IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 47, NO. 6, JUNE 2000
701
Analysis of Synaptic Quantal Depolarizations in
Smooth Muscle Using the Wavelet Transform
Priya Vaidya, K. Venkateswarlu, Uday B. Desai, Senior Member, IEEE, and Rohit Manchanda*
Abstract—The time-frequency characteristics of synaptic
potentials contain valuable information about the process of
neurotransmission between nerves and their target organs. For
example, at the synapse between autonomic nerves and smooth
muscle, two central issues of neurophysiology, i.e., 1) the probability of neurotransmitter release and 2) the quantal behavior of
transmission can be deduced from analysis of the rising phases
of evoked excitatory junction potentials (eEJP’s) recorded from
smooth muscle. eEJP rising phases are marked by prominent
inflexions, which reflect these features of neuronal activity. Since
these inflexions contain time-varying frequency information, we
have applied recent techniques of time-frequency analysis based
upon wavelet transforms to eEJP’s recorded from the guinea-pig
vas deferens in vitro. We find that these techniques allow accurate
and convenient characterization of neuronal release sites, and that
their probability of release falls between 0.001–0.004. We have
also analyzed eEJP’s recorded in the presence of the chemical
1-heptanol, which reveals quantal depolarizations. These results
have helped clarify the nature of the quantal depolarizations that
underly eEJP’s. The present method offers significant advantages
over those previously employed for these tasks, and holds promise
as a novel approach to the analysis of synaptic potentials.
Index Terms—Neuromuscular transmission, signal processing,
smooth muscle, synaptic potentials, wavelet transform.
I. INTRODUCTION
T
HE RELAY of information from a neuron to its target cell
at the junction between the two, the synapse, is mediated
by a chemical substance [the neurotransmitter, (NTr)] released
from the nerve terminals [1]. Two central factors determine the
efficacy and the eventual outcome of the process of neurotransmission. On the neuronal side, the probability of NTr release
from specialized release sites is a variable that determines significantly the amount of NTr released and, therefore, the input
to the target cells. At the level of the target cells, the electrical
properties of postsynaptic cell membranes determine the cell’s
electrical response to activation by NTr. Both these issues can
be examined by investigating the properties of the synaptic or
junction potentials. These potentials are transient changes of
membrane potential of the target cells produced by the action
of NTr’s which change the conductance of postsynaptic memManuscript received March 25, 1998; revised January 3, 2000. This work was
supported by the Department of Science and Technology, Government of India,
under project SP/SO/NO6/93. Asterisk indicates corresponding author.
P. Vaidya is with the School of Biomedical Engineering, Indian Institute of
Technology, Bombay, Powai, Mumbai 400076, India.
*R. Manchanda is with the School of Biomedical Engineering, Indian
Institute of Technology, Bombay, Powai, Mumbai 400076, India (e-mail:
rmanch@cc.iitb.ernet.in).
U. B. Desai is with the Department of Electrical Engineering, Indian Institute
of Technology, Bombay, Powai, Mumbai 400076, India.
Publisher Item Identifier S 0018-9294(00)04405-0.
branes to various ions, thus, generating transmembrane currents
and potential changes.
In particular, the rising phases of junction potentials are often
not linear but are marked by sudden changes of slope, or inflexions, during their course. This endows the rising phases with distinctive phases of depolarization, which we term component depolarizations (CD’s). Analysis of these inflexions and CD’s has
raised some interesting questions about synaptic function. This
is well exemplified in the case of neurotransmission from mammalian autonomic nerves to smooth muscle organs. Thus, in the
guinea-pig vas deferens, an organ that is conveniently explored
electrophysiologically, the following issues have been raised. 1)
The probability of NTr release from release sites located in axonal
varicosities of autonomic neurons is suggested to be remarkably
low, falling in the range of 0.001 to 0.03 [5]. This contrasts strikingly with the situation at the somatic neuromuscular junctions in
the end plates of skeletal muscle, where release probabilities are
much higher, being closer to unity. 2) The quantal depolarization
in smooth muscle is suggested to have a time course widely different from the evoked depolarization that occurs following nerve
stimulation. This is also an unusual feature. At synapses NTr is
released, and acts, in irreducible units or quanta, each quantum
corresponding to the transmitter content of a membranous storage
vesicle present in the neuronal terminal. Usually, single vesicles
of transmitter are released randomly in time, and produce the
unitary spontaneous junction potentials in target cells. An example is the well-known miniature end plate potential (mEPP) in
skeletal muscle cells. Nerve stimulation causes the synchronized
release of several quanta such that the evoked junction potential is
roughly an integral multiple of the spontaneous one, but follows
the same time course. Such a relation exists between the evoked
end plate potential (eEPP) and the mEPP in skeletal muscle and
between analogous events at other synapses [1].
