SFit – Single Value Decomposition analysis software
SFit is complete and easy to use data analysis software to study complex 3D rapid kinetics data. Typically these data consist of an optical measurement, e.g. absorbance, as a function of both reaction time and wavelength. They may be obtained from transient recordings of this optical signal with fast diode array spectrometers or alternatively are reconstructed from a collection of single wavelength transient kinetic traces.
Raw data form large 3D arrays whose analysis requires sophisticated methods such as included in SFit.
SFit includes the following procedures:
- Data handling and initial treatment
- Singular Value Decomposition (SVD)
- Global multiexponential fitting of the SVD treated data
- Introduction and evaluation of kinetic models
Figure 1: Raw data form large 3D arrays
Sfit: data handling
SFit uses Bio-Logic file formats but includes a procedure to import data from most other spectrometers and data acquisition systems. It also features a sophisticated graphic interface for an easy visualisation of the files.
Once acquired, the data can be prepared before treatment.
This includes: modification of data range, background correction, smoothing, and transformation to logarithmic time scale and many more…..
SFit: fast SVD analysis
Direct analysis of the original 3D rapid kinetics array of data would require simultaneous (global) fitting of all the kinetics traces recorded at all wavelengths (hundreds of values) . However, because of the high redundancy of the data a drastic size reduction can be obtained by using Singular Value Decomposition (SVD).
In this procedure the original array of data A is transformed into a matrix product:
A = U x S x V where U and V are orthogonal matrixes containing kinetics and spectral information respectively, S being a scale factor vector that allows evaluation of the number of significant spectral species involved in the reaction.
For more information on SVD : http://en.wikipedia.org/wiki/Singular_value_decomposition
SFit: global multiexponential fitting
Once reduced by SVD, rapid kinetics analysis becomes highly simplified. Instead of hundreds of kinetics traces, what remain to be fitted are transitions between a few spectral species as in figure 3.1 (typically 2 to 5 species only). Sfit is unique as it proposes two fitting procedures based on Levenberg-Marquardt or Simplex algorithms. This allows very precise determination of the set of rapid kinetics constants involved in the reaction.
SFit: kinetic models
The spectral vectors V obtained after SVD analysis (figure 3.2) do not correspond to real spectral species but are rather mathematical entities resulting from the decomposition. Real spectral species are in fact linear combinations of these spectral vectors.
To get the real spectral species and their amplitudes (absorbance) requires an input from the user which has to make a choice of a reaction models. Kinetics of transitions between these species are linear combination of exponentials terms with rates constants such as evaluated by the global multiexponential fitting.
SFit offers a complete choice of kinetic Models such as: parallel system, fully sequential system, partly sequential or branched kinetics as following: