Linear cell growth in Escherichia coli

Influence of homeostatic mechanisms of bacterial growth and division on structural properties of microcolonies: A computer simulation study

Bacterial growth and division generally occur by the process known as binary fission, in which the cells grow polarly until they divide into two daughter cells. Although this process is affected by factors that introduce stochastic variability in both growth rate and daughter cell length, the fact is that the size distribution in growing bacteria remains stable over time. This suggests the existence of homeostatic mechanisms that contribute to maintaining a stable size distribution. Those known as sizer and adder stand out among these mechanisms whose relevance is not entirely determined. In this work, computer simulations using an agent-based model are used to study the effect of these homeostatic mechanisms on the geometrical and structural properties of the developing microcolonies, focusing on the early stages of its development. Also, we examine the effect of linear or exponential dependence with the time of cellular growth on these properties. From our study, we deduce that these mechanisms do not have a noticeable impact on the properties studied, which could be due to the importance that stochastic factors play in the cell division and growth process. In addition, we discuss how competition between cell growth and diffusion is a key aspect in explaining the structure and geometry of developing bacterial microcolonies. The results of the study will help to clarify which processes and parameters should be considered relevant when designing simulation models.

Determination of Mutation Rates with Two Symmetric and Asymmetric Mutation Types

We revisit our earlier paper, with two of the coauthors, in which we proposed an unbiased and consistent estimator μ^n for an unknown mutation rate μ of microorganisms. Previously, we proved that the associated sequence of estimators μ^n converges to μ almost surely pointwise on a nonextinct set Ω0. Here, we show that this sequence converges also in the mean square with respect to conditional probability measure P0·=P·∩Ω0/PΩ0 and that, with respect to P0, the estimator is asymptotically unbiased. We further assume that a microorganism can mutate or turn to a different variant of one of the two types. In particular, it can mean that bacteria under attack by a virus or chemical agent are either perishing or surviving, turning them to stronger variant. We propose estimators for their respective types and show that they are a.s. pointwise and L2-consistent and asymptotically unbiased with respect to measure P0.

Microfluidic time-lapse analysis and reevaluation of the Bacillus subtilis cell cycle

Recent studies taking advantage of automated single-cell time-lapse analysis have reignited interest in the bacterial cell cycle. Several studies have highlighted alternative models, such as Sizer and Adder, which differ essentially in relation to whether cells can measure their present size or their amount of growth since birth. Most of the recent work has been done with Escherichia coli. We set out to study the well-characterized Gram-positive bacterium, Bacillus subtilis, at the single-cell level, using an accurate fluorescent marker for division as well as a marker for completion of chromosome replication. Our results are consistent with the Adder model in both fast and slow growth conditions tested, and with Sizer but only at the slower growth rate. We also find that cell size variation arises not only from the expected variation in size at division but also that division site offset from mid-cell contributes to a significant degree. Finally, although traditional cell cycle models imply a strong connection between the termination of a round of replication and subsequent division, we find that at the single-cell level these events are largely disconnected.

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.

Threshold effect of growth rate on population variability of Escherichia coli cell lengths

A long-standing question in biology is the effect of growth on cell size. Here, we estimate the effect of Escherichia coli growth rate (r) on population cell size distributions by estimating the coefficient of variation of cell lengths (CV_L) from image analysis of fixed cells in DIC microscopy. We find that the CV_L is constant at growth rates less than one division per hour, whereas above this threshold, CV_L increases with an increase in the growth rate. We hypothesize that stochastic inhibition of cell division owing to replication stalling by a RecA-dependent mechanism, combined with the growth rate threshold of multi-fork replication (according to Cooper and Helmstetter), could form the basis of such a threshold effect. We proceed to test our hypothesis by increasing the frequency of stochastic stalling of replication forks with hydroxyurea (HU) treatment and find that cell length variability increases only when the growth rate exceeds this threshold. The population effect is also reproduced in single-cell studies using agar-pad cultures and 'mother machine'-based experiments to achieve synchrony. To test the role of RecA, critical for the repair of stalled replication forks, we examine the CV_L of E. coli ΔrecA cells. We find cell length variability in the mutant to be greater than wild-type, a phenotype that is rescued by plasmid-based RecA expression. Additionally, we find that RecA-GFP protein recruitment to nucleoids is more frequent at growth rates exceeding the growth rate threshold and is further enhanced on HU treatment. Thus, we find growth rates greater than a threshold result in increased E. coli cell lengths in the population, and this effect is, at least in part, mediated by RecA recruitment to the nucleoid and stochastic inhibition of division.

