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.

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.

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.

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.

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.

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.

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.

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.

Quantitative Analysis of Actin Cable Length in Yeast.

Polarized actin cables in S. cerevisiae are linear bundles of crosslinked actin filaments that are assembled by two formins, Bnr1 (localized to the bud neck), and Bni1 (localized to the bud tip). Actin is polymerized at these two sites, which results in cables extending along the cell cortex toward the back of the mother cell. These cables serve as polarized tracks for myosin-based transport of secretory vesicles and other cargo, from the mother cell to the growing daughter cell. Until recently, descriptions of actin cable morphology and architecture have largely been qualitative or descriptive in nature. Here, we introduce a new quantitative method that enables more precise characterization of actin cable length. This technological advance generates quantitative datasets that can be used to determine the contributions of different actin regulatory proteins to the maintenance of cable architecture, and to assess how different pharmacological agents affect cable arrays. Additionally, these datasets can be used to test theoretical models, and be compared to results from computational simulations of actin assembly. Graphical abstract: Illustration of actin cable length and morphology analysis. (A) Representative maximum intensity projection image of S. cerevisiae fixed and stained with fluorescently-conjugated phalloidin to label F-actin (displayed in color), and fluorescently-conjugated Concanavalin A to label the cell wall (displayed in grey scale). Lengths of actin cables traced from the bud neck to their ends are indicated (dashed lines). (B) Inverted grey scale image of F-actin labelled with fluorescently-conjugated phalloidin and the cell wall traced in black. The length (purple) and end-to-end distance (green) of a single actin cable is indicated. Scale bar, 2 µm. (C-E) Actin cable length (C), end-to-end distance (D), and tortuosity (E) from hypothetical datasets, where each data point represents an individual cable and larger symbols represent the mean from each hypothetical experiment. Error bars, 95% confidence intervals.

How to assemble a scale-invariant gradient.

Intracellular protein gradients serve a variety of functions, such as the establishment of cell polarity or to provide positional information for gene expression in developing embryos. Given that cell size in a population can vary considerably, for the protein gradients to work properly they often have to be scaled to the size of the cell. Here, we examine a model of protein gradient formation within a cell that relies on cytoplasmic diffusion and cortical transport of proteins toward a cell pole. We show that the shape of the protein gradient is determined solely by the cell geometry. Furthermore, we show that the length scale over which the protein concentration in the gradient varies is determined by the linear dimensions of the cell, independent of the diffusion constant or the transport speed. This gradient provides scale-invariant positional information within a cell, which can be used for assembly of intracellular structures whose size is scaled to the linear dimensions of the cell, such as the cytokinetic ring and actin cables in budding yeast cells.

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.

Fundamental limits on the rate of bacterial growth and their influence on proteomic composition.

Despite abundant measurements of bacterial growth rate, cell size, and protein content, we lack a rigorous understanding of what sets the scale of these quantities and when protein abundances should (or should not) depend on growth rate. Here, we estimate the basic requirements and physical constraints on steady-state growth by considering key processes in cellular physiology across a collection of Escherichia coli proteomic data covering ≈4,000 proteins and 36 growth rates. Our analysis suggests that cells are predominantly tuned for the task of cell doubling across a continuum of growth rates; specific processes do not limit growth rate or dictate cell size. We present a model of proteomic regulation as a function of nutrient supply that reconciles observed interdependences between protein synthesis, cell size, and growth rate and propose that a theoretical inability to parallelize ribosomal synthesis places a firm limit on the achievable growth rate. A record of this paper's transparent peer review process is included in the supplemental information.

Scaling of subcellular actin structures with cell length through decelerated growth.

How cells tune the size of their subcellular parts to scale with cell size is a fundamental question in cell biology. Until now, most studies on the size control of organelles and other subcellular structures have focused on scaling relationships with cell volume, which can be explained by limiting pool mechanisms. Here, we uncover a distinct scaling relationship with cell length rather than volume, revealed by mathematical modeling and quantitative imaging of yeast actin cables. The extension rate of cables decelerates as they approach the rear of the cell, until cable length matches cell length. Further, the deceleration rate scales with cell length. These observations are quantitatively explained by a 'balance-point' model, which stands in contrast to limiting pool mechanisms, and describes a distinct mode of self-assembly that senses the linear dimensions of the cell.

Analysis of biological noise in the flagellar length control system.

