Variations In Cell Density Research Articles

Variations in cell density in the ganglion cell layer of the retina as a function of ocular pigmentation.

Ocular melanin regulates retinal development, including cell density gradients in the central retina, a region essential for normal visual acuity. In albinos this region is underdeveloped and peak cell numbers are reduced. It is not known whether there is a dosage relationship between pigmentation and the degree of this underdevelopment, as studies of the retinal effects of albinism have commonly used rodents. These have poorly developed central regions even in the wild type. Rabbits, however, have a unique, highly specialized, visual streak in the central retina where cell density gradients are very steep and these are reduced in albinos. Here, cell densities in the ganglion cell layer of separate groups of rabbits, with different levels of ocular pigmentation and known mutations of the tyrosinase gene coding sequence, were examined. These revealed reductions in peak cell densities and/or in the regions over which high cell densities were maintained in all hypopigmented phenotypes. There was no dosage relationship between levels of pigmentation and deficits in the ganglion cell layer as animals with relatively small reductions in retinal pigment had deficits comparable to those found in albinos. The greatest variability between pigmentation phenotypes was between the two completely unpigmented strains. Consequently, although pigment may regulate the development of the central retina, this study failed to show that it does so in a dose-dependent manner.

Changes of the ganglioside pattern and content in human fibroblasts by high density cell population subculture progression.

In this study we show that the ganglioside content and pattern of human skin fibroblasts change along the process of cell subculture progression by varying the cell density. GM3, GD3 and GD1a were components of the total cell ganglioside mixtures extracted from cells, but GD1a was in all the extracts a minor component or very scant. Other gangliosides present in traces were not characterised. The fibroblast ganglioside content of 52 pools of cells obtained from 5 different cell lines cultured at variable cell density ranged from 2.0 to 13.1 nmoles per mg of cell protein. The molar ratio between GM3 and GD3 varied from 418 to 0.6 in the ganglioside mixtures, as determined by densitometric quantitative analysis after thin layer chromatographic separation. Both the ganglioside content and the GM3/GD3 molar ratio were constant along several passages of subculture progression performed by plating cells collected at confluence. Instead, when the subculture progression was performed by plating cells collected at a few days after reaching confluence, a progressive increase of the ganglioside content was observed. GD3 increased proportionally more than GM3 so that a progressive decrease of the ratio between GM3 and GD3 was observed. In some experiments, GD3 was very scant at the beginning of the progression, while it was near 30% after 5 passages under these conditions. The progressive increase of GD3 along the high density cell population subculture progression was associated to a moderate increase of the mRNA GD3 synthase.

The corneal surface of aquatic vertebrates: microstructures with optical and nutritional function?

The anterior surface of the mammalian cornea plays an important role in maintaining a smooth optical interface and consequently a sharp retinal image. The smooth surface is produced by a tear film, which adheres to a variety of microprojections, which increase the cell surface area, improve the absorbance of oxygen and nutrients and aid in the movement of metabolic products across the outer cell membrane. However, little is known of the structural adaptations and tear film support provided in other vertebrates from different environments. Using field emission scanning electron microscopy; this study examines the density and surface structure of corneal epithelial cells in representative species of the classes Cephalaspidomorphi, Chondrichthyes, Osteichthyes, Amphibia, Reptilia, Aves and Mammalia, including some Marsupialia. Variations in cell density and the structure and occurrence of microholes, microridges, microplicae and microvilli are described with respect to the demands placed upon the cornea in different aquatic environments such as marine and freshwater. A progressive decrease in epithelial cell density occurs from marine (e.g. 29348 cells mm(-2) in the Dover sole Microstomius pacficus) to estuarine or freshwater (e.g. 5999 cells mm(-2) in the black bream Acanthopagrus butcheri) to terrestrial (e.g. 2126 cells mm(-2) in the Australian koala Phascolarctos cinereus) vertebrates, indicating the reduction in osmotic stress across the corneal surface. The microholes found in the Southern Hemisphere lampreys, namely the pouched lamprey (Geotria australis) and the shorthead lamprey (Mordacia mordax) represent openings for the release of mucus, which may protect the cornea from abrasion during their burrowing phase. Characteristic of marine teleosts, fingerprint-like patterns of corneal microridges are a ubiquitous feature, covering many types of sensory epithelia (including the olfactory epithelium and the oral mucosa). Like microplicae and microvilli, microridges stabilize the tear film to maintain a smooth optical surface and increase the surface area of the epithelium, assisting in diffusion and active transport. The clear interspecific differences in corneal surface structure suggest an adaptive plasticity in the composition and stabilization of the corneal tear film in various aquatic environments.

