Evidence for the generality of linear cell growth

Fundamental principles in bacterial physiology-history, recent progress, and the future with focus on cell size control: a review

Bacterial physiology is a branch of biology that aims to understand overarching principles of cellular reproduction. Many important issues in bacterial physiology are inherently quantitative, and major contributors to the field have often brought together tools and ways of thinking from multiple disciplines. This article presents a comprehensive overview of major ideas and approaches developed since the early 20th century for anyone who is interested in the fundamental problems in bacterial physiology. This article is divided into two parts. In the first part (sections 1-3), we review the first 'golden era' of bacterial physiology from the 1940s to early 1970s and provide a complete list of major references from that period. In the second part (sections 4-7), we explain how the pioneering work from the first golden era has influenced various rediscoveries of general quantitative principles and significant further development in modern bacterial physiology. Specifically, section 4 presents the history and current progress of the 'adder' principle of cell size homeostasis. Section 5 discusses the implications of coarse-graining the cellular protein composition, and how the coarse-grained proteome 'sectors' re-balance under different growth conditions. Section 6 focuses on physiological invariants, and explains how they are the key to understanding the coordination between growth and the cell cycle underlying cell size control in steady-state growth. Section 7 overviews how the temporal organization of all the internal processes enables balanced growth. In the final section 8, we conclude by discussing the remaining challenges for the future in the field.

Organelle size scaling of the budding yeast vacuole is tuned by membrane trafficking rates

Organelles serve as biochemical reactors in the cell, and often display characteristic scaling trends with cell size, suggesting mechanisms that coordinate their sizes. In this study, we measure the vacuole-cell size scaling trends in budding yeast using optical microscopy and a novel, to our knowledge, image analysis algorithm. Vacuole volume and surface area both show characteristic scaling trends with respect to cell size that are consistent among different strains. Rapamycin treatment was found to increase vacuole-cell size scaling trends for both volume and surface area. Unexpectedly, these increases did not depend on macroautophagy, as similar increases in vacuole size were observed in the autophagy deficient mutants atg1Δ and atg5Δ. Rather, rapamycin appears to act on vacuole size by inhibiting retrograde membrane trafficking, as the atg18Δ mutant, which is defective in retrograde trafficking, shows similar vacuole size scaling to rapamycin-treated cells and is itself insensitive to rapamycin treatment. Disruption of anterograde membrane trafficking in the apl5Δ mutant leads to complementary changes in vacuole size scaling. These quantitative results lead to a simple model for vacuole size scaling based on proportionality between cell growth rates and vacuole growth rates.

Loss of a 20S proteasome activator in Saccharomyces cerevisiae downregulates genes important for genomic integrity, increases DNA damage, and selectively sensitizes cells to agents with diverse mechanisms of action

Cytoprotective functions of a 20S proteasome activator were investigated. Saccharomyces cerevisiae Blm10 and human 20S proteasome activator 200 (PA200) are homologs. Comparative genome-wide analyses of untreated diploid cells lacking Blm10 and growing at steady state at defined growth rates revealed downregulation of numerous genes required for accurate chromosome structure, assembly and repair, and upregulation of a specific subset of genes encoding protein-folding chaperones. Blm10 loss or truncation of the Ubp3/Blm3 deubiquitinating enzyme caused massive chromosomal damage and cell death in homozygous diploids after phleomycin treatments, indicating that Blm10 and Ubp3/Blm3 function to stabilize the genome and protect against cell death. Diploids lacking Blm10 also were sensitized to doxorubicin, hydroxyurea, 5-fluorouracil, rapamycin, hydrogen peroxide, methyl methanesulfonate, and calcofluor. Fluorescently tagged Blm10 localized in nuclei, with enhanced fluorescence after DNA replication. After DNA damage that caused a classic G2/M arrest, fluorescence remained diffuse, with evidence of nuclear fragmentation in some cells. Protective functions of Blm10 did not require the carboxyl-terminal region that makes close contact with 20S proteasomes, indicating that protection does not require this contact or the truncated Blm10 can interact with the proteasome apart from this region. Without its carboxyl-terminus, Blm10((-339aa)) localized to nuclei in untreated, nonproliferating (G(0)) cells, but not during G(1) S, G(2), and M. The results indicate Blm10 functions in protective mechanisms that include the machinery that assures proper assembly of chromosomes. These essential guardian functions have implications for ubiquitin-independent targeting in anticancer therapy. Targeting Blm10/PA200 together with one or more of the upregulated chaperones or a conventional treatment could be efficacious.

