Team SUSTC-Shenzhen

Worms Locomotion

Model

This model describes how microfluidics Gaussian distribution plate works when we use this device to test C.elegans’ preference in the plate.If the plate works, the model can further describe how much preference the C.elegans show when attraction or repellent factor is added.

Different from classical Galton board(Fig.1), it is worms rather than balls running on the plate. We use worms as the “ball”. However, when a worm is choosing a direction at the crossing, its previous choice may influence current choice due to worm’s relative long body.

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Fig. 1 The simulation of Galton board

Details:

Gaussian distribution is very common in nature and important in statistics. This distribution is tied to many natural phenomena. In our experiment, we use Gaussian plate to see C.elegans’ distribution. Then we use it to see the change of C.elegans’ distribution after adding attraction or repellent factor(Fig.2).

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Fig. 2 The Gaussian distribution A) The ideal Gaussian distribution before adding chemicals. B) The changed Gaussian distribution after adding chemicals by using the first diffusion methods, which means diacetyl diffuse in the same plate as the Gaussian chip.

Firstly, we introduced a parameter ‘k_a’ (0<=k_a<=1) to describe how much the previous choice influences the current choice (Fig.3 缺).

The ‘k_a’ is defined as the absolute value of the difference between the probability of two direction choices(Fig.4 缺).

Depend on this, we introduce an important parameter “k” (range[0,1]). The “k” is defined as the absolute value of the differences between probability of two direction choices. It means that the greater the ”k” is, the greater the influence of previous choice on the current one. When “k” is zero, the simulation model is more like Gaussian distribution.

We count the number of choices and calculate the parameter “k” without factors (attractive or repellent factor at one side) at first. Assuming that “k” does not change when we add attractive or repellent factors.Then this model can be used to stimulate C.elegans preference when adding factors with determined “k”. Meanwhile, we can analyze the amount of C.elegans attracted or repelled by the factors via introducing another parameter kxy (range[0,1]).

All parameters set above are depended on the assumption that the influence of parameters are proportional to the probability they affect the C.elegans' choice. For example, we defined “k” as the association between cross choices. If "k" equals “0”, meaning that there is no association between cross choices. If “k” equals “1”, the next cross choice is totally determined by previous choice, the result will show poly distribution( C.elegans will only show in the end channels). When “k” equals "0.5", meaning that there is 25% probability of turning right/left and 75% probability of turning left/right. “kxy” (attractive or repellent parameter) is the same as “k”.