Difference between revisions of "Team:Tianjin/Model"

 
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                                       <p> Figure8 histogram of Time-Maximum OD Value<br> </p>
 
                                       <p> Figure8 histogram of Time-Maximum OD Value<br> </p>
 
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                                       <p> Figure9 Scatter gram of Time-Maximum OD Value </p>
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                                       <p>Figure9 Scatter gram of Time-Maximum OD Value<br></p>
 
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                                 Mars Model
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                                 Mars Model*
 
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                                         Oscillation in KaiC phosphorylation is the best-observed parameter in this system and represents a key state variable for the clock in vivo. Thus we have sought to closely mimic this output in our project. Nakajima et al. <sup><a href="#re6">[6]</a></sup> suggest, given the dual function of KaiC and ‘‘cooperation between KaiA and KaiB,’’ that autonomous oscillation of KaiC phosphorylation might be achieved. We established a model based on known biological and biochemical observations and our experiments that did not involve transcription or translation. In <a href="#14">Figure14</a>, we summarized the key steps of three Kai proteins oscillation when ATP is provided in excess. It was well established that we used three circles to represent all possible combinations of three Kai proteins, just like Mars and its two satellites. This was also why we call it Mars Model.
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                                         Oscillation in KaiC phosphorylation is the best-observed parameter in this system and represents a key state variable for the clock in vivo. Thus we have sought to closely mimic this output in our project. Nakajima et al. <sup><a href="#re6">[6]</a></sup> suggest, given the dual function of KaiC and ‘‘cooperation between KaiA and KaiB,’’ that autonomous oscillation of KaiC phosphorylation might be achieved. We established a model based on known biological and biochemical observations and our experiments that did not involve transcription or translation. In <a href="#14">Figure14</a>, we summarized the key steps of three Kai proteins oscillation when ATP is provided in excess. It was well established that we used three circles to represent all possible combinations of three Kai proteins, just like Mars and its two satellites. This was also why we call it <b>Mars Model</b>.
 
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                                     Input reaction rate constants <em>k<sub>1</sub>-k<sub>12</sub></em> and initial concentration of every protein, oscillatory curve of every protein could be obtained as shown in <a href="#16">Figure16</a>.
 
                                     Input reaction rate constants <em>k<sub>1</sub>-k<sub>12</sub></em> and initial concentration of every protein, oscillatory curve of every protein could be obtained as shown in <a href="#16">Figure16</a>.
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                                    <p>Figure16 Oscillatory curve of every protein</p>
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                                      <p>Figure16 Oscillatory curve of every protein</p>
 
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                                     From <a href="#16">Figure16</a> it was known that although the peak time of each protein varies, the oscillation period of every protein is the same. Therefore, in the following analysis, we take KaiC as an example to show the change of periods.
 
                                     From <a href="#16">Figure16</a> it was known that although the peak time of each protein varies, the oscillation period of every protein is the same. Therefore, in the following analysis, we take KaiC as an example to show the change of periods.
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                                         When the reaction rate constants change slightly with temperature changing, the period shortens while amplitude shortens too. Therefore, if <em>k</em> changes disproportionately, when the temperature increases, the cycle is shortened and the oscillation is unsteady. The curve tends to be gentle with time, which means the oscillation disappears shown as<a href="#19">Figure 19</a>.
 
                                         When the reaction rate constants change slightly with temperature changing, the period shortens while amplitude shortens too. Therefore, if <em>k</em> changes disproportionately, when the temperature increases, the cycle is shortened and the oscillation is unsteady. The curve tends to be gentle with time, which means the oscillation disappears shown as<a href="#19">Figure 19</a>.
 
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                                    <p>Figure19  The disappearance of oscillation with temperature changing</p>
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                                      <p>Figure19  The disappearance of oscillation with temperature changing</p>
 
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                                         Phosphorylase in yeasts may have promoting effect to the phosphorylation of protein and yeasts offer enough ATP/ADP in vivo, which increase the rate of phosphorylation. Therefore, <em>k<sub>4</sub></em>may increases in yeasts, which makes oscillation cycle shortens shown as <a href="#20">Figure20</a>.
 
                                         Phosphorylase in yeasts may have promoting effect to the phosphorylation of protein and yeasts offer enough ATP/ADP in vivo, which increase the rate of phosphorylation. Therefore, <em>k<sub>4</sub></em>may increases in yeasts, which makes oscillation cycle shortens shown as <a href="#20">Figure20</a>.
 
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                                  <p>Figure20 Period changes with phosphorylation rate changing</p>
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                                      <p>Figure20 Period changes with phosphorylation rate changing</p>
 
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                                     When the oscillation system is transplanted into yeasts, the supply rate of KaiA , KaiB and KaiC may increase and the relating reaction rate constants are <em>k<sub>2</sub></em>, <em>k<sub>3</sub></em> and <em>k<sub>1</sub></em>. They will increase with the supply rate of three Kai proteins increasing and the result is shown as <a href="#21">Figure21</a>.
 
                                     When the oscillation system is transplanted into yeasts, the supply rate of KaiA , KaiB and KaiC may increase and the relating reaction rate constants are <em>k<sub>2</sub></em>, <em>k<sub>3</sub></em> and <em>k<sub>1</sub></em>. They will increase with the supply rate of three Kai proteins increasing and the result is shown as <a href="#21">Figure21</a>.

Latest revision as of 13:01, 6 December 2018

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MODEL

Overview

The models we built included four parts. First, we established a fluorescent protein model to screen out the most suitable fluorescent protein, the main modeling method here is grayscale analysis. Then, for the large amount of measured OD values, we drew the growth curve of yeasts and it fitted logistic model. It described the growth situation of the yeasts after plasmid introduction, and we compare it with yeasts without any foreign plasmid. The growth curve also offers the best measuring point and the best measuring interval. What’s more, we drew the degradation curve of the fluorescent protein, which helps us know different characteristics of the two chosen fluorescent proteins better. Finally, we constructed a model to illustrate the oscillation of KaiA, KaiB and KaiC protein called Mars Model, it explained the reason why the cycle reduced in yeasts nicely. Modeling work integrated with experiments tightly made our project complete and convincing.