By John Wagner, Christopher Fall, Eric Marland, John Tyson
This textbook presents an advent to dynamic modeling in molecular phone biology, taking a computational and intuitive process. special illustrations, examples, and workouts are integrated in the course of the textual content. Appendices containing mathematical and computational options are supplied as a reference device.
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Additional resources for Computational Cell Biology
Fall and Joel E. Keizer In Chapter 1 we introduced models of simple channel behavior but ignored the idea that something might ﬂow through such a channel. In this chapter we will learn how to model current ﬂowing through ion channels and how to include the feedback regulation of the channel behavior by voltage. But let us be very clear about what we are modeling in this chapter. Only in the most idealized sense are we modeling the behavior of excitable cells like neurons. In fact, we will be creating point models of patches of membrane, with only implicit consideration through the use of ion concentrations of the idea that the membrane encloses a compartment.
The portion of the transmembrane protein that forms the “gate” is sensitive to membrane potential, allowing the pore to be in an open or closed state. cillations and other complex behaviors that often motivate study of such biological phenomena. These techniques are covered in several chapters and in the appendices. Rigorous analysis of complicated differential equations requires specialized training, because there are many subtleties that are appreciated only with experience. Similarly, choosing proper numerical methods and selecting valid simpliﬁcations requires caution.
13) where f∞ k+ k+ and τ + k− 1 . 14) Because ionic channels are composed of proteins with charged amino acid side chains, the potential difference across the membrane can inﬂuence the rate at which the transitions from the open to closed state occur. According to the Arrhenius expression for the rate constants, the membrane potential V contributes to the energy barrier for these transitions: − V+ − V− and k− ∝ exp . 16) − where k+ o and ko are independent of V. 16) into the expressions for f∞ and τ and rearranging, we obtain 1 , + exp((α − β)V) 1 + k− /k o o 1 1 · .