Length control emerges from cytoskeletal network geometry.

Many cytoskeletal networks consist of individual filaments that are organized into elaborate higher-order structures. While it is appreciated that the size and architecture of these networks are critical for their biological functions, much of the work investigating control over their assembly has focused on mechanisms that regulate the turnover of individual filaments through size-dependent feedback. Here, we propose a very different, feedback-independent mechanism to explain how yeast cells control the length of their actin cables. Our findings, supported by quantitative cell imaging and mathematical modeling, indicate that actin cable length control is an emergent property that arises from the cross-linked and bundled organization of the filaments within the cable. Using this model, we further dissect the mechanisms that allow cables to grow longer in larger cells and propose that cell length-dependent tuning of formin activity allows cells to scale cable length with cell length. This mechanism is a significant departure from prior models of cytoskeletal filament length control and presents a different paradigm to consider how cells control the size, shape, and dynamics of higher-order cytoskeletal structures.

Recycling of bacterial RNA polymerase by the Swi2/Snf2 ATPase RapA.

Free-living bacteria have regulatory systems that can quickly reprogram gene transcription in response to changes in the cellular environment. The RapA ATPase, a prokaryotic homolog of the eukaryotic Swi2/Snf2 chromatin remodeling complex, may facilitate such reprogramming, but the mechanisms by which it does so are unclear. We used multiwavelength single-molecule fluorescence microscopy in vitro to examine RapA function in the Escherichia coli transcription cycle. In our experiments, RapA at <5 nM concentration did not appear to alter transcription initiation, elongation, or intrinsic termination. Instead, we directly observed a single RapA molecule bind specifically to the kinetically stable post termination complex (PTC)-consisting of core RNA polymerase (RNAP)-bound sequence nonspecifically to double-stranded DNA-and efficiently remove RNAP from DNA within seconds in an ATP-hydrolysis-dependent reaction. Kinetic analysis elucidates the process through which RapA locates the PTC and the key mechanistic intermediates that bind and hydrolyze ATP. This study defines how RapA participates in the transcription cycle between termination and initiation and suggests that RapA helps set the balance between global RNAP recycling and local transcription reinitiation in proteobacterial genomes.

RNA polymerase sliding on DNA can couple the transcription of nearby bacterial operons.

DNA transcription initiates after an RNA polymerase (RNAP) molecule binds to the promoter of a gene. In bacteria, the canonical picture is that RNAP comes from the cytoplasmic pool of freely diffusing RNAP molecules. Recent experiments suggest the possible existence of a separate pool of polymerases, competent for initiation, which freely slide on the DNA after having terminated one round of transcription. Promoter-dependent transcription reinitiation from this pool of posttermination RNAP may lead to coupled initiation at nearby operons, but it is unclear whether this can occur over the distance and timescales needed for it to function widely on a bacterial genome in vivo. Here, we mathematically model the hypothesized reinitiation mechanism as a diffusion-to-capture process and compute the distances over which significant interoperon coupling can occur and the time required. These quantities depend on molecular association and dissociation rate constants between DNA, RNAP, and the transcription initiation factor σ70; we measure these rate constants using single-molecule experiments in vitro. Our combined theory/experimental results demonstrate that efficient coupling can occur at physiologically relevant σ70 concentrations and on timescales appropriate for transcript synthesis. Coupling is efficient over terminator-promoter distances up to ∼1,000 bp, which includes the majority of terminator-promoter nearest neighbor pairs in the Escherichia coli genome. The results suggest a generalized mechanism that couples the transcription of nearby operons and breaks the paradigm that each binding of RNAP to DNA can produce at most one messenger RNA.

Yeast ATM and ATR kinases use different mechanisms to spread histone H2A phosphorylation around a DNA double-strand break.

