Curve fitting

Based on laboratory experiments was possible to plotting fluorescence standard curve as a function of GFP concentration (Green Fluorescent Protein). This adjustment was essential to facilitated the process of obtaining the GFP molecules number just using the fluorescence values obtained in lab.

The curve that better fitted the fluorescence standard curve points was the straight: (1) $$ F_{luo}=a[GFP]+b $$

Where the parameters a and b are constants, [GFP] is GFP concentrations given by nM and F_{luo} is fluorescence in u.a. (IMAGEM 1)

The graph 1 fitting constants results and their respective uncertainties is described in table 1 on appendix (link). The result was: (2) $$ F_{luo}=113[GFP]+94$$

For further analyses we will transform this equation for GFP molecules number, resulting in the following equation: (3) $$ F_{luo}=1.85 10^⁻13[GFP]+117 $$

Using the lab results (link) of uspA and J23101, we fitted the GFP molecules number in function of PEG (polyethylene glycol) concentration with the exponential function: $$ y=y_0+Ae^((R_0)x) $$ and made the graph 2. (IMAGEM 2)

This curves have both the coefficient of determination value $$ r^2 = 0.97 $$,it is the number that indicates how well data fit a statistical model , in other words, almost 97% of the experimental dots are described by this fit. Moreover, the constants uncertainties are relatively low for both adjustment as can be seen in the tables 2 and 3 on appendix (link).

The exponential fitting curve for uspA promoter: