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Team:BIT/Modeling
From 2013.igem.org
| Modeling |
| We have established a model to match the data of our previous work. On the whole, we designed a model which can be divided into three parts. The first part is called Low-starting model. We believe that chrB protein can still can still express itself even though there is no chromate at all. So we follow this idea, and write the following equation:  In the above formula, Mr is the mRNA concentration of chrB protein, R is the concentration of chrB protein, u is the specific growth rate of E.coli. G is the concentration of chrB gene. And  are the velocity constants of the formation of substances presented by subscript. In addition, are the corresponding degradation rate constants. Finally, L1 is the ratio of the promoter occupied by RNA polymerase.The second part is named Cr-transportation model. We want to use our biological device to measure the environmental chromate concentration. Since chromate is familiar with the sulfate radical, its transportation is also familiar with sulfate radical.  C1 is the concentration of intracellular chromate. C2 is the extracellular concentration of chromate and C3 is the saturated concentration of chromium ion transport. Kc is chromium ion transport rate constant. p is the cell density. The last, but the most important, part is called Strong-starting model. Firstly, our device expresses chrB protein by the first model. So there will be a little chrB protein though the promoter has low-starting ability at this moment. Once chrB protein presents, it will chelate chromium ions, and the chelate compound will activate or promote the promoter to form chrB protein. The facilitative process can be divided into two reactions. In the first reaction, chromium ions combine with the chrB protein, forming an inducer.  In the second reaction, the inducer combines with chrB promoter, pchrB.  Kd and Kp are the degrees of dissociation of the above two complexes, respectively, and n is the Hill coefficient which indicates the induction strength. We assume that Ca means the concentration of Crn-chrB, Cb means the concentration of chrB protein, Cp means the concentration of the free promoter of chrB, and Ct means the total concentration of the promoter of chrB. So we assume the following:  M represents the strong-starting condition chrB mRNA concentration; G’ represents the concentration of chrB gene. R’ represents the strong-starting condition free chrB protein concentration. And KR’ means the new constant of rate. Finally a formula on the right side of the first representative chrB protein synthesis, the third means chrB protein in combination with chromium ions, led to a decline in unbonded protein concentration. Obviously, KR is combined with chromium ions, chrB protein concentration is directly related to, temporarily need further data to determine the relationship between, the idea is there: For example:  , where q is the proportionality coefficient.
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