The multifork Escherichia coli chromosome is a self-duplicating and self-segregating thermodynamic ring polymer.

At all but the slowest growth rates, Escherichia coli cell cycles overlap, and its nucleoid is segregated to daughter cells as a forked DNA circle with replication ongoing-a state fundamentally different from eukaryotes. We have solved the chromosome organization, structural dynamics, and segregation of this constantly replicating chromosome. It is locally condensed to form a branched donut, compressed so that the least replicated DNA spans the cell center and the newest DNA extends toward the cell poles. Three narrow zones at the cell center and quarters contain both the replication forks and nascent DNA and serve to segregate the duplicated chromosomal information as it flows outward. The overall pattern is smoothly self-replicating, except when the duplicated terminus region is released from the septum and recoils to the center of a sister nucleoid. In circular cross-section of the cell, the left and right arms of the chromosome form separate, parallel structures that lie in each cell half along the radial cell axis. In contrast, replication forks and origin and terminus regions are found mostly at the center of the cross section, balanced by the parallel chromosome arms. The structure is consistent with the model in which the nucleoid is a constrained ring polymer that develops by spontaneous thermodynamics. The ring polymer pattern extrapolates to higher growth rates and also provides a structural basis for the form of the chromosome during very slow growth.

A Fundamental Unit of Cell Size in Bacteria.

A new study clarifies a relationship between growth, gene expression, and cell size in cyanobacteria. Quite unexpectedly, cyanobacteria and Escherichia coli appear to share an invariance principle to coordinate growth and chromosome replication. This principle allows quantitative predictions of cell size across a range of growth conditions in both organisms.

Synthesis and degradation of FtsZ quantitatively predict the first cell division in starved bacteria.

In natural environments, microbes are typically non-dividing and gauge when nutrients permit division. Current models are phenomenological and specific to nutrient-rich, exponentially growing cells, thus cannot predict the first division under limiting nutrient availability. To assess this regime, we supplied starving Escherichia coli with glucose pulses at increasing frequencies. Real-time metabolomics and microfluidic single-cell microscopy revealed unexpected, rapid protein, and nucleic acid synthesis already from minuscule glucose pulses in non-dividing cells. Additionally, the lag time to first division shortened as pulsing frequency increased. We pinpointed division timing and dependence on nutrient frequency to the changing abundance of the division protein FtsZ. A dynamic, mechanistic model quantitatively relates lag time to FtsZ synthesis from nutrient pulses and FtsZ protease-dependent degradation. Lag time changed in model-congruent manners, when we experimentally modulated the synthesis or degradation of FtsZ. Thus, limiting abundance of FtsZ can quantitatively predict timing of the first cell division.

Fundamental principles in bacterial physiology-history, recent progress, and the future with focus on cell size control: a review.

Bacterial physiology is a branch of biology that aims to understand overarching principles of cellular reproduction. Many important issues in bacterial physiology are inherently quantitative, and major contributors to the field have often brought together tools and ways of thinking from multiple disciplines. This article presents a comprehensive overview of major ideas and approaches developed since the early 20th century for anyone who is interested in the fundamental problems in bacterial physiology. This article is divided into two parts. In the first part (sections 1-3), we review the first 'golden era' of bacterial physiology from the 1940s to early 1970s and provide a complete list of major references from that period. In the second part (sections 4-7), we explain how the pioneering work from the first golden era has influenced various rediscoveries of general quantitative principles and significant further development in modern bacterial physiology. Specifically, section 4 presents the history and current progress of the 'adder' principle of cell size homeostasis. Section 5 discusses the implications of coarse-graining the cellular protein composition, and how the coarse-grained proteome 'sectors' re-balance under different growth conditions. Section 6 focuses on physiological invariants, and explains how they are the key to understanding the coordination between growth and the cell cycle underlying cell size control in steady-state growth. Section 7 overviews how the temporal organization of all the internal processes enables balanced growth. In the final section 8, we conclude by discussing the remaining challenges for the future in the field.

Bending forces plastically deform growing bacterial cell walls.

