By John Wagner, Christopher Fall, Eric Marland, John Tyson
This textbook presents an creation to dynamic modeling in molecular mobilephone biology, taking a computational and intuitive method. distinctive illustrations, examples, and workouts are integrated through the textual content. Appendices containing mathematical and computational concepts are supplied as a reference software.
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Extra resources for Computational Cell Biology
03, and two different initial conditions were used, fO (0) 1 and fO (0) 0. 5. 10A. The rate at which the steady state is approached depends on the value of τ, which is 3 in these simulations. 10 (A) The exponential decay of the open fraction of channels. 5. (B) The effect of the step size in the Euler method for the simulation in panel A starting with the initial condition fO (0) 1. 5(1 + exp(−t/3)), is given by the full line. (C) Plot of the rate of change of n as a function of n. (D) Phase portrait with the arrows representing the direction and relative magnitude of the rate for each value of fO .
Nullclines are plotted in phase space, and show us the values of a pair of variables at which one of the variables does not change. 35) Note that there is a nullcline for each variable. The points of intersection of two nullclines are particularly interesting points in phase space that we will discuss below. 4. Oscillations occur at Iapp 150 pA. (B) The phase plane for the Morris-Lecar model for Iapp 150 pA. The heavy line is the limit cycle corresponding to the oscillation in (A), and the lighter lines are short trajectories that circulate in the counter– clockwise direction toward the stable limit cycle.
These tools reveal the structure, properties, and dynamical behavior of the system much as anatomical, physiological, and molecular biological techniques reveal the physical basis of the model. 7 Mechanistic cartoon of a gated ionic channel showing an aqueous pore that is selective to particular types of ions. 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.