Surface Area to Volume and Water Potential Review
Trends Microbiol. Author manuscript; available in PMC 2019 October i.
Published in final edited form as:
PMCID: PMC6150810
NIHMSID: NIHMS971050
Surface Area to Volume Ratio: A Natural Variable for Bacterial Morphogenesis
Leigh G. Harris
oneDepartment of Molecular and Prison cell Biological science, University of California at Berkeley, Berkeley, CA 94720, U.s.
Julie A. Theriot
2Department of Biochemistry, Department of Microbiology & Immunology, Howard Hughes Medical Institute, Stanford University School of Medicine, Stanford, CA 94305, Usa
Abstract
An immediately observable feature of leaner is that cell size and shape are remarkably constant and feature for a given species in a detail status, merely vary quantitatively with physiological parameters such as growth rate, indicating both genetic and ecology regulation. However, despite decades of research, the molecular mechanisms underlying bacterial morphogenesis have remained incompletely characterized. We recently demonstrated that a wide range of bacterial species exhibit a robust surface area to volume ratio (SA/Five) homeostasis. Because cell size, shape, and SA/Five are mathematically interconnected, if SA/Five is indeed the natural variable that cells actively monitor, this finding has disquisitional implications for our understanding of bacterial morphogenesis, placing fundamental constraints on the sizes and shapes that cells can prefer. In this Opinion article we talk over the broad implications that this novel perspective has for the field of bacterial growth and morphogenesis.
Quantitative Bacterial Physiology
For quantitative laboratory experiments, bacteria are extraordinarily reliable partners for scientists interested in uncovering fundamental laws governing cell growth and form. Not simply do they grow quickly, but their behavior from day to day and from culture to culture is so reproducible that all the complexities associated with their biological function can often be accurately summarized in simple mathematical equations [one,2]. In recent years there have been a number of technical advances that have made it possible to extend this quantitative assay to dynamic observations of individual cells. These advances include improved methods for culturing bacteria nether steady-country atmospheric condition for many generations on a microscope [3,4], improvements in the extraction of data from videomicroscopy experiments that enable precise, dynamic measurements on private cells [five,half dozen], and improvements in data assay and storage that have enabled even subtle variations across large populations to be compared in statistically robust ways [vii,viii].
Using this kind of approach, we investigated the growth of aberrantly shaped Caulobacter crescentus mutants, and noticed that, although their overall sizes and shapes could vary wildly, cells moved toward and maintained a specific, condition-dependent SA/V [ix]. This credible SA/V homeostasis could not be explained using models of size and shape determination current in the field, which primarily focused on width and length of rod-shaped bacteria equally separately controlled parameters [x–12]. Nosotros therefore hypothesized that SA/V might instead be the almost illuminating property to consider – the 'natural variable' for this problem. By thus reframing the question of size control in terms of SA/V homeostasis, we were able to develop a unified model of bacterial growth and class with broad explanatory powers [13], the implications of which the bacterial inquiry community has merely merely begun to explore [14–sixteen]. In this Stance commodity, we discuss the 'relative rates' mechanism by which cells appear to achieve SA/Five homeostasis, we utilize this model to reconsider reports in the literature of changes in growth rate and/or cell wall biosynthesis altering SA/V, nosotros re-examine Schaechter'southward archetype growth law relationship between cell size and growth rate from an SA/V-centric perspective, we speculate virtually what molecular cues might provide the indicate to increase or decrease SA/5 in different weather condition, and finally we propose specific molecular mechanisms that rod-shaped bacteria could employ to alter their width and length in gild to attain SA/V homeostasis.
Cell Size, Shape, and SA/V Are Interconnected Variables
In considering the origins of bacterial morphogenesis it is essential to make explicit the necessary geometric connections between size (meaning volume), shape, and SA/V. If volume is held constant, cells of dissimilar shapes will typically adopt different SA/V values (Figure 1A). However, in many species, information technology is shape and not volume that is abiding. In Escherichia coli, for instance, cell volume can vary over nearly an gild of magnitude for cells grown at dissimilar growth rates, but cells typically maintain roughly the same shape – a rod with attribute ratio 4:1 [17]. And so, if we now consider the scenario where shape is held constant, we observe that increases in volume necessarily correspond to reductions in SA/V (Effigy 1B). Thus, once shape is constrained, specification of a given volume is sufficient to determine SA/V, and vice versa. While many studies have treated volume as the actively controlled parameter in this scenario, our contempo piece of work suggests that it is probable the other way around, and that SA/V is the actively regulated variable, with size following forth as necessary [thirteen].
Size, Shape, and Surface Surface area to Volume Ratio (SA/V) Are Interconnected Backdrop. (A) When book is held abiding, irresolute the shape of an object tin can significantly alter the overall SA/V. (B) When shape is held constant, changes in book directly correspond to changes in SA/V, with larger objects having lower SA/V. (C) In the case of a rod-shaped prison cell with hemispherical end caps, increases in width and length both represent to reductions in SA/V.
Focusing specifically on rod-shaped leaner, many studies have described the impact of diverse genetic, nutritional, and pharmacological perturbations on cell width and/or length [10–12]. Yet, changes in either of these dimensions will as well pb to changes in SA/V. On their own, increases in width reduce SA/V, every bit do increases in length, albeit to a bottom caste (Figure 1C). This bear on of cell lengthening tin can be understood by considering the relative contributions of the cylindrical cell body and hemispherical end caps: as cells go longer, the contribution of the high-SA/V terminate caps is macerated and the overall SA/V goes down (meet Effigy 1C, inset). For these reasons, changes in width and length in different growth weather must always exist considered in the context of their combined impact on the overall SA/V of cells.
A 'Relative Rates' Model Quantitatively Explains SA/V Homeostasis
With the understanding that cell size, shape, and SA/V are intimately linked, and having observed individual cells alter both their size and shape in guild to motion toward a steady-land SA/Five [9], we chose to focus strictly on how cells might achieve such SA/V homeostasis. First, we knew that bacteria increase both their mass and book exponentially – that is, the rate of volume growth scales with cell volume [1,18,19]. We then realized that if nosotros make the simple assumption that the rate of surface growth too scales with cell volume, this model predicts that cells volition move toward a steady-land SA/V over fourth dimension, that is, exhibit SA/V homeostasis. At the molecular level, nosotros hypothesized that the scaling betwixt book and surface growth is due to the fact that the biosynthesis of new surface textile begins in the 3D cell cytoplasm, where cytosolic enzymes synthesize precursors of various envelope components, including the peptidoglycan (PG) cell wall [11]. In this way, the biosynthetic flux through one or more envelope synthesis pathways in the jail cell cytoplasm might limit surface growth, causing the charge per unit of surface growth to scale with volume.
