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1Neurological Sciences Institute, Oregon Health and Science University, Beaverton, Oregon; 2Plexon Inc., Dallas, Texas; and 3Laguna Beach, California
Submitted 31 January 2005; accepted in final form 28 April 2005
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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; Mainen and Sejnowski 1995) and the mechanisms that underlie it (Harris et al. 2002; Mehta et al. 2002; Pouille and Scanziani 2001; Stevens and Zador 1998).
However, it is clear that there are also slower synaptic mechanisms that can relate spike timing to signal transmission over a much slower time scale. First, not all synaptic signals are rapid; even in glutamatergic transmission, kainate receptor activation can generate excitatory postsynaptic potentials (EPSPs) at resting potential that last for hundreds of milliseconds, leading to a much longer time window for synaptic integration (Frerking and Ohliger-Frerking 2002). Second, multiple forms of activity-dependent synaptic plasticity can combine during complex activity patterns to alter the synaptic response, depending on the temporal structure of prior activity; these synaptic dynamics can cause synaptic output to depend on spike timing over several seconds (Dobrunz and Stevens 1999; Ohliger-Frerking et al. 2003; Tsodyks and Markram 1997; Varela et al. 1997; Zador and Dobrunz 1997).
One difficulty in evaluating the degree to which slower synaptic mechanisms contribute to information processing is that doing so requires an understanding of how these mechanisms are engaged during physiologically relevant patterns of activity. To date, few studies have used such patterns to characterize synaptic function. This is not because of a paucity of data; indeed, single unit recordings are made throughout the CNS. Rather, the spike patterns observed during behavioral tasks are frequently presented in a form that does not translate into useful experimental paradigms for synaptic physiology, because this is not a focus of in vivo studies.
In this study, we examined spike patterns in CA3 pyramidal cells, the presynaptic source of Schaffer collateral synapses, from awake, behaving rats during the performance of a complex behavioral task, in which correct task performance is correlated with changes in the ensemble activity of hippocampal neurons (Deadwyler et al. 1996; Wiebe and Stäubli 1999). We will address several questions. What is the level of overall activity during a complex task, and how consistent is that activity among different cells? How closely does a spike train during a complex behavior match random firing, and what are the sources of nonrandom firing? How do environmental cues change afferent activity, and how are different choices within the same general class of cue encoded? How prevalent is synchronous firing between cells, and what is the time window over which synchrony occurs? The answers to these questions will be used to construct a model for producing artificial spike trains and to make some generalizations about synaptic transmission during physiologically relevant patterns of activity.
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METHODS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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) during performance of an olfactory delayed match-to-sample task. The sequence of events involved in the task are outlined in Fig. 1 A. Briefly, the task was initiated by a nose-poke on a button in the sample arm. After a 2-s delay, an odor (the sample odor) was presented in the sample arm of a Y-maze for 10 s, followed by a variable delay. After the delay, two different odors were presented, one in each of the two test arms of the maze (the test odors). One of these test odors was the same as the sample odor, and the other was a novel odor. The rat could indicate which test arm contained the novel odor by entering a test arm and pressing a button located at the end of that arm. If the rat was correct, it was rewarded with water; if not, it was punished with a brief flash of light.
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), it has been shown that many hippocampal pyramidal neurons respond to both spatial and nonspatial cues during a complex task (Hampson et al. 1999; Wiebe and Stäubli 1999; Wood et al. 1999). In this study, cells could generate responses (defined as a change in the firing rate) to various cues during this task, for example, exposure to the sample odor, entry into a test arm, or presentation of the reward/punishment. There were also parameters within the task that differed between individual trials of the task, so that cellular responses during a cue could discriminate between different options of that parameter. There were three parameters monitored: which of two odors the rat was exposed to in the sample phase (odor-discrimination), which test arm the rat entered (location-discrimination), and whether the rat was rewarded or punished (performance-discrimination). Previous study has indicated that during this task, most cells generate responses that discriminate multiple parameters, although some cells discriminate only one parameter, respond to cues in a nondiscriminatory fashion, or do not respond to any of the monitored cues at all (Wiebe and Stäubli 1999).
Adult Long Evans rats were trained over an 
1-mo period to perform the task and were then surgically implanted with a microwire electrode array consisting of two rows of eight microwires, cemented in place with bone wax and dental cement. An uninsulated reference wire was used to eliminate low-frequency movement artifacts. After a 6- to 7-day recovery period, the animals were retrained, and recordings were performed during the task. At the end of the recordings, each rat was killed with pentobarbital sodium (100 mg/kg), and 40 µA of current was passed through the recording electrodes. The brain was fixed, removed, and sectioned to localize the electrode tips.
