Hierarchical Brain

ABCD (Absolutely Basic Coincidence Detecting) neuron

Real neurons in the human brain are complex and varied but they can be modelled for my purposes using a large number of simplified model neurons. I call these model neurons Absolutely Basic Coincidence Detecting (ABCD) neurons. An ABCD neuron has just two inputs and one output and can perform very simple coincidence detection. The purpose of this page is to show how ABCD neurons can model the coincidence detection ability of real neurons.

To be clear, ABCD neurons do not exist in reality, I have invented them as a helpful modelling tool. Using them in diagrams and descriptions makes it very much easier to show how the ability of real neurons to act as coincidence detectors can be the basis of the processing of data in the brain.

The principle

• Scientists over the years have tried to model the behaviour of neurons in the human brain using mathematics¹. I take a much simpler approach by observing two things:
  1. Every neuron has three basic elements: inputs, processing and outputs.
  2. The processing can be described as the detection of coincidences in the input signals and the outputting of a signal when a coincidence is detected.
• Inputs. A real neuron in the human brain typically has many hundreds or even thousands of inputs on its many dendrites, but I propose that, in principle, these multiple inputs can be modelled by connecting together many much simpler model neurons.
  • A real neuron with many inputs can potentially detect many thousands or even millions of different coincidences of various combinations of two or more input signals that arrive at the same time, or very nearly the same time.
    • Some of these coincidences will cause the neuron to create an action potential and pass on a signal, although many will not.
    • I propose to divide up this behaviour so that we have one model neuron per coincidence.
    
  • I define an ABCD neuron to have only two inputs so that it can detect only one coincidence, of the two inputs signals arriving at the same time, or nearly the same. So in this diagram, the ABCD neuron C has two inputs, A and B, and C detects a coincidence of A and B firing at, or very near, the same time.
    • One ABCD neuron is needed to represent the end result of a single coincidence that the real neuron can detect, and many more are needed in the correct tree-like hierarchical configuration to model the many inputs that may contribute to this.
    • A huge number of ABCD neurons may therefore be needed to fully emulate the functionality of a single real neuron.
    • It wouldn’t actually be practical to do this; nevertheless as a model it has its uses, so this page is my attempt to show that it can, in principle, be done.
  • In terms of computer or logic circuits, an ABCD neuron is very similar to an AND gate, but it is more flexible. With reference to an ABCD neuron:
    • The two incoming signals do not have to be present at exactly the same time in order to create an output signal, but they need to be close together (I do not define exactly how close).
    • The strengths of the inputs can vary, which in terms of the model neurons means that connections can be removed or replaced depending on previous events.
• Outputs. A real neuron in the human brain typically also has many outputs on its branching axon.
  • These are simply duplications of the signal so no extra ABCD neurons are needed to model this feature, only extra connections.
  • This duplication in the brain sometimes merely provides resilience, which does not need to be modelled.

The detail

• Let’s take a typical real neuron (we’ll call it N) that has hundreds or even thousands of incoming synapse connections from many different pre-synaptic neurons (so many possible incoming signals) on many dendrites at many different distances from the axon hillock, and one axon down which an action potential can travel in order to pass a signal to one or more other neurons.
  • We need to zoom in to a particular place on the membrane close to the axon hillock at one particular moment when an action potential is triggered in this neuron N. Let’s call this place P and the time T.
    • The axon hillock is the place where the axon is attached to the soma, the body of a neuron containing the nucleus.
    • The axon hillock is (normally) where the summation takes place that “decides” whether or not an action potential is sent down the axon.
  • The “decision” that is made at time T as to whether an action potential is generated or not at place P depends on the concentration of ions close to P at T (on both sides of the membrane).
    • For an action potential to be triggered near P at T, the voltage across the membrane must become positive enough (or less negative enough) to exceed the threshold for voltage-gated ion channels in the membrane near P to start to open.
    • The voltage across the membrane is created by the presence of ions near P at T.
    • See the section on Signal Production in the page about the movement of ions for much more detail on how this happens.
  • The ions found close to P at T inside the neuron can only have been generated from incoming signals via synapses into N from other neurons prior to T.
    • The ions (of both positive and negative charge, but the majority will be positive) inside the neuron that are the primary cause of the voltage change across the membrane being different from the resting potential can only have been generated from incoming signals.
    • Those signals must have been from activations of synapses coming in to N from other neurons prior to T.
    • The activation of a synapse can generally only be caused by an action potential in another neuron.
    • Each of these signals will have been either an EPSP (Excitatory PostSynaptic Potential) or an IPSP (Inhibitory PostSynaptic Potential).
    • An EPSP generates positively-charged ions inside the membrane, an IPSP generates negatively-charged ions inside the membrane, and these ions will have moved by diffusion and mixed together before they reach P at T.
    • The number of ions that reach P will primarily depend on the distance from the synapse to P.
  • Ions in the fluid outside the cell membrane near P at T could be an additional factor that influences the voltage across the membrane, and therefore whether an action potential is generated or not inside the neuron.
    • Many of these ions will be ones that have come out of this neuron via various transmembrane proteins, but the ones near the trigger point are likely to be only those that were contributing to the resting potential up to the time P.
    • Other ions generated by other events such as action potentials occurring in other neurons or other events occurring in glial cells would be very widely diffused throughout the fluid outside the membrane, so would not have a significant effect.
  • In the real world it would be impossible to plot backwards in time from T to find out where these ions came from, but, for the purposes of this modelling, we can say that that there must have been a set of synapses that were activated (had PostSynaptic Potentials - PSPs) at some time prior to T that together were capable of triggering the action potential in N at P.
    • These PSP events will have taken place at varying times prior to the triggering, and at varying distances from P, and so will have a varying strength of effect. Some synapses may have even been triggered multiple times, with many of these having an effect on the ions at P at T.
    • These exact times and distances may or may not be important to the final triggering decision, but let’s assume they all are.
    • This is the same as saying that there is a set of neurons that need to have fired, or to have raised an action potential, at times prior to T, to cause this coincidence to take place.
  • As mentioned above, some of these synapse events that contribute to this coincidence may have been inhibitory (IPSPs), which perhaps seems counterintuitive because their inclusion actually decreases the likelihood of neuron N raising an action potential, but they need to be included as events that contribute to the coincidence.
• An additional complication is the effects of neurotransmitter chemicals in the cerebrospinal fluid outside the cell membrane.
  • These chemicals will have arrived by the process called neuromodulation, and can have a major effect on the operation of synapses and the behaviour of neurons.
  • They will have been emitted by other neurons, glia cells, or even come (as hormones) from other parts of the body, before the time T.
  • So, in principle, it would be possible to trace back to the source or sources of these and then to the events that coincided to cause them to happen, and to include those event as inputs to model neurons.
• My proposition is that it is possible to create a model consisting only of ABCD neurons in a hierarchical tree-like structure that will mimic exactly the behaviour of a real-world neuron creating an action potential.
  • To do this, each PSP must be modelled as if it were a connection from a different neuron with a single connection to another neuron that eventually, via other singly-connected neurons, connects to N.
  • Sufficient intermediate layers must then be added to allow simple two-to-one coincidence detection.