Threshold effect of growth rate on population variability of Escherichia coli cell lengths

A long-standing question in biology is the effect of growth on cell size. Here, we estimate the effect of Escherichia coli growth rate (r) on population cell size distributions by estimating the coefficient of variation of cell lengths (CV_L) from image analysis of fixed cells in DIC microscopy. We find that the CV_L is constant at growth rates less than one division per hour, whereas above this threshold, CV_L increases with an increase in the growth rate. We hypothesize that stochastic inhibition of cell division owing to replication stalling by a RecA-dependent mechanism, combined with the growth rate threshold of multi-fork replication (according to Cooper and Helmstetter), could form the basis of such a threshold effect. We proceed to test our hypothesis by increasing the frequency of stochastic stalling of replication forks with hydroxyurea (HU) treatment and find that cell length variability increases only when the growth rate exceeds this threshold. The population effect is also reproduced in single-cell studies using agar-pad cultures and 'mother machine'-based experiments to achieve synchrony. To test the role of RecA, critical for the repair of stalled replication forks, we examine the CV_L of E. coli ΔrecA cells. We find cell length variability in the mutant to be greater than wild-type, a phenotype that is rescued by plasmid-based RecA expression. Additionally, we find that RecA-GFP protein recruitment to nucleoids is more frequent at growth rates exceeding the growth rate threshold and is further enhanced on HU treatment. Thus, we find growth rates greater than a threshold result in increased E. coli cell lengths in the population, and this effect is, at least in part, mediated by RecA recruitment to the nucleoid and stochastic inhibition of division.

Scaling laws governing stochastic growth and division of single bacterial cells

Uncovering the quantitative laws that govern the growth and division of single cells remains a major challenge. Using a unique combination of technologies that yields unprecedented statistical precision, we find that the sizes of individual Caulobacter crescentus cells increase exponentially in time. We also establish that they divide upon reaching a critical multiple (≈ 1.8) of their initial sizes, rather than an absolute size. We show that when the temperature is varied, the growth and division timescales scale proportionally with each other over the physiological temperature range. Strikingly, the cell-size and division-time distributions can both be rescaled by their mean values such that the condition-specific distributions collapse to universal curves. We account for these observations with a minimal stochastic model that is based on an autocatalytic cycle. It predicts the scalings, as well as specific functional forms for the universal curves. Our experimental and theoretical analysis reveals a simple physical principle governing these complex biological processes: a single temperature-dependent scale of cellular time governs the stochastic dynamics of growth and division in balanced growth conditions.

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.

Scaling properties of cell and organelle size

How size is controlled is a fundamental question in biology. In this review, we discuss the use of scaling relationships-for example, power-laws of the form y∝x(α)-to provide a framework for comparison and interpretation of size measurements. Such analysis can illustrate the biological and physical principles underlying observed trends, as has been proposed for the allometric dependence of metabolic rate or limb structure on organism mass. Techniques for measuring size at smaller length-scales continue to improve, leading to more data on the control of size in cells and organelles. Size scaling of these structures is expected to influence growth patterns, functional capacity and intracellular transport. Furthermore, organelles such as the nucleus, mitochondria and endoplasmic reticulum show widely varying morphologies that affect their scaling properties. We provide brief summaries of these issues for individual organelles, and conclude with a discussion on how to apply this concept to better understand the mechanisms of size control in the cellular environment.

