Chem. Senses 27: 789-801,
2002
© Oxford University Press 2002
Oscillatory Current Responses of Olfactory Receptor Neurons to Odorants and Computer Simulation Based on a Cyclic AMP Transduction Model
Animal Behaviour and Intelligence, Division of Biological Sciences, Graduate School of Science, Hokkaido University, Sapporo 060-0810, Japan 1 Present address: Department of Fisheries, Wildlife and Conservation Biology, University of Minnesota, 200 Hodson Hall, 1980 Folwell Avenue, St Paul, MN 55108, USA
Correspondence to be sent to: Dr Noriyo Suzuki, Animal Behavior and Intelligence, Division of Biological Sciences, Graduate School of Science, Hokkaido University, Sapporo 060-0810, Japan. e-mail: suzuki{at}sci.hokudai.ac.jp
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Abstract |
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Neural oscillatory activities triggered by odorant stimulation have been often reported at various levels of olfactory nervous systems in vertebrates. To elucidate the origin of neural oscillations, we studied first the oscillatory properties of current responses of isolated olfactory receptor neurons (ORNs) of the rainbow trout to amino acid odorants, using a whole-cell voltage-clamp technique and found that the damped current oscillations were intrinsic in both ciliated and microvillous ORNs and occurred when ORNs were stimulated by odorants at high intensities. Continuous wavelet analysis using the Gabor function revealed that the dominant frequency of oscillations was 1.89 ± 0.50 Hz (mean ± SD, n = 92). There was no significant difference in oscillation frequency between the two types of ORNs and between different perfusion conditions with standard and Na+-free (choline) Ringer's solutions, but there was a slight difference in oscillation frequency between different holding potential conditions of negative and positive potentials. We then performed a computer simulation of the current responses with a cAMP olfactory transduction model. The model was based on the assumption that the current responses of ORNs were linearly related to the sum of concentrations of active cyclic-nucleotide-gated channels and Ca2+-activated Cl- channels, and was expressed by 12 differential equations with 44 different parameters. The simulation revealed that the oscillations of current responses of ORNs were mainly due to the oscillatory properties of intracellular cAMP and Ca2+ concentrations. The necessary reaction component for the oscillations in the transduction model was direct inhibition of adenylate cyclase activity by Ca2+. High Ca2+ efflux by the Na+—Ca2+ exchanger and cAMP-phosphodiesterase activity were most influential on the oscillations. The simulation completely represented the characteristics of current responses of ORNs: odorant-intensity-dependent response, intensity-dependent latency and adaptation. Thus, the simulation is generally applicable to current and voltage responses of ORNs equipped with cAMP olfactory transduction pathway in other vertebrate species. The simulation programs for Macintosh (cAMP 9.2.7 and 9.2.8 for MacOS 8.1 or later) and cAMP JAVA applet versions based on cAMP 9.2.8 have been published on the world wide web (http://bio2.sci.hokudai.ac.jp/bio/chinou1/noriyo_home.html).
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Introduction |
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TopAbstractIntroductionMaterials and methodsResultsDiscussionAppendixDefinition of functions and...References |
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Since the pioneering work on olfactory physiology by Adrian (Adrian, 1955
), neural
oscillatory activities triggered by odorant stimulation have often been
reported at various levels of olfactory nervous systems in a wide variety of
vertebrates: fish (Sutterlin and
Sutterlin, 1971; Tucker and
Suzuki, 1972); amphibians (Ottoson,
1956,
1959a; Takagi and Shibuya,
1960a,
b,
1961;
Hamilton and Kauer, 1989);
reptiles (Tucker, 1975a,
b); birds
(Shibuya and Tucker, 1967);
and mammals (Adrian, 1956;
Ottoson, 1959b;
Mathews, 1972).
The oscillatory activities in the peripheral and higher olfactory nervous
system have recently been restudied in order to determine their role in
odorant information coding. The oscillations of electro-olfactograms (EOGs)
occur in their decay phases in response to different odorants and their
dominant frequencies are 28 Hz in the channel catfish
(Parker et al., 1999)
and 16 Hz in the toad (Nakazawa et
al., 2000). It has been shown
(Parker et al., 2000)
that the dominant frequency of oscillations of summated impulse responses of
small populations of olfactory receptor neurons (ORNs) to amino acid odorants
was 13-37 Hz and that the oscillations were triggered and enhanced by
trisodium citrate with its action of Ca2+ chelation from the
surface of the olfactory epithelium. Optical recordings of odorant responses
from different loci in the turtle olfactory bulb have shown that there are
three different oscillations with different frequencies in the olfactory bulb
(Lam et al., 2000).