One of the hallmarks of DNA damage is the rapid spreading of phosphorylated histone H2A (γ-H2AX) around a DNA double-strand break (DSB). In the budding yeast Saccharomyces cerevisiae, nearly all H2A isoforms can be phosphorylated, either by Mec1ATR or Tel1ATM checkpoint kinases. We induced a site-specific DSB with HO endonuclease at the MAT locus on chromosome III and monitored the formation of γ-H2AX by chromatin immunoprecipitation (ChIP)-qPCR in order to uncover the mechanisms by which Mec1ATR and Tel1ATM propagate histone modifications across chromatin. With either kinase, γ-H2AX spreads as far as ∼50 kb on both sides of the lesion within 1 h; but the kinetics and distribution of modification around the DSB are significantly different. The total accumulation of phosphorylation is reduced by about half when either of the two H2A genes is mutated to the nonphosphorylatable S129A allele. Mec1 activity is limited by the abundance of its ATRIP partner, Ddc2. Moreover, Mec1 is more efficient than Tel1 at phosphorylating chromatin in trans-at distant undamaged sites that are brought into physical proximity to the DSB. We compared experimental data to mathematical models of spreading mechanisms to determine whether the kinases search for target nucleosomes by primarily moving in three dimensions through the nucleoplasm or in one dimension along the chromatin. Bayesian model selection indicates that Mec1 primarily uses a three-dimensional diffusive mechanism, whereas Tel1 undergoes directed motion along the chromatin.

Non-genetic variability in microbial populations: survival strategy or nuisance?

The observation that phenotypic variability is ubiquitous in isogenic populations has led to a multitude of experimental and theoretical studies seeking to probe the causes and consequences of this variability. Whether it be in the context of antibiotic treatments or exponential growth in constant environments, non-genetic variability has significant effects on population dynamics. Here, we review research that elucidates the relationship between cell-to-cell variability and population dynamics. After summarizing the relevant experimental observations, we discuss models of bet-hedging and phenotypic switching. In the context of these models, we discuss how switching between phenotypes at the single-cell level can help populations survive in uncertain environments. Next, we review more fine-grained models of phenotypic variability where the relationship between single-cell growth rates, generation times and cell sizes is explicitly considered. Variability in these traits can have significant effects on the population dynamics, even in a constant environment. We show how these effects can be highly sensitive to the underlying model assumptions. We close by discussing a number of open questions, such as how environmental and intrinsic variability interact and what the role of non-genetic variability in evolutionary dynamics is.

Control of filament length by a depolymerizing gradient.

Cells assemble microns-long filamentous structures from protein monomers that are nanometers in size. These structures are often highly dynamic, yet in order for them to function properly, cells maintain them at a precise length. Here we investigate length-dependent depolymerization as a mechanism of length control. This mechanism has been recently proposed for flagellar length control in the single cell organisms Chlamydomonas and Giardia. Length dependent depolymerization can arise from a concentration gradient of a depolymerizing protein, such as kinesin-13 in Giardia, along the length of the flagellum. Two possible scenarios are considered: a linear and an exponential gradient of depolymerizing proteins. We compute analytically the probability distributions of filament lengths for both scenarios and show how these distributions are controlled by key biochemical parameters through a dimensionless number that we identify. In Chlamydomonas cells, the assembly dynamics of its two flagella are coupled via a shared pool of molecular components that are in limited supply, and so we investigate the effect of a limiting monomer pool on the length distributions. Finally, we compare our calculations to experiments. While the computed mean lengths are consistent with observations, the noise is two orders of magnitude smaller than the observed length fluctuations.

Chromosome-refolding model of mating-type switching in yeast.

Chromosomes are folded into cells in a nonrandom fashion, with particular genetic loci occupying distinct spatial regions. This observation raises the question of whether the spatial organization of a chromosome governs its functions, such as recombination or transcription. We consider this general question in the specific context of mating-type switching in budding yeast, which is a model system for homologous recombination. Mating-type switching is induced by a DNA double-strand break (DSB) at the MAT locus on chromosome III, followed by homologous recombination between the cut MAT locus and one of two donor loci (HMLα and HMRa), located on the same chromosome. Previous studies have suggested that in MATa cells after the DSB is induced chromosome III undergoes refolding, which directs the MAT locus to recombine with HMLα. Here, we propose a quantitative model of mating-type switching predicated on the assumption of DSB-induced chromosome refolding, which also takes into account the previously measured stochastic dynamics and polymer nature of yeast chromosomes. Using quantitative fluorescence microscopy, we measure changes in the distance between the donor (HMLα) and MAT loci after the DSB and find agreement with the theory. Predictions of the theory also agree with measurements of changes in the use of HMLα as the donor, when we perturb the refolding of chromosome III. These results establish refolding of yeast chromosome III as a key driving force in MAT switching and provide an example of a cell regulating the spatial organization of its chromosome so as to direct homology search during recombination.

