Recent genetic and bioinformatic studies have led to the discovery that many bacterial species encode the genes required to produce sphingolipids. Shotgun lipidomic studies have identified numerous sphingolipid species with novel structures that do not exist in eukaryotic organisms. The impacts of these lipids on the biophysical properties of bacterial membranes have not yet been determined. In this study, we purify a novel anionic bacterial sphingolipid, ceramide phosphoglycerate (CPG), and investigate its effect on membrane zeta potential and bending stiffness. CPG and its precursor, ceramide 1-phosphate (C1P), are shown to increase the magnitude of the membrane zeta potential. These sphingolipids also increase the stiffness of these membranes, with CPG increasing rigidity more than C1P or ceramide. This work provides experimental and computational methods of lipid isolation and characterization that may be broadly applicable to a variety of uncharacterized bacterial sphingolipids.

Genetic screens are powerful approaches to unveiling new biological insight and ordered redundant transposon libraries have emerged as a primary tool for performing screens of known genetic saturation. Newer sequencing methods based on combinatorial pooling have lowered the cost and time required to generate these libraries. Caulobacter crescentus is a gramnegative bacterium that has served as a model for understanding bacterial physiology with a myriad of genetic tools. To add to this collection of tools, we created CauloKO - the first ordered, transposon library in C. crescentus. CauloKO includes insertion mutants in 86% of all non-essential genes and 77% of all open reading frames of strain CB15. CauloKO insertion mutants were validated using Sanger sequencing. We also present phenotypic analysis of the CauloKO library using a crystal violet screen for biofilm mutants, which both confirmed previous results and identified new mutants for future studies. This combined approach revealed that the CauloKO library shows promise for screening applications, particularly for phenotypes that require monoclonal populations of cells.

The crowded bacterial cytoplasm is composed of biomolecules that span several orders of magnitude in size and electrical charge. This complexity has been proposed as the source of the rich spatial organization and apparent anomalous diffusion of intracellular components, although this has not been tested directly. Here, we use biplane microscopy to track the 3D motion of self-assembled bacterial genetically encoded multimeric nanoparticles (bGEMs) with tunable size (20 to 50 nm) and charge (-3,240 to +2,700 e) in live Escherichia coli cells. To probe intermolecular details at spatial and temporal resolutions beyond experimental limits, we also developed a colloidal whole-cell model that explicitly represents the size and charge of cytoplasmic macromolecules and the porous structure of the bacterial nucleoid. Combining these techniques, we show that bGEMs spatially segregate by size, with small 20-nm particles enriched inside the nucleoid, and larger and/or positively charged particles excluded from this region. Localization is driven by entropic and electrostatic forces arising from cytoplasmic polydispersity, nucleoid structure, geometrical confinement, and interactions with other biomolecules including ribosomes and DNA. We observe that at the timescales of traditional single molecule tracking experiments, motion appears subdiffusive for all particle sizes and charges. However, using computer simulations with higher temporal resolution, we find that the apparent anomalous exponents are governed by the region of the cell in which bGEMs are located. Molecular motion does not display anomalous diffusion on short time scales and the apparent subdiffusion arises from geometrical confinement within the nucleoid and by the cell boundary.

The universally conserved α-oxoaldehydes glyoxal (GO) and methylglyoxal (MGO) are toxic metabolic byproducts whose accumulation can lead to cell death. In the absence of a known, natural inducer of the GO-specific response in prokaryotes, we exploited RNA-seq to define a GO response in the bacterial pathogen Pseudomonas aeruginosa. The highest upregulated operon consisted of the known glyoxalase (gloA2) and an antibiotic monooxygenase (ABM) domain of unknown function - renamed here Aldehyde responsive quorum-sensing Inhibitor (ArqI). The arqI-gloA2 operon is highly specific to GO induction and ArqI protein responds by migrating to the flagellar pole. An ArqI atomic structure revealed several unique features to the ABM family, including a 'pinwheel' hexamer harboring a GO-derived post-translational modification on a conserved arginine residue (Arg49). Induction of ArqI abrogates production of the Pseudomonas Quinolone Signal (PQS) quorum sensing molecule and was found to directly interact with PqsA; the first enzyme in the PQS biosynthesis pathway. Finally, we use a sepsis model of infection to reveal a survival requirement for arqI-gloA2 in blood-rich organs (heart, spleen, liver and lung). Here we define a global GO response in a pathogen, identify and characterize the first GO-specific operon and implicate its role in PQS production and host survival.

Understanding the mechanisms that dictate the localization of cytoskeletal filaments is crucial for elucidating cell shape regulation in prokaryotes. The actin homolog MreB plays a pivotal role in maintaining the shape of many rod-shaped bacteria such as Escherichia coli by directing cell-wall synthesis according to local curvature cues. However, the basis of MreB’s curvature-dependent localization has remained elusive. Here, we develop a biophysical model for the energetics of a filament binding to a surface that integrates the complex interplay between filament twist and bending and the two-dimensional surface geometry. Our model predicts that the spatial localization of a filament like MreB with substantial intrinsic twist is governed by both the mean and Gaussian curvatures of the cell envelope, which strongly covary in rod-shaped cells. Using molecular dynamics simulations to estimate the mechanical properties of MreB filaments, we show that their thermodynamic preference for regions with lower mean and Gaussian curvatures matches experimental observations for physiologically relevant filament lengths of ~50 nm. We find that the experimentally measured statistical curvature preference is maintained in the absence of filament motion and after a cycle of depolymerization, repolymerization, and membrane rebinding, indicating that equilibrium energetics can explain MreB localization. These findings provide critical insights into the physical principles underlying cytoskeletal filament localization and suggest design principles for synthetic shape-sensing nanomaterials.

