@article {26199,
	title = {Computing Optimal Properties of Drugs Using Mathematical Models of Single Channel Dynamics},
	journal = {Computational and Mathematical Biophysics},
	volume = {6},
	year = {2018},
	month = {10/2018},
	pages = { 41-64},
	publisher = {DE GRUYTER},
	abstract = {Single channel dynamics can be modeled using stochastic differential equations, and the dynamics\&nbsp;of the state of the channel (e.g. open, closed, inactivated) can be represented using Markov models. Such\&nbsp;models can also be used to represent the effect of mutations as well as the effect of drugs used to alleviate\&nbsp;deleterious effects of mutations. Based on the Markov model and the stochastic models of the single channel,\&nbsp;it is possible to derive deterministic partial differential equations (PDEs) giving the probability density functions\&nbsp;(PDFs) of the states of the Markov model. In this study, we have analyzed PDEs modeling wild type (WT)\&nbsp;channels, mutant channels (MT) and mutant channels for which a drug has been applied (MTD). Our aim is\&nbsp;to show that it is possible to optimize the parameters of a given drug such that the solution of the MTD model\&nbsp;is very close to that of the WT: the mutation{\textquoteright}s effect is, theoretically, reduced significantly. We will present the\&nbsp;mathematical framework underpinning this\&nbsp;methodology and apply it to several examples. In particular, we\&nbsp;will show that it is possible to use the method to, theoretically, improve the properties of some well-known\&nbsp;existing drugs.},
	author = {Tveito, Aslak and Maleckar, Molly and Glenn T. {Lines}}
}
