Neurons can add their inputs. In a traditional neuron model, you add up all the inputs, run the result through a threshold, boom you're done.
But the most elementary control system requires multiplication, to set the gain. Question: can neurons multiply?
Subtraction is easy, it's just an inhibitory neuron. Division is easy too, it's a "shunt" that involves a chloride channel. But what about multiplication?
Multiplication takes two forms. The first is homosynaptic. There's only one synapse, and what it's multiplying is the membrane potential. To make this work you need the appropriate combination of voltage gated conductances. The second for of multiplication is hetero synaptic, or "trans-synaptic". It involves two inputs, A * B. We have several options:
1. We can add A to itself B times, using transmitter duration as a mechanism.
2. We can scale A by B, using a second messenger as a mechanism.
3. We can use a membrane electrical mechanism, like a dendritic spike.
4. We can use a glial cell and the calcium dynamics of glutamate, if we only need excitatory multiplication.
5. We can use a circuit
Each of these methods is nonlinear. At best it has a linear "region". Which method fo brains use?
The answer comes to us from the lowly fruit fly. The T4 neuron in its visual system is a multiplier. However it works by inverting inhibition. Which is a version of (5). Instead of A * B, it does A / (1/B). This is a perfect reason to have triadic synapses. With two shunts you can have a multiplier.
But the most elementary control system requires multiplication, to set the gain. Question: can neurons multiply?
Subtraction is easy, it's just an inhibitory neuron. Division is easy too, it's a "shunt" that involves a chloride channel. But what about multiplication?
Multiplication takes two forms. The first is homosynaptic. There's only one synapse, and what it's multiplying is the membrane potential. To make this work you need the appropriate combination of voltage gated conductances. The second for of multiplication is hetero synaptic, or "trans-synaptic". It involves two inputs, A * B. We have several options:
1. We can add A to itself B times, using transmitter duration as a mechanism.
2. We can scale A by B, using a second messenger as a mechanism.
3. We can use a membrane electrical mechanism, like a dendritic spike.
4. We can use a glial cell and the calcium dynamics of glutamate, if we only need excitatory multiplication.
5. We can use a circuit
Each of these methods is nonlinear. At best it has a linear "region". Which method fo brains use?
The answer comes to us from the lowly fruit fly. The T4 neuron in its visual system is a multiplier. However it works by inverting inhibition. Which is a version of (5). Instead of A * B, it does A / (1/B). This is a perfect reason to have triadic synapses. With two shunts you can have a multiplier.
