A simple model to describe transient differences between cell number and biomass growth rates of Escherichia coli

Information on the response of a microbial culture to dynamic environmental conditions is necessary for the design of transient operation processes. However, most attempts at modelling culture response have been directed at describing the steady-state behavior. Thus, there is a need for adequate dynamic models for process design. Simulations of nutrient shifts were completed using a "single-cell" model for Escherichia coli. It was discovered that the specific mass growth rate and the specific number of cells growth rate were different under transient conditions, whereas at steady state (balanced growth) these rates are equivalent. Using these observations, a simple delay model to describe the transient behavior of the two growth rates is formulated and tested. The model contains as state variables only the readily measurable macroscopic quantities (biomass, cell number, and limiting nutrient). This model agreed well with the predictions of the single-cell model.     

Cell cycle and cell size dependence of susceptibility to hydrodynamic forces

Exposure of animal cells to intense hydrodynamic forces exerted in turbulent capillary flow, and by controiled agitation and aeration, resulted in preferential destruction of S and G(2) cells and the extent of destruction of these cells was dependent upon the intensity of the action. The loss of these cells was possibly due to their larger size. However, the appearance of large numbers of membrane-bound vesicular structures similar to apoptotic bodies as well as cells with low DNA stainability (in a sub-G(1) peak) suggested that the action of adverse hydrodynamic forces on these large cells may at least in part be to induce an apoptotic response. (c) 1995 John Wiley & Sons, Inc.     

Scaling of offspring number and mass to plant and animal size: model and meta-analysis

The scaling of reproductive parameters to body size is important for understanding ecological and evolutionary patterns. Here, we derived allometric relationships for the number and mass of seeds, eggs and neonates from an existing model on population production. In a separate meta-analysis, we collected 79 empirical regressions on offspring mass and number covering different taxa and various habitats. The literature review served as a validation of the model, whereas, vice versa, consistency of isolated regressions with each other and related ecological quantities was checked with the model. The total offspring mass delivered in a reproductive event scaled to adult size with slopes in the range of about 3/4 to 1. Exponents for individual seed, egg and neonate mass varied around 1/2 for most heterotherms and between 3/4 and 1 for most homeotherms. The scaling of the progeny number released in a sowing, clutch or litter was opposite to that of their size. The linear regressions fitted into a triangular envelope where maximum offspring mass is limited by the size of the adult. Minimum seed and egg size scaled with weight exponents of approximately 0 up to 1/4. These patterns can be explained by the influence of parents on the fate of their offspring, covering the continuum of r-strategists (pelagic–aquatic, arial, most invertebrates, heterotherms) and K-strategists (littoral–terrestrial, some invertebrates, homeotherms).     

Growth autocorrelation and animal size variation

It has long been recognized that variability in animal size is affected by how individual growth rate is autocorrelated in time. Earlier studies have attributed the mechanism generating the autocorrelation primarily to size‐dependent growth rate and autocorrelation in resource abundance. All of these studies have shown that positive autocorrelation in individual growth rate always translates into increased variability in size. We show that energy reserves in individuals induce growth autocorrelation by acting like a low pass filter between the resource and the internal energy that is available for metabolism, growth and reproduction. However, the reserve also reduces the variance in growth rate. Consequently, reserve‐induced growth autocorrelation has relatively little effect on size variability in the population, contradicting existing ideas about the relationship between the growth autocorrelation and size variability.     

Cell size, cell cycle and transition probability in mouse fibroblasts

This paper describes the relationship between cell size and cell division in two situations. In the first, quiescent cells were sorted on the basis of cell size using a fluorescence-activated cell sorter and returned to culture. The results of this type of experiment are compatible with the idea that once cells have completed a size-dependent lag, the rate of entry of cells into S phase is controlled by a rate-limiting random event (or transition).The second kind of experiment follows the kinetics of complete cell cycles in rapidly proliferating cells whose mothers had been sorted on the basis of cell size. The cells born of small mother cells have longer cycle times than cells derived from large mothers. The difference in the cycle time of these two classes was due to differences in the B phase of the cell cycle [containing S, G2, M and part of G1 (G1B)], transition probability being the same in both size classes. Our results show that S, G2 and M are unaffected by size, thus confining the effect of size to G1B. It seems probable that the variability of B phase in cloned cell populations is partly due to variations of cell size at division, and correlations between the cycle times of sister cells result because sibling cells are more similar in size than unrelated cells. The major factor controlling cell division in mouse fibroblasts is shown, however, to be the transition probability; size has a more minor role.     