In smooth muscle, however, the evoked event, termed the excitatory junction potential (eEJP), is some sixfold to tenfold more
prolonged than the spontaneously occurring, presumably unitary
event, which is the spontaneous EJP (sEJP). This interesting discrepancy is thought to arise from the peculiar electrical behavior
of smooth muscle, whose transfer function is thought to change
depending upon the pattern of transmitter release [15], [16].
Speculations such as the above have relied substantially on
close scrutiny of the CD’s in the rising phase of eEJP’s. These
CD’s are held to uniquely characterize or “fingerprint” individual
neuronal release sites, thus, aiding estimation of the probability
of activation of these sites [5]. Additionally, analysis of CD’s and
their comparison to rising phase of sEJP’s has stimulated the contention that the quantal depolarization is sEJP-like, hence, substantially briefer and grossly different from the eEJP [2].
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The extraction of functional information from CD’s requires
analysis of the changes in slope and the precise time of occurrence of these changes [5]. Clearly, the problem can be regarded
as one involving the extraction of time-frequency information
from the eEJP’s. However, the methods presently used for this
purpose suffer from significant disadvantages, related mainly
to subjectivity and cumbersome nature of signal detection
and analysis (see Section IV). We felt, therefore, that it was
warranted to explore the application of recent wavelet transform (WT)-based methods of time-frequency analysis to this
problem. Such methods are reported to have a high sensitivity
to the time-frequency content of analysand signals [12]. We
have investigated their use in automating and improving the
required signal processing tasks, and their contribution to the
aforementioned issues of neurophysiology and neuroeffector
transmission.
In this paper, we report that the use of WT-based time-frequency analysis succeeds in providing the information of interest with accuracy and reliability, and also aids automation
of data processing. Our analysis has been performed on eEJP’s
recorded from the guinea-pig vas deferens in vitro, evoked both
under control (normal) conditions and under the influence of
a chemical, 1-heptanol, that has been suggested to reveal the
quantal evoked depolarizations underlying eEJP’s [14].
were collected on computer at 1 kHz using SCAN (Synaptic
Current Analysis Software, supplied by Dr. J. Dempster,
Strathclyde University, Glasgow) driving an analog-to-digital
(A/D) card (PCL 209, Dynalog Microsystems, Mumbai, India)
installed on a PC-AT 80 486 compatible. eEJP’s were collected
using the external triggering option supported by SCAN and
the A/D card. Collection was triggered using a pretrigger pulse
which preceded the stimulus pulse by 5 ms.
B. Detection and Characterization of Component
Depolarizations: Theory
To detect and characterize the CD’s in the rising phase of
eEJP’s, we carried out WT-based time-frequency analysis on
the signals. The wavelet transform
, represents a signal
, which
in terms of a family of functions
, called the basic wavelet.
are the translates and dilates of
Following Mallat [12], [13], we have
(1)
is taken to be a quadratic spline, also
and the basic wavelet
, a cubic
specified as the derivative of a smoothing function
spline
(2)
II. METHODS
A. Electrophysiological Recording and Data Collection
The eEJP’s were recorded as previously described [14].
Briefly, male Hartley guinea-pigs weighing 400–550 g were
stunned and exsanguinated, and the vasa deferentia were
dissected out along with the innervating branch of hypogastric
nerve. The vas was pinned out on the silicone rubber base of a
Perspex organ bath in which recordings were carried out. The
tissue was continuously superfused with physiological Krebs
at 2–3 ml/min (composition in mM: NaCl 118.4, KCl 4.7,
MgCl 1.2, CaCl 2.5, NaHCO 25.0, NaH PO 0.4, glucose
11.1, bubbled with 95% O and 5% CO , pH 7.3–7.4). The
temperature of the solution in the bath was recorded by placing
a thermistor near the tissue and maintained at 35 C–37 C by
heating the liquid paraffin in a surrounding Perspex jacket
using a proportional temperature control system. Solutions
of 1-heptanol (S.D. Fine Chemicals, Mumbai) were made up
by vigorous shaking with Krebs at the time of experiment
and were applied to tissue by switching the inflow to the
heptanol-containing reservoir. Intracellular recordings of
membrane potential changes were obtained by use of glass
high impedance (20–60 M ) microelectrodes filled with 3 M
KCl. eEJP’s were evoked by stimulating the hypogastric nerve
supramaximally using rectangular voltage pulses (amplitude
5–10 V and pulsewidth 0.01–0.1 ms) delivered through bipolar
Ag–AgCl ring electrodes at 0.7 Hz. With supramaximal stimulation, the amplitude of eEJP’s was not depressed even for
stimulation periods lasting for an hour or more. Signals were
fed to an intracellular electrometer (IE-201, Warner Instrument
Corp., Hamden, CT.) through its high-impedance headstage
), and recorded on a DAT recorder (DTR-1204,
(
Bio-logic, Claix, France, bandwidth dc 22 kHz). The data
The WT of
as [12], [13]
at scale and position , can now be expressed
(3)
, at scale , is
Thus, the dyadic wavelet transform
proportional to the derivative of the original signal smoothed
at scale . The maxima of the absolute value of the WT cor, which are
respond to the sharply varying points of
essentially the points of inflexion in the original signal [12]. In
practice, we use the discrete wavelet transform (DWT) at dyadic
, and belong
scale ; that is defined as
to the set of integers. Now, the computation of DWT can be
achieved using a subband filter structure based on discrete filand the scaling
ters and corresponding to the wavelet
. In the implementation, the related discrete filters
function
and
were derived by putting (
) zeros between each
[12]. Thus, downsampling
of the coefficients filters and
was not done and, hence, the data length was held constant at
each scale . The WT was obtained and corresponding modulus maxima (MM) (local maxima of the DWT modulus) were
also found. A presence of inflexion is registered when the corresponding MM is present at all scales. In practice, we start with
, and
the coarse scale,
,
trace the MM all the way to the first scale
the finest scale. The location of the traced MM at the finest scale
gives the point of inflexion.
C. Implementation
We have done wavelet transform analysis on eEJP’s recorded
from five different cells. Each data set included at least several
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VAIDYA et al.: ANALYSIS OF SYNAPTIC QUANTAL DEPOLARIZATION
703
Fig. 1. Illustration of procedure adopted for analysis of smooth muscle
synaptic potentials. As described in Section II-B, we have used the algorithm
proposed by Mallat to compute the DWT. We have used the quadratic spline to
be the basic wavelet for transformation. Refer [12] for the detailed explanation
of the DWT. (a) Experimentally recorded eEJP; (b) De-noised version of eEJP
in a, showing retention of features of interest (inflexions in rising phase); (c)
First trace corresponds to the DWT of the signal at first scale. This is called the
finest scale in Wavelet transform terminology, i.e., we detect the high-frequency
contents in the signal at this scale. The successive waveforms in Fig. 1(c) are
obtained by computing the DWT at next three scales (basically focusing on
lower frequencies). (d) First trace is the MM plot corresponding to first trace in
Fig. 1(c). The MM are defined to be the local maxima of the DWT modulus.
Hence, the first signal waveform obtained in Fig. 1(d) is generated using the
first waveform in Fig. 1(c) by calculating local maxima of the DWT modulus.
The successive traces correspond to the traces in Fig. 1(c) at different scales.
hundred eEJP’s. However, the data presented in the paper are
from a single cell, one which provided especially dramatic examples of CD’s and quantal EJP’s (qEJP’s, see Section III-C),
and in which it was possible to record over 1500 eEJP’s continuously during the introduction and removal of heptanol. The
recordings contained considerable noise at frequencies higher
than the frequencies of interest. This noise was removed using a
standard WT-based denoising algorithm [9], as described in [7].
