Robustness and accuracy of cell division in Escherichia coli in diverse cell shapes

Scaling of stochastic growth and division dynamics: A comparative study of individual rod-shaped cells in the Mother Machine and SChemostat platforms

Microfluidic platforms enable long-term quantification of stochastic behaviors of individual bacterial cells under precisely controlled growth conditions. Yet, quantitative comparisons of physiological parameters and cell behaviors of different microorganisms in different experimental and device modalities is not available due to experiment-specific details affecting cell physiology. To rigorously assess the effects of mechanical confinement, we designed, engineered, and performed side-by-side experiments under otherwise identical conditions in the Mother Machine (with confinement) and the SChemostat (without confinement), using the latter as the ideal comparator. We established a protocol to cultivate a suitably engineered rod-shaped mutant of Caulobacter crescentus in the Mother Machine and benchmarked the differences in stochastic growth and division dynamics with respect to the SChemostat. While the single-cell growth rate distributions are remarkably similar, the mechanically confined cells in the Mother Machine experience a substantial increase in interdivision times. However, we find that the division ratio distribution precisely compensates for this increase, which in turn reflects identical emergent simplicities governing stochastic intergenerational homeostasis of cell sizes across device and experimental configurations, provided the cell sizes are appropriately mean-rescaled in each condition. Our results provide insights into the nature of the robustness of the bacterial growth and division machinery.

Dynamic proteome trade-offs regulate bacterial cell size and growth in fluctuating nutrient environments

Bacteria dynamically regulate cell size and growth to thrive in changing environments. While previous studies have characterized bacterial growth physiology at steady-state, a quantitative understanding of bacterial physiology in time-varying environments is lacking. Here we develop a quantitative theory connecting bacterial growth and division rates to proteome allocation in time-varying nutrient environments. In such environments, cell size and growth are regulated by trade-offs between prioritization of biomass accumulation or division, resulting in decoupling of single-cell growth rate from population growth rate. Specifically, bacteria transiently prioritize biomass accumulation over production of division machinery during nutrient upshifts, while prioritizing division over growth during downshifts. When subjected to pulsatile nutrient concentration, we find that bacteria exhibit a transient memory of previous metabolic states due to the slow dynamics of proteome reallocation. This allows for faster adaptation to previously seen environments and results in division control which is dependent on the time-profile of fluctuations.

The bacterial nucleoid-associated proteins, HU, and Dps, condense DNA into context-dependent biphasic or multiphasic complex coacervates

The bacterial chromosome, known as its nucleoid, is an amorphous assemblage of globular nucleoprotein domains. It exists in a state of phase separation from the cell's cytoplasm, as an irregularly-shaped, membrane-less, intracellular compartment. This state (the nature of which remains largely unknown) is maintained through bacterial generations ad infinitum. Here, we show that HU, and Dps, two of the most abundant nucleoid-associated proteins (NAPs) of Escherichia coli, undergo spontaneous complex coacervation with different forms of DNA/RNA, both individually and in each other's presence, to cause accretion and compaction of DNA/RNA into liquid-liquid phase separated (LLPS) condensates in vitro. Upon mixing with nucleic acids, HU-A and HU-B form (a) bi-phasic heterotypic mixed condensates in which HU-B helps to lower the C_sat of HU-A; and also (b) multi-phasic heterotypic condensates, with Dps, in which de-mixed domains display different contents of HU and Dps. We believe that these modes of complex coacervation that are seen in vitro can serve as models for the in vivo relationships amongst NAPs in nucleoids, involving local and global variations in the relative abundances of the different NAPs, especially in de-mixed sub-domains that are characterized by differing grades of phase separation. Our results clearly demonstrate some quantitative, and some qualitative, differences in the coacervating abilities of different NAPs with DNA, potentially explaining (i) why E. coli has two isoforms of HU, and (ii) why changes in the abundances of HU and Dps facilitate the lag, logarithmic and stationary phases of E. coli growth.

Cell Sorting-Directed Selection of Bacterial Cells in Bigger Sizes Analyzed by Imaging Flow Cytometry during Experimental Evolution

Cell morphology is an essential and phenotypic trait that can be easily tracked during adaptation and evolution to environmental changes. Thanks to the rapid development of quantitative analytical techniques for large populations of cells based on their optical properties, morphology can be easily determined and tracked during experimental evolution. Furthermore, the directed evolution of new culturable morphological phenotypes can find use in synthetic biology to refine fermentation processes. It remains unknown whether and how fast we can obtain a stable mutant with distinct morphologies using fluorescence-activated cell sorting (FACS)-directed experimental evolution. Taking advantage of FACS and imaging flow cytometry (IFC), we direct the experimental evolution of the E. coli population undergoing continuous passage of sorted cells with specific optical properties. After ten rounds of sorting and culturing, a lineage with large cells resulting from incomplete closure of the division ring was obtained. Genome sequencing highlighted a stop-gain mutation in amiC, leading to a dysfunctional AmiC division protein. The combination of FACS-based selection with IFC analysis to track the evolution of the bacteria population in real-time holds promise to rapidly select and culture new morphologies and association tendencies with many potential applications.

Extracting, quantifying, and comparing dynamical and biomechanical properties of living matter through single particle tracking

A panoply of new tools for tracking single particles and molecules has led to an explosion of experimental data, leading to novel insights into physical properties of living matter governing cellular development and function, health and disease. In this Perspective, we present tools to investigate the dynamics and mechanics of living systems from the molecular to cellular scale via single-particle techniques. In particular, we focus on methods to measure, interpret, and analyse complex data sets that are associated with forces, materials properties, transport, and emergent organisation phenomena within biological and soft-matter systems. Current approaches, challenges, and existing solutions in the associated fields are outlined in order to support the growing community of researchers at the interface of physics and the life sciences. Each section focuses not only on the general physical principles and the potential for understanding living matter, but also on details of practical data extraction and analysis, discussing limitations, interpretation, and comparison across different experimental realisations and theoretical frameworks. Particularly relevant results are introduced as examples. While this Perspective describes living matter from a physical perspective, highlighting experimental and theoretical physics techniques relevant for such systems, it is also meant to serve as a solid starting point for researchers in the life sciences interested in the implementation of biophysical methods.