Numerical Design of Auto-Catalyst Substrate for Improved Conversion Performance Using Radially Variable Cell Density

The optimal design of auto-catalyst needs a good compromise between the pressure drop and flow uniformity in the substrate. One of the effective methods to achieve this goal is to use the concept of radially variable cell density. But this method has not been examined its usefulness in terms of chemical behavior and conversion performance. In this work, two-dimensional performance prediction of catalyst coupled with turbulent reacting flow simulation has been used to evaluated the benefits of this method n the flow uniformity and conversion efficiency. The results showed that two cell combination of 93cpsc and 62 cpsc was the most effective for improved pressure drop and conversion efficiency due to balanced space velocity and efficient usage of geometric surface area of channels. It was also found that large temperature difference between the bricks in case that the edge of the frontal face of brick has too much lower cell density(less than 67% of cell density of the center of the brick). This study has also demonstrated that the present computational results show the better prediction accuracy in terms of CO, HC and NO conversion efficiencies compared to those of conventional 1-D adiabatic model by comparison with experimental results.

Interstitial Fluid Pressure, Fraction of Necrotic Tumor Tissue, and Tumor Cell Density in Human Melanoma Xenografts

Interstitial fluid pressure (IFP) has been shown to differ substantially between individual tumors, but the tumor properties governing the intertumor heterogeneity in IFP have not been identified conclusively. The purpose of the work reported here was to investigate whether the fraction of necrotic tissue and the density of tumor cells are major determinants of the intertumor heterogeneity in IFP. The study was based on the hypothesis that the resistance against fluid flow in the tumor interstitium is influenced significantly by these parameters. Xenografted tumors of four human melanoma lines (A-07, D-12, R-18, U-25) were included in the study. Tumors showing large variation in necrotic fraction but similar cell densities (D-12, U-25) were used to study the influence of necrosis on IFP, whereas tumors showing no or insignificant necrosis but large variation in cell density (A-07, R-18) were used to search for correlations between IFP and cell density. IFP was recorded using the wick-in-needle technique. Necrotic fraction and cell density were measured by stereological analysis of histological sections using an image processing system. Significant correlations between IFP and necrotic fraction were not found, implying that the IFP of tumors is not influenced significantly by the development of necrosis. The R-18 tumors, which had a high cell density, showed a significantly higher IFP than the A-07 tumors, which had a low cell density. Significant correlations between IFP and cell density were not found when individual tumors of the same line were considered. These two observations suggest that the IFP of tumors depends on the cell density, but the cell density is probably not a major determinant of the IFP.

Culturing of human vascular endothelial cells strongly affects their endothelin-1 and prostacyclin production.

Cultured human umbilical vein endothelial cells (HUVECs) are a widely used model to study the regulation of endothelial production of vasoactive substances such as endothelin-1 (ET-1) and prostacyclin (PGI2) in human. As even short term culturing is known to affect the function of many cell types, we studied whether there are differences in the production of ET-1 and PGI2 between freshly isolated HUVECs and HUVECs cultured for two passages, and whether variation in cell density affects the production of ET-1 and PGI2 by these cells. At confluency, freshly isolated HUVECs produced only from one-tenth to one-fifth of ET-1, but 46-86 times more PGI2 (p < 0.001), when compared to respective productions by similar amounts of cultured HUVECs. When the cell density of freshly isolated HUVECs was lowered either by diluting the cell suspension or by plating the same amount of cells on different size wells, the production of ET-1 increased: lowering cell density to one-tenth led to 18 fold increase in ET-1 production (p < 0.001). PGI2 production was not affected by cell density. Thus our data imply that the production of both ET-1 and PGI2 are differently regulated in freshly isolated and cultured HUVECs, and that cell density is an important determinant in the regulation of ET-1 production.

