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1Department of Pharmacology and Toxicology, Michigan State University, East Lansing, Michigan 48823; and 2Department of Pharmacology, Faculty of Medicine, Hacettepe University, 06100 Ankara, Turkey
Submitted 24 February 2003; accepted in final form 12 March 2003
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMETHODSRESULTSDISCUSSIONACKNOWLEDGMENTSREFERENCES |
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONACKNOWLEDGMENTSREFERENCES |
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; Tuckwell
1988), fractal point processes are characterized by long-range
correlations among events extending over more than one time scale
(Bassingthwaighte et al. 1994;
Liebovitch 1998;
West 1990). In recent studies
from our laboratory (Das et al.
2003; Lewis et al.
2001), it was demonstrated that the spike trains of single
preganglionic cervical sympathetic neurons (PSNs) and sympathetic premotor
neurons located in the rostral ventrolateral medulla (RVLM) and medullary
raphe of cats with an intact neuraxis fit the model of a fractal point
process. This was revealed by using Fano factor analysis, which tests for a
power law relationship (straight line on a log-log plot) between fluctuations
in spike counts and the window length used to count spikes. The slope of the
line is the power to which fluctuations in spike counts measured over short
periods (approximately 1 s) are proportional to those measured on longer time
scales (≥100 s). Such time-scale invariant behavior reflects a form of
memory in that the current value of the measured property (spike counts or
interspike interval) is related to past values in a time frame defined by the
range of window sizes comprising the power law in the Fano factor curve. The current study was designed to determine the level(s) of the neuraxis from which the fractal firing patterns of PSNs and medullary sympathetic premotor neurons arise. For this purpose, we used Fano factor analysis to determine whether the spike trains of these neurons exhibit fractal properties after cervical spinal cord transection. The results demonstrate that fractal activity in the sympathetic nervous system can be generated independently in the brain and spinal cord.
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METHODS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONACKNOWLEDGMENTSREFERENCES |
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The experimental protocols described below were approved by the
All-University Committee on Animal Use and Care of Michigan State University.
The experiments were performed on 12 baroreceptor-intact cats anesthetized by
intraperitoneal injection of a mixture of diallylbarbiturate (60 mg/kg),
urethane (240 mg/kg), and monoethyl urea (240 mg/kg). A surgical state of
anesthesia was indicated by the failure of noxious stimuli (pinch,
cauterization of skin and muscle) applied to the head to desynchronize
spindles and delta-slow wave activity in the frontal-parietal
electroencephalogram (Gebber et al.
1999; Steriade and Llinas
1988). In the six cats in which recordings were made from PSNs,
the spinal cord was transected at the level of the seventh cervical segment.
These cats breathed spontaneously after spinal cord transection. In the six
cats in which recordings were made from RVLM and raphe neurons, the spinal
cord was transected at the fourth cervical segment. These animals were
artificially ventilated and paralyzed with gallamine triethiodide (4 mg/kg iv,
initial dose); bilateral pneumothoracotomy was performed to minimize movement
artifacts at the recording sites.
Blood pressure was measured from the femoral artery, and norepinephrine bitartrate (20 µg/ml in 3% dextran) was infused continuously into a femoral vein at a rate sufficient to maintain mean blood pressure close to 100 mmHg after spinal transection. Body temperature was maintained near 37°C with a heat lamp, and end-tidal CO2 was in the range of 4–5% (Traverse Medical Monitors Capnometer, model 2200) in both spontaneously breathing and artificially ventilated cats.
PSN recordings
Multiunit activity was recorded from thin strands teased from the left
preganglionic cervical sympathetic nerve using the method described by Koley
et al. (1989). The recordings
were made from the central end of the cut strand with bipolar platinum
electrodes and a capacity-coupled preamplifier band-pass of 300–3,000
Hz. Spike-sorting software (Run Technologies, Mission Viejo, CA) was used
off-line to separate the spikes of different preganglionic fibers making up
the multiunit recording field. Spikes were grouped into separate files based
on spike height, width, shape, depolarization velocity, and other
characteristics. A minimum interspike interval (ISI) of ≥60 ms was taken as
an indication that the spikes in a file arose from a single fiber
(Mannard and Polosa 1973).
