Neurons and Axon-Dendrite Connections: Exploring Complexities in Neural Networks

Understanding the intricacies of neural connections in the brain is no small feat. Many descriptions of neurons and their connections present simplified models, especially for educational purposes. However, such simplifications can sometimes lead to misconceptions, such as the one you've brought to light with your question: ‘In the brain if each neuron has 1 axon and M dendrites and each axon connects to exactly 1 dendrite from a different neuron then this leads to a contradiction: for N neurons total of axons N1 but also total of axons NM. What gives?'

Neurons and Their Complexity

Both neurons and the brain are remarkably complex systems, and to truly understand them, we need to delve into their intricate details. The traditional diagrams often used to illustrate neurons are overly simplified, focusing on the key components but often omitting critical nuances that can lead to misunderstandings.

A neuron, as illustrated in many textbooks, consists of a body with multiple dendrites that receive signals, and an axon that transmits these signals to other neurons or cells. However, this oversimplified model can be misleading. Here are some key elements that are often omitted:

1. Axon Hillocks and Multiple Axons

A neuron's cell body may have one or more axon hillocks, each of which can start the propagation of an action potential to the axon. It's not uncommon for an axon to split into two or more axons. Each axon can branch and deliver signals to various destinations, such as synapse sites (telodendria), where neurotransmitters are released.

2. Dendrites and Branching

Each neuron can also have multiple dendrites, which project from the cell body. These dendrites can also branch, and each branch can connect to other neurons or cells. This branching allows for complex network interactions and information processing.

3. Dendritic Spines and Synaptic Complexity

Dendrites often have dendritic spines along their length, which are small protrusions where synapses typically occur. Because of these spines, a single dendrite can have multiple synapses, and more than one axon terminal can terminate on a spine, meaning that a single synapse may involve multiple axonal inputs.

Addressing the Paradox: A More Detailed Explanation

Your question highlights a potential paradox in the simplified model, but when we consider the actual complexity of neurons and synaptic connections, the contradiction resolves. Let's break it down:

Assuming each neuron has 1 axon and M dendrites, if each axon connects to exactly 1 dendrite from a different neuron, the number of connections is limited by the number of neurons. However, due to the branching nature of axons and dendrites, each axon can connect to multiple dendrites over its length, resolving the alleged contradiction.

Neuron Geometry and Synaptic Pathways

For a more detailed understanding, consider the image of a pyramidal neuron, which has a single axon hillock but can branch into multiple axons and dendrites. This branching allows for complex and redundant synaptic pathways, which is crucial for the robustness and efficiency of neural networks.

By examining the more complex geometry of neurons, we can see that there are no free floating, unconnected axons or dendrites in the brain. Glial cells quickly remove or bind these structures, maintaining the integrity of synaptic connections.

Conclusion

The apparent contradiction in the number of axons and dendrites is resolved by understanding the branching and complex network of these structures. Neurons and their connections are far more intricate than the simplified models often presented, and they are designed to enable efficient and robust information processing in the brain.

For a deeper dive, it's essential to explore detailed research papers and diagrams that capture the true complexity of neural networks. While such detailed explanations may seem overwhelming, they are necessary to fully grasp the marvels of the brain's computational power.