Stochastic Turing patterns of trichomes in Arabidopsis leaves.

Biological patterns that emerge during the morphogenesis of multicellular organisms can display high precision at large scales, while at cellular scales, cells exhibit large fluctuations stemming from cell-cell differences in molecular copy numbers also called demographic noise. We study the conflicting interplay between high precision and demographic noise in trichome patterns on the epidermis of wild-type Arabidopsis thaliana leaves, as a two-dimensional model system. We carry out a statistical characterization of these patterns and show that their power spectra display fat tails-a signature compatible with noise-driven stochastic Turing patterns-which are absent in power spectra of patterns driven by deterministic instabilities. We then present a theoretical model that includes demographic noise stemming from birth-death processes of genetic regulators which we study analytically and by stochastic simulations. The model captures the observed experimental features of trichome patterns.

Target search by an imported conjugative DNA element for a unique integration site along a bacterial chromosome during horizontal gene transfer.

Integrative and conjugative elements (ICEs) are mobile genetic elements that can transfer by conjugation to recipient cells. Some ICEs integrate into a unique site in the genome of their hosts. We studied quantitatively the process by which an ICE searches for its unique integration site in the Bacillus subtilis chromosome. We followed the motion of both ICEBs1 and the chromosomal integration site in real time within individual cells. ICEBs1 exhibited a wide spectrum of dynamical behaviors, ranging from rapid sub-diffusive displacements crisscrossing the cell, to kinetically trapped states. The chromosomal integration site moved sub-diffusively and exhibited pronounced dynamical asymmetry between longitudinal and transversal motions, highlighting the role of chromosomal structure and the heterogeneity of the bacterial interior in the search. The successful search for and subsequent recombination into the integration site is a key step in the acquisition of integrating mobile genetic elements. Our findings provide new insights into intracellular transport processes involving large DNA molecules.

Robust stochastic Turing patterns in the development of a one-dimensional cyanobacterial organism.

Under nitrogen deprivation, the one-dimensional cyanobacterial organism Anabaena sp. PCC 7120 develops patterns of single, nitrogen-fixing cells separated by nearly regular intervals of photosynthetic vegetative cells. We study a minimal, stochastic model of developmental patterns in Anabaena that includes a nondiffusing activator, two diffusing inhibitor morphogens, demographic fluctuations in the number of morphogen molecules, and filament growth. By tracking developing filaments, we provide experimental evidence for different spatiotemporal roles of the two inhibitors during pattern maintenance and for small molecular copy numbers, justifying a stochastic approach. In the deterministic limit, the model yields Turing patterns within a region of parameter space that shrinks markedly as the inhibitor diffusivities become equal. Transient, noise-driven, stochastic Turing patterns are produced outside this region, which can then be fixed by downstream genetic commitment pathways, dramatically enhancing the robustness of pattern formation, also in the biologically relevant situation in which the inhibitors' diffusivities may be comparable.

Transcript degradation and noise of small RNA-controlled genes in a switch activated network in Escherichia coli.

Post-transcriptional regulatory processes may change transcript levels and affect cell-to-cell variability or noise. We study small-RNA downregulation to elucidate its effects on noise in the iron homeostasis network of Escherichia coli In this network, the small-RNA RyhB undergoes stoichiometric degradation with the transcripts of target genes in response to iron stress. Using single-molecule fluorescence in situ hybridization, we measured transcript numbers of the RyhB-regulated genes sodB and fumA in individual cells as a function of iron deprivation. We observed a monotonic increase of noise with iron stress but no evidence of theoretically predicted, enhanced stoichiometric fluctuations in transcript numbers, nor of bistable behavior in transcript distributions. Direct detection of RyhB in individual cells shows that its noise is much smaller than that of these two targets, when RyhB production is significant. A generalized two-state model of bursty transcription that neglects RyhB fluctuations describes quantitatively the dependence of noise and transcript distributions on iron deprivation, enabling extraction of in vivo RyhB-mediated transcript degradation rates. The transcripts' threshold-linear behavior indicates that the effective in vivo interaction strength between RyhB and its two target transcripts is comparable. Strikingly, the bacterial cell response exhibits Fur-dependent, switch-like activation instead of a graded response to iron deprivation.

Spatial fluctuations in expression of the heterocyst differentiation regulatory gene hetR in Anabaena filaments.