This phenomenological 'relative rates' model tin be formulated mathematically, and makes several experimentally testable, nontrivial predictions (Figure 2A). Specifically, SA/V at steady state is expected to be equal to the ratio β/α, where α is the exponential volume growth rate of cells and β is the rate of surface material synthesis per unit of measurement volume. Essentially, this means that, at steady state, SA/5 will be adamant by the ratio of surface growth to volume growth. Considering nosotros look both α and β to vary in unlike physiological conditions, we can plot what we predict will happen when cells are shifted between conditions (Figure 2B). After the shift, cells are initially not at the 'correct' SA/5 for their terminal status (βlast/αconcluding), and the model predicts that cells will movement toward that value in a trajectory that is described past a decomposable exponential function with decay abiding equal to αfinal. Dynamic, single-cell imaging of distantly related bacterial species undergoing dissimilar types of physiological perturbations revealed that cells indeed move toward a new steady-state SA/V in this manner, providing potent, quantitative support for this mechanism of SA/5 homeostasis [13]. Given the predictive power of this model, we propose that SA/V is the critical natural variable to consider when looking at bacterial morphogenesis. Importantly, achieving a item SA/V does not dictate 1 specific size or shape, but rather the range of sizes and shapes that cells tin can adopt (Effigy 1). Thus, any questions of bacterial size and shape determination must be considered inside the context of their combined impact on SA/V.
The Relative Rates of Surface and Volume Growth Dictate the Surface Surface area to Book Ratio (SA/V) of Bacterial Cells. (A) A 'relative rates' model for SA/Five homeostasis assumes that both volume and surface surface area grow at rates proportional to the electric current jail cell volume, with scaling factors α and β respectively. This model makes the quantitative prediction that cells volition move toward a terminal steady-land SA/5 in a trajectory described past a decaying exponential with decay constant α, and that the final SA/Five will be equal to the ratio of the scaling factors β/α. These quantitative predictions were borne out by dynamic, single-cell imaging [13]. (B) This diagram depicts the predictions of the model, that cells volition change SA/V depending on the relative rates of surface and book synthesis. For instance, during a nutritional upshift, the rate of volume synthesis increases relatively more than than the rate of surface synthesis, leading to an overall drop in SA/V and larger cells on average.
PG Synthesis Connects Surface Growth to Cell Volume
The central hypothesis underlying the 'relative rates' model is that surface growth rate scales with cell volume. Information technology is critical, therefore, to identify the molecular mechanisms that give rising to this scaling. Given the hypothesis that the flux through one or more than surface biosynthesis pathways in the cytoplasm sets the rate of surface growth, we wondered whether cell wall biosynthesis might be the primary pathway mediating this connection. The cell wall is a stiff, covalently linked network composed of PG that surrounds the cell, counteracts turgor pressure level, and is a major structural component of the jail cell envelope. Additionally, PG precursor synthesis begins in the cytoplasm, afterward which precursors are fastened to a lipid ballast (undecaprenyl phosphate, Und-P), flipped across the cytoplasmic membrane into the periplasm, and incorporated into the surrounding network [eleven,12]. For these reasons, PG biosynthesis was an bonny candidate for linking volume to the rate of surface growth.
Recently, a multifariousness of pharmacological and genetic experiments from our laboratory and others back up the proposal that PG biosynthesis does indeed serve as a meaning connection between volume and surface growth rate. When diverse bacterial species were treated with very low doses of the antibody fosfomycin, which inhibits the first committed step of PG biosynthesis, cells continued growing their volume essentially uninterrupted (i.e., α did not modify), simply slowed down the rate of surface growth per unit book (i.eastward., β was reduced) [13]. This implies that the scaling between volume and surface growth, at least in this authorities, is adamant by the flux through the PG biosynthesis pathway. Furthermore, cells treated with fosfomycin became larger and reduced their SA/V as predicted by the 'relative rates' model, where SA/Fivesteady-state = β/α. While information technology may seem counterintuitive that cells treated with a cell wall biosynthesis inhibitor should become bigger, this makes sense from an SA/V-axial indicate of view: because volume continued growing at the aforementioned rate while surface growth was slightly reduced, SA/V had to go down considering cells simply had less surface material available to encapsulate the same corporeality of volume. Remarkably, three extremely divergent species – the Gram-negatives C. crescentus and Escherichia coli and the Gram-positive Listeria monocytogenes – all responded to fosfomycin in the aforementioned way, reducing their SA/Five by increasing both their width and length in a dose-dependent manner, implying that the ability to flexibly alter dimensions in response to PG precursor availability is a widely conserved trait.
Other groups have likewise observed that changes in the flux through the PG biosynthesis pathway can lead to alterations in cellular SA/Five. Our fosfomycin results have been replicated past others [17], and it has as well been shown in Bacillus subtilis that depletion of MurB, the second enzyme in the PG biosynthesis pathway, leads to wide, elongated cells [20]. Recently, a comprehensive, CRISPRi-based analysis of essential genes in B. subtilis revealed that knockdowns of several different enzymes in the PG biosynthesis pathway also led to wider cells, and that, of all essential genes, but jail cell wall biosynthesis and patterning genes were significantly enriched in this metric [21]. Additionally, a two-component arrangement in Vibrio cholerae was identified, WigKR, that allows cells to tune the expression of the entire PG biosynthesis pathway. Activation of the system increased cell wall content and led to a 20% reduction in cell width, while blocking the system led to a comparable increase in prison cell width [22]. These results are exactly what the 'relative rates' model would predict: increased PG production led to sparse cells with high SA/V, while reduced PG product led to wide cells with low SA/V.
The in a higher place examples all back up the notion that PG biosynthesis serves as a meaning link between prison cell volume and surface growth, and that PG availability somehow mediates changes in SA/V. Interestingly, disruption of tardily steps in the biosynthesis of two other envelope constituents – O-antigen and enterobacterial mutual antigen (ECA) – have also been shown to increase cell size [23,24]. Notwithstanding, in both cases it was shown that these effects are also ultimately due to a reduction in PG biosynthesis. O-antigen, ECA, PG, and many other surface constituents are synthesized in a similar manner, where precursors are attached to the same lipid anchor, Und-P, earlier existence incorporated into their concluding structures. Disruption of late steps in the O-antigen and ECA biosynthesis pathways leads to a buildup of Und-P-linked expressionless terminate intermediates, which sequester Und-P away from PG biosynthesis [23,24]. The authors of these studies demonstrated that the observed increases in prison cell size are due specifically to reduced product of PG, not the other envelope constituents, further supporting the proposal that PG biosynthesis provides the primary molecular link between jail cell volume and surface growth in the 'relative rates' model. Additional details of envelope biosynthesis pathways that go through Und-P-linked intermediates, and interesting possible implications of contest between these pathways and PG biosynthesis, accept recently been reviewed [15].
Growth Rate Plays a Disquisitional Role in Size Determination
Then far we have focused on the role of surface material biosynthesis in determining SA/5 and cell size. However, it is the ratio of surface growth (β) to volume growth (α) that sets the steady-state SA/V of cells. Therefore, changes in volume growth rate can likewise accept profound impacts on SA/V and thus jail cell size. Because of this, it is of import to always consider the possibility that changes in cell size in response to a genetic or pharmacological perturbation could exist due primarily to changes in growth charge per unit. For example, it has been proposed that fatty acid (FA) biosynthesis, a necessary precursor to synthesis of membrane lipids, is involved in setting prison cell size considering disruption of this pathway leads to a reduction in cell size and an increase in SA/5 [25,26]. However, this perturbation also leads to a severe growth charge per unit defect – a fifty% reduction in α. Because SA/V ~ β/α, this driblet in α could cause an increase in SA/V, and hence the observed reduction in cell size.
