Variability of motor neuron spike timing maintains and shapes contractions of the accessory radula closer muscle of Aplysia

Abstract

The accessory radula closer (ARC) muscle of Aplysia has long been studied as a typical "slow" muscle, one that would be assumed to respond only to the overall, integrated spike rate of its motor neurons, B15 and B16. The precise timing of the individual spikes should not much matter. However, but real B15 and B16 spike patterns recorded in vivo show great variability that extends down to the timing of individual spikes. By replaying these real as well as artificially constructed spike patterns into ARC muscles in vitro, we examined the consequences of this spike-level variability for contraction. Replaying the same pattern several times reproduces precisely the same contraction shape: the B15/B16-ARC neuromuscular transform is deterministic. However, varying the timing of the spikes produces very different contraction shapes and amplitudes. The transform in fact operates at an interface between "fast" and "slow" regimens. It is fast enough that the timing of individual spikes greatly influences the detailed contraction shape. At the same time, slow integration of the spike pattern through the nonlinear transform allows the variable spike timing to determine also the overall contraction amplitude. Indeed, the variability appears to be necessary to maintain the contraction amplitude at a robust level. This phenomenon is tuned by neuromodulators that tune the speed and nonlinearity of the transform. Thus, the variable timing of individual spikes does matter, in at least two, functionally significant ways, in this "slow" neuromuscular system.

Figure 1.

A single extra or missing motor neuron spike dramatically alters ARC muscle contraction. A, Representative example with short regular spike trains. Motor neuron B16 was stimulated by intracellular current injection to fire a 2-s-long train at a basal frequency of 5 Hz (left), which was then modified by the insertion (middle) or omission (right) of a single spike in the middle of the train. B, Group data of measurements of peak contraction amplitude from all experiments like that in A. Triplets of control, extra-spike, and missing-spike contractions were recorded as in A with different basal firing frequencies (each repeated twice in some muscles), with both motor neurons B15 and B16, and in some preparations with both of the ARC muscles. In all cases, the motor neuron spike train was 2 s long. The peak amplitude of each contraction was normalized to the peak amplitude elicited in the same muscle by the same motor neuron firing its control, unmodified train at 10 Hz. Beyond this, all values were treated as independent measurements. Each point plotted is the mean ± SE of 10 measurements from six muscles from four preparations. Statistical significance was tested with two-way ANOVA, followed by pairwise multiple comparisons using the Holm–Sidak test. The overall differences between the control (gray circles), extra-spike (black circle), and missing-spike (open circles) conditions, for both B15 (left) and B16 (right), were all highly significant (p < 0.001); ∗∗∗p < 0.001, ∗∗p < 0.01, and ∗p < 0.05, for the difference between the extra-spike and control or the missing-spike and control values at a particular frequency. C, Representative example with longer regular spike trains. As in A except that motor neuron B16 was fired for 10 s.

Figure 2.

Intraburst variability of motor neuron B16 spike timing during feeding motor programs in vitro. Reanalysis of a dataset of motor programs elicited by electrical stimulation of the esophageal nerve recorded by Horn et al. (2004) (see also Zhurov et al., 2005a). A, Motor neuron B16 spike patterns recorded intracellularly during the radula-protraction phases of four representative programs, with the corresponding instantaneous firing frequency function (f_B16), computed by assigning to each time point in an interspike interval the reciprocal of the duration of that interspike interval. B, Distribution of all B16 interspike intervals during protraction phases in the entire dataset, subject however to the following selection criterion. Because the B16 firing frequency often gradually increases over the first part of protraction (Brezina et al., 2005; Zhurov et al., 2005a,b), only the second half of each protraction was considered and accepted only if it contained ≥30 interspike intervals. This left from the original dataset a subset of 31,226 interspike intervals from the second halves of 583 protractions from 28 experiments, included in the distribution shown. The distribution is scaled so as to approximate the probability density function. The thin vertical lines mark the 10th, 25th, 50th (median), 75th, and 90th percentiles. C, The corresponding distribution of the differences between successive B16 interspike intervals, normalized by the mean interval in each protraction half. Computed from the same data as in B, this distribution therefore contains 31,226 − 583 = 30,643 interspike interval differences. The first and last bars contain pooled smaller and larger values, respectively, indicated by the small left- and right-pointing arrows.

Figure 3.

