Protein overabundance is driven by growth robustness.

Protein expression levels optimize cell fitness: Too low an expression level of essential proteins will slow growth by compromising essential processes; whereas overexpression slows growth by increasing the metabolic load. This trade-off naïvely predicts that cells maximize their fitness by sufficiency, expressing just enough of each essential protein for function. We test this prediction in the naturally-competent bacterium Acinetobacter baylyi by characterizing the proliferation dynamics of essential-gene knockouts at a single-cell scale (by imaging) as well as at a genome-wide scale (by TFNseq). In these experiments, cells proliferate for multiple generations as target protein levels are diluted from their endogenous levels. This approach facilitates a proteome-scale analysis of protein overabundance. As predicted by the Robustness-Load Trade-Off (RLTO) model, we find that roughly 70% of essential proteins are overabundant and that overabundance increases as the expression level decreases, the signature prediction of the model. These results reveal that robustness plays a fundamental role in determining the expression levels of essential genes and that overabundance is a key mechanism for ensuring robust growth.

Noise robustness and metabolic load determine the principles of central dogma regulation.

The processes of gene expression are inherently stochastic, even for essential genes required for growth. How does the cell maximize fitness in light of noise? To answer this question, we build a mathematical model to explore the trade-off between metabolic load and growth robustness. The model provides insights for principles of central dogma regulation: Optimal protein expression levels for many genes are in vast overabundance. Essential genes are transcribed above a lower limit of one message per cell cycle. Gene expression is achieved by load balancing between transcription and translation. We present evidence that each of these regulatory principles is observed. These results reveal that robustness and metabolic load determine the global regulatory principles that govern gene expression processes, and these principles have broad implications for cellular function.

Noise robustness and metabolic load determine the principles of central dogma regulation.

The processes of gene expression are inherently stochastic, even for essential genes required for growth. How does the cell maximize fitness in light of noise? To answer this question, we build a mathematical model to explore the trade-off between metabolic load and growth robustness. The model predicts novel principles of central dogma regulation: Optimal protein expression levels for many genes are in vast overabundance. Essential genes are transcribed above a lower limit of one message per cell cycle. Gene expression is achieved by load balancing between transcription and translation. We present evidence that each of these novel regulatory principles is observed. These results reveal that robustness and metabolic load determine the global regulatory principles that govern central dogma processes, and these principles have broad implications for cellular function.

Noise robustness and metabolic load determine the principles of central dogma regulation.

The processes of gene expression are inherently stochastic, even for essential genes required for growth. How does the cell maximize fitness in light of noise? To answer this question, we build a mathematical model to explore the trade-off between metabolic load and growth robustness. The model predicts novel principles of central dogma regulation: Optimal protein expression levels for many genes are in vast overabundance. Essential genes are transcribed above a lower limit of one message per cell cycle. Gene expression is achieved by load balancing between transcription and translation. We present evidence that each of these novel regulatory principles is observed. These results reveal that robustness and metabolic load determine the global regulatory principles that govern central dogma processes, and these principles have broad implications for cellular function.

The one-message-per-cell-cycle rule: A conserved minimum transcription level for essential genes.

The inherent stochasticity of cellular processes leads to significant cell-to-cell variation in protein abundance. Although this noise has already been characterized and modeled, its broader implications and significance remain unclear. In this paper, we revisit the noise model and identify the number of messages transcribed per cell cycle as the critical determinant of noise. In yeast, we demonstrate that this quantity predicts the non-canonical scaling of noise with protein abundance, as well as quantitatively predicting its magnitude. We then hypothesize that growth robustness requires an upper ceiling on noise for the expression of essential genes, corresponding to a lower floor on the transcription level. We show that just such a floor exists: a minimum transcription level of one message per cell cycle is conserved between three model organisms: Escherichia coli, yeast, and human. Furthermore, all three organisms transcribe the same number of messages per gene, per cell cycle. This common transcriptional program reveals that robustness to noise plays a central role in determining the expression level of a large fraction of essential genes, and that this fundamental optimal strategy is conserved from E. coli to human cells.

