154 
PRESYNAPTIC NEURAL INFORMATION PROCESSING 
L. R. Carley 
Department of Electrical and Computer Engineering 
Carnegie Mellon University, Pittsburgh PA 15213 
ABSTRACT 
The potential for presynaptic information processing within the arbor 
of a single axon will be discussed in this paper. Current knowledge about 
the activity dependence of the firing threshold, the conditions required for 
conduction failure, and the similarity of nodes along a single axon will be 
reviewed. An electronic circuit model for a site of low conduction safety in 
an axon will be presented. In response to single frequency stimulation the 
electronic circuit acts as a lowpass filter. 
I. INTRODUCTION 
The axon is often modeled as a wire which imposes a fixed delay on a 
propagating signal. Using this model, neural information processing is 
performed by synaptically summing weighted contributions of the outputs 
from other neurons. However, substantial information processing may be 
performed in by the axon itself. Numerous researchers have observed 
periodic conduction failures at norma.,[ physiological impulse activity rates 
(e.g., in cat 1, in frog 2, and in man'). The oscillatory nature of these 
conduction failures is a result of the dependence of the firing threshold on 
past impulse conduction activity. 
The simplest view of axonal (presynaptic) information processing is 
as a switch: the axon will either conduct an impulse or not. The state of 
the switch depends on how past impulse activity modulates the firing 
threshold, which will result in conduction failure if firing threshold is bigger 
than the incoming impulse strength. In this way, the connectivity of a 
synaptic neural network could be modulated by past impulse activity at 
sites of conduction failure within the network. More sophisticated 
presynaptic neural information processing is possible when the axon has 
more than one terminus, implying the existence of branch points within the 
axon. Section II will present a general description of potential for 
presynaptic information processing. 
The after-effects of previous activity are able to vary the connectivity 
of the axonal arbor at sites of low conduction safety according to the 
temporal pattern of the impulse train at each site (Raymond and Lettvin, 
1978; Raymond, 1979). In order to understand the information processing 
potential of presynaptic networks it is necessary to study the after-effects 
of activity on the firing threshold. Each impulse is normally followed by a 
brief refractory period (about 10 ms in frog sciatic nerve) of increased 
American Institute of Phmic 1 c,gg 
155 
threshold and a longer superexcitable period (about I s in frog sciatic 
nerve) during which the threshold is actually below its resting level. 
During prolonged periods of activity, there is a gradual increase in firing 
threshold which can persist long (> I hour in frog nerve) after cessation 
of impulse activity (Raymond and Lettvin, 1978). In section III, the 
methods used to measure the firing threshold and the after-effects of 
activity will be presented. 
In addition to understanding how impulse activity modulates sites of 
low conduction safety, it is important to explore possible constraints on 
the distribution of sites of low conduction safety within the axon's arbor. 
Section IV presents results from a study of the distribution of the after- 
effects of activity along an axon. 
Section V presents an electronic circuit model for a region of low 
conduction safety within an axonal arbor. It has been designed to have a 
firing threshold that depends on the past activity in a manner similar to the 
activity dependence measured for frog sciatic nerve. 
II. PRESYNAPTIC SIGNAL PROCESSING 
Conduction failure has been observed in many different organisms, 
including man, at normal physiological activity rates. TM The after- 
effects of activity can "modulate" conduction failures at a site of low 
conduction safety. One common place where the conduction safety is low 
is at branch points where an impedance mismatch occurs in the axon. 
In order to clarify the meaning of presynaptic information processing, 
a simple example is in order. Parnas reported that in crayfish a single 
axon separately activates the medial (DEA. and lateral (DEAL) branches 
of the deep abdominal extensor muscles. '" At low stimulus frequencies 
(below 40-50 Hz) impulses travel down both branches; however, each 
impulse evokes much smaller contractions in DEAL than in DEAM resulting 
in contraction of DEAM without significant contraction of DEAL. At higher 
stimulus frequencies conduction in the branch leading to DEAM fails and 
DEAL contracts without DEAM contracting. Both DEAL and DEAM can be 
stimulated separately by stimulus patterns more complicated than a single 
frequency. 
