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| − | <div class="container-fluid page-heading" style="background-image: url(https://static.igem.org/mediawiki/2016/f/f4/T--BNU-China--project.jpg);"> | + | <div class="main-container" > |
| − | <h3> Modeling </h3> | + | <div class="container-fluid page-heading" style="background-image: url(https://static.igem.org/mediawiki/2018/e/e3/T--BNU-China--attribution.jpg);text-align:left;"> |
| | + | <!--<h3 style="font-family:Helvetica;text-align:left"> Attributions </h3>--> |
| | + | <!--<img src = "https://static.igem.org/mediawiki/2018/e/e3/T--BNU-China--attribution.jpg" alt = "model"/>--> |
| | </div> | | </div> |
| | + | <div class="page-story"> |
| | + | <article id="achievement" class="col-lg-10 col-lg-offset-1 col-md-12 col-md-offset-0 col-sm-offset-0 col-sm-12"> |
| | + | <header class="page-header"> |
| | + | <h1>Attributions</h1> |
| | + | <br></br> |
| | + | <p>Hello，This is BNU-China.</p> |
| | + | <p>There are 28 team members this year, 18 of which learning life science, 2 of which learning mathematics, 2 of which learning physics, 4 of which learning information science and technology, and also we have a student learning chemistry and a student major in art. </p> |
| | + | <p>We had a great year together, from the brainstorming at the beginning to intensive experiments, and finally we wrote draft and made wiki. IGEM brought us not only skills, but also a group of friends who could fight together. This Attribution page is to document all the effort.</p> |
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| − | <div class="page-story">
| + | </header> |
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| − | <article id="project" class="col-lg-10 col-lg-offset-1 col-md-12 col-md-offset-0 col-sm-offset-0 col-sm-12">
| + | <h2>Attributions</h2> |
| − | <header class="page-header">
| + | <div class="panel-group"> |
| − | </header>
| + | <div class="panel panel-info attributions"> |
| − | | + | <div class="panel-heading"> |
| − | <p> In order to reach the goal of minimizing the average degradation rate of E. coli, i.e. the highest average expression level of our target gene, we chose to simulate the behaviors of individual E. coli by a segregated population competition model, furthermore used the method of cellular automaton, while incorporating several modulating model parts into steps of cell reproduction, to get the population of different E. coli at each time step.</p> | + | <h4>What We Have Accomplished</h4> |
| − | <p> To specify, we first distinguish the E.coli by their plasmid numbers, under the assumption that individual behaviors are alike within the group with the same plasmid numbers. Then, by getting the ribosome bind rate through mechanism model and the growth promoting effect through 3- dimensional random walk model, we adjusted the E. coli’s individual growth rate. Meanwhile, queue theory is used for exploring the relationship between intracellular plasmid number and target gene expression level. What’s more, a fall-off mechanism is incorporated by energy estimation, when considering the subsequent translation of glucose dehydrogenase, which serves as a growth promoter of E.coli.</p> | + | </div> |
| − | <p id = " Main"> After repeating the process of reproduction in a reasonable period of time, the population of E.coli with various plasmids can be simulated, therefore provide us with the population’s information as time goes on.</p> | + | <div class="panel-body"> |
| − | <h2>Main model<h2>
| + | <p>The whole team could be divided into 5 groups: wet lab group, modeling group, human practice group, wiki group and art design group.</p> |
| − | <p> The whole population of E. coli are separated into 100 different groups, with $N(i)$ E. coli attributed to the $i^{th}$ group, in which they all possess $i$ plasmids at current time. Each group of E.coli was regarded as a distinct population, under the assumption that individuals are alike within, i. e. their gene expression level, growth rate are basically the same under similar circumstances. One minute is set as a time step. For each group of E.coli, a fraction of the population will go through the process of plasmid replication and dividend at each time step, through which the fraction is determined by the level of E. coli’s growth rate $\mu(i, S)$, who is closely related to the E.coli’s type and culture concentration. </p> | + | <p>Shaobo Yang, Wei Zhang, Min Wei are the team leaders, they have worked together to manage the whole process.</p> |
