental sequence and proliferative behaviour of these cells of  the 
mononuclear phagocyte cell line have been extensively studied both in vivo and in 
vitro in our laboratory [2,3,7). The results of these investigations were used to 
construct the block diagram in Figure 1. In addition to proliferating cells, each 
subpopulation includes a subcompartment of  nonproliferating cells. Such a model was
TABLE 1. Total Number of Monoblasts, Promonocytes, and 
Macrophages3
Kinetics of Cultured Mononuclear Phagocytes 229
Day
Monoblasts
x  1 0 3
Promonocytes 
x  I03
Macrophages 
x  I03
Total 
x  I03
0 0 . 0 0 1 0 . 0 0 1
4 0.03 0.03 0.07 0.13
7 0 . 2 0.4 l . l 1.7
10 0 . 2 1.1 4.0 5.3
14 0.4 2 . 0 5.3 7.7
17 0.3
*rt 
r 
1 5.9 8.7
21 0.3
oc• 8.9 13.0
“Values are means o f  normalized data o f  four experiments,  each done in 
triplicate 17 1; the initial number o f  monoblasts is taken as one cell at day 0 .
r
MONOBLASTS 1 ' PROMONOCYTES 1 1 DIVIDING i i MACRO-> ' * ‘ 'LJMUNULt bb , iMACROPh a GES' I m i A r r p
PHAGES
Fig. 1. Schematic presentation o f  the proliferation and maturation o f  cells o f  the mononuclear phago­
cyte cell line. B =  monoblast; P =  promonocyte; M =  macrophage: Q =  quiescent, nondividing cells;
a ,  /3, and 7  =  mean number o f  proliferative cells formed at mitosis; t  = cell death.
TABLE 2. Labelling of Cells ¡11 Mononuclear Phagocyte 
Colonies“
Day
Labelled cells
Monoblasts
(%)
Promonocytes
(%)
Macrophages
(%)
4 39 36 10
7 34 34 16
10 30 26 12
14 23 21 12
17 N D h 9 9
21 ND 6 4
aIncubated for 1 hour at 37°C in medium containing 0.1 ¡iCi/ml 
(3H|thymidine.
hND: not determined, because these cells cannot be identified with 
certainty.
thought to explain the course of the labelling indices (Table 2); and with the final 
parameter values (see below) selected in the present study, the labelling indices indeed 
showed the expected qualitative behaviour.
230 van Furth et al
The letters B, P, and M in Figure 1 indicate monoblasts, promonocytes, and 
macrophages, respectively; Q refers to quiescent, nondividing, cells; and the possible 
cell loss is indicated by f .  For this model we preferred the concept of quiescent (Q) 
cells to that of  G0 cells; if a quiescent cell survives, it leaves this subcompartment 
randomly with parameter \ q .  Parameters a ,  /3, and 7  represent the fraction of the 
daughter cells formed at mitosis that return to the cell cycle; thus 2 -a , 2-/3, and 2-y 
represent the numbers of  new nondividing (Q) cells. It was previously assumed that 
mononuclear phagocytes beyond the promonocyte stage do not proliferate in vitro. 
However, the 1 -hr [3H]thymidine labelling indices of the macrophages in liquid 
cultures are higher than 10% during the first 2 weeks of  culture (Table 2); this 
indicates that there is some proliferative activity within this compartment. These cells 
were named dividing macrophages.
