Name
Title | ||
|---|---|---|
The influence of the A-current on the dynamics of an oscillator-follower inhibitory network. |
Abstract | ||
|---|---|---|
The transient potassium A-current is present in almost all neurons and plays an essential role in determining the timing and frequency of action potential generation. We use a three-variable mathematical model to examine the role of the A-current in a rhythmic inhibitory network, as is common in central pattern generation. We focus on a feed-forward architecture consisting of an oscillator neuron inhibiting a follower neuron. We use separation of time scales to demonstrate that the trajectory of the follower neuron within each cycle can be tracked by analyzing the dynamics on a 2-dimensional slow manifold that as determined by the two slow model variables: the recovery variable and the inactivation of the A-current. The steady-state trajectory, however, requires tracking the slow variables across multiple cycles. We show that tracking the slow variables, under simplifying assumptions, leads to a one-dimensional map of the unit interval with at most a single discontinuity depending on g(A), the maximal conductance of the A-current, or other model parameters. We demonstrate that, as the value of g(A) is varied, the trajectory of the follower neuron goes through a set of bifurcations to produce n:m periodic solutions where the follower neuron becomes active m times for each n cycles of the oscillator. Using a generalized Pascal triangle, each n:m trajectory can be constructed as a combination of solutions from a higher level of the triangle. |
Year | DOI | Venue |
|---|---|---|
2009 | 10.1137/090760994 | SIAM J. Applied Dynamical Systems |
Keywords | Field | DocType |
action potential,feed forward,potassium,bioinformatics,phase plane,steady state,oscillation,bifurcation,biomedical research,central pattern generator,mathematical model,oscillations | Slow manifold,Oscillation,Control theory,Discontinuity (linguistics),Unit interval,Phase plane,Maxima,Trajectory,Mathematics,Bifurcation | Journal |
Volume | Issue | ISSN |
8 | 4 | 1536-0040 |
Citations | PageRank | References |
1 | 0.36 | 5 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Yu Zhang | 1 | 1 | 0.36 |
| Amitabha Bose | 2 | 56 | 17.79 |
| Farzan Nadim | 3 | 68 | 20.17 |