Local field potential (LFP) oscillations are often accompanied by synchronization of activity within a widespread cerebral area. Thus, the LFP and neuronal coherence appear to be the result of a common mechanism that underlies neuronal assembly formation. We used the olfactory bulb as a model to investigate: (1) the extent to which unitary dynamics and LFP oscillations can be correlated and (2) the precision with which a model of the hypothesized underlying mechanisms can accurately explain the experimental data. For this purpose, we analyzed simultaneous recordings of mitral cell (MC) activity and LFPs in anesthetized and freely breathing rats in response to odorant stimulation. Spike trains were found to be phase-locked to the gamma oscillation at specific firing rates and to form odor-specific temporal patterns. The use of a conductance-based MC model driven by an approximately balanced excitatory-inhibitory input conductance and a relatively small inhibitory conductance that oscillated at the gamma frequency allowed us to provide one explanation of the experimental data via a mode-locking mechanism. This work sheds light on the way network and intrinsic MC properties participate in the locking of MCs to the gamma oscillation in a realistic physiological context and may result in a particular time-locked assembly. Finally, we discuss how a self-synchronization process with such entrainment properties can explain, under experimental conditions: (1) why the gamma bursts emerge transiently with a maximal amplitude position relative to the stimulus time course; (2) why the oscillations are prominent at a specific gamma frequency; and (3) why the oscillation amplitude depends on specific stimulus properties. We also discuss information processing and functional consequences derived from this mechanism.
Recent experiments under awake conditions indicate that there is little effective spatial contrast in the firing rate of neurons in olfactory structures [1] and even in auditory primary sensory structures [2], which suggests a limited role for the mean firing rate in sensory function. In addition, it has recently been shown in the retina that the sole firing rate is not sufficient to code for behavioral performance [3]. Furthermore, the role of spike timing for plasticity [4] and coding [5] suggests that the temporal structure of neuronal activity may be crucial for perception. In particular, various functional studies have reported that fast local field potential (LFP) oscillations, particularly those in the gamma band (40–80 Hz) that correlate with perception [6] and attention [7], simultaneously induce a greater synchrony in the firing of cells, thereby having a greater impact on downstream structures [7]. In the mammalian olfactory bulb (OB), odorant stimulation induces LFP oscillations both in the gamma (40–80 Hz) and beta (15–35 Hz) ranges. There is, however, significant disparity in the reports regarding the conditions in which these oscillations are expressed. In anesthetized animals, gamma and beta LFP oscillations are odor-induced and appear alternately along the respiratory cycle, with gamma bursts specifically occurring during the inspiration/expiration (I/E) transition [8], [9]. In the awake rat, gamma and beta LFP oscillations exist spontaneously, and odors evoke increases [10] or decreases [11] of amplitude in the gamma frequency range. In insects [5], [12] and to a lesser extent in fish [13], spiking activity has been shown to be strongly linked to the oscillation which plays therefore a crucial role in coding. In rodents the role of these oscillation has been primarily described to reflect the experience of the animal [14], [15]. Despite the findings of phase/time relationships between mitral (MC) spiking activity and the oscillation or between MC pairs [16]–[18], a better description of these relationships across the MC population is needed before demonstrating that such temporal activity can support an odor code. Our approach focused on gamma oscillations in anesthetized rats, which are not very different from oscillations recorded under behaving conditions [19]. The aim of the current study was two-fold: (1) to analyze the fine temporal relationships between the spiking of an MC population and gamma oscillations in anesthetized, freely-breathing rats in response to odorant stimulation and (2) to build a biophysical model of MC activity under the same in vivo conditions to explain the data. Our data showed that during the transient periods of gamma oscillation, a specific subset of MCs exhibited specific periodic firing phase patterns that could be grouped in a small number of types. Furthermore, the pattern types exhibited by a particular MC are qualitatively related to the nature of the odorant stimulus. These different types of patterns constitute the signature of an entrainment of these cells by an input oscillation [20], [21], whose origin can be attributed to the inhibitory granular input [17]. In the model, we verify that this scenario of entrainment effectively reproduces the experimental observations. We further explored the model' s dependence on MC input activity and intrinsic properties, showing that our model robustly exhibited an optimum of entrainment when the oscillation frequency was within the gamma range. Overall, these results provide a detailed quantitative description of the complex MC firing activity at the population level and, at the same time, a theoretical explanation of the links between MC spike trains and gamma LFP oscillations evoked under freely breathing conditions in the OB. Furthermore, these results constitute an important underlying mechanism if future research shows that such a firing activity can support odor coding in behaving conditions.