In back up of this idea, in that location is evidence that the reduction in jail cell size in response to FA inhibition is mediated by the minor-molecule alarmones (p)ppGpp. These molecules are function of the stringent response in bacteria, and slow growth by dramatically altering the transcriptional contour of cells and facilitating a transition to a slow-growing state [27]. Similar to E. coli, C. crescentus typically slows down growth and reduces cell size in response to FA inhibition. However, in a (p)ppGpp null strain, cells no longer grew slowly or became modest during FA inhibition [28]. This implies that the decrease in growth is mediated through (p)ppGpp, and that the reduction in size is indeed due to the affect on growth rate, not another outcome of FA inhibition. Interestingly, when a like experiment was performed in Eastward. coli, (p)ppGpp null cells exposed to a FA biosynthesis inhibitor lost membrane integrity and were killed at higher rates than wild-type cells [25]. This suggests that, for this species and inhibitor concentration, cells must slow down their volume growth using (p)ppGpp, lest book growth outpace membrane capacity. More broadly, this example highlights the potential of (p)ppGpp signaling to coordinate book growth with the physiological state of the cell, potentially tuning cytoplasmic expansion to go on information technology in balance with other biosynthetic rates [27].
A Re-test of Schaechter's Growth Police
The observation that growth charge per unit has a profound bear upon on prison cell size is not new. Indeed, it was showtime reported lx years ago that E. coli cells grown chop-chop in nutrient-rich medium are larger than those grown slowly in nutrient-poor medium [29]. Specifically, it was observed that, for E. coli and closely related species, the average volume of cells appears to increase exponentially with growth charge per unit when the nutritional content of the growth medium is varied. This relationship, termed Schaechter's growth police force, has held up beautifully over the years, and recent work from Si et al. – using multiplexed turbidostats to mensurate the size and shape of E. coli cells growing at steady country in different media conditions – confirmed that the boilerplate prison cell volume appears to increment exponentially with growth rate (reproduced in Figure 3A) [17]. All the same, it is non just volume that varies monotonically with growth rate in these conditions. In addition to being large, fast-growing cells also accept lower SA/V values (reproduced in Effigy 3B) [17]. Biochemically, this drib in SA/V corresponds to less envelope textile per unit dry out cell mass. In fact, the amount of surface material per unit dry out weight was measured to be inversely proportional to growth rate [xxx]. This supports the thought that large, fast-growing cells are simply producing less surface material (PG) compared to book (mass) – that is, β/α is lower. Interestingly, these experimental results were invoked in several theoretical papers in the 1970s in order to explain the changes in cell size observed when growth rates are shifted [31,32], similar to the recently proposed 'relative rates' model.
A Linear Dependence of the Surface Area to Volume Ratio (SA/5) on Growth Rate Could Underlie Classically Observed Trends between Cell Size and Growth Rate. (A) Boilerplate cell volume versus growth charge per unit and SA/5 versus growth charge per unit for Due east. coli cells growing at steady state in different media conditions [17]. Each signal represents the average value for many cells from an experiment conducted in the indicated growth medium. The solid blue line represents an exponential fit to the data, and the extracted relationship is indicated in the gray box. The blue dashed line indicates the predicted dependence of SA/5 on growth rate given the exponential fit between volume and growth charge per unit, and assuming a rod shaped cell with 4:1 aspect ratio. (B) The same data as in (A), but hither SA/Five versus growth rate was fit with a linear role (solid orangish line). The extracted human relationship is indicated in the grayness box. The orangish dashed line indicates the predicted dependence of volume on growth charge per unit given the linear human relationship betwixt SA/V and growth rate, and assuming a rod shaped cell with iv:1 aspect ratio. (C) Predicted dependence of surface synthesis (β) on growth rate (α) when growth rate is varied by changing media conditions. Assuming a linear human relationship betwixt SA/V and α where g and b are constants, and combining this with the conclusion from the 'relative rates' model that at steady country SA/V is equal to the ratio β/α, we predict that β has a parabolic dependence on α. We can and so use the values of 1000 and b extracted from (B) and plot the predicted dependence of β on α for the data from Si et al. [17]. Known competing trends betwixt substrate availability and biosynthesis enzyme concentrations could contribute to the shape of this dependence.
Given our evidence that SA/Five homeostasis underlies size determination, nosotros wondered whether Schaechter's observation that size varies with growth rate might actually be due to SA/V varying with growth charge per unit. To investigate this, we examined the correlation between SA/Five and growth rate using measurements from Si et al., and observed a remarkably simple relationship: SA/5 appears to decrease linearly with growth rate (Effigy 3B). This linear trend fits the data simply as well every bit an exponential fit to book (Effigy 3A), meaning that even this very high quality dataset does not accept the resolution to distinguish betwixt these ii models. Although it is not immediately clear why SA/V should vary linearly with growth rate, we can interpret this observation inside the context of the 'relative rates' model every bit follows. If SA/5 is linear with respect to growth rate (α), and given that SA/Five is equal to β/α, we tin can conclude that β has a parabolic dependence on α in these conditions (Effigy 3C). In other words, the amount of surface cloth synthesized per unit cytoplasm (β) increases with α at slow growth rates, simply tapers off at rates close to the maximal growth charge per unit for E. coli. Specifically, using the information from Si et al. we find that β = α (−2.8 α + 9.38). Substantially, β is comprised of i component that increases with growth rate (α), convolved with a component that decreases with growth rate (−2.8 α + 9.3). There are several intriguing hints from the literature about why this might be the case, which nosotros highlight below.
First, we recall that increases in α correspond to increases in nutritional content of the medium. We therefore propose that the increasing component of β could be due to the increased availability of raw cloth available for PG biosynthesis – that is, the substrates for this reaction. For the decreasing component, we hypothesize that the concentration of surface biosynthesis enzymes decreases linearly with growth rate. It is well documented that the relative concentrations of many enzymes decrease with increasing growth rate [33,34]. This is because the global RNA/protein ratio increases linearly with growth rate equally an increasing fraction of the jail cell mass is composed of ribosomes, allowing cells to accomplish faster growth rates. Additionally, more of the proteome itself is defended to ribosome-associated proteins at fast growth rates, further reducing the relative concentration of other enzymes [34]. These changes in cell composition are both quantitative and reproducible, and if the relative concentrations of PG biosynthesis enzymes indeed decrease linearly with growth rate, and then this enzyme activity decrease, combined with the increasing availability of substrates, could readily explain the parabolic dependence of β on α. Future piece of work must directly measure both enzyme and substrate concentrations at different growth rates, and decide whether these trends can in fact explicate the observed dependence of SA/V – and thus size – on growth rate.
What is the Molecular Cue to Modulate SA/V?
