Moment-flux models for bacterial chemotaxis in large signal gradients

Effect of receptor cooperativity on methylation dynamics in bacterial chemotaxis with weak and strong gradient

We study methylation dynamics of the chemoreceptors as an Escherichia coli cell moves around in a spatially varying chemoattractant environment. We consider attractant concentration with strong and weak spatial gradient. During the uphill and downhill motion of the cell along the gradient, we measure the temporal variation of average methylation level of the receptor clusters. Our numerical simulations we show that the methylation dynamics depends sensitively on the size of the receptor clusters and also on the strength of the gradient. At short times after the beginning of a run, the methylation dynamics is mainly controlled by short runs which are generally associated with high receptor activity. This results in demethylation at short times. But for intermediate or large times, long runs play an important role and depending on receptor cooperativity or gradient strength, the qualitative variation of methylation can be completely different in this time regime. For weak gradient, both for uphill and downhill runs, after the initial demethylation, we find methylation level increases steadily with time for all cluster sizes. Similar qualitative behavior is observed for strong gradient during uphill runs as well. However, the methylation dynamics for downhill runs in strong gradient show highly nontrivial dependence on the receptor cluster size. We explain this behavior as a result of interplay between the sensing and adaptation modules of the signaling network.

A Mathematical Description of Bacterial Chemotaxis in Response to Two Stimuli

Bacteria are often exposed to multiple stimuli in complex environments, and their efficient chemotactic decisions are critical to survive and grow in their native environments. Bacterial responses to the environmental stimuli depend on the ratio of their corresponding chemoreceptors. By incorporating the signaling machinery of individual cells, we analyze the collective motion of a population of Escherichia coli bacteria in response to two stimuli, mainly serine and methyl-aspartate (MeAsp), in a one-dimensional and a two-dimensional environment, which is inspired by experimental results in Y. Kalinin et al., J. Bacteriol. 192(7):1796-1800, 2010. Under suitable conditions, we show that if the ratio of the main chemoreceptors of individual cells, namely Tar/Tsr, is less than a specific threshold, the bacteria move to the gradient of serine, and if the ratio is greater than the threshold, the group of bacteria moves toward the gradient of MeAsp. Finally, we examine the theory with Monte Carlo agent-based simulations and verify that our results qualitatively agree well with the experimental results in Y. Kalinin et al. (2010).

Effect of receptor clustering on chemotactic performance of E. coli: Sensing versus adaptation

We show how the competition between sensing and adaptation can result in a performance peak in Escherichia coli chemotaxis using extensive numerical simulations in a detailed theoretical model. Receptor clustering amplifies the input signal coming from ligand binding which enhances chemotactic efficiency. But large clusters also induce large fluctuations in total activity since the number of clusters goes down. The activity and hence the run-tumble motility now gets controlled by methylation levels which are part of adaptation module rather than ligand binding. This reduces chemotactic efficiency.

A model of strongly biased chemotaxis reveals the trade-offs of different bacterial migration strategies

Many bacteria actively bias their motility towards more favourable nutrient environments. In liquid, cells rotate their corkscrew-shaped flagella to swim, but in surface attached biofilms cells instead use grappling hook-like appendages called pili to pull themselves along. In both forms of motility, cells selectively alternate between relatively straight 'runs' and sharp reorientations to generate biased random walks up chemoattractant gradients. However, recent experiments suggest that swimming and biofilm cells employ fundamentally different strategies to generate chemotaxis: swimming cells typically suppress reorientations when moving up a chemoattractant gradient, whereas biofilm cells increase reorientations when moving down a chemoattractant gradient. The reason for this difference remains unknown. Here we develop a mathematical framework to understand how these different chemotactic strategies affect the distribution of cells at the population level. Current continuum models typically assume a weak bias in the reorientation rate and are not able to distinguish between these two strategies, so we derive a model for strong chemotaxis that resolves how both the drift and diffusive components depend on the underlying chemotactic strategy. We then test predictions from our continuum model against individual-based simulations and identify further refinements that allow our continuum model to resolve boundary effects. Our analyses reveal that the strategy employed by swimming cells yields a larger chemotactic drift, but the strategy used by biofilm cells allows them to more tightly aggregate where the chemoattractant is most abundant. This new modelling framework provides new quantitative insights into how the different chemical landscapes experienced by swimming and biofilm cells might select for divergent ways of generating chemotaxis.

Modeling Transport of Chemotactic Bacteria in Granular Media with Distributed Contaminant Sources

Chemotaxis has the potential to improve bioremediation strategies by enhancing the transport of pollutant-degrading bacteria to the source of contamination, leading to increased pollutant accessibility and biodegradation. This computational study extends work reported previously in the literature to include predictions of chemotactic bacterial migration in response to multiple localized contaminant sources within porous media. An advection-dispersion model, in which chemotaxis was represented explicitly as an additional advection-like term, was employed to simulate the transport of bacteria within a sand-packed column containing a distribution of chemoattractant sources. Simulation results provided insight into attractant and bacterial distributions within the column. In particular, it was found that chemotactic bacteria exhibited a distinct biased migration toward contaminant sources that resulted in a 30% decrease in cell recovery, and concomitantly an enhanced retention within the sand column, compared to the nonchemotactic control. Model results were consistent with experimental observations. Parametric studies were conducted to provide insight into the influence of chemotaxis parameters on bacterial migration and cell percent recovery. The model results provide a better understanding of the effect of chemotaxis on bacterial transport in response to distributed contaminant sources.

Feedback between motion and sensation provides nonlinear boost in run-and-tumble navigation

Many organisms navigate gradients by alternating straight motions (runs) with random reorientations (tumbles), transiently suppressing tumbles whenever attractant signal increases. This induces a functional coupling between movement and sensation, since tumbling probability is controlled by the internal state of the organism which, in turn, depends on previous signal levels. Although a negative feedback tends to maintain this internal state close to adapted levels, positive feedback can arise when motion up the gradient reduces tumbling probability, further boosting drift up the gradient. Importantly, such positive feedback can drive large fluctuations in the internal state, complicating analytical approaches. Previous studies focused on what happens when the negative feedback dominates the dynamics. By contrast, we show here that there is a large portion of physiologically-relevant parameter space where the positive feedback can dominate, even when gradients are relatively shallow. We demonstrate how large transients emerge because of non-normal dynamics (non-orthogonal eigenvectors near a stable fixed point) inherent in the positive feedback, and further identify a fundamental nonlinearity that strongly amplifies their effect. Most importantly, this amplification is asymmetric, elongating runs in favorable directions and abbreviating others. The result is a “ratchet-like” gradient climbing behavior with drift speeds that can approach half the maximum run speed of the organism. Our results thus show that the classical drawback of run-and-tumble navigation—wasteful runs in the wrong direction—can be mitigated by exploiting the non-normal dynamics implicit in the run-and-tumble strategy.

Countless bacteria, larvae and even larger organisms (and robots) navigate gradients by alternating periods of straight motion (runs) with random reorientation events (tumbles). Control of the tumble probability is based on previously-encountered signals. A drawback of this run-and-tumble strategy is that occasional runs in the wrong direction are wasteful. Here we show that there is an operating regime within the organism’s internal parameter space where run-and-tumble navigation can be extremely efficient. We characterize how the positive feedback between behavior and sensed signal results in a type of non-equilibrium dynamics, with the organism rapidly tumbling after moving in the wrong direction and extending motion in the right ones. For a distant source, then, the organism can find it fast.