The one-message-per-cell-cycle rule: A conserved minimum transcription level for essential genes.

The inherent stochasticity of cellular processes leads to significant cell-to-cell variation in protein abundance. Although this noise has already been characterized and modeled, its broader implications and significance remain unclear. In this paper, we revisit the noise model and identify the number of messages transcribed per cell cycle as the critical determinant of noise. In yeast, we demonstrate that this quantity predicts the non-canonical scaling of noise with protein abundance, as well as quantitatively predicting its magnitude. We then hypothesize that growth robustness requires an upper ceiling on noise for the expression of essential genes, corresponding to a lower floor on the transcription level. We show that just such a floor exists: a minimum transcription level of one message per cell cycle is conserved between three model organisms: Escherichia coli, yeast, and human. Furthermore, all three organisms transcribe the same number of messages per gene, per cell cycle. This common transcriptional program reveals that robustness to noise plays a central role in determining the expression level of a large fraction of essential genes, and that this fundamental optimal strategy is conserved from E. coli to human cells.

The in vivo measurement of replication fork velocity and pausing by lag-time analysis.

An important step towards understanding the mechanistic basis of the central dogma is the quantitative characterization of the dynamics of nucleic-acid-bound molecular motors in the context of the living cell. To capture these dynamics, we develop lag-time analysis, a method for measuring in vivo dynamics. Using this approach, we provide quantitative locus-specific measurements of fork velocity, in units of kilobases per second, as well as replisome pause durations, some with the precision of seconds. The measured fork velocity is observed to be both locus and time dependent, even in wild-type cells. In this work, we quantitatively characterize known phenomena, detect brief, locus-specific pauses at ribosomal DNA loci in wild-type cells, and observe temporal fork velocity oscillations in three highly-divergent bacterial species.

Omnipose: a high-precision morphology-independent solution for bacterial cell segmentation.

Advances in microscopy hold great promise for allowing quantitative and precise measurement of morphological and molecular phenomena at the single-cell level in bacteria; however, the potential of this approach is ultimately limited by the availability of methods to faithfully segment cells independent of their morphological or optical characteristics. Here, we present Omnipose, a deep neural network image-segmentation algorithm. Unique network outputs such as the gradient of the distance field allow Omnipose to accurately segment cells on which current algorithms, including its predecessor, Cellpose, produce errors. We show that Omnipose achieves unprecedented segmentation performance on mixed bacterial cultures, antibiotic-treated cells and cells of elongated or branched morphology. Furthermore, the benefits of Omnipose extend to non-bacterial subjects, varied imaging modalities and three-dimensional objects. Finally, we demonstrate the utility of Omnipose in the characterization of extreme morphological phenotypes that arise during interbacterial antagonism. Our results distinguish Omnipose as a powerful tool for characterizing diverse and arbitrarily shaped cell types from imaging data.

Genome-wide protein-DNA interaction site mapping in bacteria using a double-stranded DNA-specific cytosine deaminase.

DNA-protein interactions are central to fundamental cellular processes, yet widely implemented technologies for measuring these interactions on a genome scale in bacteria are laborious and capture only a snapshot of binding events. We devised a facile method for mapping DNA-protein interaction sites in vivo using the double-stranded DNA-specific cytosine deaminase toxin DddA. In 3D-seq (DddA-sequencing), strains containing DddA fused to a DNA-binding protein of interest accumulate characteristic mutations in DNA sequence adjacent to sites occupied by the DNA-bound fusion protein. High-depth sequencing enables detection of sites of increased mutation frequency in these strains, yielding genome-wide maps of DNA-protein interaction sites. We validated 3D-seq for four transcription regulators in two bacterial species, Pseudomonas aeruginosa and Escherichia coli. We show that 3D-seq offers ease of implementation, the ability to record binding event signatures over time and the capacity for single-cell resolution.