The theory of "fallible trees", which has been discussed by Lettvin, 
McCulloch and Pitts, Raymond, and Waxman and Grossman among 
others, suggests that one axon which branches many times forms an 
information processing element with one input and many outputs. Thus, 
the after-effects of previous activity are able to vary the connectivity of 
the axonal arbor at regions of low conduction safety according to the 
temporal pattern of the impulse train in each branch. The transfer function 
of the fallible tree is determined by the distribution of sites of low 
conduction safety and the distribution of superexcitability and depressibility 
at those sites. Thus, a single axon with 1000 terminals can potentially be 
in 2  different states as a function of the locations of sites of conduction 
failure within the axonal arbor. And, each site of low conduction safety is 
156 
modulated by the past impulse activity at that site. 
Fallible trees have a number of interesting properties. They can be 
used to cause different input frequencies to excite different axonal 
terminals. Also, fallible trees, starting at rest, will preserve timing 
information in the input signal; i.e., starting from rest, all branches will 
respond to the first impulse, 
III. AFTER-EFFECTS OF ACTIVITY 
In this section, the firing threshold will be defined and an experimental 
method for its measurement will be described. In addition, the after- 
effects of activity will be characterized and typical results of the 
characterization process will be given. 
The following method was used to measure the firing threshold. 
Whole nerves were placed in the experimental setup (shown in figure 1). 
The whole nerve fiber was stimulated with a gross electrode. The 
response from a single axon was recorded using a suction microelectrode. 
Firing threshold was measured by applying test stimuli through the gross 
stimulating electrode and looking for a response in the suction 
microelectrode. 
Motor- 
driven 
vernier 
micrometer 
J Fixed-clration 
variable-amplitude 
current stimulator Am lifter 
electrode JJJ A 
0-4 mm diameterJJJ Suction electrode j/I/ J t / Reference 
' ' le axon '  suction 
>11! Sing %/// electrode 
I nnnnnnnnnnnnnno0nn' '  i I 
Velcro  Ag-AgCl Plate  Sponge 
Figure 1. Drawing of the experimental recording chamber. 
Threshold Hunting, a process for choosing the test stimulus strength, 
was used to characterize the axons. 6 It uses the following paradigm. A 
test stimulus which fails to elicit a conducting impulse causes a small 
increase the strength of subsequent test stimuli. A test stimulus which 
157 
elicits an impulse causes a small decrease in the strength of subsequent 
test stimuli. Conditioning Stimuli, ones large enough to guarantee firing an 
impulse, can be interspersed between test stimuli in order to achieve a 
controlled overall activity rate. Rapid variations in threshold following one 
or more conditioning impulses can be measured by slowly increasing the 
time delay between the conditioning stimuli and the test stimulus. Several 
phases follow each impulse. First, there is a refractory period of short 
duration (about 10ms in frog nerve) during which another impulse cannot 
be initiated. Following the refractory period the axon actually becomes 
more excitable than at rest for a period (ranging from 200ms to ls in frog 
nerve, see figure 2). The superexcitable period is measured by applying a 
conditioning stimulus and then delaying by a gradually increasing time 
delay and applying a test stimulus (see figure 3). There is only a slight 
increase in the peak of the superexcitable period following multiple 
impulses. 7 The superexcitability of an axon was characterized by the % 
decrease of the threshold from its resting level at the peal< of the 
superexcitable period. 
0 250 500 750 
INTERVAl_ 
Figure 2. Typical superexcitable 
period in axon from frog sciatic 
rtsrvo. 
Figure 3. Stimulus pattern used 
for measuring superexcitability. 
