Spike firing allometry in avian intrapulmonary chemoreceptors: matching neural code to body size
1 Department of Biological Sciences, Northern Arizona University, Flagstaff,
AZ 86011-5640 USA
2 Division of Biological Sciences, The University of Montana, Missoula, MT
59812 USA
3 Department of Respiratory Care, Boise State University, Boise, ID 83725
USA
4 Department of Biology, Bates College, Lewiston, ME 04240 USA
5 Division of Physiology, Department of Medicine, University of California
San Diego, La Jolla, CA 92093-0623 USA
* Author for correspondence (e-mail: steven.hempleman{at}nau.edu)
Accepted 14 June 2005
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Summary |
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Key words: allometry, body size, bird, intrapulmonary chemoreceptors, neural coding
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Introduction |
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An exception to frequency scaling occurs in the nervous systems of animals.
Maximal action potential (spike) generation rate in neurons is relatively
fixed in animals of varying size because of the highly conserved genetics and
kinetics of voltage-gated ion channels. Ion channel kinetics and gating are
key determinants of transmembrane ionic fluxes, and control the width, shape
and refractory periods of action potentials. The interplay of expressed ion
channels in axonal membranes sets a practical upper limit for spike frequency
at approximately 300 s1 in most neurons, but normal
discharge rates are usually much slower even in very small animals
(Hille, 1992).
Action potential spike trains are the mechanism for long distance
information transmission in the nervous system. In general, neural information
may be `rate coded,' with average spike rate over a time period encoding
stimulus intensity, or `time coded,' with the occurrence of a single spike (or
spike burst) encoding the occurrence of a rapid stimulus transition
(Rieke et al., 1999). Rate and
time codes are not mutually exclusive: `partially adapting' sensory neurons
are common, and have both tonic (rate coded) and phasic (time coded) discharge
responses (see below).
Rate codes are probably the most intuitive spike coding format in the
nervous system (Rieke et al.,
1999). This is the code observed in `tonic' sensory receptors that
detect slowly changing sensory input. However, a rate code requires
transmission of relatively many action potentials to describe the sensory
stimulus, because the stimulus amplitude is encoded as time-averaged spike
discharge rate. Since it takes time to generate these action potentials, the
maximal stimulus frequency that can be rate encoded is considerably less than
the maximum possible spike discharge frequency.
As the stimulus frequency increases, a rate code becomes inadequate (not
enough time for the needed number of spikes), but a timing code can still
transmit information. In a timing code, the occurrence of one spike or a rapid
burst of spikes indicates that an abrupt phasic change in stimulus intensity
has occurred (Rieke et al.,
1999). However, time coding is ineffective for indicating steady
(tonic) stimulus levels.
The range of stimulus frequencies that can be encoded by a sensory neuron may be thought of as its `bandwidth'. Since rate codes accurately represent low (tonic) stimulus frequencies, and timing codes accurately represent high (phasic) stimulus frequencies, the bandwidth of a neuron can be broadened by incorporating features of both rate and time coding. This broadening of bandwidth is seen in sensory receptors that are partially adapting having both phasic and tonic responses.
Limited sensory bandwidth may have adverse fitness consequences if detection of fast sensory input is needed to avoid predation, detect prey or mates, or maintain homeostasis. It is not surprising, then, that several mechanisms for neural coding of rapid signals have evolved. These include the phasically responding (partially and rapidly adapting) receptors mentioned previously. Other mechanisms include specialized sensory organs that are `tuned' to detect higher stimulus frequencies. For example, in the vertebrate ear, sensory hair cells arrayed along the basilar membrane of the cochlea use an anatomical place code (their position along the frequency-tuned membrane) to encode stimulus frequency, and a rate code (their spike discharge rate) to encode stimulus amplitude.
We hypothesized that some phasic physiological traits, like breathing
rates, which scale to approximately
Mb1/4
(Lindstedt and Calder, 1981),
are slow enough in large animals to be adequately represented using a neural
rate code, but are rapid enough in small animals to require at least some
elements of a neural timing code for effective signal processing. If true,
this would provide the first evidence for allometric scaling of neural coding.
