Prediction by Promoter Logic in Bacterial Quorum Sensing

Quorum-sensing systems mediate chemical communication between bacterial cells, coordinating cell-density-dependent processes like biofilm formation and virulence-factor expression. In the proteobacterial LuxI/LuxR quorum sensing paradigm, a signaling molecule generated by an enzyme (LuxI) diffuses between cells and allosterically stimulates a transcriptional regulator (LuxR) to activate its cognate promoter (pR). By expressing either LuxI or LuxR in positive feedback from pR, these versatile systems can generate smooth (monostable) or abrupt (bistable) density-dependent responses to suit the ecological context. Here we combine theory and experiment to demonstrate that the promoter logic of pR – its measured activity as a function of LuxI and LuxR levels – contains all the biochemical information required to quantitatively predict the responses of such feedback loops. The interplay of promoter logic with feedback topology underlies the versatility of the LuxI/LuxR paradigm: LuxR and LuxI positive-feedback systems show dramatically different responses, while a dual positive/negative-feedback system displays synchronized oscillations. These results highlight the dual utility of promoter logic: to probe microscopic parameters and predict macroscopic phenotype

Students’ Epistemic Connections Between Science Inquiry Practices and Disciplinary Ideas in a Computational Science Unit

Teaching science inquiry practices, especially the more contemporary ones, such as computational thinking practices, requires designing newer learning environments and appropriate pedagogical scaffolds. Using such learning environments, when students construct knowledge about disciplinary ideas using inquiry practices, it is important that they make connections between the two. We call such connections epistemic connections, which are about constructing knowledge using science inquiry practices. In this paper, we discuss the design of a computational thinking integrated biology unit as an Emergent Systems Microworlds (ESM) based curriculum. Using Epistemic Network Analysis, we investigate how the design of unit support students’ learning through making epistemic connections. We also analyze the teacher’s pedagogical moves to scaffold making such connections. This work implies that to support students’ epistemic connections between science inquiry practices and disciplinary ideas, it is critical to design restructured learning environments like ESMs, aligned curricular activities and provide appropriate pedagogical scaffolds

Model-independent predictions.

<p>Each stack of histograms relates to predictions and terminal response measurements of a different feedback loop shown in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002361#pcbi-1002361-g001" target="_blank">Fig. 1C–E</a>. In all stacks, grey histograms show model-independent predictions over 1000 trials. Note that the predictions are of deterministic steady-states, while the measurements include the effects of cell-to-cell variability; measured histograms are thus broader than predicted ones. (A) Rec-RFB. Orange histograms show observed LuxR::YFP levels. Numbers on the right indicate aTc levels in ng/ml. Our predictions match the observed fluorescence intensities as well as the threshold aTc level within a factor of two, even though both the input and output are varied by over an order of magnitude. (B) Aut-RFB. Orange histograms show observed LuxR::YFP levels for ON-history cells, white histograms show observed LuxR::YFP levels for OFF-history cells; the intersection is hatched. Numbers on the right indicate IPTG levels in µM. LuxR::YFP levels are predicted to be low independent of IPTG, but are observed to be induced starting from IPTG∼50 µM. There is no evidence of hysteresis. (C) Aut-IFB. Blue histograms show observed LuxI::CFP levels for ON-history cells, white histograms show observed LuxI::CFP levels for OFF-history cells; the intersection is hatched. Numbers on the right indicate IPTG levels in µM. For the Aut-IFB case, we sometimes detect three intersections of the input-output characteristic with the line of equivalence, an indication of multistability and hysteresis; the low and high intersections are predicted stable values, the middle intersection is an unstable threshold (e.g. see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002361#pcbi-1002361-g005" target="_blank">Fig. 5D</a>). Percent values show the fraction of trials that generate such multistable predictions. The actual terminal response is indeed observed to be hysteretic: histograms from OFF-history cells and ON-history cells are non-overlapping for IPTG = 10 µM and 50 µM.</p

The interplay of regulation, promoter logic, and feedback.

<p>(A) Response types for the LuxR-feedback topology, with LuxI as the regulator. (B) Response types for the LuxI-feedback topology, with LuxR as the regulator. Each panel shows an identical slice of parameter space: the Hill coefficient of LuxR-DNA binding is varied along the <i>x</i>-axis; the transcription rate of the regulator is varied along the <i>y</i>-axis; all other parameters are fixed at their autonomous loop values given in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002361#pcbi.1002361.s011" target="_blank">Table S3</a>. The parameters corresponding to our autonomous loop experiments are shown as seven partly overlapping white dots, whose positions are identical in the two panels: their <i>x</i>-coordinates are given by the fitted Hill coefficient  = 1.45; their <i>y</i>-coordinates are given by the seven IPTG-induced pLac transcription rates, obtained using Eq. S4 with parameters from <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002361#pcbi.1002361.s012" target="_blank">Table S4</a>. The boundaries between the four DDR types are computed numerically; any differences in these DDR boundaries between the two panels can be attributed to topology alone. Both LuxR-feedback and LuxI-feedback topologies can generate all four types of density-dependent responses; however, given the same microscopic parameters the two topologies can show distinct behaviors. The observed LuxR-feedback responses happens to fall near the monostable type M boundary, while the observed LuxI-feedback responses are solidly within the bistable type B region. Generically, for a given ‘hard-wired’ value of the LuxR-feedback response will be either type M (smooth) or type B (abrupt). In contrast, as long as is sufficiently high, the LuxI-feedback system can be tuned between smooth and abrupt responses by varying the regulator level . Moreover, the LuxI-feedback system can achieve abrupt responses over a broader range of values. These figures are qualitatively unchanged for other values of the fixed parameters (Supporting Information, <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002361#pcbi.1002361.s013" target="_blank">Text S1</a>: Bifurcation analysis of feedback loops).</p

Model-based predictions.

