King-Alman rate equation generator

The King-Altamn rate equation generator, despite its apparently obscure and technical immediate application, is one of the most sophisticated examples of pure programming I have ever produced. Much of the fron end is extremely simple, and it is only the heart of the engine, which is used to calculate the elements of each term in the denominator of the rate equation, which is of any real interest to any non-biochemists. I will attempt an explanation of the complexity of the problem with which I was faced, and how I eventually solved it. Essentially, this situation was this: a number of terms, each constructed from one element from each 'level' have to be collected. Each 'level' can contain up to 10 elements, and there can be up to ten levels. starting at the first level, the program must make its way to the last, collecting elements on its way. If it chooses always to always go down the left-most branch, then one valid term will be generated. If it chooses to go down the left-most branch for all but the last, where it travles down the second-left-most branch, another combination is generated. What we have, essentially then, is a branching tree problem: at each fork, where the program has two or more choices on its next path, effectively what is required is for the procedure that makes the decisions, and simultaneously collects the elements, to run copies of itself for every branch in the level below it. These, in turn, will be completely capable of handling the branches below them. And so on, until the maximum, tenth, level. The classical approach I would make to problems of this sort would be one of specific coding; introducing a FOR loop control variable for each stage of the procedure, and controlling each individually. Although this would allow for greatly simplified coding, the code structure is manifestly inelegant and overcomplicated, and it lacks the wholeness that truly defines pure code at its best. It also becomes increasingly complex if the code ever had to be extended for more than 10 levels, and soon becomes unmanagable, if only in the volume of code, for many more than three times this number. It also is rather tedious to write, and being prepared for a challenge, I accepted a different route. Here, a small procedure adds the element it finds to the growing string of the term its compiling, and then makes exact copies of itself for every branch below the current level. I implemented this is Delphi through a procedure that, when ready to spawn new versions of itself, simply called itself with an indication of which level to start on, and passing on the term it carries to all its progeny. Ultimately, and with a little experimentation, this approach (to my surprise) seemed to work, and (to bring this rapidly to conclusion) can generate rate equations from the simple rmodel reversible michaelis-menton equation to the complex ones of inhibiton or multiple substrates, or beyond. For those interested in how to program a mechanism into the generor, the method is to identify all different enzyme forms in your mechanism; ie. free enzyme, enzyme bound to substrate etc; and plug them in the top list, remembering to ignore isomerisation. If the enzyme form can be converted to another with a pseudo-first order rate constant, then find the origin form on the left and the destination on top, and put the constant name in there. The program employs reserved 'words', such as 'a' and 'p' for substrate and product, that you can use if making use of the automatic factorisation. Note this generator only produces the denominator-the numerators are often trivially derived using the method of Wong and Haines. The rate generator is available for download with full source for Delphi 4 below.

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