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'.

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.

Measurement of live bacteria by Nomarski interference microscopy and stereologic methods as tested with macroscopic rod-shaped models

A new method is proposed to measure bacterial cells under growth conditions. Bacterial cells, suspended in their growth medium, were attached to a cover slip with poly-L-lysine. The cover slip was inverted and placed on a glass microscope slide. To prevent dehydration of the medium, the edges of the cover slip were sealed to the microscope slide with clear fingernail polish. The bacteria on the slide were then quickly photographed with a Leitz light microscope, using Nomarski optics. The photographic negatives were then projected at a standard distance through a lens system, and the projected images of the whole cells were outlined by hand onto graph paper. The profile images so transcribed onto the graph paper were in effect transverse sections of each of the cells. Using stereologic grid and point counting techniques, the area of the cell transverse section as well as the perimeter or circumference of the transverse section were estimated. Formulae were developed so that both the volume and surface area of the whole cell could be ascertained from these area and circumference measurements. Since the efficacy of any measurements of surface area and volume of microscopic rod-shaped bacterial cells could be questioned, macroscopic rod-shaped models were used to test the theory and formulae and to compare this method with other commonly used cell-sizing techniques. This technique could be used in any study of bacterial cell size or changes in cell size (e.g., osmotic shifts).

Elongation and surface extension of individual cells of Escherichia coli B/r: comparison of theoretical and experimental size distributions

The way individual cells grow and divide uniquely determines the (time-invariant) cell size distribution of populations in steady-state exponential growth. In the preceding article, theoretical distributions were derived for two exponential and six linear models containing a small number of adjustable parameters but no assumptions other than that all cells obey the same growth law. The linear models differ from each other with respect to the timing of the presumptive doubling in their growth rate, the exponential models--according to whether there is or is not a part of the cell that does not contribute to the growth rate. Here we compared the size distributions predicted by each of these models with those of cell length and surface area measured by electron microscopy; the quality of the fit, as determined by the mean-square successive-differences test and the chi 2 goodness-of-fit test, was taken as a measure of the adequacy of the model. The actual data came from two slow-growing E. coli B/r cultures, an A strain (pi = 125 min) and a K strain (pi = 106 min), and a correction was introduced in each to account for the distortion caused by the finite size of the picture frame. The parameter estimates produced by the various models are quite reliable (cv less than 0.1%); we discuss them briefly and compare their values in the two strains. All the length extension models were rejected outright whereas most of the surface growth versions were not. When the same models were tested on A-strain data from a faster growing culture (tau = 21 min), those models that provided an adequate fit to the cell surface area data proved equally satisfactory in the case of cell length. These findings are evaluated and shown to be consistent with cell surface area rather than cell length being the dimension under active control. Three surface area models, all linear, are rejected--those in which doubling of the growth rate occurs with a constant probability from cell birth, at a particular cell age, and precisely at cell division. The evidence in the literature that appears to contradict this last result, rejection of the simple linear surface growth model, is shown to be faulty. The 16 original models are here reduced to five, two involving exponential surface growth and three linear, and possible reasons are presented for our inability to discriminate further at this stage.

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

Increase in the mean cell mass of undivided cells was determined during the division cycle of Escherichia coli B/rA. Cell buoyant densities during the division cycle were determined after cells from an exponentially growing culture were separated by size. The buoyant densities of these cells were essentially independent of cell age, with a mean value of 1.094 g ml-1. Mean cell volume and buoyant density were also determined during synchronous growth in two different media, which provided doubling times of 40 and 25 min. Cell volume and mass increased linearly at both growth rates, as buoyant density did not vary significantly. The results are consistent with only one of the three major models of cell growth, linear growth, which specifies that the rate of increase in cell mass is constant throughout the division cycle.

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.