Bacterial RNA polymerase can retain σ70 throughout transcription.

Production of a messenger RNA proceeds through sequential stages of transcription initiation and transcript elongation and termination. During each of these stages, RNA polymerase (RNAP) function is regulated by RNAP-associated protein factors. In bacteria, RNAP-associated σ factors are strictly required for promoter recognition and have historically been regarded as dedicated initiation factors. However, the primary σ factor in Escherichia coli, σ(70), can remain associated with RNAP during the transition from initiation to elongation, influencing events that occur after initiation. Quantitative studies on the extent of σ(70) retention have been limited to complexes halted during early elongation. Here, we used multiwavelength single-molecule fluorescence-colocalization microscopy to observe the σ(70)-RNAP complex during initiation from the λ PR' promoter and throughout the elongation of a long (>2,000-nt) transcript. Our results provide direct measurements of the fraction of actively transcribing complexes with bound σ(70) and the kinetics of σ(70) release from actively transcribing complexes. σ(70) release from mature elongation complexes was slow (0.0038 s(-1)); a substantial subpopulation of elongation complexes retained σ(70) throughout transcript elongation, and this fraction depended on the sequence of the initially transcribed region. We also show that elongation complexes containing σ(70) manifest enhanced recognition of a promoter-like pause element positioned hundreds of nucleotides downstream of the promoter. Together, the results provide a quantitative framework for understanding the postinitiation roles of σ(70) during transcription.

Distribution of Initiation Times Reveals Mechanisms of Transcriptional Regulation in Single Cells.

Transcription is the dominant point of control of gene expression. Biochemical studies have revealed key molecular components of transcription and their interactions, but the dynamics of transcription initiation in cells is still poorly understood. This state of affairs is being remedied with experiments that observe transcriptional dynamics in single cells using fluorescent reporters. Quantitative information about transcription initiation dynamics can also be extracted from experiments that use electron micrographs of RNA polymerases caught in the act of transcribing a gene (Miller spreads). Inspired by these data, we analyze a general stochastic model of transcription initiation and elongation and compute the distribution of transcription initiation times. We show that different mechanisms of initiation leave distinct signatures in the distribution of initiation times that can be compared to experiments. We analyze published data from micrographs of RNA polymerases transcribing ribosomal RNA genes in Escherichia coli and compare the observed distributions of interpolymerase distances with the predictions from previously hypothesized mechanisms for the regulation of these genes. Our analysis demonstrates the potential of measuring the distribution of time intervals between initiation events as a probe for dissecting mechanisms of transcription initiation in live cells.

Deciphering Transcriptional Dynamics In Vivo by Counting Nascent RNA Molecules.

Deciphering how the regulatory DNA sequence of a gene dictates its expression in response to intra and extracellular cues is one of the leading challenges in modern genomics. The development of novel single-cell sequencing and imaging techniques, as well as a better exploitation of currently available single-molecule imaging techniques, provides an avenue to interrogate the process of transcription and its dynamics in cells by quantifying the number of RNA polymerases engaged in the transcription of a gene (or equivalently the number of nascent RNAs) at a given moment in time. In this paper, we propose that measurements of the cell-to-cell variability in the number of nascent RNAs provide a mostly unexplored method for deciphering mechanisms of transcription initiation in cells. We propose a simple kinetic model of transcription initiation and elongation from which we calculate nascent RNA copy-number fluctuations. To demonstrate the usefulness of this approach, we test our theory against published nascent RNA data for twelve constitutively expressed yeast genes. Rather than transcription being initiated through a single rate limiting step, as it had been previously proposed, our single-cell analysis reveals the presence of at least two rate limiting steps. Surprisingly, half of the genes analyzed have nearly identical rates of transcription initiation, suggesting a common mechanism. Our analytical framework can be used to extract quantitative information about dynamics of transcription from single-cell sequencing data, as well as from single-molecule imaging and electron micrographs of fixed cells, and provides the mathematical means to exploit the quantitative power of these technologies.

