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A STOCHASTIC BRANCHING MODEL WITH FORMATION OF SUBUNITS APPLIED TO THE GROWTH OF INTESTINAL CRYPTS
被引:37
作者
:
LOEFFLER, M
论文数:
0
引用数:
0
h-index:
0
机构:
INST THEORET PHYS,W-6900 HEIDELBERG,GERMANY
INST THEORET PHYS,W-6900 HEIDELBERG,GERMANY
LOEFFLER, M
[
1
]
GROSSMANN, B
论文数:
0
引用数:
0
h-index:
0
机构:
INST THEORET PHYS,W-6900 HEIDELBERG,GERMANY
INST THEORET PHYS,W-6900 HEIDELBERG,GERMANY
GROSSMANN, B
[
1
]
机构
:
[1]
INST THEORET PHYS,W-6900 HEIDELBERG,GERMANY
来源
:
JOURNAL OF THEORETICAL BIOLOGY
|
1991年
/ 150卷
/ 02期
关键词
:
D O I
:
10.1016/S0022-5193(05)80330-3
中图分类号
:
Q [生物科学];
学科分类号
:
07 ;
0710 ;
09 ;
摘要
:
The intestinal epithelium is one of the most rapidly regenerating tissues in mammals. Cell production takes place in the intestinal crypts which contain about 250 cells. Only a minority of 1-60 proliferating cells are able to maintain a crypt over a long period of time. However, so far attempts to identify these stem cells were unsuccessful. Therefore, little is known about their cellular growth and selfmaintenance properties. On the other hand, the crypts appear to exhibit a life cycle which starts by fission of existing crypts and ends by fission or extinction. Data on these processes have recently become available. Here, we demonstrate how these data on the life cycle of the macroscopic crypt structure can be used to derive a quantitative model of the microscopic process of stem cell growth. The model assumptions are: (1) stem cells undergo a time independent supracritical Markovian branching process (Galton-Watson process); (2) a crypt divides if the number of stem cells exceeds a given threshold and the stem cells are distributed to both daughter crypts according to binomial statistics; (3) the size of the crypt is proportional to the stem cell number. This model combining two different stochastic branching processes describes a new class of processes whose stationary stability and asymptotic behavior are examined. This model should be applicable to various growth processes with formation of subunits (e.g. population growth with formation of colonies in biology, ecology and sociology). Comparison with crypt data shows that intestinal stem cells have a probability of over 0·8 of dividing asymmetrically and that the threshold number should be 8 or larger. © 1991 Academic Press Limited.
引用
收藏
页码:175 / 191
页数:17
相关论文
共 25 条
[1]
CELL PROLIFERATION STUDIES IN INTESTINAL EPITHELIUM OF RAT .2. THEORETICAL ASPECTS
CAIRNIE, AB
论文数:
0
引用数:
0
h-index:
0
CAIRNIE, AB
LAMERTON, LF
论文数:
0
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0
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0
LAMERTON, LF
STEEL, GG
论文数:
0
引用数:
0
h-index:
0
STEEL, GG
[J].
EXPERIMENTAL CELL RESEARCH,
1965,
39
(2-3)
: 539
-
&
[2]
FISSION OF CRYPTS IN SMALL-INTESTINE OF IRRADIATED MOUSE
CAIRNIE, AB
论文数:
0
引用数:
0
h-index:
0
机构:
QUEENS UNIV, DEPT BIOL, KINGSTON, ONTARIO, CANADA
QUEENS UNIV, DEPT BIOL, KINGSTON, ONTARIO, CANADA
CAIRNIE, AB
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0
引用数:
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0
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QUEENS UNIV, DEPT BIOL, KINGSTON, ONTARIO, CANADA
QUEENS UNIV, DEPT BIOL, KINGSTON, ONTARIO, CANADA
MILLEN, BH
[J].
CELL AND TISSUE KINETICS,
1975,
8
(02):
: 189
-
196
[3]
MUTATION SELECTION AND NATURAL-HISTORY OF CANCER
CAIRNS, J
论文数:
0
引用数:
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IMPERIAL CANC RES FUND,BURTONHOLE LANE,MILL HILL,LONDON NW7,ENGLAND
IMPERIAL CANC RES FUND,BURTONHOLE LANE,MILL HILL,LONDON NW7,ENGLAND
CAIRNS, J
[J].
