Chemotaxis is the movement up a concentration gradient of chemo-attractants (e.g. malate in our project) and away from repellents (e.g. 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’[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.

Each chemoreceptor 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 chemo-attractant concentration.

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2.1 Objective

Use the modelling of chemotaxis pathway to determine the threshold chemoattractant concentration that the bacteria with 8uM chemoreceptor can detect and the saturation level of chemoattractant where bacteria become inactive. As it is believed that the auxin should be placed at a region near the (0.25 cm [4]), therefore it is crucial to determine whether our bacteria will be able to stay close to the seed.

2.2 Description

Figure 1[1]: Chemotaxis signaling components and pathways for E.coli.

The chemotaxis pathway in E. coli is demonstrated in Figure 1.Chemoreceptors form stable ternary complexes with the CheA and CheW proteins to generate signals that control the direction of rotation of the flagellar motors [5]. The signalling groups currency is in the form of phosphoryl (p), made available to the CheY and CheB effector proteins through autophosphorylation of CheA[1].CheY-p initiates flagellar responses by interacting with the motor to enance the probability of ‘run’ [1]. CheB-p is part of a sensory adaptation circuit that terminates motor responses [1]. Therefore, studying of methylation level, phosphorylation level of CheB and CheY are important to understand chemotaxis of single cell. The model based on Spiro et al. (1997) [1] was used to identify candidates of the chemotaxis receptor pathway.

In addition, 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), CheYp_wt is defined as wild type CheYp[5].

2.3 Results and discussion

Based on the Spiro model, the methylation level of receptors, phosphorylation level of CheY and CheB were studied from Spiro’s model (Figure 2).

Fig.2(a):The phosphorylation level of CheY. Fig.2(b):Phosphorylation of CheB.Fig.2(c):Methylation level of Chemoreceptor. Fig.2(d): The probablity of of bacteria in the running state at different levels of CheYp. Fig.2(a)(b)(c) shows 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 the bacterium start become inactive.

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3.1 Objective

Model the chemotaxis of bacteria population dynamics in two conditions, experimental and natural.It will inform our project about how and where we can place our bacteria.

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.

3.2 Description

This part of modelling focused on creating the movement model of a bacteria population for chemotaxis. 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 Hz, and decreases to almost zero as he bacteria move up a chemotatic gradient [5]. In order to accurately built this model, the following assumptions are made based on literature:

1) During the directed movement phase, the mean speed of an E. coli equals 24.1 μm/s, varying speed between 17.3 μm/s and 30.9 μm/s [7]. Whereas during the tumbling phase, the speed is significantly smaller and can be neglected.

2) E. coli usually take the previous second as their basis on deciding whether the concentration has increased or not. Therefore, in our model the bacteria will be able to compare the concentration of chemoattractant at t second and t-1 second.

3) In our model, we ignored that E. coli do not travel in a straight line during a run, but take curved paths due to unequal firing of flagella.

4) Our model did not consider the growth and dividing of bacteria. And the tendency of bacteria to congregate into a small area due to quorum sensing is also neglected.

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 Hz. 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 as an exponential function of chemostatic constant, bacteria velocity , concentration differentce between adjacent time points and angle between that two time points. Therefore, we can conclude the above description into the following statement [8]:

Under laboratory conditions, the chemoattractant diffuses from the source, hence the distribution pattern of chemoattratctant changes with time. In this case, the error function (Equation 2) was used to describe the non-steady state chemoattractant distribution.

However, in real soil conditions, malate is used as the chemoattractant. Malate is constantly secreted from the root tip, and the concentration is 3 mM[9]. In this case, the malate source is always replenished due to continuous secretion from the seed and the distribution pattern can be considered as steady (i.e. independent of time). The steady-state Keler-Segel model was used to demonstrate this distribution (Equation 3).

3.2 Results and Discussion

Under laboratory conditions, a simulation of chemotaxis of 100 bacteria placed 6 cm away from a 5 mM malate source is shown in the movie below.

The distribution of malate in real soil is displayed in Fig. 3. And the paths of bacteria chemotaxis with placing bacteria at different positions in steady state malate distribution is demonstrated in Fig.4. Fig.4 shows that the chemotaxis is inefficient with bacteria at position in between 0.0028 m and 0.0012 m due to the small concentration change between time points in steady state malate environment. The green line shows that the bacteria can be maintained close to the seed when it is placed at distance < 0.012, therefore it is suggested for our project the bacteria should be placed at the distance <0.012

Fig.3(a):Distribution of malate vs. distance. Fig.3(b):Distribution of malate with radius. Fig.3(b)shows the position of lower threshold (1e-8 M, radius = 0.028 m)where the bacteria start to response to malate and the saturation level (1e-5 M,radius = 0.012)where the chemoreceptors start to lose efficiency.

Fig.4:Chemotaxis with plaing bacteria at different starting position. Blue: 2×10⁵s chemotaxis starts at radius = 0.015 m (0.0125s chemotaxis starts at radius = 0.008 m (<0.012)

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[1] Peter A. Spiro, John S. Parkinson, Hands G. Othmer. ‘A model of exciatation and adaptation in bacterial chemotaxis’. Proc. Natl. Acd. Sci. USA, Vol. 94, pp. 7263-7268, July 1997. Biochemistry

[2] Blocks S. M., Segall J. E. and Berg H.C. (1982) Cell 31, 215-226.

[3] Stock J. B. and Surette M. G. (1996) ‘Escherichia coli and salmonella: Cellular and molecular biology’. Am. Soc. Microbiol., Washington, DC).

[4] Andrea Schnepf. ‘3D simulation of nutrient uptake’

[5] M D Levin, C J Morton-Firth, W N Abouhamad, R B Bourret, and D Bray, ‘Origins of individual swimming behavior in bacteria.’

[6] Vladimirov N, Lovdok L, Lebiedz D, Sourjik V (2008) ‘Dependence of Bacterial Chemotaxis on Gradient Shape and Adaptation Rate’ PloS Comput Biol 4(12): e1000242. Doi:10.1371/journal.pcb1.1000242.

[7] Zenwen Liu and K. Papadopoulos. ‘Unidirectional Motility of Escherichia coli’. APPLIED AND ENVIRONMENTAL MICROBIOLOGY, Oct. 1995, p. 3567–3572 Vol. 61, No. 100099-2240/95/$04.0010 Copyright q 1995, American Society for Microbiology

[8] https://2009.igem.org/Team:Aberdeen_Scotland/chemotaxis

[9] Enrico Martinoia and Doris Rentsch. ‘Malate Compartmentation-Responses to a Complex Metabolism’ Annual Review of Plant Physiology and Plant Molecular Biology Vol. 45: 447-467 (Volume publication date June 1994) DOI: 10.1146/annurev.pp.45.060194.002311

[10] C.J. Brokaw. ‘Chemotaxis of bracken spermatozoids: Implications of electrochemical orientation’.

[11] D.L.Jones, A.M. Prabowo, L.V.Kochian, ‘Kinetics of malate transport and decomposition in acid soils and isolated bacterial populations the effect of microorganisms on root exudation of malate under Al stress.’ Plant and Soil 182:239-247, 1996.

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