Under nitrogen deprivation, filaments of the cyanobacterium Anabaena undergo a process of development, resulting in a one-dimensional pattern of nitrogen-fixing heterocysts separated by about ten photosynthetic vegetative cells. Many aspects of gene expression before nitrogen deprivation and during the developmental process remain to be elucidated. Furthermore, the coupling of gene expression fluctuations between cells along a multicellular filament is unknown. We studied the statistics of fluctuations of gene expression of HetR, a transcription factor essential for heterocyst differentiation, both under steady-state growth in nitrogen-rich conditions and at different times following nitrogen deprivation, using a chromosomally-encoded translational hetR-gfp fusion. Statistical analysis of fluorescence at the individual cell level in wild-type and mutant filaments demonstrates that expression fluctuations of hetR in nearby cells are coupled, with a characteristic spatial range of circa two to three cells, setting the scale for cellular interactions along a filament. Correlations between cells predominantly arise from intercellular molecular transfer and less from cell division. Fluctuations after nitrogen step-down can build up on those under nitrogen-replete conditions. We found that under nitrogen-rich conditions, basal, steady-state expression of the HetR inhibitor PatS, cell-cell communication influenced by the septal protein SepJ and positive HetR auto-regulation are essential determinants of fluctuations in hetR expression and its distribution along filaments. A comparison between the expression of hetR-gfp under nitrogen-rich and nitrogen-poor conditions highlights the differences between the two HetR inhibitors PatS and HetN, as well as the differences in specificity between the septal proteins SepJ and FraC/FraD. Activation, inhibition and cell-cell communication lie at the heart of developmental processes. Our results show that proteins involved in these basic ingredients combine together in the presence of inevitable stochasticity in gene expression, to control the coupled fluctuations of gene expression that give rise to a one-dimensional developmental pattern in this organism.

Sub-cellular mRNA localization modulates the regulation of gene expression by small RNAs in bacteria.

Small non-coding RNAs can exert significant regulatory activity on gene expression in bacteria. In recent years, substantial progress has been made in understanding bacterial gene expression by sRNAs. However, recent findings that demonstrate that families of mRNAs show non-trivial sub-cellular distributions raise the question of how localization may affect the regulatory activity of sRNAs. Here we address this question within a simple mathematical model. We show that the non-uniform spatial distributions of mRNA can alter the threshold-linear response that characterizes sRNAs that act stoichiometrically, and modulate the hierarchy among targets co-regulated by the same sRNA. We also identify conditions where the sub-cellular organization of cofactors in the sRNA pathway can induce spatial heterogeneity on sRNA targets. Our results suggest that under certain conditions, interpretation and modeling of natural and synthetic gene regulatory circuits need to take into account the spatial organization of the transcripts of participating genes.

Location of the unique integration site on an Escherichia coli chromosome by bacteriophage lambda DNA in vivo.

The search for specific sequences on long genomes is a key process in many biological contexts. How can specific target sequences be located with high efficiency, within physiologically relevant times? We addressed this question for viral integration, a fundamental mechanism of horizontal gene transfer driving prokaryotic evolution, using the infection of Escherichia coli bacteria with bacteriophage λ and following the establishment of a lysogenic state. Following the targeting process in individual live E. coli cells in real time revealed that λ DNA remains confined near the entry point of a cell following infection. The encounter between the 15-bp-long target sequence on the chromosome and the recombination site on the viral genome is facilitated by the directed motion of bacterial DNA generated during chromosome replication, in conjunction with constrained diffusion of phage DNA. Moving the native bacterial integration site to different locations on the genome and measuring the integration frequency in these strains reveals that the frequencies of the native site and a site symmetric to it relative to the origin are similar, whereas both are significantly higher than when the integration site is moved near the terminus, consistent with the replication-driven mechanism we propose. This novel search mechanism is yet another example of the exquisite coevolution of λ with its host.

Effects of post-transcriptional regulation on phenotypic noise in Escherichia coli.

Cell-to-cell variations in protein abundance, called noise, give rise to phenotypic variability between isogenic cells. Studies of noise have focused on stochasticity introduced at transcription, yet the effects of post-transcriptional regulatory processes on noise remain unknown. We study the effects of RyhB, a small-RNA of Escherichia coli produced on iron stress, on the phenotypic variability of two of its downregulated target proteins, using dual chromosomal fusions to fluorescent reporters and measurements in live individual cells. The total noise of each of the target proteins is remarkably constant over a wide range of RyhB production rates despite cells being in stress. In fact, coordinate downregulation of the two target proteins by RyhB reduces the correlation between their levels. Hence, an increase in phenotypic variability under stress is achieved by decoupling the expression of different target proteins in the same cell, rather than by an increase in the total noise of each. Extrinsic noise provides the dominant contribution to the total protein noise over the total range of RyhB production rates. Stochastic simulations reproduce qualitatively key features of our observations and show that a feed-forward loop formed by transcriptional extrinsic noise, an sRNA and its target genes exhibits strong noise filtration capabilities.