Engineering challenges in high density cell culture systems

High density cell culture systems offer the advantage of production of bio-pharmaceuticals in compact bioreactors with high volumetric production rates; however, these systems are difficult to design and operate. First of all, the cells have to be retained in the bioreactor by physical means during perfusion. The design of the cell retention is the key to performance of high density cell culture systems. Oxygenation and media design are also important for maximizing the cell number. In high density perfusion reactors, variable cell density, and hence the metabolic demand, require constant adjustment of perfusion rates. The use of cell specific perfusion rate (CSPR) control provides a constant environment to the cells resulting in consistent production. On-line measurement of cell density and metabolic activities can be used for the estimation of cell densities and the control of CSPR. Issues related to mass transfer and mixing become more important at high cell densities. Due to the difference in mass transfer coefficients for oxygen and CO(2), a significant accumulation of dissolved CO(2) is experienced with silicone tubing aeration. Also, mixing is observed to decrease at high densities. Base addition, if not properly done, could result in localized cell lysis and poor culture performance. Non-uniform mixing in reactors promotes the heterogeneity of the culture. Cell aggregation results in segregation of the cells within different mixing zones. This paper discusses these issues and makes recommendations for further development of high density cell culture bioreactors.

Biofilm structural heterogeneity visualized by three microscopic methods

The structural heterogeneity of a microbial biofilm was demonstrated by scanning electron microscopy, confocal scanning laser microscopy (CSLM), and cryoembedding followed by sectioning and microscopic examination. Biofilm was composed of a binary population of Pseudomonas aeruginosa and Klebsiella pneumoniae grown in a continuous flow annular reactor. The three microscopic methods provided a consistent picture of the biofilm as a non-uniform structure characterized by variable thickness and variable local cell and polymer densities. Significant changes in these parameters occurred in the biofilm over distances of 10 μm or less. Though the biofilm was several hundred microns thick in places, areas of bare substratum were also observed on the same sample coupon. Cell-free pores and channels in the biofilm interior were evident. Specific staining of cellular nucleic acids with ethidium bromide and extracellular polymeric substances (EPS) with calcofluor showed that cell and EPS distributions did not always overlap. The ethidium bromide-stained region was contained within the larger region of calcofluor staining; thus, some cell-free areas actually were filled with EPS. CSLM and cryoembedding approaches are superior to SEM in their ability to image the biofilm interior and in their potential to provide quantitative information.

Longitudinal variation in cell density and mossy fiber reorganization in the dentate gyrus from temporal lobe epileptic patients

Variation in cell loss and mossy fiber reorganization was examined along the longitudinal axis of the dentate gyrus from temporal lobe epileptic (TLE) patients. Previous evidence has indicated that the anterior hippocampus is prone to seizure activity. We compared granule and hilar cell number in addition to Timm stain density of the molecular layer and hilus in more anterior and more posterior specimens of hippocampus obtained from patients surgically treated for intractable epilepsy by the removal of the anterior half of the hippocampus. Granule cells/mm in the more anterior specimen were less than or equal to those in the more posterior specimen locations in 77% of the patients, while there was no significant difference in hilar neuron density between the two blocks. These results demonstrate a significantly greater pathology in the granule cell layer in more anterior specimens and no difference in pathology for hilar neurons. Molecular layer Timm stain density was significantly greater in the more anterior specimen of 71% of the patients. The molecular layer Timm stain density ratio was inversely related to hilar cell density in more anterior specimens, whereas in more posterior specimens there was no significant relationship with hilar cell density. Our observations show that although differences exist among TLE patients for these neuroanatomic measures, pathology was greater in more anterior specimens. The latter result is consistent with the conclusion that seizure activity may originate in the anterior region of the hippocampus in a majority of patients.

Differential Regulation of Plasminogen Activation in Normal Keratinocytes and SCC-4 Cells by Fibroblasts

