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

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.

Different Amounts of DNA in Newborn Cells of Escherichia coli Preclude a Role for the Chromosome in Size Control According to the "Adder" Model

According to the recently-revived adder model for cell size control, newborn cells of Escherichia coli will grow and divide after having added a constant size or length, ΔL, irrespective of their size at birth. Assuming exponential elongation, this implies that large newborns will divide earlier than small ones. The molecular basis for the constant size increment is still unknown. As DNA replication and cell growth are coordinated, the constant ΔL could be based on duplication of an equal amount of DNA, ΔG, present in newborn cells. To test this idea, we measured amounts of DNA and lengths of nucleoids in DAPI-stained cells growing in batch culture at slow and fast rates. Deeply-constricted cells were divided in two subpopulations of longer and shorter lengths than average; these were considered to represent large and small prospective daughter cells, respectively. While at slow growth, large and small prospective daughter cells contained similar amounts of DNA, fast growing cells with multiforked replicating chromosomes, showed a significantly higher amount of DNA (20%) in the larger cells. This observation precludes the hypothesis that ΔL is based on the synthesis of a constant ΔG. Growth curves were constructed for siblings generated by asymmetric division and growing according to the adder model. Under the assumption that all cells at the same growth rate exhibit the same time between initiation of DNA replication and cell division (i.e., constant C+D-period), the constructions predict that initiation occurs at different sizes (Li) and that, at fast growth, large newborn cells transiently contain more DNA than small newborns, in accordance with the observations. Because the state of segregation, measured as the distance between separated nucleoids, was found to be more advanced in larger deeply-constricted cells, we propose that in larger newborns nucleoid separation occurs faster and at a shorter length, allowing them to divide earlier. We propose a composite model in which both differential initiation and segregation leads to an adder-like behavior of large and small newborn cells.

Bacterial shape maintenance: an evaluation of various models

In this article, we examine a large number of combinations of growth models, with separate attention to cell volume, cylindrical surface-area, polar caps, nascent poles, onset of constriction, precision of cell division and interdivision-time dispersion, for Escherichia coli cells growing in steady state at various doubling times. Our main conclusion is striking, and quite general: exponential cylindrical surface-area growth is not possible, irrespective of the behaviour of cell volume, the polar regions, the nascent poles, or any other feature of cell growth-such cells never reach steady state. The same is true of linear cylindrical surface-area growth, regardless of when during the cell cycle the doubling in growth rate takes place. Only after the introduction of feedback into the surface-area growth law, do the cultures attain steady state, all of them. The other components of the models contribute only marginally to the properties of the steady state. Thus, whether the feedback applies just to the cylindrical portion of the cell or to its entire surface area affects only the coefficient of variation of cell radius and the radius-volume correlation. The dynamics of old-pole maintenance, constant area or constant shape, influences the radius-length and radius-volume correlations and, to a much lesser extent, the coefficients of variation of cell radius and length; how the nascent poles grow, whether linearly or exponentially, does not seem to matter at all. The absolute dimensions of the cells are set by the growth rate of the culture and have almost no effect when the feedback is taken to apply to the entire cell surface area; when it is limited to the cylindrical portion of the cell, however, both radius-length and radius-volume correlations increase with increasing doubling time. Comparison with published values was inconclusive. The nature of cell surface-area growth has therefore been settled, but whether the volume increases by simple-exponential or by pseudo-exponential growth, or whether the old poles maintain a constant shape or a constant area during the cell cycle, can be determined only with more precise experimental data. The form of nascent-pole growth is not resolvable by present techniques.

Polarized light scattering for rapid observation of bacterial size changes

The effect of changing growth conditions on the diameter of rod-shaped bacteria was studied in vivo with the use of polarized light scattering. The value of a ratio of scattering matrix elements was measured as a function of scattering angle at various times after nutritional "upshift" for two strains of Escherichia coli cells. The peak locations of the scattering function were calibrated against the diameter for rod-shaped bacteria. The peaks moved toward smaller angles as a function of time after upshift, indicating that the diameter was increasing. Under special conditions, substantial peak shifts occurred within a few minutes of growth condition change, indicating a rapid onset of growth in diameter. The rate of increase of the diameters after upshift was obtained from the angular shift of peak location. This rate was approximately 14 nm/min for E. coli K12 and approximately 9 nm/min for E. coli B/r at 37 degrees C. The rate of diameter increase is smaller at lower temperatures. Experiments with Bacillus megaterium showed that any diameter change after nutritional upshift at 37 degrees C is limited to at most a very small increase, at least for the strain and medium tested.