Photoperiodic time measurement is the ability of plants and animals to measure differences in day versus night length (photoperiod) and use that information to anticipate critical seasonal transformations, such as annual temperature cycles. This timekeeping phenomenon triggers adaptive responses in higher organisms, such as gonadal stimulation, flowering, and hibernation. Unexpectedly, we observed this capability in cyanobacteria—unicellular prokaryotes with generation times as short as 5 to 6 hours. Cyanobacteria exposed to short, winter-like days developed enhanced resistance to cold mediated by desaturation of membrane lipids and differential programs of gene transcription, including stress response pathways. As in eukaryotes, this photoperiodic timekeeping required an intact circadian clockwork and developed over multiple cycles of photoperiod. Therefore, photoperiodic timekeeping evolved in much simpler organisms than previously appreciated and enabled genetic responses to stresses that recur seasonally.

Understanding the mechanisms that dictate the localization of cytoskeletal filaments is crucial for elucidating cell shape regulation in prokaryotes. The actin homolog MreB plays a pivotal role in maintaining the shape of many rod-shaped bacteria such as Escherichia coli by directing cell-wall synthesis according to local curvature cues. However, the basis of MreB's curvature-dependent localization has remained elusive. Here, we develop a biophysical model for the energetics of filament binding to a surface that integrates the complex interplay between filament twist and bending and the two-dimensional surface geometry. Our model predicts that the spatial localization of a filament like MreB with substantial intrinsic twist is governed by both the mean and Gaussian curvatures of the cell envelope, which strongly covary in rod-shaped cells. Using molecular dynamics simulations to estimate the mechanical properties of MreB filaments, we show that their thermodynamic preference for regions with lower mean and Gaussian curvatures matches experimental observations for physiologically relevant filament lengths of ∼50 nm. We find that the experimentally measured statistical curvature preference is maintained in the absence of filament motion and after a cycle of depolymerization, repolymerization, and membrane rebinding, indicating that equilibrium energetics can explain MreB localization. These findings provide critical insights into the physical principles underlying cytoskeletal filament localization, and suggest new design principles for synthetic shape sensing nanomaterials. Significance statement:The protein MreB, a homolog of eukaryotic actin, regulates the shape of bacteria like Escherichia coli by guiding new cell-wall insertion based on local curvature cues. However, the mechanism by which a nanometer-scale MreB filament "senses" the micron-scale curvature of the cell wall has remained a mystery. We introduce a biophysical model of the energetics of twisted and bent filaments bound to curved surfaces, which predicts that localization of filaments like MreB is sensitive to both mean and Gaussian curvature. The model captures experimentally measured curvature enrichment patterns and explains how MreB naturally localizes to saddle-shaped regions without energy-consuming processes. Beyond cell shape regulation, our work suggests design principles for synthetic systems that can sense and respond to surface shape.

Protein turnover is critical for proteostasis, but turnover quantification is challenging, and even in well-studied E. coli, proteome-wide measurements remain scarce. Here, we quantify the turnover rates of ~3200 E. coli proteins under 13 conditions by combining heavy isotope labeling with complement reporter ion quantification and find that cytoplasmic proteins are recycled when nitrogen is limited. We use knockout experiments to assign substrates to the known cytoplasmic ATP-dependent proteases. Surprisingly, none of these proteases are responsible for the observed cytoplasmic protein degradation in nitrogen limitation, suggesting that a major proteolysis pathway in E. coli remains to be discovered. Lastly, we show that protein degradation rates are generally independent of cell division rates. Thus, we present broadly applicable technology for protein turnover measurements and provide a rich resource for protein half-lives and protease substrates in E. coli, complementary to genomics data, that will allow researchers to study the control of proteostasis.

Fluctuating environments that consist of regular cycles of co-occurring stress are a common challenge faced by cellular populations. For a population to thrive in constantly changing conditions, an ability to coordinate a rapid cellular response is essential. Here, we identify a mutation conferring an arginine-to-histidine (Arg to His) substitution in the transcription terminator Rho. The rho R109H mutation frequently arose in Escherichia coli populations experimentally evolved under repeated long-term starvation conditions, during which the accumulation of metabolic waste followed by transfer into fresh media results in drastic environmental pH fluctuations associated with feast and famine. Metagenomic sequencing revealed that populations containing the rho mutation also possess putative loss-of-function mutations in ydcI , which encodes a recently characterized transcription factor associated with pH homeostasis. Genetic reconstructions of these mutations show that the rho allele confers plasticity via an alkaline-induced reduction of Rho function that, when found in tandem with a Δ ydcI allele, leads to intracellular alkalization and genetic assimilation of Rho mutant function. We further identify Arg to His substitutions at analogous sites in rho alleles from species that regularly experience neutral to alkaline pH fluctuations in their environments. Our results suggest that Arg to His substitutions in Rho may serve to rapidly coordinate complex physiological responses through pH sensing and shed light on how cellular populations use environmental cues to coordinate rapid responses to complex, fluctuating environments.

The shape a bacterial cell assumes is an essential component in its ability to interact with its physical environment. For many bacterial species, shape is genetically encoded in the action of a small number of cell shape determining proteins. These proteins guide the building of a rigid peptidoglycan cell wall of a given geometry. We use a computational imaging framework to reconstruct the 3D shape of individual cells from fluorescence microscopy images and determine where a secondary fluorescent probe is enriched. In the straight-rod bacterium Escherichia coli, the bacterial actin MreB is enriched in areas with low Gaussian curvature, avoiding the poles. Disrupting MreB's interactions with the transmembrane protein RodZ alters MreB's geometric localization and cells lose their characteristic rod-like morphology. In the helical-rod bacterium Helicobacter pylori, the bactofilin CcmA is preferentially enriched at regions of small positive Gaussian curvature along the outer or major helical axis. Disrupting CcmA interaction partners results in less CcmA on the membrane, altered geometric localization of CcmA, and loss of the characteristic helical morphology of cells. These results are consistent with a model of cell shape determination that includes proper geometric localization of bacterial cytoskeletal proteins.