Medullary neuron recordings
The dorsal surface of the medulla was exposed by removing portions of the
occipital bone and cerebellum. The obex and midline were used as landmarks for
placement of the recording tungsten microelectrode (FHC; approximately
3-m
tip impedance) with a David Kopf Instruments microdrive. The
reference electrode was a gold-plated disc placed on the skull.
Capacity-coupled preamplification with a band-pass of 100–3,000 Hz was
used. On-line analog discrimination was used to isolate the action potentials
(≥1.5 ms in duration) of single neurons. Extracellular recordings were made
from RVLM neurons located approximately 3.5 mm to the left of midline,
5–6 mm rostral to the obex, and within 2.5 mm of the ventral surface.
Raphe neuron recordings were made on the midline, 2–3.5 mm rostral to
the obex, and within 3.5 mm of the ventral surface. These are the regions in
which we have located single neurons with spinal axons and naturally occurring
activity correlated to the heart beat and postganglionic sympathetic nerve
discharge in cats with an intact neuraxis (Barman and Gebber
1985,
1992,
1997).
In four cats, time-controlled collision of spontaneous and stimulus-induced
action potentials was used as a test for antidromic activation of individual
RVLM or raphe neurons with electrical pulses delivered through concentric
bipolar electrodes (Rhodes model NE100; 0.5-mm exposed tips) to the
dorsolateral funiculus (left side) of the third cervical spinal segment. As
described by Barman and Gebber
(1985,
1997), antidromic activation is
indicated when the minimum interval between a spontaneous action potential and
the stimulus (2 x threshold) that always elicits a response just exceeds
the sum of the onset latency of the stimulus-induced action potential and the
axonal refractory period (estimated by paired shocks activation). Medullary
neuronal recording sites were identified using the histological techniques
described by Barman and Gebber
(1985,
1992).
Spike train analysis
The action potentials of single PSNs and medullary neurons were represented
by standardized 5-V square-wave pulses (2 ms in duration). From time series of
these pulses, we counted the number of spikes in time windows of designated
length and measured ISIs using software written in our laboratory by Lewis
(Gebber et al. 1999;
Lewis et al. 2001).
We used Fano factor analysis to test whether the fluctuations in spike
counts occurred randomly or were time scale invariant (fractal) in nature. The
Fano factor, F(T), as defined by Teich
(1989,
1992), is the ratio of the
variance of the number of spikes to the mean number of spikes in time windows
of a designated length, T
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,
1992). For a periodic process,
F(T) approaches zero as the window size is increased due to
decreasing variance. For a fractal process, F(T) increases
as a power of the window size and may reach values ≥1.0 (Teich
1989,
1992). This reflects the
greater variance of spike counts with increasing window size. The power law
relationship appears as a straight line on the log-log scale with a positive
slope, 
. , the scaling exponent, is the power to which
fluctuations in spike counts on one time scale are proportional to those on
longer time scales. The correlation coefficient (r value) is used as
a test for linearity on the log-log scale, and linear regression is used to
calculate .
Whether a power law relationship in the Fano factor curve reflects
long-range correlations of events is tested by constructing surrogate data
sets in which the ISIs have been randomly shuffled. Specifically, we assigned
random numbers to the ISIs in the original time series and then sorted the
random numbers by size. This creates a randomized data set whose mean ISI, ISI
variance, and ISI histogram are identical to those of the original spike
train, but with no correlations among events
(Teich and Lowen 1994). If
shuffling the data eliminates the power law relationship, it is concluded that
long-range correlations existed among the original ISIs. On the other hand, if
shuffling does not affect the Fano factor curve, it can be assumed that the
power law simply reflected the distribution of ISIs, which is the same for the
original data and its surrogates (Teich
1989; Teich et al.
1997). We routinely compared the curve for the original spike
train with those for 10 surrogates.
ISI histograms and arterial pulse (AP)-triggered histograms of single
neuron activity were constructed as described by Barman et al.
(2002) and Lewis et al.
(2001).
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RESULTS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONACKNOWLEDGMENTSREFERENCES |
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In six spinal cats, we recorded from 123 strands teased from the preganglionic cervical sympathetic nerve. Only 10 of these strands exhibited multiunit activity rising above background noise. Spike sorting was used to separate the discharges of 16 single PSNs from these strands. None of these neurons had cardiac-related activity. This was expected because baroreceptor reflex control of PSN activity was disrupted by transection of the cervical spinal cord.
