1.3 Quantitative effect of non-constant time constant Say that a particular neuron, X, has a set of synapses that fire when either stimulus A or stimulus B is present. The sequence of events is this: 1. X's resting membrane potential is -62mV. 2. Stimulus A occurs and raises the voltage to -55mV. Then, it stops, and the voltage begins to fall. 3. 20ms after stimulus A ends, stimulus B immediately adds an additional 8mV. (It's not actually immediately, but for the purposes of this question, please treat it that way.) X's threshold is -50mV. As you can see, stimulus A by itself is not enough to increase the membrane potential to threshold. However, let's see if the additional 8mV provided by stimulus B is enough to get the membrane to threshold. In other words, please calculate the final membrane potential in the following two scenarios, and say whether it hits threshold:

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### 1.3 Quantitative Effect of Non-Constant Time Constant

Say that a particular neuron, X, has a set of synapses that fire when either stimulus A or stimulus B is present. The sequence of events is as follows:

1. **X’s resting membrane potential is -62mV.**
2. **Stimulus A occurs** and raises the voltage to -55mV. Then, it stops, and the voltage begins to fall.
3. **20ms after stimulus A ends,** stimulus B immediately adds an additional 8mV. (It's not actually immediately, but for the purposes of this question, please treat it that way.)

X’s threshold is -50mV. As you can see, stimulus A by itself is not enough to increase the membrane potential to threshold. However, let’s see if the additional 8mV provided by stimulus B is enough to get the membrane to threshold. In other words, please calculate the final membrane potential in the following two scenarios, and say whether it hits threshold:

1. With a time constant of **40ms**.
2. With a time constant of **4ms**.
Transcribed Image Text:### 1.3 Quantitative Effect of Non-Constant Time Constant Say that a particular neuron, X, has a set of synapses that fire when either stimulus A or stimulus B is present. The sequence of events is as follows: 1. **X’s resting membrane potential is -62mV.** 2. **Stimulus A occurs** and raises the voltage to -55mV. Then, it stops, and the voltage begins to fall. 3. **20ms after stimulus A ends,** stimulus B immediately adds an additional 8mV. (It's not actually immediately, but for the purposes of this question, please treat it that way.) X’s threshold is -50mV. As you can see, stimulus A by itself is not enough to increase the membrane potential to threshold. However, let’s see if the additional 8mV provided by stimulus B is enough to get the membrane to threshold. In other words, please calculate the final membrane potential in the following two scenarios, and say whether it hits threshold: 1. With a time constant of **40ms**. 2. With a time constant of **4ms**.
Expert Solution
Step 1: Introduction:

The time constant of a membrane is a measure of how quickly it responds to a stimulus. A longer time constant means that the membrane will take longer to reach its final state. A shorter time constant means that the membrane will reach its final state more quickly.

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