In choosing to focus on SA/V when formulating the 'relative rates' model, we remained doubter about what morphological changes cells apply to achieve a specific SA/V. In reality, rod-shaped bacteria accept two major dimensions that they tin can alter in social club to change their SA/V – length and width (Figure 1). Much work has already been washed to identify genes that are involved in width and length control, and many mutations only seem to alter one or the other dimension, implying that width and length control are somewhat independent processes [12]. However, we consistently observed cells irresolute both length and width in order to reach whatsoever SA/V was necessary [xiii]. What molecular mechanisms might underlie these changes in dimension, and how do they conform quantitatively to the predictions of the 'relative rates' model? In the rest of this Stance commodity, we suggest ways that cells could achieve SA/5 homeostasis, with an emphasis on reconciling what is already known nearly the molecular mechanisms of width and length control in rod-shaped bacteria with the phenomenological observation of SA/Five homeostasis.
We can think of at least two general classes of mechanism, which are not mutually exclusive, that could permit cells to find whether their SA/V is consonant with the electric current rates of surface and volume synthesis: mechanisms that are sensitive to turgor pressure, and those that are sensitive to PG forerunner availability. In both cases, an imbalance in the rates of surface synthesis and book growth would pb to changes in a cell-scale property that could bespeak to cells to alter their pattern of growth in an advisable manner to alter their SA/V (Figure 4). Nosotros will focus exclusively on mechanisms involving PG precursor availability because more experiments take been performed on this topic, providing molecular clues nigh how precursors might influence cell width and length control. In contrast, picayune is known virtually the impact of turgor pressure level on bacteria, though it has been shown to modify cell growth [35,36]. In the future, it volition be important to identify the molecular ramifications of changes in turgor pressure level, and determine if such changes play a role in SA/5 homeostasis.
Changes in Peptidoglycan (PG) Forerunner Levels and/or Turgor Pressure Could Serve as a Betoken to Cells to Modify Their Surface Area to Volume Ratio (SA/Five). If SA/5 is too high, that is, SA/5 >β/α, surface synthesis is besides slow and book synthesis is too fast to be compatible with the current SA/V. Thus, in this case, at that place will potentially be a lack of bachelor peptidoglycan (PG) precursors and/or backlog turgor pressure. Conversely, if SA/V is also low, that is, SA/Five <β/α, surface synthesis is too fast and volume synthesis is too slow. In this scenario, in that location could exist an accumulation of excess PG precursors and/or a drop in turgor pressure level. In this style, cells could use changes in either of these properties to decide whether they should alter their length and width to achieve the correct SA/V.
Length and width command mechanisms that respond to the relative availability of PG precursors are highly-seasoned for several reasons. First, the prove presented above suggests that the flux through the PG biosynthetic pathway provides the molecular link between cell volume and surface growth, making this pathway an ideal candidate for orchestrating SA/V homeostasis. Second, the level of precursors in a jail cell would exist expected to change depending on whether the prison cell is at the correct SA/5 (Effigy 4). Third, the same puddle of PG precursors is used by the lateral and septal PG insertion machineries, which catalyze the elongation and division of cells respectively. Because of this, width and length could be modulated separately, merely in a concerted fashion, by these two dissimilar machineries both responding to changes in the shared puddle of PG precursors. This idea is similar to the 'two competing sites' model, which states that competition between the elongation and septation machineries dictates the residuum betwixt elongation and segmentation [37]. Edifice on this model, nosotros suggest that, every bit PG precursors become more or less available, these machineries would both reply, tuning length and width every bit necessary to reach the proper SA/Five. Nosotros believe that this type of coordinated response to changes in the shared pool of PG precursors could underlie the remarkable ability of some bacterial species to maintain a abiding attribute ratio across a wide range of sizes and growth rates [17]. Interestingly, when C. crescentus cells were genetically prevented from dividing, cells became very long, a morphological change that would pb to a driblet in SA/V if cells remained the same width (Effigy 1C). All the same, as cells became longer, they also became thinner and maintained the same SA/Five [13]. Thus, changes in width and length can be decoupled, merely cells still retain the ability to achieve SA/V homeostasis – if non with one dimension, and then with the other. This result supports a fluid sharing of PG precursors between the lateral and septal insertion machineries that robustly facilitates SA/V homeostasis. In the adjacent sections nosotros therefore consider mechanisms of width and length command separately, though in the time to come it will be critical to determine how and to what extent these systems interact in both fourth dimension and infinite.
How Might Width Be Modulated in Response to SA/Five Requirements?
Nigh rod-shaped leaner under normal, constant atmospheric condition elongate by incorporating new PG into their sidewall such that they elongate at a specific width. The lateral PG insertion machinery is therefore an obvious candidate effector of width control. During lateral wall synthesis, lipid-anchored PG precursors are polymerized into a growing glycan strand by a processive enzyme with PG transglycosylase (PGT) activity. This nascent strand is then cross-linked into the surrounding network through its peptide side chains past an enzyme with transpeptidase (TP) activity. The bacterial actin homolog MreB polymerizes into curt filaments or patches that bind to the cytoplasmic confront of the membrane and coordinate the circumferential movement of the Rod complex, a grouping of proteins that is known to help maintain width control and rod shape by promoting constrained lateral insertion, perchance by ensuring that strong glycan strands are inserted in their characteristic circumferential orientation [10,11,38] (Figure 5A).
The Residuum between Activity of 2 Different Peptidoglycan (PG) Insertion Machineries and Alterations in the Molecular Properties of PG Could Contribute to Changes in Jail cell Width. (A) The Rod system inserts lateral wall material and is known to promote rod-like growth at a fixed width. Recently, it was shown that bifunctional penicillin-bounden proteins (PBPs) insert fabric independent of the Rod system. Information technology is thus possible that, while the Rod system promotes constrained lateral insertion, the bifunctional PBPs promote unconstrained, or expansive insertion. In this style, simply past tuning the relative activities of these unlike systems based on the surface area to volume ratio (SA/V) requirements, cells could flexibly modify their width. (B) A diversity of different molecular alterations to the PG network could atomic number 82 to changes in the overall cell width over time.
An interesting detailed hypothesis for how cells could change width in response to PG forerunner levels is suggested by a series of contempo experiments showing that, while the Rod circuitous contains both PGT and TP enzymes, another class of enzymes is bifunctional and contains both of these activities in a single protein [39,xl]. Furthermore, these bifunctional penicillin-binding proteins (PBPs) do not appear to be governed by MreB. Thus, while the Rod complex promotes constrained lateral insertion, it is possible that bifunctional PBPs act as free agents, polymerizing and cross-linking PG in a way that does not seem to exist width-constrained, leading to expansive lateral insertion. In principle and then, cells could alter their width past tuning the balance betwixt these ii different modes of lateral wall incorporation (Figure 5A). Critically, recent piece of work showed that lipid-anchored PG precursors appear to recruit MreB to the membrane in B. subtilis [41]. This could create a homeostatic mechanism where low levels of PG precursors recruit less MreB to the cell surface, causing the bifunctional PBPs to have over and leading to prison cell widening. Conversely, loftier levels of PG precursors would recruit additional MreB and tilt the balance of synthesis toward the Rod complex, thereby causing the cells to narrow. More experiments are needed to test whether a homeostatic mechanism like the one described hither does indeed facilitate width modulation in response to SA/Five requirements.
