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Learning about the basics of theoretical neuroscience from the youtube lectures from Michale Fee's introduction to neural computation course.
We're considering a very simplified model of a neuron, where it's just a spherical shell (no ion channels) and the only way to inject current into it is via an electrode that takes charges from a saline solution and pumps them into the neuron.
This simplified model corresponds to the neuon being a capacitor.
It's then said that "As positive charges build up on the inside of the membrane, they repel positive charges away from the outside of the membrane"
My question: why is it that only positive charges are pumped into the neuron from the saline solution? Why aren't any negative charges pumped in?
Both positive and negative charges are pumped in; in fact, you can't really do one without doing the other, it just happens in different places. When you "pump in positive" charge you are making the electrode contiguous with the inside of the cell more positive while making a ground electrode in your bath more negative. If you "pump in negative" then the opposite happens.
Here's an example current-clamp experiment in a biological setting, where you measure voltage while injecting current to a cell. In this experiment, there is 0 current at the start, then either a positive or negative current is applied for a couple hundred milliseconds, and then the current returns to zero. If you inject a positive current, the cell depolarizes (voltage becomes less negative), and sufficient current will lead to action potentials ("spikes") if you had a biological neuron or if you implemented voltage-gated channels in your circuit. If you inject a negative current, the cell hyperpolarizes (voltage becomes more negative).
In equilibrium there are more positive ions on the outside of the cell as on the inside. This is where the potential is set to zero. Now you can use both types of ions. Positive as well as negative. When you pump in negative ions the potetial difference will grow. But then no signal will run along the neuron's axon. When the small channels are opened only positive ions will flow. The constant potential difference is kept up by Vm. If the channels in the real neurons are opened when the cell body has given a signal for this, the positive ions flow to the inside and this gives a change in potential. This ingoing of ions propagates through the axon. The potential Vm is for a short while reduced to zero and the channels open. The positive ions flow in, causing a flowing in in the direction of signal propagation. This short inflow propagation is the signal. Shortly after the initial ions have flown in the are pulled out again by Vm and the stationary potential difference is established again. Like the potential difference in a battery (which works with ions too, but instead there are electrons flowing between the + and - terminals, instead of the positive ions in the neuron). So a short in and outflow finds place when a signal (a potential spikewhich is essentially a zero potential spike but because we set the equilibrium potential to zero this is a potential spike).
Why does your pictured model say that a positive current flows inside? Well, in the zero potential state (which is a atate with more positive ions on the outside of the membrane than on the inside) there is no current flowing. This unevenly distribution is caused by an electric potential due to negative charges. The channels are closed to maintain this difference. The positive ions are drawn from the inside through a one way door so to speak. The moment they are drawn to the outside (by an electric field) the door is shut behind their back so they can't go back to the inside. Only when the channels are opened the ions can flow back. When the channels are open they can be pulled back to the outside again when the channels are still open. This happens shortly after ions have flown in. The net result is a pitential peak. The Vm in your model is the driving force of the positive ion movement. But why are no negative ions involved in the flow between the two sides of the membrane? Why are only positive ions flowing in and pulled out? Because they are needed to pull the ions out of the inside of the cell. They constitute the Vm and in your model only the positive charges flowing in are considered. This is not how it goes though. The positive ions flow in (positive current) because the membrane has opened for them (channels are opened). But then they fast flow back again ( negative current) to contribute to a new potential difference. This is also caused by Vm and I don't see this in the model you give. Now what constitutes Vm in reality? Something to think about!
The answer is: Because this happens in a true neuron. Only positive ions rush in (this momentary rush-in gives the spike potential, a short time in which the potential goes from the rest potential to zero) during a signal traveling. The in-rush of positive ions travels down the axon to inform another neuron. The non-zero rest potential is the restored shortly after the rush-in by other means, so not by ions passing through the channels back again. That's why it takes a short while before a new spike can be sent.
I am not sure if I get the pictured model completely. The Vm pictured resembles the rest potential. The circle resembes the cell body. But the capacitor is misleading. It might rsesemble both sides of the membrane (which indeed have the capacity to store charge) but drawing it outside the cell and connected to the cell is misleading. The cell itself is a capacitor. The circle, that is. You can't separate the capacitor and the body (circle). The is a non-zero rest potential. A loaded capacitor so to speak. Then the plates of the capacitor are connected (which in the model happens via the circle but in reality finds place in the circle). Then the plates are recharged again. Again via the circle. It is Vm that recharges the capacitor, but remember it is the circle itself that is the capacitor (it would have been clearer if the cell was drawn as two concentric circles). A new rest potential is installed. Of course some positive ions have to flow out the neuron too. It would get pretty crowde if the always rush in when a signal travels. So there will be also ions outward, that is a negative current will be seen alsi (if inward if plus).
Of the various types of excitable cells that respond to chemical signals, neurons are perhaps the most familiar. When electrical signals reach the end of neurons, they trigger the release of chemical messengers called neurotransmitters. Each neurotransmitter then diffuses from its point of release on one side of the synapse to the cell on the other side of the synapse. If the neurotransmitter binds to an ion channel receptor on the target cell, the related ion channel opens, and an electrical signal propagates itself along the length of the target cell.
Neurons have ion channel receptors specific to many kinds of neurotransmitters. Some of these neurotransmitters act in an excitatory capacity, bringing their target cells ever closer to signal propagation. Other neurotransmitters exert an inhibitory effect, counteracting any excitatory input and lessening the chance that the target cell will fire.
Skeletal muscle cells also rely on chemical signals in order to generate electrical signals. These cells have synapses that are packed with receptors for acetylcholine, which is the primary neurotransmitter released by motor neurons. When acetylcholine binds to the receptors on a skeletal muscle cell, ion channels in that cell open, and this launches a sequence of events that results in contraction of the cell.
In contrast to neurons and skeletal muscle cells, some excitable cells have ion channels that open in response to mechanical stimuli rather than chemical signals. These the hair cells of the mammalian inner ear and the touch receptor cells of both human finger pads and Venus fly traps. Cells that respond to touch have their ion channel receptors clustered at the position where contact usually occurs.
Excitable cells, such as fast-acting neurons and muscle cells, have specialized channels that open in response to a signal and permit rapid ion movement across the cell membrane. The opening of just a single ion channel alters the electrical charge on both sides of the membrane. The resulting charge differential then causes adjacent voltage-sensitive channels to open in chain-reaction fashion, creating a self-propagating electrical signal that travels down the entire length of the cell. Sometimes, this sequence of events is triggered when a chemical signal — such as a neurotransmitter — binds to an ion channel receptor on cell's surface. Other times, a cell's ion channels open in response to mechanical (rather than chemical) stimuli.