Simultaneous recordings of EOGs or summated impulse responses of small
populations of ORNs (peripheral waves—PWs) and summated impulse
responses of small populations of neurons at different bulbar loci (local
field potentials—LFPs) to volatile odorants in the salamander
(Dorries and Kauer, 2000) and
amino acid odorants in the channel catfish
(Nikonov and Caprio, 2001;
Nikonov et al., 2002)
have shown that the PWs and the LFPs are cross-correlated; the frequency and
magnitude of the LFPs increased with PWs and their oscillations are
phase-locked. These studies suggest that the oscillations of both levels share
a common source and are modulated together and that their common source might
be the oscillatory properties of individual ORNs in the olfactory
epithelium.
The characteristic frequency ranges of neural oscillations in different
nervous systems are basically determined by two types of features; one is
patterns of connectivity between neurons and the dynamic properties of the
intervening synapses and the other is the network rhythmicity that arises via
the coupling of oscillatory subunits, each of which possesses an intrinsically
determined frequency preference, although these two features are not mutually
exclusive since network connectivity could reinforce the patterns of
excitation produced by coupled oscillators
(Hutcheon and Yarom, 2000). In
the olfactory nervous system, such independent and intrinsic oscillatory
activities have actually been observed in isolated ORNs
(Frings and Lindemann, 1988)
and in the olfactory bulb slice preparation
(Desmaisons et al.,
1999). Reisert and Matthews (Reisert and Matthews,
1997,
2001a,
b) reported that the
oscillation frequency of isolated ORNs in response to a prolonged odorant
stimulation of 30 s was 0.083-0.28 Hz in the frog and 0.42-2.70 Hz in the
mouse. They suggested that the oscillations might be due to the
Na+—Ca2+ ion exchanger (NCX) mechanisms in the
membrane of ORNs. We also have noticed the oscillations superimposed on
current responses of isolated ORNs from the rainbow trout in our previous
patch-clamp studies (Sato and Suzuki,
2000,
2001).
In the present work, we studied the oscillatory properties of current responses of isolated ORNs from the rainbow trout and performed a computer simulation of current responses of ORNs based on a cAMP transduction model in order to elucidate the origin of oscillations in ORNs. The simulation studies revealed that the oscillations of current responses of ORNs are mainly due to the oscillatory properties of intracellular cAMP and Ca2+ concentrations and that the necessary reaction component for the oscillations in the transduction model is the direct inhibition of adenylate cyclase (AC) activity by Ca2+. High Ca2+ effluxes by NCX and cAMP-phosphodiesterase (cAMP-PDE) activity were most influential on the oscillations. The simulation completely represented the characteristics of current responses of ORNs: odorant-intensity-dependent response, intensity-dependent latency and adaptation.
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Materials and methods |
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TopAbstractIntroductionMaterials and methodsResultsDiscussionAppendixDefinition of functions and...References |
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Whole-cell current recordings of isolated ORNs from rainbow trout
The ORNs of rainbow trout (fork length, 17-20 cm; weight, 60-90 g) obtained
from a local fishery were isolated for whole-cell patch-clamp recordings. Cell
isolation by the Ca2+-free solution method and whole-cell
voltage-clamp recordings using a pressure ejection stimulation system were
performed as described previously (Sato and Suzuki,
2000,
2001). Briefly, both types of
ORNs—ciliated (cORNs) and microvillous (mORNs)—were isolated and
stimulated focally at their cilia or microvilli with a quadruple amino acid
mixture (1.0 or 10 mM: L-Glu, L-Arg, L-Ala and L-Nva) in the perfusion of
standard Ringer's solution (in mM: NaCl, 100; KCl, 3; CaCl2, 2;
MgCl2, 1; D-glucose, 10; HEPES, 5; NaOH, 2.2; pH 7.4) or
Na+-free (choline) Ringer's solution (in mM: choline-Cl, 100; KCl,
3; CaCl2, 2; MgCl2, 1; D-glucose, 10; HEPES, 5; NaOH,
2.2; pH 7.4) in order to record Ca2+-activated Cl- ion
channel current responses. The calibration of the waveforms of ejected odorant
pulses, examined by measuring liquid junction currents and voltages, confirmed
that there were no measurable bumps superimposed on the odorant pulses. The
recording pipette was filled with K+-internal solution (in mM: KCl,
93; EGTA-2K, 5; HEPES, 5; ATP-2Na, 1.0; GTP-Na, 0.1; KOH, 2.26; pH 7.4] and
its resistance was 8-12 M
. The recording pipette was connected via a
silver—silver-chloride (Ag—AgCl) wire to the headstage of a
patch-clamp amplifier (CEZ-2200; Nihon Kohden, Tokyo). The reference electrode
was an Ag—AgCl plate immersed in the bath solution. Current signals were
low-pass filtered at 3 kHz and stored on magnetic tape using a PCM data
recorder (DC-13 kHz bandwidth; PCM-501ES; Sony, Tokyo) for later off-line
analysis.