Cell walls define a cell's shape in bacteria. The walls are rigid to resist large internal pressures, but remarkably plastic to adapt to a wide range of external forces and geometric constraints. Currently, it is unknown how bacteria maintain their shape. In this paper, we develop experimental and theoretical approaches and show that mechanical stresses regulate bacterial cell wall growth. By applying a precisely controllable hydrodynamic force to growing rod-shaped Escherichia coli and Bacillus subtilis cells, we demonstrate that the cells can exhibit two fundamentally different modes of deformation. The cells behave like elastic rods when subjected to transient forces, but deform plastically when significant cell wall synthesis occurs while the force is applied. The deformed cells always recover their shape. The experimental results are in quantitative agreement with the predictions of the theory of dislocation-mediated growth. In particular, we find that a single dimensionless parameter, which depends on a combination of independently measured physical properties of the cell, can describe the cell's responses under various experimental conditions. These findings provide insight into how living cells robustly maintain their shape under varying physical environments.

Physical manipulation of the Escherichia coli chromosome reveals its soft nature.

Replicating bacterial chromosomes continuously demix from each other and segregate within a compact volume inside the cell called the nucleoid. Although many proteins involved in this process have been identified, the nature of the global forces that shape and segregate the chromosomes has remained unclear because of limited knowledge of the micromechanical properties of the chromosome. In this work, we demonstrate experimentally the fundamentally soft nature of the bacterial chromosome and the entropic forces that can compact it in a crowded intracellular environment. We developed a unique "micropiston" and measured the force-compression behavior of single Escherichia coli chromosomes in confinement. Our data show that forces on the order of 100 pN and free energies on the order of 10(5) k(B)T are sufficient to compress the chromosome to its in vivo size. For comparison, the pressure required to hold the chromosome at this size is a thousand-fold smaller than the surrounding turgor pressure inside the cell. Furthermore, by manipulation of molecular crowding conditions (entropic forces), we were able to observe in real time fast (approximately 10 s), abrupt, reversible, and repeatable compaction-decompaction cycles of individual chromosomes in confinement. In contrast, we observed much slower dissociation kinetics of a histone-like protein HU from the whole chromosome during its in vivo to in vitro transition. These results for the first time provide quantitative, experimental support for a physical model in which the bacterial chromosome behaves as a loaded entropic spring in vivo.

Tools and methods for high-throughput single-cell imaging with the mother machine.

Despite much progress, image processing remains a significant bottleneck for high-throughput analysis of microscopy data. One popular platform for single-cell time-lapse imaging is the mother machine, which enables long-term tracking of microbial cells under precisely controlled growth conditions. While several mother machine image analysis pipelines have been developed in the past several years, adoption by a non-expert audience remains a challenge. To fill this gap, we implemented our own software, MM3, as a plugin for the multidimensional image viewer napari. napari-MM3 is a complete and modular image analysis pipeline for mother machine data, which takes advantage of the high-level interactivity of napari. Here, we give an overview of napari-MM3 and test it against several well-designed and widely used image analysis pipelines, including BACMMAN and DeLTA. Researchers often analyze mother machine data with custom scripts using varied image analysis methods, but a quantitative comparison of the output of different pipelines has been lacking. To this end, we show that key single-cell physiological parameter correlations and distributions are robust to the choice of analysis method. However, we also find that small changes in thresholding parameters can systematically alter parameters extracted from single-cell imaging experiments. Moreover, we explicitly show that in deep learning-based segmentation, 'what you put is what you get' (WYPIWYG) - that is, pixel-level variation in training data for cell segmentation can propagate to the model output and bias spatial and temporal measurements. Finally, while the primary purpose of this work is to introduce the image analysis software that we have developed over the last decade in our lab, we also provide information for those who want to implement mother machine-based high-throughput imaging and analysis methods in their research.

Tools and methods for high-throughput single-cell imaging with the mother machine.