Intraburst variability of motor neuron B15 and B16 spike timing during spontaneous feeding in vivo. Reanalysis of a chronic recording by Horn et al. (2004) of electrical activity in the ARC muscle during an entire ∼2.5 h meal comprising 749 cycles of feeding behavior, then decomposed by Brezina et al. (2005) into the instantaneous firing frequency functions of the motor neurons B15 and B16. A, Representative segment of 13 cycles of the instantaneous firing frequency functions with a schematic representation of the individual spikes. Of the total of 8951 B15 and 26,455 B16 interspike intervals in the 2.5 h meal, 7847 B15 and 25,116 B16 intervals were identified as intraburst intervals, here defined simply as intervals <1 s. This definition, less restrictive than the complete definition of Brezina et al. (2005), implicitly allowed a somewhat different number of bursts (722 for B15, 953 for B16) than cycles (749). B, Distributions of all 7847 B15 (left) and 25,116 B16 (right) intraburst interspike intervals. Plot details as in Figure 2B. C, The corresponding distributions of the 7125 B15 (left) and 24,163 B16 (right) successive intraburst interspike interval differences, normalized by the means of all of the B15 and B16 intraburst interspike intervals. Plot details as in Figure 2C.

Figure 4.

Motor neuron B15 and B16 spike patterns with different timing produce different ARC muscle contraction shapes. A, Representative experiment with motor neuron B15. A, Top, The six motor neuron B15 spike patterns that were used in the experiment, shown schematically. Each pattern had 100 spikes, a nominal mean spike frequency f = 7 Hz, and thus a nominal duration of 14.29 s. The irregular patterns 1–5 were constructed by drawing the successive interspike intervals from the positive part of a Gaussian distribution with mean 1/f = 142.9 ms and SD 1/(4f) = 35.7 ms. The regular pattern 6 was constructed with the same mean interspike interval but SD = 0 (see Results, Variable motor neuron spike timing maintains contraction amplitude). A, Middle, The resulting ARC muscle contraction waveforms. The motor neuron was fired with each spike pattern 11 times in succession, with 1 min rest intervals between the repetitions. Repetition 1 was discarded (see below). The waveforms produced by repetitions 2–11 are shown (offset from each other by an arbitrary fixed amount for clarity) down each column. After a rest interval of >1 min, this was repeated with each of the other spike patterns, as shown across the columns. A, Bottom, The superimposed deviations (differences) of each of the 10 individual contraction waveforms from the ensemble mean of the waveforms in each column, plotted on the same scale as the individual waveforms. B, Representative experiment with motor neuron B16. As in A, except with patterns of 100 B16 spikes at a nominal mean frequency f = 9 Hz. C, Group data for distances between contraction waveforms, and the spike patterns that produced them, from the entire series of experiments. All experiments were done as in A and B, with six different spike patterns per experiment. However, as noted in Results (Motor neuron spike patterns with different timing produce different muscle contraction shapes), there was some tendency for the contraction waveforms produced by successive repetitions of the same pattern to change, usually to decrease in amplitude. Whenever the peak amplitude of the contraction waveform produced by repetition 11 of a pattern differed by >20% from that produced by repetition 2, all repetitions of the pattern were discarded. For the same reason, repetition 1, which followed a longer period of rest and often produced a significantly larger contraction waveform, was routinely discarded. Altogether, this left a dataset of 10 repetitions each of 125 patterns in 28 experiments with motor neuron B15 and 10 repetitions each of 210 patterns in 50 experiments with B16. (The experiments were done with different mean spike frequencies f̄, ranging from 5 to 17 Hz with B15 and 6 to 17 Hz with B16, but all were pooled here.) The spike pattern actually recorded during each of these repetitions was converted into the instantaneous firing frequency function by assigning to each time point in an interspike interval the reciprocal of the duration of that interspike interval (see Figs. 2A, 3A). The instantaneous firing frequency function was then sampled at m time points from the time of the first spike over an interval equal to the duration of the longest pattern in the entire experiment (because the patterns were constructed from random interspike intervals, their durations were not exactly identical), every 10 ms, in A for example for a total of 1430 samples. The contraction waveform produced by the pattern was sampled in the same way. The root mean square distance d between the sampled amplitudes a of two patterns or waveforms 1 and 2 was computed using the following equation: This was done for all pairwise combinations of patterns or waveforms within each experiment. From all of these distances, four mean values were then computed within each experiment: d̄_{spikes,same pattern}, the mean distance between spike patterns that were nominally the same, that is, were repetitions of each other; d̄_{spikes,different pattern}, the mean distance between patterns that were nominally different; d̄_{contr,same pattern}, the mean distance between contraction waveforms produced by patterns that were nominally the same; and d̄_{contr,different pattern}, the mean distance between waveforms produced by patterns that were nominally different. To allow pooling across multiple experiments, these mean distances were further normalized by the mean amplitude of all of the patterns or waveforms in the experiment. Plotted in C, finally, are the means ± SD of the four normalized mean distances from the 28 experiments with motor neuron B15 (bars 1–4) and from the 50 experiments with B16 (bars 5–8). Statistical significance was tested with two-way ANOVA, followed by pairwise multiple comparisons using the Holm–Sidak test; ∗∗∗p < 0.001.