Clearly, spike rate codes are well known in sensory systems dealing with low
frequency signals (tonic receptors), and spike timing codes are well known in
sensory systems dealing with high frequency signals (phasic or adapting
receptors); however, the transition between these two coding systems in a
single sensory system due to variation in body mass (i.e. allometry of neural
coding) has never been investigated. We tested for neural coding allometry by
measuring action potential spike trains from sensory neurons (intrapulmonary
chemoreceptors, IPC) that detect lung CO2 oscillations linked to
breathing rate, in birds ranging in body mass from 0.045 kg to 5.23 kg. We
found that phasic action potential discharge pattern (peak discharge rate and
magnitude of spike frequency adaptation, both in units of spikes
s1) scaled between
Mb0.23 and
Mb0.26, like breathing rate. We suggest
that body-mass-dependent changes in the neural coding of phasic signals
preserves information transmission rates for high frequency signals in IPC
(and perhaps other) sensory neurons.
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Materials and methods |
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Surgical preparation and unidirectional ventilation
Birds were restrained in dorsal recumbency and polyethylene catheters
inserted into the left brachial artery and vein using a local anesthetic
(Lidocaine HCl). Each bird was then anesthetized with sodium pentobarbital
(2090 mg kg1 i.v. initially; supplementary doses of
415 mg kg1 h1 i.v. or as needed).
In some quail, induction of surgical anesthesia with pentobarbital was
followed by injections of urethane (12 mg min1 i.v.
or as needed). Arterial blood pressure and body temperature in most birds were
continuously monitored during and following induction of deep surgical
anesthesia (Kilgore et al.,
1985). Colonic temperature (Tb) was regulated
to 41±1°C in all birds except lovebirds, where
Tb was regulated to 40±1°C.
Unidirectional ventilation followed previously described procedures
(Hempleman and Bebout, 1994;
Hempleman et al., 2000
). In
birds where each lung was independently ventilated, airflow through the two
lungs exceeded reported ventilatory flow rates by an average factor of
1.11.9. All lovebirds, most of the quail and two ducks were
unidirectionally ventilated with a continuous stream of warmed, humidified gas
that was delivered via an endotracheal tube, and exited the opened
interclavicular air sac (Hempleman et al.,
2000
; Shoemaker and Hempleman,
2001
). Insufflation rates exceeded published ventilatory flow
rates in these birds by a factor of 45. Carbon dioxide was added to the
ventilatory gas stream going to the left lung or through the trachea with an
electronic valve to make step changes in lung CO2 concentration
between low (01%) and high (5%7%;
Hempleman and Bebout, 1994
;
Hempleman et al., 2000
).
Arterial blood gases were periodically assessed to ensure the adequacy of
ventilation. Arterial samples were anaerobically drawn into heparinized
syringes and analyzed with a blood gas system
(Hempleman and Bebout, 1994
).
CO2 and O2 concentrations in the ventilation streams
were measured with a respiratory mass spectrometer or separate gas analyzers
(Hempleman and Bebout,
1994
).
Neural recording
Extracellular single-unit action potentials were recorded from fine vagal
filaments under mineral oil using Pt-Ir and Ag-AgCl electrodes coupled with a
Grass HIP511 high impedance differential probe to a Grass P511K AC
preamplifier (West Warwick, RI, USA). Vagal filaments were divided by
micro-dissection until action potentials from only a single IPC were evident
in the electrical recording. IPC were identified by their prompt response to
step reductions in ventilatory CO2, and single IPC action
potentials were identified by the constant shape and amplitude of their spike
waveform (Hempleman and Bebout,
1994; Hempleman et al.,
2000
; Shoemaker and Hempleman,
2001
). Occurrence times of action potentials and CO2
stimulus steps were recorded on-line using an Intel 8085-based interrupt
driven assembly language program sampling at 14 500 s1
(Hempleman and Bebout, 1994
;
Hempleman et al., 2000
;
Shoemaker and Hempleman,
2001
). Data were analyzed off-line to produce cycle triggered
stimulus histograms (averaged spike frequency vs time) and raster
plots (spike occurrence vs time) of IPC spike activity (e.g.