A bstract Integrins are crucial for eukaryotic cell attachment and motility within the extracellular matrix (ECM) via focal-adhesion formation, with their evolutionary emergence important for the development of multicellularity. Intriguingly, single gliding cells of the predatory deltaproteobacterium Myxococcus xanthus form bacterial focal-adhesion (bFA) sites; therein, helically-trafficked motors become immobilized at anchored locations through Glt apparatus association with cell-surface integrin αI-domain-like adhesin CglB. Using traction-force, bead-force, and total internal reflection-fluorescence microscopies combined with biochemical approaches, we herein identify the von Willebrand A domain-containing cell-surface lipoprotein CglD to be a β-integrin-like outer-membrane lipoprotein that functionally associates with and anchors the trans-envelope Glt–CglB gliding apparatus, stabilizing and efficiently anchoring this assembly at bFAs. Calcium dependence governs CglD importance, consistent with its integrated ECM eukaryotic cartilage oligomeric matrix protein domains. CglD thus confers mechanosensory and mechanotransductory capabilities to the gliding apparatus, helping explain bFA-mediated trans-envelope force transduction, from inner-membrane-embedded motors to the cell surface.

The skin microbiome provides vital contributions to human health. However, the spatial organization and viability of its bacterial components remain unclear. Here, we apply culturing, imaging, and molecular approaches to human and mouse skin samples, and find that the skin surface is colonized by fewer viable bacteria than predicted by bacterial DNA levels. Instead, viable skin-associated bacteria are predominantly located in hair follicles and other cutaneous invaginations. Furthermore, we show that the skin microbiome has a uniquely low fraction of viable bacteria compared to other human microbiome sites, indicating that most bacterial DNA on the skin surface is not associated with viable cells Additionally, a small number of bacterial families dominate each skin site and traditional sequencing methods overestimate both the richness and diversity of the skin microbiome. Finally, we performed an in vivo skin microbiome perturbation-recovery study using human volunteers. Bacterial 16S rRNA gene sequencing revealed that, while the skin microbiome is remarkably stable even in the wake of aggressive perturbation, repopulation of the skin surface is driven by the underlying viable population. Our findings help explain the dynamics of skin microbiome perturbation as bacterial DNA on the skin surface can be transiently perturbed but is replenished by a stable underlying viable population. These results address multiple outstanding questions in skin microbiome biology with significant implications for future efforts to study and manipulate it.

The predatory deltaproteobacterium Myxococcus xanthus uses a helically-trafficked motor at bacterial focal-adhesion (bFA) sites to power gliding motility. Using total internal reflection fluorescence and force microscopies, we identify the von Willebrand A domain-containing outer-membrane (OM) lipoprotein CglB as an essential substratum-coupling adhesin of the gliding transducer (Glt) machinery at bFAs. Biochemical and genetic analyses reveal that CglB localizes to the cell surface independently of the Glt apparatus; once there, it is recruited by the OM module of the gliding machinery, a heteroligomeric complex containing the integral OM β barrels GltA, GltB, and GltH, as well as the OM protein GltC and OM lipoprotein GltK. This Glt OM platform mediates the cell-surface accessibility and retention of CglB by the Glt apparatus. Together, these data suggest that the gliding complex promotes regulated surface exposure of CglB at bFAs, thus explaining the manner by which contractile forces exerted by inner-membrane motors are transduced across the cell envelope to the substratum.

Chronic infection of the stomach with the bacterium Helicobacter pylori can cause gastric cancers and ulcers, and the helical shape of H. pylori cells promotes stomach colonization. A helical shape promoting protein complex includes peptidoglycan-hydrolases, a peptidoglycan precursor synthesis enzyme, non-enzymatic transmembrane proteins, and the cytoplasmic bactofilin CcmA. Bactofilins are highly conserved spontaneously polymerizing cytoskeletal proteins in bacteria. Using a combination of CcmA deletion analysis, in vitro polymerization, and in vivo co-immunoprecipitation experiments we show that the bactofilin domain and N-terminal region of CcmA are required for helical cell shape and the bactofilin domain is sufficient for polymerization and interactions with transmembrane proteins Csd5 and Csd7. The CcmA N-terminal region inhibits interaction with Csd7. Deletion of the N-terminal region of CcmA increases CcmA-Csd7 interactions and destabilizes the peptidoglycan-hydrolase Csd1. Using super-resolution microscopy, we found that Csd5 recruits CcmA to the cell envelope and promotes CcmA enrichment at the major helical axis. Thus, a combination of CcmA protein-protein and interpolymer interactions regulate CcmA localization and peptidoglycan-hydrolase stability to generate the helical shape of H. pylori cells.

Pseudomonas aeruginosa is a significant threat in healthcare settings where it deploys a wide host of virulence factors to cause disease. Many virulence-related phenotypes such as pyocyanin production, biofilm formation, and twitching motility have been implicated in causing disease in a number of hosts. In this study, we investigate these three virulence factors in a collection of 22 clinical strains isolated from blood stream infections. Despite the fact that all 22 strains caused disease and came from the same body site of different patients, they show significant variability in assays for each of the three specific phenotypes examined. There was no significant correlation between the strength of the three phenotypes across our collection, suggesting that they can be independently modulated. Furthermore, strains deficient in each of the virulence-associated phenotypes examined could be identified. To understand the genetic basis of this variability we sequenced the genomes of the 22 strains. We found that the majority of genes responsible for pyocyanin production, biofilm formation, and twitching motility were highly conserved among the strains despite their phenotypic variability, suggesting that the phenotypic variability is likely due to regulatory changes. Our findings thus demonstrate that no one lab-assayed phenotype of pyocyanin production, biofilm production, and twitching motility is necessary for a P. aeruginosa strain to cause blood stream infection and that additional factors may be needed to fully predict what strains will lead to specific human diseases.

