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Subneural Models: Synapses and Spines 
In an address to the annual meeting of the American Psychological Association in 2002, psychologist and 
neuroscientist Joseph LeDoux of New York University said, 
If who we are is shaped by what we remember, and if memory is a function of the brain, then synapses—the 
interfaces through which neurons communicate with each other and the physical structures in which 
memories are encoded—are the fundamental units of the self....Synapses are pretty low on the totem pole of 
how the brain is organized, but I think they're pretty important....The self is the sum of the brain's individual 
subsystems, each with its own form of "memory," together with the complex interactions among the 
subsystems. Without synaptic plasticity—the ability of synapses to alter the ease with which they transmit 
signals from one neuron to another—the changes in those systems that are required for learning would be 
impossible.
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Although early modeling treated the neuron as the primary unit of transforming information, the tide has turned 
toward emphasizing its subcellular components. Computational neuroscientist Anthony J. Bell, for example, argues: 
Molecular and biophysical processes control the sensitivity of neurons to incoming spikes (both synaptic 
efficiency and post-synaptic responsivity), the excitability of the neuron to produce spikes, the patterns of 170 
spikes it can produce and the likelihood of new synapses forming (dynamic rewiring), to list only four of the 
most obvious interferences from the subneural level. Furthermore, transneural volume effects such as local 
electric fields and the transmembrane diffusion of nitric oxide have been seen to influence, responsively, 
coherent neural firing, and the delivery of energy (blood flow) to cells, the latter of which directly correlates 
with neural activity. The list could go on. I believe that anyone who seriously studies neuromodulators, ion 
channels, or synaptic mechanism and is honest, would have to reject the neuron level as a separate computing 
level, even while finding it to be a useful descriptive level.
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Indeed, an actual brain synapse is far more complex than is described in the classic McCulloch-Pitts neural-net 
model. The synaptic response is influenced by a range of factors, including the action of multiple channels controlled 
by a variety of ionic potentials (voltages) and multiple neurotransmitters and neuromodulators. Considerable progress 
has been made in the past twenty years, however, in developing the mathematical formulas underlying the behavior of 
neurons, dendrites, synapses, and the representation of information in the spike trains (pulses by neurons that have 
been activated). Peter Dayan and Larry Abbott have recently written a summary of the existing nonlinear differential 
equations that describe a wide range of knowledge derived from thousands of experimental studies.
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Well-
substantiated models exist for the biophysics of neuron bodies, synapses, and the action of feedforward networks of 
neurons, such as those found in the retina and optic nerves, and many other classes of neurons. 
Attention to how the synapse works has its roots in Hebb's pioneering work. Hebb addressed the question, How 
does short-term (also called working) memory function? The brain region associated with short-term memory is the 
prefrontal cortex, although we now realize that different forms of short-term information retention have been identified 
in most other neural circuits that have been closely studied. 
Most of Hebb's work focused on changes in the state of synapses to strengthen or inhibit received signals and on 
the more controversial reverberatory circuit in which neurons fire in a continuous loop.
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Another theory proposed by 
Hebb is a change in state of a neuron itself—that is, a memory function in the cell soma (body). The experimental 
evidence supports the possibility of all of these models. Classical Hebbian synaptic memory and reverberatory 
memory require a time delay before the recorded information can be used. In vivo experiments show that in at least 
some regions of the brain there is a neural response that is too fast to be accounted for by such standard learning 
models, and therefore could only be accomplished by learning-induced changes in the soma.
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Another possibility not directly anticipated by Hebb is real-time changes in the neuron connections themselves. 
Recent scanning results show rapid growth of dendrite spikes and new synapses, so this must be considered an 
important mechanism. Experiments have also demonstrated a rich array of learning behaviors on the synaptic level that 
go beyond simple Hebbian models. Synapses can change their state rapidly, but they then begin to decay slowly with 
continued stimulation, or in some a lack of stimulation, or many other variations.
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Although contemporary models are far more complex than the simple synapse models devised by Hebb, his 
intuitions have largely proved correct. In addition to Hebbian synaptic plasticity, current models include global 
processes that provide a regulatory function. For example, synaptic scaling keeps synaptic potentials from becoming 
zero (and thus being unable to be increased through multiplicative approaches) or becoming excessively high and 
thereby dominating a network. In vitro experiments have found synaptic scaling in cultured networks of neocortical, 
hippocampal, and spinal-cord neurons.
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Other mechanisms are sensitive to overall spike timing and the distribution of 
potential across many synapses. Simulations have demonstrated the ability of these recently discovered mechanisms to 
improve learning and network stability. 
The most exciting new development in our understanding of the synapse is that the topology of the synapses and 
the connections they form are continually changing. Our first glimpse into the rapid changes in synaptic connections 
was revealed by an innovative scanning system that requires a genetically modified animal whose neurons have been 
engineered to emit a fluorescent green light. The system can image living neural tissue and has a sufficiently high 
resolution to capture not only the dendrites (interneuronal connections) but the spines: tiny projections that sprout from 
the dendrites and initiate potential synapses. 
Neurobiologist Karel Svoboda and his colleagues at Cold Spring Harbor Laboratory on Long Island used the 
scanning system on mice to investigate networks of neurons that analyze information from the whiskers, a study that 
provided a fascinating look at neural learning. The dendrites continually grew new spines. Most of these lasted only a 
day or two, but on occasion a spine would remain stable. "We believe that the high turnover that we see might play an 
important role in neural plasticity, in that the sprouting spines reach out to probe different presynaptic partners on 
neighboring neurons,” said Svoboda. "If a given connection is favorable, that is, reflecting a desirable kind of brain 
rewiring, then these synapses are stabilized and become more permanent. But most of these synapses are not going in 
the right direction, and they are retracted."
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Another consistent phenomenon that has been observed is that neural responses decrease over time, if a particular 
stimulus is repeated. This adaptation gives greatest priority to new patterns of stimuli. Similar work by neurobiologist 
Wen-Biao Gan at New York University's School of Medicine on neuronal spines in the visual cortex of adult mice 
shows that this spine mechanism can hold long-term memories: "Say a 10-year-old kid uses 1,000 connections to store 
a piece of information. When he is 80, one-quarter of the connections will still be there, no matter how things change. 
That's why you can still remember your childhood experiences." Gan also explains, "Our idea was that you actually 
don't need to make many new synapses and get rid of old ones when you learn, memorize. You just need to modify the 
strength of the preexisting synapses for short-term learning and memory. However, it's likely that a few synapses are 
made or eliminated to achieve long-term memory."
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The reason memories can remain intact even if three quarters of the connections have disappeared is that the 
coding method used appears to have properties similar to those of a hologram. In a hologram, information is stored in 
a diffuse pattern throughout an extensive region. If you destroy three quarters of the hologram, the entire image 
remains intact, although with only one quarter of the resolution. Research by Pentti Kanerva, a neuroscientist at 
Redwood Neuroscience Institute, supports the idea that memories are dynamically distributed throughout a region of 
neurons. This explains why older memories persist but nonetheless appear to "fade," because their resolution has 
diminished.