The oscillation pattern is affected by the change in the diffusion coefficient.

<p>(A) There are large changes in the oscillation pattern at low and high diffusion coefficients. At low diffusion coefficients, virtually no oscillation is seen. Right panels show representative oscillations. (B) At diffusion coefficients from 10⁻¹² to 10⁻¹¹ m²/s, the oscillation frequency stays unchanged. At higher diffusion coefficient, however, the oscillation frequency becomes lower, and at lower diffusion coefficient, it becomes higher. (C) At diffusion coefficient lower than 10⁻¹² m²/s, the amplitude of the first peak increases as the diffusion coefficient increases. But it stays unchanged at higher diffusion coefficients. (D) The time to the first peak stays unchanged until the diffusion coefficient is increased to 10⁻¹¹ m²/s, and at higher diffusion coefficient, it increases drastically. (E) <i>τ_p</i> and <i>τ_d</i> increase by the increases in the diffusion coefficient.</p

The oscillation pattern is changed by the change in the location of the IκBs synthesis.

<p>(A) The IκBs synthesis proceeds in the same compartment as the nuclear membrane in the control condition (bottom panel). If its location is moved to the plasma membrane keeping other parameters unchanged, the oscillation pattern is changed (middle and top panels). The loci of IκBs synthesis are shown in red compartments. (B) The changes in the oscillation frequency, amplitude of the first peak, and the time to the first peak are quantitatively shown in the top, middle, and bottom panels, respectively.</p

The oscillation pattern is altered by the change in the nuclear transport.

<p>(A) There is a large change in the oscillation pattern by the change in the nuclear transport. Representative oscillations are shown in the right panels. (B) Oscillation frequency becomes larger as transport increases. (C) The amplitude of the first peak becomes larger at larger transport values. (D) The time to the first peak changed largely by the change in the transport. (E) <i>τ_p</i> and <i>τ_d</i> also show large change by the change in the transport. These data are not available at smaller nuclear transport values.</p

3D model requires a different parameter set from that used in the temporal model.

<p>(A) 3D model of spherical cell with diameter of 50 µm, which is divided into compartments enabling reaction-diffusion simulation. Red compartments indicate the nuclear membrane compartments. (B) Middle panel is the 3D simulation result with the same reaction rate constants as in the temporal model. The simulation result shows much lower oscillation frequency as compared to the temporal model shown in the top panel. Bottom panel is the oscillation in the 3D simulation with modified reaction rate constants. (C) No combination of diffusion coefficient and the location of IκBs protein synthesis (blue plane) gives comparable oscillation frequency as in the temporal model (orange plane). The range of D is 10⁻¹³ to 10⁻¹⁰ m²/s with three locations of IκBs protein synthesis, which are indicated by three icons. (D) We defined oscillation frequency <i>f</i>, height of the first peak <i>A₀</i>, time to the first peak <i>t_fp</i>, decay time constant of the peak <i>τ_p</i>, and decay time constant <i>τ_d</i> of successive amplitudes <i>A₀</i>, <i>A₁</i>, <i>A₂</i>…., as parameters characterizing nuclear NF-κB oscillation.</p

The oscillation pattern is altered by the change in N/C ratios.

<p>(A) Oscillation time courses are plotted for varying N/C ratios from 2.9 to 19% with the amplitude shown in color for higher and lower in red and blue, respectively. Representative oscillations are shown on the right. This representation shows overall oscillation pattern. There is no change in the oscillation frequency by changing N/C ratios which is seen by a regular color interval among different N/C ratios. The damping of the oscillation is faster in smaller N/C volume ratios which is supported by disappearance of the periodic color change at the later time in smaller N/C ratios. At higher N/C ratios, however, the oscillation lasts for more than 10 hrs. (B) There is no change in the oscillation frequency (<i>f</i>) with changes in the N/C ratio. (C) The amplitude of the first peak (<i>A₀</i>) becomes smaller at larger N/C values. (D) The time to the first peak (<i>t_fp</i>) also stays almost unchanged by the change in N/C. (E) The decay time constants of the peaks (<i>τ_p</i>) and successive amplitudes (<i>τ_d</i>) of oscillation becomes larger at larger N/C ratios. <i>τ_p</i> and <i>τ_d</i> at larger N/Cs could not be extracted from the simulated oscillation.</p

Analysis of TLR3 pathway in macrophages.

<p>A) Schematic representation of the determined TLR3 pathway topology in macrophages. dsRNA or poly (I∶C) stimulated TLR3 triggers TRIF dependant response by the recruitment of TRIF to the cytoplasmic domain of the receptor which then allows RIP1, TRAF6, TBK1 and TRAF3 to bind with TRIF. This results in the activation of MAP kinases (MKK1/2, MKK3/6 and MKK4/7) and IκB kinase complex; MKK1/2, MKK3/6 and MKK4/7 activate ERK, JNK and p38, respectively and IκBα degradation releases NF-κB. TBK1 phosphorylates IRF-3 and 7. ERK, JNK and p38 translocate to the nucleus and activate the transcription factor AP-1, and NF-κB, IRF-3 and IRF-7 translocate to the nucleus. AP-1 and NF-κB bind to the promoter regions of cytokine genes such as <i>Tnf</i> and <i>Il6</i> while IRF-3, IRF-7 together with NF-κB bind to the promoter region of chemokine genes such as <i>Cxcl10</i> and <i>Ccl5</i> and induce their transcription. Protein-protein interactions between molecules at the two signaling branches analyzed are highlighted in brown and blue. The dotted lines indicate weak activation (see maintext). B), C) and D) show simulations of NF-κB, JNK and p38 activation, respectively, in wildtype (WT). The <i>x</i>-axis represents the time in minutes and the <i>y</i>-axis represents the relative activation profile.</p

The modeling strategy.

<p>See maintext for details.</p

Prediction of missing steps prior to poly (I∶C)/TLR3 binding.

<p>A) Schematic representation of TLR3 model after adding three signaling intermediates upstream of TLR3 representing uncharacterized cellular processes (blue) and TLR3-ectodomain dimerization (red dotted) (see maintext). Note: from our model, it is not possible to equate the three intermediary steps to represent exactly three actual biological events, since spatial transport processes might be one of candidates for the time delay. B), C) and D) show simulations of NF-κB, JNK and p38 activation, respectively, in the wildtype (WT) (black), TRAF6 KO (green), TRADD KO (orange). The <i>x</i>-axis represents the time in minutes and the <i>y</i>-axis represents the relative activation profile.</p

A novel pathway is crucial for MAP kinases activation in poly (I∶C) stimulated macrophages.

<p>A) Schematic representation of the final TLR3 model after adding novel pathway (blue) from TRIF activates MAP kinases. B), C) and D) show simulations of NF-κB, JNK and p38 activation, respectively, of the final macrophages TLR3 model with novel pathway, in wildtype (WT) (black), TRAF6 KO (green) and TRADD KO (orange). The <i>x</i>-axis represents the time in minutes and the <i>y</i>-axis represents the relative activation profile.</p

The final <i>in silico</i> TLR3 model reactions and parameter values.

<p>The final <i>in silico</i> TLR3 model reactions and parameter values.</p