Introducing new exchange models



One of the primary goals in LineShapeKin development was to make it easy to extend the package to suit specific needs of an academic researcher. Current implementation of the package uses simple 1:1 binding model. However, real binding equilibria may be complex. Simple binding models have that inherent advantage that it is possible to develop analytical solutions to the mass law equations to extract equilibrium concentrations of components needed for building K-matrices. More complicated models are hard to analytically solve. Therefore I introduced a way of building the exchange models when one relies on numeric solution of the mass law equations. No surprise, this is slower about 20x. However, the benefit is that all you need is to write the equations out and express binding constants through the set of equilibrium concentrations you will need in K-matrix. For example see 1:1 equilibrium model that still functions both ways - analytical and numeric (see a 'mode' switch in the header).

The line shape fitting using numeric solution to mass law equations is unarguably inefficient. However, 'simulation' mode is still fast enough to serve as  a good instructional/exploration tool. If you have enough patience you can fit real data in the numeric mode and see if it is worth it to sit down and derive analytical solution to the exchange process you deal with. The key benefit is that you will get the idea of the result with relatively modest effort.

One of the difficult issues with complex models that one needs very precise data to substantiate use of the more complex model. Normally it is considered to be very difficult to fit data to 3- and more state equilibria (unless you have outrageously clear-cut case) because information content of spectral line shapes is limited. However, if many nuclei experience same multi-step kinetics, one can fit all data globally and have much better definition of the model parameters even for complicated exchange processes. LineShapeKin was coded from ground up to handle global fitting procedure. It will be exciting to use this capability together with complex models. Faster processors and replacement of numeric minimization with analytical solutions for the models will certainly make analysis of complex kinetic processes very feasible.


To be done:

  1. Modify prepare-residue-data etc. for handling multiple starting peaks (for complex models)