QSoas tips and tricks: generating smooth curves from a fit

Often, one would want to generate smooth data from a fit over a small number of data points. For an example, take the data in the following file. It contains (fake) experimental data points that obey to Michaelis-Menten kinetics: $$v = \frac{v_m}{1 + K_m/s}$$ in which \(v\) is the measured rate (the y values of the data), \(s\) the concentration of substrate (the x values of the data), \(v_m\) the maximal rate and \(K_m\) the Michaelis constant. To fit this equation to the data, just use the fit-arb fit:

QSoas> l michaelis.dat
QSoas> fit-arb vm/(1+km/x)

After running the fit, the window should look like this:

Now, with the fit, we have reasonable values for \(v_m\) (vm) and \(K_m\) (km). But, for publication, one would want to generate "smooth" curve going through the lines... Saving the curve from "Data.../Save all" doesn't help, since the data has as many points as the original data and looks very "jaggy" (like on the screenshot above)... So one needs a curve with more data points.

Maybe the most natural solution is simply to use generate-buffer together with apply-formula using the formula and the values of km and vm obtained from the fit, like:

QSoas> generate-buffer 0 20
QSoas> apply-formula y=3.51742/(1+3.69767/x)

By default, generate-buffer generate 1000 evenly spaced x values, but you can change their number using the /samples option. The two above commands can be combined to just one call to generate-buffer:

QSoas> generate-buffer 0 20 3.51742/(1+3.69767/x)

This works, but it is quite cumbersome and it is not going to work well for complex formulas or the results of differential equations or kinetic systems...

This is why to each fit- command corresponds a sim- command that computes the result of the fit using a "saved parameters" file (here, michaelis.params, but you can also save it yourself) and buffers as "models" for X values:

QSoas> generate-buffer 0 20
QSoas> sim-arb vm/(1+km/x) michaelis.params 0

This strategy works with every single fit ! As an added benefit, you even get the fit parameters as meta-data, which are displayed by the show command:

QSoas> show 0
Dataset generated_fit_arb.dat: 2 cols, 1000 rows, 1 segments, #0
Flags: 
Meta-data:	commands =	 sim-arb vm/(1+km/x) michaelis.params 0	fit =	 arb (formula: vm/(1+km/x))	km =	 3.69767
	vm =	 3.5174

They also get saved as comments if you save the data.

Important note: the sim-arb command will be available only in the 3.0 release, although you can already enjoy it if you use the github version.

About QSoas

QSoas is a powerful open source data analysis program that focuses on flexibility and powerful fitting capacities. It is released under the GNU General Public License. It is described in Fourmond, Anal. Chem., 2016, 88 (10), pp 5050–5052. Current version is 2.2. You can download its source code and compile it yourself or buy precompiled versions for MacOS and Windows there.