thats_karlo wrote:I thought when model fires an action potential its amplitude has to be constant during firing pattern and even for different set of model parameters.
In a model, and also in a real cell, the total membrane ionic current must be equal and opposite to the total membrane capacitive current (because of conservation of charge). For a single compartment model, or an electrically compact cell, this fact can be expressed by the equation
where the i_x are the currents attributable to each of the ionic species x.
At any point where v reaches a maximum or minimum, dv/dt is 0. Therefore at any maximum or minimum of membrane potential, the sum of all ionic currents must be 0.
Imagine a single compartment model with three ionic currents: sodium, potassium, and leak. Then at the spike peak, 0 = gNa * (v - eNa) + gK * (v - eK) + gL * (v - eL) where gx and ex are the membrane conductance and equilibrium potential for ionic species x. Solving for v gives v = (gNa*eNa + gK * eK + gL * eL)/(gNa + gK + gL).
1. the denominator is the total membrane conductance gm
2. gNa/gm, gK/gm, and gL/gm are the fractions of membrane conductance that are attributable to sodium, potassium, and leak.
3. membrane potential at the peak of the spike is the average of the ionic equilibrum potentials, weighed by their fractional contribution to total membrane conductance. In other words, the peak membrane potential is the weighted sum of the ionic equilibrium potentials at the time of the spike peak.
At the peak of the spike, membrane potential will be closest to the equilibrium potential of whichever ionic species makes the biggest contribution to total membrane conductance. Anything that makes gK larger, or gNa smaller, at the peak of the spike, will reduce the peak amplitude of the spike.
What do you think happens to gK activation during injection of a sustained depolarizing current? And what do you think happens to gNa inactivation during injection of a sustained depolarizing current? Can you use a model to test your predictions? e.g. by demonstrating the time course of gK and gNa during repetitive spiking?
This really belongs under General Questions and Discussions about Computational Neuroscience; I will move this thread to that area, and leave a "shadow topic" in its original location.