The spike train of a single PSN was considered to contain long-range
correlations providing that 1) a power law extending over more than
one time scale (decade on log scale) was present in the Fano factor curve and
2) shuffling the ISIs to produce surrogate data sets eliminated the
power law. The spike train was considered not to be fractal if these
conditions were not met when the number of spikes in the time series was
≥2,000. The rationale for using this number is based on our work with brain
stem sympathetic premotor neurons (Lewis
et al. 2001) and PSNs (Das et
al. 2003) in cats with an intact neuraxis showing that the
percentage of spike trains of such neurons with fractal properties reached 100
when the time series contained ≥2,000 spikes. On this basis, the spike
trains of seven PSNs were classified as fractal. The time series for the other
nine PSNs contained <2,000 spikes, and their Fano factor curves did not
show a power law. As such, we were unable to classify their spike trains as
either fractal or nonfractal.
The results in Fig. 1 are
representative of those obtained for five of the seven PSNs with fractal spike
trains. In this case, the time series of ISIs was 2,980 s in length and
contained 3,283 intervals (Fig.
1A). The ISI histogram
(Fig. 1B) had a
coefficient of variation (CV) of 1.66, a value exceeding that (1.0) expected
for a pure exponential distribution (Cox
and Lewis 1966; Tuckwell
1988). The minimum and modal ISIs were 125 and 286 ms,
respectively, and the mean discharge rate was 1.1 Hz. The Fano factor curve
derived from the original spike train (single black trace in
Fig. 1C) was flat
( = 0), with F(T) near 1.0 for window sizes up to
approximately 50 ms. This feature is consistent with a Bernoulli process with
a low probability of success (Lewis et al.
2001; Teich 1992).
That is, for window sizes less than the minimum ISI, the spike count is either
zero or one, with the former more likely to occur. After a small dip below
1.0, F(T) rose to a value near 100 at the largest window
size. In contrast, the Fano factor curves for the 10 surrogate data sets (gray
region in Fig. 1C)
approached an asymptote at a much lower value (near 3.0) of
F(T). The differences between the Fano factor curve for the
original time series and those for the surrogates reflect the long-range
correlations existing among ISIs in the original spike train
(Teich and Lowen 1994). The
slope () of the Fano factor curve for the original spike train was 0.90
for window sizes between 25 and 497 s.
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Figure 2 shows one of two
cases in which the ISI histogram was gamma-like in shape (CV < 1.0). In
these cases, the power law in the Fano factor curve for the original spike
train also was eliminated by shuffling the ISIs. The time series of ISIs for
this PSN was 1,890 s in length and contained 1,864 intervals
(Fig. 2A). The ISI
histogram had a CV of 0.64 (Fig.
2B). The minimum and modal ISIs were 75 and 678 ms,
respectively, and mean discharge rate was 1.0 Hz. The Fano factor curve for
the original spike train (single black trace in
Fig. 2C) dipped to
values <1.0 beginning at a window size near the minimum ISI, and
F(T) reached its lowest value (0.35) at a window size near 3
s. The dip is larger than that in Fig.
1C, and this reflects the greater symmetry of gamma-like
distributions (Teich 1992).
The power law relationship in the Fano factor curve began at a window size
near 4 s and extended over more than one decade to 315 s, thus meeting the six
nonoverlapping window requirement we set as the minimum for accurate
determination of F(T), which reached a maximum value near 10
in this case. The slope of the power law was 0.77. In contrast, the Fano
factor curves for the 10 surrogate data sets were flat at window sizes >4 s
(gray region in Fig.
2C) and, for the most part, F(T)
remained below 1.0.
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The properties of the fractal spike trains of seven PSNs are summarized in
Table 1. The data for the five
PSNs whose ISI histograms had a CV >1.0 (PSN-A) are grouped separately from
the data for the two PSNs whose ISI histograms were gamma-like in shape
(PSN-B). The characteristics ( and window size range) of the Fano
factor curves for the two groups refer to that portion that deviated from the
curves for the corresponding surrogates. Of the properties listed, only the
CVs of the ISI distributions for PSN-A and PSN-B were clearly different.