Recordings were made using a multichannel neuronal acquisition processor system (Plexon, Dallas, TX) that performed on-line multichannel spike sorting. Neural activity and behavioral responses were digitized and time-stamped for subsequent computer processing. Spikes were isolated using time–amplitude window discrimination and waveform template matching; no more than four single units could be isolated per microwire. Single units were isolated and separated into pyramidal cells and interneurons based on a linear cut-off in the relationship between mean firing rate and spike width, as described (Wiebe and Stäubli 1999).
An initial characterization of this data set has been published (Wiebe and Stäubli 1999). In this study, the data were further analyzed using a quantitative analysis of spike timing. Spike trains for individual cells were separated and analyzed using Neuroexplorer (Plexon) and user-written programs in SigmaPlot (Jandel Scientific). All data are presented as means ± SE. Significance was assessed at P < 0.05.
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RESULTS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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We will first consider several general properties of CA3 pyramidal cell activity during a behavioral task (outlined in Fig. 1A; for details of the task, see METHODS). We will address several questions. What is the overall level of activity, and how does it correlate with cell function? Which ISIs are observed during the task, and how consistent is the ISI distribution across different cells? How does the ISI distribution change as a function of the mean firing rate? The answers to these questions will allow us to relate cellular activity in vivo with the stimulation protocols used in vitro to monitor synaptic function.
What are the firing rates of CA3 pyramidal cells during a behavioral task?
It has been reported since the earliest studies of hippocampal pyramidal cells in awake, unrestrained rats that essentially all hippocampal pyramidal cells fire in irregular patterns with sustained firing rates <10 Hz and that there is a qualitatively large variability in overall firing rate for different neurons (Ranck 1973). Consistent with this finding, we observed that different CA3 pyramidal cells had highly variable mean levels of activity even during a single trial of the task, as shown for several cells recorded simultaneously in Fig. 1B. The mean firing rate for all 766 CA3 pyramidal cells available in recordings from 18 animals was 0.97 ± 0.05 Hz, considerably higher than that typically used in studies of synaptic transmission (0.05–0.2 Hz, typically 0.1 Hz). However, because cross-cell variability in the firing rate extended over several orders of magnitude, the mean has limited value in describing the population. To provide a more complete quantitative description of the population of CA3 pyramidal cells, we measured the distribution of firing rates from the population of CA3 pyramidal cells recorded in each animal and averaged this distribution for all animals that had a large enough population of CA3 pyramidal cells to accurately measure that distribution (n = 13; Fig. 1C). This average distribution reveals that firing around 1 Hz is most common, and most (75%) cells fire at rates >0.2 Hz.
Does the function of a cell predict its firing rate?
An obvious mechanism for explaining the large variability in firing rate would be that different cells encode different numbers of functional parameters during performance of the task and are therefore active to different degrees. To evaluate this possibility, we considered the impact of functional responses during the task on cellular activity. We first considered the possibility that cells that generated discriminatory responses based on different parameters might have different mean firing rates. However, we did not observe any difference in mean firing rate between cells that selectively discriminated between odor, location, or performance (data not shown).
However, it remains possible that cells might have higher firing rates if they respond to more parameters during the task. For those cells with sufficient data to do so, we separated the cells into five functional categories: cells that did not respond to (or discriminate based on) any of the cues that were monitored (n = 86); cells that responded to one or more cues but that did not discriminate based on odor, location, or performance (0 parameters; n = 211); cells that responded in a discriminatory fashion based on only one of the three parameters (1 parameter; n = 52); cells that responded in a discriminatory fashion based on two of the three parameters (2 parameters; n = 89); and cells that responded in a discriminatory fashion based on all three parameters monitored (3 parameters; n = 276). We found that nonresponsive cells had lower mean firing rates than did responsive cells, and cells that discriminated all three parameters had higher mean firing rates that did cells discriminating fewer parameters; the intermediate three categories had indistinguishable mean firing rates when compared with each other (Fig. 2 A). However, the mean firing rates of these different categories differed by roughly an order of magnitude, whereas the total variability in mean firing rate encompassed a much larger range, over three orders of magnitude. As a result, mean firing rates were poor predictors of cell function (Fig. 2B). These results indicate that the mean firing rate of a cell does depend weakly on its function, but the majority of the variability in the mean firing rate is determined by some other factor; moreover, the overall firing rate of a cell during the task is independent of the specific identity of the parameter(s) that it encodes.