Analysis of oscillatory properties of current responses
Current response data for a period of 5 or 15 s were first low-pass
filtered at 40 Hz (4 dB/oct, Butterworth) and digitized at 200 Hz sampling
speed using PowerLab Chart 3.6.8 (AD Instruments, Mountain View, CA) on a
Power Macintosh computer and the data for each record were transformed into
the file format for Igor Pro 4.0 (WaveMetrics, Lake Oswego, OR). The data
files were then displayed as Igor Pro graphs and their decay phase was fitted
by a double exponential function curve. The data of the fitted function curve
were subtracted from the decay phase data of the record and the residue data
for the decay phase were obtained for each record and transformed into a text
file format. The text files were then subjected to a continuous wavelet
analysis using a JAVA software MEM—maximum entropy method
(Ishikawa, 2000)—with
the eighth-order Gabor function (Mallat,
1999). The power density of the frequency for each record was
analyzed at eight levels, each of which was divided into four divisions, in
the frequency range between 0.19 and 32.02 Hz. The analyzed data for each
record were displayed on a computer screen as an 8 bit grayscale diagram with
axes of frequency on ordinate and time on abscissa. The text files of the
residue data of records were also subjected to the calculation of mean of root
mean square (RMS) for the evaluation of signal fluctuation by PowerLab Chart
4.1.1. The statistical evaluation of frequency analysis data was performed
using StatView 4.5 (SAS Institute, Cary, NC).
Development of simulation programs
Simulation programs of the current responses for a Power Macintosh computer
were developed with REALbasic 3.5J (REAL Software, Austin, TX) based on a cAMP
transduction pathway model for the current responses
(Figure 3). The model was
constructed on the basis of cAMP second messenger system models for neurons at
different levels of the nervous system
(Cooper et al., 1995;
Bhalla and Iyengar, 1999),
using some of the parameter values in the references cited in review articles
(Zufall et al., 1994;
Nakamura, 2000) and
empirically determined parameter values. Although most functional molecules in
the olfactory transduction pathway are thought to be concentrated in the
membranes of olfactory cilia or microvilli, it was assumed in the present
model that these functional molecules are evenly distributed in the cell
(Bhalla and Iyengar, 1999). The
unit conductances of cyclic-nucleotide-gated (CNG) ion channels and
Ca2+-activated Cl- (CAC) ion channels were also ignored,
so that the whole-cell current responses were assumed to be linearly related
to the sum of concentrations of active CNG and CAC channels for an ORN. In
addition, IP3-involved reaction processes and CO/cGMP-involved
processes that have been proposed to exist in the olfactory transduction
pathways in fishes (Restrepo et al.,
1990,
1993;
Lo et al., 1993;
Cadiou et al., 2000)
and mammals and amphibians (Schild et
al., 1995; Lischka et
al., 1999; Zufall and
Leinders-Zufall, 1997) were excluded to avoid complicating the
simulation procedure. Thus, the reaction processes in the model were expressed
by 12 differential equations with 44 different parameters (see Appendix). The
simulation programs for Macintosh (cAMP 9.2.7 and 9.2.8 for MacOS 8.1 or
later) and the cAMP JAVA applet versions based on cAMP 9.2.8
(http://bio2.sci.hokudai.ac.jp/bio/chinou1/noriyo_home.html)
calculate numerical solutions using the Euler integration method or the
4th-order Runge—Kutta integration method
(Gershenfeld, 1999;
Schutter, 2001) on a fixed
integration time step, usually 0.001 s or shorter and display the solutions
for 12 different functions expressed as the concentration in µM on the
ordinate versus the time in seconds on the abscissa. The time scale of the
abscissa is changeable up to 10 s for cAMP 9.2.7 and 100 s for cAMP 9.2.8. The
polarity and scale of the ordinate are changeable for the numerical solution
curves to represent similarly as actual inward current responses, especially
for the sum of concentrations of active CNG and CAC channels. The programs
also export the solution files as reversible row text tables for Igor Pro,
from which the three-dimensional graphs were obtained using its surface plot
option.
