Repressor and Activator Dynamics

<p>(A and B) Shows repressor <i>(y)</i>, activator <i>(x)</i> phase plane analysis for both designs. Nullclines and limit cycle trajectory (red line) close to the bifurcation point. Solid line, activator-nullcline; dashed line, repressor-nullcline; inset, frequency of the limit cycle oscillations as a function of the bifurcation parameter Δ. Note the difference in both designs (oscillations may arise almost with zero frequency in Design I).</p> <p>(C and D) Activator (<i>x</i>, solid blue line) and repressor (<i>y</i>, dashed red line) adimensional concentration as a function of time. We consider the following parameter values in all figures: ξ_x = 1.58, ɛ = 0.05, <i>ρ</i> = 50, σ = 1 (see Supporting Information for bifurcation diagrams associated with the emergence of oscillations).</p

Minimal Oscillatory Architecture and Its Genetic Implementation

<p>(A) An activator (red) is acting on itself and on a repressor element (blue). The repressor is in turn acting on the activator. (B) The logical elements correspond to the promoter and coding region of a given gene. This motif can be genetically implemented in two ways. An activator protein operates transcriptionally in both cases while repression is implemented at the transcriptional, Design I (C), or post-translational, Design II (D) level.</p

Effect of Noise Due to the Presence of a Small Number of Molecules of All Circuit Components

<p>CV and τ_c scaled by the deterministic oscillation periods versus biochemical noise expressed as the average number of activator molecules per period, obtained from numerical simulations. (A and C) Design I; (B and D) Design II. Filled circles correspond to a situation close to bifurcation in both designs and open squares to a value of the parameter Δ far from bifurcation. Error bars are the size of data points.</p

Phase Lag Distributions in the Oscillatory Regime

<p>(Δ = 11 in Design I and Δ = 22 in Design II) with biochemical noise at protein levels close to the deterministic limit in both models (the CV of period distribution is ~0.045 in both designs). Solid line (black): no forcing, Design I. Dashed line (red): critical forcing at ω/ω₀~0.9 in Design I. Dotted line (blue): same parameters for Design II. Design II is more difficult in being synchronized, exhibiting thus more phase diffusion.</p

Synchronization Regions (Arnold Tongues) for the Deterministic Models

<p>Only the 1:1 (red) and 1:2 (blue) stable resonance regions are shown. ω₀ is the limit cycle frequency (the undriven system is in the oscillatory regime at Δ = 11 for Design I and Δ = 22 for Design II, respectively), and ω denotes the signal frequency. The (scaled) signal amplitude δ_RS affects the repressor degradation (see Supporting Information). Positive values (top panels) increase degradation and decrease the value of Δ while negative values (bottom panels) decrease degradation and increase the value of Δ. Solid lines: critical values of signal amplitude for effectively driving the system towards the rest state.</p

Effect of Noise Due to the Presence of a Small Number of mRNA Molecules

<p>CV and τ_c, as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0020030#pcbi-0020030-g004" target="_blank">Figure 4</a>, versus biochemical noise expressed as the average number of activator mRNA molecules per period. (A and C) Design I; (B and D) Design II. Filled circles correspond to a situation close to bifurcation in both designs and open squares to a value of the parameter Δ far from bifurcation. We fix the cell volume such as the system experiences intermediate noise strengths (coinciding with the maxima seen in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.0020030#pcbi-0020030-g004" target="_blank">Figure 4</a>, where the number of activator molecules is ~500 in Design I and ~200 in Design II). Error bars are the size of data points.</p

Response in Activator Concentration <i>(x)</i> to a Short-Pulse Train

<p>(A and C) Design I; (B and D) Design II.</p> <p>(A and B) Three pulses of fixed amplitude and duration. In this example, pulses represent transient changes in repressor degradation rate, i.e., changes in parameter Δ. Pulse durations are chosen approximately as 1/10 of the oscillation period (1 time unit for Design I, and 0.2 time units for Design II, respectively). Pulse amplitudes are 1 for Design I and 0.5 for Design II in units of Δ (right y axis).</p> <p>(C) Design I: ten pulses with the same amplitude and period eliciting a large response.</p> <p>(D) Design II: three pulses with the same amplitude but slightly longer duration (0.3 time units) are able to trigger a big response.</p

Proportion of gene pairs conserved in a comparator versus intergene distance in

<p><b>Copyright information:</b></p><p>Taken from "The determinants of gene order conservation in yeasts"</p><p>http://genomebiology.com/2007/8/11/R233</p><p>Genome Biology 2007;8(11):R233-R233.</p><p>Published online 5 Nov 2007</p><p>PMCID:PMC2258174.</p><p></p> Profiles of the rate of gene pairs conserved versus their current spacer in (red) or in simulants (blue) when comparing with two comparator species for and . For the simulations the number of inversions to run was determined by comparing observed synteny conservation rates against inversion number as shown in Figure 1. For our five focal species we also restricted analysis to cases where both of the orthologues of the gene pair are on the same chromosome in the comparator species, as this fits better the simulant model and permits higher orthology certainty. Each data point in the real and simulant data represents the proportion of gene pairs from 50 showing conserved synteny, after the data was rank ordered by intergene distance. After considering the first 50 we then considered ranks 2-51, 3-52, and so on. In addition, we also considered other comparators, and a much more distant comparator, (Additional data file 1)

Determinants of close non-adjacently conserved pairs versus distant adjacently conserved pairs

<p><b>Copyright information:</b></p><p>Taken from "The determinants of gene order conservation in yeasts"</p><p>http://genomebiology.com/2007/8/11/R233</p><p>Genome Biology 2007;8(11):R233-R233.</p><p>Published online 5 Nov 2007</p><p>PMCID:PMC2258174.</p><p></p> The difference between the ratio of determinant values of non-adjacently conserved genes in a close species to () and those adjacently conserved in a distant species () is plotted in red for each predictor (line between points to help visualization). This ratio is defined as the quotient between the corresponding values of the close (distant) pairs and those of the adjacently conserved pairs in the close species, that is, . We also plotted the null behavior obtained by random sampling of the combined group, close and distant, preserving group size, 10,000 times (mean, continuous blue line, ±2 standard deviations, dashed blue lines). Behavior was qualitatively robust for the , , and predictors when using and as close/distant comparator (Additional data file 1)