Circuit Elements Required for Neural Systems - Brain Theory from a Circuits and Systems Perspective - page 52

possible when inhibitory neurotransmitters are considered. Enabled logic is not as
dependent on timing. Instances of dendritic logic may occur thousands of times in
dendrites, whereas enabled logic is generally limited to active regions that can store
charge, usually a soma.
Several new symbols for circuit elements have been introduced. The usual
symbols for capacitance and resistance are used for membrane charge, membrane
conductance, and channel resistance. Controlled current source symbols are used
for membrane charging, while control circuits as in the appendix freely employ
independent voltage source symbols and ideal diodes.
A capacitor symbol represents a step in membrane capacitance, which happens
when a smaller dendrite physically connects to a larger body, such as a soma. This
is important because capacitance in the larger body accumulates charge, and also,
according to simulations, may trigger a back propagation of pulses.
Pulses, akin to solitons with fixed waveforms are produced by a continuously
active membrane, and typically flow back and forth within dendrites, but not back
into presynaptic regions.
A synapse transmits signals one way, from the presynaptic (bouton at an axon
termination) region to postsynaptic (receptor on spine) region. A excitatory synap-
tic contact is denoted by a transconductance amplifier of the non-inverting type
such that signals flow from input to output. This amplifier injects positive charge to
excite neural pulses. An inhibitory synaptic contact is denoted by an inverting
transconductance amplifier. This amplifier injects negative charge to dampen neural
pulses. These amplifiers are denoted by triangular amplifier symbols that point in
the direction of signal flow.
A postsynaptic receptor can accumulate LTP, denoted by a capacitor with initial
static charge, indicating a receptor region that is precharged so that it is easier to
trigger. LTP is thought to be important to long-term memory and learning.
An STM neuron is denoted with an oval symbol. STM neurons are modeled as
having a shortfall of internal ions in its dendrites and also by an insulated membrane
so that a longer dendritic pulse results; this enables the triggering of an extended
burst of pulses at a maximal rate to be sent down the axon. Burst durations vary and
depend on internal parameters.
Symbols for neurotransmitters were introduced in conjunction with enabled NOT
gates: (+) for excitatory, ( ) for inhibitory, and (0) for no neurotransmitters. Neural-

synaptic circuit elements are the subject of simulation experiments described in the
appendix, and will be used to model long-term memory, simulated qubits, and
various systems such as cue editors and recall referees as in subsequent chapters.

References

1. Burger JR (2009) Human memory modeled with standard analog and digital circuits: inspira-
tion for man-made computers. Wiley, Hoboken, NJ
2. Kandel ER (2006) In search of memory: the emergence of a new science of mind. W. W
Norton & Co, New York