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All graphs obtained by the various software packages in the present study were further processed for presentation using Canvas 6 graphics software (Deneba, Miami, FL).
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Results |
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Oscillations of whole-cell inward current responses
Figure 1A illustrates
typical whole-cell current responses of a cORN to the amino acid mixture puff
with a 25 ms duration at a holding potential of -60 mV. The amplitude of
inward current response increased with increased odorant intensity, as the
odorant intensity was shown to relate linearly to the ejection pressure
(Sato and Suzuki, 2000). Since
the responses were all phasic, with a fast rise and slower exponential decay,
the decay phases of responses were fitted by different double exponential
function curves. The fitted function curve data were subtracted from the decay
phase data of the record and the residue data for the decay phase were
obtained. The corresponding residue noises to the original responses in
Figure 1A are shown in
Figure 1B. The signal
fluctuation measured by the mean of RMS for these residue noises increased
with increased odorant intensity and the residue noises became more
oscillatory with increases of signal fluctuation, i.e. the oscillations
occurred in high odorant intensity ranges. The positive correlation between
the current response peak and the signal fluctuation of residual noises
(r = 0.78, n = 23 records from four cORNs) also indicated
that the oscillations appeared in the responses of ORNs when stimulated by
odorants in high intensity. The residue noise records were then subjected to
wavelet analysis and displayed as power density diagrams for frequency versus
time relation, as shown in Figure
1C.
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Figure 2A shows whole-cell current responses of an mORN to the amino acid mixture with different prolonged stimulus durations (1, 3 and 5 s; 1 kgf/cm2) at a holding potential of -60 mV and the fitted double exponential function curves to their decay phases. The residue noise was subjected to wavelet analysis to show its dominant frequency (Figure 2B).
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Oscillation frequency of whole-cell current responses
Table 1 summarizes the oscillation frequencies of whole-cell current responses determined by wavelet analysis under different recording conditions. The mean of theoscillation frequencies of current response records from 41 ORNs (31 cORNs and 10 mORNs) was 1.89 ± 0.50 Hz (mean ± SD, n = 92, range 0.98-3.51). There was no statistical difference in the mean frequency between different types of ORNs [cORNs, 1.95 ± 0.25 Hz (n = 41, range 0.98-3.51); mORNs, 1.85 ± 0.22 Hz (n = 21, range 1.36-3.51); P > 0.3, Mann—Whitney U-test] or between different perfusion conditions [standard Ringer's solution, 1.92 ± 0.49 Hz (n = 62, range 0.98-3.15); Na-free (choline) Ringer's solution, 1.86 ± 0.28 Hz (n = 28, range 1.36-2.93); P > 0.5, Mann—Whitney U-test], but there was a statistical difference in the mean frequency between different holding potentials [-60 mV, 1.91 ± 0.25 Hz (n = 71, range 0.98-3.51); +20 mV, 1.59 ± 0.15 Hz (n = 13, range 1.36-2.58); P < 0.01, Mann—Whitney U-test].
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Simulation of whole-cell current responses
As described in Materials and methods, the simulation programs were developed on the basis of a cAMP transduction model for current responses of ORNs, where it was assumed that the sum of concentrations of active CNG and CAC channels was linearly related to the whole-cell inward current response (Figure 3). The solutions for 12 differential equations using 44 different parameters (see Appendix) were calculated by the Euler or 4th-order Runge—Kutta integration methods at 1 ms integration time step. No obvious differences in the solutions obtained by these two methods were observed at 1 ms step integration. Figure 4 shows one set of solutions when the initial values of the 12 functions and 44 parameters were set up as defaults for the programs shown in the Appendix. Odorant stimuli (od) with a 25 ms duration at different concentrations ranging from 0.01 to 10 000 µM (10-8 and 10-2 M) were applied in 20 logarithmic steps. The resulting function changes were phasic, with an initial fast rise and a slower exponential decay and return to the initial level within 6 s. For od concentrations >10 µM, the damped oscillations were superimposed on the decay phases of the changes. Marked oscillations occurred in five functions: the concentrations of active CNG channels (x); active CAC channels (y); active AC (v); cAMP (u); and free Ca2+ (q). Oscillations also occurred in the sum of concentrations of active CNG and CAC channels (x + y) in od concentrations >10 µM (Figure 4A—F), although the contribution of the concentration of active CAC channels to the sum of concentrations of (x + y) was small compared to the concentration of active CNG channels (note that the scale maximum in Figure 4C is one-hundredth of that in Figure 4B). Less marked oscillations were observed in concentrations of active PKA (s) and calcium—calmodulin complex (p) in od concentrations >10 µM (graphs not shown). The changes of all 12 functions, including the five functions with marked oscillations, became saturated in od concentrations >1000 µM.
