系统与计算神经科学作业3

Systems and Computational Neuroscience

Tsinghua University

Homework #3

The paramecium has a resting potential (RP) and an action potential (AP) similar to many neural potentials. In typical pond water, the figure shows the AP and the RP for the cell. If one varies the extracellular potassium or the extracellular calcium, the results are shown in the lower part of the figure. Assume that the cell is only permeable to these two ions and water. Answer these:

(a) In the resting state which is true: PK > PCa, PK = PCa, or PK < PCa?

PK > PCa is true. Because according to the RP curve shown in the figure below, the slope of RP curve of K is bigger than that of Ca, it means in the resting state the extracellular concentration of calcium has less influence on the resting potential, which indicates that the permeability of calcium is smaller than that of potassium.

(b) What about at the peak of the AP?

PK < PCa is true. Because according to the AP-overshoot curve shown in the figure below, the slope of AP-overshoot curve of Ca is bigger than that of K, it means in the action state the extracellular concentration of potassium has less influence on the action potential, which indicates that the permeability of potassium is smaller than that of calcium.

(c) Compared to the ionic concentrations of pond water, is [K]in greater than, less than or equal to [K]out? Explain.

[K]in > [K]out

In the resting state, the equilibrium potential is negative, which means the electrical gradient drives potassium inside the cell. So the chemical gradient rises and is opposite against the electrical gradient. Due to the chemical gradient, some potassium move out of the cell. Thus, [K]in > [K]out.

(d) Answer the same for calcium.

[Ca]in < [Ca]out

When calcium channels open, the potential rises and finally action potential occurs. This indicates calcium diffuse into the cell due to the chemical gradient. Thus, [Ca]in < [Ca]out.

(e) When the posterior end of the organism is mechanically tapped, the membrane transiently hyperpolarizes. What permeability changes might be responsible?

The change of PK might be responsible. When PK increases, the chemical gradient drives more potassium out of the cell, this follows the rise of the electrical gradient. And finally, the membrane transiently hyperpolarizes.