Methods to monitor bacterial growth and replicative rates at the single-cell level

The heterogeneity of bacterial growth and replicative rates within a population was proposed a century ago notably to explain the presence of bacterial persisters. The term "growth rate" at the single-cell level corresponds to the increase in size or mass of an individual bacterium while the "replicative rate" refers to its division capacity within a defined temporality. After a decades long hiatus, recent technical innovative approaches allow population growth and replicative rates heterogeneity monitoring at the single-cell level resuming in earnest. Among these techniques, the oldest and widely used is time-lapse microscopy, most recently combined with microfluidics. We also discuss recent fluorescence dilution methods informing only on replicative rates and best suited. Some new elegant single cell methods so far only sporadically used such as buoyant mass measurement and stable isotope probing have emerged. Overall, such tools are widely used to investigate and compare the growth and replicative rates of bacteria displaying drug-persistent behaviors to that of bacteria growing in specific ecological niches or collected from patients. In this review, we describe the current methods available, discussing both the type of queries these have been used to answer and the specific strengths and limitations of each method.

Asymmetric peptidoglycan editing generates cell curvature in Bdellovibrio predatory bacteria

Peptidoglycan hydrolases contribute to the generation of helical cell shape in Campylobacter and Helicobacter bacteria, while cytoskeletal or periskeletal proteins determine the curved, vibrioid cell shape of Caulobacter and Vibrio. Here, we identify a peptidoglycan hydrolase in the vibrioid-shaped predatory bacterium Bdellovibrio bacteriovorus which invades and replicates within the periplasm of Gram-negative prey bacteria. The protein, Bd1075, generates cell curvature in B. bacteriovorus by exerting LD-carboxypeptidase activity upon the predator cell wall as it grows inside spherical prey. Bd1075 localizes to the outer convex face of B. bacteriovorus; this asymmetric localization requires a nuclear transport factor 2-like (NTF2) domain at the protein C-terminus. We solve the crystal structure of Bd1075, which is monomeric with key differences to other LD-carboxypeptidases. Rod-shaped Δbd1075 mutants invade prey more slowly than curved wild-type predators and stretch invaded prey from within. We therefore propose that the vibrioid shape of B. bacteriovorus contributes to predatory fitness.

Kinetic Modeling of Saccharomyces cerevisiae Central Carbon Metabolism: Achievements, Limitations, and Opportunities

Central carbon metabolism comprises the metabolic pathways in the cell that process nutrients into energy, building blocks and byproducts. To unravel the regulation of this network upon glucose perturbation, several metabolic models have been developed for the microorganism Saccharomyces cerevisiae. These dynamic representations have focused on glycolysis and answered multiple research questions, but no commonly applicable model has been presented. This review systematically evaluates the literature to describe the current advances, limitations, and opportunities. Different kinetic models have unraveled key kinetic glycolytic mechanisms. Nevertheless, some uncertainties regarding model topology and parameter values still limit the application to specific cases. Progressive improvements in experimental measurement technologies as well as advances in computational tools create new opportunities to further extend the model scale. Notably, models need to be made more complex to consider the multiple layers of glycolytic regulation and external physiological variables regulating the bioprocess, opening new possibilities for extrapolation and validation. Finally, the onset of new data representative of individual cells will cause these models to evolve from depicting an average cell in an industrial fermenter, to characterizing the heterogeneity of the population, opening new and unseen possibilities for industrial fermentation improvement.

Localization, Assembly, and Activation of the Escherichia coli Cell Division Machinery

Decades of research, much of it in Escherichia coli, have yielded a wealth of insight into bacterial cell division. Here, we provide an overview of the E. coli division machinery with an emphasis on recent findings. We begin with a short historical perspective into the discovery of FtsZ, the tubulin homolog that is essential for division in bacteria and archaea. We then discuss assembly of the divisome, an FtsZ-dependent multiprotein platform, at the midcell septal site. Not simply a scaffold, the dynamic properties of polymeric FtsZ ensure the efficient and uniform synthesis of septal peptidoglycan. Next, we describe the remodeling of the cell wall, invagination of the cell envelope, and disassembly of the division apparatus culminating in scission of the mother cell into two daughter cells. We conclude this review by highlighting some of the open questions in the cell division field, emphasizing that much remains to be discovered, even in an organism as extensively studied as E. coli.

Continuous rate modeling of bacterial stochastic size dynamics

Bacterial division is an inherently stochastic process with effects on fluctuations of protein concentration and phenotype variability. Current modeling tools for the stochastic short-term cell-size dynamics are scarce and mainly phenomenological. Here we present a general theoretical approach based on the Chapman-Kolmogorov equation incorporating continuous growth and division events as jump processes. This approach allows us to include different division strategies, noisy growth, and noisy cell splitting. Considering bacteria synchronized from their last division, we predict oscillations in both the central moments of the size distribution and its autocorrelation function. These oscillations, barely discussed in past studies, can arise as a consequence of the discrete time displacement invariance of the system with a period of one doubling time, and they do not disappear when including stochasticity on either division times or size heterogeneity on the starting population but only after inclusion of noise in either growth rate or septum position. This result illustrates the usefulness of having a solid mathematical description that explicitly incorporates the inherent stochasticity in various biological processes, both to understand the process in detail and to evaluate the effect of various sources of variability when creating simplified descriptions.

Rapid detection and identification of bacteria directly from whole blood with light scattering spectroscopy based biosensor

Bacterial infections are one of the major causes of death worldwide. The identification of a bacterial species that is the source of an infection generally takes a long time, and often exceeds the treatment window for seriously ill patients. Many of these deaths are preventable if the bacterial species can be identified quickly. Here we present an optical spectroscopic method for rapid detection and identification of bacteria directly from whole blood using a light scattering spectroscopy technique. This technique was originally developed to detect pre-cancerous changes in epithelial tissues, characterize changes in tissue on the cellular scale, and characterize biological structures comparable to or smaller than a single wavelength. We demonstrate here that not only can an inexpensive light scattering spectroscopy-based biosensor rapidly detect and identify four bacteria species in the blood, responsible for the majority of death causing infections, but that species-level identification can potentially be made based on approximately one thousand bacterial cells per milliliter of blood. Observing entire colonies or performing susceptibility testing is therefore not required.

Lab-on-a-chip based mechanical actuators and sensors for single-cell and organoid culture studies

All living cells constantly experience and respond to mechanical stresses. The molecular networks that activate in cells in response to mechanical stimuli are yet not well-understood. Our limited knowledge stems partially from the lack of available tools that are capable of exerting controlled mechanical stress to individual cells and at the same time observing their responses at subcellular to molecular resolution. Several tools such as rheology setups, micropipetes, and magnetic tweezers have been used in the past. While allowing to quantify short-time viscoelastic responses, these setups are not suitable for long-term observations of cells and most of them have low throughput. In this Perspective, we discuss lab-on-a-chip platforms that have the potential to overcome these limitations. Our focus is on devices that apply shear, compressive, tensile, and confinement derived stresses to single cells and organoid cultures. We compare different design strategies for these devices and highlight their advantages, drawbacks, and future potential. While the majority of these devices are used for fundamental research, some of them have potential applications in medical diagnostics and these applications are also discussed.