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Characteristics of (x + y) changes in the simulation
Figure 5 shows three-dimensional presentations of (x + y) changes, of which the polarity of y-axes was reversed to mimic actual whole-cell inward current responses. The changes in (x + y) increased with increased od concentrations and the damped oscillations were superimposed on their decay phases in od concentrations >10 µM. The changes saturated in od concentrations >1000 µM. The latency for (x + y) changes became shorter (from 181.8 to 22.7 ms) with increased od concentration. The frequency of damped oscillations increased slightly (from 0.98 to 1.39 Hz) with increased od concentration (Figure 5A). These characteristics of (x + y) changes simulated well the odorant intensity relation of actual inward current responses shown in Figure 1.
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A search for the limiting reaction components in the transduction model for the oscillations of (x + y) changes was performed by disconnecting the feedback loops (dotted line loops in Figure 3). After many trials and errors in running the programs, direct inhibition of AC activity by Ca2+ was found to be only one limiting reaction for the oscillations. This is clearly shown in Figure 5B, where the maximal Ca2+ inhibition rate constant (A3max) was varied from 0 to 40 s-1 at 100 µM od stimulus with a 25 ms duration. The oscillations did not occur at 0 of A3max. Reaction components in the model that affected the oscillations and their frequency of (x + y) were the Ca2+ efflux rate by NCX (ef) and the endogenous concentration of cAMP-PDE (apd). The oscillations occurred in an ef range >4.5 s-1, where od stimulus was set at 100 µM and 25 ms duration. The frequency of oscillations slightly increased up to 1.62 Hz at an ef range of 20 s-1 (Figure 5C). When apd was set at 0 µM, there was almost no oscillation in the od concentration range from 0.01 to 10 000 µM (Figure 5D). On the other hand, the occurrence of oscillations of (x + y) was little influenced by calmodulin-involved feedback loops. An example is shown in Figure 5E, where the endogenous concentration of calmodulin (cam) was changed from 1 µM as the default value to 0 µM in order to disconnect the calmodulin-involved feedback loops, calmodulin dependent phosphodiesterase (CAM-PDE) and calmodulin dependent kinase II (CAM-kinase II).
The decay speed of (x + y) changes and the damping factor of the oscillations in responses to odorant stimuli >1 s long were strongly dependent on the rate constant of odorant dissociation from the receptor (os2) and on the endogenous concentrations of calmodulin (cam), CAM-PDE (cpd) and CAM-kinase II (ckk) in the calmodulin-involved feedback loops. Figure 5F shows the (x + y) changes with increases of od concentration from 0.01 to 10 000 µM with a 3 s duration, where os2, cam, cpd and ckk were set at 20 s-1 and 2.2, 2.2 and 2.2 µM, respectively. Figure 5F simulates well the actual inward current responses when stimulated by odorants with durations >1 s shown in Figure 2.
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Discussion |
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TopAbstractIntroductionMaterials and methodsResultsDiscussionAppendixDefinition of functions and...References |
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Oscillations depended on electrophysiological properties of ORNs
Oscillations superimposed on the inward current responses of isolated ORNs
from rainbow trout occurred in both cORNs and mORNs when stimulated by amino
acid odorants at high intensity. The dominant frequency of oscillations in
both types of ORNs did not differ significantly. This similarity of
oscillation properties was probably due to the similarity of
electrophysiological properties of the I—V relations and
reversal potentials for the amino acid odorant between both types of ORNs
(Sato and Suzuki, 2000,
2001). In addition, there was
no significant difference in oscillation frequency between different perfusion
conditions for different ion channel current recordings, indicating that both
types of ORNs have the same kinds of efferent ion channels—CNG and CAC
channels—in their transduction pathways, although these two types of
ORNs might have different types of odorant receptors
(Sato and Suzuki, 2001). On
the other hand, the oscillation frequency was significantly different in
different holding potential conditions. The dominant frequency of oscillation
at -60 mV was slightly higher than at +20 mV. The results were also attributed
to the voltage-dependent characteristics of the current responses to amino
acid odorants, in which the decay speed of the current responses was faster in
negative holding potential ranges than in positive potential ranges. Thus, the
oscillation frequency of whole-cell current responses depended superficially
on their electrophysiological characteristics.
