3D Spatial Exploration by E. coli Echoes Motor Temporal Variability

Unraveling bacterial strategies for spatial exploration is crucial for understanding the complexity in the organization of life. Bacterial motility determines the spatiotemporal structure of microbial and controls infection spreading and the microbiota organization in guts or in soils. Most theoretical approaches for modeling bacterial transport rely on their run-and-tumble motion. For Escherichia coli, the run-time distribution is reported to follow a Poisson process with a single characteristic time related to the rotational switching of the flagellar motors. However, direct measurements on flagellar motors show heavy-tailed distributions of rotation times stemming from the intrinsic noise in the chemotactic mechanism. Currently, there is no direct experimental evidence that the stochasticity in the chemotactic machinery affects the macroscopic motility of bacteria. In stark contrast with the accepted vision of run and tumble, here we report a large behavioral variability of wild-type E. coli, revealed in their three-dimensional trajectories. At short observation times, a large distribution of run times is measured on a population and attributed to the slow fluctuations of a signaling protein triggering the flagellar motor reversal. Over long times, individual bacteria undergo significant changes in motility. We demonstrate that such a large distribution of run times introduces measurement biases in most practical situations. Our results reconcile the notorious conundrum between run-time observations and motor-switching statistics. We finally propose that statistical modeling of transport properties, currently undertaken in the emerging framework of active matter studies, should be reconsidered under the scope of this large variability of motility features.

Popular Summary

Bacterial motion determines the changing structure of microbial communities and controls infection spreading as well as microbiota organization in ecosystems. E. coli bacteria explore their environment using a “run-and-tumble” strategy: a sequence of straight paths (runs) and sudden changes in swimming direction (tumbles) that happen when motors driving the cell’s tail-like flagellum change rotation direction for a short time. While this random walk is classically described as a process with a single characteristic run time, the flagellar motor rotation switching, responsible for reorientations, displays a wide distribution of times. To address this paradox, we built a 3D tracking microscope suited to follow swimming bacteria for as long as tens of minutes.

Our results reconcile individual motor rotation and bacterial spatial exploration in three dimensions. We reveal a continuous variation of exploration “moods” for individual bacteria, characterized by periods of frequent directional changes alternating with periods of persistent swimming. The dynamics can be explained by important fluctuations in the number of certain proteins inside the cell that are responsible for the motor switching.

Future research will address the importance of these realistic run-and-tumble statistics in the macroscopic transport of bacteria. Bacterial persistent swimming may help to explain the onset of medical emergencies as well as bacterial anomalous transport in confined environments, such as narrow capillaries and porous media. This knowledge could be relevant to emerging technologies for targeted drug delivery or for understanding the spreading of biocontaminants in soils.

Figure 1

Lagrangian 3D tracking of bacteria and analysis conditions. (a) RP437 wild-type E. coli displaying very different typical trajectories: persistent trajectory (bact 1: ${\tau }_p=12\mathrm{s}$) and nonpersistent trajectory (bact 2: ${\tau }_p=0.7\mathrm{s}$). (b) Sketch of the part of the track used for analysis and angles used for computing $C(\mathrm{\Delta }t)=⟨\widehat{p}(t)·\widehat{p}(t+\mathrm{\Delta }t)⟩=⟨\cos \theta (\mathrm{\Delta }t)⟩$, using a sliding window for an average on time $t$.

Figure 2

Details of a typical trajectory. (a) 3D trajectory and its projection on the $x\text{−}y$ plane, (b) velocity vs time, and (c) velocity distribution. The marks every 5 s in the 3D track are references for comparison with (b).

Figure 3

Swimming orientation correlations. Experiments I. (a) Correlation function $C(\mathrm{\Delta }t)$ obtained for 30 tracks of different RP437 bacteria in M9G, showing a large distribution of persistence times. The correlation functions are fitted with an exponential decay $\exp (-\tau /{\tau }_p)$ to extract the persistence times ${\tau }_p$. The dotted line corresponds to ${\tau }_p=1.5\mathrm{s}$ as expected from Ref. [1]. Inset: Correlation functions as a function of $\mathrm{\Delta }t$ rescaled by ${\tau }_p$. The dashed line is $\exp (-x)$. (b) Persistence times for individual bacteria of wild-type strains RP437 and AB1157 and smooth swimmer mutant CR20 in different media (MB, MB-S, and M9G). Circles and uncertainty bars correspond to the mean and 68% confidence intervals for each group. The blue background region designates the cutoff from Brownian diffusion. The dotted line corresponds to the expected ${\tau }_p=1.5\mathrm{s}$ also represented in (a). Uncertainty bars indicate the mean and confidence interval at 68%.

Figure 4

Analysis for long tracks. Experiments II. (a) Sketch indicating the pieces of track from the same trajectory selected for demonstrating the behavioral variability. (b) ${\tau }_p$ for pieces of track from the same trajectories, for 33 different RP437 bacteria in MB-S. The color represents the starting time of the measurement. Each bacterium displays a large variation of persistence times.

Figure 5

Heuristic view of the behavioral variability model. (a) Timescales of the tumbling process and the CheY-P concentration governing them. The switching time ${\tau }_s$ represents the local average of the stochastic run times ${\tau }_{\mathrm{CCW}}$. The switching time ${\tau }_s$ stays relatively constant during the memory time $T_Y$ and evolves as a function of the normalized CheY-P concentration: $\delta X=([Y]-[Y_0])/{\sigma }_Y$. (b) 2D projection of the simulated 3D trajectory where the $\delta X$ fluctuations drive the tumbling process. The insets correspond to different levels of [$\delta X$]: Inset I depicts a low CheY-P level, and inset II depicts a high CheY-P level.

Figure 6

Determination of the memory time from experiments II. (a) Persistence times ${\tau }_p$ computed over pieces of span 20 s and shifted 5 s for two different bacteria. Gaps larger than 5 s between consecutive points correspond to lapses in which the bacteria are swimming close to surfaces. (b) Persistence times self-correlation function $C_p$ using pieces of 20 s. Points represent the average over the ensemble of bacteria. (c) Correlation time of the persistence times as a function of the lengths of the pieces. We extract the memory time to be $T_Y=19.0\pm 1.3\mathrm{s}$.

Figure 7

Probability density function of the logarithm of persistence times $(\ln {\tau }_p)$. (a) The values ${\tau }_p$ are extracted from pieces of track from experiments II that last 20 s. Simulations using two different models are shown: The Poisson model does not reproduce the experiments, while the BV model reproduces the main features. (b) The experimental distribution corresponds to the combined RP437 bacteria in all media, from Fig. 3 in experiments I. “BV model experiment constraints” are determined from the same simulations of “BV model” but analyzing pieces of trajectories that follow the experimental constraints in this case. It reproduces experiments I without additional free parameters.

Figure 8

Average run duration as a function of the threshold in bacterial velocity (cutoff $V$). The runs are identified as continuous parts of the track where $V>\mathrm{cutoff}V$. The plot demonstrates that an arbitrary choice of velocity drops along the trajectory leads to arbitrary run-time duration. Inset: Log-normal plot.