Synapse Types

Free C++ source code for the firing rate neuron model is available.

Introduction

So far there has been a good deal of discussion about the properties and behaviors of the different neuron types. However, unless there is a way to connect these different neurons together into a network, then they are useless. It is only through the complex, dynamic interactions of the entire neural network that the biomechanical organism can generate survival behaviors. This section attempts to explain the types of synapses that are used to connect the model neurons into networks. There are three basic types of synapses, but the first one will be looked at in two different ways. The first is the regular synapse as it is used to excite other neurons. The other aspect of the regular synapse is when it is used to inhibit other neurons. The second major type of synapse is the gated synapse. And finally there is the modulatory synapse.

Excitatory Synapse

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Figure 2. This is a graph of the output from a normal neuron with externally applied input currents of -4 na, 2 na, 4 na, 6 na, and 8 na in 100 ms intervals with the following neuron properties: Cm = 1 nf, Gm = 100 nS, Vth = 0 mv, Fmin = 0 Hz, Gain = 10 V^-1

The excitatory synapse is a regular synapse. It causes the post-synaptic neuron to be depolarized by injecting a positive current into it. The strength of the synapse is given below the synapse line as 5 na. This means that if neuron 1 is firing at its peak value of 1 Hz then it will be injecting 5 na of current into neuron 2. Lower values for the firing frequency will inject proportionally less current. So if the firing rate is 0.5 Hz then it will be injecting 2.5 na. In figure 2 the first two axis of this graph show the currents for neuron 1 and then the currents for neuron 2. On the voltage and firing frequency axis, neuron 1's output is in red, and neuron 2's output is in green. The graph shows that current is injected into neuron 1 causing it to fire. This is transmitted through the axon and injects current into neuron B. Neuron 2's firing frequency lags slightly behind the firing frequency for 1. This is because it takes time to for current injected into neuron 1 to begin having an effect. Once it does this is propogated to neuron 2. This is not due to any synaptic transmission delay. Synaptic delays are not modeled in this system.

Inhibitory Synapse

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Figure 3. This is a graph of the output from a normal neuron with externally applied input currents of -4 na, 2 na, 4 na, 6 na, and 8 na in 100 ms intervals with the following neuron properties: Cm = 1 nf, Gm = 100 nS, Vth = 0 mv, Fmin = 0 Hz, Gain = 10 V^-1

The inhibitory synapse is also a regular synapse. However, it causes other neurons to be less likely to fire. It uses a filled circle on the target neuron to tell which direction the current will flow. For the example above the negative current will go from neuron 3 to neuron 4. This synapse works exactly like the excitatory synapse except it injects negative currents instead of positive currents. In figure 3 the first two axis of this graph show the currents for neuron 3 and then the currents for neuron 4. On the voltage and firing frequency axis, neuron 3's output is in red, and neuron 4's output is in green. Neuron 4 is a tonic neuron that maintians a constant firing frequency. Neuron 3 is then injected with a series of different currents that cause it to fire. This is transmitted through the axon and negative current is injected into neuron 4. The negative current pulls the membrane potential down and reduces the firing frequency of neuron 4. The thing to notice here is that as the firing frequency of 3 increases the firing rate of 4 decreases.

Regular Synapse Properties

All the synapses in this module are derived from the Link object and share the properties of that item. For a description of these properties please see the text that discusses the Link properties.

Gated Synapse

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Figure 4. This is a graph of the output from a normal neuron with externally applied input currents of -4 na, 2 na, 4 na, 6 na, and 8 na in 100 ms intervals with the following neuron properties: Cm = 1 nf, Gm = 100 nS, Vth = 0 mv, Fmin = 0 Hz, Gain = 10 V^-1

The gated synapse works like a basic switch or transistor. A gated synapse is always associated with one or more other synapses that are entering the target neuron. In the example above, the gated synapses are between neuron 6 and 7 and neuron 8 and 9. They are symbolized using a triangle with an attached line. The synapse that is actually gated is associated with the other synapse that goes from neuron 5 to neuron 6 and 8. The gate can either be on by default or off by default. If it is on by default then when neuron 9 fires it will block the current of neuron 5 from entering neuron 8. But if neuron 9 is silent then the current from neuron 5 is free to enter neuron 8. If the gated synapse is off by default then the above works in just the opposite manner. The first example uses a gated synapse that is off by default and the second example uses a gated synapses that is on by default.

