Hello,
I am measuring thermal stability of a small protein (131 aa) using circular dichroism following the loss of its secondary structure. The data obtained is normalized to be within 0 and 1 where 0 is folded protein and 1 is completely unfolded. The CD of the fully unfolded state was calculated from a different experiment on the same batch and taken as reference. Once plotting my data in Graphpad Prism 9, I am fitting a standard 4PL curve using non-linear regression, constraining the regression to use 0 as bottom value and 1 as top value (see attached file). The Tm is reported as IC50 in this screenshot because this formula is often use for calculating IC50 and EC50. However, the resulted fitted line seems to not being able to represent correctly my data. I performed this experiment twice and the replicate test is showing that the model is inadequately representing the data. Should I look for a different equation to model my data? Or am I making a mistake in performing this regression? Thank you for the help!
If your protein has multiple domains that have different melting temperatures, the curve would appear as a composite of multiple curves.
Thank you Adam B Shapiro for your answer. This protein is a small homodimer, so I don't think there should be a significant deviation from a sigmoidal curve.
To ascertain that your model is applicable to your data, plot the residuals (y-\hat{y}) against the independent variable, they should be randomly distributed. You can perform a “runs-test” as a non-parametric test, or (more work, but also more powerful) a t-test to compare the residuals with the standard deviation of the data. Both methods test for H0: The data are reasonably well described by the regression curve, against H1: The data significantly deviate from the regression curve.
Most commercial software performs non-linear curve fitting with the Marquardt-Levenberg algorithm. I had this fail me on occasions and found that Nelder-Mead's simplex-algorithm is more reliable (DOI:10.1093/comjnl/7.4.308). Disadvantage: you need to get the errors of the fitting parameters from bootstrapping (10.1016/0076-6879(92)10009-3), ML gives them directly.
Thank you for your help Engelbert Buxbaum . I performed the runs test and indeed it resulted that data significantly deviate from the data. However, I changed the model to fit an asymmetric sigmoidal curve (5PL curve) and now the fit seems to be much more correct.
Hello Fabrizio Casilli Clearly, an S model would fit your data better. Look at the attached image.
LogXb = LogEC50 + (1/HillSlope)*Log((2^(1/S))-1)
Numerator = Top - Bottom
Denominator = (1+10^((LogXb-X)*HillSlope))^S
Y = Bottom + (Numerator/Denominator)
- Badges
- Science topic
- Similar topics
- Physics
- Condensed Matter Physics
- Solid State Physics
- PEAKS