Fig 1.
In vitro TCR neuron response to injected frozen noise.
Left panel: Spike trains induced in a TCR cell by frozen noise with identical amplitude and various DC offsets; trace is a 3 s extract from a standard 300 s recording. Top: example trace at −50 mV. Bottom: example trace at −80 mV. Vertical bars in the panels in between mark the detected spikes in the 3 recorded replicates at 4 levels of depolarization, from top to bottom: −50, −60, −70 and −80 mV. The neuron responds earlier at more depolarized membrane potentials. Middle panel: 100 ms zoom of a single event starting at 1850 ms (zoom indicated in the left panel). Top and bottom show the event at −50 mV and −80 mV. Right panel: Cross-correllograms between a reference spike train at −80 mV and the spike trains obtained in the same cell at the different membrane states. Recordings from 5 cells (=15 traces), resulting in 10 comparisons at −80 mV, 15 comparisons at −70 and at −60 mV; only 2 cells gave sufficient results at −50 mV (6 comparisons). On depolarization the peaks shift to the left, indicating that the neurons fire earlier.
Fig 2.
Quantification of burstiness in a TCR cell spike train.
Left panels: Spike train recorded at a membrane state of −80 mV. The ISI histogram (top row) shows a first peak around 5 ms and a second one around 250 ms. The tail decays exponential (dashed line) above 300 ms; so events were considered independent if further apart than 300 ms. The Autocorrelogram (middle row) shows peaks at 5 and 10 ms. In the return map (bottom row) ISI n is plotted against ISI n+1; k-means clustering of this data provides 4 clusters and a silhouette value of 0.96. Based on the ISI histogram and the return map we used an interval of 30 ms to separate single spikes from bursts. Right: Spike train recorded at a membrane state of −50 mV. The ISI histogram (top row) indicates a single Poisson process with events independent if they were further apart than 100 ms. The autocorrelogram (middle) shows only one central peak around zero and the return map (bottom) shows an unimodal structure confirmed by a silhouette value of 0.48.
Fig 3.
Transfer function of a TCR neuron in vitro.
Impedance of the TCR neuron calculated as the amplitude of the transfer function between current input and voltage output for the four defined membrane states (blue: −80 mV, green: −70 mV, red: −60 mV, black: −50 mV). Left: A small time window was cut out and interpolated around each single spike to avoid contamination of the spectra by the fast spikes. Inset: zoom with one in ten data points on the frequency range between 100 and 1000 Hz. Right: same data, but now with also a larger cut-out window around each burst including the LTS. Note the resonance peak around 5 Hz that is related to bursting: absent in the −50 mV trace and considerably reduced if we cut away the LTSs in the left panel. Error bars reflect standard error of the mean.
Fig 4.
Coherence and phase between input current and spikes or bursts.
Coherence (left column) and phase (right column) between the input current and the timing of three different activity components in the TCR cells: bursts, spikes and ‘follower’ spikes in bursts. Calculations were performed over the first 500 s of each trial and for the four different membrane states. Coherence decreases for higher frequencies. Bursts (blue traces) phase-lock mainly to low frequencies, with positive phase (upstroke). Isolated spikes (green traces) show more broadband phase locking. Spikes in a burst (red traces) seem to follow the properties of the burst to which they belong. The colour shade around a trace indicates the confidence interval (95%) based on a jackknife method.
Fig 5.
Information density carried in the TCR output signal.
Typical example of the information density as a function of frequency calculated for several relevant components in the output signal of a TCR cell at the four different membrane states (left to right as defined in Fig 3). Two different input signals were used, both contained the same frozen Gaussian noise, filtered with an exponential filter with a time constant of either τ = 10 ms (top two rows) or τ = 1 ms (bottom two rows). We calculated the information density for each isolated spike (green), each burst (blue), each event (red = either isolated spike or burst) and all spikes (black, isolated or contained in a burst). The information density was calculated either per type of activity (row 2 and 4) or over the full trace (row 1 and 3).
Fig 6.
Event Triggering Average (ETA) of membrane potential and injected current.
Left column: ETA of the membrane potential 200 ms preceeding single spikes (green),aligned at t = 0, or bursts (blue). The peak of the spike (or first spike in the burst) was used as trigger; this implies perfect coincidence of isolated spike and first spike in the burst; later spikes in the burst tend to average out. The horizontal black lines indicate the mean value of the subthreshold membrane potential calculated from the entire trial. Middle column: ETA of the input current (mean value substracted and normalized with the L2 norm) using the triggerpoints from the voltage (peak of the spikes, left column). Right column: probability distributions of a convolution of the normalized ETA with event-triggered (blue/green lines) or with a random input (black line, also called the prior). Rows indicate membrane states.
