Having had a past interest in this, I thought I would comment. Through the retrospectoscope, life is a strange and interesting thing. I became interested in math models back when I was doing research in oncology. I had some serious training as an inorganic chemist so I naturally gravitated towards that most unusual of chemotherapeutic agents, cisplatinum (Cisplatin).
The whole story of how this drug was discovered is fascinating:
In the 1960s, Barnett Rosenberg and van Camp et al at Michigan State University discovered that electrolysis of a platinum electrode produced cisplatin, which inhibited binary fission in Escherichia coli (E. coli) bacteria. The bacteria grow to 300 times their normal length but cell division fails. Rosenberg then conducted a series of experiments to test the effects various platinum coordination complexes on sarcomas artificially implanted in rats. This study found that cis-diamminedichloridoplatinum(II) was the most effective out of this group, which started the medicinal career of cisplatin.By the time I started looking at this drug in the 1980’s, it was well established in oncology for the treatment of testicular cancer. At that time it was being looked at in almost every other solid cancer, particularly in childhood tumors, including those of the brain. I even ran a clinical trial using it in relapsed brain tumors. The drug continues to be used extensively in cancer. It continues to have activity, but has monstrous side effects, particularly in children. Its congener, carboplatinum, has less side effects but is probably not as effective. While cisplatinum is curative in testicular cancer, it is not so in many other tumors.
In chemistry graduate school, one of our faculty was John O. Edwards, the then reigning guru of chemical kinetics. He put me onto an appreciation of the dynamics of the molecular world. Trust me, at a time in chemistry when X-Ray Crystallographers held sway, molecular mechanics had a hard time competing with the static view of nature.
It occurred to me that of all the ligands that might react with cis platinum, a sulfhydryl containing one would be the most likely, and the cell is replete with such ligands, including glutathione. During my study of such reactions, I found that the reaction was biphasic and began looking for a way to solve the simultaneous differential equations involved.
I still think that the reaction of sulfhydryl contiaining molecules is the key to the mechanism of action of cisplatinum, but the cross linking of DNA has been the dominant theory since the beginning. It is so dominant that it has attained the status of dogma and only a few souls in the wilderness, myself included, have bothered to question the dogma. I find this a very interesting comment on Big Science and Big Medicine. Most assuredly the damage cisplatinum does to the inner ear (the hair cells) and the kidney involve sulfhydryl binding. However, in the end, it is probably a theoretical question since it is doubtful that the drug will be in use in the future once more active biological treatments are developed.
(To be fair there has been some recent studies suggesting that the reaction of cisplatinum with sulfhydryl groups including those on GSH is too slow to account for its biological activity. I have some questions about this study but will leave it there.)
In any case, even modelling A + B -> C and C -> D as simultaneous differential equations is difficult. That’s when it became obvious that Euler’s solution became the way to handle this problem. I am quite sure that many others had worked this out long ago, but it was fun to come across something like this by yourself. Basically I came in the back door (and the sub basement) to system dynamics and the computer solution of dynamical problems exemplified by Stella and, I assume, MathLab.
Unfortunately my research on this project went nowhere, mainly because of the lack of support by the powers that be who wondered why I was questioning the orthodoxy of cisplatinum and DNA. So, I switched over to modelling the cell cycle where I also ran up against orthodoxy. The "Pipe" model of the cell cycle does very well in predicting flow cytometry results. But, orthodoxy holds sway. So, throwing up my hands, I left academic medicine. (incidentally, googling "pipe model" of the cell cycle gets you lots of references to "pipe cleaners"!!!)
I have often wondered about the theoretical basis of these simulation programs (e.g. Stella) and every other one including everything from SimCity to all the Virtual Reality sites. I guess the hypothesis is that one can divide time into smaller and smaller increments so that the approximation approaches its asymptotic limit. That is, if one has A -> B; C -> D; B ->E; D -> A; etc that one can use the starting concentration (amount) of A, B, C, D, E, etc in the rate equations and run through a cycle, then adjust the concentrations for the new values and run the cycle again. If the time increment is small enough, the generated curves should fit experiment.
I’ve always looked back with pleasure on the times when thinking about these things was more than a hobby. Unfortunately, questioning orthodoxy in science doesn't get you tenure. Only a lot of grief.