The relationships between unit activity and gamma LFP oscillations during phase-locking raise the question of whether reciprocal entrainment mechanisms exist between MC and LFP oscillations. We addressed one part of this question using a biophysical model 1) to investigate the modalities of entrainment of MC activities by granule cell activities and 2) to explain the spike train structures measured experimentally. The use of a model allowed us to perform studies that are not currently feasible with animal studies.
Our work provides converging arguments in favor of a MC entrainment, suggesting that they receive an oscillatory input in vivo. Although several groups have focused on the temporal relationship between spikes and LFP, the exploration of this entrainment phenomenon has only been partly addressed. The analysis of Eeckman and Freeman [16] differed due to the multi-unit nature of their signal. Kashiwadani et al. [18] focused more on a coding hypothesis rather than a dynamic hypothesis and used an artificial sniff, which likely affected the bulbar dynamics. One in vitro study has explored the spike/LFP relationship [17]. The network connectivity and dynamic conditions, however, could be very different from those in vivo, and it is difficult to compare in vitro oscillations to those under in vivo conditions. One potential criticism of our work is the usefulness of such a mechanism under some behavioral conditions, such as where odor presentation induces a decrease in gamma oscillations [14]. The fact that the amplitude of gamma oscillations decreases under particular conditions does not indicate that gamma oscillations are unnecessary for the system. Indeed, the amplitude decreases under particular conditions; however, beta oscillations are simultaneously enhanced, which suggests that the olfactory bulb and cortex together work in a different manner [27], [28]. There are other behavioral conditions in which gamma oscillations do not decrease but rather increase with odor presentation [10]. Experimental conditions vary widely depending on the employed paradigm, which can induce different sniffing strategies [29] or different neuromodulatory control of the MC/GC loop [30]. These different conditions are certainly responsible for the variation in the expression of gamma and beta oscillations. The aim of our study was to explore how spikes and oscillation can be phase-locked in the more general situations in which gamma oscillations are present. It would be an interesting second step to perform the same study for beta oscillations and to look for another mechanism that could be responsible for the observed spike/beta oscillation synchronization [31]. Our MC model was fitted to reproduce the quantitative and dynamic properties of MCs, based upon recent findings on MC membrane activity. It is consistent with experimental data [17], [32]–[34] and includes essential features of existing models [35]–[37]. In our model, entrainment was produced by a relatively weak oscillatory inhibitory conductance. When the cell has an input well above the threshold, it fires regularly and even periodically in response to a constant input. Under these conditions, and when the oscillatory input is sufficiently weak, the neuronal response can be predicted from the phase response curve (PRC) [38], [39], which can also predict some characteristics of the tongues [40]. Since the PRC of our MC model agrees with the experimental one [41], it is likely that our model can accurately predict the MC response to such synaptic inputs. The synaptic mechanisms hypothesized in our model are based on observations made by Lagier et al. (2004) [17], who reported that a fraction of the IPSPs received by the MCs were phase-locked relative to gamma oscillations. Other possible mechanisms that could affect the MC membrane potential during gamma oscillations have been proposed: (1) a synchronous inhibition resulting from GABA release from astrocytes [42], (2) a synchronous excitation of the MCs by glutamate spillover onto lateral dendrites [43], [44], and (3) a direct influence of the LFP on membrane voltage [45], [46]. Of these possible explanations, the functional and dynamic relevance of the interactions between MCs and GCs [47] are the most likely processes to occur during gamma oscillations. Aside from this observation, an important characteristic of our model is that the time constant of the single inhibitory inputs does not play a role because it is the frequency of the oscillatory modulation of the whole inhibitory input that imposes the locking frequency. It is