In figure 4 The first two axis are for neurons 5,6, and 7. The second two axis are for neuron 5, 8, and 9. The first axis in each pair shows relevant currents and the second axis shows firing frequencies. A series of currents are applied to neuron 5 to stimulate it. The important thing to see in this graph is what happens when neurons 7 and 9 are on. In axis 2 you should notice that neuron 6 does not fire until neuron 7 is firing strongly. When 7 is firing the gate between neurons 5 and 6 is open allowing synaptic current to flow. When neuron 7 is not firing this gate is closed and synaptic current is blocked even though neuron 5 is firing.

The important thing to notice for the second portion of the graph is that when neuron 9 fires the synaptic current from 5 to 8 dries up and neuron 8 quits firing. When 9 begins firing it closes its gate and stops the current from flowing. Once it quits firing the gate is reopened and current can flow between 5 and 8 again.

If there were another neuron 20 that was firing and injecting current into 6 it would cause 6 to fire regardless of whether neuron 7 was firing or not. The gated synapse simply works like a water faucet to turn on and off some of the other synapses. The equation that describes the behavior for the gated synapses is I = (U + Sign(I_G)) * I_S . Where U is the un-gated state of the synapse, I_G is the synaptic current of the gating synapse, and I_S is the current of the gated synapse. So in the synapse above U is one. When neuron A is not firing then I = (1 + 0) * I_C = I_C, and the current from neuron C is passed through to B. But since the weight of the gated synapse is negative one, when neuron A is firing then I = (1 - 1) * I_C = 0, and the current from neuron C is blocked.

Gated Synapse Properties

All the synapses in this module are derived from the Link object and share the properties of that item. For a description of these properties please see the text that discusses the Link properties.

Modulatory Synapse

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Figure 5. This is a graph of the output from a normal neuron with externally applied input currents of -4 na, 2 na, 4 na, 6 na, and 8 na in 100 ms intervals with the following neuron properties: Cm = 1 nf, Gm = 100 nS, Vth = 0 mv, Fmin = 0 Hz, Gain = 10 V^-1

The modulatory synapse works more like a dimmer switch or an amplifier. Like the gated synapse, it is always associated with one or more other synapses that are entering the target neuron. In the example above, the modulatory synapse is symbolized using a diamond. The equation for the modulated synapse is:

(1 + I_M) * I_S  if I_M > 0
I_S / (1+ |I_M|) if I_M < 0

So if the modulating current is greater than zero then it amplifies the synaptic current. And if the modulating current is less than zero then it reduces the synaptic current. In the example network from above the weight of the modulating synapse is -2 between neuron 13 and 14. If neuron 10 is firing at a rate of 1 Hz then I_M = -2 for neuron 14. Since I_M < 0, I = I_C / (1 + 2) = I_C / 3. So the current going into neuron 13 from 10 is reduced by a third. It is important to understand that the modulatory synapse is not inhibiting neuron 13 and causing it not to fire. It is simply amplifying or reducing the amount of current that is being injected from other neurons.

Modulatory Synapse Properties

All the synapses in this module are derived from the Link object and share the properties of that item. For a description of these properties please see the text that discusses the Link properties.

Synapse Overview

Real neurons in living organisms are capable of a wide diversity of actions on other neurons. At their simplest, they just depolarize or hyperpolarize other neurons. These types of interactions are modeled nicely with a regular excitatory or inhibitory synapse connection. However, real neurons are also capable of modulating other connections to the neuron they are synapsed with. This is where the gated and modulatory synapse types come into play. Their main purpose is to allow one neuron to manipulate the connection between two other neurons. This is very important later on because it allows the higher decision functions to shut off or modulate other subsystems.