From Fig. 1 it can be seen that this procedure allowed us to retain the main features of interest in the signal. The time instants
of the inflexions were found using the algorithm proposed by
Mallat [12], described above, by tracing the significant maxima
present at the fourth-scale back to the first scale. The result of
applying the WT to a sample eEJP after denoising is shown in
Fig. 1. Modulus maxima at each scale are shown in Fig. 1(d)
and the corresponding WT in Fig. 1(c). The time instants and
peak amplitudes of the MM were stored in a look up table to
search for eEJP’s having identical or near identical frequency
characterization at the same latency after stimulation. The automated search was carried out by the K-means clustering method.
It was also possible to compute the instantaneous frequencies
( ’s) of the inflexions [8]. However, the absolute values of
were not of particular use in our analysis, since the information
of interest could be obtained from comparison of relative ’s,
represented by MM amplitudes. Hence, only the latter were used
for further analysis. Thus, the important steps in the implementation were as follows:
• denoising the records;
Fig. 2. CD’s of eEJP’s and their MM. (a) Six consecutive eEJP’s (148-153),
showing CD’s in their rising phases (e.g., asterisks). Vertical lines correspond to
the four distinct latencies at which the CD’s are observed. (b) Scatter plot of 666
Modulus Maxima obtained from analysis of 1500 eEJP’s. Note that the bands of
MM center on approximately 39, 56, 68, and 88 ms (see text for details), along
the latency axis [Fig. 2(b)]. These correspond to the four vertical lines drawn in
(a) [note different time scales in (a) and (b)].
• characterizing the inflexions by wavelet analysis;
• finding out identical inflexions using clustering.
III. RESULTS
A. Component Depolarizations of eEJP’s
In Fig. 2(a), we show six eEJP’s evoked by successive stimuli
delivered to the hypogastric nerve at 0.7 Hz. The rising phases
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of some of the eEJP’s can be seen to have prominent inflexions. These rising phases are clearly composed of more than
one component depolarization, the individual components being
separated by the inflexions which can appear as distinct steps
or notches. In the cell from which these records were taken, a
total of over 1500 eEJP’s were recorded (over about 35 min, at
0.7 Hz). The CD’s of the rising phases commenced at latencies
that fell into four distinct intervals. This is shown by the clustering of MM amplitudes for these eEJP’s into four prominent
bands, having mean s.d.(data) of 39.7 3.2 (178), 55.8
3.4 (122), 67.8 3.9 (277), 87.6 3.1 (89) ms along the latency axis [Fig. 2(b)].
In each latency band, the amplitudes of the depolarizations
varied continuously from the lowest discernible level ( 1 mV)
to 15 mV. As seen in Fig. 2(a), the configuration of the eEJP
rising phase is extremely variable from one event to the next,
because of the random appearance of different CD’s at the different latencies.
B. Detection of Identical CD’s of eEJP’s: Estimation of
Release Probabilities
Inflexions on depolarizations of eEJP’s are suspected to
represent quantal components of eEJP’s. This can be tested
by seeing if they fulfill the previously established criteria for
quantal evoked events in smooth muscle [5], namely 1) intermittency and 2) repetition of the same event at a low probability
(0.001–0.05). Intermittency of occurrence of inflexions/CD’s
at any particular latency is evident in Fig. 2(a), e.g., a CD
occurs at the fourth latency only in one record (153) of the six
shown. In order to see whether a particular CD would repeat
itself during a series of eEJP’s, we computed the MM for all
the eEJP’s and searched for matching amplitudes at particular
latencies (see Methods). On inspection of MM of long series
of eEJP’s, it was possible to detect such repetitions. When the
corresponding eEJP’s were superimposed, they were found
to possess identical CD’s in 95% of the cases. Examples of
such matches are shown in Fig. 3 for CD’s at latencies falling
in two of the four bands. In Fig. 3(a), the two eEJP’s shown
have identical CD’s in the first latency band (at a latency of 37
ms), but they differ widely in their subsequent configuration.
Fig. 3(b) shows eEJP’s with identical CD’s in the third latency
band (at a latency of 64 ms), but not at any other.