Comparison with previously observed oscillations
The oscillation frequency of isolated ORNs from rainbow trout in the
present study (1.89 Hz) was higher than those previously found in isolated
ORNs from the frog—0.10-0.12 Hz
(Frings and Lindemann, 1988)
and 0.083-0.28 Hz (Reisert and Matthews,
1997,
2001a)—and was in the
range of those found in the mouse—0.42-2.70 Hz
(Reisert and Matthews, 2001b).
Differences in oscillation frequencies might be due to the different odorant
stimulation methods used in various studies; we used short periods of
stimulation from 25 ms to 5 s with the pressure ejection method, while other
groups used a longer odorant stimulation time of 30 s or >1 min with
stepping superfusion or continuous bath application methods. The different
oscillation frequencies of ORNs in different species also suggest
species-specific differences in reaction components in olfactory transduction
pathways of ORNs (see later discussion on simulation).
Generation mechanisms of PWs
Oscillations of current responses of ORNs should directly influence both
EOG responses and nerve impulse responses of the populations of ORNs in in
vivo preparations, since EOG responses are composed of the sums of slow
potential changes of ORNs in the olfactory epithelium, and nerve impulses from
the populations of ORNs are direct outputs from ORNs triggered by current or
voltage responses of individual ORNs. The oscillation frequency of current
responses of isolated ORNs from the rainbow trout (1.89 Hz) in the present
study, however, was much lower than those of the PWs of EOGs in the channel
catfish (28 Hz) (Parker et al.,
1999;
2000) and in the toad (16 Hz)
(Nakazawa et al.,
2000), and the nerve impulse responses of small populations of
ORNs in the channel catfish (20-28 Hz)
(Nikonov and Caprio, 2001;
Nikonov et al.,
2002). The higher frequency of oscillations in the PWs could not
be explained by the simple summation of slow oscillations of individual ORNs,
because spatial and temporal excitation of individual ORNs in different
locations in the olfactory epithelium would elicit the PWs as a whole
(Parker et al.,
1999). If there are electrical connections between individual ORNs
in the olfactory epithelium as has been suggested
(Zhang et al., 2000),
the generation mechanism of the PWs would become much more complex.
Parameter setting in the simulation
The present simulation revealed that the oscillations of current responses
of ORNs are mainly due to the oscillatory properties of intracellular cAMP and
Ca2+ concentrations. The necessary reaction component for the
oscillations in the transduction model was the direct inhibition of AC
activity by Ca2+. High Ca2+ effluxes by NCX and cAMP-PDE
activity were the parameters that most influenced the oscillations. The
important role of NCX in Ca2+ efflux in the oscillations of ORNs,
as suggested by Reisert and Matthews (Reisert and Matthews,
1997,
2001a,
b), was consistent with the
previous result that the Ca2+-chelating action of trisodium citrate
on the surface of olfactory epithelium triggered and enhanced the PWs
(Parker et al.,
2000).
We used 44 different parameters in the simulation, some of which were
obtained from data available in previously published studies and the
references therein (Zufall et
al., 1994; Nakamura,
2000). Since many other parameters were unknown, we took arbitrary
but reasonable ranges of values in ORNs, as used in previous simulation
studies (Cooper et al.,
1995; Bhalla and Iyengar,
1999). For example, endogenous concentrations of enzymes such as
pka, go, ac, ckk, apd, cam and cpd were taken as 1-5 µM
per ORN. The endogenous concentrations of CNG and CAC ion channels were set at
1 µM per ORN. Unknown rate constants and their maximal rates for enzyme
reactions such as AKmax, PKmax, rg, a, A2max, A3max, ca, PDmax, CDmax
and CKmax were also set at 0.1-40 s-1. In addition, the
rate constants for Ca2+ influx (if) through CNG channels
and efflux (ef) by NCX were set at 20 and 10 s-1,
respectively. However, essentially similar simulation results were obtained in
the intracellular Ca2+ concentration range up to 300 nM
(Leinders-Zufall et al.,
1997,
1998), even if these values
were changed to the order of several thousands per second
(Hilgemann, et al.,
1991; Niggli and Lederer,
1991) when we kept the ratio of influx and efflux rates at
2:1. Thus, these empirically chosen values, conversely, have been shown
to be appropriate for the simulation of actual current responses in the
present study.