Effects of cell number and cell size on petiole length variation in a stoloniferous herb

In stoloniferous species, the length of petioles is of pivotal importance because it determines the position of leaf blades within the canopy. From a mechanistic perspective, two developmental processes, cell division and cell elongation, are responsible for the length of a given petiole. This study aimed at quantifying the relative contributions of cell division and cell elongation to genotypic and plastic variation in petiole length of the stoloniferous herb Trifolium repens. Thirty-four genotypes of T. repens were grown under high light conditions and simulated canopy shade. Cells were counted and their lengths measured on epidermal prints from fully grown petioles of leaves that had been initiated in the experimental light conditions. Cell number was the main trait explaining petiole length differences among genotypes grown under high light, while both cell number and length changed in response to shading. Our study revealed a strong negative correlation between shade-induced changes in cell number and cell length: genotypes that responded to shading by increasing cell numbers hardly changed in cell length, and vice versa. Our results suggest that genotypic and phenotypic variation in petiole length results from a complex interplay between the developmental processes of cell elongation and cell division.     

蚜虫种群时空分布动态模型

种群空间格局是昆虫种群的重要属性,是为害虫防治提供动态信息的重要前提。关于种群空间格局的时空动态,前人曾建立了富立叶模型和有阻尼自由震荡模型,但忽略了生境资源和空间资源的限制,不能很好地描述昆虫种群在自然界摆布状况的动态行为。因此,在前人研究的基础上,根据蚜虫在自然界的聚集扩散行为逐步建立了描述蚜虫种群聚集扩散规律的变幅、变周期时空分布动态模型,即:y=Ae-nt[sin(w0emtt+φ)+b]+c,并应用该模型对麦长管蚜(Sitobion avenae Fabricius)、麦二叉蚜(Schizaphis graminum Rondani)、禾缢管蚜(Rhopalosiphum padi Linnaeus)和玉米蚜(Rhopalosiphum maidis Fitch)的实验数据进行了拟合。结果表明,麦蚜种群和玉米蚜种群呈现出不同的规律,3种麦蚜均为减幅减周期的变化趋势,玉米蚜则表现为减幅增周期的变化趋势。此外,该模型的拟合效果较好(R20.942,SSE2.6)、生物意义明确,不仅可用于描述蚜虫以及蚜虫以外的其他昆虫和螨类种群的时空动态,还可准确描述不同年龄阶段和不同空间位置上种群的动态,具有普遍适用性。应用该模型考察不同种蚜虫在同一作物上的竞争情况和蚜虫与其天敌的空间分布动态,可为害虫的综合防治奠定基础;对不同小麦抗性品种上同一种蚜虫的聚集扩散行为进行刻画、分析,还可为小麦的抗性育种提供参考依据。     

Relationship between cell size, cell cycle and specific recombinant protein productivity

Centrifugal elutriation was used to produce cell cycle enrichedfractions of four commercially relevant recombinant cell lines,chosen to allow for variation in properties due to construct,expression system and parent cell type, from normally growingheterogeneous batch cultures. As these fractions had identicalculture histories and had not been subjected to any insult orstress which was likely to have adversely affected cellularmetabolism, they were ideal for further study of cellularproperties. Specific productivity, cell size and cell cyclestate of replicate elutriated fractions were measured for eachcell line. Results showed that cell size was the major cellulardeterminant of productivity for all cell lines examined. Productformation was not restricted to any particular cell cycle phaseand in all cases, production occurred irrespective of cell cyclephase. Specific productivity was lowest when the majority ofcells in the fraction were G₁, intermediate when themajority of cells in the fraction were S phase and greater whenthe majority of cells in the fraction were in G₂/M. However, the evidence suggests that size is the major cellulardeterminant of productivity; the apparent relationship betweencell cycle and productivity is secondary and can simply beascribed to the increasing size of cells as they progress thoughthe cell cycle. Thus, in addition to cell density and viabilitycell size is the cellular parameter which should be incorporatednot only into mathematical models of recombinant mammalian cellproduction processes but also into process monitoring andcontrol strategies.     