The CD’s that recurred in a series of eEJP’s were separated
by a variable number of events, e.g., 100 and 61, respectively,
for the repetitions illustrated in Fig. 3(a) and (b). In general, it
was observed that repetitions were separated by as little as 2–3
events to as many as 300–500 events, as reported earlier [5]. It
was possible to detect several similar matches between CD’s,
particularly in the first latency band. In a train of a total of 1500
eEJP’s analyzed, there were 76 such matches. Each CD, however, could occur more than twice. The distribution of numbers
of matches observed in this train of eEJP’s is provided in Table I.
The data indicate, provided each MM uniquely corresponds to
a single release site, that the overall probability of release for
sites that were reactivated varies between 0.001 and 0.004.
+
Fig. 3. Matching CD’s of eEJP’s. Modulus maxima ( and 5) detected to have
identical amplitude and latency (arrow indicating superimposed and 5) are
shown in the upper traces of both (a) and (b). [Modulus maxima traces shown
in this figure and subsequent Figs. 5 and 7 are obtained similarly as trace 4 of
Fig. 1(d) for the respective eEJP]. Corresponding eEJP’s are shown in the lower
traces indicating the serial number in a set of eEJP’s analyzed. Two examples
are shown, for latencies 37 ms (a) and 64 ms (b). Note the precise match between
the CD’s of the eEJP’s whose analysis returned identical MM.
+
TABLE I
DISTRIBUTION OF MATCHES IN A TRAIN OF
1500 eEJP’s. NUMBER OF eEJP’s OBSERVED WITH SIGNIFICANT
INFLEXIONS WERE 666
C. Effects of Heptanol on eEJP’s: Observation of Quantal
Evoked Depolarizations
The effect of heptanol on eEJP’s of the guinea-pig vas deferens makes it possible to observe more directly the quantal
depolarizations underlying the eEJP. This is because heptanol
seems to suppress the slower background depolarization during
the eEJP (see Section IV-C for details on mechanism of heptanol action), revealing rapid, sEJP-like stimulus-locked evoked
depolarizations, namely, “quantal EJP’s” or qEJP’s [14]. Examples are provided in Fig. 4, of five successive eEJP’s recorded
following the action of 2.0-mM heptanol. The signals illustrated
are from the same cell from which the examples in Figs. 2 and 3
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VAIDYA et al.: ANALYSIS OF SYNAPTIC QUANTAL DEPOLARIZATION
705
Fig. 5. Identical qEJP’s in the presence of heptanol. (a) shows MM detected
(see Figs. 1 and 3 legend for details) to have identical amplitude and latency
and 5, indicated by arrow). (b) qEJP’s
for two qEJP’s (superimposed
corresponding to the MM in a, along with background depolarization (*). (c)
Identical signals resulting after subtraction of background from qEJP’s in (b).
+
97 stimuli evoked qEJP’s, 90 at the first latency band and seven
at the fourth, illustrating their intermittent occurrence.
D. Detection of Identical qEJP’s
Fig. 4. Observation of qEJP’s revealed by 1-heptanol. (a) Five consecutive
traces (846-850) recorded in the presence of 2.0 mM heptanol, showing
intermittent qEJP’s (*). Vertical lines indicate the two latencies at which
qEJP’s were observed. (b) Scatter plot of 97 MM obtained from analysis of 500
heptanol affected signals. Note the clustering into two bands (centered around
39 and 87 ms) corresponding to the lines in (a) [note different time scales in
(a) and (b)].
were drawn. In this cell, it was possible to maintain the microelectrode insertion while carrying out the introduction of heptanol and its removal twice. As evident from Fig. 4(a), the prolonged phase of the depolarization of the eEJP is suppressed by
heptanol [e.g., compared to eEJP’s of Fig. 2(a)], while the more
rapid qEJP’s remain (asterisks), occurring intermittently.
Modulus maxima for heptanol-affected eEJP’s occurred only
at latencies clustered in two bands (first and fourth) out of the
four that were observed in control solution [Fig. 4(b)], indicating that the chemical had suppressed events at the other two
latencies considerably. qEJP’s are suggested to be the quantal
evoked depolarizations underlying eEJP’s [14]. This hypothesis
can be tested by seeing if they show the same properties of intermittence and repetition as the inflexions/CD’s of normal eEJP’s.