important to insert this mechanism into a more realistic model in order to take into consideration the spatial distribution of the physiological mechanism in dendrites. The presence of high frequency bursts of spikes in MCs is probably not due solely to the excitatory drive from the sensory input, but also to additional conductance levels beyond those present in the model. For example, the activation of an intrinsic conductance, such as T channels, would facilitate the emergence of high frequency bursts like those in our recordings. Neuronal phase-locking and pattern formation have already been described both theoretically [20], [21], [48] and experimentally [26], [49]. Our study, performed in the context of the OB with a resonant neuron, however, sheds light on important aspects that are specific to this system. First, the simulation results provide some precise explanations regarding electrophysiological properties that are not directly accessible by experimentation. The phase of the MC spikes relative to LFP oscillations is precisely distributed in the ¼ to ½ part of the LFP cycle due to their level of synaptic drive. The phase distributions extracted from simulated data (Fig. 6A) are more precise and go beyond the data that was obtained in the OB [14], [17], [18], as well as our own experimental results. We wish to point out, however, that our experimental measurement of gamma phase was not totally reliable from one particular depth to another, and could have up to ¼ of a cycle of phase shift. Indeed, gamma oscillations are generated by membrane currents flowing on either side of the MC layer, and the simultaneous recording of a gamma oscillation constantly shows a ¼ cycle phase shift when it is recorded up to 100 µm from the MC layer (Fourcaud-Trocmé and Buonviso, personal communication). In our recordings, we could not control the exact position of each electrode relative to the MC layer. As a consequence, these recording constraints, as well as the noise level, are likely to be the source of the larger spread of phases during the phase-locked experimental pattern when compared to the model prediction (see Fig. 6B). This can also explain the small discrepancies with recordings from other studies in which the LFP recording position relative to the mitral cell layer was different or more precisely controlled [16]–[18]. In all cases, however, our results are still qualitatively comparable. Second, lower levels of excitatory conductance in the model were predicted to induce a slight phase lag (corresponding to ∼5 ms) between the neurons, as shown in Fig. 6A. This phase difference is observed in the cross-correlograms that were presented by Kashiwadani et al. (1999) [18] (their Fig. 5A), and it may be achieved by differential activation of the glomerulus [18], [50], [51]. Our predictions are able to explain the result of this previous study. The model predicts that phase-locked or residual spike trains may depend on the degree of detuning (i. e. , the difference between the neuronal intrinsic firing rate and the external network frequency), the strength of coupling, and the level of noise. The continuity between the locked and residual spike trains suggests that entrainment of MCs may be fine-tuned during the gamma oscillation, and may corroborate the locking that was observed in the fish OB [13]. However, only simple phase-locking has been found in these species. Finally, in our model, increasing the global level of excitatory-inhibitory conductance favors entrainment (see Fig. 7A–B). Under anesthetized conditions, the maximal conductance should be directly related to the maximal activity of the peripheral excitation [51], [52] and to the maximum of synaptic inhibition [53], which corresponds to the inspiration/expiration transition. Taken together, these data imply that entrainment should be the strongest at this transition, which is what was observed with the gamma wave appearing around this point (Fig. 1). Interestingly, odors that elicit low theta activity (respiratory modulation), which potentially reflects weak OB activation (e. g. , low-concentration odors), generally failed to elicit gamma oscillation [9], suggesting that the theta oscillation could gate gamma activity. In the OB, MCs are directly interconnected only within glomerulus [54]–[57] and not across bulbar areas. Instead, MC spikes induce a depolarization of some GC spines, which propagates through parts of the cell to other spines and triggers both synchronous [58]–[62] and asynchronous [36], [55], [63]–[65] GABA release from granule dendrodendritic synapses