Despite much progress, image processing remains a significant bottleneck for high-throughput analysis of microscopy data. One popular platform for single-cell time-lapse imaging is the mother machine, which enables long-term tracking of microbial cells under precisely controlled growth conditions. While several mother machine image analysis pipelines have been developed in the past several years, adoption by a non-expert audience remains a challenge. To fill this gap, we implemented our own software, MM3, as a plugin for the multidimensional image viewer napari. napari-MM3 is a complete and modular image analysis pipeline for mother machine data, which takes advantage of the high-level interactivity of napari. Here, we give an overview of napari-MM3 and test it against several well-designed and widely-used image analysis pipelines, including BACMMAN and DeLTA. Researchers often analyze mother machine data with custom scripts using varied image analysis methods, but a quantitative comparison of the output of different pipelines has been lacking. To this end, we show that key single-cell physiological parameter correlations and distributions are robust to the choice of analysis method. However, we also find that small changes in thresholding parameters can systematically alter parameters extracted from single-cell imaging experiments. Moreover, we explicitly show that in deep learning based segmentation, "what you put is what you get" (WYPIWYG) - i.e., pixel-level variation in training data for cell segmentation can propagate to the model output and bias spatial and temporal measurements. Finally, while the primary purpose of this work is to introduce the image analysis software that we have developed over the last decade in our lab, we also provide information for those who want to implement mother-machine-based high-throughput imaging and analysis methods in their research.

Replication initiation in bacteria: precision control based on protein counting.

Balanced biosynthesis is the hallmark of bacterial cell physiology, where the concentrations of stable proteins remain steady. However, this poses a conceptual challenge to modeling the cell-cycle and cell-size controls in bacteria, as prevailing concentration-based eukaryote models are not directly applicable. In this study, we revisit and significantly extend the initiator-titration model, proposed thirty years ago, and explain how bacteria precisely and robustly control replication initiation based on the mechanism of protein copy-number sensing. Using a mean-field approach, we first derive an analytical expression of the cell size at initiation based on three biological mechanistic control parameters for an extended initiator-titration model. We also study the stability of our model analytically and show that initiation can become unstable in multifork replication conditions. Using simulations, we further show that the presence of the conversion between active and inactive initiator protein forms significantly represses initiation instability. Importantly, the two-step Poisson process set by the initiator titration step results in significantly improved initiation synchrony with CV~1/N scaling rather than the standard 1/N scaling in the Poisson process, where N is the total number of initiators required for initiation. Our results answer two long-standing questions in replication initiation: (1) Why do bacteria produce almost two orders of magnitude more DnaA, the master initiator proteins, than required for initiation? (2) Why does DnaA exist in active (DnaA-ATP) and inactive (DnaA-ADP) forms if only the active form is competent for initiation? The mechanism presented in this work provides a satisfying general solution to how the cell can achieve precision control without sensing protein concentrations, with broad implications from evolution to the design of synthetic cells.

Bacterial Replication Initiation as Precision Control by Protein Counting.

Balanced biosynthesis is the hallmark of bacterial cell physiology, where the concentrations of stable proteins remain steady. However, this poses a conceptual challenge to modeling the cell-cycle and cell-size controls in bacteria, as prevailing concentration-based eukaryote models are not directly applicable. In this study, we revisit and significantly extend the initiator-titration model, proposed 30 years ago, and we explain how bacteria precisely and robustly control replication initiation based on the mechanism of protein copy-number sensing. Using a mean-field approach, we first derive an analytical expression of the cell size at initiation based on three biological mechanistic control parameters for an extended initiator-titration model. We also study the stability of our model analytically and show that initiation can become unstable in multifork replication conditions. Using simulations, we further show that the presence of the conversion between active and inactive initiator protein forms significantly represses initiation instability. Importantly, the two-step Poisson process set by the initiator titration step results in significantly improved initiation synchrony with CV~1/N scaling rather than the standard 1/N scaling in the Poisson process, where N is the total number of initiators required for initiation. Our results answer two long-standing questions in replication initiation: (i) Why do bacteria produce almost two orders of magnitude more DnaA, the master initiator proteins, than required for initiation? (ii) Why does DnaA exist in active (DnaA-ATP) and inactive (DnaA-ADP) forms if only the active form is competent for initiation? The mechanism presented in this work provides a satisfying general solution to how the cell can achieve precision control without sensing protein concentrations, with broad implications from evolution to the design of synthetic cells.

Quantitative Examination of Five Stochastic Cell-Cycle and Cell-Size Control Models for Escherichia coli and Bacillus subtilis.