Any proposed mechanism for organelle size control should be able to account not only for average size but also for the variation in size. We analyzed cell-to-cell variation and within-cell variation of length for the two flagella in Chlamydomonas, finding that cell-to-cell variation is dominated by cell size, whereas within-cell variation results from dynamic fluctuations. Fluctuation analysis suggests tubulin assembly is not directly coupled with intraflagellar transport (IFT) and that the observed length fluctuations reflect tubulin assembly and disassembly events involving large numbers of tubulin dimers. Length variation is increased in long-flagella mutants, an effect consistent with theoretical models for flagellar length regulation. Cells with unequal flagellar lengths show impaired swimming but improved gliding, raising the possibility that cells have evolved mechanisms to tune biological noise in flagellar length. Analysis of noise at the level of organelle size provides a way to probe the mechanisms determining cell geometry.

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.

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.

The interplay of phenotypic variability and fitness in finite microbial populations.

In isogenic microbial populations, phenotypic variability is generated by a combination of stochastic mechanisms, such as gene expression, and deterministic factors, such as asymmetric segregation of cell volume. Here we address the question: how does phenotypic variability of a microbial population affect its fitness? While this question has previously been studied for exponentially growing populations, the situation when the population size is kept fixed has received much less attention, despite its relevance to many natural scenarios. We show that the outcome of competition between multiple microbial species can be determined from the distribution of phenotypes in the culture using a generalization of the well-known Euler-Lotka equation, which relates the steady-state distribution of phenotypes to the population growth rate. We derive a generalization of the Euler-Lotka equation for finite cultures, which relates the distribution of phenotypes among cells in the culture to the exponential growth rate. Our analysis reveals that in order to predict fitness from phenotypes, it is important to understand how distributions of phenotypes obtained from different subsets of the genealogical history of a population are related. To this end, we derive a mapping between the various ways of sampling phenotypes in a finite population and show how to obtain the equivalent distributions from an exponentially growing culture. Finally, we use this mapping to show that species with higher growth rates in exponential growth conditions will have a competitive advantage in the finite culture.

Alternative transcription cycle for bacterial RNA polymerase.

RNA polymerases (RNAPs) transcribe genes through a cycle of recruitment to promoter DNA, initiation, elongation, and termination. After termination, RNAP is thought to initiate the next round of transcription by detaching from DNA and rebinding a new promoter. Here we use single-molecule fluorescence microscopy to observe individual RNAP molecules after transcript release at a terminator. Following termination, RNAP almost always remains bound to DNA and sometimes exhibits one-dimensional sliding over thousands of basepairs. Unexpectedly, the DNA-bound RNAP often restarts transcription, usually in reverse direction, thus producing an antisense transcript. Furthermore, we report evidence of this secondary initiation in live cells, using genome-wide RNA sequencing. These findings reveal an alternative transcription cycle that allows RNAP to reinitiate without dissociating from DNA, which is likely to have important implications for gene regulation.

Length-dependent disassembly maintains four different flagellar lengths in Giardia.

With eight flagella of four different lengths, the parasitic protist Giardia is an ideal model to evaluate flagellar assembly and length regulation. To determine how four different flagellar lengths are maintained, we used live-cell quantitative imaging and mathematical modeling of conserved components of intraflagellar transport (IFT)-mediated assembly and kinesin-13-mediated disassembly in different flagellar pairs. Each axoneme has a long cytoplasmic region extending from the basal body, and transitions to a canonical membrane-bound flagellum at the 'flagellar pore'. We determined that each flagellar pore is the site of IFT accumulation and injection, defining a diffusion barrier functionally analogous to the transition zone. IFT-mediated assembly is length-independent, as train size, speed, and injection frequencies are similar for all flagella. We demonstrate that kinesin-13 localization to the flagellar tips is inversely correlated to flagellar length. Therefore, we propose a model where a length-dependent disassembly mechanism controls multiple flagellar lengths within the same cell.

Synergy between Cyclase-associated protein and Cofilin accelerates actin filament depolymerization by two orders of magnitude.

Cellular actin networks can be rapidly disassembled and remodeled in a few seconds, yet in vitro actin filaments depolymerize slowly over minutes. The cellular mechanisms enabling actin to depolymerize this fast have so far remained obscure. Using microfluidics-assisted TIRF, we show that Cyclase-associated protein (CAP) and Cofilin synergize to processively depolymerize actin filament pointed ends at a rate 330-fold faster than spontaneous depolymerization. Single molecule imaging further reveals that hexameric CAP molecules interact with the pointed ends of Cofilin-decorated filaments for several seconds at a time, removing approximately 100 actin subunits per binding event. These findings establish a paradigm, in which a filament end-binding protein and a side-binding protein work in concert to control actin dynamics, and help explain how rapid actin network depolymerization is achieved in cells.