The current carried through CAC channels is thought to contribute mostly to
the whole-cell current response to odorants in the newt at 40% of total
current (Kurahashi and Yau,
1993) and in the rat at 80% of total current
(Lowe and Gold, 1993). In the
present simulation, however, the contribution of the concentration of active
CAC channels to (x + y) was as small as one-hundredth of
that of the active CNG channels. This quite different feature in the
simulation might be due to our parameter setting: we ignored the unit
conductances of CNG and CAC channels, and the half-maximal concentration of
Ca2+ for CAC channel openings was set at 5.0 µM
(Kleene and Gesteland, 1991),
which might have been rather high for the intracellular Ca2+ change
up to 300 nM (Leinders-Zufall et al.,
1997,
1998).
Simulation of oscillations with lower frequency induced by prolonged stimulation
The present simulation matched the oscillations of current responses of
ORNs to odorants with short stimulus durations from 25 ms to 5 s and their
damped oscillation frequency was in the range of 0.98-1.62 Hz. The frequency
of current or voltage oscillations observed in frog ORNs—0.10-0.12 Hz
(Frings and Lindemann, 1988)
and 0.083-0.28 Hz (Reisert and Matthews,
1997,
2001a)—was much lower
than the frequency range of the present simulation. The damping of
oscillations during prolonged stimulation of up to 1 min or more was not
observed in these studies. We tried to simulate such low-frequency
oscillations without damping with prolonged stimulus durations of up to 60 s
with the simulation program, cAMP 9.2.8, by changing parameter settings, but
we could not find such oscillations, although damped oscillations with
frequencies as low as 0.4 Hz were obtained when od concentration,
if and ef were set at 0.1 µM, 1 s-1 and
0.1-0.5 s-1, respectively. Therefore, the present simulation model
might have needed some other transduction processes than cAMP-involved
processes such as IP3-involved processes (Restrepo et al.,
1990,
1993;
Lo et al., 1993;
Schild et al., 1995;
Lischka et al., 1999;
Cadiou et al., 2000;
Iida and Kashiwayanagi, 2000)
and CO/cGMP-involved processes (Zufall and
Leinders-Zufall, 1997). However, since the simulation completely
represented the major characteristics of current responses of ORNs to odorants
with short stimulus durations—odorant-intensity-dependent response,
intensity-dependent latency and adaptation—the present simulation is
generally applicable to current and voltage responses of ORNs equipped with
the cAMP olfactory transduction pathway in other vertebrate species.
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Appendix |
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TopAbstractIntroductionMaterials and methodsResultsDiscussionAppendixDefinition of functions and...References |
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Differential equations
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- x:
- concentration of active CNG channels (µM) = 0.0001
(x0)
- y:
- concentration of active Ca—Cl channels (µM) = 0.0001
(y0)
- z:
- concentration of odorant—receptor complex (µM) = 0.001
(z0)
- w:
- concentration of active Golf (µM) = 0.001 (w0)
- v:
- concentration of active AC (µM) = 0.001 (v0)
- u:
- concentration of cAMP (µM) = 0.001 (u0)
- s:
- concentration of active PKA (µM) = 0.001 (s0)
- r:
- concentration of inactive odorant—receptor complex (µM) =
0.001 (r0)
- q:
- concentration of intracellular calcium ions (µM) = 0.001
(q0)
- p:
- concentration of Ca4CAM (µM) = 0.001 (p0)
- o:
- concentration of active CAM-PDE (µM) = 0.001 (o0)
- n:
- concentration of active CAM-kinase II (µM) = 0.001
(n0)
- od:
- concentration of odorants (µM) = 1.0
- uod:
- concentration of unbound odorants (µM)
- rc:
- concentration of receptor (µM) = 1.0
- urc:
- concentration of unbound receptor (µM)
- os:
- rate of odorant binding to receptor (1/µMs) = 0.1
- os2:
- rate of odorant dissociation from receptor (1/s) = 2.0
- pka:
- concentration of PKA (µM) = 1.0
- is:
- concentration of inactive PKA (µM)
- ak:
- rate of PKA activation by cAMP (1/s)
- AKmax:
- maximal rate of PKA activation by cAMP (1/µMs) = 0.1
- ak2:
- rate of PKA inactivation (1/s) = 1.0
- pk:
- rate of receptor inactivation by active PKA (1/s)
- PKmax:
