A mathematical model of erythropoiesis in mice and rats. Part 4: Differences between bone marrow and spleen

In a preceding analysis we hypothesized that the most important parameter controlled by erythropoietic regulation in vivo is the degree of amplification (number of cell divisions) in the CFU-E and erythroblast cell stages. It was concluded that erythropoietic amplification in vivo is controlled according to a sigmoidal dose-response relationship with respect to the control parameter which is the haematocrit (or haemoglobin concentration). Here, this hypothesis is extended to include the differences in murine bone marrow and splenic erythropoiesis that are described and quantified by different dose-response relationships. Comparing several sets of experimental data with mathematical model simulations, this approach leads to the following conclusions: (i) in the unperturbed normal steady state at least one extra erythropoietic cell division takes place in the spleen compared with the bone marrow; (ii) a strong erythropoietic stimulus, such as severe bleeding or hypoxia, can induce five to six additional cell divisions in the spleen but only two to three additional divisions in the bone marrow; this results in a considerable increase in the spleen's contribution to erythropoiesis from about 10% in normal animals to over 40% during strong stimulation; (iii) under erythropoietic suppression, such as red cell transfusion, a similar number of cell divisions is skipped in both organs and the splenic contribution to erythropoiesis remains unchanged. In conclusion, the concept that bone marrow and spleen microenvironments differ in the dose-response relationship for erythropoietic regulation provides an explanation for the changing contribution of splenic murine erythropoiesis following a variety of experimental treatments.     

A mathematical model of erythropoiesis in mice and rats. Part 4: Differences between bone marrow and spleen

Abstract. In a preceding analysis we hypothesized that the most important parameter controlled by erythropoietic regulation in vivo is the degree of amplification (number of cell divisions) in the CFU-E and erythroblast cell stages. It was concluded that erythropoetic amplification in vivo is controlled according to a sigmoidal dose-response relationship with respect to the control parameter which is the haematocrit (or haemoglobin concentration). Here, this hypothesis is extended to include the differences in murine bone marrow and splenic erythropoiesis that are described and quantified by different dose-response relationships. Comparing several sets of experimental data with mathematical model simulations, this approach leads to the following conclusions: (i) in the unperturbed normal steady state at least one extra erythropoietic cell division takes place in the spleen compared with the bone marrow; (ii) a strong erythropoietic stimulus, such as severe bleeding or hypoxia, can induce five to six additional cell divisions in the spleen but only two to three additional divisions in the bone marrow; this results in a considerable increase in the spleen's contribution to erythropoiesis from about 10% in normal animals to over 40% during strong stimulation; (iii) under erythropoietic suppression, such as red cell transfusion, a similar number of cell divisions is skipped in both organs and the splenic contribution to erythropoiesis remains unchanged. In conclusion, the concept that bone marrow and spleen microenvironments differ in the dose-response relationship for erythropoietic regulation provides an explanation for the changing contribution of splenic murine erythropoiesis following a variety of experimental treatments.     

Developmental changes in erythropoietin receptor expression of fetal mouse liver.

Erythropoietin (EPO) stimulates proliferation and differentiation of late erythroid precursor cells (CFU-E) and thereby determines the rate of erythropoiesis. Liver is the major erythropoietic site in a fetus. We dealt with developmental changes in CFU-E and EPO receptor (EPO-R) of fetal mouse liver. The affinity of the EPO-R to EPO was unchanged during fetal development. The population size of CFU-E, the number of EPO-R per liver cell, and EPO-R mRNA decreased as gestation proceeded, in a pattern indicating that the expression of EPO-R on erythroid precursor cells in fetal mouse liver is governed mostly by the process of mRNA production.     

The kinetics of hematopoietic stem cells during and after hypoxia. A model analysis

A previously described mathematical model of the hematopoietic stem cell system has been extended to permit a detailed understanding of the data during and after hypoxia. The model includes stem cells, erythroid and granuloid progenitors and precursors. Concerning the intramedullary feedback mechanisms two basic assumptions are made: 1) The fraction "a" of CFU-S in active cell cycle is regulated. Reduced cell densities of CFU-S, progenitors or precursors lead to an accelerated stem cell cycling. Enlarged cell densities suppress cycling. 2) The self renewal probability "p" of CFU-S is also regulated. The normal steady state is described by p = 0.5, indicating that on statistical average each dividing mother stem cell is replaced by one daughter stem cell, while the second differentiates. Diminished cell densities of CFU-S or enlarged densities of progenitors and precursors induce a more intensive self renewal (p greater than 0.5), such that the stem cell number increases. The self renewal probability declines (p less than 0.5) if too many CFU-S or too few progenitors and precursors are present. The model reproduces bone marrow data for CFU-S, BFU-E, CFU-C, CFU-E, 59 Fe-uptake and nucleated cells in hypoxia and posthypoxia. Although the ratio of differentiation into the erythroid and granuloid cell lines is kept constant in the model, a changing ratio of CFU-E and CFU-C results. The model suggests that stem cells and progenitor cells are regulated by a regulatory interference of erythropoiesis and granulopoiesis.     

Selective modulation of the erythropoietic and tissue-protective effects of erythropoietin: time to reach the full therapeutic potential of erythropoietin

Erythropoietin (EPO) has been used clinically both as an erythropoietic stimulating agent in the treatment of anemia and as a tissue-protective agent in diverse clinical settings including stroke, multiple sclerosis, acute myocardial infarction and others. However, use of EPO or EPO-analogues leads to simultaneous targeting of both the erythropoietic and tissue-protective properties of EPO, and this strategy has been associated with several problems. Specifically, the benefit of correction of cancer-related anemia can be offset by the tissue-protective effects of EPO, which may lead to stimulation of cancer cell proliferation. Conversely, the benefit of tissue-protection in patients with stroke or myocardial infarction can be offset by adverse effects associated with the erythropoietic effects of EPO such as elevation of red blood cell mass, hypertension and prothrombotic phenomena. The finding that the erythropoietic and tissue-protective properties of EPO are conferred via two distinct receptor systems raises the interesting possibility of discovering novel drugs that selectively stimulate either the erythropoietic or the tissue-protective activities of EPO. This article reviews the current status of the clinical use of EPO and EPO-analogues in the treatment of cancer-related anemia and for tissue protection, outlines the distinct molecular biology of the tissue-protective and erythropoietic effects of EPO and discusses strategies of selective targeting of these activities with the goal of exploiting the full therapeutic potential of EPO.     

Estimation of circadian variations in cell cycle phase durations in murine epidermal basal cells

Circadian variations in the proliferative activity of squamous epithelia are well known. However, circadian variations in the duration of the various cell cycle phases (S, G2 and mitosis) have been disputed. The percent labelled mitoses method, which is traditionally used to obtain duration of cell cycle phases, is poorly suited for identification of circadian variations. Therefore methods combining changes in compartment size (cell cycle phase) and cellular flux through the compartments have been used. Three different methods using such data are presented. These incorporate various simplifying assumptions that cause methodological errors. Limits for use of the different methods are indicated. The use of all three methods gives comparable and pronounced circadian variations in the duration of S and G2 phase. These results are also compatible with circadian variations in the mitotic duration, but they may also represent artefacts due to sensitivity to model errors.     

Estimation of Circadian Variations In Cell Cycle Phase Durations In Murine Epidermal Basal Cells

Circadian variations in the proliferative activity of squamous epithelia are well known. However, circadian variations in the duration of the various cell cycle phases (S, G₂ and mitosis) have been disputed. the percent labelled mitoses method, which is traditionally used to obtain duration of cell cycle phases, is poorly suited for identification of circadian variations. Therefore methods combining changes in compartment size (cell cycle phase) and cellular flux through the compartments have been used. Three different methods using such data are presented. These incorporate various simplifying assumptions that cause methodological errors. Limits for use of the different methods are indicated. the use of all three methods gives comparable and pronounced circadian variations in the duration of S and G₂ phase. These results are also compatible with circadian variations in the mitotic duration, but they may also represent artefacts due to sensitivity to model errors.     

Measurement of generation-dependent proliferation rates and death rates during mouse erythroid progenitor cell differentiation

Herein, we describe an experimental and computational approach to perform quantitative carboxyfluorescein diacetate succinimidyl ester (CFSE) cell-division tracking in cultures of primary colony-forming unit-erythroid (CFU-E) cells, a hematopoietic progenitor cell type, which is an important target for the treatment of blood disorders and for the manufacture of red blood cells. CFSE labeling of CFU-Es isolated from mouse fetal livers was performed to examine the effects of stem cell factor (SCF) and erythropoietin (EPO) in culture. We used a dynamic model of proliferation based on the Smith-Martin representation of the cell cycle to extract proliferation rates and death rates from CFSE time-series. However, we found that to accurately represent the cell population dynamics in differentiation cultures of CFU-Es, it was necessary to develop a model with generation-specific rate parameters. The generation-specific rates of proliferation and death were extracted for six generations (G(0) -G(5) ) and they revealed that, although SCF alone or EPO alone supported similar total cell outputs in culture, stimulation with EPO resulted in significantly higher proliferation rates from G(2) to G(5) and higher death rates in G(2) , G(3) , and G(5) compared with SCF. In addition, proliferation rates tended to increase from G(1) to G(5) in cultures supplemented with EPO and EPO + SCF, while they remained lower and more constant across generations with SCF. The results are consistent with the notion that SCF promotes CFU-E self-renewal while EPO promotes CFU-E differentiation in culture.     

Functional heterogeneity among the T-derived lymphocytes of the mouse. V. Response kinetics of peripheral T cell subpopulations.