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The mean firing rate provides an overall view of the general activity level of the cell but does not address the variability in firing around that mean. To determine specific patterns of spiking with higher resolution, we examined the interspike interval (ISI) distributions of CA3 pyramidal cells. As with mean firing rates, individual cells had highly variable ISI distributions, as shown by nine representative cells in Fig. 3. Many studies, including our own, have approximated the firing properties of CNS neurons with random firing patterns governed by Poisson statistics; however, we observed that most ISI distributions were clearly indicative of a nonrandom firing pattern (see Fig. 4 A, gray lines, for ISI distributions expected based on homogeneous Poisson statistics), frequently having obvious structure within the distribution or strongly preferred ISIs. This observation was consistent even among cells that did not respond to any of the cues that were monitored (e.g., cell 1). Although occasionally cells had qualitatively similar ISI distributions, such as cells 4 and 8 in Fig. 3, major subpopulations of cells with similar ISI distributions were not observed (data not shown).
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The second feature that is clear from the data in Fig. 4A is that, even when averaged across cells that are matched to similar mean firing rates, the ISI distributions are not well approximated by random firing over most of the firing rates observed. For illustrative purposes, the ISI distributions expected from random firing at the appropriate frequency are shown in Fig. 4A (gray lines). The observed ISI distributions from 0.1 to 3 Hz were strongly overdispersed compared with what would be expected from random firing, with overrepresentation of both the longest and shortest ISIs. Overdispersion was modest in cells firing around 10 Hz (1% of the total population), but was still apparent on closer inspection. These results suggest that random firing patterns will cover a much smaller range of ISIs than are observed in vivo.
Sources of nonrandom activity in CA3 pyramidal cells
Up to this point, we have noted a number of ways in which the ISI distributions of CA3 pyramidal cells do not meet the expectations of random firing patterns. We therefore turned our attention to the issue of how prevalent nonrandom patterns of activity are. We considered three issues to be most important. First, over what time scale does nonrandom activity persist? Second, to what extent can long, nonrandom activity patterns be described solely by taking into account the nonrandom ISI distribution? Finally, to what extent do cellular responses to environmental cues contribute to nonrandom activity? We will address the first two questions here; the third is sufficiently complex that we will address it in a separate dedicated subsection.
How long does the occurrence of a spike affect the probability of firing?
To assess the time scale over which nonrandom patterns of activity persist, we used an autocorrelogram analysis. The autocorrelogram indicates the probability of observing a spike as a function of time, given that a spike occurred at the zero time-point. The point at which the probability of spiking becomes independent of time indicates the length of time over which nonrandom interactions between spikes occur. One common use of autocorrelograms is to detect theta oscillations, which are widely observed in the hippocampus (Buzsaki 2002; Kahana et al. 2001). Theta oscillations are prominent in recordings from CA1 pyramidal cells during performance of tasks requiring odor and spatial discrimination (Otto et al. 1991). In the CA3 pyramidal cells examined in this study, theta oscillations were somewhat less pronounced, with only a minority of analyzed cells (21 of 86 cells analyzed) showing a damped oscillation in the theta frequency range (5–10 Hz, average = 7.4 ± 0.4 Hz), which was resolvable for between 2 and 25 cycles (average = 4.2 ± 0.9 cycles; Fig. 5 A). These theta oscillations will contribute to long-lasting nonrandom activity in the minority of cells that have them.
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This slow phase indicates that there is a long-range interaction between spikes that can last for several seconds. It remains unclear whether the long-range interactions observed are caused by long-range interactions between intrinsic spiking mechanisms or long-range interactions between environmental cues that drive spiking, although we note that similar long-range interactions can be generated by sustained firing at a constant frequency (see Fig. 11D). However, regardless of the mechanism that underlies them, these long-range interactions will affect the activity pattern transmitted to the synapse.
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Given that nonrandom spiking occurs over such a long time scale, we wondered whether this indicates that there are long sequences of many nonrandom spikes that fall into a distinct pattern. To address this issue, we reasoned that nonrandom spike sequences would be manifested as a deviation from repeated random samples from the ISI distribution. We therefore examined whether the joint distribution of ISIs during spike triplets could be explained as the random superposition of two spike doublets drawn from the ISI distribution. The ISI distribution of a representative cell is shown in Fig. 6 A, and the joint distribution of two ISIs in succession during a spike triplet is shown on a color-scale in Fig. 6B for all triplets in the train. The expected distribution if each of the two ISIs in the triplet were randomly drawn from the ISI distribution is also shown (Fig. 6C).