Figure 5.

The B15–ARC neuromuscular transform is essentially identical on the two sides of the animal. Here a 20 min segment chosen at random from the real motor neuron B16 spike pattern during the spontaneous 2.5 h meal in Figure 3 was replayed simultaneously into the left and right motor neurons B15. The B16 pattern, rather than the B15 pattern, was used because the B15 pattern recorded during the 2.5 h meal, when replayed alone, was not sufficiently intense to elicit contraction in many cycles. The two pairs of records at the top show the motor neuron B15 firing and the resulting ARC muscle contractions on the two sides; the two records at the bottom expand the indicated portion of the two contraction waveforms.

Figure 6.

ARC muscle contractions produced by replaying the real, irregular and corresponding regularized motor neuron B15 and B16 spike patterns: representative experiment and analysis of distance between waveforms. A, B, Representative experiment. A 20 min segment was chosen at random from the real motor neuron B15 and B16 spike patterns during the spontaneous 2.5 h meal in Figure 3. Cycles were demarcated using the complete definition of Brezina et al. (2005) whereby each cycle contained one burst each of B15 and B16 spikes, each burst having ≥10 spikes with interspike intervals <1 s. This particular segment comprised 138 cycles. The corresponding regularized segment was constructed by replacing each real, irregular burst with a burst of the same mean frequency but with all interspike intervals equal. The experiment was then performed as follows. (1) The real, irregular segment was replayed, stimulating both motor neurons B15 and B16 simultaneously with their respective patterns. (2) The regularized segment was replayed similarly. (3) The real, irregular segment was replayed again. A rest interval of >1 min was interposed between (1) and (2) and between (2) and (3). (1) was discarded, and (2) and (3) were compared. The result that (2) produced smaller contractions than (3) was therefore conservative with respect to fatigue or other progressive decrease of the contractions during the experiment. A, The entire 20 min segment of the real, irregular motor neuron B15 and B16 spike patterns and the resulting ARC muscle contractions (top 3 records) and the corresponding segment of regularized spike patterns and contractions (bottom 3 records). B, Expansion of the indicated excerpt from A. The spike patterns are shown converted into the real, irregular (gray) and regularized (black) instantaneous firing frequency functions; the contractions are shown superimposed. C, Group data for distances between spike patterns and contraction waveforms from the entire series of experiments. Altogether, the dataset contained 1423 cycles from 18 experiments. Cycles were compared pairwise only within the same experiment and only if their spike patterns were sufficiently similar in the spike numbers and durations (and hence mean frequencies) of their B15 bursts, as well as those of their B16 bursts. The spike numbers were required to differ by no more than four spikes (the SD of the distribution of the spike number per burst over all 1423 cycles was 16.2 spikes, range of 0–150 spikes) and the burst durations by no more than 0.4 s (the SD over all cycles was 1.68 s, range of 0.11–20.95 s). These criteria allowed 1078 comparisons. For each comparison, the four distances d_{spikes, real, irregular}, between the real, irregular spike patterns; d_{spikes, regularized}, between the corresponding regularized patterns; d_{contr, real, irregular}, between the contraction waveforms produced by the real, irregular patterns; and d_{contr, regularized}, between the waveforms produced by the regularized patterns, were computed and normalized as in Figure 4C. For the spike patterns, the distances and normalizing mean amplitudes were computed separately for B15 and B16 and averaged. Plotted in the figure are the means ± SD of the four normalized distances from all 1078 comparisons (bars 1–4). Statistical significance was tested with two-way ANOVA, followed by pairwise multiple comparisons using the Holm–Sidak test; all pairwise differences (only two are indicated by ∗∗∗) were highly significant (p < 0.001).

Figure 7.

ARC muscle contractions produced by replaying the real, irregular and regularized motor neuron B15 and B16 spike patterns: representative effects of modulators. A, Effect of buccalin. A 5 min segment was chosen at random from the real motor neuron B15 and B16 spike patterns during the spontaneous 2.5 h meal in Figure 3. Cycles were demarcated, and the corresponding regularized segment was constructed as in Figure 6. The real, irregular and the regularized segments were then replayed in the same sequence as in Figure 6, twice: first under control conditions and then in the presence of 1 μm buccalin. A, Top, The real, irregular and the regularized spike pattern segments. Middle, The resulting ARC muscle contractions under control conditions. Bottom, The resulting contractions in the presence of buccalin. B, Effect of SCP. As in A, except with a 20 min segment of the spike patterns and 100 nm SCP_B. The records at right expand the indicated portion of the main records.

Figure 8.