Biochip with multi-planar electrodes geometry for differentiation of non-spherical bioparticles in a microchannel

A biosensor capable of differentiating cells or other microparticles based on morphology finds significant biomedical applications. Examples may include morphological determination in the cellular division process, differentiation of bacterial cells, and cellular morphological variation in inflammation and cancer etc. Here, we present a novel integrated multi-planar microelectrodes geometry design that can distinguish a non-spherical individual particle flowing along a microchannel based on its electrical signature. We simulated multi-planar electrodes design in COMSOL Multiphysics and have shown that the changes in electrical field intensity corresponding to multiple particle morphologies can be distinguished. Our initial investigation has shown that top-bottom electrodes configuration produces significantly enhanced signal strength for a spherical particle as compared to co-planar configuration. Next, we integrated the co-planar and top-bottom configurations to develop a multi-planar microelectrode design capable of electrical impedance measurement at different spatial planes inside a microchannel by collecting multiple output signatures. We tested our integrated multi-planar electrode design with particles of different elliptical morphologies by gradually changing spherical particle dimensions to the non-spherical. The computed electrical signal ratio of non-spherical to spherical particle shows a very good correlation to predict the particle morphology. The biochip sensitivity is also found be independent of orientation of the particle flowing in the microchannel. Our integrated design will help develop the technology that will allow morphological analysis of various bioparticles in a microfluidic channel in the future.

Applications of smartphone-based near-infrared (NIR) imaging, measurement, and spectroscopy technologies to point-of-care (POC) diagnostics

The role of point-of-care (POC) diagnostics is important in public health. With the support of smartphones, POC diagnostic technologies can be greatly improved. This opportunity has arisen from not only the large number and fast spread of cell-phones across the world but also their improved imaging/diagnostic functions. As a tool, the smartphone is regarded as part of a compact, portable, and low-cost system for real-time POC, even in areas with few resources. By combining near-infrared (NIR) imaging, measurement, and spectroscopy techniques, pathogens can be detected with high sensitivity. The whole process is rapid, accurate, and low-cost, and will set the future trend for POC diagnostics. In this review, the development of smartphone-based NIR fluorescent imaging technology was described, and the quality and potential of POC applications were discussed.

Bacterial Growth Control Mechanisms Inferred from Multivariate Statistical Analysis of Single-Cell Measurements

Analysis of single-cell measurements of bacterial growth and division often relied on testing preconceived models of cell size control mechanisms. Such an approach could limit the scope of data analysis and prevent us from uncovering new information. Here, we take an "agnostic" approach by applying regression methods to multiple simultaneously measured cellular variables, which allow us to infer dependencies among those variables from their apparent correlations. Besides previously observed correlations attributed to particular cell size control mechanisms, we identify dependencies that point to potentially new mechanisms. In particular, cells born smaller than their sisters tend to grow faster and make up for the size difference acquired during division. We also find that sister cells are correlated beyond what single-cell, size-control models predict. These trends are consistently found in repeat experiments, although the dependencies vary quantitatively. Such variation highlights the sensitivity of cell growth to environmental variations and the limitation of currently used experimental setups.

Artificial modulation of cell width significantly affects the division time of Escherichia coli

Bacterial cells have characteristic spatial and temporal scales. For instance, Escherichia coli, the typical rod-shaped bacteria, always maintains a relatively constant cell width and cell division time. However, whether the external physical perturbation of cell width has an impact on cell division time remains largely unexplored. In this work, we developed two microchannel chips, namely straight channels and ‘necked’ channels, to precisely regulate the width of E. coli cells and to investigate the correlation between cell width and division time of the cells. Our results show that, in the straight channels, the wide cells divide much slower than narrow cells. In the ‘necked’ channels, the cell division is remarkably promoted compared to that in straight channels with the same width. Besides, fluorescence time-lapse microscopy imaging of FtsZ dynamics shows that the cell pre-constriction time is more sensitive to cell width perturbation than cell constriction time. Finally, we revealed a significant anticorrelation between the death rate and the division rate of cell populations with different widths. Our work provides new insights into the correlation between the geometrical property and division time of E. coli cells and sheds new light on the future study of spatial–temporal correlation in cell physiology.

Efficiency and Robustness of Processes Driven by Nucleoid Exclusion in Escherichia coli

The internal spatial organization of prokaryotic organisms, including Escherichia coli, is essential for the proper functioning of processes such as cell division. One source of this organization in E. coli is the nucleoid, which causes the exclusion of macromolecules - e.g. protein aggregates and the chemotaxis network - from midcell. Similarly, following DNA replication, the nucleoid(s) assist in placing the Z-ring at midcell. These processes need to be efficient in optimal conditions and robust to suboptimal conditions. After reviewing recent findings on these topics, we make use of past data to study the efficiency of the spatial constraining of Z-rings, chemotaxis networks, and protein aggregates, as a function of the nucleoid(s) morphology. Also, we compare the robustness of these processes to nonoptimal temperatures. We show that Z-rings, Tsr clusters, and protein aggregates have temperature-dependent spatial distributions along the major cell axis that are consistent with the nucleoid(s) morphology and the volume-exclusion phenomenon. Surprisingly, the consequences of the changes in nucleoid size with temperature are most visible in the kurtosis of these spatial distributions, in that it has a statistically significant linear correlation with the mean nucleoid length and, in the case of Z-rings, with the distance between nucleoids prior to cell division. Interestingly, we also find a negative, statistically significant linear correlation between the efficiency of these processes at the optimal condition and their robustness to suboptimal conditions, suggesting a trade-off between these traits.

Nuclei determine the spatial origin of mitotic waves

Traveling waves play an essential role in coordinating mitosis over large distances, but what determines the spatial origin of mitotic waves remains unclear. Here, we show that such waves initiate at pacemakers, regions that oscillate faster than their surroundings. In cell-free extracts of Xenopus laevis eggs, we find that nuclei define such pacemakers by concentrating cell cycle regulators. In computational models of diffusively coupled oscillators that account for nuclear import, nuclear positioning determines the pacemaker location. Furthermore, we find that the spatial dimensions of the oscillatory medium change the nuclear positioning and strongly influence whether a pacemaker is more likely to be at a boundary or an internal region. Finally, we confirm experimentally that increasing the system width increases the proportion of pacemakers at the boundary. Our work provides insight into how nuclei and spatial system dimensions can control local concentrations of regulators and influence the emergent behavior of mitotic waves.

