 |
INTRODUCTION |
When certain neurons
are subjected to repeated presentations of an identical stimulus, the
action potentials encoding the stimulus information have variable
responses between presentations (Arieli et al. 1996
;
Britten et al. 1993
; Dean 1981
; de
Ruyter van Steveninck et al. 1997
; Hunter et al.
1998
; Mainen and Sejnowski 1995
; Rieke et
al. 1997
; Rose et al. 1969
; Schiller et
al. 1976
; Shadlen and Newsome 1998
;
Snowden et al. 1992
). While such variability is thought
to be important in the processing of information by neurons in the CNS
(de Ruyter van Steveninck et al. 1997
; Mainen and
Sejnowski 1995
; Rieke et al. 1997
;
Shadlen and Newsome 1998
), its potential role in
peripheral neurons has not been appreciated (Koltzenburg et al.
1997
; Merzenich and Harrington 1969
). One central issue is whether such variability is utilized in the transfer of information (de Ruyter van Steveninck et al. 1997
;
Gerstner et al. 1996
; Pei et al. 1996
;
Rieke et al. 1997
) or whether it is merely a stochastic
effect attributable to some underlying process. In other words, does a
neuronal system reliably encode due to or in spite of such variability?
A key to the resolution of this question is the determination of the
source of the variability, as well as the deduction of an underlying
mechanism for its generation. Here we report that when
mechanoreceptors, recorded in isolated skin, are stimulated with
mechanical sinusoids, the timing of responses in relation to the
stimulus exhibits nonstationary, wavelike variability.
 |
METHODS |
Rapidly adapting (RA) mechanoreceptor neurons were recorded in a
preparation of skin and nerve that was isolated from the hindlimb of
adult rats, and studied in vitro. Single guard hair afferents were
activated by moving hairs using periodic (sinusoidal) stimuli. We were
interested in the phase relationship between the stimuli and the
responses of individual neurons.
Preparation
Adult rats were anesthetized with pentobarbital sodium
(Nembutal), administered intraperitoneally. The experimental
preparation was an isolated sample of skin and nerve, taken from the
inner thigh, and studied in vitro. The fur along the thigh was clipped to a length of approximately 2 mm. Then the skin sample, approximately 14 mm square, was excised along with its sensory innervation, a branch
of the saphenous nerve. The sample was removed to an apparatus where it
was maintained in a bath of artificial interstitial fluid kept at room
temperature (20°C). The skin was supported from underneath by a
platinum mesh. Thus the under side of the skin was maintained in the
bath while the upper surface was dry. The cutaneous nerve was pulled
into a small oil-filled plastic chamber for recording. The nerve was
dissected into small fibers that were placed on a fine gold wire
electrode for recording. The indifferent electrode was placed in the
bath. Signals were amplified with a PARC 118 amplifier and filtered
with a Riverbend Electronics Learning Filter. Guard hair afferents were
sought by gently stroking the clipped hairs while recording from
fibers. Recordings were often made from filaments containing several
active neurons whose active hairs in the skin were far enough apart to allow them to be stimulated independently of each other.
Stimulation
When a suitable afferent was identified, the appropriate hair
was actuated with a mechanical stimulator that consisted of a Cambridge
Technology 300B lever system. This is a DC servomotor that rotates a
shaft through controlled angular displacements. The motor actuated a
60-mm-long cantilever whose tip was brought into contact with the hair.
The displacements that we used were small (<0.5 mm) so that the motion
of the tip was essentially linear. The stimulator had a mechanical
bandwidth of 0 to approximately 120 Hz. Stimuli were
displacement-controlled sinusoids. Stimulus waveforms, along with a
synchronization pulse, were generated with a Wavetek waveform
generator. The stimulus amplitude was adjusted so as to elicit one
spike per cycle and was kept constant throughout experimental runs. The
phase of each action potential was measured in relation to the stimulus
waveform (Del Prete and Grigg 1998
; Hunter et al.
1998
; Neiman et al. 1999
; Read and Siegal 1996
).
Data collection
Both mechanical and neuronal data were acquired using a
Cambridge Electronic Design micro 1401 data acquisition system. We collected four analog signals. Two signals represented actuator position and the force applied by the actuator. In addition, we acquired the synchronization pulse that denoted the start of each stimulus cycle and the amplified neural recording. The data acquisition rate for the position and force signals was 500 Hz, and the acquisition rate for the synchronization pulse and neuronal spikes was 500 kHz.
Data analysis
The phase of the ith spike relative to the
synchronization pulse is defined as
|
(1)
|
where si and
zi are the spike and syncronization times
(si > zi),
and f is the frequency of indentation. Defined in this way,
the phase has units of radians and is a measure of the threshold or
excitability of the mechanoreceptor system, i.e., it
represents the magnitude of indentation required for action potential generation.
The continuous wavelet transform (CWT) of a time series
(t) of length T is given by
|
(2)
|
It is a measure of the degree to which the function
(t) is periodic, with period proportional to the scale
parameter s, and at a particular time denoted by
. The
function
(t) is typically of Gaussian form (with compact
support), and we utilized the function
|
(3)
|
The scale parameter s in Eq. 2 is
proportional to the width of the Gaussian and is, by analogy with the
fast Fourier transform, a measure of the period of the signal.
