Schematic of a phylogenetic tree showing organisms in which IB homologs were found using BLASTP.

<p>Organisms with homologs for both IB and IB are in blue shaded region and organisms with a single homolog are in red shaded region. The branches in the schematic phylogenetic tree are not drawn to scale. (For simplicity, not all organisms with single or dual homologs are shown here. A complete list is provided in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003112#pcbi.1003112.s015" target="_blank">Table S6</a>).</p

Single feedback model variables.

*<p>average numbers of corresponding promoters.</p

The coefficient of variation (CV) in nuclear NF-B levels due to extrinsic and intrinsic fluctuations.

<p>The CV was calculated for peak (A,B) and late-phase (C,D) nuclear NF-B levels for both single and dual feedback systems. The CV due to intrinsic fluctuations was determined from at least 50 runs of the stochastic simulations at each value of IKK (A,C) and total NF-B (B,D). The CV due to extrinsic fluctuations in total NF-B and IKK levels was determined by varying the total NF-B level by for each value of IKK (A,C) and by varying IKK by for value of total NF-B (B,D).</p

Dual Delayed Feedback Provides Sensitivity and Robustness to the NF-<i>κ</i>B Signaling Module

<div><p>Many cellular stress-responsive signaling systems exhibit highly dynamic behavior with oscillatory features mediated by delayed negative feedback loops. What remains unclear is whether oscillatory behavior is the basis for a signaling code based on frequency modulation (FM) or whether the negative feedback control modules have evolved to fulfill other functional requirements. Here, we use experimentally calibrated computational models to interrogate the negative feedback loops that regulate the dynamic activity of the transcription factor NF-B. Linear stability analysis of the model shows that oscillatory frequency is a hard-wired feature of the primary negative feedback loop and not a function of the stimulus, thus arguing against an FM signaling code. Instead, our modeling studies suggest that the two feedback loops may be tuned to provide for rapid activation and inactivation capabilities for transient input signals of a wide range of durations; by minimizing late phase oscillations response durations may be fine-tuned in a graded rather than quantized manner. Further, in the presence of molecular noise the dual delayed negative feedback system minimizes stochastic excursions of the output to produce a robust NF-B response.</p></div

Response of the NF-B signaling module to transient inputs with magnitude ,

<p>(A) Time series of for a system with all feedback removed (top), a system with IB-mediated negative feedback (middle), and a system with both IB- and IB-mediated negative feedback (bottom) in response to 15 min (red), 30 min (orange), 45 min (green), and persistent (blue) stimulation. (B) The response duration as a function of the stimulus duration for the single feedback and dual feedback systems. The response duration is the amount of time exceeds a threshold level of 50 (as indicated by the dashed black lines in the graphs shown in (A).</p

Single feedback model reactions.

<p>Single feedback model reactions.</p

IB feedback model reactions.

<p>IB feedback model reactions.</p

Stochastic model simulation results for various network architectures (with 1000 total NF-B molecules).

<p>The architectures analyzed are the NF-B network with no feedback loops (A), only IB-mediated negative feedback (B), the NF-B network with both IB- and IB-mediated negative feedback (C), and an alternative auto-repressive network (D). The top panel in each group shows four typical runs of stochastic simulations for each network, the middle panel shows the mean and standard deviation for 200 runs of each network, and the bottom panel shows the corresponding coefficient of variation. The input signal, K(t), is switched from to at hrs. In A-C, the magnitude of external signal , in D, .</p

Period and decay rate of oscillations produced by the IB-mediated negative feedback system.

<p>(A) The oscillation period as a function of with min (green line) and as a function of with (red dashed line). (B) The oscillation decay rate as a function of with min (green line) and as a function of with (red dashed line).</p