Team:UCSF/Modeling
From 2013.igem.org
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- | <div id="description" style = "width:950px; height: | + | <div id="description" style = "width:950px; height:45px" align="justify"> |
- | <font face="calibri" size = "4"><center>There is one function for the low sensitivity promoter (f<sub>L</sub> | + | <font face="calibri" size = "4"><center>There is one function for the low sensitivity promoter (f<sub>L</sub>) |
- | and another for the high sensitivity promoter (f<sub>H</sub> . The other parameters for the production functions are: </center> <br> | + | and another for the high sensitivity promoter (f<sub>H</sub>) . The other parameters for the production functions are: </center> <br> </div> |
+ | <div id="description" style = "width:950px; height:200px;margin-left:40px" align="justify"> | ||
+ | <font face="calibri" size = "4"> | ||
A – basal expression level of promoter<br> | A – basal expression level of promoter<br> | ||
B – maximal expression level of promoter <br> | B – maximal expression level of promoter <br> | ||
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n<sub>R</sub> – hill coefficient for repression <br> | n<sub>R</sub> – hill coefficient for repression <br> | ||
I – Inducer concentration <br> | I – Inducer concentration <br> | ||
- | R:C – repressor/dCas9 complex. <br><p> | + | R:C – repressor/dCas9 complex. <br><p> </div> |
- | The subscripts indicate whether the parameter is a property of the low or high sensitivity promoter (L or H) or related to protein x or y. | + | |
+ | |||
+ | <div id="description" style = "width:950px; height:45px" align="justify"> | ||
+ | <font face="calibri" size = "4"><center> | ||
+ | The subscripts indicate whether the parameter is a property of the low or high sensitivity promoter (L or H) or related to protein x or y. </center> </div> | ||
</font> <br> | </font> <br> |
Revision as of 07:20, 28 October 2013
The primary goal of the modeling portion for the synthetic circuit project is to create a model that will help us figure out the right parameters, given our assumptions, which will generate the desired result, a Decision Making Circuit (Figure 1). In other words, we want a circuit that exhibits behavior A given a certain input and behavior B when the input is changed. A computer model can help us rapidly prototype by providing an environment where we can test out different promoters and repression strengths in the computer before we spend the time building and testing strains in the lab. The circuit is designed to produce different outputs according to different levels of inducer by utilizing the CRISPRi system. In lower concentrations of inducer, the guide RNA (gRNA) will be made to repress RFP. In higher concentrations of inducer, another gRNA will be made to repress GFP. The circuit should express GFP at lower inducer concentrations and RFP at high inducer concentrations, as shown in Figure 1 below.
ASSUMPTIONS: While creating the model for our system, we made five assumptions in order to simplify some of the aspects of the model:
1) protein degradation is linear;
2) protein production is based on a hill function and also depends on inducer concentration;
3) repression is governed by a hill function and depends on the concentration of dCas9 and gRNA complex;
4) that the binding and unbinding of dCas9 and gRNA complex happens much faster than the production/degradation of gRNA and fluorescent proteins (the complex is at Quasi Steady State).
5) everything diffuses quickly throughout the cell so that our differential equations depends on the concentration at any given time.
EQUATIONS
Given these assumptions we have the following equations for the system:
Fluorescent proteins:
dx – rate of degradation of GFP based on the “low” function
dy – rate of degradation of RFP based on the “high” function
The production term consists of a function that relates inducer and repressor complex to mRNA production rate and conversion factor that relates mRNA production to protein production rate.
px – conversion factor (mRNA/protein) for x (GFP)
py – conversion factor (mRNA/protein) for y (RFP)
The mRNA production functions depend on the amount of inducer and the amount of repressor complex as follows:
B – maximal expression level of promoter
k – Activation coefficient for low/high promoter
kR – half maximal effective concentration of R:C
n – hill coefficient for induction.
nR – hill coefficient for repression
I – Inducer concentration
R:C – repressor/dCas9 complex.