Regardless of whether width homeostasis is achieved using the mechanism proposed above or some other scheme, information technology will exist critical to identify the molecular alterations in the PG itself that are responsible for these width changes. The PG network has many physical properties that could, in principle, be modulated enzymatically at the local level to produce global changes in cell width. These are summarized in Figure 5B, and include changes in glycan strand length, orientation, or anisotropy, which would modify the mechanical backdrop of the network, equally well equally more than general chemical properties such every bit the density of PG strands, their degree of cantankerous-linking, or chemical modification. The spatiotemporal regulation of insertion site placement and the stretching of PG strands as they are being laid downward could as well take profound impacts on the shape and mechanical properties of the network and consequently prison cell width [42]. Piecing apart how these properties reply to changes in PG precursor availability – and also turgor pressure – volition exist critical to empathise how the phenomenon of SA/V homeostasis is achieved at the molecular level.
How Might Length Exist Modulated in Response to SA/V Requirements?
In addition to modulating their width, a diverse array of bacterial species also alter their length in response to SA/V requirements [xiii,17,23,24,43]. Indeed, C. crescentus, E. coli, and L. monocytogenes all increase their length in a dose-dependent manner when grown in the presence of a PG biosynthesis inhibitor [thirteen]. Because rod-shaped bacteria abound through alternating phases of elongation and septation, this dose-dependent increase in length implies that cells delay division when PG precursors are scarce, suggesting that the availability of PG precursors tin can play a role in partition timing. Considering such a role for PG precursors in sectionalisation would, in principle, allow cells to fluidly modulate their length in response to SA/5 requirements, we sought to define a mechanism that might facilitate such coupling.
While the 'relative rates' model predicts what will happen to SA/5 when averaged over multiple cells and jail cell cycles, on an individual cell basis, SA/V is expected to oscillate over the cell cycle. During elongation, SA/V will necessarily go downward considering more of the cell is composed of depression-SA/V cylindrical cell body (Figure 1C), and then septation and the synthesis of two new daughter cell poles will enhance the ratio again (Effigy 6). Experimental evidence suggests that while book growth, α, seems to exist abiding throughout the cell cycle, the observed rate of surface incorporation into the wall, βincorporated, appears to fluctuate, speeding upwards particularly during constriction, when the loftier-SA/Five end caps are being built [13,xviii,44–46]. However, we have no reason to assume that the underlying rate of PG biosynthesis is cell-cycle regulated. Nosotros therefore hypothesize that there is some constant rate of surface material synthesis, βsynthesized, which is unchanged across the cell cycle (blue dashed line in Figure 6). If this is the instance, nosotros predict that cells would produce excess surface textile during elongation, leading to a build-up of surface material in the cytoplasm during this phase of the cell cycle. During septation, this excess would be used upward during the surface-intensive process of end-cap construction, returning the level of accumulated material back to baseline (Effigy 6).
A Surface Material Aggregating Threshold Underlying Division Timing Could Couple Prison cell Length to the Surface Area to Volume Ratio (SA/V) Requirements of the Cell. During the prison cell cycle, natural variations in SA/V could lead to the aggregating of excess surface material if the underlying rate of surface material biosynthesis is abiding. Cells could then use this accumulated material to trigger division once a threshold is reached, thus tying sectionalisation timing to surface material availability. The traces shown here stand for to an ideal rod with hemispherical end caps growing exponentially.
If this is true, and cells indeed accumulate excess surface material in their cytoplasm during elongation, nosotros realized that accumulation of a threshold amount of excess textile could serve as a checkpoint for constriction initiation, allowing cells to couple division timing to the availability of PG precursors and thus the SA/V requirements of the cell. For example, in the instance of PG biosynthesis inhibition, if cells were treated with increasing concentrations of drug, they would have to grow for longer times before reaching the same threshold. This would pb to a dose-dependent increment in cell length, equally nosotros have observed. Additionally, in that location is some evidence that length control is imposed at the point of constriction initiation [xiii,47,48], supporting the idea that at that place is a checkpoint prior to constriction initiation. Finally, several contempo reports accept found that bacteria appear to abound according to an adder pattern, where cells add, on average, the same amount of volume during each cell cycle earlier dividing [7,8,49,50]. If cells trigger partition after accumulating a threshold corporeality of excess surface material, this scheme mathematically produces an adder pattern between cell birth and constriction initiation [xiii]. Thus, division according to this blazon of mechanism could potentially explicate both the adder behavior that has been seen for a diverseness of bacterial species growing at steady state, as well as the dynamic changes in length that we have observed for diverse species in shifting physiological weather.
Although the mechanism described above is an attractive model that could explain a wide range of observations, information technology has yet to be experimentally tested. In the future, it will be critical to straight measure out the levels of different PG precursors across the prison cell cycle to determine if whatever of these species accrue during elongation. Additionally, it will exist of import to determine if there is a PG precursor 'sensor' that measures the accumulated precursors and is responsible for triggering division. Bacterial partition is orchestrated past the FtsZ ring, which forms at midcell, recruits a number of accompaniment proteins to grade the divisome, and eventually begins to constrict [51]. We therefore favor the hypothesis that some late-arriving component of the divisome might sense accumulated PG precursors and trigger the FtsZ ring to brainstorm constriction. Furthermore, our proposed model is predicted to produce an adder pattern merely when the threshold is a sure amount of excess surface material, not a sure concentration [13]. Considering the FtsZ ring remains relatively abiding in size as cells grow, a sensor that is part of the FtsZ ring could thus enable cells to sense a specific amount, not concentration, of material. Finally, loftier-throughput, loftier-resolution single-cell imaging will be required to determine if sectionalization timing does indeed appear to be imposed at the point of constriction initiation, and if and so, how this gives ascension to the observed adder design.
What Role Does Chromosome Replication Play in Partitioning Timing?
This proposal – that bacteria divide in response to surface material accumulation and SA/V requirements – is very different from traditional models of the bacterial cell bicycle where partitioning timing is intimately linked to chromosome replication. Particularly in E. coli, the Cooper–Helmstetter model of division timing has predominated, which states that after E. coli cells initiate another round of chromosome replication, it takes a prepare corporeality of time (the C menstruum), to replicate their chromosomes, and that cells then divide a fixed amount of time subsequently (the D period) [52]. From this perspective, the initiation of chromosome replication is the central issue of the Due east. coli jail cell bicycle, and with every initiation effect a corresponding division effect is 'scheduled' to happen C+D minutes later. After this model was proposed in 1968, Donachie pointed out that a abiding C+D flow, combined with the apparent exponential dependence of book on growth charge per unit known as Schaechter's growth law (Effigy 3), implies that cells initiate another round of chromosome replication at a fixed volume per origin of replication [53]. Experimental studies have since confirmed that East. coli cells do indeed initiate chromosome replication once they attain a critical book per origin of replication [17,54,55], and for wild-type Eastward. coli growing at moderate to fast growth rates the C+D period is remarkably constant [55,56]. Notwithstanding, the full general constancy of the C+D period has been called into question. Although the C period does announced to remain the aforementioned in almost conditions, various physiological and morphological perturbations have been identified that change the D catamenia in complex and unpredictable ways [13,17,57–59]. These data propose that, although the D flow originally appeared to exist a fundamental constant of bacterial sectionalisation, information technology is quite variable in unlike contexts.