Unstable activator model for size control of the cell cycle

An unstable activator model for the size-control of cellular events is presented. An effector is synthesised at a rate proportional to cell volume and degraded at a rate in proportion to its own concentration and the number of nuclei (or genome equivalents) so that at equilibrium its concentration changes two-fold over one cell cycle. Triggering of the controlled event occurs when a critical concentration is achieved. Provided turnover of the effector is rapid the cell will correctly monitor its nuclear concentration under all conditions.     

Cell number, cell size and hormone levels in semi-isogenic mutants of Lycopersicon pimpinellifolium differing in fruit size

Tomato fruit growth parameters, cell number and cell size, and hormone levels [IAA, abscisic acid (ABA), zeatin (Z)/zeatin riboside (ZR), isopentenyladenosine (i-Ado)/isopentenlyadenine (i-Ade)], in the wild-type ( Lycopersicon pimpinellifolium Mill.) and a semi-isogenic mutant (mutant III) differing in fruit size were investigated during fruit development. An image-processing system was used for the determination of cell number and single cell size per fruit and hormone levels were measured by radioimmuno-assay (RIA). The bigger fruits of mutant III showed higher cell numbers throughout fruit development and cells enlarged faster than in wild-type fruits. During the first 10 days of fruit growth, the main cell division period after fertilization, high concentrations of cytokinins were found, these being correlated with high cell division activity. There were only slight differences in IAA and ABA levels in the different sized fruits. The results emphasized the importance of the cell number per fruit at anthesis as a determining factor of final fruit size in tomatoes. A possible relationship between cytokinins and subsequent fruit development is discussed.     

Gene copy number and cell cycle arrest

The cell cycle is an orderly sequence of events which ultimately lead to the division of a single cell into two daughter cells. In the case of DNA damage by radiation or chemicals, the damage checkpoints in the G1 and G2 phases of the cell cycle are activated. This results in an arrest of the cell cycle so that the DNA damage can be repaired. Once this is done, the cell continues with its usual cycle of activity. We study a mathematical model of the DNA damage checkpoint in the G2 phase which arrests the transition from the G2 to the M (mitotic) phase of the cell cycle. The tumor suppressor protein p53 plays a key role in activating the pathways leading to cell cycle arrest in mammalian systems. If the DNA damage is severe, the p53 proteins activate other pathways which bring about apoptosis, i.e., programmed cell death. Loss of the p53 gene results in the proliferation of cells containing damaged DNA, i.e., in the growth of tumors which may ultimately become cancerous. There is some recent experimental evidence which suggests that the mutation of a single copy of the p53 gene (in the normal cell each gene has two identical copies) is sufficient to trigger the formation of tumors. We study the effect of reducing the gene copy number of the p53 and two other genes on cell cycle arrest and obtain results consistent with experimental observations.     

微藻光密度与细胞密度及生物质的关系

以四种常见微藻,小球藻(Chlorella sp.XQ-20044)、栅藻(Scenedesmus sp.SS-200716)、绿球藻(Chlorococcum sp.)和螺旋藻(Spirulina sp.CH-164)为实验材料,用梯度稀释法测定对数生长期不同浓度藻液的光密度(OD)、细胞密度和生物质干重(DW),在光自养分批培养模式下对4种微藻进行OD-波长(350—800 nm)扫描,同时测定细胞密度和生物质干重,分析藻液OD与细胞密度、生物质干重的关系。结果表明:在任何波长下,对数生长期的4种微藻细胞密度与OD值、生物质干重与OD值的变化都不成比例,波长不同其拟合曲线偏离直线的程度不同。但是,在435 nm处这种关系最接近直线,可以用直线方程近似描述(R20.98),其它波长处细胞密度-OD、干重-OD的关系都可以用二项式方程很好地描述(R20.99)。因此,光密度法适用于连续和半连续培养,可以用435 nm处测得的OD值计算细胞密度与干重。但是在分批培养模式下,4种微藻DW/OD比值随着培养时间均逐渐上升。小球藻DW/OD540为0.19—0.44 g/L,栅藻DW/OD540为0.36—0.53 g/L,绿球藻DW/OD540为0.48—0.75 g/L,螺旋藻DW/OD560为0.46—0.74 g/L,因此分批培养模式下采用测定藻液OD值反映细胞密度和生物质的方法不适用,只有直接测定细胞密度和生物质才是准确的。研究结果为正确使用分光光度法监测微藻生长提供依据。     

