Circuit Elements Required for Neural Systems - Brain Theory from a Circuits and Systems Perspective - page 48

Fig. 3.17 Two synapses can
constitute an OR gate
The Possibility of Synaptic Logic
Synapses make contact to spines on a given dendritic branch. The possibility of
synaptic weights has been promoted [ 5 , 6 ] but is discounted in this topic, owing to
a membrane that either pulses or it does not. And when it pulses, it provides a
standard pulse. However, standardized pulses from adjacent synapses (on spines)
may very well proceed to undergo dendritic logic.
Synaptic logic, which the author considers to be dendritic logic, might be said to
be occurring when adjacent active spines provide pulses to dendritic membrane that
is either active or inactive. If membrane is active, an OR gate results with the circuit
model in Fig. 3.17 . If the membrane is passive for a short distance, a dendritic AND
gate might result. Note that these are in fact examples of dendritic logic.
To an electrical engineer, the figure is reminiscent of hard-wired diode logic, but
the underlying physics is completely different. The signals are bursts of pulses.
Either input A, input B, or both can initiate a burst of pulses in the dendrite to
produce a propagation at Y. Note that synapses send pulses one way and thus avoid
back propagations.
Enabled Logic in Dendrites and Soma
Enabled logic depends on applying charge to an input capacitance until a triggering
threshold is reached. In particular, an AND gate is achieved if one input supplies
half of the required charge, and the other input supplies the other half to trigger a
pulse burst. Enabled logic does not required that pulses arrive simultaneously, so in
this sense it is simpler. However, pulses must still arrive within a certain time frame
or existing charge will dissipate. A place to accumulate charge is required, often
taken to be the capacitance of the larger soma in a neuron; there is only one soma
per neuron, so there will be fewer enabled gates per neuron.
Enabled logic is akin to artificial neural network concepts under which (usually
DC) inputs are added together linearly to reach a threshold. However, the
weightings of the inputs are usually fixed in enabled logic, since pulse bursts
from active membrane generally have fixed waveforms. Specialized neurons may
produce differing counts of pulses in a burst, and even differing waveforms,
however, so more exotic forms of weightings may be possible.