Operationally, the meaning of the wavelet transform can be illustrated
as follows. Since the CWT is a function of both time and scale,
consider fixing the width of the Gaussian in Eq. 2 by
letting s = 1 and superimposing it along with the time
series at time t = 0. Then the CWT for
= 0 and
s = 1 is obtained by integrating Eq. 2 over
time, and physically, this corresponds to the degree to which the
Gaussian function and the time series overlay; i.e., the value of their convolution (the prefactor 1/
s is necessary for
normalization purposes so that the transformed signal will have the
same "energy" for each s). The Gaussian (at scale
s = 1) is then translated in time to the location
t =
, and the integral is recomputed to obtain the
CWT at t =
and s = 1 in the
time-frequency plane. This procedure is repeated until the Gaussian has
been translated to the end of the time series, resulting in the
calculation of the CWT for fixed s, i.e.,
(
,
s = 1). Then, s is increased by a small
value and the entire procedure is repeated. Note that this is a
continuous transform, and therefore both
and s must be
incremented continuously. However, since the CWT is obtained numerically, both parameters are increased by a sufficiently small step
size, which corresponds to sampling the time-scale plane.
 |
RESULTS |
Data were collected from 14 neurons, and the results presented
below are representative of the qualitative features observed in all of
the neurons. Figure 1 shows the phase
behavior of a typical neuron. The response shows a gradual,
time-dependent increase in phase, a signature of the adaptation
process. In addition, the variability of the response increases with
time. We find that there is significant structure to the variability,
which is seen to exhibit waves (Fig. 1, inset). To quantify
the properties of the waves, Fourier analysis was utilized. The power
spectrum of an entire data run of 300-s exhibits peaks at 0.18 and 0.50 Hz (Fig. 1B). Since the time series appears to be
nonstationary, we investigated the temporal properties associated with
the oscillations by partitioning the data into four sequential segments
and analyzing each independently. We found significant qualitative
differences in the power spectra generated from quarter segments in the
data sets. For example, the power spectrum obtained using the first quarter of the time series in Fig. 1A does not clearly
exhibit the 0.18- and 0.50-Hz maxima seen in Fig. 1B.
However, analysis of the second and third quarter segments reveals
significant power at these frequencies and, in addition, the birth of
substantial peaks at low frequencies. Analysis of the fourth quarter
segment exhibits maxima at 0.18 and 0.50 Hz, but relatively little
low-frequency content.

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Fig. 1.
Typical phase data from a mechanoreceptor. A trigger pulse is generated
at the beginning of each actuation cycle, so that data collection
periods contain the times of the trigger pulse and any subsequent
action potentials. The phase, which represents the excitability of the
mechanoreceptor response, is defined as i = (si zi)2 f, where
si and
zi are the spike and trigger times
(si > zi), and f is the
frequency of actuation. A: data for a 15-Hz stimulus
frequency. During the entire run, the phase is bounded by /2 as the
mechanoreceptor is responding to the inward motion of the indenter. The
phase slowly increases, indicating a slow decrease in excitability,
which is likely due to adaptation. Inset: a section of
the data is displayed at higher resolution, elucidating oscillations in
the phase data. B: the power spectrum of the phase data
in A. There are 2 distinct maxima at 0.18 and 0.50 Hz,
along with a strong peak at very low frequency.
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|
Wavelet analysis is well-suited for describing a nonstationary time
series such as the phase data in Fig. 1A. While the
classical Fourier technique yields information only in the frequency
domain, the wavelet approach quantifies periodicity in both the time
and frequency domains and is thus capable of elucidating the nature of
the time-dependent oscillatory regions noted above (see the caption of
Fig. 2 for the definition of the
continuous wavelet transform). Figure 2 shows the fluctuations in
frequency and power during the run depicted in Fig. 1. We observe phase
oscillations of several different frequencies and find that, at times,
these waves exhibit a significant frequency drift. Such a variable
response is of interest for two primary reasons. First, since the
current opinion on population coding is that the function of a
population of neurons is to produce responses in phase with a common
stimulus, variability in the responses of single afferents should
adversely affect this function. Further work is thus needed to
determine what effect the waves have on the degree of synchronous
behavior observed in groups of cells with a common stimulus. Second,
the waves may provide insight into peripheral mechanisms involved in
mechanoreceptor activation.

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Fig. 2.
Time-period diagrams obtained from a continuous wavelet analysis of the
phase data in Fig. 1A. A: there are
oscillations of several different periods, and, at times, there is
significant frequency drift. The frequency drift is quite noticeable
from 40 to 100 s and again from 150 to 200 s. The regions
from 100 to 140 s and 200 to 250 s indicate coexisting waves
of several different periods. B: a blowup of the time
scale reveals more precisely dominant periods of approximately 2 and
6-8 s, respectively. These correspond to the peaks in the power
spectrum of Fig. 1B.