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RVLM neurons with cardiac-related activity
The Fano factor curves for 8 of the10 RVLM neurons with cardiac-related activity identified in three spinal cats contained a power law that was eliminated by shuffling the ISIs. Although the spike trains of the other two neurons contained >2,000 spikes, their Fano factor curves deviated only slightly from those of the surrogates, and we were hesitant to classify them as either fractal or nonfractal. Figure 3 shows the results for one of the eight RVLM neurons with a fractal spike train. Note that the neuron had cardiac-related activity, as reflected by the sharp peaks in the AP-triggered histogram of neuronal discharges (Fig. 3A). The original time series of ISIs (936 s in length) is shown in Fig. 3B. The ISI histogram (Fig. 3C) for this RVLM neuron had a modal interval (282 ms) that exceeded that between heart beats (246 ms). The CV of the ISI histogram was 0.52, and mean firing rate was 2.6 Hz. The Fano factor curve in Fig. 3D contained a power law relationship that was eliminated by shuffling the ISIs in the original time series. The power law had a slope of 0.78 for window sizes between approximately 2.5 and 156 s, and F(T) reached a value of 6.3 at the largest window size.
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The properties of the spike trains of the eight RVLM neurons with fractal properties are summarized in Table 1. On the average, the RVLM neurons had higher firing rates than PSNs and their ISI histograms had lower CVs as compared with the PSN-A group.
We were successful in antidromically activating seven of eight RVLM neurons
with cardiac-related activity by electrical activation of sites in the
dorsolateral funiculus of the third cervical spinal segment. An example is
shown in Fig. 4. This neuron
was activated with a constant onset latency (14.5 ms) by spinal stimulation
(Fig. 4A,
1–3) and faithfully followed paired stimuli separated by no
<4 ms (Fig. 4B3).
The latter value provides an estimate of the neuronal refractory period. A
response at the recording site failed to occur when the interval between a
spontaneous action potential and the spinal stimulus was 16 ms
(Fig. 4B1), but an
action potential was elicited when the interval (19 ms) just exceeded the sum
of the latency of the stimulus-induced response and the neuronal refractory
period (Fig. 4B2).
Thus the response of the RVLM neuron to spinal stimulation was mediated
antidromically. The axonal conduction velocity was 2.1 m/s in this case.
Axonal conduction velocities averaged 2.9 ± 0.3 m/s (range
2.0–3.9 m/s) for the seven neurons. This value is similar to that for
RVLM neurons with activity correlated to the cardiac-related rhythm in
postganglionic sympathetic nerve discharge in cats with an intact neuraxis
(Barman and Gebber 1997).
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Raphe neurons with cardiac-related activity
Of the 11 medullary raphe neurons with cardiac-related activity identified in three spinal cats, the Fano factor curves for 8 neurons contained a power law that was eliminated by shuffling the ISIs. The spike trains of the other three neurons contained <2,000 spikes. Thus they could not be classified as nonfractal despite the absence of a power law in their Fano factor curves. Figure 5 shows the results for a raphe neuron with a fractal spike train. This neuron had strong cardiac-related activity as evidenced by the high peak-to-background ratio in the AP-triggered histogram of neuronal discharge (Fig. 5A). The time series of ISIs was 1,089 s in length and contained 1,562 intervals (Fig. 5B). The ISI histogram was multimodal (Fig. 5C). The primary peak at 262 ms was identical to that of the period between heart beats while the secondary peaks were close to multiples of this value. The secondary peaks reflect the fact that the neuron missed firing in a variable number of cardiac cycles. The Fano factor curve for the original spike train contained a power law with a slope of 0.69 for window sizes between approximately 3 and 182 s (single black trace in Fig. 5D). Note that shuffling the ISIs in the original spike train eliminated the power law (gray region in Fig. 5D).
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The properties of the spike trains of eight raphe neurons with fractal properties are summarized in Table 1. Mean firing rate and the mean CV of ISI histograms for these neurons were similar to those of RVLM neurons with cardiac-related activity.
