We investigated how respiratory rhythms and the recruitment of short-term synaptic plasticity at bulb-to-cortex synapses affect the transfer of olfactory bulb population activity to the cortex. We initially characterized the synaptic responses from principle neurons (n=32) in L2 of anterior olfactory cortex (AOC, n=6) and piriform cortex (APC, n=26) during lateral olfactory tract (LOT) stimulation. Based on our results, we created simulated mitral/tufted cell (M/T) population currents that were used to drive spiking in cortical principal neurons (n=19). We then explored how the interactions between the timescales of short-term plasticity at M/T synapses and respiratory rhythms give rise to different cortical responses.
Short-term synaptic plasticity at lateral olfactory tract (LOT) synapses
The transfer of odor information represented by M/T spike trains is likely influenced by the short-term plasticity at synapses between M/T cells and cortical neurons in the lateral olfactory tract (LOT). To characterize plasticity at these synapses, we stimulated the LOT (Layer 1a) with a train of Poisson distributed pulses (7 s duration, mean rate: 10 Hz). This stimulus is advantageous because it allows the quantification of short-term plasticity over a range of stimulus frequencies (1–100 Hz) using a variety of inter-pulse intervals (IPI) between 10 and 1000 ms. These IPIs are consistent with inter-spike intervals found in M/T spike trains that have instantaneous firing rates ranging from 1–200 Hz (Cury et al., 2010
; Carey and Wachowiak, 2011
, Shusterman et al., 2011
). We measured short-term plasticity as the ratio of the amplitude of each EPSP of the train relative to the first EPSP of the train (relative amplitude, RA). Changes in RA that were greater than 1 indicated short-term facilitation, while RA values less than 1 indicated depression. When we assessed the average RA across the train we found that the distribution of synapse types was strikingly trimodal (). This was surprising because previous reports have described these inputs dichotomously as either facilitating or depressing (Bower and Haberly, 1986
; Hasselmo and Bower, 1990
; Suzuki and Bekkers, 2006
). We found facilitation-dominant synapses (F, n=7, red) that had an average RA of 1.45 ± 0.06 () and values near 1 for only the shortest IPIs (). Facilitating-depressing synapses (FD, n=10, green) had an average RA of 0.93 ± 0.03 and RA values <1 for short IPIs and RA>1 for longer IPIs. Depression-dominant synapses (D, n=15, blue) had an average RA of 0.44 ± 0.02 and rarely had RA values >1 for any IPI. Example traces recorded from neurons receiving each type of synapse are shown in .
Short-term plasticity at LOT synapses
The EPSPs of depression-dominant synapses had significantly greater initial amplitudes (D: 7.8 ± 4.4 mV) than synapses that showed facilitation (F & FD: 2.4 ± 2.3 mV, p<0.01) but the synaptic decays did not differ (τα
: facilitating: 14.3 ± 1.3 ms, depressing: 14.5 ± 1.4 ms, p: 0.90, see Eq. 1
, Methods). The majority of neurons that received solely depressing input (n=15) were regular spiking (adaptation ratio <=1, see Methods) consistent with semilunar cells. Alternatively, most neurons that received facilitating inputs (n=17) were bursting neurons (adaptation ratio >4) suggestive of pyramidal cells. Since these results are consistent with previous characterizations synaptic inputs to principal neurons in piriform cortex, we focus the remainder of the study on the general role of short-term plasticity in information coding rather than the specific differences between pyramidal and semilunar cells.