<p>(A,D) Intersections of input-output characteristics (IOCs: black curves, generated using Eq. 6, <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002361#pcbi.1002361.s011" target="_blank">Table S3</a>, and Eq. S4, <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002361#pcbi.1002361.s012" target="_blank">Table S4</a>) with lines of equivalence (red lines, generated using Eq. S3, <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002361#pcbi.1002361.s011" target="_blank">Table S3</a>). Datapoints show CFP values from the PLF; fluorescence values are background-subtracted. Since the promoters driving the regulators have lower maximal transcription rates than pR, datapoints lie in a low band of regulator values. Fitted IOCs appear to have the same maximal value because the half-saturation concentration for LuxR-DNA binding is ∼1 LuxR molecule per cell, far below available total LuxR (Supporting Information, <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002361#pcbi.1002361.s013" target="_blank">Text S1</a>: AHL and LuxR biochemistry). (B,C,E) Predicted (curves) and measured (datapoints) terminal responses for the three feedback loops. Each datapoint gives the mean fluorescence of a cell population; error bars represent standard deviations over replicates. (A) For predicting LuxR-feedback response, the IOC is a vertical slice of the PLF (keeping aTc and LuxI fixed, while varying IPTG and LuxR); for example, we show IOCs corresponding to aTc = 0 ng/ml and 50 ng/ml (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002361#pcbi-1002361-g003" target="_blank">Fig. 3C</a>). (B) Feedback response of Aut-RFB. White datapoints show the terminal response of OFF-history cells; orange datapoints show the terminal response of ON-history cells. There is no evidence of hysteresis; we infer that all DDRs are monostable, type M. (C) Feedback response of Rec-RFB. Orange datapoints show measured terminal responses. We infer that all DDRs are monostable, type M. (D) For predicting LuxI-feedback response, the IOC is a horizontal slice of the PLF (keeping IPTG and LuxR fixed, while varying aTc and LuxI); for example, we show IOCs corresponding to IPTG = 10 µM and 100 µM (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002361#pcbi-1002361-g003" target="_blank">Fig. 3C</a>). (E) Feedback response of Aut-IFB. White datapoints show the terminal response of OFF-history cells; blue datapoints show the terminal response of ON-history cells; the grey box highlights the hysteretic region. We infer that DDRs in the hysteretic IPTG range are bistable, type B±, while those below and above this range are type B− and B+ respectively. (F) Quantifying hysteresis for autonomous feedback loops Aut-RFB (orange) and Aut-IFB (blue). We show p-values from a T-test quantifying the differences between the terminal responses of ON-history and OFF-history cells over replicates; the dotted line shows p = 0.05. Only the Aut-IFB system shows significant hysteresis (grey box).</p

Density-dependent responses and feedback loops.

<p>(A) The response of a quorum-sensing system is encapsulated by its transcriptional output, from the moment of inoculation upto its terminal density . Four different types of density-dependent responses can arise: (M) monostable, where transcription smoothly increases with cell density; (B+) bistable, with a threshold density at which transcription abruptly increases; (B±) bistable and hysteretic at the terminal density, where high and low transcription states co-exist; (B−) bistable but un-induced even at the terminal density, since the potentially bistable region is never reached. Solid lines are stable fixed points, dotted lines are unstable fixed points, and grey boxes indicate bistable density ranges. In our experiments we infer DDRs from the measured terminal responses. These figures were generated for the autonomous LuxI-feedback system using Eq. S18 and parameters from <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002361#pcbi.1002361.s011" target="_blank">Table S3</a>. Here  = 0.05 (OD₆₀₀) to match the autonomous loop experiments, while are varied as follows. M: {0.1,0.6}; B+: {0.04,1.6}; B±: {0.01,1.4}; B−: {0.002,1.5}. (B) Constructs used in this study. In sender cells (Sen), LuxI is expressed from the aTc-inducible pTet promoter. In feedforward receiver cells (Rec-FF), LuxR is expressed from the IPTG-inducible pLac promoter, and CFP is expressed from the pR promoter. (C) In the feedback receiver cells (Rec-RFB), LuxR is expressed in feedback from the pR promoter. (D,E) In autonomous feedback systems (Aut-RFB and Aut-IFB) either LuxR or LuxI is expressed in feedback from the pR promoter, while the other protein is expressed from the pLac promoter. Detailed construct maps are given in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002361#pcbi.1002361.s009" target="_blank">Tables S1</a>, <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002361#pcbi.1002361.s010" target="_blank">S2</a>.</p

Examples of feedback and regulation in LuxI/LuxR quorum-sensing systems.

<p>Examples of feedback and regulation in LuxI/LuxR quorum-sensing systems.</p