Of the eight raphe neurons with fractal spike trains and cardiac-related
activity, two were tested for spinal axons. Both of these neurons were
antidromically activated by stimuli applied to the dorsolateral funiculus of
the third cervical spinal segment. Their axonal conduction velocities of 1.5
and 2.1 m/s fell within the range previously reported for raphe neurons with
activity correlated to the cardiac-related rhythm in postganglionic
sympathetic nerve discharge in cats with an intact neuraxis
(Barman and Gebber 1997).
Medullary neurons without cardiac-related activity
We used Fano factor analysis to test for fractal properties of the spike trains of three RVLM and five raphe neurons in four spinal cats whose discharges were not cardiac-related. The curves for all but one (an RVLM neuron) of these units contained a power law extending over more than one time scale that was eliminated by shuffling the ISIs in the original time series. The scaling exponent of the power law averaged 0.67 ± 0.07 for these seven neurons, a value similar to those for RVLM and raphe neurons with cardiac-related activity (see Table 1). These neurons were located close to RVLM and raphe neurons with cardiac-related activity identified in the same experiments.
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONACKNOWLEDGMENTSREFERENCES |
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;
Lewis et al. 2001), Fano
factor analysis was used to demonstrate time-scale invariant correlations
among ISIs of both PSNs and medullary sympathetic premotor neurons in cats
with an intact neuraxis. Because sympathetic nerve activity in the cat is
markedly reduced after high spinal transection
(Alexander 1946;
Zhong et al. 1991), one might
assume that the fractal firing patterns of the PSNs arose in supraspinal
circuits. However, it is also possible that fractal firing patterns of spinal
neurons were transmitted to the medulla where they influenced the timing of
RVLM and raphe neuronal activity generated by other sources. A third
possibility is that both supraspinal and spinal neurons in sympathetic
circuits independently generated fractal firing patterns. As demonstrated in
the current study, PSNs as well as putative medullary sympathetic premotor
neurons exhibited fractal firing patterns in cats subjected to cervical spinal
cord transection. The fact that shuffling of the ISIs in the original spike
trains of these neurons eliminated the power law in their Fano factor curves
supports the view that complexly ordered sequences of action potentials can be
generated independently at both spinal and supraspinal levels of the circuits
controlling sympathetic nerve activity. Such fractal activity might arise from
properties inherent to individual neurons
(Liebovitch and Koniarek 1992;
Lowen et al. 1997) or of the
networks in which they are embedded (West
1990).
RVLM and raphe neurons with fractal firing patterns and cardiac-related
activity in spinal cats likely were sympathetic premotor neurons for the
following reasons. First, these neurons were located in the same regions of
the RVLM and raphe that contained neurons with activity correlated to the
cardiac-related rhythm in sympathetic nerve discharge of cats with an intact
neuraxis (Barman and Gebber
1985,
1992,
1997). Second, the RVLM and
raphe neurons in cats with an intact neuraxis had fractal firing patterns that
were similar (see Table 1 in Lewis et al.
2001) to those reported here for neurons in spinal cats. The
similarity of the slopes of the power law in the Fano factor curves suggests
that the fractal firing patterns of RVLM and raphe sympathetic premotor
neurons in intact cats were largely independent of spinal feedback they may
have received. Third, of the 10 RVLM and raphe neurons with cardiac-related
activity tested in spinal cats, 9 had axons that descended to at least the
third cervical spinal segment. Moreover, their axonal conduction velocities
were in the range of those of RVLM-spinal and raphespinal neurons with
sympathetic nerve-related activity that were antidromically activated by
stimuli applied to the thoracic intermediolateral nucleus in cats with an
intact neuraxis (Barman and Gebber
1997).
Cervical spinal cord transection in barbiturate anesthetized cats markedly
and uniformly reduces the discharges of the inferior cardiac, renal, splenic,
and vertebral sympathetic nerves (Zhong et
al. 1991). As such, it is not surprising that of the 123 strands
dissected from the preganglionic cervical sympathetic nerve in six spinal
cats, only 10 showed activity that exceeded background noise. From these
strands, we were able to isolate the spike trains of 16 single PSNs, 7 of
which could be classified as fractal. Thus at least some PSNs can generate
fractal firing patterns characterized by long-range correlations among ISIs in
the absence of fractal inputs from the brain stem. Nonetheless, many PSNs
undoubtedly were silenced by spinal transection. All such neurons can be
assumed to have had fractal firing patterns before spinal transection in view
of our results in cats with an intact neuraxis
(Das et al. 2003). In that
study, fluctuations in spike counts and ISIs were fractal for all single PSN
time series that contained ≥2,000 spikes. Thus the fractal firing patterns
of PSNs silenced by spinal transection may have been entirely dependent on
their fractal inputs from the brain stem.