To obtain the timescales of plasticity for each type of synapse we fit the relationship between the RA of a given EPSP in the train and the preceding IPI using a phenomenological model for short-term plasticity (Markram et al., 1998
; see Methods). The premise of the model is that on any given stimulus pulse the relative synaptic strength (RA) is the product of the maximum efficacy (E
) of a synapse, the proportion of efficacy utilized (u
) on the current pulse that becomes immediately unavailable for the next pulse, and the proportion that remains available (r
) (, green circles). For facilitating synapses (F, FD), u
is incremented on each pulse and decays to its initial value (U
) according to the time constant for facilitation, τfac
, (Eq. 4
, , open circles). For solely depressing synapses (D), u=U
and the proportion utilized on each pulse is constant. For both facilitating and depressing synapses, r,
is decremented by u,
recovers between pulses according to the time constant, τrec
, , black circles). The values of E, U,
, and τrec
were obtained from model fits to each data set and the means are reported for each synapse type (F, FD, and D) in . Facilitating synapses (F, FD) were described by two time constants (τfac
) while solely depressing synapses (D) are described by just one, τrec
Thus, all synapses (F, FD, D) recover from short-term depression described by τrec
but only a subset of synapses (F, FD) express facilitation described by τfac
For the synaptic responses shown in , the predicted change in RA based on the model is plotted versus time. The fitting procedure minimized the root mean squared error (RMSE) between the predicted (dashed line) and recorded (solid colored lines) RA for a given sequence of stimulus pulses. Overall, the synaptic responses were well-fit by the model as the average RMSE for facilitating synapses was 0.12 ± 0.02 and for depressing synapses, 0.02 ± 0.005. The relationship between the predicted and recorded amplitudes (, right) was linear which also indicates a good fit between model and data (facilitating synapses: R: 0.7 ± 0.03; depressing synapses: R: 0.8 ± 0.03). F-synapses had a significantly shorter time constant for depression, τrec: 86 ± 16 ms, than FD (163 ± 26 ms) or D (147 ± 18 ms, p<0.05) synapses. F-synapses also had a significantly longer time constant for facilitation, τfac: 1171 ± 94 ms, than FD-synapses (910 ± 38 ms, p<0.05). In the following sections, we use this model to explore how short-term synaptic plasticity in a simulated population of M/T inputs influences information transfer between the olfactory bulb and the cortex.
Simulated population input from the olfactory bulb
To investigate how synaptic dynamics influence the responses of cortical neurons to olfactory bulb inputs, we used the short-term plasticity model to simulate the synaptic current from a presynaptic population of 20 M/T cells. This current was then directly injected to real pyramidal or semilunar cortical neurons. The main advantage of driving cortical responses with simulated population currents is that each M/T spike train is simulated independently of the other population inputs. This better represents the response heterogeneity of the M/T population (Padmanabhan and Urban, 2010
). The spike trains of individual M/T cells were simulated using time varying Poisson processes with baseline spike rates randomly chosen from a Gaussian distribution (mean rate of 10 Hz and SD of 5 Hz). To simulate odor evoked increases in firing rate, 2, 6, 10 or 14 Hz was added to this baseline rate. To mimic firing patterns during respiration, these increases in firing rate were sinusoidally modulated at 2 Hz (passive breathing) or 8 Hz (active sniffing). Altogether, this resulted in simulated presynaptic M/T firing rates that, when averaged across cycles and the population were 12, 16, 20 or 24 Hz. In , we show the rhythmicity of the simulated spike rate of the M/T population over a number of 2 or 8 Hz cycles. Although average spike rates ranged between 12 and 24 Hz, the instantaneous firing rates of individual M/T cells could be much higher (10–100 Hz, ). These average and instantaneous firing rates are consistent with odor-evoked changes in firing rate recorded in awake animals (Rinberg et al., 2006
; Davison and Katz, 2007
; Fuentes et al., 2008
; Cury and Uchida, 2010
; Shusterman et al., 2011
Simulated M/T population currents
To generate current stimuli to drive the cortical neurons, the individual M/T spike trains were convolved with alpha function “synaptic” currents (). For each M/T input, the synaptic currents were scaled based on the preceding IPI according to values of τfac, and τrec that were comparable to the recorded values for F, FD and D synapses (, ). Finally, these individual synaptic current waveforms were summed to create population excitatory currents (50 s duration) that were directly injected into cortical neurons (). In the next section, we characterize the spike responses of cortical neurons to these simulated M/T population currents.
Differential cortical responses with simulated 2 Hz versus 8 Hz respiratory rhythms
To investigate how short-term plasticity and respiratory rhythms influence the cortical coding of presynaptic firing rates, we assessed the firing rates of cortical spike trains in response to our sinusoidally modulated M/T population currents. The mean and phase-locked cortical firing rates as well as statistical analyses for all combinations of synapse type, presynaptic rate, and simulated respiration frequency, are presented in .
