Team:SCAU-China/Model/Stress-Model

MESEG

Stress Model

Overview

The selective autophagy pathway of Chlamydomonas is mediated by receptors. In the situation of dietary enrichments and autophagy-inducing factor deficiency, Atg13 is phosphorylated by TORC1 kinase, and lead to the decreased activity of Atg1 kinase. Under Nitrogen starvation, TORC1 kinase is inhibited. The interaction betweeen phosphorylated Atg13 and Atg1 results in the ativation of Atg1, and further induce Atg8 lipidation into Atg8-PE which indicates that Chlamydomonas grow from normal stage to autophagy stage.

Figure 1: Cd2+ absorption pathway




Validation in growth


For the above complicated molecular mechanism, we primarily used engineered yeast to observe the effect of different vectors on yeast growth by measuring the OD600 value of yeast containing different fusion proteins, and obtained the following growth curves.

Figure 2: Line chart of engineered yeast growth


Figure 3: Fitting plot of engineered yeast with ‘loess’


For the identical vector, we induced it into Chlamydomonas for culture, observed its growth effect, and achieved the growth curve of Chlamydomonas fitted by logistics method.

Figure 4: Fitting plot of engineered Chlamydomonas with ‘logistics’





Stress model conspectus


For engineered Chlamydomonas, the growth curve can greatly represent its working recovery time and then guide the delivery time and recovery time of engineered Chlamydomonas device. The parameters of the working limits measurement of engineered Chlamydomonas under different heavy metal ion concentration gradients are estimated, using these obtained parameters, we can infer the growth curves of engineered Chlamydomonas under other unknown heavy metal concentrations. Therefore, we established the following stress model of engineered Chlamydomonas.

From T0 to T1: Engineered Chlamydomonas grows under nutritional adequacy and limited environmental capacity. Assuming that Chlamydomonas are in normal stage. The relative density of engineered Chlamydomonas is G, the renewal rate of Chlamydomonas is only related to the light intensity, which is set under a specific light intensity λ1 is a constant value, the death rate be δ_1 G. At T1 time, the relative density of Chlamydomonas reached the maximum GM. We call it the growth saturation point.

From T1 to T2: the growth rate of engineered Chlamydomonas is equal to the death rate, and its relative density remained at the maximum GM. At t2 time, engineered Chlamydomonas are put into the sewage for cadmium ion adsorption, which is also the starting point for inducing engineered Chlamydomonas from normal stage to autophagy stage.

From T2 to T3: engineered Chlamydomonas will have three states: normal stage, autophagy stage and absorption saturation stage. Appropriate level of autophagy is conducive to cell survival. However, excessive autophagy can induce programmed cell apoptosis. Assuming that the relative density in normal stage is x, the growth rate is λ_2 and the death rate is δ_2 X; The rate of entering the autophagy phase is k_1 X. Let the relative density in autophagy phase be y; The death rate is δ_3 Y, the rate of entering the absorption saturation period is k_2 Y. Let the relative density in the absorption saturation period be Z; The death rate is δ_4 Z. Engineered Chlamydomonas in autophagy stage and absorption saturation stage could not grow normally. T3 time is the minimum time when the engineered Chlamydomonas population reaches the maximum absorption saturation point, and it is also the time when the engineered Chlamydomonas can be recovered.

\begin{matrix} \left\{\begin{array}{c} \Large{\frac{d G}{d t}=\lambda_{1}-\delta_{1} \mathrm{G} }\\ \Large{\mathrm{G}\left(\mathrm{t}_{0}\right)=0} \end{array}\right.\end{matrix}
\begin{matrix} \left\{\begin{array}{c} \mathrm{G}(\mathrm{t})=\mathrm{G}_{\mathrm{M}}\left(1-\mathrm{e}^{-\lambda_{1} \mathrm{t}}\right) \\ \mathrm{G}_{\mathrm{M}}=\frac{\lambda_{1}}{\delta_{1}} \end{array}\right. \end{matrix}
\begin{matrix} \left\{\begin{aligned} \frac{d G}{d t} &=0 \\ \mathrm{G}\left(\mathrm{t}_{1}\right) &=\mathrm{G}_{\mathrm{M}}\\ \mathrm{G}(\mathrm{t})=\mathrm{G}_{\mathrm{M}} \end{aligned}\right. \end{matrix}
\begin{matrix} \begin{array}{c} \frac{d}{G(t)=X(t)+Y(t)+Z(t)} \\ {\frac{d X}{d t}=-k_{1} X-\delta_{2} X} \\ {\frac{d Y}{d t}=k_{1} X-k_{2} Y-\delta_{3} Y} \\ {\frac{d Z}{d t}=k_{2} Y-\delta_{4} Z} \\ {G\left(t_{2}\right)=G_{\mathrm{M}}} \\ {X\left(t_{2}\right)=\mathrm{G}\left(\mathrm{t}_{2}\right)} \\ {Y\left(t_{2}\right)=0} \\ \qquad Z\left(t_{2}\right)=0 \end{array} \end{matrix}
\begin{matrix} \mathrm{X}(\mathrm{t})=\mathrm{G}_{\mathrm{M}} \mathrm{e}^{-\left(\mathrm{k}_{1}+\delta 2\right) \mathrm{t}} \end{matrix}
\begin{matrix} \mathrm{Y}(\mathrm{t})=\frac{\mathrm{G}_{\mathrm{M}} \mathrm{k}_{1}}{\mathrm{k}_{1}-\mathrm{k}_{2}+\delta_{2}-\delta_{3}}\left(\mathrm{e}^{-\left(\mathrm{k}_{2}+\delta_{3}\right) \mathrm{t}}-\mathrm{e}^{-\left(\mathrm{k}_{1}+\delta_{2}\right) \mathrm{t}}\right) \end{matrix}
\begin{matrix} \mathrm{Z}(\mathrm{t})=\frac{\frac{\mathrm{G}_{\mathrm{M}} \mathrm{k}_{1}}{\mathrm{k}_{1}+\delta_{2}-\delta_{4}}\left(\mathrm{e}^{-\delta_{4} \mathrm{t}}-\mathrm{e}^{-\left(\mathrm{k}_{1}+\delta_{2}\right) \mathrm{t}}\right)+\frac{\mathrm{G}_{\mathrm{M}} \mathrm{k}_{1} \mathrm{k}_{2}}{\mathrm{k}_{2}+\delta_{3}-\delta_{4}}\left(1+\mathrm{e}^{\left(\delta_{4}-\delta_{3}-\mathrm{k}_{2}\right) \mathrm{t}}\right)}{\mathrm{k}_{1}-\mathrm{k}_{2}+\delta_{2}-\delta_{3}} \end{matrix}

Based on the setting parameters above, we preliminarily want to use neural network model to learn and explore the internal relationship between various growth conditions of Chlamydomonas and its work recovery time. After model learning, if the growth conditions such as cadmium ion concentration are input, the model will give the simulated work recovery time, and then guide to when to recover the device. However, on account of the lack of data sets, we did not really build the machine learning model. This idea was also put forward to the team in the cooperation with SJTong to help their team improve their projects. For details, please refer to the collaboration part.


Figure 5: Concept model of Chlamydomonas work recovery time; X aixs: Cd2+ concentration; Y aixs: Time(hours); Z aixs: OD600 of Chlamydomonas sample