Antenna Mechanism of Length Control of Actin Cables.

Actin cables are linear cytoskeletal structures that serve as tracks for myosin-based intracellular transport of vesicles and organelles in both yeast and mammalian cells. In a yeast cell undergoing budding, cables are in constant dynamic turnover yet some cables grow from the bud neck toward the back of the mother cell until their length roughly equals the diameter of the mother cell. This raises the question: how is the length of these cables controlled? Here we describe a novel molecular mechanism for cable length control inspired by recent experimental observations in cells. This "antenna mechanism" involves three key proteins: formins, which polymerize actin, Smy1 proteins, which bind formins and inhibit actin polymerization, and myosin motors, which deliver Smy1 to formins, leading to a length-dependent actin polymerization rate. We compute the probability distribution of cable lengths as a function of several experimentally tuneable parameters such as the formin-binding affinity of Smy1 and the concentration of myosin motors delivering Smy1. These results provide testable predictions of the antenna mechanism of actin-cable length control.

Mechanism of transcriptional repression at a bacterial promoter by analysis of single molecules.

The molecular basis for regulation of lactose metabolism in Escherichia coli is well studied. Nonetheless, the physical mechanism by which the Lac repressor protein prevents transcription of the lactose promoter remains unresolved. Using multi-wavelength single-molecule fluorescence microscopy, we visualized individual complexes of fluorescently tagged RNA polymerase holoenzyme bound to promoter DNA. Quantitative analysis of the single-molecule observations, including use of a novel statistical partitioning approach, reveals highly kinetically stable binding of polymerase to two different sites on the DNA, only one of which leads to transcription. Addition of Lac repressor directly demonstrates that bound repressor prevents the formation of transcriptionally productive open promoter complexes; discrepancies in earlier studies may be attributable to transcriptionally inactive polymerase binding. The single-molecule statistical partitioning approach is broadly applicable to elucidating mechanisms of regulatory systems including those that are kinetically rather than thermodynamically controlled.

Stochastic models of transcription: from single molecules to single cells.

Genes in prokaryotic and eukaryotic cells are typically regulated by complex promoters containing multiple binding sites for a variety of transcription factors leading to a specific functional dependence between regulatory inputs and transcriptional outputs. With increasing regularity, the transcriptional outputs from different promoters are being measured in quantitative detail in single-cell experiments thus providing the impetus for the development of quantitative models of transcription. We describe recent progress in developing models of transcriptional regulation that incorporate, to different degrees, the complexity of multi-state promoter dynamics, and its effect on the transcriptional outputs of single cells. The goal of these models is to predict the statistical properties of transcriptional outputs and characterize their variability in time and across a population of cells, as a function of the input concentrations of transcription factors. The interplay between mathematical models of different regulatory mechanisms and quantitative biophysical experiments holds the promise of elucidating the molecular-scale mechanisms of transcriptional regulation in cells, from bacteria to higher eukaryotes.

Ultrasensitivity of microtubule severing due to damage repair.

Microtubule-based cytoskeletal structures aid in cell motility, cell polarization, and intracellular transport. These functions require a coordinated effort of regulatory proteins which interact with microtubule cytoskeleton distinctively. In-vitro experiments have shown that free tubulin can repair nanoscale damages of microtubules created by severing proteins. Based on this observation, we theoretically analyze microtubule severing as a competition between the processes of damage spreading and tubulin-induced repair. We demonstrate that this model is in quantitative agreement with in-vitro experiments and predict the existence of a critical tubulin concentration above which severing becomes rare, fast, and sensitive to concentration of free tubulin. We show that this sensitivity leads to a dramatic increase in the dynamic range of steady-state microtubule lengths when the free tubulin concentration is varied, and microtubule lengths are controlled by severing. Our work demonstrates how synergy between tubulin and microtubule-associated proteins can bring about specific dynamical properties of microtubules.