The helical shape of Helicobacter pylori cells promotes robust stomach colonization; however, how the helical shape of H. pylori cells is determined is unresolved. Previous work identified helical-cell-shape-promoting protein complexes containing a peptidoglycan-hydrolase (Csd1), a peptidoglycan precursor synthesis enzyme (MurF), a non-enzymatic homolog of Csd1 (Csd2), non-enzymatic transmembrane proteins (Csd5 and Csd7), and a bactofilin (CcmA). Bactofilins are highly conserved, spontaneously polymerizing cytoskeletal bacterial proteins. We sought to understand CcmA’s function in generating the helical shape of H. pylori cells. Using CcmA deletion analysis, in vitro polymerization, and in vivo co-immunoprecipitation experiments, we identified that the bactofilin domain and N-terminal region of CcmA are required for helical cell shape and the bactofilin domain of CcmA is sufficient for polymerization and interactions with Csd5 and Csd7. We also found that CcmA’s N-terminal region inhibits interaction with Csd7. Deleting the N-terminal region of CcmA increases CcmA-Csd7 interactions and destabilizes the peptidoglycan-hydrolase Csd1. Using super-resolution microscopy, we found that Csd5 recruits CcmA to the cell envelope and promotes CcmA enrichment at the major helical axis. Thus, CcmA helps organize cell-shape-determining proteins and peptidoglycan synthesis machinery to coordinate cell wall modification and synthesis, promoting the curvature required to build a helical cell.

Bacterial species have diverse cell shapes that enable motility, colonization and virulence. The cell wall defines bacterial shape and is primarily built by two cytoskeleton-guided synthesis machines, the elongasome and the divisome. However, the mechanisms producing complex shapes, like the curved-rod shape of Vibrio cholerae , are incompletely defined. Previous studies have reported that species-specific regulation of cytoskeleton-guided machines enables formation of complex bacterial shapes such as cell curvature and cellular appendages. In contrast, we report that CrvA and CrvB are sufficient to induce complex cell shape autonomously of the cytoskeleton in V. cholerae . The autonomy of the CrvAB module also enables it to induce curvature in the Gram-negative species Escherichia coli , Pseudomonas aeruginosa , Caulobacter crescentus and Agrobacterium tumefaciens . Using inducible gene expression, quantitative microscopy and biochemistry, we show that CrvA and CrvB circumvent the need for patterning via cytoskeletal elements by regulating each other to form an asymmetrically localized, periplasmic structure that binds directly to the cell wall. The assembly and disassembly of this periplasmic structure enables dynamic changes in cell shape. Bioinformatics indicate that CrvA and CrvB may have diverged from a single ancestral hybrid protein. Using fusion experiments in V. cholerae , we find that a synthetic CrvA/B hybrid protein is sufficient to induce curvature on its own, but that expression of two distinct proteins, CrvA and CrvB, promotes more rapid curvature induction. We conclude that morphological complexity can arise independently of cell-shape specification by the core cytoskeleton-guided synthesis machines.

