Neurons and their modeling

I recently wrote an article about how memory works in the brain . A few comments said that I did not sufficiently disclose the topic of the features of a biological neuron. And I decided to fix my mistake.

This article is a list of the main mechanisms that distinguish biological neurons from a simple model with bond weights and an activation threshold. I will tell you how to correct the model if you need to take these features into account.

We start here with this simple picture:

1. We have different neurons

Problem: There are many types of neurotransmitters in the brain, and each neuron has its own set of receptors.


Solution: Colorize the balls of neurons, thus highlighting those that respond to a specific neurotransmitter. If you need several neurotransmitters for one neuron - paint it in several colors. If each neurotransmitter in its own way affects the charge of the neuron, create a function of the charge of the neuron for each neurotransmitter. Describe a neuron with the composition of these functions.

2. A charge leaks from neurons

Problem: A real neuron does not store all charged particles for an infinite amount of time, but gradually discharges.

Solution: Set the function of the discharge of the neuron from time to time. If necessary, you can have one for each neuron. But in general, the charge leaks due to the potential difference, so the situation there is like with a self-discharge capacitor - we will have something like:$$$U(t) = U_0*e^{-t/RC}$, where U is the potential difference between the neuron and the environment, t is time, R is the resistance of the membrane, C is the capacity of the neuron-membrane-environment system. By the way, this has already been done .

3. Neurons can be activated without signal from other neurons

Problem: Since the real neuron is not worried about where the neurotransmitters came from, it can be activated by itself, simply from the release of neurotransmitters into the brain.

Solution: Add a thing that, when activated, will increase the charge of all neurons. Color it in the color of the desired neurotransmitter. Activate when you need to simulate an external source of neurotransmitter.

4. There are neurons that do not have dendrites

Problem: Some neurons do not receive an input signal from others at all, activating only from the level of neurotransmitters.

Solution: See paragraph above.

5. Neurogenesis

Problem: New neurons and connections grow in the brain. And they die, by the way, too.

Solution: Add dynamically new neurons and connections if you need to simulate neurogenesis. To simulate the reverse process - delete.

6. Connections between neurons - not static

Problem: When neurons are activated, connections between them are strengthened or weakened. It depends on the order of activation. If the activation direction is direct, i.e. first, a neuron is activated from which the arrow leaves, and then the one into which it enters - the connection is strengthened. If the opposite is weakening.

Solution: Reduce or increase the weight of the connection, depending on the order of activation. And yes, the weight can be zero. This means that the connection is so weak that the activation of one neuron does not affect the other. But potentially, we can enhance this connection through direct activations from the outside - therefore, you can’t simply remove it.

7. Long-term memory

Problem: The real brain can "fix" the state of communication, and thus ensures the availability of long-term memory. The process is called Late Long-Term Potentiation.

Solution: Remember the value of the weight at the time of "fixing" the connection. Return the strength of the connection to it after strengthening or weakening of the connection. If the connection is fixed again - update the saved value.

8. Forgetting information from long-term memory

Problem: The real brain is able to degrade even the connections received by the previous mechanism.

Solution: Run the degradation of communication using the mechanism of clause 6. (activation in the opposite direction of communication order) and record the result using clause 7.

9. Substances

Problem: Holders of real brains sometimes eat pills that regulate natural neurotransmitters or are their structural counterparts. For example, SSRI antidepressants increase the amount of serotonin acting on neurons, and cerucal blocks dopamine receptors.

Solution: To weaken or amplify all signals for neurons of the corresponding color. For example, we blocked dopamine - we reduce the charge of all dopamine neurons, 90 percent. We took a serotonin reuptake inhibitor - we increase all serotonin bonds by 30 percent. We took a structural analogue of serotonin - we increase again, but already by 3 times.

10. Any other problem

Is neuron charging non-linear? Create a function and use it to describe the increase in charge. Want to describe the effect of other entities on neurons? Add them to your model. The essence will not change - you will always have neurons and connections between them. You can customize their behavior, depending on your needs.

Want to bring it closer to the real? A list of 9 points above will help. You don’t need it, because your task is to recognize the pictures? Forget about all these nuances. Want a memory similar to a memory in a biological brain? Consider points 5 through 8. Not enough accuracy? Dig deeper into neuroscience, go down another level and refine the model. Model the synapse, model the behavior of the receptors. There is room for maneuver.

Much has already been modeled before, you can use these results. It took something specific that neither I nor anyone else described - do it yourself.

But, if you do not need such accuracy - forget it. You do not need to over-engineer just because now you have a set of new shiny hammers. This is the same as using GR to simulate a brick fall from a nine-story building. Yes, relativistic effects will work for this case as well. But you will seriously complicate your task, and in return you will receive an increase in accuracy by 0.0000001%.

Keep it simple and straightforward.

PS
If you want to look at an example of using such a model, then in this article I modeled memory in a biological brain using some of the points listed above.