Correlation between protein concentration and bacterial cell size can reveal mechanisms of gene expression

Classically, gene expression is modeled as a chemical process with reaction rates dependent on the concentration of the reactants (typically, DNA loci, plasmids, RNA, enzymes, etc). Other variables like cell size are in general ignored. Size dynamics can become an important variable due to the low number of many of these reactants, imperfectly symmetric cell partitioning and molecule segregation. In this work we measure the correlation between size and protein concentration by observing the gene expression of the RpOD gene from a low-copy plasmid in Escherichia coli during balanced growth in different media. A positive correlation was found, and we used it to examine possible models of cell size dynamics and plasmid replication. We implemented a previously developed model describing the full gene expression process including transcription, translation, loci replication, cell division and molecule segregation. By comparing with the observed correlation, we determine that the transcription rate must be proportional to the size times the number of plasmids. We discuss how fluctuations in plasmid segregation, due to the low copy number, can impose limits in this correlation.

Microfluidic Single-Cell Analytics

What is the impact of cellular heterogeneity on process performance? How do individual cells contribute to averaged process productivity? Single-cell analysis is a key technology for answering such key questions of biotechnology, beyond bulky measurements with populations. The analysis of cellular individuality, its origins, and the dependency of process performance on cellular heterogeneity has tremendous potential for optimizing biotechnological processes in terms of metabolic, reaction, and process engineering. Microfluidics offer unmatched environmental control of the cellular environment and allow massively parallelized cultivation of single cells. However, the analytical accessibility to a cell's physiology is of crucial importance for obtaining the desired information on the single-cell production phenotype. Highly sensitive analytics are required to detect and quantify the minute amounts of target analytes and small physiological changes in a single cell. For their application to biotechnological questions, single-cell analytics must evolve toward the measurement of kinetics and specific rates of the smallest catalytic unit, the single cell. In this chapter, we focus on an introduction to the latest single-cell analytics and their application for obtaining physiological parameters in a biotechnological context from single cells. We present and discuss recent advancements in single-cell analytics that enable the analysis of cell-specific growth, uptake, and production kinetics, as well as the gene expression and regulatory mechanisms at a single-cell level.

Comparison of Escherichia coli surface attachment methods for single-cell microscopy

For in vivo, single-cell imaging bacterial cells are commonly immobilised via physical confinement or surface attachment. Different surface attachment methods have been used both for atomic force and optical microscopy (including super resolution), and some have been reported to affect bacterial physiology. However, a systematic comparison of the effects these attachment methods have on the bacterial physiology is lacking. Here we present such a comparison for bacterium Escherichia coli, and assess the growth rate, size and intracellular pH of cells growing attached to different, commonly used, surfaces. We demonstrate that E. coli grow at the same rate, length and internal pH on all the tested surfaces when in the same growth medium. The result suggests that tested attachment methods can be used interchangeably when studying E. coli physiology.

Intracellular morphogens: Specifying patterns at the subcellular scale

The notion that graded distributions of signals underlie the spatial organization of biological systems has long been a central pillar in the fields of cell and developmental biology. During morphogenesis, morphogens spread across tissues to guide development of the embryo. Similarly, a variety of dynamic gradients and pattern-forming networks have been discovered that shape subcellular organization. Here we discuss the principles of intracellular pattern formation by these intracellular morphogens and relate them to conceptually similar processes operating at the tissue scale. We will specifically review mechanisms for generating cellular asymmetry and consider how intracellular patterning networks are controlled and adapt to cellular geometry. Finally, we assess the general concept of intracellular gradients as a mechanism for positional control in light of current data, highlighting how the simple readout of fixed concentration thresholds fails to fully capture the complexity of spatial patterning processes occurring inside cells.

Structural basis for the coordination of cell division with the synthesis of the bacterial cell envelope

Bacteria are surrounded by a complex cell envelope made up of one or two membranes supplemented with a layer of peptidoglycan (PG). The envelope is responsible for the protection of bacteria against lysis in their oft-unpredictable environments and it contributes to cell integrity, morphology, signaling, nutrient/small-molecule transport, and, in the case of pathogenic bacteria, host-pathogen interactions and virulence. The cell envelope requires considerable remodeling during cell division in order to produce genetically identical progeny. Several proteinaceous machines are responsible for the homeostasis of the cell envelope and their activities must be kept coordinated in order to ensure the remodeling of the envelope is temporally and spatially regulated correctly during multiple cycles of cell division and growth. This review aims to highlight the complexity of the components of the cell envelope, but focusses specifically on the molecular apparatuses involved in the synthesis of the PG wall, and the degree of cross talk necessary between the cell division and the cell wall remodeling machineries to coordinate PG remodeling during division. The current understanding of many of the proteins discussed here has relied on structural studies, and this review concentrates particularly on this structural work.

The E. coli MinCDE system in the regulation of protein patterns and gradients

Molecular self-organziation, also regarded as pattern formation, is crucial for the correct distribution of cellular content. The processes leading to spatiotemporal patterns often involve a multitude of molecules interacting in complex networks, so that only very few cellular pattern-forming systems can be regarded as well understood. Due to its compositional simplicity, the Escherichia coli MinCDE system has, thus, become a paradigm for protein pattern formation. This biological reaction diffusion system spatiotemporally positions the division machinery in E. coli and is closely related to ParA-type ATPases involved in most aspects of spatiotemporal organization in bacteria. The ATPase MinD and the ATPase-activating protein MinE self-organize on the membrane as a reaction matrix. In vivo, these two proteins typically oscillate from pole-to-pole, while in vitro they can form a variety of distinct patterns. MinC is a passenger protein supposedly operating as a downstream cue of the system, coupling it to the division machinery. The MinCDE system has helped to extract not only the principles underlying intracellular patterns, but also how they are shaped by cellular boundaries. Moreover, it serves as a model to investigate how patterns can confer information through specific and non-specific interactions with other molecules. Here, we review how the three Min proteins self-organize to form patterns, their response to geometric boundaries, and how these patterns can in turn induce patterns of other molecules, focusing primarily on experimental approaches and developments.