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.

Shape changes in Escherichia coli B/r A during agar filtration

We have investigated the phenomenon of shape distortion in a sample of 1,552 Escherichia coli B/r A cells in balanced exponential growth, during preparation for electron microscopy by agar filtration. Mixed preparations of bacterial cells and polystyrene latex spheres were shadow cast at low angle and the resulting shadows used to obtain quantitative estimates for the dimensions of the dehydrated cells; these then serve as a basis for a model of its shape in three dimensions. A statistical analysis of the projections of clustered cells and the intervening fissures, in nonshadow-cast preparations, provides an estimate of the effects of drying. The average width of the dehydrated cell (450 nm) is about 20 nm greater than the diameter of the live bacterium, whereas its length (1,398 nm) is approximately 40 nm less.

Relationship between size of parent at cell division and relative size of its progeny in Escherichia coli

This article examines the empirical basis for the assumption of independence between the relative size (length or surface area) of a newborn cell w and the absolute size of its mother at cell division. Random samples from two strains of Escherichia coli B/r cells in steady-state exponential growth, covering a range of doubling times, were fixed in osmium tetroxide and prepared for electron microscopy by agar filtration. Length and diameter of over 3000 constricted cells were measured from the electron micrographs and cell surface area computed by assuming an idealized geometry of right circular cylinders with hemispherical polar caps. In general, these strains were found to divide into two daughter cells with a precision that is independent of the size of the mother. In addition, both a normal and a symmetrical beta-distribution were shown to fit the observed size distributions of w rather well; theoretical grounds for preferring the latter are discussed.

Aggregation of Escherichia coli B/r A during agar filtration: effect on morphometric measurements

We have investigated the phenomenon of particle aggregation in a sample of 71,038 Escherichia coli B/r A cells in balanced exponential growth, during preparation for electron microscopy by agar filtration. The bacteria were photographed in a transmission electron microscope and the dimensions and spatial relationships among all the members of each aggregate were recorded using an interactive image processing system. The proportion of aggregated cells, 22%, is much greater than that found by direct count in a light microscope (7%), implying that most aggregation takes place during the preparation stages. The aggregated cells are about 1% narrower than the free cells, because of mutual compression, and 1.5% longer, because of a selection bias in favor of longer cells. From a statistical analysis of the data, we conclude that the clustering of cells into aggregates in the course of sample preparation is the result of random encounters during the settling on the collodion membrane and of the changing surface tension during the drying process. A method is proposed to correct morphometric measurements for the distortion caused by cellular aggregation of this kind.

Synthesis of the cell surface during the division cycle of rod-shaped, gram-negative bacteria

When the growth of the gram-negative bacterial cell wall is considered in relation to the synthesis of the other components of the cell, a new understanding of the pattern of wall synthesis emerges. Rather than a switch in synthesis between the side wall and pole, there is a partitioning of synthesis such that the volume of the cell increases exponentially and thus perfectly encloses the exponentially increasing cytoplasm. This allows the density of the cell to remain constant during the division cycle. This model is explored at both the cellular and molecular levels to give a unified description of wall synthesis which has the following components: (i) there is no demonstrable turnover of peptidoglycan during cell growth, (ii) the side wall grows by diffuse intercalation, (iii) pole synthesis starts by some mechanism and is preferentially synthesized compared with side wall, and (iv) the combined side wall and pole syntheses enclose the newly synthesized cytoplasm at a constant cell density. The central role of the surface stress model in wall growth is distinguished from, and preferred to, models that propose cell-cycle-specific signals as triggers of changes in the rate of wall synthesis. The actual rate of wall synthesis during the division cycle is neither exponential nor linear, but is close to exponential when compared with protein synthesis during the division cycle.