Article Figures and data Abstract Editor's evaluation eLife digest Introduction Results Discussion Materials and methods Appendix 1 Appendix 2 Data availability References Decision letter Author response Article and author information Metrics Abstract Collection of high-throughput data has become prevalent in biology. Large datasets allow the use of statistical constructs such as binning and linear regression to quantify relationships between variables and hypothesize underlying biological mechanisms based on it. We discuss several such examples in relation to single-cell data and cellular growth. In particular, we show instances where what appears to be ordinary use of these statistical methods leads to incorrect conclusions such as growth being non-exponential as opposed to exponential and vice versa. We propose that the data analysis and its interpretation should be done in the context of a generative model, if possible. In this way, the statistical methods can be validated either analytically or against synthetic data generated via the use of the model, leading to a consistent method for inferring biological mechanisms from data. On applying the validated methods of data analysis to infer cellular growth on our experimental data, we find the growth of length in E. coli to be non-exponential. Our analysis shows that in the later stages of the cell cycle the growth rate is faster than exponential. Editor's evaluation In this manuscript, the authors describe a generative model-based framework to better analyze stochastic growth data, including bacterial cell growth. They show how this framework can be applied to gain insight into the processes underlying these phenomena. This work is well-supported by simulations and data analysis and will likely be of interest to those trying to understand the processes governing bacterial growth, as well as those studying stochastic growth processes in biology more broadly. https://doi.org/10.7554/eLife.72565.sa0 Decision letter eLife's review process eLife digest All cells – from bacteria to humans – tightly control their size as they grow and divide. Cells can also change the speed at which they grow, and the pattern of how fast a cell grows with time is called ‘mode of growth’. Mode of growth can be ‘linear’, when cells increase their size at a constant rate, or ‘exponential’, when cells increase their size at a rate proportional to their current size. A cell’s mode of growth influences its inner workings, so identifying how a cell grows can reveal information about how a cell will behave. Scientists can measure the size of cells as they age and identify their mode of growth using single cell imaging techniques. Unfortunately, the statistical methods available to analyze the large amounts of data generated in these experiments can lead to incorrect conclusions. Specifically, Kar et al. found that scientists had been using specific types of plots to analyze growth data that were prone to these errors, and may lead to misinterpreting exponential growth as linear and vice versa. This discrepancy can be resolved by ensuring that the plots used to determine the mode of growth are adequate for this analysis. But how can the adequacy of a plot be tested? One way to do this is to generate synthetic data from a known model, which can have a specific and known mode of growth, and using this data to test the different plots. Kar et al. developed such a ‘generative model’ to produce synthetic data similar to the experimental data, and used these data to determine which plots are best suited to determine growth mode. Once they had validated the best statistical methods for studying mode of growth, Kar et al. applied these methods to growth data from the bacterium Escherichia coli. This showed that these cells have a form of growth called ‘super-exponential growth’. These findings identify a strategy to validate statistical methods used to analyze cell growth data. Furthermore, this strategy – the use of generative models to produce synthetic data to test the accuracy of statistical methods – could be used in other areas of biology to validate statistical approaches. Introduction The last decade has seen a tremendous increase in the availability of high-quality large datasets in biology, in particular in the context of single-cell level measurements. Such data are complementary to ‘bulk’ measurements made over a population of cells. They have led to new biological paradigms and motivated the development of quantitative models (Osella et al., 2017; Facchetti et al., 2017; Ho et al., 2018; Soifer et al., 2016; Jun et al., 2018; Amir and Balaban, 2018; Kohram et al., 2021). Nevertheless, they have also led to new challenges in data analysis, and here we will point out some of the pitfalls that exist in handling such data. In particular, we will show that the commonly used procedure of binning data and linear regression may hint at specific functional relations between the two variables plotted that are inconsistent with the true functional relations. As we shall show, this may come about due to the ‘hidden’ noise sources that affect the binning procedure and the phenomenon of ‘inspection bias’ where certain bins have biased contributions. One of our main take home messages is the significance of having an underlying model (or models) to guide/test/validate data analysis methods. The underlying model is referred to as a generative model in the sense that it leads to similar data to that observed in the experiments. The importance of a so-called generative model has been beautifully advocated in the context of astrophysical data analysis (Hogg et al., 2010), yet biology brings in a plethora of exciting differences: while in physics noise from measurement instruments often dominates, in the biological examples we will dwell on here it is the intrinsic biological noise that can obscure the mathematical relation between variables when not handled properly. In the following, we will illustrate this rather philosophical introduction on a concrete and fundamental example, albeit e pluribus unum. We will focus on the analysis of the Escherichia coli growth curves obtained via high throughput optical microscopy. Nevertheless we anticipate the conceptual points made here – and demonstrated on a particular example of interest – will translate to other types of measurements, which make use of microscopy but also beyond. Binning corresponds to grouping data based on the value of the x-axis variable, and finding the mean of the fluctuating y-axis variable for this group. By removing the fluctuations of the y-variable, the binning process often aims to expose the ‘true’ functional relation between the two variables which can be used to infer the underlying biological mechanism. While binning may provide a smooth non-linear relation between variables, linear regression is used to find a linear relationship between the variables. In addition to binning, we use the ordinary least squares regression where the slope and the intercept of the best linear fit line are obtained by minimizing the squared sum of the difference between the dependent variable raw data and the predicted value. Here, the best fit/the best linear fit is obtained using the raw data and not the binned data. Similar to binning, the assumption underlying linear regression is that our knowledge of x-axis variable is precise while the noise is in the y-axis variable. It is important to discuss the sources of fluctuations in the y-axis variable before we proceed. In biology, fluctuations in the variables arise inevitably from the intrinsic variability within a cell population. Cells growing in the same medium and environment have different characteristics (e.g. growth rate) due to the stochastic nature of biochemical reactions in the cell (Kiviet et al., 2014). For example, the division event is controlled by stochastic reactions, whose variability leads to cell dividing at a size smaller or larger than the mean. In this paper, when modeling the data, we will consider the intrinsic noise as the only source of variability and assume that the measurement error is much smaller than the intrinsic variation in the population. One example of the use of binning and linear regression is shown in Figure 1A where size at division (Ld) vs size at birth (Lb) is plotted using experimental data obtained by Tanouchi et al. for E. coli growing at 25 °C (Tanouchi et al., 2017). In Figure 1A, the functional relation between length at division and length at birth for E. coli is observed to be linear and close to Ld=Lb+Δ⁢L (see the Experimental data section for details). The relation obtained allows us to hypothesize a coarse-grained biological model known as the adder model as shown in Figure 1B in which the length at division is set by addition of length Δ⁢L from birth (Soifer et al., 2016; Harris and Theriot, 2016; Si et al., 2019; Amir, 2014; Campos et al., 2014; Taheri-Araghi et al., 2015; Eun et al., 2018). This previously discussed example demonstrates and reiterates the use of statistical analysis on single-cell data to understand the underlying cell regulation mechanisms. Using statistical methods such as binning and linear regression, other phenomenological models apart from adder have also been proposed in E. coli where the division length (Ld) is not directly ‘set’ by that at birth (Ho and Amir, 2015; Micali et al., 2018; Witz et al., 2019). The phenomenological models, in turn, can be related to mechanistic (molecular-level) models of cell size and cell cycle regulation (Barber et al., 2017). Recent work has shed light on the subtleties involved in interpreting the linear regression results for the Ld vs Lb plot where seemingly adder behavior in length can be obtained from a sizer model (division occurring on reaching a critical size) due to the interplay of multiple sources of variability (Facchetti et al., 2019). This issue is similar in spirit to those we highlight here. Figure 1 Download asset Open asset Utility of binning and linear regression. (A) Length at division (Ld) vs length at birth (Lb) is plotted using data obtained by Tanouchi et al., 2017. Raw data is shown as blue dots. We find the trend in binned data (red) to be linear with the underlying best linear fit (yellow) following the equation, Ld=1.09⁢Lb+2.24⁢μ⁢m. This is close to the adder behavior with an underlying equation given by Ld=Lb+Δ⁢L, where Δ⁢L is the mean size added between birth and division (shown as black dashed line). B. A schematic of the adder mechanism is shown where the cell grows over its generation time (Td) and divides after addition of length Δ⁢L from birth. This ensures cell size homeostasis in single cells. The volume growth of single bacterial cells has been typically assumed to be exponential (Godin et al., 2010; Wang et al., 2010; Campos et al., 2014; Cermak et al., 2016; Soifer et al., 2016; Iyer-Biswas et al., 2014). Assuming ribosomes to be the limiting component in translation, growth is predicted to be exponential and growth rate depends on the active ribosome content in the cell (Scott et al., 2010; Lin and Amir, 2018; Metzl-Raz et al., 2017). Under the assumption of exponential growth, the size at birth (Lb), the size at division (Ld), and the generation time (Td) are related to each other by, (1) ln⁡(LdLb)=λ⁢Td, where λ is the growth rate. Understanding the mode of growth is important for example, due to its potential effects on cell size homeostasis. Exponentially growing cells cannot employ a mechanism where they control division by timing a constant duration from birth but such a mechanism is possible in case of linear growth (Amir, 2014; Kafri et al., 2016; Ho et al., 2018). Linear regression performed on ln⁡(LdLb) vs ⟨λ⟩⁢Td plot, where ⟨λ⟩ is the mean growth rate, was used to infer the mode of growth in the archaeon H. salinarum (Eun et al., 2018), and in the bacteria M. smegmatis (Logsdon et al., 2017) and C. glutamicum (Messelink et al., 2020), for example. If the best linear fit follows the y = x trend, the resulting functional relation might point to growth being exponential. A corollary to this is the rejection of exponential growth when the slope and intercept of the best linear fit deviate from one and zero, respectively (Messelink et al., 2020). Thus, binning and linear regression applied on single-cell data appear to provide information about the underlying biology, in this case, the mode of cellular growth. We will test the validity of such inference by analyzing synthetic data generated using generative models. We find that linear regression performed on the plot ln⁡(LdLb) vs ⟨λ⟩⁢Td, surprisingly, does not provide information about the mode of growth. Nonetheless, we show that other methods of statistical analysis such as binning growth rate vs age plots are adequate in addressing the problem. Using these validated methods on experimental data, we find that E. coli grows non-exponentially. In later stages of the cell cycle, the growth rate is higher than that in early stages. Results Statistical methods like binning and linear regression should be interpreted based on a model To illustrate the pitfalls associated with binning, we use data from recent experiments on E. coli where the length at birth, the length at division and the generation time were obtained for multiple cells (see Experimental methods and [Tiruvadi-Krishnan et al., 2021]). Phase-contrast microscopy was used to obtain cell length at equal intervals of time. Note that we consider length to reflect cell size in this paper rather than other cell geometry characteristics such as surface area and volume. The length growth rate that we elucidate in the paper can be different from the cell volume growth rate as shown in Appendix 1 assuming a simple cell morphology and exponential growth. Using the same cell morphology, we also find the length growth rate to be identical to cell surface growth rate. To investigate if the cell growth was exponential, we plotted ln⁡(LdLb) vs ⟨λ⟩⁢Td for cells growing in M9 alanine minimal medium at 28 °C (⟨Td⟩ = 214 min). The linear regression of these data yields a slope of 0.3 and an intercept of 0.4 as shown in Figure 2A. The binned data and the best linear fit deviate significantly from the y = x line (see Supplementary file 1). Additionally, the binned data follows a non-linear trend and flattens out at longer generation times. We also found similar deviations in the binned data and best linear fit in glycerol medium (⟨Td⟩ = 164 min) shown in Figure 2—figure supplement 1A, and glucose-cas medium (⟨Td⟩ = 65 min) shown in Figure 2—figure supplement 1B. Qualitatively similar results have been recently obtained for another bacterium, C. glutamicum, in Messelink et al., 2020. These results might point to growth being non-exponential. Figure 2 with 2 supplements see all Download asset Open asset Plots that could potentially lead to misinterpreting exponential growth. (A, B) Data is obtained from experiments in M9 alanine medium (⟨Td⟩ = 214 min, N = 816 cells). (A) ln⁡(LdLb) vs ⟨λ⟩⁢Td plot is shown. The blue dots are the raw data, the red correspond to the binned data trend, the yellow line is the best linear fit obtained by performing linear regression on the raw data and the black dashed line is the y = x line. A priori, non-linear trend in binned data might point to growth being non-exponential. (B) ⟨λ⟩⁢Td vs ln⁡(LdLb) plot is shown for the same experiments. (C, D) Simulations of exponentially growing cells following the adder model are carried out for N = 2500 cells. The parameters used are provided in the Simulations section. (C) ln⁡(LdLb) vs ⟨λ⟩⁢Td plot is shown. The trend in binned data shown in red is non-linear and the best linear fit of raw data (yellow) deviates from the y = x line (black dashed line). The black dotted line is the expected trend obtained from theory (Equation 2). For parameters used in the simulations here, the black dotted line follows ln⁡(LdLb)=1.26⁢⟨λ⟩⁢Td-0.38⁢(⟨λ⟩⁢Td)2. (D) ⟨λ⟩⁢Td vs ln⁡(LdLb) plot is shown with binned data in red and the best linear fit on raw data in yellow closely following the expected trend of y = x line (black dashed line). The theoretical binned data trend (black dotted line) is expected to follow the y = x trend. In all of these plots, the binned data is shown only for those bins with more than 15 data points in them. Next, we will approach the same problem but with a generative model. We will first show that the ln⁡(LdLb) vs ⟨λ⟩⁢Td binned plot could not distinguish exponential growth from non-exponential growth. For that purpose, we use a previously studied model (Eun et al., 2018) which considers growth to be exponential with the growth rate distributed normally and independently between cell cycles with mean growth rate ⟨λ⟩ and standard deviation CVλ⟨λ⟩. CVλ is thus the coefficient of variation (CV) of the growth rate and is assumed to be small. To maintain a narrow distribution of cell size, cells must employ regulatory mechanisms. In our model, we assume that, barring the noise due to stochastic biochemical reactions, cells attempt to divide at a particular size Ld given size at birth Lb. Keeping the model as generic as possible, we can write Ld as a function of Lb, f(Lb) which can be thought of as a coarse-grained model for the regulatory mechanism. Amir, 2014 provides a framework to capture the regulatory mechanisms by choosing f(Lb) = 2 Lb1-α⁢L0α. L0 is the typical size at birth and α, which can take values between 0 and 2, reflects the strength of regulation strategy. α = 0 corresponds to the timer model where division occurs on average after a constant time from birth, and α = 1 is the sizer model where a cell divides upon reaching a critical size. α = 1/2 can be shown to be equivalent to the adder model where division is controlled by addition of constant size from birth (Amir, 2014). In addition to the deterministic function (f) specifying division, the size at division is affected by noise (ζ⟨λ⟩) in division timing. We assume it has a Gaussian distribution with mean zero and standard deviation σn⟨λ⟩ and that it is independent of the growth rate. Thus, the generation time (Td) can be mathematically written as Td=1λ⁢ln⁡(f⁢(Lb)Lb)+ζ⟨λ⟩ and is influenced by growth rate noise and division timing noise. Note that replacing the time additive division timing noise with a size additive division timing noise will not affect the results qualitatively (see ‘Model’ and ‘Exponential growth’ sections for details and Supplementary file 1 for variable definitions). For perfectly symmetrically dividing cells whose sizes are narrowly distributed, we find the trend in the binned data for ln⁡(LdLb) vs ⟨λ⟩Td plot to be (see section ‘Predicting the results of statistical constructs applied on ln⁡(LdLb) vs ⟨λ⟩Td and ⟨λ⟩Td vs ln⁡(LdLb)’), (2) y=x(1+1−xln⁡(2)1+22−ασn2CVλ2ln2⁡(2)). Fixing C⁢Vλ = σn = 0.15, we show using simulations in Figure 2C the non-linear trend in the binned data even though we assumed exponential growth. Similarly, on performing linear regression on the raw data of ln⁡(LdLb) vs ⟨λ⟩⁢Td plot, we find that the slope of the best linear fit is not equal to one and the intercept is non-zero (see Equation 27 and 28 and Figure 2C). Equation 2 shows that the trend in the binned data depends on the ratio of growth rate noise and division timing noise. The slope is equal to one and intercept is zero only if the noise in growth rate is negligible as compared to the division timing noise. In experiments that is rarely the case, hence, the binned data trend and the best linear fit deviate from the y = x line even though growth might be exponential. Thus, we cannot rule out exponential growth in the E. coli experiments despite the binned data trend being non-linear and the best-fit line