Division plane placement in pleomorphic archaea is dynamically coupled to cell shape

One mechanism for achieving accurate placement of the cell division machinery is via Turing patterns, where nonlinear molecular interactions spontaneously produce spatiotemporal concentration gradients. The resulting patterns are dictated by cell shape. For example, the Min system of Escherichia coli shows spatiotemporal oscillation between cell poles, leaving a mid-cell zone for division. The universality of pattern-forming mechanisms in divisome placement is currently unclear. We examined the location of the division plane in two pleomorphic archaea, Haloferax volcanii and Haloarcula japonica, and showed that it correlates with the predictions of Turing patterning. Time-lapse analysis of H. volcanii shows that divisome locations after successive rounds of division are dynamically determined by daughter cell shape. For H. volcanii, we show that the location of DNA does not influence division plane location, ruling out nucleoid occlusion. Triangular cells provide a stringent test for Turing patterning, where there is a bifurcation in division plane orientation. For the two archaea examined, most triangular cells divide as predicted by a Turing mechanism; however, in some cases multiple division planes are observed resulting in cells dividing into three viable progeny. Our results suggest that the division site placement is consistent with a Turing patterning system in these archaea.

Keeping replication on par with division in Bacillus

Spatially, division site selection is one of the most precisely controlled processes in bacterial physiology. Despite its obvious importance to the production of properly sized, viable daughter cells, the mechanisms underlying division site selection have remained largely mysterious. Molecular Microbiology, Hajduk et al. provide new insight into this essential process. Overturning previous models, including one of their own, they discover that two factors involved in chromosome remodeling - the ParB-like protein Spo0J, and the nucleoid-associated protein Noc - work together to coordinate early steps in DNA replication with establishment of a medial division site in the Gram-positive bacterium, Bacillus subtilis.

Shape and Size Control of Artificial Cells for Bottom-Up Biology

Bottom-up biology is an expanding research field that aims to understand the mechanisms underlying biological processes via in vitro assembly of their essential components in synthetic cells. As encapsulation and controlled manipulation of these elements is a crucial step in the recreation of such cell-like objects, microfluidics is increasingly used for the production of minimal artificial containers such as single-emulsion droplets, double-emulsion droplets, and liposomes. Despite the importance of cell morphology on cellular dynamics, current synthetic-cell studies mainly use spherical containers, and methods to actively shape manipulate these have been lacking. In this paper, we describe a microfluidic platform to deform the shape of artificial cells into a variety of shapes (rods and discs) with adjustable cell-like dimensions below 5 μm, thereby mimicking realistic cell morphologies. To illustrate the potential of our method, we reconstitute three biologically relevant protein systems (FtsZ, microtubules, collagen) inside rod-shaped containers and study the arrangement of the protein networks inside these synthetic containers with physiologically relevant morphologies resembling those found in living cells.

Reproduction of Large-Scale Bioreactor Conditions on Microfluidic Chips

Microbial cells in industrial large-scale bioreactors are exposed to fluctuating conditions, e.g., nutrient concentration, dissolved oxygen, temperature, and pH. These inhomogeneities can influence the cell physiology and metabolism, e.g., decelerate cell growth and product formation. Microfluidic systems offer new opportunities to study such effects in great detail by examining responses to varying environmental conditions at single-cell level. However, the possibility to reproduce large-scale bioreactor conditions in microscale cultivation systems has not yet been systematically investigated. Hence, we apply computational fluid dynamics (CFD) simulations to analyze and compare three commonly used microfluidic single-cell trapping and cultivation devices that are based on (i) mother machines (MM), (ii) monolayer growth chambers (MGC), and (iii) negative dielectrophoresis (nDEP). Several representative time-variant nutrient concentration profiles are applied at the chip entry. Responses to these input signals within the studied microfluidic devices are comparatively evaluated at the positions of the cultivated cells. The results are comprehensively presented in a Bode diagram that illustrates the degree of signal damping depending on the frequency of change in the inlet concentration. As a key finding, the MM can accurately reproduce signal changes that occur within 1 s or slower, which are typical for the environmental conditions observed by single cells in large-scale bioreactors, while faster changes are levelled out. In contrast, the nDEP and MGC are found to level out signal changes occurring within 10 s or faster, which can be critical for the proposed application.

The Min-protein oscillations in Escherichia coli: an example of self-organized cellular protein waves

In the rod-shaped bacterium Escherichia coli, selection of the cell centre as the division site involves pole-to-pole oscillations of the proteins MinC, MinD and MinE. This spatio-temporal pattern emerges from interactions among the Min proteins and with the cytoplasmic membrane. Combining experimental studies in vivo and in vitro together with theoretical analysis has led to a fairly good understanding of Min-protein self-organization. In different geometries, the system can, in addition to standing waves, also produce travelling planar and spiral waves as well as coexisting stable stationary distributions. Today it stands as one of the best-studied examples of cellular self-organization of proteins.This article is part of the theme issue 'Self-organization in cell biology'.

Minimal in vitro systems shed light on cell polarity

Cell polarity - the morphological and functional differentiation of cellular compartments in a directional manner - is required for processes such as orientation of cell division, directed cellular growth and motility. How the interplay of components within the complexity of a cell leads to cell polarity is still heavily debated. In this Review, we focus on one specific aspect of cell polarity: the non-uniform accumulation of proteins on the cell membrane. In cells, this is achieved through reaction-diffusion and/or cytoskeleton-based mechanisms. In reaction-diffusion systems, components are transformed into each other by chemical reactions and are moving through space by diffusion. In cytoskeleton-based processes, cellular components (i.e. proteins) are actively transported by microtubules (MTs) and actin filaments to specific locations in the cell. We examine how minimal systems - in vitro reconstitutions of a particular cellular function with a minimal number of components - are designed, how they contribute to our understanding of cell polarity (i.e. protein accumulation), and how they complement in vivo investigations. We start by discussing the Min protein system from Escherichia coli, which represents a reaction-diffusion system with a well-established minimal system. This is followed by a discussion of MT-based directed transport for cell polarity markers as an example of a cytoskeleton-based mechanism. To conclude, we discuss, as an example, the interplay of reaction-diffusion and cytoskeleton-based mechanisms during polarity establishment in budding yeast.

An integrative view of cell cycle control in Escherichia coli

Bacterial proliferation depends on the cells' capability to proceed through consecutive rounds of the cell cycle. The cell cycle consists of a series of events during which cells grow, copy their genome, partition the duplicated DNA into different cell halves and, ultimately, divide to produce two newly formed daughter cells. Cell cycle control is of the utmost importance to maintain the correct order of events and safeguard the integrity of the cell and its genomic information. This review covers insights into the regulation of individual key cell cycle events in Escherichia coli. The control of initiation of DNA replication, chromosome segregation and cell division is discussed. Furthermore, we highlight connections between these processes. Although detailed mechanistic insight into these connections is largely still emerging, it is clear that the different processes of the bacterial cell cycle are coordinated to one another. This careful coordination of events ensures that every daughter cell ends up with one complete and intact copy of the genome, which is vital for bacterial survival.

