Difference between revisions of "Team:Tianjin/Model"

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                                     <p>The resulting growth rate function is $$r(x) = r(1 - {x \over x_m}) $$  Replacing intrinsic growth rate with r(x), get $${dx \over dt} = rx(1 - {x \over x_m}) , x(0) = x_0          (3)$$ <br></p>
 
                                     <p>The resulting growth rate function is $$r(x) = r(1 - {x \over x_m}) $$  Replacing intrinsic growth rate with r(x), get $${dx \over dt} = rx(1 - {x \over x_m}) , x(0) = x_0          (3)$$ <br></p>
 
                                     <p>
 
                                     <p>
                                         Factor <em>rx</em> in the function shows the growth trend of yeast amount itself, while factor (1 - {x \over x_m}) reflects the block effects of resources and environment to the yeast quantity growth. Obviously, the bigger x is, the former factor is bigger and the latter factor is smaller. The growth of yeast amount is the result of the two factors.<br>
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                                         Factor <em>rx</em> in the function shows the growth trend of yeast amount itself, while factor (1 - <em>x/x<sub>m</sub></em>) reflects the block effects of resources and environment to the yeast quantity growth. Obviously, the bigger x is, the former factor is bigger and the latter factor is smaller. The growth of yeast amount is the result of the two factors.<br>
 
                                     </p>
 
                                     </p>
 
                                     <p>
 
                                     <p>

Revision as of 14:11, 16 October 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.