| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
|
|
|
|||||||
|
|||||||||
1Monell Chemical Senses Center, Philadelphia, Pennsylvania 19104; 2Center for Neurobiology and Behavior, Columbia University, New York 10032; and 3Department of Physiology and Biophysics and Fishberg Research Center for Neurobiology, Mount Sinai School of Medicine, New York, New York 10029
Submitted 10 December 2003; accepted in final form 20 February 2004
 |
ABSTRACT |
|---|
 TOP ABSTRACT INTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
|---|
|
INTRODUCTION |
|---|
|
TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
|---|
Here we quantify and analyze the variability in the cyclical consummatory feeding behavior of Aplysia. This behavior comprises subtypes such as biting, swallowing, and rejection of unsuitable food, all driven by the same central pattern generator (CPG) and performed with the same neuromuscular plant. Since its first description by Kupfermann (1974)
, extensive studies have revealed much about the behavior and the neuromuscular mechanisms that produce it (reviewed by Chase 2002; Elliott and Susswein 2002; Hooper et al. 1999; Kupfermann et al. 1997). However, its variability has not been systematically studied.
The previous work in the system, indeed, leads to two differing expectations as to the variability. On the one hand, the neuromuscular system contains mechanisms—in particular, numerous endogenous neuromodulators—that tune its operating parameters for optimal functional performance. Furthermore, the tuning differs in the different subtypes of feeding behavior (Brezina and Weiss 2000; Brezina et al. 1996, 2000a, b; Hooper et al. 1999). This might suggest that the operating parameters are constrained to a narrow range of values in each subtype, so that if we examine successive cycles of a particular subtype, performed under the same circumstances, we will find them all to be very similar. On the other hand, many of the modulatory tuning processes, as well as basal processes in the neuromuscular transform—the transform of motor neuron spike patterns to muscle contractions—and in the CPG, have slow dynamics (Brezina et al. 2000a, 2003a). The history dependency of these processes might then be expected to produce cycles which, with different histories, are different from one another. Indeed this is predicted by mathematical models of the modulation in the system (Brezina et al. 2003a,b).
If there is variability, it might not be random, but might have a distinct spatiotemporal structure in the multidimensional space of the various parameters. This structure, in turn, might help us identify something that is at present unknown in this or indeed most behaviors, that is, the higher-order variables that the nervous system is attempting to control to make the behavior successful (see, e.g., Scholz and Schöner 1999; Todorov and Jordan 2002).
In this paper we therefore study the variability of the Aplysia feeding behavior. We begin with reduced preparations that, although lacking the full mechanical and sensory integrity of the intact animal, allow access to several internal levels of the neuromuscular system. We are able to record feeding-related neuromuscular activity simultaneously at three levels—the overall cycling of the CPG, motor neuron firing, and muscle contraction. We then use chronically implanted electrodes to extend our findings to intact animals fed in a semicontrolled manner or engaged in spontaneous feeding. Finally we return to the reduced preparations where we can perturb aspects of the neuromuscular function for a more analytical examination.
In connection with this order of approach, we emphasize another aspect of our strategy in this paper. In the intact animal, behavior emerges from an interaction between the nervous system, body, and environment (Chiel and Beer 1997). In such a coupled system, there are likely to be multiple layers of variability (Beer et al. 1999) that will be very difficult to separate. In particular, in a behavior that, in its several subtypes and parametric adaptability, is as responsive to environmental demands as Aplysia feeding behavior, it is difficult to be sure that the observed variability is not being driven simply by variations in the environment. For this reason, we focus here on experimental paradigms that attempt to keep the external stimuli to the system as constant as possible. This is of course easier to accomplish in the reduced preparations without sensory feedback. For the same reason, we pay relatively little attention to conventional global measures of variability that lump together many, possibly heterogeneous, cycles. Rather, we concentrate on a local measure, the pairwise differences between the successive cycles in a sequence, which provide, in essence, their own internal control. Remarkably, we find that, even with a constant stimulus in the reduced preparations that reveal in an unmediated manner the operation of the CPG, successive cycles are very different. Under these controlled conditions, this fact of large central variability can be established relatively unambiguously. The central variability can then be followed as it emerges in the overall neuromuscular variability in the intact, freely behaving animal.
|
METHODS |
|---|
|
TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
|---|
EXPERIMENTS.
The preparation was the standard preparation used for recording motor neuron-elicited contractions of the ARC (accessory radula closer, or I5) muscle (e.g., Cohen et al. 1978; Orekhova et al. 2003; Weiss et al. 1979), here combined with extracellular nerve recording and stimulation. Briefly, the preparation consisted of the bilateral buccal ganglia, the ARC muscles, and the connecting buccal nerves 3 through which the buccal motor neurons B15 and B16 innervate the ARC muscle. The cerebral ganglion, connected to the buccal ganglia by the cerebral–buccal connectives, was also retained. The buccal ganglia (but not the cerebral ganglion) were desheathed. One ARC muscle was pinned out in a separate subchamber and connected to an isotonic transducer (Model 60-3000, Harvard Apparatus, Holliston, MA) to measure the length of the muscle with a light counterbalancing load. The ipsilateral motor neurons B15 and B16 were impaled with standard intracellular microelectrodes and their membrane voltage was monitored with an intracellular amplifier (Axoclamp 2A/B, Axon Instruments, Union City, CA). Electrical activity in three buccal nerves, i.e., the I2 nerve, the ipsilateral buccal nerve 2, and the radula nerve (for nomenclature see Cohen et al. 1978; Hurwitz et al. 1994), was recorded differentially through suction electrodes connected to an extracellular amplifier (Differential AC Amplifier Model 1700, A-M Systems, Carlsborg, WA). (The radula nerve records are not used in this paper.) The extracellular amplifier, under the control of a separate stimulator (Grass S48/S88, Astro-Med, West Warwick, RI), was also used to stimulate the ipsilateral esophageal nerve. All signals were sampled and recorded simultaneously by a computer using Digidata 1322A data-acquisition hardware and pCLAMP 8/9 software (Axon Instruments). Most experiments were done at 15–16°C, although some were done at room temperature with no obvious difference.
