Six Species, Five Rate Fit

Uprecedented, Unmatched, and Almost Unbelievable

For decades, it has been the solid opinion of good science that fitting a data set with more than four species is effectively impossible and certainly impractical. Many times over the years, we have stated that good experiments must be as simple as possible to yield trustworthy results.

Samples sent to Olis in November, 1998, by a faculty member at the University of Washington turned our world upside down. We took a stopped-flow shot and proceeded to fit the data to a three species fit. The results said that the data were too complicated to produce a fit with only three exponentials. So, we tried our four species fit. Again, the residuals showed us that the reaction was more complicated than four species, three rates.

Inspired by 'real world' data which might actually support a five species, four rate equation, Dr. Iain Matheson quickly implemented this case. Unbelievably, this fit still showed structure in the residuals, although on an exceedingly small scale (Y axis from 0.002 to -0.002 AU).

Dr. Matheson returned to his computer and implemented a six species, five rate fit. As with the other equations, this involved writing the rate equations in differential form, extracting the matrix of rate constants involved in the reaction, and solving this matrix (!) using Matrix Exponentiation. He returned to the real-world data and tried the new fit. A sixth species was found! A fifth rate was found! And the residuals, now with a Y axis range of 0.001 to -0.001, have no structure, letting us know that the fit is correct.

In addition to showing you the fits, the residuals, and the species, we are also showing you the concentration of each species as a function of time. This final image shows the rapid disappearance of species one, the coming and going of the intermediate forms, and the increasing concentration from zero to 100% of the final species.

These data illustrate many exciting points:

1. The new Olis 3D fitting algorithms by Matheson can handle enormous data matrices, fit them in seconds to complicated data sets, provide the right answer, and provide the right tools for evaluating the results.

   

2. The new Olis 3D fitting algorithms by Matheson can be built upon, quickly and correctly, to support an ever-increasing number of cases. If the model can be expressed as a set of differential equations with first order or pseudo first order rate constants, it can be incorporated into Matheson's fits and solved by Matrix Exponentiation.

3. The methods implemented by Matheson are the most modern and powerful Global fitting methods ever invented, using Downhill Simplex and Matrix Exponentiation.

4. The Olis RSM 1000 obtains extraordinary time-resolved data. The linearity of the spectrophotometer must be extraordinarily high, the photometric accuracy must be extraordinarily high, and the S/N is obviously extraordinarily high to produce data sufficiently good to support a six species, five rate case.

   

5. With the Olis RSM 1000 collecting millisecond spectral scans, one has all the information for analysis he needs following a single stopped-flow shot!! Can you imagine how many shots, how many sample preparations, how many months would be required to get the correct answer if we were using a single wavelength detection system for this experiment?! It would be—effectively—impossible to trust any results. We challenge our friends and our international competitors to prove otherwise!

6. Olis is a company with elastic legs! As Professor Britton Chance noted years ago: "You can move in ways which are impossible for our bulkier colleagues to do." If your ideas make sense, we can implement them immediately, accurately, and successfully. We are not turning to the scientist at the University of Washington to pay for the addition of these two new equations, but thanking him for putting us in the position to develop and demonstrate ever better data tools for our clients.