The Synchronization of Replication and Division Cycles in Individual E. coli Cells.

Isogenic E. coli cells growing in a constant environment display significant variability in growth rates, division sizes, and generation times. The guiding principle appears to be that each cell, during one generation, adds a size increment that is uncorrelated to its birth size. Here, we investigate the mechanisms underlying this "adder" behavior by mapping the chromosome replication cycle to the division cycle of individual cells using fluorescence microscopy. We have found that initiation of chromosome replication is triggered at a fixed volume per chromosome independent of a cell's birth volume and growth rate. Each initiation event is coupled to a division event after a growth-rate-dependent time. We formalize our findings in a model showing that cell-to-cell variation in division timing and cell size is mainly driven by variations in growth rate. The model also explains why fast-growing cells display adder behavior and correctly predict deviations from the adder behavior at slow growth.

Regulatory elements coordinating initiation of chromosome replication to the Escherichia coli cell cycle.

Escherichia coli coordinates replication and division cycles by initiating replication at a narrow range of cell sizes. By tracking replisomes in individual cells through thousands of division cycles in wild-type and mutant strains, we were able to compare the relative importance of previously described control systems. We found that accurate triggering of initiation does not require synthesis of new DnaA. The initiation size increased only marginally as DnaA was diluted by growth after dnaA expression had been turned off. This suggests that the conversion of DnaA between its active ATP- and inactive ADP-bound states is more important for initiation size control than the total free concentration of DnaA. In addition, we found that the known ATP/ADP converters DARS and datA compensate for each other, although the removal of them makes the initiation size more sensitive to the concentration of DnaA. Only disruption of the regulatory inactivation of DnaA mechanism had a radical impact on replication initiation. This result was corroborated by the finding that termination of one round of replication correlates with the next initiation at intermediate growth rates, as would be the case if RIDA-mediated conversion from DnaA-ATP to DnaA-ADP abruptly stops at termination and DnaA-ATP starts accumulating.

Time-resolved imaging-based CRISPRi screening.

Our ability to connect genotypic variation to biologically important phenotypes has been seriously limited by the gap between live-cell microscopy and library-scale genomic engineering. Here, we show how in situ genotyping of a library of strains after time-lapse imaging in a microfluidic device overcomes this problem. We determine how 235 different CRISPR interference knockdowns impact the coordination of the replication and division cycles of Escherichia coli by monitoring the location of replication forks throughout on average >500 cell cycles per knockdown. Subsequent in situ genotyping allows us to map each phenotype distribution to a specific genetic perturbation to determine which genes are important for cell cycle control. The single-cell time-resolved assay allows us to determine the distribution of single-cell growth rates, cell division sizes and replication initiation volumes. The technology presented in this study enables genome-scale screens of most live-cell microscopy assays.

In situ genotyping of a pooled strain library after characterizing complex phenotypes.

In this work, we present a proof-of-principle experiment that extends advanced live cell microscopy to the scale of pool-generated strain libraries. We achieve this by identifying the genotypes for individual cells in situ after a detailed characterization of the phenotype. The principle is demonstrated by single-molecule fluorescence time-lapse imaging of Escherichia coli strains harboring barcoded plasmids that express a sgRNA which suppresses different genes in the E. coli genome through dCas9 interference. In general, the method solves the problem of characterizing complex dynamic phenotypes for diverse genetic libraries of cell strains. For example, it allows screens of how changes in regulatory or coding sequences impact the temporal expression, location, or function of a gene product, or how the altered expression of a set of genes impacts the intracellular dynamics of a labeled reporter.

Simulated single molecule microscopy with SMeagol.

UNLABELLED: SMeagol is a software tool to simulate highly realistic microscopy data based on spatial systems biology models, in order to facilitate development, validation and optimization of advanced analysis methods for live cell single molecule microscopy data. AVAILABILITY AND IMPLEMENTATION: SMeagol runs on Matlab R2014 and later, and uses compiled binaries in C for reaction-diffusion simulations. Documentation, source code and binaries for Mac OS, Windows and Ubuntu Linux can be downloaded from http://smeagol.sourceforge.net CONTACT: johan.elf@icm.uu.se SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Single-particle tracking reveals that free ribosomal subunits are not excluded from the Escherichia coli nucleoid.