An example

• As an example, the left-hand side of this picture shows a greatly simplified diagram of four real neurons that each connect to three others, so that the three can detect many different coincidences in the four inputs. The right-hand side is a diagram of the equivalent detection of just one of those coincidences using ABCD neurons.
  • In the left-hand diagram, signals from neurons A, B, C and D can all affect neurons X, Y and Z.
  • Therefore neurons X, Y and Z can each detect coincidences on any two or more of their inputs.
  • In this example, there are eleven possible coincidences of two or more inputs (A&B, A&C, A&D, B&C, B&D, C&D, A&B&C, A&B&D, A&C&D, B&C&D, A&B&C&D), but real neurons can potentially have hundreds or even thousands of different inputs, so the number of possible coincidences detected can be huge.
• The right-hand side is how ABCD neurons can model just one coincidence of the eleven possibilities - the last one of all four A&B&C&D firing at the same time. However, in the left-hand diagram, all of X, Y and Z are capable of detecting all the same coincidences. Real neurons have duplication and therefore redundancy and resilience, but one neuron can detect thousands of different coincidences. ABCD neurons do not have any duplication and one ABCD neuron can only detect one coincidence.
• To create a complete model of N, this process would have to be done for each possible combination of PSPs that could cause an action potential in N, which, if there are thousands of incoming synapses, could amount to many millions of combinations.
• See afferent processing example 1 for my proposals for how neurons detect coincidences.

Summary

• My proposal above details how, in principle, it should be possible to model a real neuron using a combination of many of my proposed simple ABCD neurons.
• The result would be a tree-like structure consisting of potentially many millions of ABCD neurons just to model one real neuron, but I am not proposing that this exercise is actually done.
• The reason for defining the ABCD neuron is so that I can give examples and draw diagrams (see afferent processing examples) that show how basic coincident detection provided by ABCD neurons is sufficient for all the data processing that is required by my hierarchical structure, and therefore that this can also potentially be performed by real neurons.

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References For information on references, see structure of this website - references

1. ^ This area of research, known as computational neuroscience, aims to discover how the brain encodes information and to develop neuronal models using mathematics, but I think there have sometimes been some problems with the assumptions made about the way the brain encodes information.
   Spiking Neuron Models (Single Neurons, Populations, Plasticity) - Gerstner and Kistler 2002
   doi: 10.1017/CBO9780511815706 viewable online at Spiking Neuron Models or see GoogleScholar.
   This book is a good review of the field at the time it was published. It reviews many techniques used for modelling the neurons in the brain. The two following quotes are from the introductory chapter:
   Page 13-14 under the heading “1.4 The Problem of Neuronal Coding”, first paragraph: “In every small volume of cortex, thousands of spikes are emitted each millisecond.... What is the information contained in such a spatio-temporal pattern of pulses? What is the code used by the neurons to transmit that information? How might other neurons decode the signal? As external observers, can we read the code and understand the message of the neuronal activity pattern?”
   And two paragraphs later: “The concept of mean firing rates has been successfully applied during the last 80 years. It dates back to the pioneering work of Adrian [1920s] who showed that the firing rate of stretch receptor neurons in the muscles is related to the force applied to the muscle.”
   The second quote shows that the firing rate of neurons that are connected to muscles is relevant because it has been shown to be proportional to the force produced in the muscle. It is also true that the firing rate of incoming signals from various senses is important because it gives information about the relevance and strength of the signal. Early researchers probably therefore assumed that the firing rate or pattern (“Spatio-temporal pattern”) of neurons within the brain (“In every small volume of cortex”) was also relevant and that they somehow encoded a particular message or some specific property of a message.
   However, it is very difficult to imagine or identify a mechanism in the brain that could usefully translate a particular rate or pattern of firing into something else that could be relevant. The only thing it could be translated to would be the firing of a single other neuron, which would be pointless, why not just activate this in the first place? The only effect multiple spikes can have is a reinforcement; multiple spikes in quick succession will obviously increase the chances of the target neuron(s) raising action potentials themselves.

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Page last uploaded Wed Jan 31 07:24:59 2024 MST