In the real motor neuron B15 and B16 spike patterns, variable spike timing maintains ARC muscle contraction amplitude: group data for the effects of spike pattern regularization and modulators. Experiments were performed as in Figure 7. Altogether, the dataset contained 1423 cycles from 18 experiments under control conditions (same as analyzed in Fig. 6C), 793 cycles from 8 experiments in the presence of 100 nm, 1 μm, or 10 μm SCP_B (the different concentrations had qualitatively similar effects and were pooled), 492 cycles from 9 experiments in the presence of 100 nm or 1 μm buccalin A, and 818 cycles from 8 experiments in the presence of both SCP_B and buccalin A. In each cycle, contraction amplitude was measured from the first B15 or B16 spike in that cycle to the first spike in the subsequent cycle; the baseline contraction amplitude at the first spike in that cycle was subtracted (Brezina et al., 2005). Top, Percentage of the cycles with above-zero contraction amplitude. Bottom, Mean ± SE of the mean contraction amplitude in each cycle normalized by the mean amplitude of the corresponding real, irregular contraction under control conditions. Cycles in which the latter was 0 were excluded. This was acceptable because contractions were eliminated but generally not newly created under the other conditions except with SCP, where the exclusion probably underestimated the total amount of contraction that was produced by the spike pattern. For the mean contraction amplitudes, statistical significance was tested with two-way ANOVA, followed by pairwise multiple comparisons using the Holm–Sidak test. The overall difference between the real, irregular and the regularized amplitudes was highly significant (p < 0.001), as was that difference under each of the individual modulator conditions (∗∗∗p < 0.001). All other individual differences were also highly significant (p < 0.001) except those between bars 1 and 7 (p < 0.05) and between bars 2 and 4, and bars 6 and 8 (p > 0.05).

Figure 9.

Mechanism of contraction amplitude maintenance and its sharpening by the modulators. A, Representative experiment. Motor neuron B16 was stimulated to fire for 2 s at 10 Hz (bottom) every 60 s, and the resulting ARC muscle contractions were recorded (superimposed above) first under control conditions, then in the presence of 10 μm SCP_B, and finally in the presence of both 10 μm SCP_B and 1 μm buccalin A. Also shown is the relaxation phase of the contraction recorded in both SCP and buccalin scaled to the same peak amplitude as the control contraction. B, Group data from all experiments like that in A summarizing the relationship between motor neuron firing frequency and peak contraction amplitude and its modification by the modulators. In each experiment, motor neuron B15 or B16 was fired successively at each of the frequencies plotted, first under control conditions, then in the presence of 10 μm SCP_B or 1 μm buccalin A, and finally in the presence of both modulators. Measurements of peak contraction amplitude were normalized by the peak amplitude of the control contraction elicited by the same motor neuron firing at 10 Hz. Shown are means ± SE from 6 control, 8 SCP, 3 buccalin, and 12 SCP plus buccalin experiments with motor neuron B15 (left), and 4 control, 4 SCP, 4 buccalin, and 8 SCP plus buccalin experiments with motor neuron B16 (right). Statistical significance was tested with two-way ANOVA. For both B15 and B16, the four frequency–amplitude relationships were all significantly different from one another (p < 0.01).

Figure 10.

The results found in this paper are explained by a nonlinear neuromuscular transform operating at the interface between fast and slow regimens. Illustration with a minimal model in which the contraction amplitude c at time t is given by as the sum of a series of elementary contraction kernels, identical α functions (Dayan and Abbott, 2001) with time constant τ, elicited by n spikes occurring at times t_i = {t₁, t₂, …, t_n}. A, Right shows the elementary kernels with τ = 0.001 (fast), 0.1 (intermediate), and 10 (slow; only partly visible) (arbitrary units). Column 1 in B and C shows three irregular spike patterns (a–c in B, repeated as e–g in C), all with n = 30 spikes at a mean frequency f̄ = 10 (arbitrary units), constructed by drawing the successive interspike intervals from the positive part of a Gaussian distribution with mean and SD 1/f̄. The corresponding regular pattern is also shown (d, h). Columns 2–4 in B and C then show the contraction waveforms c(t) produced by these spike patterns with τ = 0.001 (fast, column 2), 0.1 (intermediate, column 3), and 10 (slow, column 4; only partly visible). In this construction, the peak amplitude factor a in the above equation was set to 1/(eτ), so that the elementary kernels all had a contraction area of 1, and the contraction waveforms therefore all had the same area, regardless of τ. However, to make them all equally visible, the three elementary kernels in A (right) and the columns 2–4 of B and C are shown on different vertical scales. In B, no threshold was applied; in C, the contraction waveform c(t) was passed through a piecewise linear threshold function with the threshold amplitude set to 3/(eτ), i.e., three times the peak amplitude of the elementary kernel. The threshold function is shown schematically in A (left).