onto other MCs. This peak of GABA release is about ¾ of the gamma cycle (∼ = 12 ms) after the peak of spiking (according to the spike (Fig. 4E) and IPSP (Fig. 4G) phase distributions in [17]). The slow component of inhibition [55], [64]–[66] may contribute to the global tonic inhibition level that is present in the OB. This synaptic activity suggests that the effective interaction between MCs is inhibition, and that the OB could be approximately modeled as a network of inhibitory coupled MCs. Our results raise the question of the origin of gamma oscillatory activity in the OB. Do entrained MCs participate in the creation of this rhythm? If so, how? Two models have been recently proposed [35], [36]. In [35], a network of inhibitory coupled MCs is applied to in vitro recordings, in which the gamma oscillation is continuous and evoked by single stimulation. In [36], the particular tendency of MCs to synchronize their firing when their stochastic inputs become correlated was studied. Neither of these models, however, has been shown to induce the spiking activity that we report here. This is also the case for the general mechanisms that have been proposed for oscillation generation in inhibitory [67]–[69] and excitatory-inhibitory networks [69]–[71]. It has to be noted that, in these studies, a large heterogeneity in the population intrinsic firing rates usually prevents the formation of an oscillation, and that the case of a resonant neuron is not considered. Our results, however, suggest the following two hypotheses. First, if MCs behave like oscillators, a possible mechanism for the emergence of the oscillation may be provided by the transition towards synchrony, a phenomenon that is generally observed in a network of coupled heterogeneous oscillators [20], [72]. Second, the model predicts that intrinsic MC properties (according to Fig. 7D and 8) lead to a maximal entrainment in the gamma frequency range. Indeed, a non resonant neuron (i. e. an integrate-and-fire model) does not exhibit this behavior (data not shown). From this property, it can be seen that among the MC population that exhibits quite heterogeneous frequencies (see Fig. 4), MCs firing with intrinsic firing rate in the range of 40–70 Hz are better entrained than MCs firing at lower or higher frequencies. The rhythm could be created when this entrained MC population becomes sufficiently large. Other studies in anesthetized rats have shown that MCs can be segregated into two populations according to whether they phase-lock to gamma oscillations or to beta oscillations, which is likely due to their position relative to the receptive field of the odor [31]. Here, we show that, among MCs that lock to the gamma oscillation, locking is finely tuned depending on the various conditions that control MC entrainment, one of them being the nature of the odor. A subset of the MC population can therefore be entrained and phase-locked at gamma frequencies with patterns depending on the intrinsic firing rate of the MC, which is similar to the previously described rate-specific synchrony [26]. The resulting phase-locked activity map may overlap with the glomerular activity map. This is suggested by our results, which show that pattern types are partially reproducible for the same cell and the same odor. The glomerular map is likely forwarded to MCs as a “rate code” map that is readable by downstream structures. The phase-locked activity map, however, appears to be more elaborate than the simple glomerular map. In particular, the main characteristic of the phased-locked activity map is that it can be modulated by various parameters: such as the conductance level (Fig. 7), the MC intrinsic firing rate (Figs. 4 and 5), and/or the degree of GC-MC coupling (Fig. 5C). It is therefore likely that this phase-locked activity map is modifiable by plasticity mechanisms and central control [10]. Based on the adjustment of the spike phases, the mechanisms described here would result in population activity that is readable by decoding structures which function as coincidence detectors. Pyramidal cells of the piriform cortex have such detection properties [73]. In addition, synaptic integration by pyramidal dendrites is more sensitive to pattern-like inputs, as shown in other sensory systems [74], [75]. Thus, our model of a phase-locked map of MC activity across the OB supports the idea developed by Zou and Buck [76] that pyramidal cells could integrate odorant features using a combination of coincident MC inputs (as argued also in [77]) in a way similar to the mushroom bodies of insects [78], [79].
