Directional persistence of chemotactic bacteria in a traveling concentration wave

Abstract

Chemotactic bacteria are known to collectively migrate towards sources of attractants. In confined convectionless geometries, concentration "waves" of swimming Escherichia coli can form and propagate through a self-organized process involving hundreds of thousands of these microorganisms. These waves are observed in particular in microcapillaries or microchannels; they result from the interaction between individual chemotactic bacteria and the macroscopic chemical gradients dynamically generated by the migrating population. By studying individual trajectories within the propagating wave, we show that, not only the mean run length is longer in the direction of propagation, but also that the directional persistence is larger compared to the opposite direction. This modulation of the reorientations significantly improves the efficiency of the collective migration. Moreover, these two quantities are spatially modulated along the concentration profile. We recover quantitatively these microscopic and macroscopic observations with a dedicated kinetic model. Suspended Escherichia coli bacteria that swim in convection-free geometries such as capillaries or microchannels, collectively migrate towards nutrient-rich regions, in the form of propagating concentration waves (1-4). In homogeneous environments, the individual trajectories of these bacteria can be described by a random walk consisting in a succession of "runs" during which they swim in straight lines, and "tumbles" characterized by random [although not complete (5)] reorientations (6). The modulation of run lengths in response to temporal variations of chemoattractant concentrations (7) biases this random walk, driving the bacteria up spatial gradients (5). The collective wavelike behaviors emerge for high enough concentrations (8) and have been so far qualitatively described by several semiempirical models based on the production of chemoattractants by the bacteria themselves (3,(8)(9)(10)(11)(12). Nevertheless, a direct validation of these ideas still requires experimental data describing individual bacteria within these populations.In the present work, we use a microfluidics-based approach that allows to simultaneously track the trajectories of hundreds of individual bacteria while measuring the global characteristics of the wave. We then derive a kinetic model that quantitatively describes the observations at both scales.The experiments were conducted with the motile and chemotactic strain RP437 (5) and its mutants, in linear silicone polydimethylsiloxane (PDMS) microchannels (500 μm × 100 μm × 1.8 cm). The channels were first filled with homogeneous suspensions of cells grown to midlog phase (∼5 · 10 8 cells∕mL) in M9 minimal medium supplemented with D-Glucose and Casamino Acids (13), and immediately sealed.As a reference, we measured the mean run [respectively (resp.) tumble] duration τ run (resp. τ tumble ) and the run velocity (V run ) before centrifugation, in the absence of gradient, for each experiment. The distributions of run and tumble durations we...

Fast, high-throughput measurement of collective behaviour in a bacterial population

“…The probability of a tumble is in turn lowered, because the phosphorylated form of CheY (CheY-P) binds to the flagellar motor to induce a motor reversal, hence a tumble. Recent results have shown that the reorientation during a tumble is also reduced when running towards an attractant [19]. Both effects contribute to create a chemotactic drift in the run/tumble random walk in the presence of certain chemical stimuli.…”

Variation of swimming speed enhances the chemotactic migration of Escherichia coli

“…The mathematical model incorporates both mechanisms which lead to net drift velocity, namely, modulation of tumble frequency (TF), and swimming speed (SS) while accounting for directional persistence during tumbling. While modulation of tumble frequency is essential in achieving a net drift, Saragosti et al (2011) have shown that the turn angles for cells moving up the gradient of attractants are lower than for those moving in the opposite direction leading to a directional persistence and an enhanced drift. A further increase in swimming speed (irrespective of direction) would also contribute to increased drift velocities.…”

“…Four different gradients were obtained by using four different concentrations of 2Dg liquid plugs, namely, 100, 500, 1000 and 10000 lM. The experimental system is very robust (Vuppala et al 2010a, b;Saragosti et al 2011;Masson et al 2012) and does not require the use of pumps or complex microfluidic channels to establish a steady gradient. The existence of a stable linear gradient was confirmed by performing a similar experiment with fluorescent glucose [2-(N-(7-nitrobenz-2-oxa-1,3-diazol-4-yl)amino)-2-deoxy-glucose,2-NBDG].…”

“…The angular distribution of tumble angles is observed to follow a gamma distribution in agreement with previous studies (Berg and Brown 1972). The model also incorporates directional persistence wherein the tumble angle was higher for cells moving down the gradient compared to cells moving in the opposite direction (Saragosti et al 2011). The measured tumble angle distribution of cells moving up and down the gradient were used in the model.…”

“…Thus to study the response exclusively through the Trg receptor, we expose the two strains of cells, namely, wild type K12 and a mutant Dtrg, to varying concentrations and gradients of a non-metabolizable analogue of glucose, namely, 2-Deoxy-D-glucose (2Dg) (Adler and Epstein 1974). While it is well known that the modulation of tumble frequency causes a net drift, recent experiments by Saragosti et al (2011) have shown that the cells also exhibit directional persistence wherein the tumble angle is lower for cells moving up the gradient. Further, we have shown recently that the swimming speed (or run speed) of E. coli varies with varying uniform concentrations of glucose and 2Dg (Deepika et al 2015).…”