Mathematical Analysis o f Proliferation of Mononuclear Phagocytes
Mathematical analysis of the quantitative data for the monoblasts, promono­
cytes, and macrophages, was performed with the DEMO (deterministic model) 
program, written entirely in Fortran and implemented on UNIVAC and ECLIPSE 
computers [5]. The model is based on hypothetical internal subcompartments in each 
phase of  the cell cycle. The system is described by first-order differential equations, 
and the program is developed around DGEAR, a subroutine obtained from the 
commercial IMSL (International Mathematical and Statistical Libraries, Inc.). The 
behaviour of  monoblasts, promonocytes, and macrophages, as shown schematically • 
in Figure 1, can be described by the following equations:
monoblasts:
^  =  -A ,<B>Bi(t) +  aXk ® B k(t) 
dt
dBj(t)
dt
\ j (B)Bj(t) +  Ai—l (B)Bj —l(t), \ = 2 .............k
=  -  X Q < B > Q B ( t )  -  ^ q (B )Q b  ( t )  +  (2 _  a)Ak' B>Bk(t) (1)
promonocytes:
=  - X i ,P)Pi(t) +  Xq (B)Q b (t) +  /3Xm (P|Pm(t)
^ 7^  =  - X j (P,Pi(t) +  Xj-i(P) P i - l ( t ) ,  i =  2, . . . , 111 
dt
d Q P(t) =  _ x Q (P,Qp(t)  -  MQ(P,Qp(t) + (2 - /3)Xm (P,Pm(t) (2)
dt
Kinetics of Cultured Mononuclear Phagocytes
dividing macrophages:
231
dMl(t!  =  - \ i (M)M i(t)  +  Xn,P)Qp(t) + 7Xn' M)Mn(t)
dt
+  Xi- i <M)M i — 1 (t), 1 = 2 --------- n (3)
dt
macrophages:
=  - w T ’QMCt) +  (2 -  7)Xn'M)Mn(t) (4)dt
In these equations, B| (t) is the number of monoblasts in a subcompartment i at time 
t; the number of cells in the other compartments is similarly denoted. Other parame­
ters are defined in Table 3.The solution of the differential equations was performed 
with initial values according to the real measurements; i.e., all initial values except 
those of  monoblasts were zero (the total number of monoblasts at t =  0 was 
normalized to unity). The parameters \  in the various compartments were calculated 
with the program using the cell cycle times given in Table 3 [5].
No direct experimental information is available on the cell loss from the 
population. However, to find a mathematical solution consonant with the measured 
behaviour of  the subpopulations, it was necessary to reduce “ n o w ” from monoblasts 
to promonocytes on the basis of  cell loss. Macrophages in the population also had to 
be “ killed” to keep their number at the observed level. Even then, there was a slight 
tendency of the calculated line to overshoot the data points (Fig. 2).
TABLE 3. Kinetic Parameters Used in the Simulation
(X <$>)
Cell loss factors 
„ (B)M Q 
„ <P)M Q 
,/ (NT)
12.00 hr
12.00 hr
12.00 hr
Cell cycle times 
Monoblasts1'
Promonocytes1*
Dividing macrophages
Mean number o f  proliferative cells formed at mitosis
«o
ft.
To
Parameter for transition o f  quiescent monoblasts to promonocytes
(X '%)
Parameter for transition o f  quiescent promonocytes to dividing macrophages
1.5
1.5 
2.0
0.1 hr I
0.1 hr- 1
0.3 h r " 1 
0
0.03 h r " 1
“Experimentally determined ( 1 ]. 
^Initial values o f  a, ß, and 7 .
232 van Furth et al
er
LU
CD
LUo
10000  -
5 0 0 0  -
1000  -
500
100  -
50 -
10 -
5 -
M A C R O P H A G E S  . e
1
PROMONOCYTES
0
MONOBLASTS
l 1 i 1 1 J_I_1_l
10 15 20
TIME (days)
Fig. 2. Growth o f  monoblast,  promonocyte,  and macrophage populations in bone marrow cultures 
incubated for 2 I days in the presence o f  CSF-I .  Symbols refer to counted numbers o f  monoblasts ( • ) ,  
promonocytes ( ■ ) ,  and macrophages ( A ) ;  the solid, dashed, and dotted lines represent the calculated 
growth pattern.
The feedback signal in the present model was derived from the number of 
monoblasts by progressively reducing parameters a?, /i, and 7  in the following way:
a 1 +  (a0 -  1)(1 -  C(t)) (5)
ß  =1  +  (ßa -  1)(1 -  C(t)) (6)
7 = To( l - C ( t ) )  (7)
y B;(t) + Qß(t)
C(t)
V B j ( o o )  +  Q b ( o o )
(8)
These are arbitrary assumptions, and they may be (probably are) biologically un­
sound. From the mathematical point of view, however, the relevant assumption is
Kinetics of Cultured Mononuclear Phagocytes 233
that a  and (3 approach unity when the population grows, and 7 approaches zero. This 
ast assumption means that dividing macrophages eventually evolve to a mere transit 
population, i.e., the cells divide just once and hence produce only nonproliferating 
end-cells (i.e., macrophages).