Out of 500 stimuli delivered during the action of heptanol, only
Amongst the MM for the 97 qEJP’s observed during the action of heptanol, 11 pairs were found to be identical, ten at the
first latency band and one at the fourth. Fig. 5 shows an example
of the repetition of a qEJP in the first latency band (at the latency
of 37 ms) that occurred twice during the action of heptanol, the
second occurrence coming 123 stimuli after the first. Verification of the identity of the qEJP’s by superimposition presents
the problem that the sharp depolarization of the qEJP is usually
riding on a slower background depolarization, which modifies
the shape of its decay phase. In order to perform a robust comparison, we have subtracted an appropriate background depolarization from the records containing the qEJP’s. The background
depolarization was chosen from events evoked just preceding
or following the qEJP’s. These events did not possess noticeable inflexions, and in time course followed closely the basal
depolarizations underlying the qEJP’s [asterisk in Fig. 5(b)].
Fig. 5(c) shows the qEJP’s superimposed after subtraction of
background, demonstrating their identically (within the limits
imposed by residual noise). (In Figs. 6 and 8, a similar subtraction of background depolarization was carried out to determine
the true time course of CD’s and sEJP’s.)
Similar to the case mentioned for eEJP’s in Section III-B, a
particular qEJP could be reactivated at event intervals ranging
from very short (e.g., within two stimuli of each other) to very
long (e.g., about 200 stimuli out of about 500 stimuli delivered
during the action of heptanol).
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Fig. 7. qEJP identical to a CD of an eEJP. (a) MM detected (see Figs. 1 and
3 legend for details) to have identical amplitude and latency (40 ms; arrow) for
a qEJP ( ) and an eEJP (5). (b) Original signals superimposed to show exact
match between corresponding depolarizations of qEJP (dashed line) and eEJP
(continuous line).
+
Fig. 6. Showing a qEJP identical to an sEJP. (a) The qEJP (*) and background
depolarization (arrow). (b) The qEJP after subtraction of the background, (c)
an sEJP that occurred randomly in the same cell. (d) subtracted qEJP and sEJP
superimposed, demonstrating identicality of the signals.
E. Detection of qEJP’s Identical to sEJP’s
The definitive evidence that a qEJP is a quantal event would
be to find a match between this signal and a randomly generated
sEJP, since the sEJP is believed to be the quantal depolarization
in smooth muscle [6], [15], [16].
It was possible to detect qEJP’s whose rising phases returned
MM identical to those of certain sEJP’s recorded in the same
cell. Subtraction of appropriate background depolarization
[arrow in Fig. 6(a)] yielded the true configuration of the qEJP
[Fig. 6(b)]. A randomly occurring sEJP is shown in Fig. 6(c).
Superimposition of the qEJP and sEJP, after shifting the sEJP,
shows that these events were identical in all respects such
as amplitude, rise, and decay [Fig. 6(d)]. These observations
indicate strongly that qEJP’s represent quantal evoked depolarizations in smooth muscle cells.
F. Detection of CD’s Identical to qEJP’s/sEJP’s: Quantal
Nature of CD’s
Since the sEJP and qEJP are quantal events, the proposed
quantal nature of the CD’s of the eEJP [5] can, therefore, be
verified by matching them with sEJP’s or with qEJP’s observed
in the presence of heptanol. Fig. 7 shows an example of a match
obtained between a CD of a control eEJP and a qEJP in the
presence of heptanol, as indicated by their identical MM.
Furthermore, it was possible to detect eEJP’s whose rising
phases provided MM identical to those of certain sEJP’s
recorded in the same cell. Following subtraction of background
depolarization similar to that outlined for qEJP’s above, we
show a CD of an eEJP identical to an sEJP occurring in the same
Fig. 8. An sEJP identical to a CD of an eEJP. (a) CD of eEJP (*) and
background depolarization (arrow); see Section III-D for details. (b) CD
after subtraction of background. (c) sEJP ( ) and background depolarization
(arrow). (d) sEJP after subtraction of background. (e) and (f) Signals resulting
after subtraction in (b) and (d), shown superimposed on a compressed time
scale (e) and on an expanded scale (f). The eEJP and sEJP were identified for
matching on the basis of identical MM.
cell (Fig. 8). Thus, the sharp CD’s of the eEJP are also quantal
depolarizations of the smooth muscle cells (see Section IV).
