Increase in cell mass during the division cycle of Escherichia coli B/rA

Hunting the Cell Cycle Snark

In this very personal hunt for the meaning of the bacterial cell cycle, the snark, I briefly revisit and update some of the mechanisms we and many others have proposed to regulate the bacterial cell cycle. These mechanisms, which include the dynamics of calcium, membranes, hyperstructures, and networks, are based on physical and physico-chemical concepts such as ion condensation, phase transition, crowding, liquid crystal immiscibility, collective vibrational modes, reptation, and water availability. I draw on ideas from subjects such as the 'prebiotic ecology' and phenotypic diversity to help with the hunt. Given the fundamental nature of the snark, I would expect that its capture would make sense of other parts of biology. The route, therefore, followed by the hunt has involved trying to answer questions like "why do cells replicate their DNA?", "why is DNA replication semi-conservative?", "why is DNA a double helix?", "why do cells divide?", "is cell division a spandrel?", and "how are catabolism and anabolism balanced?". Here, I propose some relatively unexplored, experimental approaches to testing snark-related hypotheses and, finally, I propose some possibly original ideas about DNA packing, about phase separations, and about computing with populations of virtual bacteria.

AFM Microfluidic Cantilevers as Weight Sensors for Live Single Cell Mass Measurements

Reliably measuring small mass changes at the single-cell level is challenging. In this manuscript, we report the use of microfluidic cantilevers in liquid with sub-nanogram scale weight sensing capability for the measurement of cellular mass changes of living single cells. With this instrumentation, we were able to perform fast mass measurements within 3 minutes. We show results of mass measurements of polystyrene and metal beads of various sizes (smallest weight measured at 280 ± 95 pg) and live single-cell mass measurements in a physiologically relevant environment. We also performed finite element analysis to simulate and optimize the structural design and materials of cantilevers. Our simulation results indicate that using polymer materials, such as SU8 and polyimide, could improve the minimal detectable mass by 3-fold compared to conventional silicon cantilevers. The simulations also suggest that smaller dimensions of length, width, and thickness would improve the mass detection capability of microfluidic cantilevers.

Extending applications of AFM to fluidic AFM in single living cell studies

In this article, a review of a series of applications of atomic force microscopy (AFM) and fluidic Atomic Force Microscopy (fluidic AFM, hereafter fluidFM) in single-cell studies is presented. AFM applications involving single-cell and extracellular vesicle (EV) studies, colloidal force spectroscopy, and single-cell adhesion measurements are discussed. FluidFM is an offshoot of AFM that combines a microfluidic cantilever with AFM and has enabled the research community to conduct biological, pathological, and pharmacological studies on cells at the single-cell level in a liquid environment. In this review, capacities of fluidFM are discussed to illustrate (1) the speed with which sequential measurements of adhesion using coated colloid beads can be done, (2) the ability to assess lateral binding forces of endothelial or epithelial cells in a confluent cell monolayer in an appropriate physiological environment, and (3) the ease of measurement of vertical binding forces of intercellular adhesion between heterogeneous cells. Furthermore, key applications of fluidFM are reviewed regarding to EV absorption, manipulation of a single living cell by intracellular injection, sampling of cellular fluid from a single living cell, patch clamping, and mass measurements of a single living cell.

A biphasic growth model for cell pole elongation in mycobacteria

Mycobacteria grow by inserting new cell wall material in discrete zones at the cell poles. This pattern implies that polar growth zones must be assembled de novo at each division, but the mechanisms that control the initiation of new pole growth are unknown. Here, we combine time-lapse optical and atomic force microscopy to measure single-cell pole growth in mycobacteria with nanometer-scale precision. We show that single-cell growth is biphasic due to a lag phase of variable duration before the new pole transitions from slow to fast growth. This transition and cell division are independent events. The difference between the lag and interdivision times determines the degree of single-cell growth asymmetry, which is high in fast-growing species and low in slow-growing species. We propose a biphasic growth model that is distinct from previous unipolar and bipolar models and resembles “new end take off” (NETO) dynamics of polar growth in fission yeast.

Mycobacteria grow by inserting new cell wall material at the cell poles. Here, Hannebelle et al. combine time-lapse optical and atomic force microscopy to show that single-cell growth is biphasic due to a lag phase of variable duration before the new pole transitions from slow to fast growth.