| − | <p> After each time step $dt$, the population change of the $i^{th}$ group $\frac{dN}{dt}$ is constituted with two parts: E.coli with $i$ plasmids produced by parent cell in other groups, and the E.coli with $j(\neq i)$ plasmids produced by parent cell in the $i^{th}$ group. </p> | + | <p>Wei Zhang, Ranfei Fu, Miao Yang have found the novel growth factor GDH and found the way to produce SA. Shaobo Yang, Zhe Feng measured the growth curve of GDH. Kefan Fang, Quyi Jiang, Shujuan Jiang detected the interaction between emrR and PemrR. Kefan Fang alse constructed the final plasmid and worked on the modeling collaboration with HBUT. Shaobo Yang, Yadi Liu, Yang Miao have successfully measured the degeneration rate of GDH and constructed one of the final SAM plasmids. Wei Zhang，Ranfei Fu, Kecheng Zhang, Yuanxu Jiang have detected the function of CI and constructed the final plasmid. Min Wei, Yunzhu Meng, Xiaohan Shao have working on yeast display and the VHB-plasmids growth curve, TGATG expression rate, GDH protein detection. Chenyu Liu, Anqing Duan were working on all those parts.</p> |
| − | <p> Given a random distribution mechanism of plasmids into son cells, the distribution rate $\delta_{i, j}$, which stands for the probability of parent E.coli in $i^{th}$ group producing son E. coli in $j^{th}$ group. We then multiply this probability to the fraction of population who replicates, to get the change in population respectively as $$\frac{dN(i)}{dt} = \sum_{j \neq i}^{N_{p, max}}\delta_{i, j} \mu(j, S) N(j) - (1-2(\frac{1}{2})^i) \mu(i, S) N(i)$$</p> | + | <p>Zhiruo Wang, Shangyang Li, Sirui Chen, Ziqin Yue constituted the modeling group and showed the GDH growth curve model, the TGATG expression model and the SA-emrR model.</p> |
| − | <p>Meanwhile, the consumed substrate can also be describe in an ODE as $$\frac{dS}{dt} = -\frac{1}{Ys} \sum_{i=0}^{N_{p,max}} \frac{dN(i)}{dt}$$</p>
| + | <p>Yue Peng, Yunzhu Meng, Yadi Liu, Min Wei, Zhe Feng, Kecheng Zhang have done a great achievement in human practice. They helped us put our result into the reality.</p> |
| − | <p> Programs simulating this process is done at each time step, and each group’s population is well-known. We selected ten representative groups (E. coli with 1, 20, 40, 60, 80, 100, 120, 140, 160, 180, 200 plasmids) and have their population drawn in the curves below.</p> | + | <p>Yuxuan Fan, Shuhan Hu, Anlin Chen, Yuhang Wu were all producing our wiki. |
| − | <figure class="text-center" id = "Probability">
| + | Shujuan Jiang, Jiajing Li, Qianxi Li have worked on the art design and the great collaboration between UCAS.</p> |
| − | <img src="https://static.igem.org/mediawiki/2018/1/1b/T--BNU-China--image_modeling_1.jpg" width="65%">
| + | </p> |
| − | <figcaption> | + | </div> |
| | + | </div> |
| | + | <div class="panel panel-info attributions"> |
| | + | <div class="panel-heading"> |
| | + | <h4>General Support</h4> |
| | + | </div> |
| | + | <div class="panel-body"> |
| | + | <p>Thanks for the great support from the College of Life Science and Liyun College, Beijing Normal University.</p> |
| | + | </div> |
| | + | </div> |
| | + | <div class="panel panel-info attributions"> |
| | + | <div class="panel-heading"> |
| | + | <h4>Project Support and Advice</h4> |
| | + | </div> |
| | + | <div class="panel-body"> |
| | + | <p> Thanks to Prof. Xudong Zhu, Prof. Dong Yang, Prof. Benqiong Xiang and our teacher Xiaoran Hao, Jinbo Chen，all these professors and teachers offered us important guidance as well as detailed advice on our experiments, we appreciated them sincerely. </p> |
| | + | </div> |
| | + | </div> |
| | + | <div class="panel panel-info attributions"> |
| | + | <div class="panel-heading"> |
| | + | <h4>Fundraising Help and Advice</h4> |
| | + | </div> |
| | + | <div class="panel-body"> |
| | + | <p>Thanks for the great fundraising support from the College of Life Science and Liyun College, Beijing Normal University.</p> |
| | + | </div> |
| | + | </div> |
| | + | <div class="panel panel-info attributions"> |
| | + | <div class="panel-heading"> |
| | + | <h4>Lab Support</h4> |
| | + | </div> |
| | + | <div class="panel-body"> |
| | + | <p>Thanks for the lab support from the College of Life Science and Liyun College, Beijing Normal University. Our instructor Prof. Xudong Zhu, Prof. Dong Yang, Prof. Benqiong Xiang, Xiaoran Hao, Jinbo Chen helped us to maintain a great environment. </p> |
| | + | </div> |
| | + | </div> |
| | + | <div class = "panel panel-info attributions"> |
| | + | <div class = "panel-heading"> |
| | + | <h4>Difficult Technique Support</h4> |
| | + | </div> |
| | + | <div class = "panel-body"> |
| | + | <p> Thanks for the technique support from the College of Life Science and Liyun College, Beijing Normal University.</p> |
| | + | </div> |
| | + | <div> |
| | + | <div class = "panel panel-info attributions"> |
| | + | <div class = "panel-heading"> |
| | + | <h4>Project Advisor Support</h4> |
| | + | </div> |
| | + | <div class = "panel-body"> |
| | + | <p> Our advisor Chenxi Li, Qiaohong Xie, Nan Rong gave us a great training along our experiment and they also helped us a lot in our project. Many thanks to them!</p> |
| | + | </div> |
| | + | <div> |
| | + | <div class = "panel panel-info attributions"> |
