Cell division and cell growth in size

Summary and conclusion The coefficient of correlation between cell length and percentage mitosis in root-tips ofZea mays was found to be high and negative: r=–0·577±0·075. This value taken together with correlated data justifies the generality that cell division and cell size are inversely related. An analysis of the bases of the relation brings the conclusion that in an increasing cell population where growth in cell number and growth in cell size are taking place simultaneously, cell division is the independent and cell size the dependent variable. That is to say, other things being equal, the size of the cells is a result of the rate of cell multiplication. The explanation of this is given in the text.     

Proliferation controls in a linear growth system: theoretical studies of cell division in the cartilage growth plate

The columnar arrangement of dividing cells in the epiphyseal cartilage plates of growing bones provides a model of a linear proliferation system. One factor which determines the rate of cell production, and hence the rate of growth, is the size of the proliferating population. In this one dimensional system this size is equal to the length of the proliferation zone. Two possible mechanisms for a differentiation control that sets a limit to the length of this zone have been tested in computer simulations. While a diffusion gradient control is consistent with cell kinetic measurements a division limit based on an inheritable growth substance is shown to require further development before the model fits experimental data.Cell division in the columns produces linear clones of cells. If the final length of a bone is set by a limit on the number of divisions that the cartilage stem cells can make, then the number of cells per clone is crucial in determining overall bone growth. The parameters that affect linear clone size have been investigated in computer simulations. Clone size depends largely on the relative division rate of stem cells to proliferation zone cells — but the data on stem cell division rates are generally unreliable.The analysis could be applied to other linear proliferating systems.     

Control of the timing of cell division in fission yeast : Cell size mutants reveal a second control pathway

Strains of Schizosaccharomyces pombe carrying the wee 1 mutation divide at a reduced cell size compared with the wild-type. In this paper, we investigate the mechanism which determines the time of division and cell size at division in wee 1 strains, using three experimental approaches. The evidence suggests that the wild-type control (a cell size control over entry into nuclear division) is absent in wee 1 strains. Instead, a mechanism operates which comprises a cell size control over the initiation of S phase plus a minimum incompressible period in G2 (“timer”) from S phase to nuclear division. The elements of this second control mechanism exist in wild-type cells, though the control is not normally expressed. In particular, the G2 interval in wild-type cells is normally longer than that in wee 1 cells, but can be reduced to this minimum value by delaying S phase. Thus there are two independent controls over entry into nuclear division, one of which operates in wild-type, and the other in wee 1 cells.     

Control of cell length in Bacillus subtilis.

During inhibition of deoxyribonucleic acid synthesis in Bacillus subtilis 168 Thy-minus Tryp-minus, the rate of length extension is constant. A nutritional shift-up during thymine starvation causes an acceleration in the linear rate of length extension. During a nutritional shift-up in the presence of thymine, the rate of length extension gradually increases, reaching a new steady state at about 50 min before the new steady-state rate of cell division is reached. The steady-state rates of nuclear division and length extension are reached at approximately the same time. The ratio of average cell length to numbers of nuclei per cell in exponential cultures is constant over a fourfold range of growth rates. These observations are consistent with: (i) surface growth zones which operate at a constant rate of length extension under any one growth condition, but which operate at an absolute rate proportional to the growth rate of the culture, (ii) a doubling in number of growth zones at nuclear segregation, and (iii) a requirement for deoxyribonucleic acid replication for the doubling in a number of sites.     

Rate maintenance of cell division in Escherichia coli B/r: analysis of a simple nutritional shift-down.

A competitive (nonmetabolizable) inhibitor of glucose uptake, alpha-methylglucoside, was used to limit the growth of Escherichia coli. Cell division during such a nutritional shift-down was studied in batch cultures and with the "baby-machine" technique. Following a brief delay, the rate of division was maintained for 60 to 70 min in batch cultures and for an extended period in the baby machine. Decreases in cell size were due, in part, to a possible reduction in the mass per chromosome origin at the time of replication initiation and a shorter time interval between initiation and the subsequent division. These unusual findings suggest that this method for abrupt change in growth rate without modifying repression patterns is useful for studying the control of various aspects of the bacterial cell.     

The relationship between cell size and cell division in the yeast Saccharomyces cerevisiae.

Cell numbers in synchronous cultures of yeast cultured at fast growth rates increase from N to 2N after the first division and from 2N to 4N after the second division. At these fast growth rates, there are equal numbers of parents and daughters. In contrast, at slow growth rates the cell number increases from N to 2N after one division and from 2N to 3N rather than 4N after the second division. Moreover, the percentage of daughters increases with decreasing growth rate. Thus, slowly growing cultures actually consist of two sub-populations having different cell cycle transit times. These observations are predicted if a yeast cell requires a critical size before a particular cell cycle event can be completed and that after completion of this event cell division occurs following a period of time independent of growth rate.     