NATURE,
1975,
255
(5505)
: 197
-
200
[4]
GROWTH, FISSION AND THE STABLE SIZE DISTRIBUTION
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论文数:
0
引用数:
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0
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NATL INST WATER SUPPLY,2260 AD LEIDSCHENDAM,NETHERLANDS
DIEKMANN, O
LAUWERIER, HA
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0
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0
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0
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NATL INST WATER SUPPLY,2260 AD LEIDSCHENDAM,NETHERLANDS
LAUWERIER, HA
ALDENBERG, T
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0
h-index:
0
机构:
NATL INST WATER SUPPLY,2260 AD LEIDSCHENDAM,NETHERLANDS
ALDENBERG, T
METZ, JAJ
论文数:
0
引用数:
0
h-index:
0
机构:
NATL INST WATER SUPPLY,2260 AD LEIDSCHENDAM,NETHERLANDS
METZ, JAJ
[J].
JOURNAL OF MATHEMATICAL BIOLOGY,
1983,
18
(02)
: 135
-
148
[5]
ON THE EXTINCTION TIME DISTRIBUTION OF A BRANCHING-PROCESS IN VARYING ENVIRONMENTS
FUJIMAGARI, T
论文数:
0
引用数:
0
h-index:
0
FUJIMAGARI, T
[J].
ADVANCES IN APPLIED PROBABILITY,
1980,
12
(02)
: 350
-
366
[6]
ON SOME CLASSES OF POPULATION-SIZE-DEPENDENT GALTON-WATSON PROCESSES
HOPFNER, R
论文数:
0
引用数:
0
h-index:
0
机构:
UNIV MAINZ,D-6500 MAINZ,FED REP GER
UNIV MAINZ,D-6500 MAINZ,FED REP GER
HOPFNER, R
[J].
JOURNAL OF APPLIED PROBABILITY,
1985,
22
(01)
: 25
-
36
[7]
A NOTE ON THE PROBABILITY OF EXTINCTION IN A CLASS OF POPULATION-SIZE-DEPENDENT GALTON-WATSON PROCESSES
HOPFNER, R
论文数:
0
引用数:
0
h-index:
0
HOPFNER, R
[J].
JOURNAL OF APPLIED PROBABILITY,
1985,
22
(04)
: 920
-
925
[8]
SOME RESULTS ON POPULATION-SIZE-DEPENDENT GALTON-WATSON PROCESSES
HOPFNER, R
论文数:
0
引用数:
0
h-index:
0
HOPFNER, R
[J].
JOURNAL OF APPLIED PROBABILITY,
1986,
23
(02)
: 297
-
306
[9]
JAGERS P, 1975, BRANCHING PROCESSES
[10]
LIMIT THEOREMS FOR DECOMPOSABLE MULTI-DIMENSIONAL GALTON-WATSON PROCESSES
KESTEN, H
论文数:
0
引用数:
0
h-index:
0
KESTEN, H
STIGUM, BP
论文数:
0
引用数:
0
h-index:
0
STIGUM, BP
[J].
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS,
1967,
17
(02)
: 309
-
&
←
1
2
3
→
共 25 条
[1]
CELL PROLIFERATION STUDIES IN INTESTINAL EPITHELIUM OF RAT .2. THEORETICAL ASPECTS
CAIRNIE, AB
论文数:
0
引用数:
0
h-index:
0
CAIRNIE, AB
LAMERTON, LF
论文数:
0
引用数:
0
h-index:
0
LAMERTON, LF
STEEL, GG
论文数:
0
引用数:
0
h-index:
0
STEEL, GG
[J].
EXPERIMENTAL CELL RESEARCH,
1965,
39
(2-3)
: 539
-
&
[2]
FISSION OF CRYPTS IN SMALL-INTESTINE OF IRRADIATED MOUSE
CAIRNIE, AB
论文数:
0
引用数:
0
h-index:
0
机构:
QUEENS UNIV, DEPT BIOL, KINGSTON, ONTARIO, CANADA
QUEENS UNIV, DEPT BIOL, KINGSTON, ONTARIO, CANADA
CAIRNIE, AB
MILLEN, BH
论文数:
0
引用数:
0
h-index:
0
机构:
QUEENS UNIV, DEPT BIOL, KINGSTON, ONTARIO, CANADA
QUEENS UNIV, DEPT BIOL, KINGSTON, ONTARIO, CANADA
MILLEN, BH
[J].