- maximal rate of receptor inactivation by active PKA (1/µMs) =
1.0
- pk2:
- rate of reversal of receptor inactivation (1/s) = 0.1
- go:
- concentration of Golf (µM) = 1.0
- iw:
- concentration of inactive Golf (µM)
- rg:
- rate of activation of Golf by odorant—receptor complex (1/µMs)
= 10
- rg2:
- rate of inactivation of Golf (1/s) = 2.0
- ac:
- concentration of AC (µM) = 5.0
- iv:
- concentration of inactive AC (µM)
- a:
- rate of AC activation by active Golf (1/µMs) = 2.0
- ckk:
- concentration of CAM-kinase II (µM) = 1.0
- in:
- concentration of inactive CAM-kinase II (µM)
- a2:
- rate of AC inactivation by CAM-kinase II (1/s)
- A2max:
- maximal rate of AC inactivation by CAM-kinase II (1/µMs) = 1
0
- a3:
- rate of AC inactivation by calcium ions (1/s)
- A3max:
- maximal rate of AC inactivation by calcium ions (1/s) = 40
- ca:
- rate of cAMP synthesis by active AC (1/s) = 40
- apd:
- concentration of cAMP-PDE (µM) = 1.0
- pd:
- rate of cAMP hydrolysis by cAMP-PDE (1/s)
- PDmax:
- maximal rate of cAMP hydrolysis by cAMP-PDE (1/µMs) = 10
- cng:
- concentration of CNG channels (µM) = 1.0
- ix:
- concentration of inactive CNG channels (µM)
- cn:
- rate of CNG channel activation by cAMP (1/s)
- CNmax:
- maximal rate of CNG channel activation by cAMP (1/s) = 5.0
- cn2:
- rate of CNG channel inactivation (1/s) = 10
- cam:
- concentration of CAM (µM) = 1.0
- cc:
- rate of calcium binding to CAM (1/µMs) = 0.1
- cc2:
- rate of calcium dissociation from CAM (1/s) = 1.0
- cm:
- rate of CNG channel inactivation by Ca4CAM (1/s)
- CMmax:
- maximal rate of CNG channel inactivation by Ca4-CAM (1/µMs) =
10
- if:
- rate of calcium ion influx through CNG channels (1/s) = 20
- ef:
- rate of calcium ion efflux by NCX (1/s) = 10
- cac:
- concentration of Ca—Cl channels (µM) = 1.0
- iy:
- concentration of inactive Ca—Cl channels (µM)
- cl:
- rate of Ca—Cl channel activation by calcium ions (1/s)
- CLmax:
- maximal rate of Ca—Cl channel activation by calcium ions (1/s) =
5.0
- cl2:
- rate of Ca—Cl channel inactivation (1/s) = 10
- cpd:
- concentration of CAM-PDE (µM) = 1.0
- io:
- concentration of inactive CAM-PDE (µM)
- cp:
- rate of CAM-PDE activation by Ca4CAM (1/s)
- CPmax:
- maximal rate of CAM-PDE activation by Ca4CAM (1/µMs) = 10
- cp2:
- rate of CAM-PDE inactivation (1/s) = 0.01
- cd:
- rate of cAMP hydrolysis by CAM-PDE (1/s)
- CDmax:
- maximal rate of cAMP hydrolysis by CAM-PDE (1/µMs) = 20
- ck:
- rate of CAM-kinase II activation by Ca4CAM (1/s)
- CKmax:
- maximal rate of CAM-kinase II activation by Ca4CAM (1/µMs) =
10
- ck2:
- rate of CAM-kinase II inactivation (1/s) = 0.01
- K1:
- concentration of cAMP at which CNG channel activation is half-maximal
(µM) = 3.4
- K2:
- concentration of calcium ions at which Ca—Cl channel activation
is half-maximal (µM) = 5.0
- K3:
- concentration of calcium ions at which AC inhibition is half-maximal
(µM) = 0.2
- N1,2,3:
- Hill coefficients for the processes = 1.4, 2 and 3
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Definition of functions and parameters, and default settings of these values for numerical calculation |
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TopAbstractIntroductionMaterials and methodsResultsDiscussionAppendixDefinition of functions and...References |
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Acknowledgments |
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We thank Dr Yasuhiro Ishikawa (Ishikawa Medical Clinic, Saitama, Japan) for his kind guidance during the use of MEM wavelet analysis software. We also thank Dr Michio Yazawa (Division of Chemistry, Hokkaido University) for valuable comments on the construction of the cAMP transduction model and Dr Shin Tochinai (Division of Biological Science, Hokkaido University) for uploading the cAMP 9.2.7 and 9.2.8 simulation programs and the cAMP JAVA applet versions to our web site (http://bio2.sci.hokudai.ac.jp/bio/chinou1/).
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References |
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TopAbstractIntroductionMaterials and methodsResultsDiscussionAppendixDefinition of functions and...References |
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Accepted August 7, 2002
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