| | + | <div class = "panel-heading"> |
| | + | <h4>Wiki Support</h4> |
| | + | </div> |
| | + | <div class = "panel-body"> |
| | + | <p>Thanks for Yuxuan Fan, Shuhan Hu, Anlin Chen, Yuhang Wu, who are major in information science and technology.</p> |
| | + | </div> |
| | + | <div> |
| | + | <div class = "panel panel-info attributions"> |
| | + | <div class = "panel-heading"> |
| | + | <h4>Presentation Coaching</h4> |
| | + | </div> |
| | + | <div class = "panel-body"> |
| | + | <p> Thanks for our instructor Prof. Xudong Zhu, Prof. Dong Yang, Prof. Benqiong Xiang, Xiaoran Hao, Jinbo Chen for training us to make a impressive presentation. Prof. Sen Li, Prof. Fei Dou also teach us how to make it better, thanks a lot to them!</p> |
| | + | </div> |
| | + | <div> |
| | + | <div class = "panel panel-info attributions"> |
| | + | <div class = "panel-heading"> |
| | + | <h4>Human Practices Support</h4> |
| | + | </div> |
| | + | <div class = "panel-body"> |
| | + | <p>Thanks to Bluapha, LooKChem, ZJUT, OUC, UCAS, UESTC, Fuxing Hospital for helping us doing human practice. We have learned a lot in this process.</p> |
| | + | </div> |
| | + | <div> |
| | + | <div class = "panel panel-info attributions"> |
| | + | <div class = "panel-heading"> |
| | + | <h4>Thanks and acknowledgements for all other people involved in helping make a successful iGEM team.</h4> |
| | + | </div> |
| | + | <div class = "panel-body"> |
| | + | <p>Last bu not least,</p> |
| | + | <p>We would like to thank all the people who came to our lab and gave us useful feedback.</p> |
| | + | </div> |
| | + | <div> |
| | + | </div> |
| | + | |
| | | | |
| − | </figcaption>
| + | </article> |
| − | </figure> | + | </div> |
| − | <h2>Probability of distribution<h2>
| + | |
| − | <p>The loss of plasmids during reproduction, is mainly due to the uneven distribution of plasmids into two son E.coli after plasmid replication. Therefore, it is important to give the probability of each possible situation. To be more specified, the probability of a i-plasmid parent producing a j-plasmid son has to be calculated. </p>
| + | |
| − | <p>Plasmids’ self-replication has to take place ahead, for a empirical formula of replication number is given $$CopyNum(i) = \frac{V_m (i-1)}{K_m+i-1} - (i-1)\mu(i,S)$$ to describe the average plasmid copy number of E.coli with $i$ plasmids. </p>
| + | |
| − | <p>Then, treating the plasmid distribution process as totally random distribution, the allocation of n plasmids into two son E.coli can be viewed as Bernoulli experiment for n times, from which the probability of i-plasmid parent producing a j-plasmid son is $$\delta_{i,j}=2C_i^j (\frac{1}{2})^j(\frac{1}{2})^{i-j}=\frac{C_i^j}{2^{i-1}}$$. If we mark each row by their intracellular plasmid number, and each column by the plasmid number of their offspring, a distribution possibility table can be listed. However, since the table is too large and lack of readability, we display it more intuitively by using a 3-dimensional plot, in which the x-axis is the plasmid number of parent E.coli, while the y-axis is the number of plasmids possessed by one of its son, the height of each point stands for the possibility of above reproduction.</p>
| + | |
| − | <figure class="text-center" id = "E">
| + | |
| − | <img src="https://static.igem.org/mediawiki/2018/6/61/T--BNU-China--image_modeling_2_change.jpg" width="65%">
| + | |
| − | <figcaption>
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| − |
| + | |
| − | </figcaption>
| + | |
| − | </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>Equipped with theoretical formula, the change of individual growth rate with respect to several factors can be simulated:</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%">
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| − | <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>
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| − |
| + | |
| − | </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%">
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| − | <figcaption>
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| − | </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%">
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| − | <figcaption>
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| − | </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>
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| − | <figure class="text-center">
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| − | <img src="https://static.igem.org/mediawiki/2018/1/11/T--BNU-China--image_modeling_7.jpg" width="65%">
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| − | <figcaption>
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| − | </figcaption>
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| − | </figure>
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