By Christopher P. Fall, Eric S. Marland, John M. Wagner, John J. Tyson
This textbook offers an creation to dynamic modeling in molecular phone biology, taking a computational and intuitive process. designated illustrations, examples, and workouts are integrated during the textual content. Appendices containing mathematical and computational strategies are supplied as a reference tool.
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By making even smaller changes in Iapp and testing the stability of the steady state, it is possible to locate the speciÞc values at which the stability of the steady state changes. This procedure could become very laborious, and so numerical algorithms have been developed that allow investigation of bifurcations to be done automatically. 9D, the characteristic values of the membrane potential are plotted on the ordinate as a function of Iapp . The thin full and dashed lines are the steady—state values of V for each value of Iapp , with the full lines representing stable steady states and the dashed lines unstable states.
The same is true for Iapp = 60 pA. We know that a point on a nullcline corresponds to a point at which the variable of interest is not changing, and so it makes sense that the intersection of nullclines represents a combination of variables for which the system as a whole does not change. The intersection of the nullclines for Iapp = 60 pA and Iapp = 300 pA are examples of Þxed points, and represent stable steady states. What is diﬀerent about the intersection of nullclines obtained when Iapp = 150 pA?
28). 7), then changed to various test potentials for a Þxed interval (40 ms), and Þnally returned to the holding potential. The value of the holding potential generally is chosen so that there is little or no current through the channel. This greatly simpliÞes the interpretation of the current at the test voltages. 8 Depolarization-induced electrical activity in giant barnacle muscle Þbers; the arrows indicated the start and end of the depolarizating currents. Reprinted from [Morris and Lecar, 1981].
Computational Cell Biology by Christopher P. Fall, Eric S. Marland, John M. Wagner, John J. Tyson