We examine five quantitative models of the cell-cycle and cell-size control in Escherichia coli and Bacillus subtilis that have been proposed over the last decade to explain single-cell experimental data generated with high-throughput methods. After presenting the statistical properties of these models, we test their predictions against experimental data. Based on simple calculations of the defining correlations in each model, we first dismiss the stochastic Helmstetter-Cooper model and the Initiation Adder model, and show that both the Replication Double Adder (RDA) and the Independent Double Adder (IDA) model are more consistent with the data than the other models. We then apply a recently proposed statistical analysis method and obtain that the IDA model is the most likely model of the cell cycle. By showing that the RDA model is fundamentally inconsistent with size convergence by the adder principle, we conclude that the IDA model is most consistent with the data and the biology of bacterial cell-cycle and cell-size control. Mechanistically, the Independent Adder Model is equivalent to two biological principles: (i) balanced biosynthesis of the cell-cycle proteins, and (ii) their accumulation to a respective threshold number to trigger initiation and division.

Self-avoiding polymer trapped inside a cylindrical pore: Flory free energy and unexpected dynamics.

We study the elastic and dynamic behavior of a self-avoiding chain confined inside a cylindrical pore using a Flory-type approach and molecular-dynamics simulations. In the Hookean regime, we find that the effective spring constant of the chain is given by keff approximately N(-1)D(-gamma), where N is the number of monomers and D the diameter of the pore. While the Flory approach reproduces the earlier scaling result gamma=1/3, our simulations confirm a more recent numerical result gamma approximately 0.9 for the computationally accessible regimes. In the absence of hydrodynamic interactions, the relaxation dynamics of a stretched-and-released chain in this regime is characterized by a global relaxation time tauR approximately N2Dgamma with the same exponent gamma for keff. We also discuss how chain relaxation under confinement is influenced by hydrodynamic interactions. In the presence (or absence) of the hydrodynamic interaction, the finite-size effect observed in keff is shown to persist in chain relaxation, resulting in tauR markedly different from previous results.

Control of Bacillus subtilis Replication Initiation during Physiological Transitions and Perturbations.

Bacillus subtilis and Escherichia coli are evolutionarily divergent model organisms whose analysis has enabled elucidation of fundamental differences between Gram-positive and Gram-negative bacteria, respectively. Despite their differences in cell cycle control at the molecular level, the two organisms follow the same phenomenological principle, known as the adder principle, for cell size homeostasis. We thus asked to what extent B. subtilis and E. coli share common physiological principles in coordinating growth and the cell cycle. We measured physiological parameters of B. subtilis under various steady-state growth conditions with and without translation inhibition at both the population and single-cell levels. These experiments revealed core physiological principles shared between B. subtilis and E. coli Specifically, both organisms maintain an invariant cell size per replication origin at initiation, under all steady-state conditions, and even during nutrient shifts at the single-cell level. Furthermore, the two organisms also inherit the same "hierarchy" of physiological parameters. On the basis of these findings, we suggest that the basic principles of coordination between growth and the cell cycle in bacteria may have been established early in evolutionary history.IMPORTANCE High-throughput, quantitative approaches have enabled the discovery of fundamental principles describing bacterial physiology. These principles provide a foundation for predicting the behavior of biological systems, a widely held aspiration. However, these approaches are often exclusively applied to the best-known model organism, E. coli In this report, we investigate to what extent quantitative principles discovered in Gram-negative E. coli are applicable to Gram-positive B. subtilis We found that these two extremely divergent bacterial species employ deeply similar strategies in order to coordinate growth, cell size, and the cell cycle. These similarities mean that the quantitative physiological principles described here can likely provide a beachhead for others who wish to understand additional, less-studied prokaryotes.

Mechanistic Origin of Cell-Size Control and Homeostasis in Bacteria.