Characterizing stochastic cell-cycle dynamics in exponential growth.

Two powerful and complementary experimental approaches are commonly used to study the cell cycle and cell biology: One class of experiments characterizes the statistics (or demographics) of an unsynchronized exponentially growing population, while the other captures cell-cycle dynamics, either by time-lapse imaging of full cell cycles or in bulk experiments on synchronized populations. In this paper, we study the subtle relationship between observations in these two distinct experimental approaches. We begin with an existing model: A single-cell deterministic description of cell-cycle dynamics where cell states (i.e., periods or phases) have precise lifetimes. We then generalize this description to a stochastic model in which the states have stochastic lifetimes, as described by arbitrary probability distribution functions. Our analyses of the demographics of an exponential culture reveal a simple and exact correspondence between the deterministic and stochastic models: The corresponding state ages in the deterministic model are equal to the exponential mean of the age in the stochastic model. An important implication is therefore that the demographics of an exponential culture will be well fit by a deterministic model even if the state timing is stochastic. Although we explore the implications of the models in the context of the Escherichia coli cell cycle, we expect both the models as well as the significance of the exponential-mean lifetimes to find many applications in the quantitative analysis of cell-cycle dynamics in other biological systems.

An interbacterial DNA deaminase toxin directly mutagenizes surviving target populations.

When bacterial cells come in contact, antagonism mediated by the delivery of toxins frequently ensues. The potential for such encounters to have long-term beneficial consequences in recipient cells has not been investigated. Here, we examined the effects of intoxication by DddA, a cytosine deaminase delivered via the type VI secretion system (T6SS) of Burkholderia cenocepacia. Despite its killing potential, we observed that several bacterial species resist DddA and instead accumulate mutations. These mutations can lead to the acquisition of antibiotic resistance, indicating that even in the absence of killing, interbacterial antagonism can have profound consequences on target populations. Investigation of additional toxins from the deaminase superfamily revealed that mutagenic activity is a common feature of these proteins, including a representative we show targets single-stranded DNA and displays a markedly divergent structure. Our findings suggest that a surprising consequence of antagonistic interactions between bacteria could be the promotion of adaptation via the action of directly mutagenic toxins.

Correspondence between thermodynamics and inference.

We expand upon a natural analogy between Bayesian statistics and statistical physics in which sample size corresponds to inverse temperature. This analogy motivates the definition of two statistical quantities: a learning capacity and a Gibbs entropy. The analysis of the learning capacity, corresponding to the heat capacity in thermal physics, leads to insight into the mechanism of learning and explains why some models have anomalously high learning performance. We explore the properties of the learning capacity in a number of examples, including a sloppy model. Next, we propose that the Gibbs entropy provides a natural device for counting distinguishable distributions in the context of Bayesian inference. We use this device to define a generalized principle of indifference in which every distinguishable model is assigned equal a priori probability. This principle results in a solution to a long-standing problem in Bayesian inference: the definition of an objective or uninformative prior. A key characteristic of this approach is that it can be applied to analyses where the model dimension is unknown and circumvents the automatic rejection of higher-dimensional models in Bayesian inference.

Bifunctional Immunity Proteins Protect Bacteria against FtsZ-Targeting ADP-Ribosylating Toxins.

ADP-ribosylation of proteins can profoundly impact their function and serves as an effective mechanism by which bacterial toxins impair eukaryotic cell processes. Here, we report the discovery that bacteria also employ ADP-ribosylating toxins against each other during interspecies competition. We demonstrate that one such toxin from Serratia proteamaculans interrupts the division of competing cells by modifying the essential bacterial tubulin-like protein, FtsZ, adjacent to its protomer interface, blocking its capacity to polymerize. The structure of the toxin in complex with its immunity determinant revealed two distinct modes of inhibition: active site occlusion and enzymatic removal of ADP-ribose modifications. We show that each is sufficient to support toxin immunity; however, the latter additionally provides unprecedented broad protection against non-cognate ADP-ribosylating effectors. Our findings reveal how an interbacterial arms race has produced a unique solution for safeguarding the integrity of bacterial cell division machinery against inactivating post-translational modifications.