Fig. 1). Statistical analyses
(ANOVA and linear regression) were performed using SAS JMP-IN (v.4) on a
Microsoft Windows 2000 platform.
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Allometric equations for phasic discharge during down-steps in ventilatory CO2
Cycle triggered stimulus histograms from each IPC were used to tabulate
species mean values of two indices of phasic discharge to a CO2
down-step: (1) peak discharge rate and (2) magnitude of spike frequency
adaptation, both in units of inverse time (s1;
Fig. 1C). Spike frequency
adaptation is the burst-like roll-off in spike frequency after a stimulus step
despite maintained stimulus intensity
(Hille, 1992). These indices
were compared among species with ANOVA. We fit measurements of body mass
(Mb) and peak discharge rate or magnitude of spike
frequency adaptation (y) to the allometric equation
(y=aMbb) using a log-log regression
[log(y)=bx(logMb)+log(a)] to obtain the
power function (b) and the proportionality constant (a).
Phylogenetically independent contrast analysis of phasic discharge data
Since linear regression of multi-species data assumes phylogenetic
independence of subjects, violations of independence may affect the accuracy
and confidence limits of the calculated mass exponent (b) and phylogenetic
constant (a) (Garland et al.,
1993). Some birds in our study had closer phylogenetic ties than
others (Frappell et al., 2001
),
so we tested the effect of phylogenetic relatedness using PDAP (Phenotypic
Diversity Analysis Programs), version 6.0 (Garland et al.,
1993
,
1999
;
Garland and Ives, 2000
) running
in DOS on a Pentium III based Dell Optiplex GX150 PC. Phylogenetically
corrected allometric mass exponents and constants (with their standard errors)
calculated with PDAP are reported below.
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Results |
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Fig. 3 shows the mean peak IPC discharge rates from the five species we studied (symbols wholly or partly red) and also includes mean peak IPC discharge rates from the avian species published in the literature (emu, chicken, muscovy duck, mallard duck and Pekin duck: symbols wholly or partly in green). One species, Anas platyrhynchos, representing the wild mallard duck and domestic Pekin duck, was studied by us and also by others (Table 2). The average of all mean peak discharge rates for Anas platyrhynchos IPC, weighted by the number of observations in each study, is shown as a green square with a red border in Fig. 3. Regression analyses included all data plotted in Fig. 3.
Phylogenetic correction produced negligible changes in the allometric regression equations for peak frequency and the magnitude of spike frequency adaptation, but did increase the estimates of the standard error (Table 3). With CO2 step decreases, log-log regression analysis with phylogenetic correction showed that peak IPC discharge rate scaled to Mb0.231 (Fig. 3, heavy gray line, r2=0.715), and the magnitude of IPC spike frequency adaptation scaled to Mb0.224 (Fig. 4, heavy gray line, r2=0.761). The phylogenetically corrected mass exponent for peak frequency was again different from zero (P<0.05), but the 95% confidence interval for the corrected magnitude of spike frequency adaptation mass exponent marginally included zero (P=0.055). This is considered further in the Discussion.
We observed both tonic IPC and phasically adapting IPC in all of the species studied; however, the magnitude of the adaptation differed among species (P<0.05), as noted above and shown in Figs 2 and 4. Fig. 5A shows spike discharge characteristics of a partially adapting quail IPC: it has a prompt on-response to the stimulus, and the magnitude of spike frequency adaptation is large. Fig. 5B shows a minimally adapting (tonic) quail IPC from our study: it maintains a steady discharge at a given CO2 stimulus, with little adaptation.
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Discussion |
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For effective sensory feedback, spike trains of IPC must encode information
about lung CO2 that oscillates between 0% and
6% at the
normal breathing frequency, which varies with metabolic rate and size
(Powell et al., 1981
). We
found that the allometric scaling of IPC peak frequency and the magnitude of
IPC spike frequency adaptation ranged from
Mb0.224 to
Mb0.263, which matched the allometric
scaling of breathing rate at about
Mb1/4. On the one hand this might be
expected because mass-scaling exponents of this size and sign are
characteristic of most biological frequencies (e.g. heart rate, breathing
rate, gait frequency). However, to our knowledge this is the first time that
allometric scaling of phasic peak spike discharge frequency and the magnitude
of spike frequency adaptation has been reported in any class of neurons. The
observation suggests a mechanism for continuous adjustment of neural coding in
sensory spike trains, from a rate code when stimulus signals are of low
frequency relative to the maximal possible action potential discharge rate,
towards a time code when stimulus signals driving action potential discharge
have a higher frequency. Over the body mass range we studied here, most
allometric adjustments to IPC discharge occurred in terms of peak frequency.