Transcription templated assembly of the nucleolus in the C. elegans embryo.

The nucleolus is a multicomponent structure made of RNA and proteins that serves as the site of ribosome biogenesis within the nucleus. It has been extensively studied as a prototype of a biomolecular condensate whose assembly is driven by phase separation. While the steady-state size of the nucleolus is quantitatively accounted for by the thermodynamics of phase separation, we show that experimental measurements of the assembly dynamics are inconsistent with a simple model of a phase-separating system relaxing to its equilibrium state. Instead, we show that the dynamics are well described by a model in which the transcription of ribosomal RNA actively drives nucleolar assembly. We find that our model of active transcription-templated assembly quantitatively accounts for the rapid kinetics observed in early embryos at different developmental stages, and for different RNAi perturbations of embryo size. Our model predicts a scaling of the time to assembly with the volume of the nucleus to the one-third power, which is confirmed by experimental data. Our study highlights the role of active processes such as transcription in controlling the placement and timing of assembly of membraneless organelles.

Strong intranucleoid interactions organize the Escherichia coli chromosome into a nucleoid filament.

The stochasticity of chromosome organization was investigated by fluorescently labeling genetic loci in live Escherichia coli cells. In spite of the common assumption that the chromosome is well modeled by an unstructured polymer, measurements of the locus distributions reveal that the E. coli chromosome is precisely organized into a nucleoid filament with a linear order. Loci in the body of the nucleoid show a precision of positioning within the cell of better than 10% of the cell length. The precision of interlocus distance of genomically-proximate loci was better than 4% of the cell length. The measured dependence of the precision of interlocus distance on genomic distance singles out intranucleoid interactions as the mechanism responsible for chromosome organization. From the magnitude of the variance, we infer the existence of an as-yet uncharacterized higher-order DNA organization in bacteria. We demonstrate that both the stochastic and average structure of the nucleoid is captured by a fluctuating elastic filament model.

RNA polymerase sliding on DNA can couple the transcription of nearby bacterial operons.

DNA transcription initiates after an RNA polymerase (RNAP) molecule binds to the promoter of a gene. In bacteria, the canonical picture is that RNAP comes from the cytoplasmic pool of freely diffusing RNAP molecules. Recent experiments suggest the possible existence of a separate pool of polymerases, competent for initiation, which freely slide on the DNA after having terminated one round of transcription. Promoter-dependent transcription reinitiation from this pool of post-termination RNAP may lead to coupled initiation at nearby operons, but it is unclear whether this can occur over the distance- and time-scales needed for it to function widely on a bacterial genome in vivo. Here, we mathematically model the hypothesized reinitiation mechanism as a diffusion-to-capture process and compute the distances over which significant inter-operon coupling can occur and the time required. These quantities depend on previously uncharacterized molecular association and dissociation rate constants between DNA, RNAP and the transcription initiation factor σ 70 ; we measure these rate constants using single-molecule experiments in vitro. Our combined theory/experimental results demonstrate that efficient coupling can occur at physiologically relevant σ 70 concentrations and on timescales appropriate for transcript synthesis. Coupling is efficient over terminator-promoter distances up to ∼ 1, 000 bp, which includes the majority of terminator-promoter nearest neighbor pairs in the E. coli genome. The results suggest a generalized mechanism that couples the transcription of nearby operons and breaks the paradigm that each binding of RNAP to DNA can produce at most one messenger RNA. SIGNIFICANCE STATEMENT: After transcribing an operon, a bacterial RNA polymerase can stay bound to DNA, slide along it, and reini-tiate transcription of the same or a different operon. Quantitative single-molecule biophysics experiments combined with mathematical theory demonstrate that this reinitiation process can be quick and efficient over gene spacings typical of a bacterial genome. Reinitiation may provide a mechanism to orchestrate the transcriptional activities of groups of nearby operons.