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; Ranck 1973), and the remaining 4 showed a more complex or diffuse pattern of nonrandom triplets. As a control to ensure that these nonrandom triplets are not artifacts caused by undersampling or overbinning, we shuffled the sequence of ISIs in the original data set to remove any nonrandom triplets (data not shown) and subtracted the expected distribution from the new shuffled data set (Fig. 6E). In a total population of 21 cells, the difference between the expected distribution and the shuffled distribution was clearly smaller (P < 10–5) than that seen using unshuffled data, and there is no structure to the difference function after shuffling the data. The fraction of spikes that are genuinely involved in nonrandom spiking, as opposed to sampling or binning errors, was calculated by subtracting the fraction of nonrandom triplets in the shuffled data set from the fraction of nonrandom triplets in the actual data set. These nonrandom patterns that were unaccounted for by random sampling from the ISI distribution were a small minority of the total spiking (<10%), indicating that the vast majority of spiking (>90%) could be predicted by random sampling from the ISI distribution.
To determine if the nonrandom patterns are associated with responses to environmental cues, we compared the nonrandom triplets in responsive cells to the triplets in nonresponsive cells (Fig. 6F). We found that nonrandom triplets were significantly more frequent in cells that responded to a monitored environmental cue during the task (n = 14) than in those that did not (n = 7). We conclude that most spiking in CA3 pyramidal cells (>90%) can be described as random sampling from a nonrandom ISI distribution; however, a small minority of spikes are generated by patterned sequences that cannot be readily predicted by the overall ISI distribution, and these patterned sequences are more frequent in cells that respond to environmental cues, suggesting that they may be associated with cellular responses to environmental cues.
Responses to environmental cues
Up to this point, spike trains have mainly been considered without regard to whether or where responses occur and what the properties of those responses are. We now turn our attention to characterizing cellular responses to environmental cues, with a focus on three questions. First, what is the time-course over which cells respond to a cue, and how complex is that response as a function of time? Second, how does the presence or absence of a cellular response affect the ISI distribution? Finally, how do cellular responses differ during discrimination of cues that are functionally similar?
How do CA3 pyramidal cells respond to environmental cues?
To determine the time-course of cellular responses to environmental cues, we examined two types of responses in detail: responses to the onset of the sample odor (Fig. 7 A) and responses to leaving the maze sample arm (Fig. 7B). For this analysis, we only examined cells that did not discriminate in their responses based on any of the parameters monitored. For these cells, responses were fairly stereotypical. Raster plots from representative cells that responded to these phases of the task are shown in Fig. 7, A1 and B1, respectively, and average responses from those representative cells are shown in Fig. 7, A2 and B2. The average responses for all cells that responded to these cues are shown in Fig. 7, A3 (n = 109) and B3 (n = 92). The time-courses of the cellular responses were complex in both cases. It is not clear from this data whether such temporally complex responses during maze performance are due to a simple relationship between firing and complex stimuli or to a complex relationship between firing and simple stimuli; however, the conclusion that cellular responses to behavioral cues during a task are temporally complex is independent of the mechanism underlying that complexity.
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To more quantitatively consider the firing patterns involved in responses, we examined whether specific ISIs were associated with cellular responses. As an initial attempt to ascertain this information, we compared the total ISI distributions of cells that did not show a response to any of the cues during the task (n = 86; Fig. 8 A1) with those that did (n = 628; Fig. 8A2). The difference between these distributions shows ISIs that were more common among responsive cells as positive values and ISIs that were more common among nonresponsive cells as negative values (Fig. 8A3). Cells that had responses clearly showed a prominent shift toward intermediate frequencies, with both short and long ISIs having a larger representation in cells that did not respond.
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The analysis in Fig. 8A provides an estimate of how cellular responses change the ISI distribution, but does so by comparing data from different cells. To provide a within-cell comparison of responses and baseline periods, we selected cells that only responded to entry into the test arms during the task (n = 34). The ISI distribution of a representative cell during the entire trial is shown in Fig. 8B1 and during the task before test-arm entry in Fig. 8B2. These two distributions are very similar, indicating that the majority of spiking occurs during the nonresponse phase of the task. However, the ISI distribution following task arm entry (Fig. 8B3) showed a prominent increase in intermediate ISIs and a prominent decrease in the longest ISIs, consistent with results from cross-cell comparisons. This increase in intermediate ISIs was more obvious when the linear difference index was calculated, comparing ISIs before and during the test phase (Fig. 8B4). There was qualitative agreement between the cross-cell (Fig. 8A) and within-cell (Fig. 8B) comparisons, in that both showed a shift during responses from long and short ISIs to intermediate ISIs, with a maximal increase in ISIs of a few hundred milliseconds during the responses. Quantitative differences between the two methods are possibly due to the fact that all within-cell comparisons were only during test-arm entry, whereas the cross-cell comparisons were used for all cells that responded to any of several different cues, potentially with different temporal statistics.
How do cells discriminate between different options of the same cue?
