Experimental evidence for amplitude and frequency modulation.

<p>(A and B) Example data showing amplitude modulation from [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004222#pcbi.1004222.ref010" target="_blank">10</a>]. (A) Single-cell nuclear localization of Msn2 transcription factor in response to H₂O₂ stress as a function of time. The stimulus profile (input) is a step change applied at <i>t</i> = 0 (inset) which applies to all figure panels. (B) Average time trace for different concentrations of H₂O₂ stress. (C and D) Example data showing frequency modulation from [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004222#pcbi.1004222.ref015" target="_blank">15</a>]. (C) Single-cell nuclear localization of Crz1 in response to calcium stress as a function of time, showing bursts of Crz1. (D) The average frequency of bursts against calcium concentration, showing an increased frequency with increased concentration. (Inset) Burst duration distribution for low (blue bars) and high (red bars) concentration. Both histograms are well described by the Gamma distribution <math><mrow><mi>h</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><mi>t</mi><mi>e</mi><mrow><mo>−</mo><mi>t</mi><mo>/</mo><msub><mi>τ</mi><mi>b</mi></msub></mrow></mrow></math>, with <i>τ</i>_<i>b</i> = 70s (black solid line), demonstrating that pulse duration is independent of calcium concentration. Experimental data in arbitrary units (AU) of fluorescence.</p

First three moments of the protein distribution in concentration sensing from the master equation.

<p>Averages (A,B), variance (C,D), and skewness (E,F) as a function of the frequency of binding events, <i>f</i> = <i>k</i>₊<i>c</i>₀/(1+<i>k</i>₊<i>c</i>₀/<i>k</i>₋). (Insets) Magnification of small-noise approximation region (fast switching). Analytical results for CM (blue) and numerical results for BM (red) as function of the frequency of binding events (logarithmic scale). Two regimes are shown: <i>k</i>₋ = 10 <i>k</i>₊<i>c</i>₀ (<i>α</i> = 100<i>s</i>⁻¹, <i>γ</i> = 1<i>s</i>⁻¹, <i>ζ</i> from 1000 to 1) (left column) and <i>k</i>₋ = 0.1 <i>k</i>₊<i>c</i>₀ (<i>α</i> = 10<i>s</i>⁻¹, <i>γ</i> = 1<i>s</i>⁻¹, <i>ζ</i> from 1000 to 1) (right column). Averages from CM and BM are constrained to be equal, <i>i.e</i>. <math><mrow><mi>ζ</mi><mo>=</mo><mi>α</mi><msubsup><mi>k</mi><mo>−</mo><mrow><mo>−</mo><mn>1</mn></mrow></msubsup></mrow></math>. Variances of CM and BM exhibit two different regimes for fast switching: for <i>k</i>₊<i>c</i>₀ < <i>k</i>₋ BM is more accurate than CM (inset in C), while for <i>k</i>₊<i>c</i>₀ > <i>k</i>₋ CM is generally more accurate (inset in D), except for <i>ζ</i> = 1. Third moments show that, for large noise, the probability distributions become asymmetric.</p

Two regimes in incoherent feedforward loop based on the small-noise approximation.

<p>Output noise, <i>i.e</i>. relative variance of <i>x</i> (top) and <i>y</i> (bottom), as function of the non-dimensional ramp time <i>u</i>₁<i>t</i>/<i>u</i>₀ for <i>k</i>₊<i>c</i>₀ < <i>k</i>₋<i>i.e</i>. ⟨<i>τ</i>_<i>b</i>⟩ < ⟨<i>τ</i>_<i>u</i>⟩ (left) and <i>k</i>₊<i>c</i>₀ > <i>k</i>₋<i>i.e</i>. ⟨<i>τ</i>_<i>b</i>⟩ > ⟨<i>τ</i>_<i>u</i>⟩ (right). CM and BM are shown by blue and red lines respectively. (A,B) BM is more accurate than AM for <i>k</i>₊<i>c</i>₀ = 10⁷<i>s</i>⁻¹ and <i>k</i>₋ = 6.7 × 10⁷<i>s</i>⁻¹. (C,D) CM is more accurate then BM for <i>k</i>₊<i>c</i>₀ = 10⁷<i>s</i>⁻¹ and <i>k</i>₋ = 6.7 × 10⁶<i>s</i>⁻¹. Remaining parameters: <i>k</i>₊<i>c</i>₁ = 10⁵<i>s</i>⁻², <i>k</i>_<i>x</i> = 5<i>s</i>⁻¹ and <i>k</i>_<i>y</i> = 10<i>s</i>⁻¹.</p

Advantages and disadvantages of amplitude and frequency modulation.

<p>AM may be less noisy than FM (A,B), but FM may allow coordinated expression of many genes (C,D) [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004222#pcbi.1004222.ref015" target="_blank">15</a>, <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004222#pcbi.1004222.ref019" target="_blank">19</a>]. (A) In AM, low/high stimuli result in low/high levels of transcription factor (TF) inside the nucleus. (B) In AM, different nuclear TF concentrations (blue and red curves) lead to gene expression of proteins A and B (see orange and green promoter functions respectively) with variable ratios (order of dot and square changes). (C) In FM, the stimulus strength only affects the frequency of bursts, not their amplitude. (Inset) Schematic of TF (purple dots) binding promoter <i>P</i>_<i>A</i> of gene <i>A</i> (orange) and promoter <i>P</i>_<i>B</i> of gene <i>B</i> (green) with different binding strengths. (D) In FM, the nuclear TF concentration is always the same during a burst, only the frequency of occurrence changes. As a consequence, the protein ratio stays constant.</p

The two regimes in the linear pathway model based on the master equation.