Biochemical and genetic data show that ribosomes closely follow RNA polymerases that are transcribing protein-coding genes in bacteria. At the same time, electron and fluorescence microscopy have revealed that ribosomes are excluded from the Escherichia coli nucleoid, which seems to be inconsistent with fast translation initiation on nascent mRNA transcripts. The apparent paradox can be reconciled if translation of nascent mRNAs can start throughout the nucleoid before they relocate to the periphery. However, this mechanism requires that free ribosomal subunits are not excluded from the nucleoid. Here, we use single-particle tracking in living E. coli cells to determine the fractions of free ribosomal subunits, classify individual subunits as free or mRNA-bound, and quantify the degree of exclusion of bound and free subunits separately. We show that free subunits are not excluded from the nucleoid. This finding strongly suggests that translation of nascent mRNAs can start throughout the nucleoid, which reconciles the spatial separation of DNA and ribosomes with cotranscriptional translation. We also show that, after translation inhibition, free subunit precursors are partially excluded from the compacted nucleoid. This finding indicates that it is active translation that normally allows ribosomal subunits to assemble on nascent mRNAs throughout the nucleoid and that the effects of translation inhibitors are enhanced by the limited access of ribosomal subunits to nascent mRNAs in the compacted nucleoid.

Transcription-factor binding and sliding on DNA studied using micro- and macroscopic models.

Transcription factors search for specific operator sequences by alternating rounds of 3D diffusion with rounds of 1D diffusion (sliding) along the DNA. The details of such sliding have largely been beyond direct experimental observation. For this purpose we devised an analytical formulation of umbrella sampling along a helical coordinate, and from extensive and fully atomistic simulations we quantified the free-energy landscapes that underlie the sliding dynamics and dissociation kinetics for the LacI dimer. The resulting potential of mean force distributions show a fine structure with an amplitude of 1 k(B)T for sliding and 12 k(B)T for dissociation. Based on the free-energy calculations the repressor slides in close contact with DNA for 8 bp on average before making a microscopic dissociation. By combining the microscopic molecular-dynamics calculations with Brownian simulation including rotational diffusion from the microscopically dissociated state we estimate a macroscopic residence time of 48 ms at the same DNA segment and an in vitro sliding distance of 240 bp. The sliding distance is in agreement with previous in vitro sliding-length estimates. The in vitro prediction for the macroscopic residence time also compares favorably to what we measure by single-molecule imaging of nonspecifically bound fluorescently labeled LacI in living cells. The investigation adds to our understanding of transcription-factor search kinetics and connects the macro-/mesoscopic rate constants to the microscopic dynamics.

Lost in presumption: stochastic reactions in spatial models.

Physical modeling is increasingly important for generating insights into intracellular processes. We describe situations in which combined spatial and stochastic aspects of chemical reactions are needed to capture the relevant dynamics of biochemical systems.

Thermodynamic modeling of variations in the rate of RNA chain elongation of E. coli rrn operons.

Previous electron-microscopic imaging has shown high RNA polymerase occupation densities in the 16S and 23S encoding regions and low occupation densities in the noncoding leader, spacer, and trailer regions of the rRNA (rrn) operons in E. coli. This indicates slower transcript elongation within the coding regions and faster elongation within the noncoding regions of the operon. Inactivation of four of the seven rrn operons increases the transcript initiation frequency at the promoters of the three intact operons and reduces the time for RNA polymerase to traverse the operon. We have used the DNA sequence-dependent standard free energy variation of the transcription complex to model the experimentally observed changes in the elongation rate along the rrnB operon. We also model the stimulation of the average transcription rate over the whole operon by increasing rate of transcript initiation. Monte Carlo simulations, taking into account initiation of transcription, translocation, and backward and forward tracking of RNA polymerase, partially reproduce the observed transcript elongation rate variations along the rrn operon and fully account for the increased average rate in response to increased frequency of transcript initiation.

The Escherichia coli chromosome moves to the replisome.