All experiments were performed in accordance with the guidelines of the European Communities Council. Male Wistar rats (150–350 g) obtained from Charles River Labs (L' Arbresle) were anesthetized with urethane (i. p. 1. 5 mg/kg, with additional supplements as needed) and placed in a stereotaxic apparatus. The dorsal region of the OB was exposed. Bulbar activity was recorded as a broadband signal (0. 1–5 kHz) using 16-channel silicon probes (NeuroNexus Technologies, Ann Arbor, MI) with a homemade, 16-channel DC amplifier. The data were digitally sampled at 10 kHz and acquired on a PC using the IOtech acquisition system (Wavebook, IOtech, Cleveland, OH). Probes were placed in the lateral or medial part of the OB at a depth that maximized the number of channels located in the mitral cell layer (MCL). The respiration signal was recorded using a homemade flowmeter based on a fast response time thermodilution airflow sensor. Odors were delivered through a dilution olfactometer (440 ml/min). The recording protocol was as follows: 5 s of spontaneous activity, 5 s of odor-evoked activity, and 5 s of post-stimulus activity. Each sampling included stimulation by simple linear aliphatic compounds. The varying features of odorants were either the number of carbons in the main chain (chain length: 5,6, 7 and 10 C) or the functional group associated with the chain (alcohol, ester, aldehyde or ketone). Additional odors have been used, including isoamyl acetate, p-cymene, and eugenol. All odors were delivered in front of the animal' s nose at a fraction of 18. 10−2 of the saturated vapor pressure. The time delay between each odor presentation was at least one minute. The MC model was derived from a previous study [35], which was derived in turn from [85]. The model uses parameters from [86], [87]. Its essential features are (1) spiking activity through sodium spikes, (2) bursting activity (Fig. 11A), (3) its current-frequency response (Fig. 11B), (4) resonant properties as revealed through sub-threshold oscillations (Fig. 11C), and (5) phase response curve (Fig. 11D). The method to compute the resonance frequency is to linearize the system of dynamical equations around its equilibrium for a given membrane potential and to extract this frequency from the imaginary part of complex eigenvalue λ (Imag (λ) /2π). The method to compute the phase response curve [39] was to impose a small instantaneous voltage deviation along the period of spiking (here equal to 25 ms). We reduced the number of variables in the model from nine to four by removing each of the variables individually and checking that the simpler model retained the essential features listed above; at the same time, some of the parameters were adjusted as necessary. The main characteristics were preserved as depicted in Fig. 11. The remaining variables were the membrane potential (V), the activation gating variable of the fast rectifying potassium current (mKf), the activation (mKs) and the inactivation (hKs) gating variable of the slow potassium current. The dynamics is described in Eqs. 5–8: (5) (6) (7) (8) Isyn is the synaptic current and is detailed later. The gating variable parameters are given by: The maximal conductance of the ionic channels was gNa = 500 S/m2; gNaP = 1. 1 S/m2; gKs = 310e S/m2; gKA = 100 S/m2; gKf = 100 S/m2. The leak conductance is gL = 0. 1 S/m2. The product is approximated to 0. 004. The reverse ionic potentials are EK = −70 mV and ENa = 45 mV, and the membrane reverse potential is EL = −66. 5 mV. The membrane capacitance is 0. 01 F/cm2. In terms of amplitude, to assess the synaptic inputs that the MCs receive under in vivo conditions, the MC model input resistance was verified to be consistent with the order of magnitude of synaptic inputs that an MC actually receives. Experimentally, the input resistance of an MC was found to be 115 MΩ [88]. We assumed that a limited part of the total membrane area was responsible for the input resistance and that axial resistance (or intracellular resistivity) was negligible for this neuronal small portion. This portion included the soma and proximal dendrites and corresponded to 10% of the total area or ∼15. 103 µm2 [89], [90] given that, beyond a distance of about 100 µm from the soma on either the primary or secondary dendrite, synaptic inputs are not conveyed to the soma [91]. This experimental “effective” input resistance becomes 1. 72 Ω. m2 when related to the membrane unit area. Our model is consistent with experiments since its input resistance measured at hyperpolarized membrane potential is 1. 