Spatio-temporal coherence of circadian clocks and temporal control of differentiation in Anabaena filaments.

Circadian clock arrays in multicellular filaments of the heterocyst-forming cyanobacterium Anabaena sp. strain PCC 7120 display remarkable spatio-temporal coherence under nitrogen-replete conditions. To shed light on the interplay between circadian clocks and the formation of developmental patterns, we followed the expression of a clock-controlled gene under nitrogen deprivation, at the level of individual cells. Our experiments showed that differentiation into heterocysts took place preferentially within a limited interval of the circadian clock cycle, that gene expression in different vegetative intervals along a developed filament was discoordinated, and that the circadian clock was active in individual heterocysts. Furthermore, Anabaena mutants lacking the kaiABC genes encoding the circadian clock core components produced heterocysts but failed in diazotrophy. Therefore, genes related to some aspect of nitrogen fixation, rather than early or mid-heterocyst differentiation genes, are likely affected by the absence of the clock. A bioinformatics analysis supports the notion that RpaA may play a role as master regulator of clock outputs in Anabaena, the temporal control of differentiation by the circadian clock and the involvement of the clock in proper diazotrophic growth. Together, these results suggest that under nitrogen-deficient conditions, the clock coherent unit in Anabaena is reduced from a full filament under nitrogen-rich conditions to the vegetative cell interval between heterocysts.IMPORTANCECircadian clocks, from unicellular organisms to animals, temporally align biological processes to day and night cycles. We study the dynamics of a circadian clock-controlled gene at the individual cell level in the multicellular filamentous cyanobacterium Anabaena, under nitrogen-stress conditions. Under these conditions, some cells along filaments differentiate to carry out atmospheric nitrogen fixation and lose their capability for oxygenic photosynthesis. We found that clock synchronization is limited to organismic units of contiguous photosynthetic cells, contrary to nitrogen-replete conditions in which clocks are synchronized over a whole filament. We provided evidence that the circadian clock regulates the process of differentiation, allowing it to occur preferentially within a limited time window during the circadian clock period. Lastly, we present evidence that the signal from the core clock to clock-regulated genes is conveyed in Anabaena as in unicellular cyanobacteria.

Stability and gene strand bias of lambda prophages and chromosome organization in Escherichia coli.

Temperate phage-mediated horizontal gene transfer is a potent driver of genetic diversity in the evolution of bacteria. Most lambdoid prophages in Escherichia coli are integrated into the chromosome with the same orientation with respect to the direction of chromosomal replication, and their location on the chromosome is far from homogeneous. To better understand these features, we studied the interplay between lysogenic and lytic states of phage lambda in both native and inverted integration orientations at the wild-type integration site as well as at other sites on the bacterial chromosome. Measurements of free phage released by spontaneous induction showed that the stability of lysogenic states is affected by location and orientation along the chromosome, with stronger effects near the origin of replication. Competition experiments and range expansions between lysogenic strains with opposite orientations and insertion loci indicated that there are no major differences in growth. Moreover, measurements of the level of transcriptional bursts of the cI gene coding for the lambda phage repressor using single-molecule fluorescence in situ hybridization resulted in similar levels of transcription for both orientations and prophage location. We postulate that the preference for a given orientation and location is a result of a balance between the maintenance of lysogeny and the ability to lyse.IMPORTANCEThe integration of genetic material of temperate bacterial viruses (phages) into the chromosomes of bacteria is a potent evolutionary force, allowing bacteria to acquire in one stroke new traits and restructure the information in their chromosomes. Puzzlingly, this genetic material is preferentially integrated in a particular orientation and at non-random sites on the bacterial chromosome. The work described here reveals that the interplay between the maintenance of the stability of the integrated phage, its ability to excise, and its localization along the chromosome plays a key role in setting chromosomal organization in Escherichia coli.

Caught in the act: the lifetime of synaptic intermediates during the search for homology on DNA.

Homologous recombination plays pivotal roles in DNA repair and in the generation of genetic diversity. To locate homologous target sequences at which strand exchange can occur within a timescale that a cell's biology demands, a single-stranded DNA-recombinase complex must search among a large number of sequences on a genome by forming synapses with chromosomal segments of DNA. A key element in the search is the time it takes for the two sequences of DNA to be compared, i.e. the synapse lifetime. Here, we visualize for the first time fluorescently tagged individual synapses formed by RecA, a prokaryotic recombinase, and measure their lifetime as a function of synapse length and differences in sequence between the participating DNAs. Surprisingly, lifetimes can be approximately 10 s long when the DNAs are fully heterologous, and much longer for partial homology, consistently with ensemble FRET measurements. Synapse lifetime increases rapidly as the length of a region of full homology at either the 3'- or 5'-ends of the invading single-stranded DNA increases above 30 bases. A few mismatches can reduce dramatically the lifetime of synapses formed with nearly homologous DNAs. These results suggest the need for facilitated homology search mechanisms to locate homology successfully within the timescales observed in vivo.