Division-Based, Growth Rate Diversity in Bacteria

To investigate the nature and origins of growth rate diversity in bacteria, we grew Escherichia coli and Bacillus subtilis in liquid minimal media and, after different periods of ¹⁵N-labeling, analyzed and imaged isotope distributions in individual cells with Secondary Ion Mass Spectrometry. We find a striking inter- and intra-cellular diversity, even in steady state growth. This is consistent with the strand-dependent, hyperstructure-based hypothesis that a major function of the cell cycle is to generate coherent, growth rate diversity via the semi-conservative pattern of inheritance of strands of DNA and associated macromolecular assemblies. We also propose quantitative, general, measures of growth rate diversity for studies of cell physiology that include antibiotic resistance.

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.

Generation and filtering of gene expression noise by the bacterial cell cycle

Background

Gene expression within cells is known to fluctuate stochastically in time. However, the origins of gene expression noise remain incompletely understood. The bacterial cell cycle has been suggested as one source, involving chromosome replication, exponential volume growth, and various other changes in cellular composition. Elucidating how these factors give rise to expression variations is important to models of cellular homeostasis, fidelity of signal transmission, and cell-fate decisions.

Results

Using single-cell time-lapse microscopy, we measured cellular growth as well as fluctuations in the expression rate of a fluorescent protein and its concentration. We found that, within the population, the mean expression rate doubles throughout the cell cycle with a characteristic cell cycle phase dependent shape which is different for slow and fast growth rates. At low growth rate, we find the mean expression rate was initially flat, and then rose approximately linearly by a factor two until the end of the cell cycle. The mean concentration fluctuated at low amplitude with sinusoidal-like dependence on cell cycle phase. Traces of individual cells were consistent with a sudden two-fold increase in expression rate, together with other non-cell cycle noise. A model was used to relate the findings and to explain the cell cycle-induced variations for different chromosomal positions.

Conclusions

We found that the bacterial cell cycle contribution to expression noise consists of two parts: a deterministic oscillation in synchrony with the cell cycle and a stochastic component caused by variable timing of gene replication. Together, they cause half of the expression rate noise. Concentration fluctuations are partially suppressed by a noise cancelling mechanism that involves the exponential growth of cellular volume. A model explains how the functional form of the concentration oscillations depends on chromosome position.

Electronic supplementary material

The online version of this article (doi:10.1186/s12915-016-0231-z) contains supplementary material, which is available to authorized users.

A bacteriophilic resin, synthesis and E. coli sequestration study

The polycationic pyridinium-Merrifield resinIwas prepared and subjected to bacteria sequestration studies. Its efficiency was demonstrated by capillary electrophoresis titrations, and the effectiveness of the sequestration was shown by confocal microscopy.

The potential for biologically catalyzed anaerobic methane oxidation on ancient Mars

This study examines the potential for the biologically mediated anaerobic oxidation of methane (AOM) coupled to sulfate reduction on ancient Mars. Seven distinct fluids representative of putative martian groundwater were used to calculate Gibbs energy values in the presence of dissolved methane under a range of atmospheric CO2 partial pressures. In all scenarios, AOM is exergonic, ranging from -31 to -135 kJ/mol CH4. A reaction transport model was constructed to examine how environmentally relevant parameters such as advection velocity, reactant concentrations, and biomass production rate affect the spatial and temporal dependences of AOM reaction rates. Two geologically supported models for ancient martian AOM are presented: a sulfate-rich groundwater with methane produced from serpentinization by-products, and acid-sulfate fluids with methane from basalt alteration. The simulations presented in this study indicate that AOM could have been a feasible metabolism on ancient Mars, and fossil or isotopic evidence of this metabolic pathway may persist beneath the surface and in surface exposures of eroded ancient terrains.

Mathematical modeling of bacterial cell cycle: the problem of coordinating genome replication with cell growth

In this paper, we perform an analysis of bacterial cell-cycle models implementing different strategies to coordinately regulate genome replication and cell growth dynamics. It has been shown that the problem of coupling these processes does not depend directly on the dynamics of cell volume expansion, but does depend on the type of cell growth law. Our analysis has distinguished two types of cell growth laws, "exponential" and "linear", each of which may include both exponential and linear patterns of cell growth. If a cell grows following a law of the "exponential" type, including the exponential V(t) = V(0) exp (kt) and linear V(t) = V(0)(1 + kt) dynamic patterns, then the cell encounters the problem of coupling growth rates and replication. It has been demonstrated that to solve the problem, it is sufficient for a cell to have a repressor mechanism to regulate DNA replication initiation. For a cell expanding its volume by a law of the "linear" type, including exponential V(t) = V(0) + V(1) exp (kt) and linear V(t) = V(0) + kt dynamic patterns, the problem of coupling growth rates and replication does not exist. In other words, in the context of the coupling problem, a repressor mechanism to regulate DNA replication, and cell growth laws of the "linear" type displays the attributes of universality. The repressor-type mechanism allows a cell to follow any growth dynamic pattern, while the "linear" type growth law allows a cell to use any mechanism to regulate DNA replication.