deviating from the y = x line. Why does a non-linear relationship in the binned data for the plot ln⁡(LdLb) vs ⟨λ⟩⁢Td arise even for exponential growth? According to the model, Ld is determined by a deterministic strategy, f(Lb) and a time/size additive division timing noise. The noise component which affects Ld and subsequently the quantity ln⁡(LdLb) is thus the noise in division timing and not the growth rate. The generation time (Td) plotted on the x-axis is influenced by the noise in division timing as well as the noise in growth rate. Binning assumes that for a fixed value of the x-axis variable, the noise from other sources affects only the y-axis variable (the binned variable). Similarly for linear regression, the underlying assumption is that the independent variable on x-axis is precisely known while the dependent variable on the y-axis is influenced by the independent variable and from external factors other than the independent variable. In this case, only ⟨λ⟩⁢Td plotted on x-axis is influenced by growth rate noise while both ⟨λ⟩⁢Td and ln⁡(LdLb) are influenced by noise in division time. This does not fit the assumption for binning and linear regression and hence, the best linear fit for ln⁡(LdLb) vs ⟨λ⟩⁢Td plot might deviate from the y = x line even in the case of exponential growth. Another way of explaining the deviation from the linear y = x trend is by inspection bias, which arises when certain data is over-represented (Stein and Dattero, 2018). Cells which have a longer generation time than the mean will most likely have a slower growth rate. Thus, in Figure 2A and C, at larger values of ⟨λ⟩⁢Td or Td, the bin averages are biased by slower growing cells, thus making ln⁡(LdLb) or λ⁢Td to be lower than expected. This provides an explanation for the flattening of the trend. It follows from the previous discussion that if one bins data by ln⁡(LdLb) then the assumption for binning is met. Both of the variables ⟨λ⟩⁢Td and ln⁡(LdLb) are influenced by the noise in division time but ⟨λ⟩⁢Td plotted on the y-axis is also influenced by the growth rate noise. Thus, the y-axis variable, ⟨λ⟩⁢Td is determined by the x-axis variable, ln⁡(LdLb), and an external source of noise, in this case, the growth rate noise. Thus, based on our model, we expect the trend in binned data and linear regression performed on the interchanged axes to follow the y = x trend for exponentially growing cells (see section ‘Predicting the results of statistical constructs applied on ln⁡(LdLb) vs ⟨λ⟩Td and ⟨λ⟩Td vs ln⁡(LdLb)’). Indeed, on interchanging the axis and plotting ⟨λ⟩⁢Td vs ln⁡(LdLb) for synthetic data, we find that the trend in the binned data and the best linear fit closely follows the y = x line (Figure 2D). We also find that the best linear fit follows the y = x line in the case of alanine (Figure 2B), glycerol (Figure 2—figure supplement 1A) and glucose-cas (Figure 2—figure supplement 1B). A change from non-linear behavior to that of linear on interchanging the axes is also observed in a related problem where growth rate (λ) and inverse generation time (1Td) are considered (Figure 2—figure supplement 2 and Section ‘Interchanging axes in growth rate vs inverse generation time plot might lead to different interpretations’). Thus far, we showed for a range of models where birth controls division that the binned data trend for ln⁡(LdLb) as function of ⟨λ⟩⁢Td is non-linear and dependent on the noise ratio σnC⁢Vλ in the case of exponential growth. On interchanging the axes the binned data trend agrees with the y = x line independent of the growth rate and division time noise. However, we will show next that this agreement with the y = x trend cannot be used as a ‘smoking gun’ for inferring exponential growth from the data. To investigate this further, let us consider linear growth, which has also been suggested to be followed by E. coli cells (Mitchison, 2005; Abner et al., 2014). The underlying equation for linear growth is, (3) Ld-Lb=λ′⁢Td, where λ′ is the the elongation speed that is, d⁢Ld⁢t. For cells growing linearly, the best linear fit for the plot ⟨λ⟩⁢Td vs ln⁡(LdLb) is expected to deviate from the y = x line. As before, we fix ⟨λ⟩ to be the mean of 1Td⁢ln⁡(LdLb), agnostic of the linear mode of growth. Surprisingly, we found that for the class of models where birth controls division by a strategy f(Lb) and cells grow linearly, the best linear fit for ⟨λ⟩⁢Td vs ln⁡(LdLb) agrees closely with the y = x trend. On carrying out analytical calculations based on this model, we obtain the slope and the intercept of the ⟨λ⟩⁢Td vs ln⁡(LdLb) plot to be 32⁢ln⁡(2)≈ 1.04 and –0.03 respectively, which is very close to that for exponential growth (see section ‘Differentiating linear from exponential growth’). This is shown for simulations of linear growth with cells following an adder model in Figure 3A. Given no information about the underlying model, Figure 3A could be interpreted as cells undergoing exponential growth contrary to the assumption of linear growth in simulations. Thus, when handling experimental data, cells undergoing either exponential or linear growth might seem to agree closely with the y = x trend. Deforet et al., 2015 used the linear binned data trend in case of ⟨λ⟩⁢Td vs ln⁡(LdLb) plot to infer exponential growth but as we showed in this section, the linear trend does not rule out linear growth. This again reiterates our message of having a generative model to guide the data analysis methods such as binning and linear regression. For completeness, we also test the utility of ln⁡(LdLb) vs ⟨Td⟩⁢λ and its interchanged axes plots to elucidate the mode of growth (Appendix 2). We find that binning and linear regression applied on these plots can not differentiate between exponential and linear growth. Figure 3 with 3 supplements see all Download asset Open asset Differentiating linear growth from exponential growth. (A) ⟨λ⟩Td vs ln⁡(LdLb) plot is shown for simulations of linearly growing cells following the adder model for N = 2500 cell cycles. The binned data (red) and the best linear fit on raw data (yellow) closely follows the y = x trend (black dashed line) which could be incorrectly interpreted as cells undergoing exponential growth. (B) The binned data trend for growth rate vs age plot is shown as purple circles for simulations of N = 2500 cell cycles of exponentially growing cells following the adder model. We observe the trend to be nearly constant as expected for exponential growth (purple dotted line). Since the growth rate is fixed at the beginning of each cell cycle in the above simulations, we do not show error bars for each bin within the cell cycle. Also shown as green squares is the growth rate vs age plot for simulations of N = 2500 cell cycles of linearly growing cells following the adder model. As expected for linear growth, the binned growth rate decreases with age as λ∝11+a⁢g⁢e (green dotted line). The binned growth rate trend (shown as magenta diamonds) is also found to be nearly constant as expected (shown as magenta dotted line) for the simulations of exponentially growing cells following the adder per origin model. We also show that the binned growth rate trend (red triangles) increases for simulations of the adder model with the cells undergoing faster than exponential growth. The trend is in agreement with the underlying growth rate function (shown as red dotted line) used in the simulations of super-exponential growth. Thus, the plot growth rate vs age provides a consistent method to identify the mode of growth. Parameters used in the above simulations of exponential, linear and super-exponential growth are derived from the experimental data in alanine medium. Details are provided in the Simulations section. To conclude the discussion of linear growth, we note that the natural plot for this growth regime is ⟨λl⁢i⁢n⟩⁢Td vs ld-lb and the plot obtained on interchanging the axes (see the Linear growth section and Figure 3—figure supplement 1A and B). Here lb, ld and λl⁢i⁢n are defined to be quantities Lb, Ld and λ′, respectively, normalized by the mean length at birth. For cells growing exponentially, the best linear fit for the ⟨λl⁢i⁢n⟩⁢Td vs ld-lb plot is expected to deviate from the y = x line. This is indeed what is observed in Figure 3—figure supplement 1 where simulations of exponentially growing cells following the adder model are presented (see ‘Differentiating linear from exponential growth’ for extended discussion). In all the cases above, the problem at hand deals with distilling the biologically relevant functional relation between two variables. However, the data is assumed to be subjected to fluctuations of various sources, and it is important to ensure that the statistical construct we are using (e.g. binning) is robust to these. How can we know a priori whether the statistical method is appropriate and a ‘smoking gun’ for the functional relation we are conjecturing? The examples shown above suggest that performing statistical tests on synthetic data obtained using a generative model is a convenient and powerful approach. Note that in cases such as the ones studied here where analytical calculations may be performed, one may not even need to perform any numerical simulations to test the validity of the methods. Growth rate vs age plots are consistent with the underlying growth mode In the last section, we showed that the plots ln⁡(LdLb) vs ⟨λ⟩⁢Td and ⟨λ⟩⁢Td vs ln⁡(LdLb) are not decisive in identifying the mode of growth. Recent works on B. subtilis (Nordholt et al., 2020) and fission yeast (Knapp et al., 2019) have used differential methods of quantifying growth namely growth rate ( = 1L⁢d⁢Ld⁢t) vs age plots and elongation speed (=d⁢Ld⁢t) vs age plots to probe the mode of growth within a cell cycle. Here, L denotes the size of the cell after time t from birth in the cell cycle and age denotes the ratio of time t to Td within a

