Boosting Functional Response Models for Location, Scale and Shape with an Application to Bacterial Competition

We extend Generalized Additive Models for Location, Scale, and Shape (GAMLSS) to regression with functional response. This allows us to simultaneously model point-wise mean curves, variances and other distributional parameters of the response in dependence of various scalar and functional covariate effects. In addition, the scope of distributions is extended beyond exponential families. The model is fitted via gradient boosting, which offers inherent model selection and is shown to be suitable for both complex model structures and highly auto-correlated response curves. This enables us to analyze bacterial growth in \textit{Escherichia coli} in a complex interaction scenario, fruitfully extending usual growth models.Comment: bootstrap confidence interval type uncertainty bounds added; minor changes in formulation

Gene expression noise in a complex artificial toxin expression system

Gene expression is an intrinsically stochastic process. Fluctuations in transcription and translation lead to cell-to-cell variations in mRNA and protein levels affecting cellular function and cell fate. Here, using fluorescence time-lapse microscopy, we quantify noise dynamics in an artificial operon in Escherichia coli, which is based on the native operon of ColicinE2, a toxin. In the natural system, toxin expression is controlled by a complex regulatory network;upon induction of the bacterial SOS response, ColicinE2 is produced (cea gene) and released (cel gene) by cell lysis. Using this ColicinE2-based operon, we demonstrate that upon induction of the SOS response noise of cells expressing the operon is significantly lower for the (mainly) transcriptionally regulated gene cea compared to the additionally post-transcriptionally regulated gene cel. Likewise, we find that mutations affecting the transcriptional regulation by the repressor LexA do not significantly alter the population noise, whereas specific mutations to post-transcriptionally regulating units, strongly influence noise levels of both genes. Furthermore, our data indicate that global factors, such as the plasmid copy number of the operon encoding plasmid, affect gene expression noise of the entire operon. Taken together, our results provide insights on how noise in a native toxin-producing operon is controlled and underline the importance of post-transcriptional regulation for noise control in this system

CsrA and its regulators control the time-point of ColicinE2 release in Escherichia coli

The bacterial SOS response is a cellular reaction to DNA damage, that, among other actions, triggers the expression of colicin - toxic bacteriocins in Escherichia coli that are released to kill close relatives competing for resources. However, it is largely unknown, how the complex network regulating toxin expression controls the time-point of toxin release to prevent premature release of inefficient protein concentrations. Here, we study how different regulatory mechanisms affect production and release of the bacteriocin ColicinE2 in Escherichia coli. Combining experimental and theoretical approaches, we demonstrate that the global carbon storage regulator CsrA controls the duration of the delay between toxin production and release and emphasize the importance of CsrA sequestering elements for the timing of ColicinE2 release. In particular, we show that ssDNA originating from rolling-circle replication of the toxin-producing plasmid represents a yet unknown additional CsrA sequestering element, which is essential in the ColicinE2-producing strain to enable toxin release by reducing the amount of free CsrA molecules in the bacterial cell. Taken together, our findings show that CsrA times ColicinE2 release and reveal a dual function for CsrA as an ssDNA and mRNA-binding protein, introducing ssDNA as an important post-transcriptional gene regulatory element

Effects of stochasticity and division of labor in toxin production on two-strain bacterial competition in Escherichia coli

In phenotypically heterogeneous microbial populations, the decision to adopt one or another phenotype is often stochastically regulated. However, how this stochasticity affects interactions between competing microbes in mixed communities is difficult to assess. One example of such an interaction system is the competition of an Escherichia coli strain C, which performs division of labor between reproducers and self-sacrificing toxin producers, with a toxin-sensitive strain S. The decision between reproduction or toxin production within a single C cell is inherently stochastic. Here, combining experimental and theoretical approaches, we demonstrate that this stochasticity in the initial phase of colony formation is the crucial determinant for the competition outcome. In the initial phase (t < 12h), stochasticity influences the formation of viable C clusters at the colony edge. In the subsequent phase, the effective fitness differences (set primarily by the degree of division of labor in the C strain population) dictate the deterministic population dynamics and consequently competition outcome. In particular, we observe that competitive success of the C strain is only found if (i) a C edge cluster has formed at the end of the initial competition phase and (ii) the beneficial and detrimental effects of toxin production are balanced, which is the case at intermediate toxin producer fractions. Our findings highlight the importance of stochastic processes during the initial phase of colony formation, which might be highly relevant for other microbial community interactions in which the random choice between phenotypes can have long-lasting consequences for community fate

Amount of colicin release in Escherichia coli is regulated by lysis gene expression of the colicin E2 operon.