Damped oscillations in the adaptive response of the iron homeostasis network of E. coli.

Living organisms often have to adapt to sudden environmental changes and reach homeostasis. To achieve adaptation, cells deploy motifs such as feedback in their genetic networks, endowing the cellular response with desirable properties. We studied the iron homeostasis network of E. coli, which employs feedback loops to regulate iron usage and uptake, while maintaining intracellular iron at non-toxic levels. Using fluorescence reporters for iron-dependent promoters in bulk and microfluidics-based, single-cell experiments, we show that E. coli cells exhibit damped oscillations in gene expression, following sudden reductions in external iron levels. The oscillations, lasting for several generations, are independent of position along the cell cycle. Experiments with mutants in network components demonstrate the involvement of iron uptake in the oscillations. Our findings suggest that the response is driven by intracellular iron oscillations large enough to induce nearly full network activation/deactivation. We propose a mathematical model based on a negative feedback loop closed by rapid iron uptake, and including iron usage and storage, which captures the main features of the observed behaviour. Taken together, our results shed light on the control of iron metabolism in bacteria and suggest that the oscillations represent a compromise between the requirements of stability and speed of response.

Impaired cell-cell communication in the multicellular cyanobacterium Anabaena affects carbon uptake, photosynthesis, and the cell wall.

Cell-cell communication is an essential attribute of multicellular organisms. The effects of perturbed communication were studied in septal protein mutants of the heterocyst-forming filamentous cyanobacterium Anabaena sp. PCC 7120 model organism. Strains bearing sepJ and sepJ/fraC/fraD deletions showed differences in growth, pigment absorption spectra, and spatial patterns of expression of the hetR gene encoding a heterocyst differentiation master regulator. Global changes in gene expression resulting from deletion of those genes were mapped by RNA sequencing analysis of wild-type and mutant strains, both under nitrogen-replete and nitrogen-poor conditions. The effects of sepJ and fraC/fraD deletions were non-additive, and perturbed cell-cell communication led to significant changes in global gene expression. Most significant effects, related to carbon metabolism, included increased expression of genes encoding carbon uptake systems and components of the photosynthetic apparatus, as well as decreased expression of genes encoding cell wall components related to heterocyst differentiation and to polysaccharide export.

Robust, coherent, and synchronized circadian clock-controlled oscillations along Anabaena filaments.

Circadian clocks display remarkable reliability despite significant stochasticity in biomolecular reactions. We study the dynamics of a circadian clock-controlled gene at the individual cell level in Anabaena sp. PCC 7120, a multicellular filamentous cyanobacterium. We found significant synchronization and spatial coherence along filaments, clock coupling due to cell-cell communication, and gating of the cell cycle. Furthermore, we observed low-amplitude circadian oscillatory transcription of kai genes encoding the post-transcriptional core oscillatory circuit and high-amplitude oscillations of rpaA coding for the master regulator transducing the core clock output. Transcriptional oscillations of rpaA suggest an additional level of regulation. A stochastic one-dimensional toy model of coupled clock cores and their phosphorylation states shows that demographic noise can seed stochastic oscillations outside the region where deterministic limit cycles with circadian periods occur. The model reproduces the observed spatio-temporal coherence along filaments and provides a robust description of coupled circadian clocks in a multicellular organism.

Host responses influence on the induction of lambda prophage.

Inactivation of bacteriophage lambda CI repressor leads almost exclusively to lytic development. Prophage induction can be initiated either by DNA damage or by heat treatment of a temperature-sensitive repressor. These two treatments also cause a concurrent activation of either the host SOS or heat-shock stress responses respectively. We studied the effects of these two methods of induction on the lytic pathway by monitoring the activation of different lambda promoters, and found that the lambda genetic network co-ordinates information from the host stress response networks. Our results show that the function of the CII transcriptional activator, which facilitates the lysogenic developmental pathway, is not observed following either method of induction. Mutations in the cro gene restore the CII function irrespective of the induction method. Deletion of the heat-shock protease gene ftsH can also restore CII function following heat induction but not following SOS induction. Our findings highlight the importance of the elimination of CII function during induction as a way to ensure an efficient lytic outcome. We also show that, despite the common inhibitory effect on CII function, there are significant differences in the heat- and SOS-induced pathways leading to the lytic cascade.