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IV. DISCUSSION
WT-based analysis has been applied previously to a variety
of biomedical signals, including heart sounds, electromyogram,
brain evoked potentials, and the ECG [11]. Amongst bioelectric signals, the applications so far have been restricted to surface recorded signals. Cellular level electrophysiological signals, such as junction potentials, have not been analyzed before
with a view to exploring neuronal function and the electrical behavior of target cells. Our results show that time-frequency techniques can be usefully employed in the analysis of cellular level
bioelectric signals to infer properties of nerve and muscle biophysics. In Section IV-A, we discuss below the merits of these
techniques in the present application and prospects for its future
use.
A. Requirement of the Technique and Comparison to Earlier
Methods
Assessment of release probability of autonomic neurons is
usually based on accurate shape-matching of evoked signals obtained by either of two methods. The first type of matching is
between “discrete events” (DE’s) which are the first time derivatives of the rising phases of eEJP’s [2], [5]. The second is between “excitatory junction currents” (EJC’s), the extracellularly
recorded equivalents of synaptic potentials [3]. The identification of matched DE’s or EJC’s has in the past been a time consuming and laborious process. It has involved the screening and
short listing of candidate signals from large series of events
based upon visual inspection, followed by verification of suspected matching, again by visual examination. This becomes
cumbersome and unsatisfactory when dealing with large series
of signals, within which two signals that match may be separated from each other sometimes by hundreds of other events.
A further problem with DE analysis is that these signals are obtained after analog filtering whose characteristics are not accurately defined in the literature [2], [5].
Because of these uncertainties, estimates of probabilities
of release from autonomic nerve release sites have undergone
sweeping revisions, based upon the criteria used for identification and classification, from an earlier value of as high as 0.5
[2] to as low as 0.001 in subsequent work [5]. In view of these
problems, there has existed a requirement for a rapid, objective
and robust method of analysis, preferably automated, that will
facilitate the required characterization.
Our method offers two significant advantages over those
normally used to perform these tasks. First, automation of
the generation of MM from eEJP’s and their classification in
look-up tables facilitates the first-pass detection of candidate
signals whose phases of depolarization would be likely to
match with each other. Thus, in our study, eEJP’s with identical
CD’s separated by as many as 200–300 intervening events
could be rapidly and conveniently marked out using this
method, a task that would have incurred much greater time
and effort if done purely visually. Second, the method does not
suffer from the limitation of subjective assessment in the initial
step of identifying such eEJP’s, ensuring greater reliability. It
is noteworthy that our estimates of probability of activation of
release sites are in accord with those reported from the most
707
rigorous analyses of DE’s and EJC’s to date [10]. We cross
checked the results returned by MM clustering against the
original signals, to verify the presence of presumably matching
depolarizations. The success rate was found to be 95%, i.e.,
in 5% of the cases in which a match was expected, it was not
confirmed on inspection of the eEJP’s. The reason for these
“failures” remains to be investigated; however, it does not
detract from the utility of the method in detecting possible
matches.
B. Identification of Quantal Evoked Depolarizations
Preliminary analysis had indicated [14], that the alkanol
1-heptanol reveals the qEJP’s in smooth muscle. This result
constitutes the first direct intracellular detection of quantal
evoked depolarizations in smooth muscle.
The present analysis has helped substantiate this hypothesis
by showing that the accepted criteria for quantal evoked depolarizations in smooth muscle are satisfied by qEJP’s (see Section III). Thus, we have established that a depolarization identical to the sEJP is indeed the quantal event underlying the eEJP
in smooth muscle. The relatively brief qEJP would then occupy
mainly the rising phase of the eEJP, the remainder of the eEJP
being generated by passive decay of neurotransmitter-injected
charge through the smooth muscle membrane impedance, as
postulated earlier [6]. Our results, therefore, establish the usefulness of time-frequency methods in addressing issues related
to the electrical behavior of postsynaptic elements.
C. Mechanism of Heptanol Effect
Our results point also to the potential utility of the new
method in exploring the biophysical effects of drug action.