Many CA3 pyramidal cells can discriminate between different options of a behaviorally relevant parameter. There are two different mechanisms by which cellular responses could discriminate between two options: first, the cellular responses to the two options might have similar time-courses, but differences in response amplitude; alternatively, responses to each option might have distinct time-courses. To differentiate between these two possibilities, we examined the time-courses of responses to either of two choices in cells that showed discriminatory responses to environmental cues. We found that results were variable; there were some cells that showed discriminatory responses that were different in their time-course (Fig. 9 A), but others that showed discriminatory responses that were similar in time-course but differed in magnitude (Fig. 9B).
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Synchrony between cells
Up to this point, we have considered the firing of individual neurons in isolation. This is because most forms of short-term, activity-dependent synaptic plasticity that have been described are independent of the number of fibers activated. However, it is clear that the timing of spikes in one cell relative to another is a critical factor in temporal summation, a major mechanism for population coding that is also a factor underlying the associative properties of many forms of long-term synaptic plasticity. We therefore consider two major questions regarding the correlated firing of different CA3 pyramidal cells. First, how common is tightly coupled firing between cells? Second, how precise is correlated firing, and over what time scale does correlated firing persist?
Precisely correlated firing between cells is rare
To determine the extent to which cells are precisely correlated in their firing, we examined 202 cross-correlations between 43 CA3 pyramidal cells in eight separate clusters. Representative cross-correlograms are shown in Fig. 10 A. In many cross-correlograms (90 of 202), there was little if any resolvable correlated firing between cells (Fig. 10A, top left). However, in a minority of cross-correlograms, there was a strong and precise correlation in firing between cells (37 of 202; Fig. 10A, top right). Precisely correlated firing could be caused by synchrony, in which two cells fire at the same time or by the existence of a "synfire" chain, in which cells in a network are strongly connected so that firing in one cell leads to subsequent firing in another cell with a highly precise latency (Ikegaga et al. 2004). We did not observe precisely correlated firing with a nonzero latency, indicating that precisely correlated firing was invariably caused by synchrony. This argues against synfire chains as a common mechanism of correlated firing between CA3 pyramidal cells. We note that even in the cases where synchrony was clearly evident in the cross-correlogram, the probability that any given spike in one cell was synchronous with a spike in the other cell was still modest (<0.2 for most cases).
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While precise cross-correlations were infrequent, many cells had correlated firing that was imprecise. Some of these correlations (25 of 202) were asymmetrical, with a strong tendency for one cell to fire before the other (Fig. 10A, middle left); however, other correlations (46 of 202) were symmetrical, indicating that overall, the cells fired together but with imprecise timing (Fig. 10A, middle right). Some correlations (22 of 202) were also observed with oscillations in the theta frequency range (Fig. 10A, bottom left), although the amplitude of these oscillations was invariably very weak. The categories defined here were not mutually exclusive, and cells could express both precise and loose coupling simultaneously (Fig. 10A, bottom right).
To quantify the prevalence of correlated cell firing, we examined the probability of synchronous firing as function of the time window used to define synchrony. Only nonrandom synchrony, defined as cross-correlations exceeding the baseline of the cross-correlogram (established at ±1 s), was analyzed. When the window of synchrony was narrow (±10 ms), most cell pairs (76%) had a modest (<3%) probability of synchronous firing, and 97% of the cell pairs had a probability of synchronous firing of <20% (Fig. 10B, top). However, when the window of synchrony was broadened to 100 ms, the fraction of cell pairs with a modest probability of synchronous firing dropped to 54%, and the remaining cell pairs had a probability of synchronous firing that was much higher, even exceeding 1 in some cases (indicating that firing of a spike in 1 cell was often accompanied by firing of multiple spikes in the other; Fig. 10B, bottom). When the average probability of synchronous firing plotted as a function of the time window of synchrony for all cell pairs, the probability of synchronous firing was strongly dependent on the precision of the window used to define synchrony, with loosely coupled spiking occurring over hundreds of milliseconds (Fig. 10C).
These results indicate that precisely correlated firing in CA3 pyramidal cells is uncommon, although loosely correlated firing is widespread. Loosely correlated firing could be caused by weak network activity or uncorrelated responses of multiple cells to the same complex environmental cues. The timing of this loose coupling is sufficiently imprecise that temporal summation of rapid PSPs, like those mediated by AMPA receptors, is unlikely to be affected much by it. However, imprecisely correlated firing could have a strong effect on temporal summation of slow PSPs, like those mediated by kainate receptors.