Measurement of adherent cell mass and growth

The characterization of physical properties of cells such as their mass and stiffness has been of great interest and can have profound implications in cell biology, tissue engineering, cancer, and disease research. For example, the direct dependence of cell growth rate on cell mass for individual adherent human cells can elucidate the mechanisms underlying cell cycle progression. Here we develop an array of micro-electro-mechanical systems (MEMS) resonant mass sensors that can be used to directly measure the biophysical properties, mass, and growth rate of single adherent cells. Unlike conventional cantilever mass sensors, our sensors retain a uniform mass sensitivity over the cell attachment surface. By measuring the frequency shift of the mass sensors with growing (soft) cells and fixed (stiff) cells, and through analytical modeling, we derive the Young's modulus of the unfixed cell and unravel the dependence of the cell mass measurement on cell stiffness. Finally, we grew individual cells on the mass sensors and measured their mass for 50+ hours. Our results demonstrate that adherent human colon epithelial cells have increased growth rates with a larger cell mass, and the average growth rate increases linearly with the cell mass, at 3.25%/hr. Our sensitive mass sensors with a position-independent mass sensitivity can be coupled with microscopy for simultaneous monitoring of cell growth and status, and provide an ideal method to study cell growth, cell cycle progression, differentiation, and apoptosis.

Distinguishing between linear and exponential cell growth during the division cycle: single-cell studies, cell-culture studies, and the object of cell-cycle research

BACKGROUND

Two approaches to understanding growth during the cell cycle are single-cell studies, where growth during the cell cycle of a single cell is measured, and cell-culture studies, where growth during the cell cycle of a large number of cells as an aggregate is analyzed. Mitchison has proposed that single-cell studies, because they show variations in cell growth patterns, are more suitable for understanding cell growth during the cell cycle, and should be preferred over culture studies. Specifically, Mitchison argues that one can glean the cellular growth pattern by microscopically observing single cells during the division cycle. In contrast to Mitchison's viewpoint, it is argued here that the biological laws underlying cell growth are not to be found in single-cell studies. The cellular growth law can and should be understood by studying cells as an aggregate.

RESULTS

The purpose or objective of cell cycle analysis is presented and discussed. These ideas are applied to the controversy between proponents of linear growth as a possible growth pattern during the cell cycle and the proponents of exponential growth during the cell cycle. Differential (pulse) and integral (single cell) experiments are compared with regard to cell cycle analysis and it is concluded that pulse-labeling approaches are preferred over microscopic examination of cell growth for distinguishing between linear and exponential growth patterns. Even more to the point, aggregate experiments are to be preferred to single-cell studies.

CONCLUSION

The logical consistency of exponential growth--integrating and accounting for biochemistry, cell biology, and rigorous experimental analysis--leads to the conclusion that proposals of linear growth are the result of experimental perturbations and measurement limitations. It is proposed that the universal pattern of cell growth during the cell cycle is exponential.