Recycling of Bacterial RNA Polymerase by the Swi2/Snf2 ATPase RapA.

Free-living bacteria have regulatory systems that can quickly reprogram gene transcription in response to changes in cellular environment. The RapA ATPase, a prokaryotic homolog of the eukaryote Swi2/Snf2 chromatin remodeling complex, may facilitate such reprogramming, but the mechanisms by which it does so is unclear. We used multi-wavelength single-molecule fluorescence microscopy in vitro to examine RapA function in the E. coli transcription cycle. In our experiments, RapA at < 5 nM concentration did not appear to alter transcription initiation, elongation, or intrinsic termination. Instead, we directly observed a single RapA molecule bind specifically to the kinetically stable post-termination complex (PTC) -- consisting of core RNA polymerase (RNAP) bound to dsDNA -- and efficiently remove RNAP from DNA within seconds in an ATP-hydrolysis-dependent reaction. Kinetic analysis elucidates the process through which RapA locates the PTC and the key mechanistic intermediates that bind and hydrolyze ATP. This study defines how RapA participates in the transcription cycle between termination and initiation and suggests that RapA helps set the balance between global RNAP recycling and local transcription re-initiation in proteobacterial genomes. SIGNIFICANCE: RNA synthesis is an essential conduit of genetic information in all organisms. After transcribing an RNA, the bacterial RNA polymerase (RNAP) must be reused to make subsequent RNAs, but the steps that enable RNAP reuse are unclear. We directly observed the dynamics of individual molecules of fluorescently labeled RNAP and the enzyme RapA as they colocalized with DNA during and after RNA synthesis. Our studies show that RapA uses ATP hydrolysis to remove RNAP from DNA after the RNA is released from RNAP and reveal essential features of the mechanism by which this removal occurs. These studies fill in key missing pieces in our current understanding of the events that occur after RNA is released and that enable RNAP reuse.

Length control emerges from cytoskeletal network geometry.

Many cytoskeletal networks consist of individual filaments that are organized into elaborate higher order structures. While it is appreciated that the size and architecture of these networks are critical for their biological functions, much of the work investigating control over their assembly has focused on mechanisms that regulate the turnover of individual filaments through size-dependent feedback. Here, we propose a very different, feedback-independent mechanism to explain how yeast cells control the length of their actin cables. Our findings, supported by quantitative cell imaging and mathematical modeling, indicate that actin cable length control is an emergent property that arises from the cross-linked and bundled organization of the filaments within the cable. Using this model, we further dissect the mechanisms that allow cables to grow longer in larger cells, and propose that cell length-dependent tuning of formin activity allows cells to scale cable length with cell length. This mechanism is a significant departure from prior models of cytoskeletal filament length control and presents a new paradigm to consider how cells control the size, shape, and dynamics of higher order cytoskeletal structures.

Effect of promoter architecture on the cell-to-cell variability in gene expression.

According to recent experimental evidence, promoter architecture, defined by the number, strength and regulatory role of the operators that control transcription, plays a major role in determining the level of cell-to-cell variability in gene expression. These quantitative experiments call for a corresponding modeling effort that addresses the question of how changes in promoter architecture affect variability in gene expression in a systematic rather than case-by-case fashion. In this article we make such a systematic investigation, based on a microscopic model of gene regulation that incorporates stochastic effects. In particular, we show how operator strength and operator multiplicity affect this variability. We examine different modes of transcription factor binding to complex promoters (cooperative, independent, simultaneous) and how each of these affects the level of variability in transcriptional output from cell-to-cell. We propose that direct comparison between in vivo single-cell experiments and theoretical predictions for the moments of the probability distribution of mRNA number per cell can be used to test kinetic models of gene regulation. The emphasis of the discussion is on prokaryotic gene regulation, but our analysis can be extended to eukaryotic cells as well.