The plasminogen activator (PA)/plasmin system is thought to be involved in processes such as tumor invasion and wound healing, during which epithelial and mesenchymal cells come close together. However, information on regulation of the PA/plasmin system during epithelial-mesenchymal interactions is scarce. Therefore, we examined the in vitro modulation of the production and activity of the components of the PA/plasmin system in squamous carcinoma cells (SCC-4) and normal human keratinocytes in relation to cell density and the presence or absence of fibroblasts (3T3 cells). There was an inverse relation between cell density and mRNA expression for urokinase-type plasminogen activator (u-PA) and u-PA receptor in both SCC-4 cells and keratinocytes. In addition, such a relation was found for plasminogen activator inhibitor types 1 (PAI-1) and 2 (PAI-2) in SCC-4 monocultures, but not in keratinocyte monocultures. In contrast to monocultures, variation of cell density did not affect the mRNA expression of the components of the PA/plasmin system in cocultures of SCC-4 cells or keratinocytes with 3T3 cells. However, the relative expression of mRNAs in co-cultures was clearly different from that in monocultures, especially at low cell density. For most of the components of the PA/plasmin system, a decrease in mRNA expression and u-PA receptor protein was observed at most cell densities, whereas for PAI-1 only in keratinocytes a marked increase was documented. Zymography of supernatants revealed that the levels of both free u-PA and PA-PAI were increased in SCC-4/3T3 co-cultures, whereas in keratinocytes/3T3 co-cultures, only levels of the PA-PAI complex were increased, while the amount of free u-PA activity decreased. This occurred despite the increase u-PA immunoreactivity and was probably caused by the markedly elevated levels of immunoreactive PAI-1. The results of the present study reveal that the production and synthesis of various components of the PA/plasmin system in keratinocytes and SCC-4 cells depend on the density of epithelial cells and are modulated by fibroblasts, probably through a direct cell-cell or cell-matrix contact. Fibroblast-induced modulations are similar in keratinocytes and SCC-4 cells except for the regulation of PAI-1, which is markedly enhanced only in keratinocytes. This suggests that the modulation of PA activity in the direct microenvironment may be different under physiologic and pathologic conditions.

A kinetic model for cell density dependent bacterial transport in porous media

A kinetic transport model with the ability to account for variations in cell density of the aqueous and solid phases was developed for bacteria in porous media. Sorption kinetics in the advective‐dispersive‐sorptive equation was described by assuming that adsorption was proportional to the aqueous cell density and the number of available sites on the solid phase, whereas desorption was proportional to the density of sorbed cells. A numerical solution to the model was tested against laboratory column data, and the performance was compared with that of a two‐site model. The kinetic model described the column data as well as the two‐site model did, but the highest efficiencies of both models were associated with experiments with the smallest sorption. Furthermore, the kinetic model accounted for cell density dependent sorption, as demonstrated by fair predictions of bacterial transport at one cell density when using parameters obtained at another cell density.

Search for cell proliferation markers suitable for cell count in continuous immobilized cell bioreactors

The control of hybridoma cell cultures in bioreactors requires the use of convenient indicators to monitor the proliferation of the biomass. In order to select appropriate indications, we followed the variations of several compounds including tumoral markers, polyamines, sialic acids, purine and pyrimidine bases, enzymes and metabolites such as glucose, lactate and amino acids, and the variations of cell density during batch culture. Significant correlations were found between the number of viable cells and alkaline phosphatase, β-glucuronidase, glucose and lactate measured in the culture medium of hybridoma strains. The correlation calculated from alkaline phosphatase and β-glucuronidase concentrations in culture medium underestimated cell number. The correlation established with glucose and lactate gave the best indication of cell proliferation in continuous culture with an immobilized cell bioreactor. Finally, the exact quantification of the biomass in these culture conditions can be obtained using the mean of glucose and lactate correlations.

A model for calculating tumour control probability in radiotherapy including the effects of inhomogeneous distributions of dose and clonogenic cell density

Most calculations of the biological effect of radiation on tumours assume that the clonogenic cell density is uniform even if account is taken of non-uniform dose distribution. In practice tumours will almost certainly have a non-uniform clonogenic cell density. The paper extends one particular model of tumour control probability (TCP) to incorporate a variable clonogenic cell density while at the same time assuming a constant 2 Gy fraction size and a uniform radiosensitivity throughout the treatment. Since there are virtually no in vivo data on the variation of density the authors consider some model situations. One clear conclusion is that a large reduction in clonogenic cell density at the edges of a tumour would permit only a very modest decrease in dose if the TCP is not to be reduced. In general the effect on TCP is a complicated function of the variation in both dose and clonogenic cell density. The authors give the equations which enable both to be included.

Effects of cell density on in vitro glucose metabolism by isolated adipocytes.

