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| | </figcaption> | | </figcaption> |
| | </figure> | | </figure> |
| − | <h2>E.coli growth rate<h2> | + | |
| − | <p>The growth rate of each E.coli can be controlled by an upper limitation of growth rate $\mu_{max}$, influenced by the number of plasmids $i$ contained, length of target gene incorporated, the culture concentration $S$, as well as the growth promoting effect $\gamma$ brought by the growth-promoter (glucose dehydrogenase). Referring to several well-established models, we form the individual growth rate at a given culture condition as $\mu(i,S) = \mu_{max} \frac{K}{K + i^n} \frac{S}{S+Ks}\gamma(i,S)$.</p> | + | <p>Under aerobic condition, bacteria grow faster after adding TorA signal peptide, and the K value has improved. As for microaerophilic environment, bacteria can maintain stable growth trend for a long time after adding TorA signal peptide.</p> |
| − | <p>Equipped with theoretical formula, the change of individual growth rate with respect to several factors can be simulated:</p>
| + | <p>All these results suggest that our new part can make VHb work better than before and give bacteria growth advance.</p> |
| − | <p>I.Change of E.coli’s Growth Rate v.s. Change of Plasmid Number</p>
| + | |
| − | <figure class="text-center">
| + | |
| − | <img src="https://static.igem.org/mediawiki/2018/8/85/T--BNU-China--image_modeling_3.jpg" width="65%">
| + | |
| − | <figcaption>
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| − |
| + | |
| − | </figcaption>
| + | |
| − | </figure>
| + | |
| − | <p>II.Change of E.coli’s Growth Rate v.s. Change of Culture Concentration</p>
| + | |
| − | <figure class="text-center" id = "Growth">
| + | |
| − | <img src="https://static.igem.org/mediawiki/2018/2/28/T--BNU-China--image_modeling_4.jpg" width="65%">
| + | |
| − | <figcaption>
| + | |
| − |
| + | |
| − | </figcaption>
| + | |
| − | </figure>
| + | |
| − | <h2>Growth promoting effect<h2>
| + | |
| − | <p>Knowing the promoter’s mechanism of increasing individual growth rate, our model wish to quantitatively figure out the extent of increase in E.coli’s growth rate with the influence of a certain amount of glucose dehydrogenase. Because of the great complexity of knowing and simulating the whole promoting process, our model only focuses on the steps influenced by the promoter, who serves as an enzyme in cellular respiration. Both the enzyme and the substrate moves randomly in the E.coli, which induced us to a 3-dimensional random walk model. The initial substrate concentration is set fixed throughout experiments, while the concentration of enzyme (i.e. the growth-promoter glucose dehydrogenase) varies among different situations, simulation with programming is done, and the average combination ratio can be calculated. </p>
| + | |
| − | <p>This value is then used as the adjustment multiplier of E.coli’s individual growth rate, since their combination stands for the happening of enzymatic reaction. By treating the substrate-enzyme combination rate as a quantified value of E.coli’s growth promoting effect, we further incorporate this term as the change of individual growth rate (no units), which means, the greater this value is, E. coli shall experience a faster growth, and the promoting effect changes, under various content of intercellular glucose dehydrogenase, as follows.</p>
| + | |
| − | <figure class="text-center" id = "Gene">
| + | |
| − | <img src="https://static.igem.org/mediawiki/2018/3/36/T--BNU-China--image_modeling_5.jpg" width="65%">
| + | |
| − | <figcaption>
| + | |
| − |
| + | |
| − | </figcaption>
| + | |
| − | </figure>
| + | |
| − | <h2>Gene expression level<h2>
| + | |
| − | <p>Following the steps mentioned above, the composition of E.coli population at each time is well known. Our goal now is to find out the relationship between individual plasmid number and the recombinant gene expression level. </p>
| + | |
| − | <p>We absorbed the queue theory in operational research, by treating the nutrients as customers, and the plasmid in each E.coli as the service station. Given the E.coli’s average nutrient intaking capacity, as well as the plasmid processing rate, the amount of nutrients taken by E.coli and processed by each plasmid are known. Then, with different intracellular plasmid numbers between different groups, the processing ability between individual E.coli can vary, indicating a bigger velocity of reaction with a greater number of plasmids contained. </p>
| + | |
| − | <p>However, more plasmids can leads to decreasing amount of allocated nutrients on average. Since the E.coli’s nutrient intake ability is fixed, more plasmid within means less nutrients sent to each of them, this will on the other hand, leads to a decrease in target gene expression level of each plasmid. </p>
| + | |
| − | <p>Programming goes along with theoretical deductions, by setting the time step as one second, E.coli’s nutrient intake ability is set as at most 10 units, and the plasmid’s average processing ability is 2 units at a time, under the assumption that the absorbed amount is totally proportional to the gene expression level. Individual E.coli with 0 to 200 plasmids are considered, and after the simulation for 3600 seconds, we count the total amount of nutrients utilized by each kind of E.coli, which reveals the total amount of target protein produced. Then the gene (taken by each plasmid) expression level within each group of E.coli can be calculate, and its change are drawn into the curve below.</p>
| + | |
| − | <figure class="text-center" id = "Ribosome">
| + | |
| − | <img src="https://static.igem.org/mediawiki/2018/0/07/T--BNU-China--image_modeling_6.jpg" width="65%">
| + | |
| − | <figcaption>
| + | |
| − |
| + | |
| − | </figcaption>
| + | |
| − | </figure>
| + | |
| − | <h2>Ribosome fall-off rate<h2>
| + | |
| − | <p>But one thing left to be mentioned is that, the express possibility of target gene can differ from the gene in charge of promoting cell growth (i.e. glucose dehydrogenase). Since the target gene can be successfully expressed as long as the promoter combines with the ribosome, while the subsequent TGATG sequence allows for a ratio of fall-off , therefore results in a decrease in the expression level of glucose dehydrogenase. </p> | + | |
| − | <p>The possibility of fall-off is relevant to the length of target gene, which situated before the TGATG sequence, while the gene of growth-promoting part is relatively fixed, which follows the TGATG sequence, and our task is trying to figure out, the change of fall-off rate with respect to the length of target gene.</p>
| + | |
| − | <p>The intensity of ribosome-sequence combination can be measured as their binding energy through translation, which we assume to be proportional as the length of target gene. Referring to [], the fraction of time that a ribosome elongates the translation process and remains in combination with subsequent sequence. $F = \frac{1}{1+C \exp(G_bind)}$, $C$ a parameter representing the ribosome-assisted unfolding coefficient, while $G_bind$ is the binding energy between given target gene and the ribosome. The curve describing the remaining rate of ribosome, with respect to the length of target gene, is shown.</p> | + | |
| − | <figure class="text-center">
| + | |
| − | <img src="https://static.igem.org/mediawiki/2018/1/11/T--BNU-China--image_modeling_7.jpg" width="65%">
| + | |
| − | <figcaption>
| + | |
| − |
| + | |
| − | </figcaption>
| + | |
| − | </figure>
| + | |
| | | | |
| | | | |
| | <div class="reference"> | | <div class="reference"> |
| − | | + | <ol> |
| | + | <li id="ref-1">Ouyang, P.; Wang, H.; Hajnal, I.; Wu, Q.; Guo, Y.; Chen, G.-Q. Increasing oxygen availability for improving poly(3-hydroxybutyrate) production by Halomonas. Metabolic Engineering 2018, 45, 20.</li> |
| | + | |
| | + | |
| | + | </ol> |
| | </div> | | </div> |
| | | | |