Exponential growth, random transitions and progress through the G1 phase: computer simulation of experimental data

At a time of increasing knowledge of gene and molecular regulation of cell cycle progression, a re-evaluation is presented concerning a phenomenon discussed before the present expanding era of cell cycle research. 'Random transition' and exponential slopes of alpha- and beta-curves were conceived in the 1970s and early 1980s to explain cell cycle progression. An exponential behaviour of the beta-curve was claimed as being necessary and sufficient for a 'random transition' in the cell cycle. In our present work, similar slopes of those curves were shown to materialize when the increase in mass of single cells was set as exponential in a structured cell cycle model where DNA replication and increase in cell mass were postulated to be two loosely coupled subcycles of the cell cycle, without introducing any 'random transition'. Findings published in the 1980s demonstrating the effect of serum depletion of 3T3 Balb-c cells were simulated and the shallower slope of the alpha- and beta-curves found experimentally could be attributed to the reduced rate of exponential growth in cell mass, rather than to a reduced 'transition probability'.

Genetic control of variation in human gingival fibroblast proliferation rate

Logarithmic proliferation rate (Days 1 to 6) of gingival fibroblasts derived from 15 pairs of monozygotic (MZ) and 9 pairs of dizygotic (DZ) human twins was compared under optimal and suboptimal growth conditions. Cell proliferation rates exhibited considerable variability among strains. For Caucasian donors (13 MZ, 6 DZ pairs) DZ twins demonstrated significantly greater (P less than 0.01) within-pair variance in cell proliferation rate compared to MZ twins when evaluated under optimal growth conditions. Heritability analysis indicated strong genetic control of proliferation rate of human gingival fibroblasts (HGF) under optimal growth conditions (1.0 +/- 0.67), whereas proliferation rate of HGF under suboptimal growth conditions revealed less genetic control (0.42 +/- 0.61). These findings emphasize the importance of carefully matching control and test HGF in assays dependent on cellular proliferation.

Variation in precursor pool size during the division cycle of Escherichia coli: further evidence for linear cell growth

The magnitudes of several pools of radioactively labeled precursors for RNA and protein synthesis were determined as a function of cell age during the division cycle of Escherichia coli 15 THU. Uracil, histidine, and methionine pools increased from low initial values for cells at birth to maxima during midcycle and then subsided again. These pools were small or nonexistent at the beginning and the end of the cycle, and their average values during the cycle were less than 4% of the total cellular radioactivity. The results are consistent with a linear pattern of growth for cells during the division cycle and provide strong evidence against exponential or bilinear growth of E. coli cells.

Leucine uptake and protein synthesis are exponential during the division cycle of Escherichia coli B/r

The rate of leucine uptake, which is a measure of protein synthesis, was measured during the division cycle of Escherichia coli B/r by the membrane elution technique. The rate of leucine uptake was exponential, indicating that protein synthesis is exponential, and not linear, during the division cycle. These results, coupled with the results of other work on the exponential rate of RNA synthesis during the division cycle, indicate that the accumulation of mass in E. coli and other gram-negative organisms is exponential during the division cycle.

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.

Kinetics of gram-negative bacterial cell elongation as measured by using the large rod "Lineola longa"

Photomicrographic data were collected to measure the kinetics of elongation of "Lineola longa," a large gram-negative rod ranging from 5 to 10 microns long, during the exponential phase of growth. Its large size makes this organism especially well suited for light microscopic observations. Because this organism is aerobic, it was necessary to ensure a saturating supply of oxygen during growth. Oxygen was supplied by using Chlorella species, in a Wheaton microculture slide, as an oxygen donor separated from the bacteria by a thin layer of agar. In another set of experiments, water-saturated air replaced Chlorella species, with similar results. Statistical analysis of the data showed that "L. longa" elongates in an exponential manner. Minicell-like structures, small spherical cells lacking DNA, were occasionally seen to be produced by aberrant septation. These minicells were seen most often at the end of the exponential-growth phase. A model of cell growth is proposed to account for these observations.