A series of computer simulations led to the selection of one set of  parameter 
values apparently consistent with the experimental data. These parameters are shown 
in Table 3. The calculated curves shown in Figure 2 fit well with the observations. 
The kinetic analysis also indicated that the first promonocytes originating in vitro 
from monoblasts appear after about 36 hr and the first macrophages 16 hr after that.
DISCUSSION
Several fates are possible for the daughter cells formed by mitosis. A daughter 
cell may proceed toward a new mitosis or revert to a resting or quiescent (Q) state, 
i.e., the mitotic cycle does not recur in the same subcompartment. Morphologically, 
a proliferative cell does not differ from a quiescent cell of the same type, but a 
quiescent daughter cell may mature to perform the function for which it was actually 
created. The final fate of any cell is death and disintegration, which can occur at any 
stage of maturity. The causes of cell death are not known.
The schematic presentation in Figure I may not reflect the true population's 
behaviour, because the growth kinetics of mononuclear phagocytes in vitro are 
complicated and at present there is too little detailed information to allow construction 
of an absolutely correct model. Some of the parameters used in this analysis can be 
determined experimentally (e.g., cell-cycle times [ 1 ]); other parameters given in 
Table 3 are determined by trial and error. For instance, the compartment of dividing
macrophages was included because a small percentage of macrophages label after 1- 
hr incubation with [3H(thymidine. The present study provides support for, but does 
not prove, the existence of these proliferating cells. For instance, these cells could be 
labelled promonocytes showing morphologic features of macrophages due to the in 
vitro conditions. Nevertheless, it is possible that a proportion of the macrophages 
arising from dividing promonocytes continue to divide in vitro because CSF-1 is 
present [4|. CSF-1 is required for the survival, proliferation, and differentiation of 
mononuclear phagocytes in bone marrow cultures (6 ).
Feedback analyses raise special problems because sufficient qualitative and 
quantitative information is lacking. From the mathematical point of view, the only 
solution is to have the artificial population to grow in a manner resembling the true 
population behaviour. It is not at all clear that cell loss is the mechanism responsible 
for the retardation of the growth rate of the subpopulations. It is possible, and even 
more likely, that the growth parameters do not remain constant. A reduction in the 
growth of mononuclear phagocytes in bone marrow cultures may be due to a relative 
CSF-1 deficiency (6 ]. We reduced the growth rate progressively in the model by 
changing parameters o\ /3, and 7 , i.e., the fraction of new proliferative cells; when 
the population grows, a  and approach unity and 7  approaches zero. This means 
that initially, dividing macrophages divide and return to the cell cycle, but eventually 
produce nonproliferating end-cells only.
The feedback signal could, of  course, be produced in another way. For example, 
this signal could arise not from monoblasts, but from the cell density in general or 
from humoral inhibitors |e .g . ,  monocyte production inhibitor (MPI) [8] or prostaglan­
234 van Furth et al
dins 13 11 whose concentration depends on the total number of (mature) cells. These 
signals could have a very complicated effect on the growth rate via changes in the 
cell cycle time. For example, it has been shown that in vivo a humoral factor [factor 
increasing monocytopoiesis (FIM)] has a stimulating effect on the monocyte produc­
tion by shortening the cell cycle time of the promonocytes [9]. In principle, many 
reasonable alternatives can be proposed for the control of the cell proliferation 
process, but very little experimental evidence is available.
It is possible that the parameter values prevailing in vitro at the time when the 
system is approaching the steady state are those that reflect most closely the population 
behaviour under undisturbed in vivo conditions. The active growth period in vitro 
might indicate population behaviour in vivo during regeneration or expansion, e.g., 
as a response to functional demands.
Even if the correct block diagram and all of the feedback mechanisms were
known, the mathematical description of the in vitro behaviour of  mononuclear phag­
ocytes would still depend on a large number of growth parameters that can be 
modified in different ways in the computer simulation to find apparently good 
agreement with experimental data. It is self-evident that most of these parameters 
must be determined experimentally; otherwise, the simulations remain of purely 
academic interest. However, a rigorous mathematical approach provides the means 
to find an explanation to the experimental results, and certainly constitutes one step 
toward a full understanding of  the kinetic behaviour of the cells of the mononuclear 
phagocyte cell line.
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Kinetic analysis of the growth of bone marrow mononuclear phagocytes in long term cultures

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