The energetics of organic synthesis inside and outside the cell

Thermodynamic modelling of organic synthesis has largely been focused on deep-sea hydrothermal systems. When seawater mixes with hydrothermal fluids, redox gradients are established that serve as potential energy sources for the formation of organic compounds and biomolecules from inorganic starting materials. This energetic drive, which varies substantially depending on the type of host rock, is present and available both for abiotic (outside the cell) and biotic (inside the cell) processes. Here, we review and interpret a library of theoretical studies that target organic synthesis energetics. The biogeochemical scenarios evaluated include those in present-day hydrothermal systems and in putative early Earth environments. It is consistently and repeatedly shown in these studies that the formation of relatively simple organic compounds and biomolecules can be energy-yielding (exergonic) at conditions that occur in hydrothermal systems. Expanding on our ability to calculate biomass synthesis energetics, we also present here a new approach for estimating the energetics of polymerization reactions, specifically those associated with polypeptide formation from the requisite amino acids.

A size-structured model of bacterial growth and reproduction

We consider a size-structured bacterial population model in which the rate of cell growth is both size- and time-dependent and the average per capita reproduction rate is specified as a model parameter. It is shown that the model admits classical solutions. The population-level and distribution-level behaviours of these solutions are then determined in terms of the model parameters. The distribution-level behaviour is found to be different from that found in similar models of bacterial population dynamics. Rather than convergence to a stable size distribution, we find that size distributions repeat in cycles. This phenomenon is observed in similar models only under special assumptions on the functional form of the size-dependent growth rate factor. Our main results are illustrated with examples, and we also provide an introductory study of the bacterial growth in a chemostat within the framework of our model.

FtsZ in bacterial cytokinesis: cytoskeleton and force generator all in one

FtsZ, a bacterial homolog of tubulin, is well established as forming the cytoskeletal framework for the cytokinetic ring. Recent work has shown that purified FtsZ, in the absence of any other division proteins, can assemble Z rings when incorporated inside tubular liposomes. Moreover, these artificial Z rings can generate a constriction force, demonstrating that FtsZ is its own force generator. Here we review light microscope observations of how Z rings assemble in bacteria. Assembly begins with long-pitch helices that condense into the Z ring. Once formed, the Z ring can transition to short-pitch helices that are suggestive of its structure. FtsZ assembles in vitro into short protofilaments that are ∼30 subunits long. We present models for how these protofilaments might be further assembled into the Z ring. We discuss recent experiments on assembly dynamics of FtsZ in vitro, with particular attention to how two regulatory proteins, SulA and MinC, inhibit assembly. Recent efforts to develop antibacterial drugs that target FtsZ are reviewed. Finally, we discuss evidence of how FtsZ generates a constriction force: by protofilament bending into a curved conformation.

Diamagnetic levitation enhances growth of liquid bacterial cultures by increasing oxygen availability

Diamagnetic levitation is a technique that uses a strong, spatially varying magnetic field to reproduce aspects of weightlessness, on the Earth. We used a superconducting magnet to levitate growing bacterial cultures for up to 18 h, to determine the effect of diamagnetic levitation on all phases of the bacterial growth cycle. We find that diamagnetic levitation increases the rate of population growth in a liquid culture and reduces the sedimentation rate of the cells. Further experiments and microarray gene analysis show that the increase in growth rate is owing to enhanced oxygen availability. We also demonstrate that the magnetic field that levitates the cells also induces convective stirring in the liquid. We present a simple theoretical model, showing how the paramagnetic force on dissolved oxygen can cause convection during the aerobic phases of bacterial growth. We propose that this convection enhances oxygen availability by transporting oxygen around the liquid culture. Since this process results from the strong magnetic field, it is not present in other weightless environments, e.g. in Earth orbit. Hence, these results are of significance and timely to researchers considering the use of diamagnetic levitation to explore effects of weightlessness on living organisms and on physical phenomena.