Modified Pearson correlation coefficient for two-color imaging in spherocylindrical cells

The revolution in fluorescence microscopy enables sub-diffraction-limit ("superresolution") localization of hundreds or thousands of copies of two differently labeled proteins in the same live cell. In typical experiments, fluorescence from the entire three-dimensional (3D) cell body is projected along the z-axis of the microscope to form a 2D image at the camera plane. For imaging of two different species, here denoted "red" and "green", a significant biological question is the extent to which the red and green spatial distributions are positively correlated, anti-correlated, or uncorrelated. A commonly used statistic for assessing the degree of linear correlation between two image matrices R and G is the Pearson Correlation Coefficient (PCC). PCC should vary from - 1 (perfect anti-correlation) to 0 (no linear correlation) to + 1 (perfect positive correlation). However, in the special case of spherocylindrical bacterial cells such as E. coli or B. subtilis, we show that the PCC fails both qualitatively and quantitatively. PCC returns the same + 1 value for 2D projections of distributions that are either perfectly correlated in 3D or completely uncorrelated in 3D. The PCC also systematically underestimates the degree of anti-correlation between the projections of two perfectly anti-correlated 3D distributions. The problem is that the projection of a random spatial distribution within the 3D spherocylinder is non-random in 2D, whereas PCC compares every matrix element of R or G with the constant mean value [Formula: see text] or [Formula: see text]. We propose a modified Pearson Correlation Coefficient (MPCC) that corrects this problem for spherocylindrical cell geometry by using the proper reference matrix for comparison with R and G. Correct behavior of MPCC is confirmed for a variety of numerical simulations and on experimental distributions of HU and RNA polymerase in live E. coli cells. The MPCC concept should be generalizable to other cell shapes.

Cell shape-independent FtsZ dynamics in synthetically remodeled bacterial cells

FtsZ is the main regulator of bacterial cell division. It has been implicated in acting as a scaffolding protein for other division proteins, a force generator during constriction, and more recently, as an active regulator of septal cell wall production. FtsZ assembles into a heterogeneous structure coined the Z-ring due to its resemblance to a ring confined by the midcell geometry. Here, to establish a framework for examining geometrical influences on proper Z-ring assembly and dynamics, we sculpted Escherichia coli cells into unnatural shapes using division- and cell wall-specific inhibitors in a micro-fabrication scheme. This approach allowed us to examine FtsZ behavior in engineered Z-squares and Z-hearts. We use stimulated emission depletion (STED) nanoscopy to show that FtsZ clusters in sculpted cells maintain the same dimensions as their wild-type counterparts. Based on our results, we propose that the underlying membrane geometry is not a deciding factor for FtsZ cluster maintenance and dynamics in vivo.

The FtsZ protein assembles into a structure known as ‘Z-ring’ at midcell for bacterial cell division. Here, Söderström et al. show that Z-ring assembly and dynamics in E. coli cells with unnatural shapes, such as squares and hearts, are generally similar to those observed in cells with normal shape.

Effects of geometry and topography on Min-protein dynamics

In the rod-shaped bacterium Escherichia coli, the center is selected by the Min-proteins as the site of cell division. To this end, the proteins periodically translocate between the two cell poles, where they suppress assembly of the cell division machinery. Ample evidence notably obtained from in vitro reconstitution experiments suggests that the oscillatory pattern results from self-organization of the proteins MinD and MinE in presence of a membrane. A mechanism built on cooperative membrane attachment of MinD and persistent MinD removal from the membrane induced by MinE has been shown to be able to reproduce the observed Min-protein patterns in rod-shaped E. coli and on flat supported lipid bilayers. Here, we report our results of a numerical investigation of patterns generated by this mechanism in various geoemtries. Notably, we consider the dynamics on membrane patches of different forms, on topographically structured lipid bilayers, and in closed geometries of various shapes. We find that all previously described patterns can be reproduced by the mechanism. However, it requires different parameter sets for reproducing the patterns in closed and in open geometries.

The precision of the symmetry in Z-ring placement in Escherichia coli is hampered at critical temperatures

Cell division in Escherichia coli is morphologically symmetric due to, among other things, the ability of these cells to place the Z-ring at midcell. Studies have reported that, at sub-optimal temperatures, this symmetry decreases at the single-cell level, but the causes remain unclear. Using fluorescence microscopy, we observe FtsZ-GFP and DAPI-stained nucleoids to assess the robustness of the symmetry of Z-ring formation and positioning in individual cells under sub-optimal and critical temperatures. We find the Z-ring formation and positioning to be robust at sub-optimal temperatures, as the Z-ring's mean width, density and displacement from midcell maintain similar levels of correlation to one another as at optimal temperatures. However, at critical temperatures, the Z-ring displacement from midcell is greatly increased. We present evidence showing that this is due to enhanced distance between the replicated nucleoids and, thus, reduced Z-ring density, which explains the weaker precision in setting a morphologically symmetric division site. This also occurs in rich media and is cumulative, i.e. combining richer media and critically high temperatures enhances the asymmetries in division, which is evidence that the causes are biophysical. To further support this, we show that the effects are reversible, i.e. shifting cells from optimal to critical, and then to optimal again, reduces and then enhances the symmetry in Z-ring positioning, respectively, as the width and density of the Z-ring return to normal values. Overall, our findings show that the Z-ring positioning in E. coli is a robust biophysical process under sub-optimal temperatures, and that critical temperatures cause significant asymmetries in division.

Analysis of Factors Limiting Bacterial Growth in PDMS Mother Machine Devices

The microfluidic mother machine platform has attracted much interest for its potential in studies of bacterial physiology, cellular organization, and cell mechanics. Despite numerous experiments and development of dedicated analysis software, differences in bacterial growth and morphology in narrow mother machine channels compared to typical liquid media conditions have not been systematically characterized. Here we determine changes in E. coli growth rates and cell dimensions in different sized dead-end microfluidic channels using high resolution optical microscopy. We find that E. coli adapt to the confined channel environment by becoming narrower and longer compared to the same strain grown in liquid culture. Cell dimensions decrease as the channel length increases and width decreases. These changes are accompanied by increases in doubling times in agreement with the universal growth law. In channels 100 μm and longer, cell doublings can completely stop as a result of frictional forces that oppose cell elongation. Before complete cessation of elongation, mechanical stresses lead to substantial deformation of cells and changes in their morphology. Our work shows that mechanical forces rather than nutrient limitation are the main growth limiting factor for bacterial growth in long and narrow channels.

