E.coli is a motile strain of bacteria, which is to say it can swim. It is able to do so by rotating its flagellum, which is a rotating tentacle like structure on the outside of cell.

Chemotaxis is the movement up concentration gradient of chemoattractants (i.e. malate in our project) and away from poisons. E.coli is too small to detect any concentration gradient between the two ends of itself, and so they must randomly head in any direction and then compare the new chemoattractant concentration at new point to the previous 3-4s point. Its motion is described by ‘runs’ and ‘tumbles’, runs refer to a smooth, straight line movement for a number of seconds, while tumble referring to reorientation of bacteria [1]. Chemoattractant increases transiently raise the probability of ‘tumble’ (or bias), and then a sensory adaptation process returns the bias to baseline, enabling the cell to detect and respond to further concentration changes. The response to a small step change in chemoattractant concentration in a spatially uniform environment increase the response time occurs over a 2s to 4s time span [2]. Saturating changes in chemoattractant can increase the response time to several minutes.

Many bacterial chemoreceptors belong to a family of transmemberane methyl-accepting chemotaxis proteins (MCPs) [3]. Each chemoreceptors on the bacterium has a periplasmic binding domain and a cytoplasmic signaling domain that communicates with the flagellar motors via a phosphorelay sequence involving the CheA, CheY, and CheZ proteins. This signalling pathway modelling result will determines the threshold chemoattractant concentration.

In addition, modelling of chemotaxis of bacteria population is also valuable for us to capture the overview of movement of bacteria around the plant root; therefore it can potentially inform our project about how and where we can place our bacteria.

1. Use the modelling result to determine, with certain numbers of chemoreceptors, the threshold of chemoattractant concentration where the bacterium is able to detect and the saturation level of chemoattractant where the all the receptors on the bacterium are occupies. As it is believed that the auxin should be placed at a region near the (0.25 cm [4]), therefore it is essential to obtain the number of chemoreceptors needed on individual bacterium that enables it to stay close enough to the seed.

2. Model the bacterial popolation dynamics in two conditions: experimental and natural. Under experiment condition, the chemoattractant diffuses all the time from the source. However, in real soil, the root produces malate all the time, therefore we assume that the distribution of chemoattractant outside the root is steady and time-independent. Hence, the modelling of bacteria population chemotaxis will be built with different patterns of chemoattractant distribution.

1. Chemotaxis pathway

Based on the Spiro model, the methylation level of receptors, phosphorylation level of CheY and CheB were studied from Spiro’s model(Figure 2). From the modelling results, we can observe that the lower threshold concentration of chemoattractant that the bacterium start to detect is 10^-8mole/L. The saturation level is 10^-5mole/L in which concentration or higher the bacteria’s movements to chemoattractant are less efficient.

The quantity that links the CheY-p concentration with the type of motion (run vs. tumble) is called bias. It is defined as the fraction of time spent on the directed movement with respect to the total movement time. The relative concentration of CheYp is converted into motor bias using a Hill function (Euqation 1)[5]. A graph describes bias against CheY-p concentration was shown in Fig. 2(d).

Fig.2(a) [Phosphorylated CheY]/ [CheY] vs. time(s)

Fig.2(b) [Phosphorylated CheB]/ [CheB] vs. time(s)

Fig.2(c) Methylation level vs. time(s)

Fig.2(d) The dependency of Bias on the concentration of CheY-p

2. Simulation of chemotaxis of bacteria population

In chemotaxis, receptors sensing an increase in the concentration of chemoattractant send a signal that suppresses tumbling, and, simultaneously, the receptor becomes more highly methylated. Conversely, a decrease in the chemoattractant concentration increases the tumble frequency and causes receptor demethylation. The tumbling frequency is approximately 1 Hertz, and decreased to almost zero as he bacteria move up a chemtoatic gradient [5].

In the model, the bacteria should be able compare the chemoattractant concentration at current point to the concentration at previous second. If the concentration decreases (i.e. C_t1-C_t2 ≤0), the bacteria will tumble with frequency 1 Hertz. If the concentration increases (C_t1-C_t2 >0), the tumble frequency decreases, and hence the probability of tumbling decreases. From equation 10 in ref [6], we known that even if C_t1-C_t2 >0, the probability of tumbling could decreases to 39%. Therefore, we can conclude the above description into the following statement [8]:

2.1. Chemotaxis of bacteria population under laboratory conditions

Under laboratory condition, the chemoattractant diffuses from the source, hence the distribution pattern of chemoattratctant changes with time. In this case, error function (Equation 2) was used to describe the non-steady chemoattractant distribution. The simulation of chemotaxis of 100 bacteria placed 6cm away from the 5mM malate is shown in the movie below.

2.2. Chemotaxis of bacteria population in Soil

Malate is used as the chemoattractant in our project, the malate is constantly secreted in the root tip, and the concentration is 3mM[9]. In this case, the malate source is always replenished due to continuous secretion from the seed, the distribution pattern can be considered as steady (i.e. independent of time), and steady state Keler-Segel model was used to demonstrate this distribution (Equation 3 and Equation 4). The distribution was displayed in Figure 3. And Figure 4 shows the position of lower threshold where the bacteria start to response to malate and the saturation level where the chemoreceptors start to loss efficiency. Finally, the animation of bacterial chemotaxis in steady chemoattractant distribution is demonstrated in video below.

Figure 3: Malate distribution (1D)

Figure 4: Malate distribution. Red: malate concentration = 10^-8M,Blue: malate concentration = 10^-5M

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