We propose that these changes in the apparent D period can be understood if we allow go of the chromosome-centric view of cell segmentation, and instead adopt a chromosome-agnostic perspective. This type of model has been put forrad by other groups [60–63], and generally states that, for Eastward. coli cells growing at steady country, the partitioning and chromosome replication cycles operate in parallel, with minimal feedback between the 2. We build on these models, and propose that cells abound and split up according to their SA/Five requirements, with chromosome replication separately keeping footstep with volume growth. Because additional rounds of chromosome replication are triggered when cells reach a critical volume per origin of replication, this organisation allows chromosome number to automatically calibration with volume, regardless of cell partition. In back up of this view, contempo studies have found that perturbations which change Due east. coli jail cell size accept remarkably niggling outcome on the Dna-to-cytoplasm ratio, indicating that chromosome replication is unaffected by such morphological perturbations [13,17,57,59]. While some groups have suggested that these changes in cell size arise because the perturbations are altering the D flow, we argue the contrary – that the perturbations directly alter cell size, and therefore lead to changes in the apparent D menstruation. From our perspective, the D period is not a fundamental biological parameter that cells actively attune, and is instead simply the time that happens to elapse from the completion of chromosome replication until sectionalization. Although this distinction can sound subtle, understanding whether division timing sets the D period or the D flow sets partitioning timing will be critical to place the molecular players underlying length command in bacteria.
We can also apply this chromosome-agnostic view of sectionalisation timing to Schaechter's growth constabulary. Historically, it has been thought that increases in prison cell size with growth charge per unit are due to chromosome replication initiating at a constant book per origin of replication followed by a constant C+D menses. In Figure 3, nosotros put forward an alternating hypothesis for Schaechter's observations – ane that does not invoke chromosome replication and instead relies on trends in SA/V. From this perspective, cell size is set independently of chromosome replication, and this dependence of jail cell size on growth rate, combined with replication initiating at a constant book per origin of replication, result in the credible C+D period actualization relatively abiding over these nutritional atmospheric condition. Along these lines, in 1991 Cooper himself wrote: 'Since 1968, when the temporal continuance of the period between termination of Deoxyribonucleic acid replication and prison cell sectionalization was noted, information technology has been idea that termination of replication may trigger invagination. This observation is consistent with the alternate proposal that there is only a coincidental relationship between termination and division. Information technology may be that the abiding D catamenia is a result of the cell evolving to accept DNA replication terminate prior to division and that there is no causal human relationship between division and termination.' [64] We agree with this alternate proposal, and argue that at that place is no genuine 'timer' mechanism underlying the D period. Rather, E. coli seems to take evolved to scale its size (via trends in SA/V? via trends in β with α?) such that enough time is always left between termination of replication and the subsequent cell division.
Another statement against a chromosome-centric model of division timing is that at that place is piddling molecular evidence for a mechanism that causes E. coli to dissever a fix amount of time later on chromosome replication. Mostly, chromosome-centric models invoke the idea that once replication is terminated, it takes a set amount of time for the chromosomes to segregate, for the divisome to form, and for the prison cell to constrict. Consistent with this, nucleoid occlusion systems have been identified which forbid the cell from cutting across unsegregated chromosomes during prison cell sectionalization [65,66]. In these systems, the presence of DNA near the FtsZ ring direct inhibits band constriction. All the same, nucleoid occlusion appears to exist more of a fail-safe mechanism that kicks in when something has gone awry during the jail cell cycle, rather than a core feature that always dictates division timing. The evidence for this is that when nucleoid occlusion is genetically removed from cells, cells are not only viable, but the boilerplate cell size does not change [65,66], implying that this system is not at play during normal cell cycles. Furthermore, when nucleoid occlusion is removed and chromosomes are prevented from replicating birthday, cells go ahead and carve up across unreplicated chromosomes, 'guillotining' them [65,66]. This means that neither chromosome replication nor segregation is required for prison cell segmentation to occur, strongly arguing confronting a 18-carat molecular timer underlying the D period dictating when the cell will divide.
Finally, it is important to proceed in listen that the Cooper–Helmstetter model of the jail cell bike merely applies to Due east. coli. Other species have very unlike chromosome replication control programs, such equally C. crescentus, where compartmentalization of daughter cells is necessary to license another round of chromosome replication [67]. Nonetheless, diverse species all delayed partitioning in response to PG biosynthesis inhibition [13], implying that the availability of PG precursors is intimately tied to partition timing in all of these species. Additionally, the 'adder' growth pattern has been observed not just for E. coli, but also for many other kinds of bacteria [7,8,50]. Thus, information technology seems unlikely that the origin of the 'adder' pattern would be rooted in a chromosome replication program unique to Due east. coli, as some have suggested [55,59]. In contrast, accumulation of backlog surface material across the jail cell cycle could be a universal feature of rod-shaped bacteria (Effigy 6), making this an bonny model that could explain why extremely divergent species all exhibit similar 'adder' behaviors and responses to PG biosynthesis inhibition. Excitingly, other bacterial shapes, such every bit growing spheres, as well subtract their SA/V during an private jail cell cycle (considering SA/V = 3/R for a sphere, as the cell radius increases SA/V goes downwardly). This raises the possibility that other shapes could also accumulate excess material during the jail cell bike, making our proposed model of division timing perhaps even more broadly applicative.
Concluding Remarks
Nosotros recently reported that a strikingly simple 'relative rates' model is able to quantitatively explicate SA/Five homeostasis in a wide range of bacterial species. This model is phenomenological and makes intuitive sense: if the electric current SA/5 is not equal to the ratio of the surface and volume growth rates, cells alter their dimensions until the proper ratio is accomplished. Many observations in the literature, where changes in PG biosynthesis or volume growth rate led to changes in cell size, can be understood in the context of this model. However, the model still lacks molecular item. In the time to come, it will be essential to identify the molecular players that enable bacterial cells to change their dimensions and exquisitely conform to the predictions of the 'relative rates' model. We believe that the availability of PG precursors is the well-nigh likely way that cells could exist able to sense whether they need to increase or subtract their SA/V. Futurity studies must place whether forerunner levels change in different physiological contexts and beyond the cell wheel, whether the mode of lateral insertion varies based on precursor availability, and whether accumulation of precursors plays a role in partition timing (see Outstanding Questions). Although much is known about the players that assist to set the width and length of cells, a unified theory of bacterial size and shape determination has been lacking; by treating SA/5 as the key natural variable, we have uncovered a powerful new framework that might finally enable a comprehensive understanding of bacterial morphogenesis.