During a period of repetitive impulse conduction, the firing threshold may 
gradually increase. After the period of increased impulse activity ends, the 
threshold gradually recovers from its maximum over the course of several 
minutes or more with complete return of the threshold to its resting level 
taking as long as an hour or two (in frog nerve) depending on the extent of 
the preceding impulse activity. The depressibility of an axon can be 
characterized by the initial upward slope of the depression and the time 
158 
constant of the recovery phase (see figure 4). The pattern of conditioning 
and test stimuli used to generate the curve in figure 4 is shown in figure 5. 
Depression may be correlated with microanatomical changes which 
occur ir the glial cells in the nodal region during periods of increased 
activity.- During periods of repetitive stimulation the size and number of 
extracellular paranodal intramyelinic vacuoles increases causing changes 
in the paranodal geometry. 
Success 
Threshold (percentage of resting level) 
2 l Failure 
160 
120. 
80- 
4O 
5 t 15 0 25 3 
Time (ram} 
Success 
Failure 
Figure 4. Typical depression in an 
axon from frog sciatic nerve. The 
average activity rate was 4 
impulses/sec between the 5 rnin 
mark and the 10 rain mark. 
burst Test 
 stimulus 
On 
5 min  Time 
off 
Figure 5. Stimulus pattern used 
for measuring depression. 
IV. CONSTRAINTS ON FALLIBLE TREES 
The basic fallible tree theory places no constraints on the distribution 
of sites of conduction failure among the branches of a single axon. In this 
section one possible constraint on the distribution of sites of conduction 
failure will be presented. Experiments have been performed in an attempt 
to determine if the extremely wide variations in superexcitability an 
depressibility found between nodes from different axons in a single nerve 
(particularly for depressibility) also occur between nodes from the same 
axon. 
A study of the distribution of the after-effects of activity along an 
unbranching length of frog sciatic nerve OnUnd only small variations in the 
after-effects along a single axon." Both superexcitability and 
depressibility were extremely consistent for nodes from along a single 
unbranching length of axon (see figures 6 and 7). This suggests that there 
may be a cell-wide regulatory system that maintains the depressibility and 
159 
superexcitability at comparable levels throughout the extent of the axon. 
Thus, portions of a fallible tree which have the same axon diameter would 
be expected to have the same superexcitability and depressibility. 
3.0 3 
9"5 
Superexcitability 
Upward slope 
Figure 6. PDF of Superexcitabili- 
ty, The upper trace represents 
the PDF of the entire population 
of nodes studied and the two 
lower traces represent the 
separate populations of nodes 
from two different axons. 
Figure 7, PDF of Depressibility, 
The upper trace represents the 
PDF of the entire population of 
nodes studied and the two lower 
traces represent the separate 
populations of nodes from two 
different axons, 
This study did not examine axons which branched, therefore it cannot be 
concluded that superexcitability and depressibility must remain constant 
throughout a fallible tree. For example, it is quite likely that the cell 
actually regulates quantities like pump-site density, not depressibility. In 
that case, daughter branches of smaller diameter might be expected to 
show consistently higher depressibility. Further research is needed to 
determine how the activity dependence of the threshold scales with axon 
diameter along a single axon before the consistency of the after-effects 
along an unbranching axon can be used as a constraint on presynaptic 
information processing networks. 
V. ELECTRICAL AXON CIRCUIT 
This section presents a simple electronic circuit which has been 
designed to have a firing threshold that depends on the past states of the 
output in a manner similar to the activity dependence measured for frog 
sciatic nerve. In response to constant frequency stimuli, the circuit acts as 
160 
a lowpass filter whose corner frequency depends on the coefficients which 
determine the after-effects of activity. 
Figure 8 shows the circuit diagram for a switched capacitor circuit 
which approximates the after-effects of activity found in the frog sciatic 
nerve. The circuit employs a two phase nonoverlapping clock,  for the 
even clock and o for the odd clock, typical of switched capacitor circuits. 
It incorporates a basic model for superexcitability and depressibility. Vnv 
represents the resting threshold of the axon. On each clock cycle the V#v 
is compared with VTH+Vo--Vs. 