CELL AND TISSUE KINETICS,
1975,
8
(02):
: 189
-
196
[3]
MUTATION SELECTION AND NATURAL-HISTORY OF CANCER
CAIRNS, J
论文数:
0
引用数:
0
h-index:
0
机构:
IMPERIAL CANC RES FUND,BURTONHOLE LANE,MILL HILL,LONDON NW7,ENGLAND
IMPERIAL CANC RES FUND,BURTONHOLE LANE,MILL HILL,LONDON NW7,ENGLAND
CAIRNS, J
[J].
NATURE,
1975,
255
(5505)
: 197
-
200
[4]
GROWTH, FISSION AND THE STABLE SIZE DISTRIBUTION
DIEKMANN, O
论文数:
0
引用数:
0
h-index:
0
机构:
NATL INST WATER SUPPLY,2260 AD LEIDSCHENDAM,NETHERLANDS
DIEKMANN, O
LAUWERIER, HA
论文数:
0
引用数:
0
h-index:
0
机构:
NATL INST WATER SUPPLY,2260 AD LEIDSCHENDAM,NETHERLANDS
LAUWERIER, HA
ALDENBERG, T
论文数:
0
引用数:
0
h-index:
0
机构:
NATL INST WATER SUPPLY,2260 AD LEIDSCHENDAM,NETHERLANDS
ALDENBERG, T
METZ, JAJ
论文数:
0
引用数:
0
h-index:
0
机构:
NATL INST WATER SUPPLY,2260 AD LEIDSCHENDAM,NETHERLANDS
METZ, JAJ
[J].
JOURNAL OF MATHEMATICAL BIOLOGY,
1983,
18
(02)
: 135
-
148
[5]
ON THE EXTINCTION TIME DISTRIBUTION OF A BRANCHING-PROCESS IN VARYING ENVIRONMENTS
FUJIMAGARI, T
论文数:
0
引用数:
0
h-index:
0
FUJIMAGARI, T
[J].
ADVANCES IN APPLIED PROBABILITY,
1980,
12
(02)
: 350
-
366
[6]
ON SOME CLASSES OF POPULATION-SIZE-DEPENDENT GALTON-WATSON PROCESSES
HOPFNER, R
论文数:
0
引用数:
0
h-index:
0
机构:
UNIV MAINZ,D-6500 MAINZ,FED REP GER
UNIV MAINZ,D-6500 MAINZ,FED REP GER
HOPFNER, R
[J].
JOURNAL OF APPLIED PROBABILITY,
1985,
22
(01)
: 25
-
36
[7]
A NOTE ON THE PROBABILITY OF EXTINCTION IN A CLASS OF POPULATION-SIZE-DEPENDENT GALTON-WATSON PROCESSES
HOPFNER, R
论文数:
0
引用数:
0
h-index:
0
HOPFNER, R
[J].
JOURNAL OF APPLIED PROBABILITY,
1985,
22
(04)
: 920
-
925
[8]
SOME RESULTS ON POPULATION-SIZE-DEPENDENT GALTON-WATSON PROCESSES
HOPFNER, R
论文数:
0
引用数:
0
h-index:
0
HOPFNER, R
[J].
JOURNAL OF APPLIED PROBABILITY,
1986,
23
(02)
: 297
-
306
[9]
JAGERS P, 1975, BRANCHING PROCESSES
[10]
LIMIT THEOREMS FOR DECOMPOSABLE MULTI-DIMENSIONAL GALTON-WATSON PROCESSES
KESTEN, H
论文数:
0
引用数:
0
h-index:
0
KESTEN, H
STIGUM, BP
论文数:
0
引用数:
0
h-index:
0
STIGUM, BP
[J].
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS,
1967,
17
(02)
: 309
-
&
←
1
2
3
→