Cortical firing rates in response to sinusoidally modulated, simulated M/T population currents
In , we show examples of cortical spike trains in response to two different presynaptic firing rates (16 Hz or 24 Hz) that were modulated by 2 Hz (left) or 8 Hz (right) rhythms (). For each synapse type, F (reds), FD (greens) and D (blues), the cycle firing rate histograms show that the peak, phase-locked, cortical firing rates (FR) increase significantly with presynaptic rate during 8 Hz, but not 2 Hz rhythms (, ** p<0.01). The cortical firing rates in response to all presynaptic rates are shown in . In the 8 Hz case, the peak, phase-locked FR increased significantly and linearly with presynaptic rate (n=14, P <0.01, ). In contrast, during 2 Hz rhythms, peak cortical FR increased minimally for presynaptic rates greater than 16 Hz (). This relationship was saturating and best fit by an exponential function (χ2: 0.12–0.29). Moreover, there was a broad range of cortical FRs (~12–20 Hz) to represent changes in presynaptic rate in the 8 Hz case but this range was significantly narrower in the 2 Hz case (~5–12 Hz, ).
Cortical spike responses to simulated M/T population currents
Summary of cortical spike responses to simulated M/T population currents
The mean firing rates of the cortical neurons increased linearly with presynaptic firing rate in both the 2 Hz and 8 Hz cases (). These increases were modest (range: ~2–6 Hz, ) compared to the range of presynaptic rates (14 Hz). In addition, the mean firing rates did not differ between the 2 Hz and 8 Hz cases (). Taken together, these results suggest that stimulus features represented by changes in presynaptic M/T firing rates can be coded by changes in mean cortical firing rates regardless of respiration frequency (2 Hz or 8 Hz) as well as by spike timing relative to the respiratory cycle at active, sniff-like frequencies (i.e. 8 Hz).
Facilitation increases the gain of the input/output relationship in cortical neurons
The relationship between cortical mean or phase-locked firing rates and presynaptic firing rate were qualitatively similar for all types of synapse. This was surprising given the extreme differences between facilitation-dominant and depression-dominant synaptic responses. However, there were quantitative differences in cortical firing rates in response to facilitating versus solely depressing inputs. F-synapses promote higher phase-locked (, , ** p<0.01) and mean firing rates (, , ** p<0.01) than solely depressing inputs. Moreover, F- and FD- synapses give rise to a significantly greater range of peak and mean cortical firing rates that represent changes in presynaptic M/T rate than depressing synapses (** p<0.01; , ). Thus, the degree of facilitation expressed in M/T-to-cortex synapses likely alters the gain of the relationship between input and output firing rates.
Contributions of synaptic plasticity and respiratory rhythms to cortical responses
To determine how plasticity and respiratory rhythm influence cortical responses, we took a step back look at how changes in presynaptic firing rate were reflected in the simulated M/T population currents. For each of the 24, sinusoidally-modulated stimuli we calculated the average current over a simulated respiratory cycle (). For all synapse types (F, reds; FD, greens; D, blues), the peak current (pA) over a simulated respiratory cycle increased with increased presynaptic firing rate but did not differ for simulated breathing cycles (2 Hz) versus simulated sniffing cycles (8 Hz) (). Facilitating inputs produced in higher peak currents and a greater range of current amplitudes to represent presynaptic rates (F-synapses: 180–280 pA; FD-synapses: 120–180 pA) compared to D-synapses (110–160 pA). This increased drive likely underlies the higher mean and phase-locked cortical firing rates in response to facilitating inputs (F, FD) versus solely depressing inputs (, ).
