By Christopher P. Fall, Eric S. Marland, John M. Wagner, John J. Tyson
This textbook presents an advent to dynamic modeling in molecular phone biology, taking a computational and intuitive procedure. certain illustrations, examples, and workouts are incorporated during the textual content. Appendices containing mathematical and computational strategies are supplied as a reference tool.
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Extra resources for Computational Cell Biology (Interdisciplinary Applied Mathematics) (v. 20)
Because the Nernst potential represents the equilibrium of the thermodynamic system, the potential diﬀerence evolves to that given by the Nernst equation regardless of the initial starting potential. This tendency for the system to move toward the equilibrium potential is the basis of the ionic battery used in the modeling of electrophysiological phenomena. In electrophysiology, the equilibrium potential is called the reversal potential, because departure from that point of zero current ßux results in the positive or negative ßow of ions.
These more complicated methods also address some other important problems such as numerical stability. There are many Þne texts on numerical analysis that discuss these issues and explain the various advantages and disadvantages of each method. As mentioned above, however, the best way to ensure an optimal and valid means of solution is to collaborate with a mathematician who has experience in scientiÞc computation or numerical analysis. There is a diﬀerent way to plot the results of solving the diﬀerential equation that frequently gives insight into the properties of the solution.
The trajectories for subthreshold initial conditions like V (0) ≤ −22 mV start at points in phase space above the V -nullcline and below the w nullcline. 12 Examples of voltage—freqency plots for the Morris—Lecar model with parameters that result in (A) Type I dynamics and (B) Type II dynamics. Note that the axes are somewhat diﬀerent. Plotted according to [Rinzel and Ermentrout, 1998a]. delayed rectiÞer K+ current. Thus the voltage begins to decrease and continues to do so because the K+ current activates as w increases.