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It is perhaps natural to conjecture that the adaptation process is
somehow responsible for the oscillatory behavior. For example, in
vertebrate auditory hair cells, the firing of an action potential induces a transport of calcium cations into the neuronal cell (Lumpkin and Hudspeth 1998
; Lumpkin et al.
1997
). These cations then act to increase the firing threshold
through their interaction with the ion channel gating process. Thus for
a periodic stimulus, each drive period could lead to a buildup of
intracellular calcium, provided passive mechanisms responsible for
export are unable to keep pace with the drive. Oscillations could then
occur if an active export process, such as the transport of calcium out of the cell by protein pumps (Lumpkin and Hudspeth
1998
), was triggered after a number of actuation cycles. If
such an adaptation mechanism is indeed related to the phase
periodicity, then the wavelet frequency response should depend on the
actuation frequency. In Fig. 3, we plot
representative time-period diagrams for actuation frequencies of 5 and
10 Hz. We observe variable periodicities of approximately 2 and 6 s for multiple stimulus frequencies. Since the stimulus represents the
only periodic signal available to the neuron, it is of interest that
the frequency of the phase response does not appear to be influenced by
the drive frequency.

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Fig. 3.
Representative time-period diagrams for actuation frequencies of 5 and
10 Hz. The data sets were obtained under identical experimental
conditions as the 15-Hz data used in Fig. 2, enabling comparison
between Fig. 3 and Fig. 2B. In all 3 data sets, we
observe periodicities of approximately 2 and 6 s, with the only
major difference being the intermittency at 5 Hz. Compared with the 10- and 15-Hz data, the 5-Hz response shows significantly fewer periodic
regions at low frequency.
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|
If the phase oscillations are linked to some metabolic process, then
one might anticipate a decrease in the frequency of the waves as the
sensory system is cooled. In Fig. 4, we
plot the power spectrum of two sets of representative phase data
obtained at two temperatures for an actuation frequency of 5 Hz. As the temperature is decreased, we observe a significant decrease of approximately 20% in the frequency of the phase response. In Fig. 5, the time-period diagram demonstrates
that the oscillatory response is slowed throughout an entire
experimental run.

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Fig. 4.
The power spectrum of 2 sets of representative data obtained at 2 temperatures for an actuation frequency of 5 Hz. There is a
temperature-induced shift from 0.81 Hz at 20.4°C to 0.62 Hz at
14.3°C. Additionally, at low frequency, there appears to be a 2nd
shift downward, although the power spectrum in this regime renders it
difficult to characterize this change quantitatively.
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Fig. 5.
Time-period diagram obtained from a wavelet analysis of the data used
for Fig. 4. In both sets, there are significant oscillations at many
different frequencies. Both sets have similar structure, and this has
been highlighted with rectangles drawn around what appear to be
complementary regions. By focusing on these regions, note that,
relative to the data at 20.4° (top), the 14.3°
(bottom) data have increased oscillatory periods at
nearly all frequencies. The time delay in the occurrence of the regions
in the bottom diagram is attributable to variations
between data runs and is not a property of the temperature
difference.
|
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DISCUSSION |
The characterization of the waves of excitability reported
here raises several significant issues. Of central importance is our
finding that structured variations occur at the periphery of the
sensory system. While variations in neuronal responses within the CNS
have been the subject of much discussion (Arieli et al.
1996
; Britten et al. 1993
; Dean
1981
; de Ruyter van Steveninck et al. 1997
;
Gerstner et al. 1996
; Mainen and Sejnowski
1995
; Pei et al. 1996
; Rieke et al.
1997
; Rose et al. 1969
; Schiller et al.
1976
; Shadlen and Newsome 1998
; Snowden
et al. 1992
), it has been assumed that periphery responses that
feed the central system are regular. Additionally, since the experiment
entailed the stimulation of individual hairs and therefore single
neurons, the oscillatory response cannot be attributed to a network of neurons. This suggests that the transduction mechanism in these sensory
neurons is more complex than is typically appreciated. The fact that
the waves appear to be independent of the stimulus frequency is
remarkable, given that the only obvious time scales present are those
set by the periodic drive and adaptation process. Perhaps the cells
possess an underlying internal clock that operates independently of the
drive. From an information-transfer point of view, the observed
temperature effects could imply that the excitability waves are
conveying useful information regarding the environment. It is also
conceivable that the oscillations could lead to fractal statistics
similar to those observed in the neuronal spike trains of other
preparations (Ivanov et al. 1999
; Teich
1989
; Teich et al. 1997
). Importantly, models
incorporating correlations in the underlying ion channel kinetics have
been shown to generate nonstationary statistics (Lowen et al.
1999
), and such models might provide insight into the
underlying mechanism for the excitability waves. Along these lines,
further studies are needed to determine whether the phenomenon is a
necessary component of the encoding apparatus or whether the system
simply tolerates its existence.
We thank N. Kopell, A. Neiman, and J. White.
This work was supported by The Fetzer Institute (J. Hasty) and National
Institute of Neurological Disorders and Stroke Grant NS-10783.
Address for reprint requests: J. Hasty, Dept. of Biomedical
Engineering, Boston University, 44 Cummington St., Boston, MA 02215 (E-mail: hasty{at}bu.edu).