The production of bacteriocins in response to worsening environmental conditions is one means of bacteria to outcompete other microorganisms. Colicins, one class of bacteriocins in Escherichia coli, are effective against closely related Enterobacteriaceae. Current research focuses on production, release and uptake of these toxins by bacteria. However, little is known about the quantitative aspects of these dynamic processes. Here, we quantitatively study expression dynamics of the Colicin E2 operon in E. coli on a single cell level using fluorescence time-lapse microscopy. DNA damage, triggering SOS response leads to the heterogeneous expression of this operon including the cea gene encoding the toxin, Colicin E2, and the cel gene coding for the induction of cell lysis and subsequent colicin release. Advancing previous whole population investigations, our time-lapse experiments reveal that at low exogenous stress levels all cells eventually respond after a given time (heterogeneous timing). This heterogeneous timing is lost at high stress levels, at which a synchronized stress response of all cells 60 min after induction via stress can be observed. We further demonstrate, that the amount of colicin released is dependent on cel (lysis) gene expression, independent of the applied exogenous stress level. A heterogeneous response in combination with heterogeneous timing can be biologically significant. It might enable a bacterial population to endure low stress levels, while at high stress levels an immediate and synchronized population wide response can give single surviving cells of the own species the chance to take over the bacterial community after the stress has ceased

Boosting functional response models for location, scale and shape with an application to bacterial competition

We extend generalized additive models for location, scale and shape (GAMLSS) to regression with functional response. This allows us to simultaneously model point-wise mean curves, variances and other distributional parameters of the response in dependence of various scalar and functional covariate effects. In addition, the scope of distributions is extended beyond exponential families. The model is fitted via gradient boosting, which offers inherent model selection and is shown to be suitable for both complex model structures and highly auto-correlated response curves. This enables us to analyse bacterial growth inEscherichia coliin a complex interaction scenario, fruitfully extending usual growth models

Boosting functional response models for location, scale and shape with an application to bacterial competition

We extend generalized additive models for location, scale and shape (GAMLSS) to regression with functional response. This allows us to simultaneously model point-wise mean curves, variances and other distributional parameters of the response in dependence of various scalar and functional covariate effects. In addition, the scope of distributions is extended beyond exponential families. The model is fitted via gradient boosting, which offers inherent model selection and is shown to be suitable for both complex model structures and highly auto-correlated response curves. This enables us to analyse bacterial growth in Escherichia coli in a complex interaction scenario, fruitfully extending usual growth models.Peer Reviewe

Characterization of interaction dynamics.

<p>The increase of the toxin producer fraction and not the ColicinE2 producer strain (C strain) growth rate determines the change in outcome distributions. Unless otherwise stated, colors indicate competition outcome (magenta: sensitive strain, green: producer strain, grey/black: coexistence), error bars represent mean ± standard deviation. (A) Sample image time series and corresponding area and relative fraction curves show C domination outcome (0.01 μg/ml MitC). Scale bar represents 400 μm. (B) Average expansion rates of single-strain colonies obtained in control experiments (no interaction). (C) Effective expansion rates of the entire S–C colony during competition (interaction present). Colors indicate the outcome of the competition: e.g., magenta indicates that >90% of S are present and responsible for colony expansion. (D) Temporal evolution of the producer fraction in the C population in high-resolution control experiments (<a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.2001457#sec004" target="_blank">Methods</a>). (E), The dependence of transition time (time taken for C to capture more than 50% on the colonized area) on inducer concentration. (B, C, E: asterisks indicate significant differences as obtained by pairwise <i>t</i>-tests; not significant (ns): <i>p</i> > 0.05, ***: <i>p</i> < 0.001, for details see <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.2001457#pbio.2001457.s015" target="_blank">S1 Data</a>).</p

Two-strain competition, strategies, and outcome.

<p>C–S competition results in four competition outcomes. The competition outcome distribution changes with increasing inducer concentration. (A) Interaction between a toxin-producing strain (C strain) and a sensitive strain (S strain) is characterized by inter-strain competition (spatial exclusion and toxin action) and intra-strain cooperation within the C strain (division of labor between reproducers and toxin producers). (B) Possible outcomes of competition experiments between sensitive (magenta) and producer (green) cells after 48 h (scale bar = 1 mm). Mitomycin C (MitC) concentrations from left to right: 0.01/0.0/0.01/0.01 μg/ml). (C) Final fraction of C after competition (dot plot) and classified outcomes (pie plots) demonstrate a transition from coexistence and dominance of S (0.0 μg/ml MitC) to dominance of the producer strain (intermediate inducer concentrations, 0.005 and 0.01 μg/ml MitC) and failure of the toxin production strategy (high inducer concentration, 0.1 μg/ml MitC).</p