Estimating the mode of growth of individual microbial cells from cell volume distributions

Two new methods are derived for inferring the mode of growth of individual microbial cells from measurements made of the volume distributions of populations. One is based on statistics of the observed distribution and has the particular advantage that it is very easy to use. The second, which requires gradient centrifugation, yields the mode of growth directly, rather than by comparison with theoretically derived distributions. Both methods have been found to be more sensitive than those previously suggested.

Cell growth, cell division and cell size homeostasis in Swiss 3T3 cells

By separating large and small 3T3 cells we show here that cell growth (in volume) after stimulation from quiescence is not 'autocatalytic'. Rather, large cells grow significantly more slowly, in relative terms, than small cells. It follows that 3T3 cells do not require a size control mechanism operating at the level of division timing in order to achieve cell size homeostasis.

Generality of the growth kinetics of the average individual cell in different bacterial populations

The kinetics of growth of all the cells in a population is reflected in the shape of the size distribution of the population. To ascertain whether the kinetics of growth of the average individual cell is similar for different strains or growth conditions, we compared the shape of normalized size distributions obtained from steady-state populations. Significant differences in the size distributions were found, but these could be ascribed either to the precision achieved at division or to a constriction period which is long relative to the total cell cycle time. The remaining difference is quite small. Thus, without establishing the pattern itself, it is concluded that the basic course of growth is very similar for the various Escherichia coli strains examined and probably also for other rod-shaped bacteria. The effects of differences in culture technique (batch or chemostat culture), growth rate, and differences among strains were not found to influence the shape of the size distributions and hence the growth kinetics in a direct manner; small differences were found, but only when the precision at division or the fraction of constricted cells (long constriction period) were different as well.

Growth pattern and cell division in Neisseria gonorrhoeae

The gram-negative coccus Neisseria gonorrhoeae was found to grow regularly in at least two dimensions. Growth proceeded at a linear rate sequentially in each dimension. Growth in the second dimension (former width) was initiated slightly before the pole-division plane distance equalled the cell width. Penicillin treatment localized presumptive growth zones to the existing septum region. It was suggested that new growth zones were always formed perpendicular to the longitudinal axis created in the incipient daughter cells of a dividing coccus. Neither penicillin nor nalidixic acid induced filaments of N. gonorrhoeae. Such structures could nevertheless be formed in the rod-shaped species Neisseria elongata. N. gonorrhoeae divides by septation; however, complete septal structures with separated cytoplasms were rather infrequent. It is proposed that N. gonorrhoeae be regarded as a short rod which always extends parallel to the actual longitudinal axis and which never undergoes a rod-sphere-rod transition.

Transport of glucose and glycine in Schizosaccharomyces pombe during the cell cycle

Cell growth and uptake of glucose and glycine during the cell cycle were studied in synchronous cultures of Schizosaccharomyces pombe. Rates of accumulation of glucose and glycine were constant during most of the cell cycle, implying a constant rate of cell mass increase. Rates of uptake of glycine appeared to double at an average cell age of 0.9 generations.

Control of membrane protein synthesis in Bacillus subtilis

In synchronous cultures of Bacillus subtilis 168/S grown on succinate as a sole carbon source (mean generation time 115 min), chromosome initiation occurs at the beginning of the cell cycle but the rate of membrane protein synthesis doubles in mid-cycle more or less coincident with nuclear segregation. In glucose-grown cultures, the doubling in rate of membrane protein synthesis occurs at about the same time as nuclear segregation and DNA initiation at the beginning of the cycle. Control of the rate of membrane synthesis by the chromosome has been demonstrated by inhibiting DNA synthesis using thymine starvation and showing that membrane protein synthesis continues at a constant rate, whereas the rate of cytoplasmic protein synthesis almost doubles. I suggest that the replication of a region at or close to the chromosome terminus is required to allow the doubling in rate of membrane synthesis.

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.