<p>(A-B) fast (<i>k</i>₊<i>c</i>₀ = 20<i>s</i>⁻¹, <i>k</i>₋ = 100<i>s</i>⁻¹, <i>γ</i> = 0.1<i>s</i>⁻¹, <i>α</i> = 100<i>s</i>⁻¹, <i>ζ</i> = 1) and (C-D) slow (<i>k</i>₊<i>c</i>₀ = 0.01<i>s</i>⁻¹, <i>k</i>₋ = 0.05<i>s</i>⁻¹, <i>γ</i> = 1<i>s</i>⁻¹, <i>α</i> = 25<i>s</i>⁻¹, <i>ζ</i> = 500) switching. (A,C) Protein number as a function of time from Gillespie simulations for CM (blue lines) and BM (red lines). (B) The probability distribution for <i>n</i> target proteins is unimodal for both AM (blue) and FM (red). (D) The probability distribution is bimodal for AM (blue) and remains unimodal for BM (red) but with a long tail in the slow switching regime.</p

Schematic view of signaling and gene regulation.

<p>(A) Cartoon of <i>S. cerevisiae</i> in presence of extracellular calcium, considered a paradigm of bursty frequency modulation. Calcium enters through plasma-membrane ion channels and can be stored (released) in (from) vacuoles. Intracellular calcium activates calcineurin, which dephosphorylates Crz1p. Once dephosphorylated, Crz1 binds inporting Nmd5p and enters the nucleus. Exportin Msn5p subsequently removes Crz1 from the nucleus. Cytoplasmic calcium pulses may correspond to Crz1 bursts in the nucleus [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004222#pcbi.1004222.ref015" target="_blank">15</a>]. Red arrows indicate movement while blue arrows stand for chemical signaling. (B) Single receptor/ion channel activity, <i>r</i>(<i>t</i>) (blue line), depends on the concentration of extra-cellular stimulus <i>c</i>. The signaling rate <i>u</i> differs between continuous (CM) and bursty modulation (BM). In CM, <i>u</i> is constant rate <i>α</i> during bound intervals, with <i>p</i>_<i>b</i> the probability of being bound. In BM, <i>ζ</i> molecules are realized at the time of binding with <i>τ</i>_bursts the duration between consecutive bursts (binding events). (C) Different regulatory networks. Linear pathway used for concentration sensing. Incoherent feedforward loop and integral feedback control allow chemical ramps to be sensed.</p

Premature Expression of Foxp3 in Double-Negative Thymocytes

<div><p>Peripheral immune regulation depends on the generation of thymic-derived regulatory T (tT_reg) cells to maintain self-tolerance and to counterbalance overshooting immune responses. The expression of the T_reg lineage defining transcription factor Foxp3 in developing tT_reg cells depends on TCR signaling during the thymic selection process of these T cells. In this study, we surprisingly identify Foxp3⁺ immature thymocytes at the double-negative (DN) stage in transcription factor 7 (Tcf7)-deficient mice. These Foxp3⁺ cells did not express a TCR (β or γδ chains), CD3 or CD5 and therefore these cells were true DN cells. Further investigation of this phenomenon in a transgenic TCR model showed that Foxp3-expressing DN cells could not respond to TCR stimulation <i>in vivo</i>. These data suggest that Foxp3 expression in these DN cells occurred independently of TCR signaling. Interestingly, these Foxp3⁺ DN cells were located in a transition state between DN1 and DN2 (CD4^-CD8^-CD3^-TCR^-CD44^highCD25^low). Our results indicate that Tcf7 is involved in preventing the premature expression of Foxp3 in DN thymocytes.</p></div

Main parameters and their values.

<p>Main parameters and their values.</p

Evidence of tip-focus splitting, growth of foci and emergence of branches, in fluorescence-imaged <i>Streptomyces coelicolor</i> expressing <i>divIVA-egfp</i>.

<p>The tip always contains a large DivIVA focus and established tips extend at an approximately constant speed. At about 12 minutes, the DivIVA tip-focus undergoes splitting, leaving behind a new focus (arrow). As the tip continues to extend, the new focus remains in place on the membrane and grows in intensity. After about 42 minutes a new branch is formed at the position of the new focus, with the new focus now sitting at the tip of the new branch. Both the new branch and the original branch now continue to extend in length. Time in hours∶minutes. Scale bar: .</p

Analysis of Foxp3⁺ DN cells in TEa-Tcf7-deficient mice.

<p>(A) Representative plots showing TCRVβ6 and TCRVα2 expression on CD4SP thymocytes from TEa-Tcf7^+/+ and TEa-Tcf7^-/- mice in the presence or absence of cognate antigen (Ag). The Tg TCR population is divided into TCR^high and TCR^low populations. (B-C) Quantification of the percentage of total (B) or TCR^high (C) TCRVβ6⁺TCRVα2⁺ cells among CD4SP thymocytes (n = 8). (D) Representative plots showing Foxp3 expression in DN TCRVβ6⁺TCRVα2⁺ thymocytes from TEa-Tcf7^+/+ and TEa-Tcf7^-/- mice in the absence of Ag. (E) Quantification of Foxp3⁺ DN TCRVβ6⁺TCRVα2⁺ thymocytes from TEa-Tcf7^+/+ and TEa-Tcf7^-/- mice in the presence or absence of Ag (n = 8). (F-G) Representative plots showing TCRVβ6 and TCRVα2 expression on DN Foxp3⁺ (F) or CD4SP Foxp3⁺ (G) thymocytes from TEa-Tcf7^+/+ and TEa-Tcf7^-/- mice in the presence or absence of Ag. Cells are pre-gated on TCRVβ6⁺TCRVα2⁺. Each dot represents one individual animal and mean is shown for all quantified data. Numbers show percentages of cells within the indicated box. NS, not significant, *** P < 0.001, **** P < 0.0001 (unpaired t-test).</p