Acknowledgments
We would like to thank members of the Theriot laboratory for thoughtful feedback, too equally Suckjoon Jun and Fangwei Si for sharing information shown in Figure three. Funding was provided by NIH R37 AI036929, the Stanford Center for Systems Biology (P50-GM107615), and HHMI.
Footnotes
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References
1. Monod J. The growth of bacterial cultures. Annu. Rev. Microbiol. 1949;3:371–394. [Google Scholar]
3. Unger MA, et al. Monolithic microfabricated valves and pumps by multilayer soft lithography. Science. 2000;288:113–116. [PubMed] [Google Scholar]
4. Balaban NQ, et al. Bacterial persistence as a phenotypic switch. Scientific discipline. 2004;305:1622–1625. [PubMed] [Google Scholar]
five. Sliusarenko O, et al. Loftier-throughput, subpixel precision assay of bacterial morphogenesis and intracellular spatio-temporal dynamics. Mol. Microbiol. 2011;fourscore:612–627. [PMC gratis article] [PubMed] [Google Scholar]
half-dozen. Ursell T, et al. Rapid, precise quantification of bacterial cellular dimensions across a genomic-scale knockout library. BMC Biol. 2017;15:17. [PMC free article] [PubMed] [Google Scholar]
seven. Campos M, et al. A constant size extension drives bacterial cell size homeostasis. Prison cell. 2014;159:1433–1446. [PMC complimentary article] [PubMed] [Google Scholar]
8. Taheri-Araghi Southward, et al. Cell-size control and homeostasis in bacteria. Curr. Biol. 2015;25:385–391. [PMC costless article] [PubMed] [Google Scholar]
9. Harris LK, et al. A Caulobacter MreB mutant with irregular cell shape exhibits compensatory widening to maintain a preferred surface expanse to volume ratio. Mol. Microbiol. 2014;94:988–1005. [PMC free commodity] [PubMed] [Google Scholar]
10. Chastanet A, Carballido-Lopez R. The actin-like MreB proteins in Bacillus subtilis: a new turn. Front end. Biosci. Sch. Ed. 2012;4:1582–1606. [PubMed] [Google Scholar]
xi. Typas A, et al. From the regulation of peptidoglycan synthesis to bacterial growth and morphology. Nat. Rev. Microbiol. 2011;x:123–136. [PMC gratis article] [PubMed] [Google Scholar]
12. Young KD. Bacterial shape: two-dimensional questions and possibilities. Annu. Rev. Microbiol. 2010;64:223–240. [PMC free article] [PubMed] [Google Scholar]
thirteen. Harris LK, Theriot JA. Relative rates of surface and volume synthesis prepare bacterial jail cell size. Cell. 2016;165:1479–1492. [PMC free commodity] [PubMed] [Google Scholar]
fourteen. Osella M, et al. Step by step, cell by cell: quantification of the bacterial cell cycle. Trends Microbiol. 2017;25:250–256. [PubMed] [Google Scholar]
xvi. Cesar S, Huang KC. Thinking large: the tunability of bacterial cell size. FEMS Microbiol. Rev. 2017;41:672–678. [PMC complimentary commodity] [PubMed] [Google Scholar]
17. Si F, et al. Invariance of initiation mass and predictability of cell size in Escherichia coli. Curr. Biol. 2017;27:1278–1287. [PMC free article] [PubMed] [Google Scholar]
18. Godin Thousand, et al. Using buoyant mass to mensurate the growth of single cells. Nat. Methods. 2010;seven:387–390. [PMC free commodity] [PubMed] [Google Scholar]
twenty. Real G, Henriques AO. Localization of the Bacillus subtilis murB factor inside the dcw cluster is important for growth and sporulation. J. Bacteriol. 2006;188:1721–1732. [PMC free article] [PubMed] [Google Scholar]
21. Peters JM, et al. A comprehensive, CRISPR-based functional analysis of essential genes in leaner. Jail cell. 2016;165:1493–1506. [PMC gratuitous commodity] [PubMed] [Google Scholar]
22. Dörr T, et al. A prison cell wall damage response mediated by a sensor kinase/response regulator pair enables beta-lactam tolerance. Proc. Natl. Acad. Sci. U. Southward. A. 2016;113:404–409. [PMC free article] [PubMed] [Google Scholar]
23. Jorgenson MA, et al. Dead-end intermediates in the enterobacterial common antigen pathway induce morphological defects in Escherichia coli by competing for undecaprenyl phosphate. Mol. Microbiol. 2016;100:i–14. [PMC free commodity] [PubMed] [Google Scholar]
24. Jorgenson MA, Young KD. Interrupting biosynthesis of O-antigen or the lipopolysaccharide core produces morphological defects in Escherichia coli past sequestering undecaprenyl phosphate. J. Bacteriol. 2016;198:3070–3079. [PMC gratis article] [PubMed] [Google Scholar]
25. Vadia South, et al. Fatty acid availability sets prison cell envelope capacity and dictates microbial cell size. Curr. Biol. 2017;27:1757–1767.e5. [PMC costless article] [PubMed] [Google Scholar]
26. Yao Z, et al. Regulation of cell size in response to nutrient availability by fatty acid biosynthesis in Escherichia coli. Proc. Natl. Acad. Sci. U. S. A. 2012;109:E2561–E2568. [PMC free article] [PubMed] [Google Scholar]
27. Gaca AO, et al. Many ways to a common end: the intricacies of (p)ppGpp metabolism and its command of bacterial homeostasis. J. Bacteriol. 2015;197:1146–1156. [PMC gratis article] [PubMed] [Google Scholar]
28. Stott KV, et al. (p)ppGpp modulates cell size and the initiation of Dna replication in Caulobacter crescentus in response to a block in lipid biosynthesis. Microbiol. Read. Engl. 2015;161:553–564. [PMC free commodity] [PubMed] [Google Scholar]
29. Schaechter M, et al. Dependency on medium and temperature of cell size and chemical composition during counterbalanced grown of Salmonella typhimurium. J. Gen. Microbiol. 1958;xix:592–606. [PubMed] [Google Scholar]
xxx. Sud IJ, Schaechter M. Dependence of the content of prison cell envelopes on the growth charge per unit of Bacillus megaterium. J. Bacteriol. 1964;88:1612–1617. [PMC free article] [PubMed] [Google Scholar]
31. Previc EP. Biochemical determination of bacterial morphology and the geometry of cell division. J. Theor. Biol. 1970;27:471–497. [PubMed] [Google Scholar]
32. Pritchard RH. Review lecture on the growth and form of a bacterial cell. Philos. Trans. R. Soc. Lond. B Biol. Sci. 1974;267:303–336. [PubMed] [Google Scholar]
33. Bremer H, Dennis PP. Modulation of chemic composition and other parameters of the cell at unlike exponential growth rates. EcoSal Plus. 2008;3 doi: 10.1128/ecosal.5.2.3. Published online September 2008. [PubMed] [CrossRef] [Google Scholar]
