Figure 1.
Häder's cyanograph experiment.
A photographic negative is projected onto a Petri dish containing a culture of photophobic filamentous cyanobacteria (Phormidium uncinatum). The trichomes cover the lighter areas of the projection while uncovering the darker areas producing a photographic positive. Petri dish is 10 cm wide. Courtesy of Donat-Peter Häder.
Figure 2.
(A) Trichomes are modeled as thin flexible rods that are discretized into sequences of 50 µm edges. Each edge is loaded with a linear spring. (B) The local bending moment is a function of the radius of curvature. (C) Trichomes can glide along their long axis and reverse their direction of movement photophobically. (D) Trichome collisions are defined between edge-vertex pairs. A vertex that penetrates an edge's volume is repulsed by equal and opposite forces between the pair.
Figure 3.
(A) Light field used for the first and second round of simulations based on a photograph of the London Tower Bridge. (B) Randomly generated light field used in the third round of simulations. The field is composed of overlapping spots that cover the whole area. Spot diameter and light intensity vary between 0.2–2 mm and 0–1 respectively. Solid white line corresponds to the domain boundary.
Table 1.
Parameter values used during simulations.
Figure 4.
Images represent 20 superimposed states of a single simulation. Simulations are run with uniform trichome populations. Each parameter value corresponds to a different simulation. Domain radius is 10 cm. The number of trichomes per simulation depends on the trichome length (the coverage of the domain is fixed) and varies between N = 1.5×104–2.8×105. Standard errors of the mean (SEMs) were very small due to the large sample sizes and are omitted. (A–C) Length and speed fixed to L = 0.5 mm and v = 10 µm.s−1 respectfully; Sensitivity varied between s = 0–1. Images correspond to s = {0.4, 0.7, 0.9} and Sup. Movies S1, S2, and S3 respectively. (D) Graph plotting trichome exposure against trichome sensitivity. The photophobic mechanism starts to become effective from s>0.4. Exposure increases roughly linearly, peaking at a 16% increase for “perfectly” sensitive trichomes. (E–G) Sensitivity and speed fixed to p = 1 and v = 10 m⋅s−1 respectfully; length varied between L = 0.1–2 mm. Images correspond to L = {0.1, 0.5, 2} mm and Sup. Movies S4, S5, and S6 respectively. (H) Log-linear plot of trichome exposure against trichome length (log2 scale).
Figure 5.
Trichome competition in the Tower Bridge field.
Each trichome (N = 1.26×105) in the domain is assigned a random length (L = 0.02–2 mm), photophobic sensitivity (s = 0–1) and gliding speed (v = 0–10 µm⋅s−1); 11 simulations were performed. Error bars are the standard deviations of simulation means. (A) Graph plotting exposure against photophobic sensitivity. For values s<0.35, trichomes are exposed to slightly less than the average light in the domain. For s>0.35, exposure increases markedly, peaking at a 12% exposure advantage for “perfectly” sensitive trichomes. (B) Graph plotting exposure against trichome length for sensitivities 0.35<s≤1. Exposure increases significantly up to 0.8 mm after which it plateaus. (C) Graph plotting exposure against gliding speed for sensitivities 0.35<s≤1. Exposure peaks at 7.5 µm⋅s−1 then plateaus. (D) Composite image of 11 simulations after 8 hours.
Figure 6.
Trichome competition in a dynamic light field.
Same initial conditions as in Figure 5, except a light field composed of overlapping circles of different light intensities is used instead of a static photograph. (A–C) Close ups of a simulation displaying the light field (greyscale) and trichomes (red). See Sup. Movie S7. Every 1/f sec the light intensity of a random spot in the domain is set to a random value I = 0–1. The spots range in diameter between 0.2–2 mm. Scale bars 1 mm. (D–F) Graphs plotting exposure against length (D), sensitivity (E) and gliding speed (F) for six different spot frequencies (0, 2, 8, 32, 128, 512). Different plot colors and symbols correspond to different frequency values, shown on the right-most axis. (G) Plot of average exposure of all trichomes as a function of spot frequency. (H–I) Contour plots demonstrating the relative importance of trichome length vs. sensitivity (H) and gliding speed vs. sensitivity (I). White contour labels indicate percentual exposure increase above average domain light.
Figure 7.
Two portions of the Tower Bridge photographic negative where longer trichomes perform better than shorter trichomes.
(A) Close up of the upper cross beams between the towers. (B) The shorter trichomes remain stuck in a finely patterned portion of the crossbeam. (C) In contrast, the longer trichomes are able to find more light below. (X) The photograph background is characterized by a smooth gradient. On the scale of an individual trichome, however, the gradient is weak and noisy. The shorter trichomes are for the most part not able to follow the gradient (Y), whereas the longer trichomes can (Z).