Evolutionarily divergent bacteria share a common phenomenological strategy for cell-size homeostasis under steady-state conditions. In the presence of inherent physiological stochasticity, cells following this "adder" principle gradually return to their steady-state size by adding a constant volume between birth and division, regardless of their size at birth. However, the mechanism of the adder has been unknown despite intense efforts. In this work, we show that the adder is a direct consequence of two general processes in biology: (1) threshold-accumulation of initiators and precursors required for cell division to a respective fixed number-and (2) balanced biosynthesis-maintenance of their production proportional to volume growth. This mechanism is naturally robust to static growth inhibition but also allows us to "reprogram" cell-size homeostasis in a quantitatively predictive manner in both Gram-negative Escherichia coli and Gram-positive Bacillus subtilis. By generating dynamic oscillations in the concentration of the division protein FtsZ, we were able to oscillate cell size at division and systematically break the adder. In contrast, periodic induction of replication initiator protein DnaA caused oscillations in cell size at initiation but did not alter division size or the adder. Finally, we were able to restore the adder phenotype in slow-growing E. coli, the only known steady-state growth condition wherein E. coli significantly deviates from the adder, by repressing active degradation of division proteins. Together, these results show that cell division and replication initiation are independently controlled at the gene-expression level and that division processes exclusively drive cell-size homeostasis in bacteria. VIDEO ABSTRACT.

Cell Boundary Confinement Sets the Size and Position of the E. coli Chromosome.

Although the spatiotemporal structure of the genome is crucial to its biological function, many basic questions remain unanswered on the morphology and segregation of chromosomes. Here, we experimentally show in Escherichia coli that spatial confinement plays a dominant role in determining both the chromosome size and position. In non-dividing cells with lengths increased to 10 times normal, single chromosomes are observed to expand > 4-fold in size. Chromosomes show pronounced internal dynamics but exhibit a robust positioning where single nucleoids reside robustly at mid-cell, whereas two nucleoids self-organize at 1/4 and 3/4 positions. The cell-size-dependent expansion of the nucleoid is only modestly influenced by deletions of nucleoid-associated proteins, whereas osmotic manipulation experiments reveal a prominent role of molecular crowding. Molecular dynamics simulations with model chromosomes and crowders recapitulate the observed phenomena and highlight the role of entropic effects caused by confinement and molecular crowding in the spatial organization of the chromosome.

Time scale of entropic segregation of flexible polymers in confinement: implications for chromosome segregation in filamentous bacteria.

We report molecular dynamics simulations of the segregation of two overlapping chains in cylindrical confinement. We find that the entropic repulsion between chains can be sufficiently strong to cause segregation on a time scale that is short compared to the one for diffusion. This result implies that entropic driving forces are sufficiently strong to cause rapid bacterial chromosome segregation.

Isolation and Characterization of Bacterial Nucleoids in Microfluidic Devices.

We report methods for isolation of Escherichia coli nucleoids in microfluidic devices, allowing characterization of nucleoids during a controlled in vivo to in vitro transition. Biochemically, nucleoids are isolated by gentle osmotic lysis, which minimally perturbs nucleoid-associated proteins (NAPs). Biophysically, nucleoids are isolated in microfluidic chambers, which mimic confinement within the cell, as well as facilitate diffusive buffer exchange around nucleoids without subjecting them to flow. These methods can be used to characterize interactions between NAPs and whole nucleoids, and to investigate nucleoid structure and dynamics in confinement. We present protocols for isolation, quantification, and perturbation of nucleoids in microfluidic confinement.

Protocol for Construction of a Tunable CRISPR Interference (tCRISPRi) Strain for Escherichia coli.

We present a protocol for construction of tunable CRISPR interference (tCRISPRi) strains for Escherichia coli. The tCRISPRi system alleviates most of the known problems of plasmid-based expression methods, and can be immediately used to construct libraries of sgRNAs that can complement the Keio collection by targeting both essential and nonessential genes. Most importantly from a practical perspective, construction of tCRISPRi to target a new gene requires only one-step oligo recombineering. Additional advantages of tCRISPRi over other existing CRISPRi methods include: (1) tCRISPRi shows significantly less than 10% leaky repression; (2) tCRISPRi uses a tunable arabinose operon promoter and modifications in transporter genes to allow a wide dynamic range with graded control by arabinose inducer; (3) tCRISPRi is plasmid free and the entire system is integrated into the chromosome; (4) tCRISPRi strains show desirable physiological properties.