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Statistical analysis
For statistical analysis GraphPad-Prism was used, testing for normality whenever sufficient replicates were available. Data were analysed by one-way or two-way ANOVA with Bonferroni or Newman–Keuls multiple comparisons tests or by t-test (Fig. 10f). Resulting P values are shown in figure legends, P<0.05 being considered significant. *<0.05, **<0.01, ***<0.001. All data shown are means±s.e.m. with ns indicated, showing variation within each group are largely similar in any one bar chart. Full statistical analysis tables not shown within the figures (Figs 4 and 5) are included as Supplementary Data File 1. Sample size was selected based on pilot studies and to be able to evaluate statistical significance (n=3 minimum; n in all cases refers to biological replicates).

Data availability
All relevant data are available from the authors on request.

Additional information
How to cite this article: Melero-Fernandez de Mera, R.M.. et al. A simple optogenetic MAPK inhibitor design reveals resonance LED Tube China between transcription-regulating circuitry and temporally-encoded inputs. Nat. Commun. 8, 15017 doi: 10.1038/ncomms15017 (2017).

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Figure 2: Design of anapole nanolaser.
Figure 2
(a) Tunability of the direct bandgap of InxGa(1?x)As as a function of the molar ratio x of InAs. (b) Pseudocolour plot of the scattering cross-section Csca of an In0.15Ga0.85As nanodisk for a varying disk diameter d and of the incident wavelength. The incident field is linearly polarized along the Ex direction. The white dashed line LED Down Light the region where the scattering is suppressed by the presence of anapole states. (c) Scattering cross-section for an In0.15Ga0.85As nanodisk of diameter d=440?nm and height h=100?nm. For these choice of parameters, the anapole wavelength coincides with the semiconductor emission wavelength λ0 (red arrow). The red shaded area shows the Lorentzian gain profile of the In0.15Ga0.85As semiconductor that is entirely contained in the scattering suppression region.
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Figure 2b illustrates the scattering cross-section Csca33 of a nanodisk of In0.15Ga0.85As with height 100?nm and different values of diameter d. The figure shows a region where the scattering of the nanodisk is suppressed in all directions (see Fig. 2b dashed line). Such special region, which extends in the visible and in the near infrared for In0.15Ga0.85As nanodisks, is sustained by the presence of non-radiating anapole states that do not possess far-field emission. This is further confirmed by the multipole decomposition of the electromagnetic fields as a function of the incident wavelength for a nanodisk with diameter d=440?nm and height h=100?nm (Supplementary Figs 2–5).

While this is normally considered detrimental for plasmonic applications like biomolecular sensing, SERS enhancement and those requiring long plasmon propagation lengths, this effect can be used advantageously for plasmonic structural colour as structures that absorb broad wavelengths of light are able to produce colours not possible from those with only narrow absorption resonances. To demonstrate the impact of rms surface roughness on the colour reflected from the nanostructure, we perform FDTD simulations of the periodic nanowell array by changing the amplitude of a uniform random height variation about the top surface of the alu<a href=""></a>minium film while maintaining a constant lateral correlation length of 15?nm. We then use the resulting spectra to predict a reflected colour through the 1932 International Commission on Illumination (CIE) colour space and colour matching functions. Further details about the surface generation and simulations can be found in the Methods section. Here, we approximate the LC region as a perfect anisotropic crystal with the slow axis (ne) parallel to the surface and at 45° with respect to a periodicity vector of the nanowell array (homogeneous LC alignment). In reality, the LC director aligns to the contours of the aluminium surface, resulting in a complex LC director tensor dependent on the local topography of the surface. However, to isolate the effects of rms surface roughness on the GCSP resonance alone, we choose to simplify this LC layer and leave it constant for the purposes of the numerical demonstration in Fig. 2a,b. By separately injecting light polarized parallel and perpendicular to this diagonal, we also isolate the fundamental modes of the plasmonic film and remove any bulk retardation/polarization rotation effects of the LC. The results for incident LED High Bay Light polarized perpendicular to the LC long-axis (90°) are shown in Fig. 2a while incident light polarized parallel (0°) to the LC orientation is shown in Fig. 2b. Line colours are determined by the CIE colour matching functions and are cascaded to show the influence of rms surface roughness on resonance location (solid black lines) and full-width-half-maximum (dotted black lines). At low values of surface roughness, the plasmonic resonance shifts less than 20?nm upon incident polarization rotation, resulting in a minute colour change. However, as the roughness of the aluminium increases, the parallel resonance red shifts more than the perpendicular case, causing a greater colour shift between the two polarization states. We explain this phenomenon with the following argument: the ?LC term of the above equation can be thought of as an effective index experienced by the plasmonic mode. For isotropic and uniform surrounding media, this term reduces to the dielectric constant of the medium. However, for anisotropic media, this term becomes an overlap integral between the plasmonic field tensor and the surrounding media’s dielectric tensor. As plasmonic fields near the metallic interface are normal to the surface, plasmon resonances depend largely on the surface normal component of the surrounding refractive index. Rough films will have local regions where the surface norm has an increased x or y component compared to the global norm. This gives the in-plane components of the surrounding media a greater contribution to the effective refractive index of the GSCP resonance. In the current case, where the surrounding media is a uniaxial crystal oriented parallel to the aluminium surface, this creates a surface roughness induced polarization dependence of the plasmonic resonance.<a href=""></a><a href=""></a><a href=""></a><a href=""></a><a href=""></a><a href=""></a><a href=""></a><a href=""></a><a href=""></a><a href=""></a>

Thermal sensing performances under mild temperature conditions. (a) Transfer (inset: output) curves according to the temperature by heat sources (TA = 25~70 °C) at VD = -20 V and VG = -20 V. (b) Drain current (ID) response according to the distance between the load-like heaters and the flexible PDLC-i-OFET devices. (c) Net drain current change (ΔID) as a function of temperature (TA): The dashed line was fitted with the power-law equation (ΔID ~ TA α) (note that more than sixteen devices were measured).
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In order to examine the response time, the distance between the heat sources and the flexible PDLC-i-OFET devices was controlled to change between 3 mm and 50 mm. As shown in Fig. 5b, the drain current at VG = -5 V and VD = -1 V was quickly increased as the heat sources approached the PDLC layers of devices for all the temperatures tested in this work. When the heat sources were moved out of the devices, the fast decay in drain current was measured. Here it is worthy to note that the different response between approaching (rise time = ~2.2 s) and receding (decay time = ~8.4 s) of the heat sources can be attributable to the different thermal cycle of heating and cooling for the flexible PDLC-i-OFET devices. Interestingly, as shown in Fig. 5c, the change of peak drain current (ΔID) as a function of approaching temperature (TA) was well fitted with a power-law type equation (ΔID ~ TAα, where α is an exponent).