Sloppy size control of the cell division cycle

In an asynchronous, exponentially proliferating cell culture there is a great deal of variability among individual cells in size at birth, size at division and generation time (= age at division). To account for this variability we assume that individual cells grow according to some given growth law and that, after reaching a minimum size, they divide with a certain probability (per unit time) which increases with increasing cell size. This model is called sloppy size control because cell division is assumed to be a random process with size-dependent probability. We derive general equations for the distribution of cell size at division, the distribution of generation time, and the correlations between generation times of closely related cells. Our theoretical results are compared in detail with experimental results (obtained by Miyata and coworkers) for cell division in fission yeast, Schizosaccharomyces pombe. The agreement between theory and experiment is superior to that found for any other simple models of the coordination of cell growth and division.     

Minimal requirements for robust cell size control in eukaryotic cells

Most cell types living in a stable environment tend to keep a constant characteristic size over successive generations. Size homeostasis requires that cells exert a tight control over the size at which they divide. Cell size control is not only robust against various noises, but also highly flexible since cell sizes can vary tremendously, notably as a function of nutrient levels. We formulated a minimal mathematical model of the eukaryotic cell cycle in which the cell size control operates through a cell growth-dependent bifurcation in the cell cycle dynamics. Such a bifurcation mechanism can readily explain the occurrence of a minimum critical size at division under limiting growth conditions. However, it also predicts that cells should become progressively larger and larger under prolific growth conditions. We argue that the cell size control can be reinforced at fast growth rates by adding a new cell cycle inhibitory activity whose strength would increase with the cell growth rate. We further show that various sources of noise may also generate a large variability in cell size at division and interdivision time that exhibit characteristic exponential tail distributions, without compromising the robustness of the cell size control.     

Cell Division of Escherichia coli BUG-6: Effect of Varying the Temperature Used as the Nonpermissive Growth Condition

When Escherichia coli BUG-6 is shifted from 30 C to 36 or 38 C, division does not stop, but the rate of division of the cell population is initially decreased followed by a period of increased rate of division before the rates characteristic of growth at 36 and 38 C are obtained. After a shift from 30 to 40 C, the rate of cell division gradually decreases over a 10-min period and then stops. The inhibition continues for 25 min, and then the cells divide rapidly before the division rate characteristic of 40 C is obtained. If filaments produced by 45 min of growth at 42 C are temporarily replaced at 30 C and then returned to 42 C, division occurs at 42 C. The amount of division is dependent on the length of the period at 30 C and can be decreased by a 3-min pulse of chloramphenicol immediately before the 42 to 30 C shift.     

Relationship between size of parent at cell division and relative size of its progeny in Escherichia coli

This article examines the empirical basis for the assumption of independence between the relative size (length or surface area) of a newborn cell w and the absolute size of its mother at cell division. Random samples from two strains of Escherichia coli B/r cells in steady-state exponential growth, covering a range of doubling times, were fixed in osmium tetroxide and prepared for electron microscopy by agar filtration. Length and diameter of over 3000 constricted cells were measured from the electron micrographs and cell surface area computed by assuming an idealized geometry of right circular cylinders with hemispherical polar caps. In general, these strains were found to divide into two daughter cells with a precision that is independent of the size of the mother. In addition, both a normal and a symmetrical beta-distribution were shown to fit the observed size distributions of w rather well; theoretical grounds for preferring the latter are discussed.     

Cell elongation and division probability during the Escherichia coli growth cycle.

A new method is presented for determining the growth rate and the probability of cell division (separation) during the cell cycle, using size distributions of cell populations grown under steady-state conditions. The method utilizes the cell life-length distribution, i.e., the probability that a cell will have any specific size during its life history. This method was used to analyze cell length distributions of six cultures of Escherichia coli, for which doubling times varied from 19 to 125 min. The results for each culture are in good agreement with a single model of growth and division kinetics: exponential elongation of cells during growth phase of the cycle, and normal distributions of length at birth and at division. The average value of the coefficient of variation was 13.5% for all strains and growth rates. These results, based upon 5,955 observations, support and extend earlier proposals that growth and division patterns of E. coli are similar at all growth rates and, in addition, identify the general growth pattern of these cells to be exponential.     

Coordination between chromosome replication and cell division in Escherichia coli.

Cell division properties of Escherichia coli B/r containing either a dnaC or a dnaI mutation were examined. Incubation at nonpermissive temperature resulted in the eventual production of cells of approximately normal size, or slightly smaller, which lacked chromosomal DNA. The cell division patterns in cultures which were grown at permissive temperature and then shifted to nonpermissive temperature were consistent with: first, division and equipartition of chromosomes by cells which were in the C and D periods at the time of the shift; second, an apparent delay in cell division; and third, commencement of the formation of chromosomeless cells. In glucose-grown cultures of the dnaI mutant, production of chromosomeless cells continued for at least 120 min, whereas in the dnaC mutant chromosomeless cells were formed during a single interval between 110 and 130 min after the temperature shift. The results are discussed in light of the hypothesis that replication of a specific chromosomal region is not an obligatory requirement for the initiation and completion of the processes leading to division in a cell which contains at least one functioning chromosome.     