However, the significantly increased magnitude of spike frequency adaptation
in smaller birds also suggests the emergence of rate coding in their IPC spike
trains.
Scaling of peak discharge frequency to phasic stimulation
We propose that scaling of peak IPC discharge rate (spikes
s1) with Mb1/4 is an
important feature of IPC neural function. IPCs detect breath-by-breath
fluctuations in lung CO2, and transmit spike-encoded feedback
information to the brainstem to help match breathing pattern to metabolic
demands (Hempleman and Posner,
2004). Because the frequency of CO2 fluctuations sensed
by IPC is set by the breathing rate (breaths s1), which
scales to Mb1/4, and this is matched by
IPC peak discharge frequency (spikes s1), which also scales
to Mb1/4, our results indicate that the
mean number of IPC spikes transmitted per breath [(spikes
s1)/(breaths s1)=(spikes
breath1)] is approximately independent of body mass
[(Mb1/4)/(Mb1/4)=Mb0].
Because action potentials are the fundamental unit of information transfer
along axons, the higher peak discharge rates in IPC of smaller birds help
compensate for the smaller birds' intrinsically shorter breath durations and
higher breathing rates.
Matching spike code to biological time
An example of the temporal challenge of increased breathing rate on IPC
spike transmission is shown in Fig.
6, modified from Stoll et al.
(1971). Here, spike discharge
from a chicken IPC was recorded while the bird was ventilated with a variable
flow of CO2 (0.41.6%) at 10, 20, 40 and 80 cycles
min1. The average breathing rate for a 1.9 kg chicken is
about 20 breaths min1
(Frappell et al., 2001
). As
shown in Fig. 6, decreasing
lung CO2 causes increases in IPC discharge rate
(Hempleman and Posner, 2004
;
Molony, 1974
). At 20 cycles
min1, changes in IPC spike frequency faithfully follow the
sinusoidal variations of carbon dioxide, and there are ample numbers of spikes
generated during the cyclic increases and decreases in CO2 to
encode the associated changes in CO2 as changes in spike frequency
(i.e. spike rate coding; Rieke et al.,
1999
). However, at higher cycle rates the changes in spike
frequency become less distinct, and there is less time for spike transmission
within each cycle. At 80 cycles min1, spike rate coding is
sparse. If this particular IPC were capable of a higher peak spike frequency
(as naturally occurs in IPC of smaller birds; Tables
1,
2), it might have retained its
ability to rate-encode CO2 changes at cycle rates of 80
min1 or above. The resting breathing rate for a 0.004 kg
hummingbird is much higher than the frequencies shown here, about 173 breaths
min1 (Frappell et al.,
2001
), so IPC in small birds somehow meet this temporal
challenge.
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Scaling the magnitude of spike frequency adaptation
We also observed Mb1/4 scaling of the
magnitude of spike frequency adaptation in IPC, which suggests yet another
mechanism for transmitting information about high frequency CO2
signals: the magnitude of IPC spike frequency adaptation is larger in smaller
birds (Table 1, Figs
2,
4).Adapting sensory neurons
(e.g. Fig. 5A) produce spikes
in response to phasic changes in their adequate stimulus (which in IPC is the
abrupt down-step of intrapulmonary CO2 that sweeps through the lung
during each inspiration), but are less responsive to tonic stimuli. Spike
frequency adaptation helps focus on the phasic features of a stimulus and
encodes them as relatively short bursts of action potentials signaling the
stimulus transition. This bursting is thought to represent a `timing code',
which allows a few spikes from a single sensory fiber to convey information
about higher stimulus frequencies than would be possible with the rate code
described above (Rieke, 1999).