Recent advances in understanding how rod-like bacteria stably maintain their cell shapes

Cell shape and cell volume are important for many bacterial functions. In recent years, we have seen a range of experimental and theoretical work that led to a better understanding of the determinants of cell shape and size. The roles of different molecular machineries for cell-wall expansion have been detailed and partially redefined, mechanical forces have been shown to influence cell shape, and new connections between metabolism and cell shape have been proposed. Yet the fundamental determinants of the different cellular dimensions remain to be identified. Here, we highlight some of the recent developments and focus on the determinants of rod-like cell shape and size in the well-studied model organisms Escherichia coli and Bacillus subtilis.

Beyond the bulk: disclosing the life of single microbial cells

Microbial single cell analysis has led to discoveries that are beyond what can be resolved with population-based studies. It provides a pristine view of the mechanisms that organize cellular physiology, unbiased by population heterogeneity or uncontrollable environmental impacts. A holistic description of cellular functions at the single cell level requires analytical concepts beyond the miniaturization of existing technologies, defined but uncontrolled by the biological system itself. This review provides an overview of the latest advances in single cell technologies and demonstrates their potential. Opportunities and limitations of single cell microbiology are discussed using selected application-related examples.

Treadmilling by FtsZ filaments drives peptidoglycan synthesis and bacterial cell division

The mechanism by which bacteria divide is not well understood. Cell division is mediated by filaments of FtsZ and FtsA (FtsAZ) that recruit septal peptidoglycan-synthesizing enzymes to the division site. To understand how these components coordinate to divide cells, we visualized their movements relative to the dynamics of cell wall synthesis during cytokinesis. We found that the division septum was built at discrete sites that moved around the division plane. FtsAZ filaments treadmilled circumferentially around the division ring and drove the motions of the peptidoglycan-synthesizing enzymes. The FtsZ treadmilling rate controlled both the rate of peptidoglycan synthesis and cell division. Thus, FtsZ treadmilling guides the progressive insertion of new cell wall by building increasingly smaller concentric rings of peptidoglycan to divide the cell.

Analysis of Noise Mechanisms in Cell-Size Control

At the single-cell level, noise arises from multiple sources, such as inherent stochasticity of biomolecular processes, random partitioning of resources at division, and fluctuations in cellular growth rates. How these diverse noise mechanisms combine to drive variations in cell size within an isoclonal population is not well understood. Here, we investigate the contributions of different noise sources in well-known paradigms of cell-size control, such as adder (division occurs after adding a fixed size from birth), sizer (division occurs after reaching a size threshold), and timer (division occurs after a fixed time from birth). Analysis reveals that variation in cell size is most sensitive to errors in partitioning of volume among daughter cells, and not surprisingly, this process is well regulated among microbes. Moreover, depending on the dominant noise mechanism, different size-control strategies (or a combination of them) provide efficient buffering of size variations. We further explore mixer models of size control, where a timer phase precedes/follows an adder, as has been proposed in Caulobacter crescentus. Although mixing a timer and an adder can sometimes attenuate size variations, it invariably leads to higher-order moments growing unboundedly over time. This results in a power-law distribution for the cell size, with an exponent that depends inversely on the noise in the timer phase. Consistent with theory, we find evidence of power-law statistics in the tail of C. crescentus cell-size distribution, although there is a discrepancy between the observed power-law exponent and that predicted from the noise parameters. The discrepancy, however, is removed after data reveal that the size added by individual newborns in the adder phase itself exhibits power-law statistics. Taken together, this study provides key insights into the role of noise mechanisms in size homeostasis, and suggests an inextricable link between timer-based models of size control and heavy-tailed cell-size distributions.

Kinetics of large-scale chromosomal movement during asymmetric cell division in Escherichia coli

Coordination between cell division and chromosome replication is essential for a cell to produce viable progeny. In the commonly accepted view, Escherichia coli realize this coordination via the accurate positioning of its cell division apparatus relative to the nucleoids. However, E. coli lacking proper positioning of its cell division planes can still successfully propagate. Here, we characterize how these cells partition their chromosomes into daughters during such asymmetric divisions. Using quantitative time-lapse imaging, we show that DNA translocase, FtsK, can pump as much as 80% (3.7 Mb) of the chromosome between daughters at an average rate of 1700±800 bp/s. Pauses in DNA translocation are rare, and in no occasions did we observe reversals at experimental time scales of a few minutes. The majority of DNA movement occurs at the latest stages of cell division when the cell division protein ZipA has already dissociated from the septum, and the septum has closed to a narrow channel with a diameter much smaller than the resolution limit of the microscope (~250 nm). Our data suggest that the narrow constriction is necessary for effective translocation of DNA by FtsK.

DNA translocases are conserved throughout bacteria. While at atomic and molecular levels they have been well characterized, their ability to partition DNA in vegetatively growing cells has remained less clear. Here we show that E. coli translocase, FtsK, can move as much as 80% (3.7 Mb) of the chromosomal DNA across the closing septum in asymmetrically dividing cells at an average rate of 1700 bp/s. The majority of DNA movement occurs at the latest stages of cell division when the septum has closed to a narrow channel. Our data implies that a narrow septal opening is needed for effective translocation of DNA by FtsK.

E. coli Cell Cycle Machinery

Cytokinesis in E. coli is organized by a cytoskeletal element designated the Z ring. The Z ring is formed at midcell by the coalescence of FtsZ filaments tethered to the membrane by interaction of FtsZ's conserved C-terminal peptide (CCTP) with two membrane-associated proteins, FtsA and ZipA. Although interaction between an FtsZ monomer and either of these proteins is of low affinity, high affinity is achieved through avidity - polymerization linked CCTPs interacting with the membrane tethers. The placement of the Z ring at midcell is ensured by antagonists of FtsZ polymerization that are positioned within the cell and target FtsZ filaments through the CCTP. The placement of the ring is reinforced by a protein network that extends from the terminus (Ter) region of the chromosome to the Z ring. Once the Z ring is established, additional proteins are recruited through interaction with FtsA, to form the divisome. The assembled divisome is then activated by FtsN to carry out septal peptidoglycan synthesis, with a dynamic Z ring serving as a guide for septum formation. As the septum forms, the cell wall is split by spatially regulated hydrolases and the outer membrane invaginates in step with the aid of a transenvelope complex to yield progeny cells.