For instance, the chemical used here, 1-heptanol, has been
reported to specifically disrupt cell-to-cell communication in
smooth muscles mediated by gap junctional channels [4]. If
heptanol blocks cell-to-cell communication one would expect
an increase in the input resistance of the tissue which would
modify the amplitude and time course of the CD’s, qEJP’s,
and sEJP’s. However, none of these changes were observed in
experiments we conducted.
The range of effects of heptanol, and our demonstration that
the qEJP is an sEJP-like quantal event, indicate an additional or
different mechanism of action for this chemical, viz. that it may
be lowering the probability of evoked transmitter release from
autonomic neurons. A more detailed application of time-frequency analysis methods to junction potentials in the presence
of heptanol should help clarify this issue.
V. CONCLUSION
Our work shows that the application of wavelet-based timefrequency analysis to cellular bioelectric signals holds promise
in exploring the biophysics of synaptic neurotransmission. Although our conclusions relate to the functioning of peripheral
autonomic neurons, these methods will be equally applicable
at other sites, including those in the central nervous system,
where time-frequency features of synaptic potentials can provide insight into physiological processes. Such studies can be
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IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 47, NO. 6, JUNE 2000
extended to the study of synaptic plasticity where neuronal release probabilities are suspected to change. Finally, the methodology should allow convenient scrutiny of the actions of either
externally introduced drugs or physiological parameters (e.g.,
Ca levels and pH) that alter the configurations of synaptic potentials and thus affect information transfer during neurotransmission.
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Priya Vaidya received the B.E. degree in electronics
and telecommunications from the Government
College of Engineering, University of Pune, India,
in 1996, and the M.Tech. degree in biomedical
engineering from the Indian Institute of Technology,
Bombay, India, in 1998. She is working toward the
Ph.D. degree in the Department of Electrical and
Computer Engineering, University of Massachusetts,
Amherst.
Her research interests are in image processing and
biomedical signal analysis.
K. Venkateswarlu received the B.E. degree in
biomedical engineering from Osmania University,
Hyderbad, India, in 1988 and the Ph.D. degree in
biomedical engineering from the Indian Intitute of
Technology, Bombay, India, in 1998.
He worked in industry as a Maintenance Engineer
from 1989 to 1992 and also taught biomedical instrumentation for a brief period in 1992. Since August
1998, he has been working as a Postdoctoral Fellow
in the Department of Urology at Albert Einstein College of Medicine of Yeshive University, New York.
His research interests include electrophysiology of smooth muscle, roles of gap
junctions in syncytial behavior of smooth muscle, and autonomic neuroeffector
mechanisms.
Uday B. Desai (S’75–M’78–SM’96) received the B.
Tech. degree from the Indian Institute of Technology,
Kanpur, India, in 1974, the M.S. degree from the
State University of New York, Buffalo, in 1976, and
the Ph.D. degree from the Johns Hopkins University,
Baltimore, MD, in 1979, all in electrical engineering.
From 1979 to 1984, he was an Assistant Professor
in the Electrical Engineering Department at Washington State University, Pullman, and an Associate
Professor at the same university from 1984 to 1987.
Since 1987, he has been a Professor in the Electrical
Engineering Department at the Indian Institute of Technology-Bombay, India.
He has held Visiting Associate Professor’s positions at Arizona State University,
Tempe, Purdue University, West Lafayette, IN, and Stanford University, Stanford, CA. His research interests are in the areas of computer vision, artificial
neural networks, image processing, adaptive signal processing and its application to communication, and wavelet analysis. He is the Editor of Modeling and
Applications of Stochastic Processes (Boston, MA: Kluwer Academic, 1986).
Rohit Manchanda received the B.A. degree (with
honors) from the University of Oxford, Oxford, U.K.,
and the M.A. degree in physiological sciences. He
received the D.Phil degree from Oxford University
in 1989, working on the electrophysiology of autonomic neurotransmission in the Department of Pharmacology.
Since 1991, he has been an Assistant Professor,
and since 1997 an Associate Professor, in the Interdisciplinary Programme in Biomedical Engineering
at the Indian Institute of Technology, Bombay, India.
His research interests are in the electrophysiolology and biophysics of neurotransmission, employing experimental as well as theoretical approaches, and in
the application of signal processing techniques to synaptic potentials.
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