Analysis of the amplitude and slope of simulated population currents
Changing the respiratory rhythm changes the rate at which odor inputs are delivered to the olfactory epithelium. Higher respiratory rates narrow the temporal window for M/T population spiking relative to the cycle. In our simulated respiratory cycles, the window is narrowed from 500 ms (2 Hz) to 125 ms (8 Hz), which has an organizing effect on spike times across the population and can increase the slope of the rising phase of the average synaptic current at the onset of the cycle. The slope of the rising phase was taken from 0–100 ms in the 2 Hz case and 0–25 ms in the 8 Hz case. As expected, the slope of the current was greater (1–3 pA/ms) in the 8 Hz case, than the 2 Hz case (<1 pA/ms). However, more importantly, the slope further increased linearly with presynaptic firing rate in the 8 Hz case but saturated in the 2 Hz case (). These results are reminiscent of the relationship between phase locked cortical FRs and presynaptic firing rate in the 8 Hz case versus 2 Hz case ().
Although changes in respiratory rhythm produce population current slopes that are generally greater in the 8 Hz case than the 2 Hz case, they do not fully explain the differential sensitivity of slope or cortical FR to changes in presynaptic rate. We next explored how synaptic plasticity might contribute to the relative insensitivity to changes in presynaptic rate in the 2 Hz case. We generated population currents of neutral (N – neither facilitating nor depressing) synaptic inputs. The population of M/T spike trains were simulated as previously described for F, FD, or D synapses except these were convolved with alpha function synaptic currents with amplitudes (20 pA) that did not vary with interpulse interval. As seen in the F, FD, and D cases, the maximum current attained over the cycle increased with increasing presynaptic firing rate and did not differ for 2 Hz versus 8 Hz cycles (). These current amplitudes (135–225 pA) were lower than those of F synapses but greater than FD or D synapses (compare with ). In the 8 Hz case, the slope of the rising phase of the neutral currents increased linearly from 0.5–2.5 pA/ms with presynaptic rate similar to F, FD, and D currents (). However, in the 2 Hz case, the slope of the neutral currents also linearly increased from 0.1 to 1 pA/ms with presynaptic rate (black circles, ), which contrasts with saturating slope values for F, FD and D synapses (). Thus, synaptic plasticity contributes substantially to the relationship between current slope and presynaptic firing rate.
Contribution of synaptic plasticity to simulated population currents
Relationship between respiratory frequency, presynaptic firing rates and synaptic scale
In the previous sections we show that cortical neurons respond differentially to changes in presynaptic firing rate when simulated M/T currents are modulated at 2 Hz (breathing) versus 8 Hz (sniffing) frequencies. We also show that both simulated respiration frequency and short-term plasticity contribute to cortical responses. However, it remains to be determined how synaptic plasticity contributes to saturating current slopes and, consequently, invariant phase-locked cortical firing rates during 2 Hz but not 8 Hz rhythms. This phenomenon occurs for all synapse types so it is unlikely that facilitation, which is only expressed in F and FD synapses, is the primary cause. For this reason, we focus on a role for short-term depression in mediating saturating cortical responses during 2 Hz modulations.
In general, as presynaptic firing rate increases, more synaptic efficacy is utilized (u) and there is less recovery of the remainder (r) between pulses (see , yellow highlight). This enhanced depression decreases overall synaptic scale and could counter the increases synaptic drive produced by higher presynaptic M/T firing rates. Such a mechanism requires substantial overlap between the timing for increased presynaptic spike activity and that of decreased synaptic scale (recruitment of depression). To ascertain the temporal relationship between presynaptic spike activity and changes in synaptic scale we plot the normalized M/T spike rate and synaptic scale against the phase (ϕ) of the simulated respiratory cycle between 0 and 2π (). When presynaptic inputs were modulated by 2 Hz rhythms, the time course of synaptic scale (F-synapses-red, FD-synapses-green, D-synapses-blue) is inversely related to M/T spike rate (black)- as spike rate increases, synaptic scale decreases (). The phase difference (Δϕ) between the peak of the M/T spike rate and the trough of synaptic scale (maximum depression) is small, 0.2π (). Thus, when M/T spike rate is maximal, synaptic amplitude is nearly minimal (scale: ~0.10). This suggests that during the 2 Hz cycle, recruited depression is optimally timed to cancel increases in M/T rates resulting in saturating cortical responses. In contrast, when population currents were modulated by 8 Hz rhythms, synaptic scale peaks early in the cycle and M/T spikes have a high probability of arriving at a time when depression is weak and synaptic amplitudes are high (Scale: 0.5–1, ). Furthermore, the phase difference between the peak spike rate and the trough of the synaptic scale is greater (Δϕ=0.6π) than in the 2 Hz case. Since the majority of M/T inputs arrive before synaptic scale is minimized, these inputs escape substantial depression and ultimately drive cortical spike responses that can code increases in presynaptic M/T firing rates.