Cell cycle,cell size and mitochondrial activity of hybridoma cells during batch cultivation

Cell cycle, cell size and rhodamine 123 fluorescence in cell populations of two batch cultures were analysed and quantified with a fluorescence-activated cell sorter (FACS). Two cultures derived from either exponential or stationary phase innocula were investigated in order to demonstrate the dependency of the subsequent cell growth on innoculum condition. The results demonstrated that the level of activity of cells in the innoculum culture could have a significant effect on cellular activity during the initial phase of the inoculated culture, as it advances through its growth cycle. Positive correlation was found between the cell size and mitochondrial activity (as measured by rhodamine 123 uptake) with S and G₂ fractions as the cell progressed through the cell cycle. The enumeration of the fractions of cell cycle phases has helped in prediction of the changes in cell numbers following perturbation of the culture condition.     

Cell cycle length, cell size, and proliferation rate in hydra stem cells

We have analyzed the cell cycle parameters of interstitial cells in Hydra oligactis. Three subpopulations of cells with short, medium, and long cell cycles were identified. Short-cycle cells are stem cells; medium-cycle cells are precursors to nematocyte differentiation; long-cycle cells are precursors to gamete differentiation. We have also determined the effect of different cell densities on the population doubling time, cell cycle length, and cell size of interstitial cells. Our results indicate that decreasing the interstitial cell density from 0.35 to 0.1 interstitial cells/epithelial cell (1) shortens the population doubling time from 4 to 1.8 days, (2) increases the [3H]thymidine labeling index from 0.5 to 0.75 and shifts the nuclear DNA distribution from G2 to S phase cells, and (3) decreases the length of G2 in stem cells from 6 to 3 hr. The shortened cell cycle is correlated with a significant decrease in the size of interstitial stem cells. Coincident with the shortened cell cycle and increased growth rate there is an increase in stem cell self-renewal and a decrease in stem cell differentiation.     

Interspecific size and number variation in pollen grains and seeds

An interspecific correlation between pollen grain size and seed size is demonstrated by means of the phylogenetic regression, which allows for phylogenetic bias. The correlation was not explained by plant size, mass of DNA per cell, style length or breeding system, although the first three of these factors all correlated with both pollen size and seed size. Two interpretations, involving pollen competition and flower size, are discussed. There is also an interspecific correlation between pollen grain number per flower and ovule number per flower. Some consequences of these correlations for the interpretation of pollen-ovule ratios and sex allocation strategies are considered.     

A population balance model describing the cell cycle dynamics of myeloma cell cultivation

A multi-staged population balance model is proposed to describe the cell cycle dynamics of myeloma cell cultivation. In this model, the cell cycle is divided into three stages, i.e., G1, S, and G2M phases. Both DNA content and cell volume are used to differentiate each cell from other cells of the population. The probabilities of transition from G1 to S and division of G2M are assumed to be dependent on cell volume, and transition probability from S to G2M is determined by DNA content. The model can be used to simulate the dynamics of DNA content and cell volume distributions, phase fractions, and substrate and byproduct concentrations, as well as cell densities. Measurements from myeloma cell cultivations, especially the FACS data with respect to DNA distribution and cell fractions in different stages, are employed for model validation.     

Geometrical constraints in the scaling relationships between genome size, cell size and cell cycle length in herbaceous plants

Plant nuclear genome size (GS) varies over three orders of magnitude and is correlated with cell size and growth rate. We explore whether these relationships can be owing to geometrical scaling constraints. These would produce an isometric GS-cell volume relationship, with the GS-cell diameter relationship with the exponent of 1/3. In the GS-cell division relationship, duration of processes limited by membrane transport would scale at the 1/3 exponent, whereas those limited by metabolism would show no relationship. We tested these predictions by estimating scaling exponents from 11 published datasets on differentiated and meristematic cells in diploid herbaceous plants. We found scaling of GS-cell size to almost perfectly match the prediction. The scaling exponent of the relationship between GS and cell cycle duration did not match the prediction. However, this relationship consists of two components: (i) S phase duration, which depends on GS, and has the predicted 1/3 exponent, and (ii) a GS-independent threshold reflecting the duration of the G1 and G2 phases. The matches we found for the relationships between GS and both cell size and S phase duration are signatures of geometrical scaling. We propose that a similar approach can be used to examine GS effects at tissue and whole plant levels.