In Escherichia coli, it is debated whether the two replisomes move independently along the two chromosome arms during replication or if they remain spatially confined. Here, we use high-throughput fluorescence microscopy to simultaneously determine the location and short-time-scale (1 s) movement of the replisome and a chromosomal locus throughout the cell cycle. The assay is performed for several loci. We find that (i) the two replisomes are confined to a region of ~250 nm and ~120 nm along the cell's long and short axis, respectively, (ii) the chromosomal loci move to and through this region sequentially based on their distance from the origin of replication, and (iii) when a locus is being replicated, its short time-scale movement slows down. This behavior is the same at different growth rates. In conclusion, our data supports a model with DNA moving towards spatially confined replisomes at replication.

MesoRD 1.0: Stochastic reaction-diffusion simulations in the microscopic limit.

SUMMARY: MesoRD is a tool for simulating stochastic reaction-diffusion systems as modeled by the reaction diffusion master equation. The simulated systems are defined in the Systems Biology Markup Language with additions to define compartment geometries. MesoRD 1.0 supports scale-dependent reaction rate constants and reactions between reactants in neighbouring subvolumes. These new features make it possible to construct physically consistent models of diffusion-controlled reactions also at fine spatial discretization. AVAILABILITY: MesoRD is written in C++ and licensed under the GNU general public license (GPL). MesoRD can be downloaded at http://mesord.sourceforge.net. The MesoRD homepage, http://mesord.sourceforge.net, contains detailed documentation and news about recently implemented features. CONTACT: johan.elf@icm.uu.se.

Stochastic reaction-diffusion kinetics in the microscopic limit.

Quantitative analysis of biochemical networks often requires consideration of both spatial and stochastic aspects of chemical processes. Despite significant progress in the field, it is still computationally prohibitive to simulate systems involving many reactants or complex geometries using a microscopic framework that includes the finest length and time scales of diffusion-limited molecular interactions. For this reason, spatially or temporally discretized simulations schemes are commonly used when modeling intracellular reaction networks. The challenge in defining such coarse-grained models is to calculate the correct probabilities of reaction given the microscopic parameters and the uncertainty in the molecular positions introduced by the spatial or temporal discretization. In this paper we have solved this problem for the spatially discretized Reaction-Diffusion Master Equation; this enables a seamless and physically consistent transition from the microscopic to the macroscopic frameworks of reaction-diffusion kinetics. We exemplify the use of the methods by showing that a phosphorylation-dephosphorylation motif, commonly observed in eukaryotic signaling pathways, is predicted to display fluctuations that depend on the geometry of the system.

Drug efflux pump deficiency and drug target resistance masking in growing bacteria.

Recent experiments have shown that drug efflux pump deficiency not only increases the susceptibility of pathogens to antibiotics, but also seems to "mask" the effects of mutations, that decrease the affinities of drugs to their intracellular targets, on the growth rates of drug-exposed bacteria. That is, in the presence of drugs, the growth rates of drug-exposed WT and target mutated strains are the same in a drug efflux pump deficient background, but the mutants grow faster than WT in a drug efflux pump proficient background. Here, we explain the mechanism of target resistance masking and show that it occurs in response to drug efflux pump inhibition among pathogens with high-affinity drug binding targets, low cell-membrane drug-permeability and insignificant intracellular drug degradation. We demonstrate that target resistance masking is fundamentally linked to growth-bistability, i.e., the existence of 2 different steady state growth rates for one and the same drug concentration in the growth medium. We speculate that target resistance masking provides a hitherto unknown mechanism for slowing down the evolution of target resistance among pathogens.

Noise-induced Min phenotypes in E. coli.

The spatiotemporal oscillations of the Escherichia coli proteins MinD and MinE direct cell division to the region between the chromosomes. Several quantitative models of the Min system have been suggested before, but no one of them accounts for the behavior of all documented mutant phenotypes. We analyzed the stochastic reaction-diffusion kinetics of the Min proteins for several E. coli mutants and compared the results to the corresponding deterministic mean-field description. We found that wild-type (wt) and filamentous (ftsZ-) cells are well characterized by the mean-field model, but that a stochastic model is necessary to account for several of the characteristics of the spherical (rodA-) and phospathedylethanolamide-deficient (PE-) phenotypes. For spherical cells, the mean-field model is bistable, and the system can get trapped in a non-oscillatory state. However, when the intrinsic noise is considered, only the experimentally observed oscillatory behavior remains. The stochastic model also reproduces the change in oscillation directions observed in the spherical phenotype and the occasional gliding of the MinD region along the inner membrane. For the PE- mutant, the stochastic model explains the appearance of randomly localized and dense MinD clusters as a nucleation phenomenon, in which the stochastic kinetics at low copy number causes local discharges of the high MinD(ATP) to MinD(ADP) potential. We find that a simple five-reaction model of the Min system can explain all documented Min phenotypes, if stochastic kinetics and three-dimensional diffusion are accounted for. Our results emphasize that local copy number fluctuation may result in phenotypic differences although the total number of molecules of the relevant species is high.