Fig 7.
Event Triggering Average (ETA), using a fast-fluctuating input current.
Repeat of the experiment in Fig 6 but now with the input filter (τ = 1 ms) and only for mixed membrane states at −70 mV (top row) and −60 mV (bottom row) as only they produced sufficient spikes and bursts for the analysis. Left column: ETA of the membrane potential 500 ms preceeding single spikes (green) or bursts (blue). Right column: ETA over the input current (mean value substracted and normalized with the L2 norm). The horizontal black line indicates the mean value of the subthreshold membrane potential calculated from the entire trial. Other details as in Fig 6.
Fig 8.
Event Triggered Covariance (ETC) of membrane potential and injected current.
ETC was calculated for bursts (left two columns) and isolated spikes (right two columns) for four different membrane states (top four rows). ETC needs far more realizations than ETA, so at −80 mV, where burst dominate, we can only give results for bursts. While at −50 mV, where bursts are rare and spikes dominate, we can only give results for spikes. Only filters for which the probability distribution was substantially different from the prior, are shown. In S3 Fig we show the corresponding eigenvalues. Bottom row: projections along the first two features for bursts at a membrane state of −80 mV (left) and for spikes at a membrane state of −50 mV (right).
Fig 9.
Comparing experimental and model spike trains.
The same computer generated frozen noise was injected into the TCR cell (solid line) and in the fine tuned model cell (dotted line). This generated comparable spike trains consisting of isolated spikes and burst in a state dependent way (rows represent the four membrane states. Open circles indicate the timepoints at which the TCR cell fired, while squares mark the moments where the model cell fired, either a spike or a burst.
Fig 10.
Comparing model and experimental spike trains.
Left two columns: reliability (coincidence factor Γ or Hunter and Milton measure RHM) between experimental traces as a function of precision at different membrane states (blue: −80 mV, green: −70 mV, red: −60 mV, black: −50 mV). The shaded areas and dotted lines denote the standard deviations. The four rows represent the different types of activity: all spikes, all events (isolated spikess and bursts), isolated spikes and finally bursts. Second column: reliability between the model traces and the experimental traces. Third column: event frequencies for the model, the experiments without the extra requirement for bursts, and with the requirement (details in Materials and methods). Right panel: distribution of the reliability values among experiments (solid line) and between model and experiments (dashed line) of bursts at a precision of 10 ms (denoted by lines at this precision, see also S1 Fig). The (dis)similarity between between experimental spike trains on the one hand and the model and the experimental spike trains on the other, was established as follows: we established the null-distribution of experimental reliability values. Next, we calculated the surface of this null-distribution up to each model-experiment reliability value (shaded area). The bottom panel gives the values of these surfaces. If experimental and model spike trains were drawn from the same distribution, the expectation value of the mean surface would be 0.5, indicated by the horizontal line. Error bars indicate standard deviations.
Fig 11.
Event-triggered T-type calcium current.
Event-triggered T-type calcium currents were calculated for the model (first column) comparable to the experimental ETAs in Fig 6; t = 0 indicates the peak of the (first) spike. Rows indicate the four different membrane states; blue traces indicate the current when a burst was induced, while green traces depict the situation for an isolated spike. The horizontal black line gives the mean value in the steady state condition. The inset zooms in around the time of initiation. The second column depicts the gating variables m (solid) and h (dashed) that underly the current using the same color code. The third column illustrates the total gating (the product m2h) that underlies the current.
Fig 12.
Effects of reducing the h-type current.
The maximum conductance of the h-type current and the mean of the input current (-700 pA) were reduced with the same factor f in the bursting regime. This resulted in a reduction of both the burst rate and the number of spikes per burst, as can be seen from the example traces in A and the event frequencies in B. Reducing the h-type current and mean input current resulted in a reduction of the width of the membrane potential distribution, while keeping the mean membrane potential at the same level (D). A stronger deviation from the mean input current was needed to trigger a burst (C). The burst-triggered potassium (E), sodium (G) and T-type (I) currents and gating (F, H and J respectively) show that this reduction in the width of the membrane potential distribution affects all three currents.
Fig 13.
In a ‘standard’ high-conductance state [28] (blue traces), the membrane potential fluctuates around a depolarized value (E). The neuron responds to excitatory input with single spikes (A), because the T-type calcium current is inactivated (C). Inhibitory input that is synchronized with (arrives just before) the excitatory input (F) can deinactivate the T-type calcium current, so that it is activated upon the arrival of excitatory input (B and D). In a ‘inhibitory’ high-conductance state (red traces) the membrane potential is not depolarized (E). Due to this lack of depolarization, the inactivation is removed from T-type calcium current and the T-current can activate for excitatory input only (C).