Please show all work! :) 1. Consider the neuron below, which has a membrane rest

Question

Please show all work! :)

1. Consider the neuron below, which has a membrane resting potential of -70mV, membrane space constant of lmm, membrane time constant of 100ms, and spike firing threshold of -65mV. The neuron receives input from three synapses. Synapse A results in an EPSP of 12mV amplitude and 2ms duration, synapse B results in an EPSP of 8mV amplitude and 1ms duration, and synapse C results in an IPSP with an amplitude of -2mV and duration of 3ms. axon hillock 0.5mm Justify your answers to the following questions mathematically (round distances to nearest 0.5mm) a) Would the cell fire an action potential if A is active? b) Would the cell fire an action potential if A and B are active simultaneously? c) Would the cell fire an action potential if B is activated twice with a delay of 2ms? d) Would the cell fire an action potential if all three are simultaneously active? e) If an excitatory synapse were also located at C, how large must the EPSP be to fire an action potential?

Explanation / Answer

a)

Yes. As the spike firing threshold is -65mV and the membrane time constant is 100ms, EPSP of 12mV for 2ms duration can definitely trigger an action potential. So, the cell can trigger action potential when A is active.

b)

Yes. A and B can trigger action potential when given simultaneously.

c)

Yes, it can as the spike threshold is -65mV and the EPSP is 8mV given twice in the interval of 2ms. As the membrane time constant is 100ms there is possibility of two spikes of duration 1ms used to trigger action potential should work well.

d)

Yes, if all the three are simultaneously given, the cell would trigger action potential as -2mV cannot reduce the spike threshold value to create action potential.

e)

If the third synapse is also excitatory, the EPSP has to be greater than 5mV to fire an action potential.

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