We studied the effect of variable isolated fat cell concentrations (from 0.17 to 1.25 x 10(6) cells/ml) on rate and pattern of basal and insulin-stimulated glucose metabolism by rat epididymal fat cells. Cell concentration did not affect total glucose utilization, but high cell concentrations increased the absolute and relative conversion of glucose to CO2 and glyceride-fatty acids by two- to threefold and decreased the conversion to lactate, pyruvate, and glyceride-glycerol when compared with values observed at low cell concentration. When effects of adenosine deaminase (ADA) and N-6(2-phenylisopropyl)adenosine (PIA) were examined, addition of ADA to incubated cells produced no significant changes in the rate or pattern of adipocyte glucose metabolism; PIA had a slight and uniform effect on the conversion of glucose to its metabolic products and minimal effect on insulin-stimulated glucose metabolism. Medium free fatty acid concentration did not change during the incubation at various cell density, but intracellular free fatty acids were found to be inversely related to fat cell density in the medium. Thus a variable fat cell density influences the pattern of adipocyte glucose metabolism in vitro. This effect may be due to variable rates of lipolysis and resulting changes in intracellular fatty acid concentration rather than to adenosine per se. This work has practical implications in the need to define cell density when carrying out in vitro measurements of adipocyte glucose conversion to products.

Modulation of glucocorticoid induction of tyrosine aminotransferase gene expression by variations in cell density

Modulation of glucocorticoid induction of tyrosine aminotransferase gene expression by variations in cell density

Metabolic chiral inversion of 2-arylpropionates in rat H4IIE and human Hep G2 hepatoma cells: Relationship to in vivo metabolism

The inversion of 2-arylpropionic acids (2-APAs) has been investigated in vitro using rat H4IIE and human Hep G2 hepatoma cells in continuous culture. The effect of substrate concentration (15–150 μg/mL), cell density (1.5–12 × 10 6 cells/dish) and serum content of the culture medium (0–20%) on inversion was examined in rat H4IIE hepatoma cells using R-ibuprofen as model compound. Increasing R-ibuprofen concentrations and decreasing serum content of the medium resulted in increased inversion whereas variation of cell density had no effect. Furthermore, rat H4IIE and human Hep G2 hepatoma cells were incubated with the individual enantiomers of ibuprofen, ketoprofen and flurbiprofen under optimized culture conditions (serum-free culture medium). The elimination rate constants ( K el ) and fractions inverted ( f 1) were determined. Although inversion occurred slowly in the tumor cells and thus long incubation periods (120 hr) were required, the hepatoma cells were nevertheless able to mimic qualitatively the species and substance specificity of inversion of 2-APAs as observed in vivo.

Modulation of glucocorticoid induction of tyrosine aminotransferase gene expression by variations in cell density.

Glucocorticoids induce tyrosine aminotransferase (TAT) in hepatoma cells. We have previously shown that both the concentration of the agonist dexamethasone (Dex) required for half-maximal induction (EC50) and the amount of agonist activity produced by the antagonist dexamethasone 21-mesylate (Dex-Mes), expressed as a percentage of maximum induction achieved by Dex, are different in Fu5-5 and HTC cells. Furthermore, both activities vary over several weeks in each cell line in an apparently random manner, but, nevertheless, are correlated by a linear semilog plot. We now find that this long term and previously unpredictable variation in both the Dex EC50 and the amount of Dex-Mes agonist activity for the induction of TAT enzyme activity can be made to occur reproducibly in 40 h or less by changing the cell density and/or amount of medium in the tissue culture plates. Thus, a higher cell density and/or a lower volume of medium produced both higher amounts of Dex-Mes agonist activity and lower EC50 values for Dex. Experiments with cells at different densities but exposed to the same medium indicated that cell density was the dominant determinant. A qualitatively identical modulation was seen at the level of TAT mRNA, but not mouse mammary tumor virus RNA. We are not aware of any previous report of cell growth conditions altering either the level of agonist activity of an antisteroid or the EC50 of a full agonist. These results further indicate that extrachromosomal parameters, such as cell-cell contact and/or a diffusable factor(s), can modulate the basic features of glucocorticoid induction of some, but not all, glucocorticoid-inducible genes.

The rate and topography of cell wall synthesis during the division cycle of Escherichia coli using N-acetylglucosamine as a peptidoglycan label.

