Frequency-Dependent Escherichia coli Chemotaxis Behavior

We study Escherichia coli chemotaxis behavior in environments with spatially and temporally varying attractant sources by developing a unique microfluidic system. Our measurements reveal a frequency-dependent chemotaxis behavior. At low frequency, the E. coli population oscillates in synchrony with the attractant. In contrast, in fast-changing environments, the population response becomes smaller and out of phase with the attractant waveform. These observations are inconsistent with the well-known Keller-Segel chemotaxis equation. A new continuum model is proposed to describe the population level behavior of E. coli chemotaxis based on the underlying pathway dynamics. With the inclusion of a finite adaptation time and an attractant consumption rate, our model successfully explains the microfluidic experiments at different stimulus frequencies.

Figure 1

Experimental setup. (a) A panoramic picture of the two-layer PDMS (polydimethylsiloxane) chip. (b) A zoomed-in view of the observation channel. The time lapse of the normalized E. coli density and attractant concentration at a control point is shown for periods $T=800\mathrm{s}$ (c) and 100 s (d). The ligand concentration is measured by adding a small amount of fluorescein into attractant stocks. Bacterial densities are determined by averaging the fluorescence intensity from the fluorescence-labeled cells in a region of $\pm 25\mu \mathrm{m}$ around the control points.

Figure 2

The spatiotemporal profiles of the cell density for different driving periods. (a) $T=100\mathrm{s}$, (b) $T=200\mathrm{s}$, (c) $T=400\mathrm{s}$, (d) $T=800\mathrm{s}$. The normalized cell density at a given position $x$ and time $t$ (scaled by $T$) is represented by the color (see color bar). $L$-aspartate concentrations at the two source channels oscillate between 0.1 and 0.9 mM with opposite phases. The gray scale stripes at the two sides of each panel show the normalized ligand concentrations at the left ($L$) and right ($R$) control point as a function of time, $t=0$ is when ligand concentration is maximum at the right control point. The cell density is measured 20 frames per period.

Figure 3

Dynamics of the center of mass (c.m.). (a) The c.m. dynamics for different driving periods ($T$) are represented by dots of different colors, lines are fits to the data with a sinusoidal function $A\cos (2\pi t+\pi +\Delta \varphi )$. The dotted black line shows the normalized ligand concentration at the right control point. (b) The phase shift $\Delta \varphi$ and (c) the normalized amplitude $A/A_{\max }$ for different $T$ are shown together with the model results. The error bars denote standard deviation of at least 4 repeats. Although $A$ is small in high-frequency conditions (e.g., $T=80\mathrm{s}$), it is still much larger than stochastic noise (see Fig. S9 in SM [15] for detail).

Figure 4

The phase shift of the cell density oscillation at the control points ($\Delta {\varphi }_{\mathrm{cp}}$) as a function of the driving period from experiments and different models.

Figure 5

The comparison of (normalized) cell density profiles for (a) $L$-aspartate and (b) MeAsp at time $t=(n+1/4)T$. There are two peaks for $L$-aspartate and one peak for MeAsp. The corresponding modeling results are shown in (c) for $L$-aspartate and (d) for MeAsp. The ligand concentration profiles and their trends at the control points are shown in the insets of (c) and (d). The period is $T=80\mathrm{s}$.