Whether the PSNs with fractal firing patterns identified in the current
study were drawn from the same populations as those with fractal spike trains
in cats with an intact neuraxis (Das et al.
2003) is problematic. The cervical sympathetic nerve is
functionally heterogenous in that it contains fibers controlling blood vessel
diameter, pupil size, nictitating membrane contraction, pilomotion, and
sweating (Bishop and Heinbecker
1932; Eccles
1935). In the cat, the background discharges of PSNs subserving
vasoconstrictor function are highly dependent on supraspinal driving inputs
(Alexander 1946;
Zhong et al. 1991). Whether
the background activity of other functional groups in the cervical nerve is
less dependent on supraspinal driving inputs is a possibility that cannot be
discounted. If so, there would have been a bias toward recording their
activity in the current study.
There were differences in the fractal firing patterns of PSNs in spinal
cats compared with those of PSNs in cats with an intact neuraxis. The
distributions of ISIs for the majority of PSNs in spinal cats had CVs
(average, 1.6) exceeding that expected for an exponential distribution. Such
distributions have also been noted for cat lateral geniculate neurons with
fractal spike trains (Teich et al.
1997). In contrast, the ISI histograms for PSNs in cats with an
intact neuraxis were gamma-like in shape (CV <1.0,
Das et al. 2003). The Fano
factor curves of most PSNs in spinal cats also differed from those of PSNs in
cats with an intact neuraxis. The curves for the original spike trains
deviated from those of corresponding surrogates at window sizes >5 s in
both spinal and intact cats. Nonetheless, after an initial dip, the curves for
the surrogate spike trains for the majority of PSNs in spinal cats approached
an asymptote at F(T) > 1.0 (see
Fig. 1). As a consequence, a
portion of the Fano factor curve for the original spike train where
F(T) exceeded a value of 1.0 overlapped with those for the
surrogates. In contrast, after the initial dip, the curves for the surrogate
spike trains for PSNs in cats with an intact neuraxis were flat and
F(T) remained below 1.0
(Das et al. 2003), a picture
similar to that for a few PSNs in the current study (see
Fig. 2).
The differences cited above might be explained if the PSNs in spinal cats were indeed drawn from populations functionally different from those sampled in cats with an intact neuraxis. Alternatively, the differences in the fractal firing patterns of PSNs in spinal versus intact cats might reflect the loss of brain stem inputs to the few PSNs that remained active after spinal transection. In this case, interruption of the descending influences might reveal the true characteristics of a spinal fractal process. Further investigation is required to distinguish between these possibilities.
Whereas Fano factor analysis is a well-established method for the detection
of time-scale invariant (i.e., fractal) behavior, mathematical constraints
prevent the variance-to-mean spike count ratio from increasing faster than
T1 (Teich et al.
1997). As a consequence, this method cannot be used to measure
scaling exponents >1.0 that are characteristic of fractal Brownian motion
rather than fractal Gaussian noise for which the scaling exponents are <1.0
(Eke et al. 2000). Moreover,
scaling exponents close to 1.0 may be underestimated when derived by Fano
factor analysis. Thus we refrained from comparing the scaling exponents of the
power laws in the Fano factor curves for PSNs and putative medullary
sympathetic premotor neurons. Nonetheless, this limitation in no way
compromises our contention that fractal firing patterns in circuits
controlling sympathetic nerve discharge can be generated at both spinal and
supraspinal levels.
