- #1

Agent M27

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## Homework Statement

We will deal here with a certain identified synapse in the CNS of the mooncalf (Bos lunaris). The post synaptic cell has voltage-sensitive channels like the squid axon-- a rapidly depolarizing, inactivating channel which conducts only sodium ions, and a slowly depolarizing, non-inactivating channel which conducts only potassium ions. For our purposes, these are the only channels present in this neuron.

Ion concentrations for mooncalf blood and for the cytoplasm if this neuron are given below:

[Na] Cyto = 5mM

[Na] Blood = 500mM

[K] Cyto = 300mM

[K] Blood = 30mM

The membrane of this neuron at resting has a conductance to sodium ions, g

_{Na}, .1mS/cm

^{2}and a conductance to potassium ions, g

_{K}, of 1mS/cm

^{2}.

After a large, rapid depolarization the maximum (peak) sodium conductance is 50 mS/cm

^{2}and the peak potassium conductance is 50 mS/cm

^{2}.

What is the max depolarization of the membrane above threshold? (Your answer must be within +-2mV)

What is the max hyperpolarization of the axon below resting? (Within +-2mV)

What is the highest value of dV/dt -- the slope of the voltage curve -- that you could possibly observe the moment the voltage trace crosses 0mV during the depolarization phase of an action potential. Assume that the membrane capacitance = 1muF/cm

^{2}.

## Homework Equations

E

_{Na}= [itex]\frac{RT}{zF}[/itex]*ln [itex]\frac{[Na]

_{o}}{[Na]

_{i}}[/itex]

## The Attempt at a Solution

E

_{K}= -56.41mV

E

_{Na}= +112.83mV

I am self studying the materials posted at MIT OCW Cellular Neurobiology and this is from problem set #1 and I am using the text by Kandel et al. "Principles of Neural Science". I started by finding the Nernst potential of the ions using the concentration figures given. However I don't really know what value they are wanting, so I don't know where to proceed from here. I know what depolarization means, but I don't know what they are asking in the quantitative sense. Also I know what threshold means, but I could not find a "threshold" value for this neuron, so I really don't know the range of acceptable values. Thanks in advance.

Joe

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