An empirical model for generating artificial spike trains
A major purpose of this study was to highlight features of in vivo spike trains that could impact synaptic function, so that these features can be incorporated into studies of synaptic physiology. Obviously, the simplest way to ensure that afferent activation in vitro closely mimics in vivo activity is to use in vivo spike trains as externally imposed stimuli. This approach has been used in the past (Dobrunz and Stevens 1999; Froemke and Dan 2002; Hampson et al. 2003; Ohliger-Frerking et al. 2003), but the heterogeneity of activity patterns seen in this data set raise the concern that data from an individual cell may not be representative of the activity patterns seen in the overall population. Here we compile the features of the available data that we consider to be most relevant and propose a simple method to generate artificial spike trains that incorporate those features.
In our view, artificial spike trains that generally mimic in vivo spiking should be designed according to the following general guidelines. 1) The population of cells is so heterogeneous that the model should be based on averaged data from many cells. 2) The average ISI distributions are overdispersed when compared with random ISI distributions, and the model should include this overdispersion. 3) Increased mean firing frequency, including during cellular responses, is predominantly caused by an increased representation of intermediate ISIs, and the model should recapitulate this feature. 4) The nonrandom ISI distribution can explain >90% of spiking, so a model that uses only the ISI distribution without regard to higher-order interactions is sufficiently accurate to mimic firing patterns at this early stage of investigation.
Based on these constraints, we constructed a simple empirical model from the available data, using the family of ISI distributions shown in Fig. 4. These distributions were organized on a third axis, mean firing rate, and interpolated to generate a continuous three-dimensional function in which the probability of a given ISI for a given overall firing rate was calculated (Fig. 11 A; see Supplemental Materials1 ). This function was sampled at different mean firing frequencies to construct firing patterns that mimic in vivo firing at those frequencies, and those patterns were spliced together appropriately to construct artificial spike trains that incorporate changes in firing rate ((Fig. 11B, raster plots). This method can be used to construct trains that successfully reproduce rapid, sharp changes in firing frequency between steady states (Fig. 11B) or cellular response waveforms from experimental recordings (Fig. 11C; response waveform from Fig. 9A). At a constant frequency of 1 Hz, the model produced an autocorrelogram that indicated nonrandom interactions between spikes over a long period, with a slow exponential phase of decay (
= 2 s), similar to that seen with real spike trains (Fig. 11D).
To what extent does the model successfully reproduce the features of the data discussed above? The model will by definition be effective over sustained firing rates ranging approximately between 0.1 and 10 Hz, encompassing the vast majority of cells. Moreover, because the model is empirical, it will reproduce the ISI distributions in Fig. 4. By definition, increased firing (e.g., during simulated responses to environmental cues) will be associated with an increased representation of intermediate ISIs. The model also reproduces the long-lasting, nonrandom interactions between spikes that are observed in the autocorrelogram and can be used to mimic simulated response waveforms of arbitrary temporal complexity.
However, we caution that there are some features of the data that will not be reproduced by the model. The model cannot describe sustained firing at frequencies that are outside the limits of the distribution in Fig. 11A. The model also will not mimic the heterogeneity in the ISI distributions of different cells, because it is based on averaged ISI distributions. The model will not reproduce the small fraction of nonrandom sequences of multiple spikes, because it is based on random sampling from the ISI distribution; however, extending the model to incorporate a given nonrandom sequence into the train would be trivial. Finally, the model in its current form mimics activity for a single afferent fiber, precluding the generation of cross-correlations between fibers. However, cross-correlations between afferents are typically weak and loose, making them irrelevant for many experimental aims, and extending the model to include a specific pattern of cross-correlations for those scenarios in which it must be taken into account would be relatively simple. We conclude that the model reproduces many properties of cell firing that we have observed, and can be extended to incorporate weak cross-correlations or nonrandom sequences, according to the specific experimental parameters for which the spike trains are being used.
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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CA3 cells have variable firing properties, but generally fire at 1 Hz
Different CA3 pyramidal cells have different firing properties, complicating description of these firing properties in general terms. Variability in the number or identity of parameters to which a cell responds accounts for only a minor fraction of the total variability in firing. ISI distributions are also highly variable, indicating that large intrinsic variability in firing within a broad population may be the most productive way of describing firing patterns in CA3 pyramidal cells.
Mean firing rates of around 1 Hz are most commonly observed in CA3 pyramidal cells. This firing rate is considerably higher than is typically used in most synaptic physiology protocols, and it remains to be seen whether the forms of short- or long-term plasticity that are generated at this level of activity are similar to those that have been widely characterized during lower frequencies of stimulation.
