Team:Hong Kong-CUHK/PROJECT MODELING

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MODELING

We are interested in simulating how E. coli undergoes positive phototaxis when expressing a photoreceptor sensory rhodopsin I (SRI) originated from Halobacterium salinarum. To simplify the model, we modeled the movement of a single bacterium only as modeling movement of a population of cells requires more numerical parameters and conditions.

Basically E. coli has only two kinds of motion, running and tumbling, which are caused by the anti-clockwise and clockwise rotation of its flagella respectively. In running state, E. coli simply runs unidirectionally (neglecting diffusion) for a certain period of time. The speed of E. coli is generally constant, while the running duration depends on light gradient exposed to. When it is in tumbling state, it stops running and rotates itself to change to a new random running direction.

The bacterium moves randomly when it is not exposed to a light gradient, in which case it switches between running and tumble states randomly. When there is a light gradient, say, it is running away from light, the bacterium has a higher probability to change from running to tumbling state. On the contrary, it has a lower chance to switch from running to tumbling state when traveling towards light. As a result, when the bacterium detects a light source, it tends to travel towards the light.

SRI was known to change between three intermediates. When SR587 accepts enough photons, it would change its shape to form an intermediate called SR373. When there is UV light, SR373 will change to another intermediate SR510. After certain time, SR510 and SR373 will change back to SR587. The ratio of the three states depends on the amount of photons up-taken by the receptor, in other words, the intensity of the light [1], as shown in the following equations.

The model is assumed to be a linear system that the transfer rates are constant.

Here M0 and M1 represent two methylation states of the transducer, EcTar. When SRI is excited by photon, it couples with HtrI-EcTar transducer (HT). The change in HT alters the autophosphorylation activity of CheA. Phosphorylated CheA (CheA-P) immediately passes the phosphoryl group to CheY and CheB. CheB-P is responsible for the HT demethylation.  The transducer is methylated and demethylated by CheR and CheB-P respectively. The different states of the receptor and methylation state of the transducer determine the activity of the transducer complex(A). The concentration of CheR does not change by the activity of HT while CheB-P does. It is assumed that the concentration of CheR is constant and the reaction only depends on the concentration of CheB.

Different combinations of methylation states and receptor states are given by a certain level of activity of the alteration of CheA autophosphorylation. The mean activity of the sensory rhodopsin transducer complex is modeled by:

At dynamic equilibrium, the concentration of CheY-P and

where [CheYPss] and [CheBPss] represent the steady-state condition concentration of CheY-P and CheB-P respectively.

Thus [CheY-P] is used to calculate the probability for E. coli to change from running state to tumbling state in the time period t à t + Δt [2].

In our system, we expect the probability for E. coli to switch from running to tumbling state will increase if the intensity of the light increases along the path of E. coli in a running state. In other words, it runs towards light for longer duration but runs away from light for shorter duration.

Conclusion
Statistically, E. coli will gradually approach light of desired wavelength.

[1] Nutsch T, Oesterhelt D, Gilles ED, Marwan W (2005). A quantitative model of the switch cycle of an archaeal flagellar motor and its sensory control. Biophys J. 89: 2307-2323.
[2] Jiang L, Ouyang Q, Tu Y (2010). Quantitative modeling of Escherichia coli chemotactic motion in environments varying in space and time. PLoS Comput Biol. 6: e1000735.
[3] Klare JP, Chizhov I, Engelhard M (2008). Microbial rhodopsins: scaffolds for ion pumps, channels, and sensors. Results Probl Cell Differ. 45: 73-122.

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