Time-scale invariant behavior that is eliminated by shuffling the data
represents a form of memory in that the current value of the ISI is related to
past values in a time frame defined by the range of the window sizes
comprising the power law in the Fano factor curve. As such, fluctuations of
the ISI are ordered in that they are statistically self-similar across
different time scales. Thus fractal spike trains differ from random series of
spikes such as a dead time modified Poisson point process which has no memory
(action potentials occur with equal probability per unit time) except for the
refractory period of the neuron (Teich
1989,
1992). Fractal spike trains
are a feature not only of PSNs and medullary sympathetic premotor neurons, but
also of cat auditory nerve fibers (Teich
1989,
1992;
Teich and Lowen 1994) and
neurons located at different levels of the cat visual system
(Teich et al. 1997). Moreover,
they have been reported for functionally unidentified neurons in the cat
mesencephalic reticular formation (Grüneis et al. 1993) and medulla (RVLM
and raphe neurons lacking cardiac-related activity in this study).
Nevertheless, it should be emphasized that the spike trains of other neurons
adhere to the classic model of a Poisson point process
(Koch 1999;
Tuckwell 1988). Examples in
the cat include primary vestibular afferent fibers
(Teich 1989) and neurons in
the superior olive (Turcott et al.
1994). Thus fractal methods such as Fano factor analysis are
essential for distinguishing fractal from Poisson point processes.
It has been suggested that time-scale invariant behavior in the spike
trains of auditory and visual sensory neurons provides a means of matching the
detection system to the expected signal which itself can be fractal
(Teich 1989;
Teich et al. 1997). The
purpose of fractal activity in the sympathetic nervous system remains a
mystery. One possibility is that fractal sympathetic activity plays a role in
generating or modulating the fractal component of heart rate variability
(Goldberger 1992;
Ivanov et al. 1999). Regarding
this possibility, Das et al.
(2003) have demonstrated
fractal fluctuations in multiunit burst amplitude and area recorded from the
postganglionic sympathetic vertebral nerve of the cat, and our unpublished
observations indicate that such is also the case for the inferior cardiac
nerve. Fractal heart rate variability is of practical importance since it is
diminished in cardiovascular diseases such as low output congestive heart
failure (Goldberger 1992;
Goldberger et al. 1996;
Ivanov et al. 1999). Thus a
potential link between fractal sympathetic nerve discharge and heart rate
variability should be investigated.
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ACKNOWLEDGMENTS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONACKNOWLEDGMENTSREFERENCES |
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This study was supported by National Heart, Lung, and Blood Institute Grants HL-13187 and HL-33266.
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FOOTNOTES |
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Address for reprint requests: G. L. Gebber, Dept. of Pharmacology and Toxicology, Michigan State Univ., East Lansing, MI 48824 (E-mail: gebber{at}msu.edu).
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REFERENCES |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONACKNOWLEDGMENTSREFERENCES |
|---|
Barman SM and
Gebber GL. Axonal projection patterns of ventrolateral medullospinal
sympathoexcitatory neurons. J Neurophysiol
53: 1551–1566,
1985.
Barman SM and
Gebber GL. Rostral ventrolateral medullary and caudal medullary raphe
neurons with activity correlated to the 10-Hz rhythm in sympathetic nerve
discharge. J Neurophysiol 68:
1535–1547, 1992.
Barman SM and
Gebber GL. Subgroups of rostral ventrolateral medullary and caudal
medullary raphe neurons based on patterns of relationship to sympathetic nerve
discharge and axonal projections. J Neurophysiol
77: 65–75,
1997.
Barman SM, Orer
HS, and Gebber GL. Differential effects of an NMDA and a non-NMDA receptor
antagonist on medullary lateral tegmental field neurons. Am J
Physiol Regul Integrat Comp Physiol 282:
R100–R113, 2002.
Bassingthwaighte JB, Liebovitch LS, and West BJ. Fractal Physiology, New York: Oxford University Press, 1994, p. 11–44.
Bishop GH and
Heinbecker P. A functional analysis of the cervical sympathetic supply to
the eye. Am J Physiol 100:
519–532, 1932.
Cox DR and Lewis PAW. The Statistical Analysis of Series of Events. New York: Wiley, 1966, p. 17–36.
Das M, Gebber
GL, Barman SM, and Lewis CD. Fractal properties of sympathetic nerve
discharge. J Neurophysiol 89:
833–840, 2003.
Eccles JC. The action potential of the superior cervical ganglion. J Physiol 85: 179–206, 1935.