[The Escherichia coli cell cycle]

This review summarizes present knowledge of the bacterial cell cycle with particular emphasis on Escherichia coli. We discuss data coming from three different types of approaches to the study of cell extension and division: The search for discrete events occurring once per division cycle. It is generally agreed that the initiation and termination of DNA replication and cell septation are discrete events; there is less agreement on the sudden doubling in rate of cell surface extension, murein biosynthesis and the synthesis of membrane proteins and phospholipids. We discuss what is known about the temporal relationship amongst the various cyclic events studied. The search for discrete growth zones in the cell envelope layers. We discuss conflicting reports on the existence of murein growth zones and protein insertion sites in the inner and outer membranes. Elucidation of the mechanism regulating the initiation of DNA replication. The concept of "critical initiation mass" is examined. We review data suggesting that the DNA is attached to the envelope and discuss the role of the latter in the initiation of DNA replication.

Length growth of two Escherichia coli B/r substrains

Length growth of synchronized Escherichia coli B/r substrain A (ATCC 12407) and B/r substrain F26 (Thy his) was followed with an electron microscope. Cells were grown with doubling times (tau) of 60 min (B/rA) and of 82 and 165 min (B/rF26). Different length growth patterns were found for the two substrains. In B/rF, the length growth rate increased about midway in the cell cycle. For tau = 165 min, the rate increase was preceded by a short period of slow growth. For B/r A (r = 60 min), this period seemed to occur at the beginning of the cell cycle. The possibility is raised that the different length growth patterns are related to different deoxyribonucleic acid replication patterns of the respective strains.

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.

Distribution of bacteria in the velocity gradient centrifuge

Cells in different parts of the cell cycle can be separated by brief centrifugation in a density stabilized gradient: the Mitchison-Vincent technique. The position of a cell in the tube depends upon its size, shape, and density, upon the gradients of density, viscosity, and centrifugal force through which it sediments, and upon time. A program to compute the velocities and integrate the velocity profile for particles of a particular size class is presented. Because enteric bacteria are a form intermediate between right cylinders and prolate ellipsoids of revolution, the program uses values for the frictional coefficient intermediate between those calculated for ellipsoids and for cylinders. The formula f=6pietab(a/b)1/2 possesses this property and because of its simplicity greatly speeds the calculations. A second program computes the distribution of masses and then of sedimentation constants for a bacterial population, expressed either as a frequency distribution or as total mass per s-class. The effect of the known variation in cell size at division is included in these calculations, which apply to organisms undergoing balanced, asynchronous growth in which mass increase is proportional to cell size. The two programs in conjunction compute the mass or cell-number profile in an arbitrary gradient. The programs have been used to design gradients to maximize the resolution of the technique.

Lag in adaptation to lactose as a probe to the timing of permease incorporation into the cell membrane

If bacteria are incapable of forming and incorporating proteins into the cytoplasmic membranes in all phases of the cell cycle, then not all cells from an asynchronous culture should be capable of growth when switched to a new carbon and energy source whose metabolism requires new membrane function. The transfer of an inducible culture to low lactose provides such a situation since the cells cannot grow unless galactoside permease can function to concentrate the lactose internally. From such experiments, it was concluded that the Y gene product of the lac operon is synthesized, incorporated, and can start functioning in active transport, at any time throughout the bulk of the cell cycle. Not only were the lags before growth re-ensued much shorter than would be expected if the membrane transport capability could only be developed in a small portion of the cycle, but brief pulses of a gratuitous inducer shortened the lags much further. Three types of Escherichia coli ML 30 culture were studied: cells that had exhausted the limiting glucose; cells taken directly from glucose-limited chemostats; and a washed suspension of highly catabolite repressed cells from cultures grown in high levels of glucose and gluconate. The growth studies reported here were performed on-line with a minicomputer. They represent at least an order of magnitude increase in accuracy in estimating growth parameters over previous instrumentation.