Kinetics of dCas9 target search in Escherichia coli.

How fast can a cell locate a specific chromosomal DNA sequence specified by a single-stranded oligonucleotide? To address this question, we investigate the intracellular search processes of the Cas9 protein, which can be programmed by a guide RNA to bind essentially any DNA sequence. This targeting flexibility requires Cas9 to unwind the DNA double helix to test for correct base pairing to the guide RNA. Here we study the search mechanisms of the catalytically inactive Cas9 (dCas9) in living Escherichia coli by combining single-molecule fluorescence microscopy and bulk restriction-protection assays. We find that it takes a single fluorescently labeled dCas9 6 hours to find the correct target sequence, which implies that each potential target is bound for less than 30 milliseconds. Once bound, dCas9 remains associated until replication. To achieve fast targeting, both Cas9 and its guide RNA have to be present at high concentrations.

Direct measurement of transcription factor dissociation excludes a simple operator occupancy model for gene regulation.

Transcription factors mediate gene regulation by site-specific binding to chromosomal operators. It is commonly assumed that the level of repression is determined solely by the equilibrium binding of a repressor to its operator. However, this assumption has not been possible to test in living cells. Here we have developed a single-molecule chase assay to measure how long an individual transcription factor molecule remains bound at a specific chromosomal operator site. We find that the lac repressor dimer stays bound on average 5 min at the native lac operator in Escherichia coli and that a stronger operator results in a slower dissociation rate but a similar association rate. Our findings do not support the simple equilibrium model. The discrepancy with this model can, for example, be accounted for by considering that transcription initiation drives the system out of equilibrium. Such effects need to be considered when predicting gene activity from transcription factor binding strengths.

Identification of enzyme inhibitory mechanisms from steady-state kinetics.

Enzyme inhibitors are used in many areas of the life sciences, ranging from basic research to the combat of disease in the clinic. Inhibitors are traditionally characterized by how they affect the steady-state kinetics of enzymes, commonly analyzed on the assumption that enzyme-bound and free substrate molecules are in equilibrium. This assumption, implying that an enzyme-bound substrate molecule has near zero probability to form a product rather than dissociate, is valid only for very inefficient enzymes. When it is relaxed, more complex but also more information-rich steady-state kinetics emerges. Although solutions to the general steady-state kinetics problem exist, they are opaque and have been of limited help to experimentalists. Here we reformulate the steady-state kinetics of enzyme inhibition in terms of new parameters. These allow for assessment of ambiguities of interpretation due to kinetic scheme degeneracy and provide an intuitively simple way to analyze experimental data. We illustrate the method by concrete examples of how to assess scheme degeneracy and obtain experimental estimates of all available rate and equilibrium constants. We suggest simple, complementary experiments that can remove ambiguities and greatly enhance the accuracy of parameter estimation.

Stochastic reaction-diffusion simulation with MesoRD.

UNLABELLED: MesoRD is a tool for stochastic simulation of chemical reactions and diffusion. In particular, it is an implementation of the next subvolume method, which is an exact method to simulate the Markov process corresponding to the reaction-diffusion master equation. AVAILABILITY: MesoRD is free software, written in C++ and licensed under the GNU general public license (GPL). MesoRD runs on Linux, Mac OS X, NetBSD, Solaris and Windows XP. It can be downloaded from http://mesord.sourceforge.net. CONTACT: johan.elf@icm.uu.se; johan.hattne@embl-hamburg.de SUPPLEMENTARY INFORMATION: 'MesoRD User's Guide' and other documents are available at http://mesord.sourceforge.net.