The observation that sustained firing at 1–10 Hz is common for CA3 pyramidal cells is surprising, because long-term depression (LTD) is reliably induced by constant frequency trains in this range in vitro (Dudek and Bear 1992; Mulkey and Malenka 1992). LTD at these synapses is difficult to induce in awake adult rats (Staubli and Scafidi 1997) for unknown reasons. One possible explanation raised by our data is that the activity patterns experienced in vivo normally cause a tonic induction of LTD that occludes externally imposed induction protocols. However, because complex spike trains differ from constant-frequency trains in their efficacy at inducing long-term synaptic plasticity (Dobrunz and Stevens 1997; Perrett et al. 2001; Sjostrom et al. 2001), the patterns seen in vivo may not induce LTD as effectively as constant frequency stimulation. It will be of interest to assess the induction of long-term plasticity in response to physiologically relevant patterns of activity.
Firing patterns of CA3 pyramidal cells are nonrandom
Firing is nonrandom in these cells, with ISI distributions showing a broader range than predicted by random firing. Others have noted nonrandom activity patterns in hippocampal pyramidal cells in a variety of contexts (Barbieri et al. 2001; Buzsaki 2002; Fenton and Muller 1998; Kahana et al. 2001; Lansky and Vaillant 2000). The majority of nonrandom firing in our study is caused by nonrandom structure in the ISI distribution. Random sampling from the ISI distribution predicts spike triplet sequences with >90% accuracy, suggesting that the ISI distribution of a cell can generate a fairly accurate artificial spike train by itself. However, the residual sequences that cannot be explained in these terms may be important for information processing, and further characterization of these sequences will be of interest.
Obviously, some nonrandom firing is generated by responses to environmental cues embedded in the overall activity. However, because the ISI distributions of nonresponsive cells were nonrandom (Fig. 8A1) and the ISI distribution of responsive cells are relatively unaffected by removal of responses (cf. Fig. 8, B1 and B2), environmental cues are likely to be a minor source of nonrandom firing. We cannot exclude the possibility that some nonrandom firing is generated by responses to unidentified cues. However, because the population of nonresponsive cells could be clearly separated from the population of responsive cells by mean firing rate, ISI distribution, and prevalence of nonrandom spike sequences, it seems unlikely that much cellular activity is dictated by environmental cues that are outside our control.
Intermediate ISIs are selectively promoted during increased activity
A third conclusion is that increased firing is represented as an increase in intermediate ISIs, for both different cells firing at different firing rates and for increased firing associated with responses to environmental cues. The shortest ISIs, which correspond to frequencies seen during complex spike bursting, are largely insensitive to overall firing rate and are less prominent during cellular responses. This argues against complex spike bursts as a major mechanism for encoding environmentally relevant cues, consistent with the observations of Harris et al. (2001).
The range of intermediate ISIs is similar to the range in which short-term plasticity is maximal, as assessed by paradigms such as paired-pulse facilitation (Creager et al. 1980). These ISIs are also a range in which kainate receptor-mediated EPSPs will undergo temporal summation, whereas AMPA receptor-mediated EPSPs will not (Frerking and Ohliger-Frerking 2002). The importance of slow synaptic mechanisms may therefore be increased in cells with a higher overall firing rate or during responses to environmental cues.
Cellular responses to environmental cues are temporally complex
During realistic behaviors, cellular responses to environmental cues are complex. Discrimination between different options within a cue is also complex, expressed mainly as differences in the time-course of the response. It will be of interest to identify features of cellular responses that are enhanced or suppressed by synaptic transmission, to determine whether synaptic transmission enhances or prevents transmission of parameter discrimination from CA3 to CA1. In this context, it is noteworthy that CA3 pyramidal cells are more specific in the cues that activate them than CA1 pyramidal cells (Barnes et al. 1990; Wiebe and Stäubli 1999).
Above a limiting frequency of afferent firing, cortical synapses transmit transitions between firing frequencies but provide the same mean depolarization at steady-state (Abbott et al. 1997; Tsodyks and Markram 1997). This does not seem to be relevant at Schaffer collateral synapses for two reasons. First, the cellular responses that we have observed are temporally complex, without simple transitions from one steady-state firing frequency to another. Second, the limiting frequencies at cortical synapses are 10–20 Hz (Abbott et al. 1997; Tsodyks and Markram 1997), well above the sustained firing rates seen here. The limiting frequency at Schaffer collateral synapses has not been determined but is probably higher than at cortical synapses, because the synaptic depression that sets the limiting frequency is modest at Schaffer collateral synapses (Selig et al. 1999).