Relationship between simulated respiration frequency, M/T spike times and synaptic plasticity
In rodents, respiratory frequencies vary from 1–12 Hz so we explored the temporal relationship between M/T spikes and synaptic scale over a range of simulated respiratory rhythms. At modulation frequencies consistent with passive respiration (1–4 Hz), we found that the phase difference between the trough of the synaptic scale and the peak presynaptic firing rate is small (Δϕ=0.2π). This suggests a substantial temporal overlap between presynaptic spiking and the recruitment of depression that can counter increases in firing rate. However, the phase difference substantially increases (Δϕ=0.4–0.6π) in a nearly step-like fashion with the transition to sniff-like, modulation frequencies (≥5 Hz, yellow box, ). This phase difference increases the probability that presynaptic spikes will drive cortical responses before depression is recruited. These results suggest that the transition from passive respiration to active sniffing creates a window of opportunity for M/T inputs to drive cortical responses that code stimulus information in phase-locked firing rates.
Cortical responses to simulated M/T burst firing delivered at 2 Hz versus 8 Hz rhythms
In the previous sections, sinusoidal modulations of presynaptic firing rate provide an intuitive explanation for how the interactions between the timescales of respiratory rhythms and short-term synaptic plasticity might influence cortical coding. We questioned whether these observations would be maintained in response to more realistic, burst-like, M/T firing patterns recorded in vivo.
Based on cycle histograms of M/T firing rates recorded during passive respiration (Carey and Wachowiak, 2011
) and active sniffing (Cury and Uchida, 2010
) in vivo
, we created two galleries of firing patterns that simulated the “bursty” spike trains of M/T cells when odors are sampled at 2 Hz () or 8 Hz (). For each population current stimulus, we randomly chose 20 patterns from a given gallery and jittered the onset of each pattern by 10 ms +/− 5 ms. This ensured that the population of simulated M/T spikes tiled the respiratory cycle () as previously described (Cury and Uchida, 2010
; Shusterman et al., 2011
). These patterns were scaled by three different peak firing rates with means of 150, 200 or 250 Hz (SD ± 50 Hz). We then used these patterns to drive Poisson distributed spike times (see methods). The resulting spike trains were convolved with alpha function currents that were scaled by synaptic plasticity as previously described. Finally, the summed population currents were injected at the somas of cortical pyramidal cells (n=5).
The characteristics of these stimuli and the elicited cortical responses were very similar to those described previously for sinusoidally-modulated firing rates. The peak cortical FR of the cycle histograms did not vary with presynaptic rate during 2 Hz rhythms but increased during 8 Hz rhythms (). Indeed, for all synapse types, the differences in peak cortical FR observed with sinusoidally-modulated inputs delivered at 2 Hz versus 8 Hz, appear amplified by the use of realistic M/T firing patterns (). Moreover, facilitation greatly enhanced the gain of these input-output relationships. As we have shown previously, the slope of the average current across cycles saturated with increasing presynaptic rate for all synapse types during 2 Hz cycles () but increased with presynaptic rate during 8 Hz cycles (). Furthermore, in the 2 Hz case, synaptic scale, which is minimized when presynaptic spike rates are maximized (Δϕ=0π, dashed line, ), can directly counteract changes in presynaptic activity. In the 8 Hz case, the recruitment of depression is delayed (Δϕ=0.4π, dashed lines, ) with respect to presynaptic spiking creating a window of opportunity to drive cortical responses. Altogether, these results suggest that short term synaptic plasticity can modulate cortical responses recorded in vivo during passive respiration or active sniffing.