Strong disorder leads to scale invariance in complex biological systems.

Despite the innate complexity of the cell, emergent scale-invariant behavior is observed in many biological systems. We investigate one example of this phenomenon: the dynamics of large complexes in the bacterial cytoplasm. The observed dynamics of these complexes is scale invariant in three measures of dynamics: mean-squared displacement (MSD), velocity autocorrelation function, and the step-size distribution. To investigate the physical mechanism for this emergent scale invariance, we explore minimal models in which mobility is modeled as diffusion on a rough free-energy landscape in one dimension. We discover that all three scale-invariant characteristics emerge generically in the strong disorder limit. (Strong disorder is defined by the divergence of the ensemble-averaged hop time between lattice sites.) In particular, we demonstrate how the scale invariance of the relative step-size distribution can be understood from the perspective of extreme-value theory in statistics (EVT). We show that the Gumbel scale parameter is simply related to the MSD scaling parameter. The EVT mechanism of scale invariance is expected to be generic to strongly disordered systems and therefore a powerful tool for the analysis of other systems in biology and beyond.

The bacterial replisome has factory-like localization.

DNA replication is essential to cellular proliferation. The cellular-scale organization of the replication machinery (replisome) and the replicating chromosome has remained controversial. Two competing models describe the replication process: In the track model, the replisomes translocate along the DNA like a train on a track. Alternately, in the factory model, the replisomes form a stationary complex through which the DNA is pulled. We summarize the evidence for each model and discuss a number of confounding aspects that complicate interpretation of the observations. We advocate a factory-like model for bacterial replication where the replisomes form a relatively stationary and weakly associated complex that can transiently separate.

Type VI Secretion System Dynamics Reveals a Novel Secretion Mechanism in Pseudomonas aeruginosa.

The type VI secretion system (T6SS) inhibits the growth of neighboring bacterial cells through a contact-mediated mechanism. Here, we describe a detailed characterization of the protein localization dynamics in the Pseudomonas aeruginosa T6SS. It has been proposed that the type VI secretion process is driven by a conformational-change-induced contraction of the T6SS sheath. However, although the contraction of an optically resolvable TssBC sheath and the subsequent localization of ClpV are observed in Vibrio cholerae, coordinated assembly and disassembly of TssB and ClpV are observed without TssB contraction in P. aeruginosa These dynamics are inconsistent with the proposed contraction sheath model. Motivated by the phenomenon of dynamic instability, we propose a new model in which ATP hydrolysis, rather than conformational change, generates the force for secretion.IMPORTANCE The type VI secretion system (T6SS) is widely conserved among Gram-negative bacteria and is a central determinant of bacterial fitness in polymicrobial communities. The secretion system targets bacteria and secretes effectors that inhibit the growth of neighboring cells, using a contact-mediated-delivery system. Despite significant homology to the previously characterized Vibrio cholerae T6SS, our analysis reveals that effector secretion is driven by a distinct force generation mechanism in Pseudomonas aeruginosa The presence of two distinct force generation mechanisms in T6SS represents an example of the evolutionary diversification of force generation mechanisms.

Noise in a phosphorelay drives stochastic entry into sporulation in Bacillus subtilis.