Mapping out Min protein patterns in fully confined fluidic chambers

The bacterial Min protein system provides a major model system for studying reaction-diffusion processes in biology. Here we present the first in vitro study of the Min system in fully confined three-dimensional chambers that are lithography-defined, lipid-bilayer coated and isolated through pressure valves. We identify three typical dynamical behaviors that occur dependent on the geometrical chamber parameters: pole-to-pole oscillations, spiral rotations, and traveling waves. We establish the geometrical selection rules and show that, surprisingly, Min-protein spiral rotations govern the larger part of the geometrical phase diagram. Confinement as well as an elevated temperature reduce the characteristic wavelength of the Min patterns, although even for confined chambers with a bacterial-level viscosity, the patterns retain a ~5 times larger wavelength than in vivo. Our results provide an essential experimental base for modeling of intracellular Min gradients in bacterial cell division as well as, more generally, for understanding pattern formation in reaction-diffusion systems.

DOI:http://dx.doi.org/10.7554/eLife.19271.001

Some proteins can spontaneously organize themselves into ordered patterns within living cells. One widely studied pattern is made in a rod-shaped bacterium called Escherichia coli by a group of proteins called the Min proteins. The pattern formed by the Min proteins allows an E. coli cell to produce two equally sized daughter cells when it divides by ensuring that the division machinery correctly assembles at the center of the parent cell. These proteins move back and forth between the two ends of the parent cell so that the levels of Min proteins are highest at the ends and lowest in the middle. Since the Min proteins act to inhibit the assembly of the cell division machinery, this machinery only assembles in locations where the level of Min proteins is at its lowest, that is, at the middle of the cell.

When Min proteins are purified and placed within an artificial compartment that contains a source of chemical energy and is covered by a membrane similar to the membranes that surround cells, they spontaneously form traveling waves on top of the membrane in many directions along to surface. It is not clear how these waves relate to the oscillations seen in E. coli. Caspi and Dekker now analyze the behavior of purified Min proteins inside chambers of various sizes that are fully enclosed by a membrane.

The results show that in narrow chambers, Min proteins move back and forth (i.e. oscillate) from one side to the other. However, in wider containers the wave motion is more common. In containers of medium width the Min proteins rotate in a spiral fashion. Caspi and Dekker propose that the spiral rotations are the underlying pattern formed by Min proteins and that the back and forth motion is caused by spirals being cut short. In other words, if a spiral cannot form because the compartment is too small then the back and forth motion emerges. Similarly, Caspi and Dekker propose that the waves emerge in larger containers when multiple spirals come together.

These findings suggest that the different patterns that Min proteins form in bacterial cells and artificial compartments arise from different underlying mechanisms. The next step will be to investigate other differences in how the patterns of Min proteins form in E. coli and in artificial compartments.

DOI:http://dx.doi.org/10.7554/eLife.19271.002

Stochastic modeling of cell growth with symmetric or asymmetric division

We consider a class of biologically motivated stochastic processes in which a unicellular organism divides its resources (volume or damaged proteins, in particular) symmetrically or asymmetrically between its progeny. Assuming the final amount of the resource is controlled by a growth policy and subject to additive and multiplicative noise, we derive the recursive integral equation describing the evolution of the resource distribution over subsequent generations and use it to study the properties of stable resource distributions. We find conditions under which a unique stable resource distribution exists and calculate its moments for the class of affine linear growth policies. Moreover, we apply an asymptotic analysis to elucidate the conditions under which the stable distribution (when it exists) has a power-law tail. Finally, we use the results of this asymptotic analysis along with the moment equations to draw a stability phase diagram for the system that reveals the counterintuitive result that asymmetry serves to increase stability while at the same time widening the stable distribution. We also briefly discuss how cells can divide damaged proteins asymmetrically between their progeny as a form of damage control. In the appendixes, motivated by the asymmetric division of cell volume in Saccharomyces cerevisiae, we extend our results to the case wherein mother and daughter cells follow different growth policies.

Multistability and dynamic transitions of intracellular Min protein patterns

Cells owe their internal organization to self-organized protein patterns, which originate and adapt to growth and external stimuli via a process that is as complex as it is little understood. Here, we study the emergence, stability, and state transitions of multistable Min protein oscillation patterns in live Escherichia coli bacteria during growth up to defined large dimensions. De novo formation of patterns from homogenous starting conditions is observed and studied both experimentally and in simulations. A new theoretical approach is developed for probing pattern stability under perturbations. Quantitative experiments and simulations show that, once established, Min oscillations tolerate a large degree of intracellular heterogeneity, allowing distinctly different patterns to persist in different cells with the same geometry. Min patterns maintain their axes for hours in experiments, despite imperfections, expansion, and changes in cell shape during continuous cell growth. Transitions between multistable Min patterns are found to be rare events induced by strong intracellular perturbations. The instances of multistability studied here are the combined outcome of boundary growth and strongly nonlinear kinetics, which are characteristic of the reaction-diffusion patterns that pervade biology at many scales.

Shape dynamics of growing cell walls

We introduce a general theoretical framework to study the shape dynamics of actively growing and remodeling surfaces. Using this framework we develop a physical model for growing bacterial cell walls and study the interplay of cell shape with the dynamics of growth and constriction. The model allows us to derive constraints on cell wall mechanical energy based on the observed dynamics of cell shape. We predict that exponential growth in cell size requires a constant amount of cell wall energy to be dissipated per unit volume. We use the model to understand and contrast growth in bacteria with different shapes such as spherical, ellipsoidal, cylindrical and toroidal morphologies. Coupling growth to cell wall constriction, we predict a discontinuous shape transformation, from partial constriction to cell division, as a function of the chemical potential driving cell wall synthesis. Our model for cell wall energy and shape dynamics relates growth kinetics with cell geometry, and provides a unified framework to describe the interplay between shape, growth and division in bacterial cells.

In Vivo study of naturally deformed Escherichia coli bacteria

A combination of light-microscopy and image processing has been applied to study naturally deformed Escherichia coli under in vivo condition and at the order of sub-pixel high-resolution accuracy. To classify deflagellated non-dividing E. coli cells to the rod-shape and bent-shape, a geometrical approach has been applied. From the analysis of the geometrical data which were obtained of image processing, we estimated the required effective energy for shaping a rod-shape to a bent-shape with the same size. We evaluated the energy of deformation in the naturally deformed bacteria with minimum cell manipulation, under in vivo condition, and with minimum influence of any external force, torque and pressure. Finally, we have also elaborated on the possible scenario to explain how naturally deformed bacteria are formed from initial to final-stage.