Universality of persistence exponents in two-dimensional Ostwald ripening.

We measured persistence exponents theta(phi) of Ostwald ripening in two dimensions, as a function of the area fraction phi occupied by coarsening domains. The values of theta(phi) in two systems, succinonitrile and brine, quenched to their liquid-solid coexistence region, compare well with one another, providing compelling evidence for the universality of the one-parameter family of exponents. For small phi, theta(phi) approximately = 0.39phi, as predicted by a model that assumes no correlations between evolving domains. These constitute the first measurements of persistence exponents in the case of phase transitions with a conserved order parameter.

Noise in timing and precision of gene activities in a genetic cascade.

Biological developmental pathways require proper timing of gene expression. We investigated timing variations of defined steps along the lytic cascade of bacteriophage lambda. Gene expression was followed in individual lysogenic cells, after induction with a pulse of UV irradiation. At low UV doses, some cells undergo partial induction and eventually divide, whereas others follow the lytic pathway. The timing of events in cells committed to lysis is independent of the level of activation of the SOS response, suggesting that the lambda network proceeds autonomously after induction. An increased loss of temporal coherence of specific events from prophage induction to lysis is observed, even though the coefficient of variation of timing fluctuations decreases. The observed temporal variations are not due to cell factors uniformly dilating the timing of execution of the cascade. This behavior is reproduced by a simple model composed of independent stages, which for a given mean duration predicts higher temporal precision, when a cascade consists of a large number of steps. Evidence for the independence of regulatory modules in the network is presented.

Precise temporal modulation in the response of the SOS DNA repair network in individual bacteria.

The SOS genetic network is responsible for the repair/bypass of DNA damage in bacterial cells. While the initial stages of the response have been well characterized, less is known about the dynamics of the response after induction and its shutoff. To address this, we followed the response of the SOS network in living individual Escherichia coli cells. The promoter activity (PA) of SOS genes was monitored using fluorescent protein-promoter fusions, with high temporal resolution, after ultraviolet irradiation activation. We find a temporal pattern of discrete activity peaks masked in studies of cell populations. The number of peaks increases, while their amplitude reaches saturation, as the damage level is increased. Peak timing is highly precise from cell to cell and is independent of the stage in the cell cycle at the time of damage. Evidence is presented for the involvement of the umuDC operon in maintaining the pattern of PA and its temporal precision, providing further evidence for the role UmuD cleavage plays in effecting a timed pause during the SOS response, as previously proposed. The modulations in PA we observe share many features in common with the oscillatory behavior recently observed in a mammalian DNA damage response. Our results, which reveal a hitherto unknown modulation of the SOS response, underscore the importance of carrying out dynamic measurements at the level of individual living cells in order to unravel how a natural genetic network operates at the systems level.

High fidelity of RecA-catalyzed recombination: a watchdog of genetic diversity.

Homologous recombination plays a key role in generating genetic diversity, while maintaining protein functionality. The mechanisms by which RecA enables a single-stranded segment of DNA to recognize a homologous tract within a whole genome are poorly understood. The scale by which homology recognition takes place is of a few tens of base pairs, after which the quest for homology is over. To study the mechanism of homology recognition, RecA-promoted homologous recombination between short DNA oligomers with different degrees of heterology was studied in vitro, using fluorescence resonant energy transfer. RecA can detect single mismatches at the initial stages of recombination, and the efficiency of recombination is strongly dependent on the location and distribution of mismatches. Mismatches near the 5' end of the incoming strand have a minute effect, whereas mismatches near the 3' end hinder strand exchange dramatically. There is a characteristic DNA length above which the sensitivity to heterology decreases sharply. Experiments with competitor sequences with varying degrees of homology yield information about the process of homology search and synapse lifetime. The exquisite sensitivity to mismatches and the directionality in the exchange process support a mechanism for homology recognition that can be modeled as a kinetic proofreading cascade.

Application of Algebraic Topology to Homologous Recombination of DNA.

Brouwer's fixed point theorem, a fundamental theorem in algebraic topology proved more than a hundred years ago, states that given any continuous map from a closed, simply connected set into itself, there is a point that is mapped unto itself. Here we point out the connection between a one-dimensional application of Brouwer's fixed point theorem and a mechanism proposed to explain how extension of single-stranded DNA substrates by recombinases of the RecA superfamily facilitates significantly the search for homologous sequences on long chromosomes.