Review lecture on the growth and form of a bacterial cell

The size, shape and composition of cells in cultures of bacteria maintained in steady states of exponential growth depend on the cultural conditions employed. Important factors influencing these parameters are the growth rate of the culture and the transit time of replication forks from one end of a chromosome to the other. The considerable progress which has been made in the last ten years in elucidating the rules governing the form and composition of cells of Escherichia coli as a function of growth rate and transit time is outlined in the Review.

Membrane synthesis in synchronous cultures of Bacillus subtilis 168

Synthesis of bacterial membranes has been investigated in Bacillus subtilis by examining incorporation of amino acids and glycerol into the protein and lipid of membranes of synchronous cultures. A simple reproducible fractionation scheme divides cellular proteins into three classes (i) truly cytoplasmic, (ii) loosely membrane bound, released by chelating agents, and (iii) tightly membrane bound. These comprise approximately 75, 10, and 15%, respectively, of cellular proteins in this organism. Incorporation of radioactivity into these fractions, using steady-state and pulse labeling has been followed during the cell cycle. Cytoplasmic proteins and the loosely membrane-bound proteins are labeled at an exponential rate throughout the cell cycle. The membrane fraction is labeled discontinuously in the cell cycle, with periods of rapid synthesis over the latter part of the cycle and a period with no net synthesis during the early part of the cycle. Pulse labeling indicates that synthesis of membrane occurs at a linear rate that doubles at a fixed time in each cycle, which coincides with the period of zero net synthesis. Rates of membrane synthesis measured by pulse labeling during the period of rapid membrane synthesis are significantly less than indicated by steady-state labeling. These discrepancies are consistent with the hypothesis that during the cell cycle certain proteins are added to the membrane from the cytoplasm and that during the period of zero net synthesis there is an efflux of proteins from the membrane. Evidence in favor of this has been presented. The activity of succinic dehydrogenase (a representative of class c) varies in a step-wise manner with periods of rapid increase, approximately coincident with bursts of membrane protein synthesis, alternating with periods without any increase in activity. The activities of malate dehydrogenase (class a) and reduced nicotinamide adenine dinucleotide dehydrogenase (class b) increased throughout the cell cycle. Phospholipid synthesis is continuous throughout the cell cycle.

Use of yeast populations fractionated by zonal centrifugation to study the cell cycle

Zonal centrifugation in a sucrose density gradient was used to separate yeast cells primarily by size and thus by age in the cell cycle. This approach provides an alternative to synchronous growth for examining the properties of cells at different stages in the cell cycle.

Control of growth rate by initial substrate concentration at values below maximum rate

The hyperbolic relationship between specific growth rate, mu, and substrate concentration, proposed by Monod and used since as the basis for the theory of steady-state growth in continuous-flow systems, was tested experimentally in batch cultures. Use of a Flavobacterium sp. exhibiting a high saturation constant for growth in glucose minimal medium allowed direct measurement of growth rate and substrate concentration throughout the growth cycle in medium containing a rate-limiting initial concentration of glucose. Specific growth rates were also measured for a wide range of initial glucose concentrations. A plot of specific growth rate versus initial substrate concentration was found to fit the hyperbolic equation. However, the instantaneous relationship between specific growth rate and substrate concentration during growth, which is stated by the equation, was not observed. Well defined exponential growth phases were developed at initial substrate concentrations below that required for support of the maximum exponential growth rate and a constant doubling time was maintained until 50% of the substrate had been used. It is suggested that the external substrate concentration initially present "sets" the specific growth rate by establishing a steady-state internal concentration of substrate, possibly through control of the number of permeation sites.

Cell growth and division. V. Error analysis of the Collins-Richmond equation

Error propagation in the Collins-Richmond equation is analyzed in order to obtain the ratio of the fractional error in rate of cell volume increase to the fractional error in each experimental variable. Typical data are analyzed numerically for the total errors resulting from counting statistics, from spectral broadening, and from volume calibration shift. The measurement of 10(4) cells can give a precision of better than 10% in the volume growth rate with a volume resolution of 3%.