"
Team:Aberdeen Scotland/Curve Fitting
From 2010.igem.org
| Line 5: | Line 5: | ||
<h1>Curve Fitting to find the Hill Coefficient for the GFP/Bbox-stem Association (n<sub style="font-size:15px">2</sub>)</h1> | <h1>Curve Fitting to find the Hill Coefficient for the GFP/Bbox-stem Association (n<sub style="font-size:15px">2</sub>)</h1> | ||
| - | <p>Based on a graph in a paper by Witherell et al.<sup style="font-size:10px">[ | + | <p>Based on a graph in a paper by Witherell et al.<sup style="font-size:10px">[1]</sup> which showed the binding curves of the MS2 stem loop we could calculate more accurately the value for n<sub style="font-size:10px">1</sub>. Our two MS2 stem loops (see Fig 1 in <a href="https://2010.igem.org/Team:Aberdeen_Scotland/Equations">Equations</a>) are 19 nucleotides apart, so our binding curve will most closely resemble that of the 8-16 construct, shown in figure 5A (filled squares).</p> |
<br> | <br> | ||
<br> | <br> | ||
| Line 43: | Line 43: | ||
<br> | <br> | ||
The reason we are not getting bistability 100% of the time, or 0% of the time, is because we have such a large range around each parameter. Each parameter value is randomly chosen from this range each time the program runs. Therefore, some combinations of parameters will give bistability and others will not. Ideally we would have a precise value for each parameter (no uncertainty). In this scenario, each time the program runs the parameters would be exactly the same. The result would either be 100% bistability or 0% bistability – either the switch always works or it doesn’t.</p> | The reason we are not getting bistability 100% of the time, or 0% of the time, is because we have such a large range around each parameter. Each parameter value is randomly chosen from this range each time the program runs. Therefore, some combinations of parameters will give bistability and others will not. Ideally we would have a precise value for each parameter (no uncertainty). In this scenario, each time the program runs the parameters would be exactly the same. The result would either be 100% bistability or 0% bistability – either the switch always works or it doesn’t.</p> | ||
| + | |||
| + | <h3>References</h3> | ||
| + | |||
| + | <sup style="font-size:10px">[1]</sup> Witherell, G.W., et al. (1990), ‘Cooperative Binding of R17 Coat Protein to RNA’, Biochemistry, Vol. 29, pp. 11051-11057 | ||
</html> | </html> | ||
Revision as of 15:10, 20 October 2010
University of Aberdeen - ayeSwitch
Curve Fitting to find the Hill Coefficient for the GFP/Bbox-stem Association (n2)
Based on a graph in a paper by Witherell et al.[1] which showed the binding curves of the MS2 stem loop we could calculate more accurately the value for n1. Our two MS2 stem loops (see Fig 1 in Equations) are 19 nucleotides apart, so our binding curve will most closely resemble that of the 8-16 construct, shown in figure 5A (filled squares).
Figure 5. A. Graph from paper by Witherell et al.[14] showing the binding curves of the MS2 stem loop. The filled squares are the 8-16 construct
which closely resembles the binding curves of our MS2 stems. B. The binding curve for the 8-16 construct was reproduced in MATLAB and the Hill
function for activators equation fitted to it (red line).
The curve fitting tool gave the following estimated parameters for β(a), K(b) and n(c):
Note that the R-square value is close to one which suggests that the fit of the curve to the data is very good.
The Hill coefficient is estimated to be 1.302 with a lower limit of 1.135 and an upper limit of 1.469. However, this is just for one MS2 stem loop and we have two. Multiplying this value by 2 we get 2.604 with a lower limit of 2.270 and an upper limit of 2.938. A value greater than 2 suggests that a protein binding to the first stem loop will make it easier for a protein to bind to the second stem loop. We say that co-operativity has been increased.
Therefore, we have n1=2.6 and n2=1.
Conclusion
Table 1 on the Parameter Space Analysis page shows that with n1=2.6 and n2=1, between 0.96% and 2.03% of the parameter combinations tested gave bistability.
However, the ideal scenario is that in table 4 on the Parameter Space Analysis page. Here, with n1=2.6 and n2=1, 51.27% to 58.04% of parameter combinations tested gave bistability.
The reason we are not getting bistability 100% of the time, or 0% of the time, is because we have such a large range around each parameter. Each parameter value is randomly chosen from this range each time the program runs. Therefore, some combinations of parameters will give bistability and others will not. Ideally we would have a precise value for each parameter (no uncertainty). In this scenario, each time the program runs the parameters would be exactly the same. The result would either be 100% bistability or 0% bistability – either the switch always works or it doesn’t.