5 Ω. m2. Previous studies have examined the kinetics of signaling to MCs and have found that MCs receive slow [64], fast, and asynchronous or simply fast inhibition from GCs [60]. In [17], it was reported that MCs receive weakly phased inhibition during gamma oscillation. From Fig. 4G of their report, we visually estimated that the amplitude of this phasic inhibition was up to 30%. The preferential phase of this oscillatory inhibition was estimated to be 359±9° of the LFP oscillation, and it showed strong statistical significance (p<10−8 by the Rayleigh test). Therefore, based on these experimental observations, our model assumes that on average, MCs receive an input current of the form (Eq. 9): (9) which is composed of a baseline conductance, including constant excitatory (gE) and inhibitory (gI) conductances, as well as a sinusoidal part, i. e. , the oscillating conductance whose amplitude is gIo and whose frequency is fosc. A white noise component was added to each excitatory and inhibitory component with amplitudes gEs and gIs, respectively, that were chosen to induce noise comparable to what is observed with in vivo intracellular voltage recording [88]. No other source of noise was added. gEs and gIs vary proportionally with gE and gI in Figs. 5 and 6. gEs is set to zero in Figs. 7 and 8. gIs is set to 0. 282 S. m−2. ms1/2 in Fig. 7B and 0. 141 S. m−2. ms1/2 in Fig. 7D. The reversal potentials of the excitatory and inhibitory synapses are EE = 0 mV and EI = −70 mV, corresponding to the reversal potentials of AMPA/NMDA receptors and GABAA receptors, respectively. Inhibitory synaptic inputs can completely stop MC firing activity [50] and reshape the temporal organization of spike trains [60]. It was therefore appropriate for our model to take into account the levels of inhibitory conductance that could have such effects on MC activity. The maximum conductance of a single synaptic input has been estimated to be on the order of 1 nS [92], [93]. A single MC has around 10,000 connections with GCs. As mentioned above, only about 10% of these inputs are conveyed to the soma [91], which corresponds to ∼1,000 synapses. Such a limited integration of the total synaptic input is consistent with other studies [94], [95]. Assuming that an MC receives inhibitory inputs from 1,000 synapses during every gamma cycle (period of ∼16 ms) and assuming an exponential time decay of 5 ms for GABAa [53], [60], it can be shown that, during the gamma oscillation, the MC average inhibitory input conductance is given by 1000*1nS*5 ms/16 ms = 312 nS. For the membrane area mentioned above, this represents gI = 20 S/m2. gE was adapted to reach a frequency up to 200 Hz, as observed in vivo. For example, Fig. 11E shows a voltage trace of the MC model that is forced by the oscillation and that receives tonic excitatory and inhibitory conductances. The amplitude of the oscillatory component gIo is discussed in the Results. For a given input, MC activities were measured after at least one second of simulation to avoid transient effects. Euler integration was used with a time step of 0. 02 ms. Simulations were performed using Matlab 7. 0 (The Mathworks, www. mathworks. com).
Olfactory function relies on a chain of neural relays that extends from the periphery to the central nervous system and implies neural activity with various timescales. A central question in neuroscience is how information is encoded by the neural activity. In the mammalian olfactory bulb, local neural activity oscillations in the 40–80 Hz range (gamma) may influence the timing of individual neuron activities such that olfactory information may be encoded in this way. In this study, we first characterize in vivo the detailed activity of individual neurons relative to the oscillation and find that, depending on their state, neurons can exhibit periodic activity patterns. We also find, at least qualitatively, a relation between this activity and a particular odor. This is reminiscent of general physical phenomena—the entrainment by an oscillation—and to verify this hypothesis, in a second phase, we build a biologically realistic model mimicking these in vivo conditions. Our model confirms quantitatively this hypothesis and reveals that entrainment is maximal in the gamma range. Taken together, our results suggest that the neuronal activity may be specifically formatted in time during the gamma oscillation in such a way that it could, at this stage, encode the odor.
neuroscience/theoretical neuroscience
biophysics/theory and simulation
neuroscience/sensory systems
computational biology/computational neuroscience
Specific Entrainment of Mitral Cells during Gamma Oscillation in the Rat Olfactory Bulb