We noticed that all birds generally had both partially adapting IPC and tonic IPC (e.g. Fig. 5A,B), but in varying proportions depending on the birds' body size. As seen in Fig. 2, the averaged CO2 step responses of IPC in large birds were mostly tonic in character with a small magnitude of spike frequency adaptation (perhaps emphasizing IPC spike rate coding at their slower breathing rates). In contrast, the averaged CO2 response of IPC in smaller birds had larger magnitudes of spike frequency adaptation and less tonic character (perhaps emphasizing IPC spike time coding at their higher breathing rates). If this allometric relationship extends to the smallest Aves, we predict that 4 g hummingbirds should have IPC with exceptionally large magnitudes of spike frequency adaptation and peak discharge to phasic stimuli, and little tonic character.
Spike frequency adaptation can be characterized by its magnitude (discussed above) and also by its rate. The rate of adaptation quantifies how rapidly spike discharge declines after a step change to a higher stimulus level. Even though the magnitude of spike frequency adaptation was mass dependent among the species (P<0.05), the relative rate of spike frequency adaptation (% change in discharge frequency over time) was not (P>0.05). This is apparent in Fig. 2.
Phylogenetic independent contrasts
We were concerned that phylogenetic non-independence among our subject
animals may have biased our estimates of allometric body mass exponents.
However, correcting the estimates using the Phenotypic Diversity Analysis
Programs (`PDAP'; Garland et al.,
1993,
1999
;
Garland and Ives, 2000
)
resulted in essentially identical mass exponents for scaling both peak
frequency and spike frequency adaptation, with somewhat larger standard errors
and confidence limits (Table
3). With phylogenetic correction, the mass exponent for peak
discharge remained significantly different from zero (P<0.05) but
the exponent for spike frequency adaptation became marginally insignificant
(P=0.055). While post-correction insignificance of the adaptation
exponent may indicate true mass independence, it is perhaps more likely
related to sample size. The adaptation exponent value remained essentially the
same at 0.22 after phylogenetic correction; and because it is common
for variance of estimated exponents to increase after phylogenetic correction
(Frappell et al., 2001
), the
marginal insignificance (5 parts in 1000) may represent a type II error, which
could be remedied by increasing sample size. In the future we hope to increase
statistical power with new experiments on larger or smaller birds to further
test the phylogenetically corrected adaptation exponent.
Possible biological basis for spike frequency scaling
Since receptor endings of IPC are probably the sites of spike initiation,
but IPC receptor endings have never been isolated or studied, we can only
speculate on the origins of allometric differences in spike coding. General
membrane biophysics suggests that peak discharge rate and spike frequency
adaptation should be dependent on the magnitude of the generator potential
produced at the sensory endings, and on the ability of the sensory neuron to
generate and recover from action potentials extremely rapidly. These actions
would be influenced by the type, number and distribution of ion channels,
transmembrane ion exchangers, and active membrane pumps expressed in the
receptor endings, which may in turn be affected by the developmental
programmes for animals of different sizes. To test these hypotheses, IPC
receptor endings must be identified, and transmembrane voltage and current
recordings made from functioning IPC. This remains a problem for future
study.
Conclusions
Maximal action potential frequency is limited in most neurons to about 300
s1 or less, due to the relatively invariant genetics of
voltage-gated Na+ and K+ channels underlying spike
generation (Hille, 1992).
Spike-frequency bandwidth limitation is known to cause variations in spike
coding strategy when comparing sensory receptors that normally respond to
tonic signals, to sensory receptors that normally respond to phasic signals.
Well-known examples, especially in mechanoreceptors, include the `rate code'
commonly associated with slowly adapting receptors, and the `timing code'
commonly associated with rapidly adapting receptors
(Rieke et al., 1999
). Here we
provide evidence for a systematic allometric shift in the neural spike code of
avian intrapulmonary chemoreceptors observed in birds of body size varying
over 2.7 orders of magnitude. The magnitudes of peak spike frequency and spike
frequency adaptation both scaled with body mass to approximately
Mb1/4. This scaling matches the known
Mb1/4 scaling of breathing rate with
body mass, and may help preserve the amount of spike-coded information
available as breath duration decreases with body mass.
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Acknowledgments |
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References |
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