34. Scott Yard, et al. Interdependence of cell growth and gene expression: origins and consequences. Scientific discipline. 2010;330:1099–1102. [PubMed] [Google Scholar]
35. Rojas E, et al. Response of Escherichia coli growth rate to osmotic shock. Proc. Natl. Acad. Sci. U. S. A. 2014;111:7807–7812. [PMC complimentary commodity] [PubMed] [Google Scholar]
36. Rojas ER, et al. Homeostatic jail cell growth is accomplished mechanically through membrane tension inhibition of cell-wall synthesis. Jail cell Syst. 2017;5:578–590.e6. [PMC free article] [PubMed] [Google Scholar]
37. Lleo MM, et al. Bacterial cell shape regulation: testing of additional predictions unique to the two-competing-sites model for peptidoglycan assembly and isolation of conditional rod-shaped mutants from some wild-type cocci. J. Bacteriol. 1990;172:3758–3771. [PMC gratis article] [PubMed] [Google Scholar]
38. Tropini C, et al. Principles of bacterial prison cell-size determination revealed by prison cell wall synthesis perturbations. Cell Rep. 2014;9:1520–1527. [PMC free article] [PubMed] [Google Scholar]
39. Meeske AJ, et al. SEDS proteins are a widespread family of bacterial cell wall polymerases. Nature. 2016;537:634–638. [PMC free article] [PubMed] [Google Scholar]
40. Cho H, et al. Bacterial cell wall biogenesis is mediated past SEDS and PBP polymerase families operation semi-autonomously. Nat. Microbiol. 2016;1:16172. [PMC free commodity] [PubMed] [Google Scholar]
41. Schirner Yard, et al. Lipid-linked cell wall precursors regulate membrane association of bacterial actin MreB. Nat. Chem. Biol. 2015;xi:38–45. [PMC gratis article] [PubMed] [Google Scholar]
42. Furchtgott Fifty, et al. Mechanisms for maintaining cell shape in rod-shaped Gram-negative bacteria. Mol. Microbiol. 2011;81:340–353. [PMC costless article] [PubMed] [Google Scholar]
43. Basan M, et al. Inflating bacterial cells by increased protein synthesis. Mol. Syst. Biol. 2015;11:836. [PMC complimentary commodity] [PubMed] [Google Scholar]
44. Cooper S. Charge per unit and topography of cell wall synthesis during the division wheel of Salmonella typhimurium. J. Bacteriol. 1988;170:422–430. [PMC complimentary article] [PubMed] [Google Scholar]
45. Wientjes FB, Nanninga N. Rate and topography of peptidoglycan synthesis during cell segmentation in Escherichia coli: concept of a leading edge. J. Bacteriol. 1989;171:3412– 3419. [PMC free article] [PubMed] [Google Scholar]
46. Woldringh CL, et al. Topography of peptidoglycan synthesis during elongation and polar cap formation in a cell partitioning mutant of Escherichia coli MC4100. Microbiology. 1987;133:575–586. [Google Scholar]
47. Reshes Yard, et al. Timing the starting time of sectionalization in E. coli : a single-cell study. Phys. Biol. 2008;5:046001. [PubMed] [Google Scholar]
48. Tsukanov R, et al. Timing of Z-band localization in Escherichia coli. Phys. Biol. 2011;eight:066003. [PubMed] [Google Scholar]
49. Amir A. Prison cell size regulation in bacteria. Phys. Rev. Lett. 2014;112:208102. [Google Scholar]
50. Deforet Thousand, et al. Cell-size homeostasis and the incremental rule in a bacterial pathogen. Biophys. J. 2015;109:521–528. [PMC complimentary article] [PubMed] [Google Scholar]
51. Haeusser DP, Margolin W. Splitsville: structural and functional insights into the dynamic bacterial Z ring. Nat. Rev. Microbiol. 2016;14:305–319. [PMC free article] [PubMed] [Google Scholar]
52. Cooper South, Helmstetter CE. Chromosome replication and the division cycle of Escherichia coli. Br. J. Mol. Biol. 1968;31:519–540. [PubMed] [Google Scholar]
53. Donachie WD. Relationship between jail cell size and time of initiation of Deoxyribonucleic acid replication. Nature. 1968;219:1077–1079. [PubMed] [Google Scholar]
54. Hill NS, et al. Cell size and the initiation of DNA replication in bacteria. PLOS Genet. 2012;8:e1002549. [PMC free commodity] [PubMed] [Google Scholar]
55. Wallden Thousand, et al. The synchronization of replication and division cycles in private E. coli cells. Cell. 2016;166:729–739. [PubMed] [Google Scholar]
56. Michelsen O, et al. Precise determinations of C and D periods by menstruation cytometry in Escherichia coli M-12 and B/r. Microbiol. Read. Engl. 2003;149:1001–1010. [PubMed] [Google Scholar]
57. Basan Yard, et al. Inflating bacterial cells by increased protein synthesis. Mol. Syst. Biol. 2015;xi:836. [PMC costless article] [PubMed] [Google Scholar]
58. Vadia Southward, Levin PA. Growth rate and cell size: a re-test of the growth law. Curr. Opin. Microbiol. 2015;24:96–103. [PMC free commodity] [PubMed] [Google Scholar]
59. Zheng H, et al. Interrogating the Escherichia coli jail cell cycle past cell dimension perturbations. Proc. Natl. Acad. Sci. U. S. A. 2016;113:15000–15005. [PMC free article] [PubMed] [Google Scholar]
lx. Adiciptaningrum A, et al. Stochasticity and homeostasis in the E. coli replication and sectionalization cycle. Sci. Rep. 2015;5:18261. [PMC free article] [PubMed] [Google Scholar]
62. Nordström K, et al. The Escherichia coli cell cycle: ane bike or multiple independent processes that are co-ordinated? Mol. Microbiol. 1991;5:769–774. [PubMed] [Google Scholar]
63. Wang JD, Levin PA. Metabolism, cell growth and the bacterial cell cycle. Nat. Rev. Microbiol. 2009;7:822–827. [PMC gratuitous article] [PubMed] [Google Scholar]
64. Cooper S. Synthesis of the cell surface during the division cycle of rod-shaped, Gram-negative bacteria. Microbiol. Rev. 1991;55:649–674. [PMC free article] [PubMed] [Google Scholar]
65. Wu LJ, Errington J. Coordination of cell segmentation and chromosome segregation past a nucleoid occlusion poly peptide in Bacillus subtilis. Cell. 2004;117:915–925. [PubMed] [Google Scholar]
66. Bernhardt TG, de Boer PAJ. SlmA, a nucleoid-associated, FtsZ binding protein required for blocking septal ring assembly over chromosomes in E. coli. Mol. Cell. 2005;18:555–564. [PMC free article] [PubMed] [Google Scholar]
67. McGrath PT, et al. Setting the stride: mechanisms tying Caulobacter cell-cycle progression to macroscopic cellular events. Curr. Opin. Microbiol. 2004;vii:192–197. [PubMed] [Google Scholar]
Source: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6150810/
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