Computing Characterizations of Drugs for Ion Channels and by Aslak Tveito, Glenn T. Lines

By Aslak Tveito, Glenn T. Lines

Flow of ions via voltage gated channels could be represented theoretically utilizing stochastic differential equations the place the gating mechanism is represented via a Markov version. The circulation via a channel could be manipulated utilizing quite a few medicinal drugs, and the impact of a given drug will be mirrored through altering the Markov version. those lecture notes offer an obtainable advent to the mathematical equipment had to care for those types. They emphasize using numerical tools and supply enough information for the reader to enforce the versions and thereby examine the impression of varied medicines. Examples within the textual content comprise stochastic calcium liberate from inner garage structures in cells, in addition to stochastic versions of the transmembrane strength. renowned Markov versions are studied and a scientific method of together with the impact of mutations is gifted. finally, the booklet indicates how you can derive the optimum homes of a theoretical version of a drug for a given mutation outlined by way of a Markov model.

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Extra info for Computing Characterizations of Drugs for Ion Channels and Receptors Using Markov Models

Sample text

It is more common to divide the calcium concentration into two values—not only one—which leads to 2 2 stochastic differential equations to be analyzed. This model will also be analyzed using Monte Carlo simulations and by a 2D deterministic system of partial differential equations representing the probability density functions of the states of the Markov model. Next, we shall couple the calcium concentration to the voltage-gated release of calcium through so-called L-type calcium channels. This model will allow us to study optimal drugs, combining the effect on calcium release and L-type channels.

To clarify what we mean by an optimal theoretical drug, we will give a few examples that will be discussed later and then we will briefly discuss the concept of a theoretical drug more generally. 1 Markov Models for Drugs: Open State and Closed State Blockers By using the notation of chemical reactions introduced above, we can explain the problem in a bit more detail. 19) kob For theoretical purposes, this drug is well defined, provided that we know the values of the parameters kob and kbo . We will often assume that these parameters are constants.

16]. 24). That is, data obtained from experiments using a particular drug are used to characterize the rates kbo and kob referred to, respectively, as the on and off rates of the drug. As mentioned above, we often view the rates as free parameters that can be optimized in order to create the best possible theoretical drug in the sense that the channel should work as much like the healthy case as possible. This way of describing a theoretically optimal drug was introduced in [99] and clearly motivated by the drug vector approach discussed in [97].

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