Precise synchrony between CA3 pyramidal cells is rare, but loosely coupled firing is common
CA3 pyramidal cells have little precisely correlated firing. The lack of precisely correlated firing indicates that extracellular stimulation of multiple afferent fibers, used in the vast majority of studies of synaptic transmission, causes afferent synchronization to a degree that does not occur in vivo. However, this method of stimulation retains its usefulness, with two caveats. First, the synaptic behavior elicited by this technique is averaged over several synapses, and cross-synapse heterogeneity will not be reflected. Second, the absolute threshold for activation of associative synaptic processes, including long-term plasticity and glutamate spillover, may be more sensitive in experiments using multifiber stimulation than it is in vivo, and the prevalence of these processes may therefore be overestimated.
Loosely correlated firing, however, is common. This correlation is sufficiently imprecise that it is unlikely to promote temporal summation of AMPA receptor-mediated synaptic transmission, although its effects on kainate receptor-mediated transmission will likely be substantial.
Loosely correlated spike timing may also be important in the induction of spike-timing dependent long-term plasticity (Bell et al. 1997; Markram et al. 1997). Correlated spike trains based on in vivo recordings can induce long-term plasticity in visual cortex (Froemke and Dan 2002), and behavioral manipulations can alter the correlated firing, thereby altering the induction of long-term potentiation (LTP) or LTD, in barrel cortex (Celikel et al. 2004). Asymmetrical cross-correlations between CA3 pyramidal cells could, at least in principle, strongly engage spike timing-dependent plasticity between CA3 pyramidal cells. However, the importance of spike timing–dependent plasticity in the hippocampus is unclear, because pairing of individual presynaptic and postsynaptic spikes does not reliably induce long-term plasticity in the hippocampus (Pike et al. 1999; Thomas et al. 1998; but see Nishiyama et al. 2000).
Model for artificial spike trains mimics spike trains observed in vivo
We have developed an empirical model for artificial spike trains that mimic those seen in vivo. This model is described at length in RESULTS, but we note here that the model can generate spike trains to mimic sustained firing over a range of frequencies and can also be used to mimic complex changes in frequency such as those seen in response to environmental cues.
We envision several experimental contexts in which this model will be useful. The model will aid in characterizing synaptic dynamics by ensuring that the appropriate frequencies and ISIs are examined. It will also allow elucidation of whether physiologically relevant patterns of activity favor or suppress the induction of long-term plasticity, relative to constant frequency trains that have been used so far. Finally, it will assist studies to define the contexts in which fast or slow EPSPs dominate cellular excitability. These studies will be helpful in defining the contribution of slow synaptic mechanisms to information processing in the CNS.
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ACKNOWLEDGMENTS |
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Present address of U. Staübli: P. O. box 820, Laguna Beach, CA 92652.
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1 The Supplementary Material for this article is available online at http://jn.physiology.org/cgi/content/full/00108.2005/DC1. 
Address for reprint requests and other correspondence: M. Frerking, Neurological Sciences Inst., Oregon Health and Science Univ., Beaverton, OR 97006 (E-mail: frerking{at}ohsu.edu)
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Barbieri R, Quirk MC, Frank LM, Wilson MA, and Brown EN. Construction and analysis of non-Poisson stimulus-response models of neural spiking activity. J Neurosci Methods 105: 25–37, 2001.[CrossRef][ISI][Medline]
Barnes CA, McNaughton BL, Mizumori SJ, Leonard BW, and Lin LH. Comparison of spatial and temporal characteristics of neuronal activity in sequential stages of hippocampal processing. Prog Brain Res 83: 287–300, 1990.[ISI][Medline]
Bell CC, Han VZ, Sugawara Y, and Grant K. Synaptic plasticity in a cerebellum-like structure depends on temporal order. Nature 387: 278–281, 1997.[CrossRef][Medline]
Best PJ, White AM, and Minai A. Spatial processing in the brain: the activity of hippocampal place cells. Annu Rev Neurosci 24: 459–486, 2001.[CrossRef][ISI][Medline]
Buzsaki G. Theta oscillations in the hippocampus. Neuron 33: 325–340, 2002.[CrossRef][ISI][Medline]
Celikel T, Szostak VA, and Feldman DE. Modulation of spike timing by sensory deprivation during induction of cortical map plasticity. Nat Neurosci 7: 534–541, 2004.[CrossRef][ISI][Medline]
Creager R, Dunwiddie T, and Lynch G. Paired-pulse and frequency facilitation in the CA1 region of the in vitro rat hippocampus. J Physiol 299: 409–424, 1980.
Deadwyler SA, Bunn T, and Hampson RE. Hippocampal ensemble activity during spatial delayed-nonmatch-to-sample performance in rats. J Neurosci 16: 354–372, 1996.
de Ruyter van Steveninck RR, Lewen GD, Strong SP, Koberle R, and Bialek W. Reproducibility and variability in neural spike trains. Science 275: 1805–1808, 1997.
