fluorescence output parameters

[cathy_joyce]

This is a question about the fluorescence output parameters when fitting stopped-flow fluorescence data using Global Explorer.
I have an enzyme reaction of the type: E+S=ES=FS=GS. E and ES have the same fluorescence; FS and GS are different (but the same as each other).
As recommended in the user manual, I use the output expression:
S1=a*((E+ES)+b*(FS+GS))+bkg
Thus, a is a scaling parameter; b is the ratio of product to substrate fluorescence; and bkg is the instrument background. I am fitting a series of traces obtained at different concentrations of S.

Usually the software comes up with values for the output parameters (a, b and bkg) that seem intuitively reasonable, BUT the standard error estimates on the values are huge (many powers of 10). Is this a peculiar quirk of the program, or does it really mean that these parameters can vary all over the map while still giving a mathematically sound solution? I haven't tested this rigorously, but it seems to me that a given experiment can give essentially the same solution, in terms of rate constants, with a whole range of different a, b, and bkg values. So maybe this means that it really doesn't matter what the output values are?

If I fix one of the output parameters, then (of course) the standard errors come into a sensible range (once one of the parameters is fixed, the values of the others are immediately obvious from the start or end points of the stopped-flow traces). So, my follow-up question is whether it is possible to measure reliably one or more of these parameters. For example, one could measure the background (bkg) parameter by noting the detector signal when no fluorescent material is in the cell. Or perhaps there is a reliable way of estimating b from emission spectra?

I'd be interested in hearing from anyone with experience of fitting fluorescence data.

[kajohnson]

The large standard errors on the scaling factors indicate that the parameters are not well defined. You can test this using several tools in KinTek Explorer. Also, compare the two example files "Tryp_synthase.mec" and "Tryp_synthase_onetrace.mec" to see the relationship between well constrained output factors and rate constants.
a. You can check the box "Plot observable traces at StdErr bounds". You will see a set of white lines drawn by the program computed at the extremes of each of the parameters (with the other parameter corresponding to the best fit at the extreme of the variable parameter). If all curves overlap with the data, then the std error estimates are not outside of a reasonable range. This display fails in some cases where standard error estimates are unrealistic, such as, 10 plus or minus 12. Even if the display looks reasonable, the std error estimates could still underestimate the error. See the instruction manual and the papers in Analytical Biochemistry for more information.
b. You can manually change one of the parameters to an extreme value, then lock it and fit the data again. Do the fitted curves follow the data and is the sum square error (chi2) comparable to the value at the best fit? If so, the extreme value of the parameter is perfectly acceptable.
c. Perform the Fitspace analysis. This is computationally more intensive, but gives a much more robust assessment of the range over which parameters can vary when fitting data. In addition the "Plot observable traces at Fitspace bounds" is more reliable in showing the effect of the allowable extremes of parameters on the fitted curves.
d. Finally, I remind you that kinetic constants and scaling factors are related. If you can do additional experiments to constrain the rates, you will be able to constrain the output factors as well. For example, we have had very good success in simultaneously fitting quench-flow and stopped-flow fluorescence data because the quench-flow data constrain the rates and that helps to constrain the output factors in fitting the fluorescence data. Also note that in the case of Tryp_synthase.mec, the data were collected at high enough substrate concentrations to allow extrapolation to define the amplitude to set then output factor for the intermediate.

We will soon be releasing a new version of the software that requires you to get an estimate of the standard deviation of your measurements (and provides tools to estimate it if is not known). In computing chi2 based upon known sigma values, one expects a good fit to give a chi2 value equal to the number of data points minus the number of fitted parameters, and thereby provides a standard for evaluation of goodness of fit. This will all be explained with the new release.

[mlarion]

Hi Dr. Johnson,
It is really nice to see how Global Kinetic Explorer has been created to deal with errors as compared to other fitting programs. We would like to use it for estimating the degree to which the microscopic rate constants are constrained by our data. We have data for substrate binding and was recorded on the Applied Photophysics machine available in our department. Therefore the first question is : Can Global Kinetic Explorer import data from Applied Photophysics machines with the extinctions .kin, .dsa, .glb, .dsb, .csv, ?

Second question is: Can Global Kinetic Explorer deal with logarithmic time acquisition and 10 000 data points?

Third question: What is the maximum number of rate constants which can be handled by the FitSpace Explorer during the calculations of space contours?

Thank you very much for your time and I am looking forward to hear from you.

[kajohnson]

KinTek Explorer can import data from any instrument so long as the data is in a text format and corresponds to one of the standards described in the instruction manual. Presumably you can export your data from the APP instrument as a text file. The .csv format may be the common comma-separated numbers format. If that is the case, import the data into MS Excel and then save it as a tab-delimited text file.

Yes, KinTek Explorer can handle logarithmic time scales...check on the logtime scale checkbox to display on the log scale, or leave it as a linear timescale. This does not effect the fitting, only the display. Fitting to 10,000 data points can be accomplished. There is no limit on the size of the data file.

The final question as to the number of rate constants that can be handled by FitSpace is harder to answer since it will depend on the data. The major problem is that if the model and rate constants are not well constrained, Fitspace will bog down in looking around in the areas of poor fit. We are still working to improve this, but for now, just try and see. Most of the information you need is derived in the first pass through the Fitspace calculation before doing the full 3-D plots, so you can stop the computation at that point.