The kinetics of the proliferative response and the appearance of effectors of helper activity after stimulation by antigen were examined in T cell subpopulations. As defined in previous papers of this series, one population, T1, is short-lived after adult thymectomy (ATx), and relatively resistant to elimination by anti-thymocyte serum (ATS). Another population, T2, is long-lived after ATx, but highly sensitive to elimination by small doses of ATS. From precursors within the T2 population, effectors of specific helper activity, after priming with antigen, appeared within 1 to 2 days and reached a maximum on day 4. The responding cells reached their peak proliferative response within 24 hr after stimulation by antigen. In contrast, helper activity arising from T1 precursors first appeared on day 3 and peaked on day 5. These cells did not reach their maximal proliferative response until 60 hr after priming. These findings indicate additional useful markers for distinguishing the T1 and T2 subpopulations and are consistent with models for T cell development in which T1 cells are virgin cells and T2 cells are memory cells.     

A quantitative model of liver regeneration in the rat

The ability of various theories to generate the kinetics of rat-liver regeneration is considered. Wound hormone and functional demand theories are shown to be either inadequate or overly complex. A simple model based on a liver-produced mitotic inhibitor is, however, able to match the experimental results on the mitotic rate and thymidine uptake of parenchymal cells in the liver as a function of time following various degrees of partial hepatectomy. The inhibitor itself would belong to the class of molecules known as chalones and differential equations describing the mechanism of its action are derived and solved numerically. The only arbitrary parameters required for the solution are those giving the halflife and dose-response curve of the inhibitor. Optimal matching of theory to data is obtained when the half-life is about 3 h and the dose-response curve is given by a negative exponential function. Experimental procedures for measuring these parameters are discussed and an explanation of the uneven distribution of mitoses in regenerating liver is given.     

Temporal pattern of changes in mitotic frequency in the epidermis and other larval tissues of Bombyx mori

Temporal changes in mitotic frequency were examined in various tissues through late larval life of Bombyx mori. From the second larval ecdysis to the third and from the third larval ecdysis to the fourth, there was a definite temporal change of mitotic pattern in each tissue. In the epidermis as well as in the tracheal epithelium, mitoses began to appear about 1 day after an ecdysis, and showed a maximum 1 to 2 days after an ecdysis. In the fat body, mitoses were observed continuously through the instars, and the mitotic frequency showed a maximum state just before an ecdysis. In the abdominal muscle the frequency was highest at about the middle of the period between two successive ecdyses. Furthermore, epidermal mitoses coincided with the time when the density of epidermal nuclei per unit area decreased to a half. This suggests that epidermal mitoses may be initiated by some process related to the increase in cell size.     

Erythropoietic progenitors capable of colony formation in culture: state of differentiation

The differentiated state of mouse erythropoietic progenitor cells (CFU-E), detected by their ability to form erythropoietin-dependent colonies in vitro, has been investigated. Transfusion-induced plethora was found to reduce the population size of CFU-E in both spleen and femoral marrow, which indicates that a significant number of CFU-E arise by differentiation processes that are themselves erythropoietin-dependent. Individual spleen colonies were found to be heterogeneous in their content of CFU-E, and the numbers of CFU-E per colony were not correlated either positively or negatively with the numbers of granulocyte-macrophage progenitors (CFU-C) present in the same colonies. The absence of a negative correlation between CFU-E and CFU-C indicates that the erythropoietic and granulopoietic pathways of differentiation are not mutually exclusive within individual spleen colonies. The numbers of CFU-E per spleen colony were also found to vary independently of the numbers of pluripotent stem cells (CFU-S) per colony; in contrast, as found previously, the numbers of CFU-C and CFU-S per colony were positively correlated. These results indicate that more randomizing events separate CFU-E from CFU-S than separate CFU-C from CFU-S, and are consistent with the view that CFU-E occupy a position on the erythropoietic pathway of differentiation that is more remote from the pluripotent stem cells than is the corresponding position of CFU-C on the granulopoietic pathway.     

Differentiation in Leaf Epidermis of Chlorophytum comosum Baker

The distribution of guard mother-cell formation has been studiedin developing abaxial epidermis in the basal meristem of theleaf of Chlorophytum comosum. It is concluded that, as tissueis displaced from the base of the leaf by growth, it passesthrough a proliferative zone in which only proliferative mitosesoccur, and then passes a boundary into a formative zone in whichformative mitoses occur, giving rise to guard mother cells,and proliferative mitoses are absent. Further distally, formativemitoses die out and in the next zone (the guard-cell zone) theonly mitoses which occur are those by which the guard mothercells give rise to the guard cells. Most distally there is azone with no mitotic activity. The probability of a cell undergoinga formative mitosis is highest at the proximal boundary of theformative zone. It is consequently suggested that the fate ofa cell on entering the formative zone depends partly on itsposition in the mitotic cycle; cells nearest to mitosis at entryare the most likely to undergo a formative mitosis during theirpassage through the formative zone. Similarly, guard mothercells which fail to undergo mitosis may be those which weremost distant from mitosis on entry into the guard cell zone.These suggestions may explain some of the elements of patternpreviously found in the mature epidermis. Chlorophytum comosum Baker, spider plant, leaf epidermis, stomata, pattern, development, formative mitosis, proliferative mitosis