Eke A, Hermán P, Bassingthwaighte JB, Raymond GM, Percival DB, Cannon M, Bala I, and Krényi I. Physiological time series: distinguishing fractal noises from motions. Eur J Physiol 439: 403–415, 2000.[Web of Science][Medline]
Gebber GL,
Zhong S, Lewis C, and Barman SM. Differential patterns of spinal
sympathetic outflow involving a 10-Hz rhythm. J
Neurophysiol 82:
841–854, 1999.
Goldberger AL. Fractal mechanisms in the electrophysiology of the heart. IEEE Med Biol 11: 47–52, 1992.
Goldberger AL, Peng C-K, Hausdorff J, Mietus J, Havlin S, and Stanley HE. Fractals and the heart. In: Fractal Geometry in Biological Systems: An Analytical Approach, edited by Iannaconne PM and Khokha M. Boca Raton, FL: CRC Press, 1996, p. 249–266.
Grüneis F, Nakao M, Yamamoto M, Musha T, and Nakahama H. An interpretation of 1/f fluctuations in neuronal spike trains during dream sleep. Biol Cybern 60: 161–169, 1989.[Medline]
Ivanov RC, Nunes Amaral LA, Goldberger AL, Havlin S, Rosenblum MG, Struzik ZR, and Stanley HE. Multifractality in human heart beat dynamics. Nature 399: 461–465, 1999.[Medline]
Koch C. Biophysics of computation. In: Information Processing in Single Neurons. New York: Oxford University Press, 1999, p. 350–373.
Koley BN, Pal P, and Koley J. High threshold baroreceptor afferents in the sympathetic nerve of monkey. Jpn J Physiol 39: 145–153, 1989.[Web of Science][Medline]
Lewis CD,
Gebber GL, Larsen PD, and Barman SM. Long-term correlations in the spike
trains of medullary sympathetic neurons. J
Neurophysiol 85:
1614–1622, 2001.
Liebovitch LS. Fractals and Chaos Simplified for the Life Sciences. New York: Oxford University Press, 1998, p. 84–87.
Liebovitch LS and Koniarek JP. Ion channel kinetics. Protein switching between conformational states is fractal in time. IEEE Eng Med Biol 11: 53–56, 1992.
Lowen SB, Cash
SS, Poo M-M, and Teich MC. Quantal neurotransmitter secretion rate
exhibits fractal behavior. J Neurosci
17: 5666–5677,
1997.
Mannard A and
Polosa C. Analysis of background firing of single sympathetic
preganglionic neurons of cat cervical nerve. J
Neurophysiol 36:
398–408, 1973.
Steriade M and
Llinas RR. The functional states of the thalamus and the associated
neuronal interplay. Physiol Rev
68: 649–742,
1988.
Teich M. Fractal character of the auditory neural spike train. IEEE Trans Biomed 36: 150–160, 1989.
Teich MC. Fractal neuronal firing patterns. In: Single Neuron Computation, edited by McKenna T, Davis J, and Zormetzer SF. Boston, MA: Academic, 1992, p. 589–625.
Teich MC, Heneghan C, Lowen SB, Ozaki T, and Kaplan E. Fractal character of the neural spike train in the visual system of the cat. J Opt Soc Am A 14: 529–546, 1997.[Web of Science][Medline]
Teich MC and Lowen SB. Fractal patterns in auditory nerve-spike trains. IEEE Eng Med Biol 13: 197–202, 1994.
Tuckwell HC. Introduction to Theoretical Neurobiology: Nonlinear and Stochastic Theories. New York: Cambridge University Press, 1988, vol. 2, p. 191–246.
Turcott RG, Lowen SB, Li E, Johnson DH, Tsuchitani C, and Teich MC. A nonstationary Poisson process describes the sequence of action potentials over long time scales in lateral-superior-olive auditory neurons. Biol Cybern 70: 209–217, 1994.[Web of Science][Medline]
West BJ. Fractal Physiology and Chaos in Medicine. Singapore: World Scientific, 1990, p. 67–78.
Zhong S, Kenney MJ, and Gebber GL. High power, low frequency components of cardiac, renal, splenic and vertebral sympathetic nerve activities are uniformly reduced by spinal cord transection. Brain Res 556: 130–134, 1991.[Web of Science][Medline]
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) elicited constant latency (14.5 ms) action potential
(
). B1: spinal stimulus failed to elicit an action potential
when interval between spontaneous action potential (