Control of stem cell proliferation: a density-dependent committment model

A Model for Heterogeneous Brain Tumor Cells that Cause Dizziness

Background::

Various models are used for brain tumors modeling. To our knowledge, no earlier work has been done on modeling the heterogeneous brain tumor that causes dizziness. However, specifying a cell using a model is not new. Unlike all earlier works in this regard, which consider analog or analog-CPU computers in the cell model, the model presented in this work fully utilizes processor computers.

Materials and Methods::

The purpose of this study is to offer a comprehensive approach for heterogeneous modeling of brain tumor cells. The model uses a brain tumor cell in Matlab and Simulink 3D software. Two heterogeneous models are presented for brain tumor cells: the imagebased cell model and computer-generated cell model. The image-based cell model is obtained through the figure altering on X-ray or ocular figures by recognizing the dissimilar states in the tumors.

Results::

The computer-generated cell model works based on locating computer produced aggregate cells into tumors. Some subdivisions for both the image-based and computer-generated cell models are presented as well.

Conclusion::

The positive and negative points of the image-based cell models and computergenerated cell models some scientific advices are presented in this work. Generally, the imagebased cell models could offer analytical facts for each state, but they are expensive and timeconsuming; besides, their performance is heavily influenced by deformation techniques. The computer-generated cell model, on the other hand, provides a higher cost of production and simplicity, but its main contribution is the overall performance and accuracy.

Independent evidence for a commitment model of clonal attenuation

We previously reported a model of clonal attenuation which assumes three classes of cells: small highly replicative cells; intermediate size cells of limited replicative potential and large non-diving cells. Computer simulations carried out with the model lead to predictions of how the relative proportion of each cell type varies throughout the in vitro replicative life span of a mass population. These predictions appear to be broadly confirmed by independent data recently reported by another laboratory.

Evidence for a universal process underlying clonal attenuation

It is shown by computer simulation that an established commitment model of clonal attenuation can account for clone size distribution data obtained from three vertebrate species--chick, hamster and human--from two evolutionarily divergent classes. The different in vitro replicative lifespans of each cell strain can be explained by differences in cell kinetics. These results suggest that the process of clonal attenuation is qualitatively similar in fibroblasts from all vertebrate species.

Clonal attenuation in chick embryo fibroblasts. Experimental data, a model and computer simulations

When cells from mass cultures of chick embryo fibroblasts are grown at very low density, some cells yield large clones while others produce smaller clones, and some cells fail to divide at all. The distribution of clone sizes is related to the number of population doublings which the donor mass culture has undergone: the more doublings which have occurred, the smaller the average clone size. In this report we describe a model which analyses this phenomenon, referred to as 'clonal attenuation', in detail. The model is based on the concept that a cell with hypothetically unlimited replicative potential--i.e. a 'stem' cell--can become 'committed' to a programme of limited replicative potential. This event is assumed to be stochastic and to have a fixed probability per stem cell division. The parameters of the model are: Pc, the probability of commitment; N, the number of differentiative divisions; and Tc, the cell-cycle times. By computer simulation, it is shown that Pc increases roughly exponentially at each successive stem cell division. According to the model, when the daughter of a stem cell becomes committed, its progeny proceed through N obligatory divisions before becoming terminally differentiated (post-mitotic). The best-fit value of N was found to be seven. The simulations also reveal that the absolute number of stem cells in the total population increases for most of the lifespan of the culture. When Pc becomes much greater than 0.5, the number of stem cells declines rapidly to zero, and the culture nears senescence. Sensitivity analysis shows that Pc can assume only a limited range of values at each stem-cell division.

Hematopoietic stem cells with high proliferative potential. Assay of their concentration in marrow by the frequency and duration of cure of W/Wv mice

THIS STUDY WAS DESIGNED TO APPROACH TWO PRIMARY QUESTIONS CONCERNING HEMATOPOIETIC STEM CELLS (HSC) IN MICE: what is the concentration of HSC with extensive proliferative potential in marrow, and how long can an HSC continue to function in an intact animal? The assay system was the W/W(v) mouse, a mouse with an inherited HSC defect, reflected in a reduction in all myeloid tissue and most particularly in a macrocytic anemia.A single chromosomally marked HSC will reconstitute the defective hematopoietic system of the W/W(v). The concentration of HSC in normal littermate (+/+) marrow was assayed by limiting dilution calculation using cure of W/W(v) as an end point (correction of anemia and erythrocytes' macrocytosis) and found to be approximately 10/10(5). This is significantly less than spleen colony forming cell (CFU-S) concentration: approximately 220/10(5) in +/+ and ranging from 50 to 270/10(5) in various other studies. Blood values were studied at selected intervals for as long as 26 mo. Of 24 initially cured mice, which were observed for at least 2 yr, 75% remained cured. However, of all cured mice, 17 lost the cure, returning to a macrocytic anemic state. Cured mice had normal numbers of nucleated and granulocytic cells per humerus and a normal concentration of CFU-S. However, cure of secondary W/W(v) recipients by this marrow was inefficient compared with the original +/+ marrow. These studies suggest the CFU-S assay over-estimates extensively proliferating HSC or perhaps does not assay such a cell. A single such HSC can not only cure a W/W(v), but can sustain the cure for 2 yr or more, despite a relative deficit of cells capable of curing other W/W(v). However, the duration of sustained cure may be finite.

A model of clonal attenuation

Two formal models of clonal attenuation [Kirkwood, T. B. L. & Holliday, R. (1975) J. Theor. Biol. 53, 481-496; Shall, S. & Stein, W. D. (1979) J. Theor. Biol. 76, 219-231] are considered in the light of recent data on the changing distribution of replicative potential among individual cultured fibroblasts on subcloning. The experimental data [Smith, J. R., Pereira-Smith, O. & Good, P. I. (1977) Mech. Ageing Dev. 6, 283-286] are shown to contradict both models. A new model, compatible with the subcloning data, is proposed. This model involves a gradual increase in the probability of commitment during cell growth in culture and a small number (about seven) of divisions following commitment. The gradual increase in commitment probability is shown to be compatible with the gradual accumulation of a gene product subject to autogenous regulation.