Pseudomonas aeruginosa is a significant threat in both healthcare and industrial biofouling. Surface attachment of P. aeruginosa is particularly problematic as surface association induces virulence and is necessary for the ensuing process of biofilm formation, which hampers antibiotic treatments. Previous efforts have searched for dispersal agents of mature biofilm collectives, but there are no known factors that specifically disperse individual surface-attached P. aeruginosa. In this study, we develop a quantitative single-cell surface-dispersal assay and use it to show that P. aeruginosa itself produces factors that can stimulate its dispersal. Through bioactivity-guided fractionation, mass spectrometry, and nuclear magnetic resonance, we elucidated the structure of one such factor, 2-methyl-4-hydroxyquinoline (MHQ). MHQ is an alkyl quinolone with a previously unknown activity and is synthesized by the PqsABC enzymes. Pure MHQ is sufficient to disperse P. aeruginosa, but the dispersal activity of natural P. aeruginosa conditioned media requires additional factors. Whereas other alkyl quinolones have been shown to act as antibiotics or membrane depolarizers, MHQ lacks these activities and known antibiotics do not induce dispersal. In contrast, we show that MHQ inhibits the activity of Type IV Pili (TFP) and that TFP targeting can explain its dispersal activity. Our work thus identifies single-cell surface dispersal as a new activity of P. aeruginosa-produced small molecules, characterizes MHQ as a promising dispersal agent, and establishes TFP inhibition as a viable mechanism for P. aeruginosa dispersal.