Using buoyant mass to measure the growth of single cells

We used a suspended microchannel resonator (SMR) combined with picoliter-scale microfluidic control to measure buoyant mass and determine the ‘instantaneous’ growth rates of individual cells. The SMR measures mass with femtogram precision, allowing rapid determination of the growth rate in a fraction of a complete cell cycle. We found that for individual cells of Bacillus subtilis, Escherichia coli, Saccharomyces cerevisiae and mouse lymphoblasts, heavier cells grew faster than lighter cells.

Cell growth and size homeostasis in proliferating animal cells

A long-standing question in biology is whether there is an intrinsic mechanism for coordinating growth and the cell cycle in metazoan cells. We examined cell size distributions in populations of lymphoblasts and applied a mathematical analysis to calculate how growth rates vary with both cell size and the cell cycle. Our results show that growth rate is size-dependent throughout the cell cycle. After initial growth suppression, there is a rapid increase in growth rate during the G1 phase, followed by a period of constant exponential growth. The probability of cell division varies independently with cell size and cell age. We conclude that proliferating mammalian cells have an intrinsic mechanism that maintains cell size.

A novel assay based on fluorescence microscopy and image processing for determining phenotypic distributions of rod-shaped bacteria

Cell population balance (CPB) models can account for the phenotypic heterogeneity that characterizes isogenic cell populations. To utilize the predictive power of these models, however, we must determine the single-cell reaction and division rates as well as the partition probability density function of the cell population. These functions can be obtained through the Collins-Richmond inverse CPB modeling methodology, if we know the phenotypic distributions of (a) the overall cell population, (b) the dividing cell subpopulation, and (c) the newborn cell subpopulation. This study presents the development of a novel assay that combines fluorescence microscopy and image processing to determine these distributions. The method is generally applicable to rod-shaped cells dividing through the formation of a characteristic constriction. Morphological criteria were developed for the automatic identification of dividing cells and validated through direct comparison with manually obtained measurements. The newborn cell subpopulation was obtained from the corresponding dividing cell subpopulation by collecting information from the two compartments separated by the constriction. The method was applied to E. coli cells carrying the genetic toggle network with a green fluorescent marker. Our measurements for the overall cell population were in excellent agreement with the distributions obtained via flow cytometry. The new assay constitutes a powerful tool that can be used in conjunction with inverse CPB modeling to rigorously quantify single-cell behavior from data collected from highly heterogeneous cell populations.

Cell shape dynamics in Escherichia coli

Bacteria are the simplest living organisms. In particular, Escherichia coli has been extensively studied and it has become one of the standard model systems in microbiology. However, optical microscopy studies of single E. coli have been limited by its small size, approximately 1 x 3 microm, not much larger than the optical resolution, approximately 0.25 microm. As a result, not enough quantitative dynamical information on the life cycle of single E. coli is presently available. We suggest that, by careful analysis of images from phase contrast and fluorescence time-lapse microscopy, this limitation can be bypassed. For example, we show that applying this approach to monitoring morphogenesis in individual E. coli leads to a simple, quantitative description of this process. First, we find the time when the formation of the septum starts, tau(c). It occurs much earlier than the time when the constriction can be directly observed by phase contrast. Second, we find that the growth law of single cells is more likely bilinear/trilinear than exponential. This is further supported by the relations that hold between the corresponding growth rates. These methods could be further extended to study the dynamics of cell components, e.g., the nucleoid and the Z-ring.

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.