The two capacitors and three switches at the bottom of figure 8 model 
the change in threshold caused by superexcitability. Note that each 
impulse resets the comparator's minus input to (1-==)Vnv, which decays 
back to VTH on subsequent clock cycles with a time constant inversely 
proportional to Is. This is a slight deviation from the actual physiological 
situation in which multiple conditioning7jmpulses will generate slightly more 
superexcitability than a single impulse. 
The two capacitors and two switches at the upper left of figure 8 
model the depressibility of the axon. The current source represents a 
fixed increment in the firing threshold with every past impulse. The 
depression voltage decays back to 0 on subsequent clock cycles with a 
time constant inversely proportional to 
o^vo 
C o 
oAvo = 
Figure 8. Circuit diagram for electrical circuit analog of nerve threshold. 
The electrical circuit exhibits response patterns similar to those of 
neurons that are conducting intermittently (see figure 9). During bursts of 
conduction, the depression voltage increases linearly until the comparator 
161 
fails to fire. The electrical axon then fails to fire until the depression 
voltage decays back to (I+(zov)VTH. The connectivity between the input 
and output of the axon is defined to be the average fraction of impulses 
which are conducted. In terms of connectivity, the electrical axon model 
acts as a lowpass filter (see figure 10). 
Figure 9. Typical waveforms for 
intermittent conduction. The 
upper trace indicates whether 
impulses are conducted or not. 
VD and Vs are the depression 
voltage and the superexcitable 
voltage respectively. 
Figure 10. Frequency response of 
electrical axon model. The 
connectivity is reflected by the 
fraction of impulses which are 
conducted out of a sequence of 
100,000 stimuli where the 
frequency is in stimuli/second. 
For a fixed stimulus frequency, the average fraction of impulses 
which are conducted by the electrical model can be predicted analytically. 
The expressions can be greatly simplified by making the assumption that 
VD increases and decreases in a linear fashion. Under that assumption, in 
terms of the variables indicated on the schematic diagram, 
P (firing) = 
oov(1 - (1 - [D ) M) 
aov(1 - (1 - Io)M) + O. D 
where M is the number of clock cycles between input stimuli, which is 
inversely proportional to the input frequency. The frequency at which only 
half of the impulses are conducted is defined as the corner frequency of 
the lowpass filter. The corner frequency is 
162 
I log (1 - D) 
f(P -- 0.5)= M =D 
log(1 -- 
oov 
Using the above equations, lowpass filters with any desired cutoff 
frequency can be designed. 
The analysis indicates that the corner frequency of the lowpass filter 
can be varied by changing the degree of conduction safety (eov) without 
changing either depressibility or superexcitability. This suggests that the 
existence of a cell-wide regulatory system maintaining the depressibility 
and superexcitability at comparable levels throughout the extent of the 
axon would not prevent the construction of a bank of lowpass filters since 
their corner frequencies could still be varied by varying the degree of 
conduction safety (oov). 
Vl. CONCLUSIONS 
Recent studies report that the primary effect of several common 
anesthetics is to abolish the activity dependene of the firing threshold 
without interfering with impulse conduction. 1 This suggests that 
presynaptic processing may play an important role in human 
consciousness. This paper has explored some of the basic ideas of 
presynaptic information processing, especially the after-effects of activity 
and their modulation of impulse conduction at sites of low conduction 
safety. A switched capacitor circuit which simulates the activity dependent 
conduction block that occurs in axons has been designed and simulated. 
Simulation results are very similar to the intermittent conduction patterns 
measured experimentally in frog axons. One potential information 
processing possibility for the arbor of a single axon, suggested by the 
analysis of the electronic circuit, is to act as a filterbank; every terminal 
could act as a lowpass filter with a different corner frequency. 
BIBLIOGRAPHY 
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163 
[2] 
Fuortes M. G. F., Action of strychnine on the "intermittent 
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[3] Culp W. and J. Ochoa, Nerves and Muscles as Abnormal Impulse 
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