Cell size homeostasis: Metabolic control of growth and cell division

Joint regulation of growth rate and cell division rate determines cell size. Here we discuss how animal cells achieve cell size homeostasis potentially involving multiple signaling pathways converging at metabolic regulation of growth rate and cell cycle progression. While several models have been developed to explain cell size control, comparison of the two predominant models shows that size homeostasis is dependent on the ability to adjust cellular growth rate based on cell size. Consequently, maintenance of size homeostasis requires that larger cells can grow slower than small cells in relative terms. We review recent experimental evidence showing that such size adjustment occurs primarily at or immediately before the G1/S transition of the cell cycle. We further propose that bidirectional feedback between growth rate and size results in cell size sensing and discuss potential mechanisms how this may be accomplished.     

A metabolic sensor governing cell size in bacteria

Nutrient availability is one of the strongest determinants of cell size. When grown in rich media, single-celled organisms such as yeast and bacteria can be up to twice the size of their slow-growing counterparts. The ability to modulate size in a nutrient-dependent manner requires cells to: (1) detect when they have reached the appropriate mass for a given growth rate and (2) transmit this information to the division apparatus. We report the identification of a metabolic sensor that couples nutritional availability to division in Bacillus subtilis. A key component of this sensor is an effector, UgtP, which localizes to the division site in a nutrient-dependent manner and inhibits assembly of the tubulin-like cell division protein FtsZ. This sensor serves to maintain a constant ratio of FtsZ rings to cell length regardless of growth rate and ensures that cells reach the appropriate mass and complete chromosome segregation prior to cytokinesis.     

Mutants altered in the control co-ordinating cell division with cell growth in the fission yeast Schizosaccharomyces pombe

Summary The control co-ordinating cell division with cell growth has been investigated in the fission yeast Schizosaccharomyces pombe. Twenty-five mutants altered in this control have been isolated which have the same growth rate as wild type but divide at a smaller cell size. The mutants define two genes wee 1 and wee 2, both of which are involved in a control initiating mitosis when the cell attains a critical size.     

Alteration of the rate of cell division independent of the rate of DNA synthesis in a mutant of Salmonella typhimurium

Summary Salmonella typhimurium strain IIG has a temperature—sensitive DNA synthesis initiation apparatus and completes rounds of DNA replication when shifted to 38°. At this temperature there is a period of apparently normal division followed by a second phase in which DNA-less cells are produced. The rate of division in this second phase can be markedly increased if a culture growing in MM is shifted to nutrient broth at the time of the temperature shift. The extra divisions induced by the nutritional shift are not due to extra replication forks being introduced by this process nor to the rapid growth of ts ⁺ revertants. It is concluded that in this strain at 38°, the rate of division can be increased without altering the rate of DNA synthesis. The extra divisions induced by the shift-up do not take place for about 90 min. The possible occurrence of such a period between the triggering of division and the division event in normal cells is discussed.     

Cell division and the production of cells lacking nuclear bodies in a mutant of Salmonella typhimurium

Summary There are two distinct division phases when the temperature-sensitive DNA synthesis initiation mutant Salmonella typhimurium strain 11G is shifted from 25° to 38°. The first phase appears to represent segregation of the nuclear bodies formed at 38°. Division in this phase takes place at the normal size and produces mainly organisms with one nuclear body. It is dependent on the termination of the rounds of replication in operation at the time of the temperature shift and sensitive to low doses of penicillin. This division phase continues for 60–75 min and then after a short lag division restarts. At first the cells undergoing the second division phase are only slightly larger than normal but they soon grow into short filaments which bud off cells at both ends even if only one nuclear body is present. The cells budded off in this division phase are about 3 long on both broth and M M. They lack nuclear bodies but have a small amount of DNA which may be exclusively in the form of a large plasmid. This second division phase is also dependent on rounds of replication being allowed to terminate at 38° and is sensitive to low levels of penicillin. It is 80–90 min after the temperature shift before the second division phase starts and this lag is maintained even if rounds of replication have been completed prior to the temperature shift by amino acid starvation at 25°. The occurrence of this lag and the demonstration (using penicillin) of potential division sites at regular intervals along 11G filaments suggest that division is initiated some time before the actual division event.     

Genetic control of the cell division cycle in the fission yeast Schizosaccharomyces pombe

Summary Twenty seven recessive temperature sensitive mutants have been isolated in Schizosaccharomyces pombe which are unable to complete the cell division cycle at the restrictive temperature. These mutants define 14 unlinked genes which are involved in DNA synthesis, nuclear division and cell plate formation. The products from most of these genes complete their function just before the cell cycle event in which they are involved. Physiological characterisation of the mutants has shown that DNA synthesis and nuclear division form a cycle of mutually dependent events which can operate in the absence of cell plate formation. Cell plate formation itself is usually dependent upon the completion of nuclear division.