Growth during the cell cycle

During the cell cycle, major bulk parameters such as volume, dry mass, total protein, and total RNA double and such growth is a fundamental property of the cell cycle. The patterns of growth in volume and total protein or RNA provide an "envelope" that contains and may restrict the gear wheels. The main parameters of cell cycle growth were established in the earlier work when people moved from this field to the reductionist approaches of molecular biology, but very little is known on the patterns of metabolism. Most of the bulk properties of cells show a continuous increase during the cell cycle, although the exact pattern of this increase may vary. Since the earliest days, there have been two popular models, based on an exponential increase and linear increase. In the first, there is no sharp change in the rate of increase through the cycle but a smooth increase by a factor of two. In the second, the rate of increase stays constant through much of the cycle but it doubles sharply at a rate change point (RCP). It is thought that the exponential increase is caused by the steady growth of ribosome numbers and the linear pattern is caused by a doubling of the structural genes during the S period giving an RCP--a "gene dosage" effect. In budding yeast, there are experiments fitting both models but on balance slightly favoring "gene dosage." In fission yeast, there is no good evidence of exponential increase. All the bulk properties, except O2 consumption, appear to follow linear patterns with an RCP during the short S period. In addition, there is in wild-type cells a minor RCP in G2 where the rate increases by 70%. In mammalian cells, there is good but not extensive evidence of exponential increase. In Escherichia coli, exponential increase appears to be the pattern. There are two important points: First, some proteins do not show peaks of periodic synthesis. If they show patterns of exponential increase both they and the total protein pattern will not be cell cycle regulated. However, if the total protein pattern is not exponential, then a majority of the individual proteins will be so regulated. If this majority pattern is linear, then it can be detected from rate measurements on total protein. However, it would be much harder at the level of individual proteins where the methods are at present not sensitive enough to detect a rate change by a factor of two. At a simple level, it is only the exponential increase that is not cell cycle regulated in a synchronous culture. The existence of a "size control" is well known and the control has been studied for a long time, but it has been remarkably resistant to molecular analysis. The attainment of a critical size triggers the periodic events of the cycle such as the S period and mitosis. This control acts as a homeostatic effector that maintains a constant "average" cell size at division through successive cycles in a growing culture. It is a vital link coordinating cell growth with periodic events of the cycle. A size control is present in all the systems and appears to operate near the start of S or of mitosis when the cell has reached a critical size, but the molecular mechanism by which size is measured remains both obscure and a challenge. A simple version might be for the cell to detect a critical concentration of a gene product.

G350 of Escherichia coli RNase P RNA contributes to Mg2+ binding near the active site of the enzyme

G350 of Escherichia coli RNase P RNA is a highly conserved residue among all bacteria and lies near the known magnesium binding site for the RNase P ribozyme, helix P4. Mutations at G350 have a dramatic effect on substrate cleavage activity for both RNA alone and holoenzyme; the G350C mutation has the most severe phenotype. The G350C mutation also inhibits growth of cells that express the mutant RNA in vivo under conditions of magnesium starvation. The results suggest that G350 contributes to Mg(2+) binding at helix P4 of RNase P RNA.

FtsZ from Escherichia coli, Azotobacter vinelandii, and Thermotoga maritima--quantitation, GTP hydrolysis, and assembly

We have cloned the ftsZ genes from Thermotoga maritima and Azotobacter vinelandii and expressed the proteins (TmFtsZ and AzFtsZ) in Escherichia coli. We compared these proteins to E. coli FtsZ (EcFtsZ), and found that several remarkable features of their GTPase activities were similar for all three species, implying that these characteristics may be universal among FtsZs. Using a calibrated protein assay, we found that all three FtsZs bound 1 mole guanine nucleotide per mole FtsZ and hydrolyzed GTP at high rates (> 2 GTP per FtsZ per min). All three required magnesium and a monovalent cation for GTP hydrolysis. Previous reports showed that EcFtsZ (and some other species) required potassium. We confirmed this specificity for EcFtsZ but found that potassium and sodium both worked for Az- and TmFtsZ. Specific GTPase activity had a striking dependence on FtsZ concentration: activity (per FtsZ molecule) was absent or low below 50 microg/ml, rose steeply from 50 to 300 microg/ml and plateaued at a constant high value above 300 microg/ml. This finding suggests that the active state requires a polymer that is assembled cooperatively at 50-300 microg/ml. A good candidate for the active polymer was visualized by negative stain electron microscopy--straight protofilaments and protofilament pairs were seen under all conditions with active GTPase. We suggest that the GTP hydrolysis of FtsZ may be coupled to assembly, as it is for tubulin, with hydrolysis occurring shortly after an FtsZ monomer associates onto a protofilament end. As a part of this study, we determined the concentration of EcFtsZ and TmFtsZ by quantitative amino acid analysis and used this to standardize the bicinchonic acid colorimetric assay. This is the first accurate determination of FtsZ concentration. Using this standard and quantitative Western blotting, we determined that the average E. coli cell has 15,000 molecules of FtsZ, at a concentration of 400 microg/ml. This is just above the plateau for full GTPase activity in vitro.

