Figure 1

The experimental setup: a set of narrow channels ($0.07\times 0.002\mathrm{cm}$), 3 cm long, microfabricated with polydimethyl-siloxane (PDMS). The 0.02 cm depth inhibits convection [25]. This was also verified using $2\mu \mathrm{m}$ size polysterene beads. Typical temperatures applied to the ends of the channels, 10 °C on the cold edge and 45 °C on the hot one. The bacterial culture, the wild-type RP437 or the mutant HCB2415 [7] E. coli, was launched from a frozen glycerol stock and grown overnight at 30 °C, in a M9 minimal medium supplemented with 1% casamino acids and 4% glucose, to an $\mathrm{O}.\mathrm{D}{.}_{600\mathrm{nm}}$ of 0.2 to 0.4 ($2–4\times {10}^8\mathrm{\text{cells}}/{\mathrm{cm}}^3$). Prior to filling the channels, the bacteria were concentrated and resuspended in fresh medium that was kept also at 30 °C. The bacteria were visualized by fluorescence microscopy using YFP (or GFP in the case of the mutant) gene inserted as a plasmid. The observation chamber was mounted on an inverted Zeiss microscope, Axiovert 35 M, while the heating and cooling blocks were connected to water baths. Imaging was done using two objectives, the $10\times$ for single cell counting, and the $2.5\times$ for wide range profiling, by collective fluorescence measurements. The initial cell density in each channel was estimated by counting the number of cells per unit volume. Images of the bacteria were acquired using an Apogee cooled CCD (Apogee Instruments Inc.).Reuse & Permissions

Figure 2

Distribution of the bacterial concentration at different times in the low concentration regime: before applying the gradient (black), $45\pm 10\min $ (red), $85\pm 10\min $ (dark green), $145\pm 10\min $ (blue), $204\pm 15\min $ (orange), and $255\pm 10\min $ (light green). Lower $x$ axis: position in the channel measured from the edge of the cooling block. Upper $x$ axis: corresponding temperature. Inset: average drift velocity of the peak $v$ as a function of the initial cell density $n$. Measurements were carried out by counting the bacteria at different locations through the channel.Reuse & Permissions

Figure 3

Fluorescence measurements of the emergence of the second mode. (a) Evolution of the second mode from the initial accumulation, with 6 minutes separation between consecutive measurements. First measurement taken 50 minutes after applying the gradient. The solid line represents the first mode, while the dashed line denotes the second mode. The inset shows the position of the second mode in time until it reaches a full rest at 14 °C, where bacterial metabolism and flagella velocity is strongly reduced. (b) Propagation of the second mode upon switching to a 30 °C uniform temperature, with 3 minutes separation between consecutive measurements. The images of the last three peaks are shown in the inset. Scale bar: 0.05 cm. The black spots in the images are PDMS pillars that act as supports in the channel.Reuse & Permissions

Figure 4

The development time of the second mode as a function of the initial cell density $n$. Wild-type bacteria (empty circles) and mutant with deleted Tsr receptor (full squares). Inset: log-log plot of the development time as a function of $n\mathrm{\text{−}}{n}_c$, where $n_c$ is the critical cell density ${10}^8\mathrm{cells}/{\mathrm{cm}}^3$ for the wild type and $2.7\times {10}^8\mathrm{\text{cells}}/{\mathrm{cm}}^3$ for the mutant [21]. Line: a power low fit with an exponent of $-0.4$.Reuse & Permissions

Figure 5

Comparison between the numerical solution and the data from two different experiments. The line depicts the solution to the Keller-Segal equations. Origin of time is the time of switching to 30 °C. The amplitude is given relative to the concentration in the peak at $t=0$. The inset depicts the position of the peak in time. Parameters used in the numerical solution: $D_b=1.7\times {10}^{-6}{\mathrm{cm}}^2/\sec $, $D_c=D_f=8\times {10}^{-5}{\mathrm{cm}}^2/\sec $, $k_c=k_f=1.2\times {10}^{-20}{\mathrm{cm}}^5/\sec $ [26], $J=4\times {10}^5/\mathrm{\text{bacterium}}/\sec $ [7], $\epsilon =0.005\mathrm{mole}/\sec $, $c_0={10}^{-5}\mathrm{M}$ [20].Reuse & Permissions