Entry into sporulation in Bacillus subtilis is governed by a phosphorelay in which phosphoryl groups from a histidine kinase are successively transferred via relay proteins to the response regulator Spo0A. Spo0A~P, in turn, sets in motion events that lead to asymmetric division and activation of the cell-specific transcription factor σF, a hallmark for entry into sporulation. Here, we have used a microfluidics-based platform to investigate the activation of Spo0A and σF in individual cells held under constant, sporulation-inducing conditions. The principal conclusions were that: (i) activation of σF occurs with an approximately constant probability after adaptation to conditions of nutrient limitation; (ii) activation of σF is tightly correlated with, and preceded by, Spo0A~P reaching a high threshold level; (iii) activation of Spo0A takes place abruptly just prior to asymmetric division; and (iv) the primary source of noise in the activation of Spo0A is the phosphorelay. We propose that cells exhibit a constant probability of attaining a high threshold level of Spo0A~P due to fluctuations in the flux of phosphoryl groups through the phosphorelay.

The Replisomes Remain Spatially Proximal throughout the Cell Cycle in Bacteria.

The positioning of the DNA replication machinery (replisome) has been the subject of several studies. Two conflicting models for replisome localization have been proposed: In the Factory Model, sister replisomes remain spatially co-localized as the replicating DNA is translocated through a stationary replication factory. In the Track Model, sister replisomes translocate independently along a stationary DNA track and the replisomes are spatially separated for the majority of the cell cycle. Here, we used time-lapse imaging to observe and quantify the position of fluorescently labeled processivity-clamp (DnaN) complexes throughout the cell cycle in two highly-divergent bacterial model organisms: Bacillus subtilis and Escherichia coli. Because DnaN is a core component of the replication machinery, its localization patterns should be an appropriate proxy for replisome positioning in general. We present automated statistical analysis of DnaN positioning in large populations, which is essential due to the high degree of cell-to-cell variation. We find that both bacteria show remarkably similar DnaN positioning, where any potential separation of the two replication forks remains below the diffraction limit throughout the majority of the replication cycle. Additionally, the localization pattern of several other core replisome components is consistent with that of DnaN. These data altogether indicate that the two replication forks remain spatially co-localized and mostly function in close proximity throughout the replication cycle. The conservation of the observed localization patterns in these highly divergent species suggests that the subcellular positioning of the replisome is a functionally critical feature of DNA replication.

Transcription leads to pervasive replisome instability in bacteria.

The canonical model of DNA replication describes a highly-processive and largely continuous process by which the genome is duplicated. This continuous model is based upon in vitro reconstitution and in vivo ensemble experiments. Here, we characterize the replisome-complex stoichiometry and dynamics with single-molecule resolution in bacterial cells. Strikingly, the stoichiometries of the replicative helicase, DNA polymerase, and clamp loader complexes are consistent with the presence of only one active replisome in a significant fraction of cells (>40%). Furthermore, many of the observed complexes have short lifetimes (<8 min), suggesting that replisome disassembly is quite prevalent, possibly occurring several times per cell cycle. The instability of the replisome complex is conflict-induced: transcription inhibition stabilizes these complexes, restoring the second replisome in many of the cells. Our results suggest that, in contrast to the canonical model, DNA replication is a largely discontinuous process in vivo due to pervasive replication-transcription conflicts.

Cytoplasmic RNA-Protein Particles Exhibit Non-Gaussian Subdiffusive Behavior.

The cellular cytoplasm is a complex, heterogeneous environment (both spatially and temporally) that exhibits viscoelastic behavior. To further develop our quantitative insight into cellular transport, we analyze data sets of mRNA molecules fluorescently labeled with MS2-GFP tracked in real time in live Escherichia coli and Saccharomyces cerevisiae cells. As shown previously, these RNA-protein particles exhibit subdiffusive behavior that is viscoelastic in its origin. Examining the ensemble of particle displacements reveals a Laplace distribution at all observed timescales rather than the Gaussian distribution predicted by the central limit theorem. This ensemble non-Gaussian behavior is caused by a combination of an exponential distribution in the time-averaged diffusivities and non-Gaussian behavior of individual trajectories. We show that the non-Gaussian behavior is a consequence of significant heterogeneity between trajectories and dynamic heterogeneity along single trajectories. Informed by theory and simulation, our work provides an in-depth analysis of the complex diffusive behavior of RNA-protein particles in live cells.