Stochastic coordination of multiple actuators reduces latency and improves chemotactic response in bacteria

Abstract

Individual neuronal, signal transduction, and regulatory pathways often control multiple stochastic downstream actuators, which raises the question of how coordinated response to a single input can be achieved when individual actuators fluctuate independently. In Escherichia coli, the bacterial chemotaxis pathway controls the activity of multiple flagellar motors to generate the run-and-tumble motion of the cell. High-resolution microscopy experiments have identified the key conformational changes adopted by individual flagella during this process. By incorporating these observations into a stochastic model of the flagellar bundle, we demonstrate that the presence of multiple motors imposes a trade-off on chemotactic performance. Multiple motors reduce the latency of the response below the time scale of the stochastic switching of a single motor, which improves performance on steep gradients of attractants. However, the uncoordinated switching of multiple motors interrupts and shortens cell runs, which thereby reduces signal detection and performance on shallow gradients. Remarkably, when slow fluctuations generated by the adaptation mechanism of the chemotaxis system are incorporated in the model at levels measured in experiments, the chemotactic sensitivity and performance in shallow gradients is partially restored with marginal effects for steep gradients. The noise is beneficial because it simultaneously generates long events in the statistics of individual motors and coordinates the motors to generate a long tail in the run length distribution of the cell. Occasional long runs are known to enhance exploration of random walkers. Here we show that they have the additional benefit of enhancing the sensitivity of the bacterium to very shallow gradients.Lévy walk | agent-based | motility | search strategy | signal processing E scherichia coli performs a random walk by controlling the rotational direction of multiple flagellar motors (1). Counterclockwise (CCW) rotation of the motors promotes formation of a coherent flagellar bundle that propels the cell forward. Clockwise (CW) rotation of any single motor causes the corresponding flagellum to change conformation, exit the bundle, and generate a reorientation event called a tumble (2, 3). Through the bacterial chemotaxis pathway, E. coli regulates the frequency of tumbles to bias its random walk in favorable directions. The core of the chemotaxis network is a two-component signal transduction system in which binding of an external attractant by clusters of transmembrane chemoreceptors leads to rapid (<1 s) inhibition of the activity of the associated histidine kinase, CheA, thereby depleting the phosphorylated form of CheY (CheY-P), a diffusible response regulator that binds to the base of the motor. Lower levels of CheY-P increase the probability that flagellar motors rotate CCW and, thus, increase the mean duration of runs in response to the attractant. The network adapts to persistent stimuli at a slower time scale (approximately 15 s) by competitive methylati...

Direct Correlation between Motile Behavior and Protein Abundance in Single Cells

“…The distribution of tumble biases was unimodal with mode at 0.2 and a standard deviation of 0.093 (Fig 1C). These values are consistent with the previously reported distribution of single flagellar motor biases from tethered cells [29] and taking into account the effect of multiple flagella that increases the cell tumble bias relative to the clockwise bias of single motors [34,35]. As expected, we observed very few cells with tumble biases outside the 0.1 to 0.4 range because the robust architecture of the chemotaxis pathway ensures that the population tumble bias is maintained within a functional range [7,36–40].…”

“…Simulations were run following a previously described method [34], with a constant swimming speed of 20 μm/s and rotational diffusion of 0.062 rad 2 /s [33]. Cells are stationary during tumbles and their orientations are uniformly randomized.…”

Chemotactic adaptation kinetics of individual Escherichia coli cells

“…The mapping that connects the conformational state of individual flagella to the cell swimming state (3, 4) has remained elusive, largely due to the lack of quantitative experimental results. Recent theoretical studies predict that cells with different numbers of flagella should exhibit different swimming behavior (38,39). Our data may provide important clues as to the way multiple motors collectively produce the swimming behavior of a cell.…”

Coordinated Switching of Bacterial Flagellar Motors: Evidence for Direct Motor-Motor Coupling?

“…Intuitively, we expect that the maximum correlation, ρ max ≡ ρ(0), increases with the input noise level ρ x / c (Fig. 2A and Ref. [9]) and the motor's sensitivity h (data not shown).…”