Biomass growth rate during the prokaryote cell cycle

The rate of biomass growth throughout the cell cycle of prokaryotes is important in the study of global regulation. Two limiting cases have generally been considered: the exponential model and the linear model. The exponential model is a logical expectation because protein, the main component of biomass of a bacterial cell, increases continuously during the cell cycle and therefore the means for synthesis of other cell components and metabolites also increases. In addition, during the cell cycle, ribosomes, the means of production of proteins, increase monotonically. As a consequence, the increase of all should be autocatalytic and the content of cell substance should be an exponential function of time. Two cellular components would not be expected to increase exponentially: the DNA and the cell envelope. The former because of the intermittent synthesis of the chromosome, and the latter because of changes in the surface-to-volume ratio with growth and division. In contrast to the exponential model, the linear model of Kubitschek postulates that the cell only increases its membrane transport capability over a brief period during the cell cycle, and, thus limited by transport, all cell components can increase only at a constant linear rate during most of the cell cycle. Other proposed models are intermediate and assume that the growth rate of the cell depends on some cell cycle event, such as the initiation of chromosome replication. The models have relevance to prokaryotes undergoing balanced growth; they may not be relevant to eukaryotic microbes or to eukaryotic cells in tissue culture that have endogenous rhythms or are controlled by protein growth factors. Logically, the models could possibly apply to a free-living cell that does not respond to environmental cues. Even under rigidly constant conditions, however, cells may try to respond to a stimulus that was periodic or regulatory under natural conditions, but is present at a constant level under the experimental culture condition. There are four classes of experiments that have been used to measure the accumulation of dry biomass or its components during the cell cycle of a bacterium, as typified by Escherichia coli. For the first class of experiments, the dimensions of living cells are measured under the microscope. So far, the experiments have been limited by the resolving power of the phase microscope, but adequate resolution should be possible with the confocal scanning light microscope or various video computer systems. Such experiments are called integral because augmentation of cell constituents is followed. The second class involves pulse-chase labeling of cells and then their separation into different phases of the cycle or age groups and measurement of the radioactivity per cell in the fractions. Such experiments are called differential in that the rate is measured directly instead of being deduced by comparing the total size at different times.(ABSTRACT TRUNCATED AT 400 WORDS)

The growth kinetics of B. subtilis

There has been considerable discussion by Kubitschek and Cooper concerning the growth rate of cells of E. coli throughout the cell cycle. Consequently, it is relevant to test Kubitschek's linear model against the exponential model espoused by Cooper (and many others) with another organism and another technique. Burdett et al. measured, by electron microscopy and computer analysis of the microphotographs, the distribution of lengths of a population of cells of Bacillus subtilis grown in 0.4% succinate in a minimal medium. The data were fitted to the extended Collins-Richmond method of Kirkwood & Burdett which subdivided the cell cycle into several phases. I have taken their results and compared them with the linear and exponential growth models for the entire cell cycle after applying correction to the data for the shape of completed and forming poles; i.e., to put the data on a cell-volume basis instead of a cell-length basis. Most of the correction involves no arbitrary assumptions. The conclusion is that global volume growth rate is nearly proportional to cell volume; i.e. growth of Bacillus subtilis is nearly exponential for almost every cell in the growing culture.

Cell volume increase in Escherichia coli after shifts to richer media

Synchronous cultures of Escherichia coli 15-THU and WP2s, which were selected by velocity sedimentation from exponential-phase cultures growing in an acetate-minimal salts medium, were shifted to richer media at various times during the cell cycle by the addition of glucose or nutrient broth. Cell numbers and mean cell volumes were measured electronically. The duration of the division cycle of the shifted generation was not altered significantly by the addition of either nutrient. Growth rates, measured as rates of cell volume increase, were constant throughout the cycle in unshifted acetate control cultures. When glucose was added, growth rates also remained unchanged during the remainder of the cell cycle and then increased abruptly at or after cell division. When nutrient broth was added, growth rates remained unchanged from periods of 0.2 to 0.4 generations and then increased abruptly to their final values. In all cases, the cell volume increase was linear both before and after the growth rate transition. The strongest support for a linear cell volume increase during the cell cycle of E. coli in slowly growing acetate cultures, however, was obtained in unshifted cultures, in complete agreement with earlier observations of cell volumes at much more rapid growth rates. Although cell growth and division are under the control of the synthesizing machinery in the cell responsible for RNA and protein synthesis, the results indicate that growth is also regulated by membrane-associated transport systems.

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.

Determination of bacterial cell volume with the Coulter Counter

Two methods were used to determine mean volumes of cells of Escherichia coli B/rA in both stationary- and exponential-phase cultures, i.e., electronic measurement with a Coulter Counter-Analyzer system and biophysical measurement of the total volume and number of cells in sedimented cell pellets. Within experimental errors, the methods gave the same mean cell volumes.