The rates of synthesis of peptidoglycan and protein during the division cycle of Escherichia coli were measured by the membrane elution technique using cells differentially labelled with N-acetylglucosamine and leucine. During the first part of the division cycle the ratio of the rates of protein and peptidoglycan synthesis was constant. The rate of peptidoglycan synthesis, relative to the rate of protein synthesis, increased during the latter part of the division cycle. These results support a simple, bipartite model of cell surface increase in rod-shaped cells. Prior to the start of constriction the cell surface increases only by lateral wall extension. After cell constriction starts, the cell surface increases by both lateral wall and pole growth. The increase in surface area is partitioned between the lateral wall and the pole so that the volume of the cell increases exponentially. No variation in cell density occurs, because the increase in surface allows a continuous exponential increase in cell volume that accommodates the exponential increase in cell mass. The results are consistent with the constant density of the growing cell and the surface stress model for the regulation of cell surface synthesis. In addition, the elution pattern suggests that the membrane elution method does work by having the cells effectively bound to the membrane by their poles.

Neuronal populations stained with the monoclonal antibody Cat-301 in the mammalian cerebral cortex and thalamus

The monoclonal antibody Cat-301 was used to examine neurons in the cerebral cortex and dorsal thalamus of several mammalian species, including Old World monkeys, cats, bush babies, guinea pigs, and rats. In each species, subpopulations of cortical and thalamic neurons are stained along the surfaces of their somata and proximal dendrites. Cat-301-positive cortical neurons include specific groups of pyramidal cells (e.g., corticospinal but not corticobulbar or callosal neurons in the monkey sensory-motor areas) and certain GABA-immunoreactive nonpyramidal cells. In the thalamus, the relay neurons projecting to the cortex and not the intrinsic neurons are stained. The Cat-301-positive neurons are nonhomogeneously distributed in the cat and monkey cortex and thalamus. In the cortex, they are densely packed in 2 bands that in most areas include layers III and V, but that in primary sensory areas include layers IV and VI. Because the density of stained neurons, their distribution, and the intensity of their staining vary among cortical areas, the borders between neighboring areas can often be detected by the differences in Cat-301 staining. Broader, regional differences are also readily apparent, for areas in the parietal and occipital lobes contain large numbers of intensely stained cells, but most areas in the frontal and temporal lobes contain fewer, more lightly stained neurons. The same broad differences are seen within the thalamus: only those nuclei reciprocally connected with intensely stained cortical areas contain large numbers of Cat-301-positive neurons. Differences among species include variations in cell density and distribution when a given cortical area or thalamic nucleus is compared between cats and monkeys. Greater differences are seen among the other species. Immunoreactive neurons in the cerebral cortex are sparse and lightly stained in guinea pigs, are restricted to the hippocampal formation in rats, and are very rare and isolated in bush babies. Similarly, Cat-301-positive thalamic neurons are restricted to only one or 2 nuclei in the guinea pig and rat and are extremely rare in the bush baby. Cat-301 stains organized groups of neurons in the cat and monkey cortex and thalamus. In addition to the laminar organization of stained cells in all cortical areas (see above), the Cat-301-positive neurons of monkey areas 17 and 18 are grouped into radial arrays. In area 17, clusters of stained cells are present in layers above and below layer IVC. These clusters lie at the centers of ocular dominance columns, within patches stained for cytochrome oxidase (CO). Most of these cells are also GABA-immunoreactive.(ABSTRACT TRUNCATED AT 400 WORDS)

Rate and topography of cell wall synthesis during the division cycle of Salmonella typhimurium

The rates of synthesis of peptidoglycan and protein during the division cycle of Salmonella typhimurium have been measured by using the membrane elution technique and differentially labeled diaminopimelic acid and leucine. The cells were labeled during unperturbed exponential growth and then bound to a nitrocellulose membrane by filtration. Newborn cells were eluted from the membrane with fresh medium. The radioactivity in the newborn cells in successive fractions was determined. As the cells are eluted from the membrane as a function of their cell cycle age at the time of labeling, the rate of incorporation of the different radioactive compounds as a function of cell cycle age can be determined. During the first part of the division cycle, the ratio of the rates of protein and peptidoglycan synthesis was constant. During the latter part of the division cycle, there was an increase in the rate of peptidoglycan synthesis relative to the rate of protein synthesis. These results support a simple, bipartite model of cell surface increase in rod-shaped cells. Before the start of constriction, the cell surface increased only by cylindrical extension. After cell constriction started, the cell surface increased by both cylinder and pole growth. The increase in surface area was partitioned between the cylinder and the pole so that the volume of the cell increased exponentially. No variation in cell density occurred because the increase in surface allowed a continuous exponential increase in cell volume that accommodated the exponential increase in cell mass. Protein was synthesized exponentially during the division cycle. The rate of cell surface increase was described by a complex equation which is neither linear nor exponential.