Mode of growth and division of Salmonella typhimurium

A temperature-sensitive strain (HD 20) of Salmonella typhimurium is described. At restrictive temperature this strain shows an envelope alteration and a defect in division associated with an increase in cell diameter. On a shift to 42 degrees C there is residual division for ca. 30 min and then no further increase in cell number. In minimal medium (MM) at 42 degrees C cell diameter remains unchanged for about one mass doubling and then increases. From measurements of cell elongation, it is concluded that such increases in diameter occur because cell volume increases exponentially at 42 degrees C but increases in the rate of elongation occur for only a short period and then elongation rate becomes constant. This conclusion is supported by the observation that HD 20 cells show no increase in diameter at 42 degrees C when cultured in media supplemented with sucrose and Mg++; normal increases in elongation rate occur in such media. A model which fits the experimental data has been constructed. This model has two main features namely (1) the elongation of individual cells is linear with the rate of elongation doubling close to division and (2) such doublings in elongation rate are linked to division such that division cannot occur if elongation rate has not doubled shortly before. In the mutant it is proposed that only a few doublings in elongation rate occur at 42 degrees C and these are responsible for the residual division. The model fits the data for cultures shifted to 42 degrees C in MM or in yeast extract casamino acids MM (YE Cas MM) and for cultures shifted to 42 degrees C and shifted up from MM to YE Cas MM. The observations on these medium shifted cultures suggest that the activity of growth zones responsible for elongation is medium dependent.

Dielectric breakdown of cell membranes

With human and bovine red blood cells and Escherichia coli B, dielectric breakdown of cell membranes could be demonstrated using a Coulter Counter (AEG-Telefunken, Ulm, West Germany) with a hydrodynamic focusing orifice. In making measurements of the size distributions of red blood cells and bacteria versus increasing electric field strength and plotting the pulse heights versus the electric field strength, a sharp bend in the otherwise linear curve is observed due to the dielectric breakdown of the membranes. Solution of Laplace's equation for the electric field generated yields a value of about 1.6 V for the membrane potential at which dielectric breakdown occurs with modal volumes of red blood cells and bacteria. The same value is also calculated for red blood cells by applying the capacitor spring model of Crowley (1973. Biophys. J. 13:711). The corresponding electric field strength generated in the membrane at breakdown is of the order of 4 . 10(6) V/cm and, therefore, comparable with the breakdown voltages for bilayers of most oils. The critical detector voltage for breakdown depends on the volume of the cells. The volume-dependence predicted by Laplace theory with the assumption that the potential generated across the membrane is independent of volume, could be verified experimentally. Due to dielectric breakdown the red blood cells lose hemoglobin completely. This phenomenon was used to study dielectric breakdown of red blood cells in a homogeneous electric field between two flat platinum electrodes. The electric field was applied by discharging a high voltage storage capacitor via a spark gap. The calculated value of the membrane potential generated to produce dielectric breakdown in the homogeneous field is of the same order as found by means of the Coulter Counter. This indicates that mechanical rupture of the red blood cells by the hydrodynamic forces in the orifice of the Coulter Counter could also be excluded as a hemolysing mechanism. The detector voltage (or the electric field strength in the orifice) depends on the membrane composition (or the intrinsic membrane potential) as revealed by measuring the critical voltage in E. coli B harvested from the logarithmic and stationary growth phases. The critical detector voltage increased by about 30% for a given volume on reaching the stationary growth phase.

Unidirectional growth and branch formation of a morphological mutant, Agrobacterium tumefaciens

Morphological characteristics of thermoconditional mutant Agrobacterium tumefaciens F-502 were investigated in relation to growth, division, and synthesis of cellular components. As a result of a shift from 27 to 37 C, mutant cells altered their morphology from short rods to elongated and branched forms; in addition, division and deoxyribonucleic acid synthesis were inhibited at 37 C. At 37 C unidirectional cell growth and branch formation occurred at one end of a cell, and the elongation rate of a cell was proportional to cell length. A hypothetical model for branch formation is presented in which the maximal elongation rate, 1.8 mum/h, at one end of a cell is an essential factor for initiation of branch formation.