Two protocols of esophageal nerve stimulation were used. In the "continuous" protocol (e.g., Fig. 1), the stimulation consisted of a long train of regular voltage pulses with parameters adjusted so as to elicit identifiable motor programs (see following text) at moderately frequent intervals while the stimulation continued. The individual voltage pulses were typically 7–10 V in amplitude, 7–15 ms in duration, delivered at 2–3 Hz. Blocks of stimulation lasting 3 min (with parameters constant within each block), separated by 7-min rest periods, were repeated as long as the motor programs continued to be elicited.
|
|
; Jing and Weiss 2001; Morgan et al. 2002; Morton and Chiel 1993a). The protraction phase of the program was defined to be coincident with the I2 nerve burst; the retraction phase was defined as lasting from the end of the I2 nerve burst to the end of the buccal nerve 2 burst. Only those blocks were analyzed that had 4 or more identified motor programs, and at least some ARC muscle contraction. Altogether, 1,076 programs in 166 blocks from 28 preparations in the continuous stimulation protocol, and 856 programs in 37 blocks from 11 preparations in the discontinuous protocol, were accepted for further analysis. Initial processing of the raw records was done in Clampfit (Axon Instruments). The programs were identified and the beginning and end times of their protraction and retraction phases were marked by eye. This appeared to be sufficiently reliable for the purposes of this paper, given that the bursts of I2 and buccal nerve 2 activity usually began and ended quite abruptly (e.g., Fig. 14). Motor neuron B15 and B16 spike times were automatically tabulated using the threshold event detection module of Clampfit 9.
Subsequent processing of the data, its collation across multiple blocks and preparations, and most statistical analysis was done in Mathematica (Wolfram Research, Champaign, IL). (The Kolmogorov–Smirnov test was run in Clampfit 9.) For some analyses, the motor neuron B15 and B16 spike times were converted to instantaneous firing frequency functions, assigning to each time point in an interspike interval the reciprocal of the duration of that interspike interval. The instantaneous ARC muscle contraction amplitude during any program was defined as –(instantaneous muscle length – muscle length at the beginning of the program); thus contraction of the muscle is positive in sign. Because different preparations, with different muscle sizes and somewhat different loads, could differ significantly in their contraction amplitudes, all contraction amplitudes were normalized by the maximal amplitude reached in that particular preparation. Other measured variables were initially not normalized, although for some analyses all variables were secondarily normalized by the mean in each stimulation block. Further details of the analysis are given in RESULTS and in the figure legends.
Esophageal motor programs in a reduced buccal-opener neuromuscular preparation
EXPERIMENTS.
The buccal-opener preparation and experiments were identical to the buccal-ARC preparation and experiments just described, with the following exceptions. Instead of the ARC muscle, the radula opener muscle complex I7–I10 (Evans et al. 1996) was used. The I9 and I10 muscles on one side (the "ipsilateral" side), plus the single I8 muscle and both I7 muscles, were left interconnected, together with a small piece of the odontophore cartilage into which the I7 muscles insert. The isotonic transducer was attached to this piece of cartilage to record the contractions of the whole complex. The contralateral I9 and I10 muscles were cut, as were all nerves except the ipsilateral buccal nerve 3, which alone remained connecting the opener muscle complex with the buccal ganglia. Instead of motor neurons B15 and B16, the ipsilateral opener motor neuron B48 (Evans et al. 1996) was recorded from intracellularly. Extracellular recordings were made from the I2 nerve and, for convenience, from the contralateral buccal nerve 2. Control recordings simultaneously from both buccal nerves 2 showed that motor-program activity appeared similarly in the contralateral as in the ipsilateral nerve. The ipsilateral esophageal nerve was stimulated with the "continuous" protocol.
DATA ANALYSIS. The same methods and criteria were used as with the buccal-ARC data, except that, because the interprogram interval preceding the program in each cycle (see Fig. 1) was also analyzed, the first program in each block, for which this interval is not well defined, was excluded from the analysis. Altogether, 741 programs in 94 blocks from 12 preparations were accepted for further analysis. The instantaneous opener muscle contraction amplitude during any cycle was defined as –(instantaneous muscle length – muscle length at the beginning of the interprogram interval).
In vivo nerve activity during ingestion of seaweed strips
EXPERIMENTS.
Chronic electrodes were implanted en passant on the radula nerve and buccal nerve 2 as described by Horn et al. (1999) and Horn and Kupfermann (2002). The signals were differentially amplified with an extracellular amplifier (Model 1700, A-M Systems) and recorded by a computer using Digidata data-acquisition hardware and AxoScope software (Axon Instruments). After the animals had adequately recovered from surgery (see Horn and Kupfermann 2002), continuous recordings were made as the food-deprived animals ingested standard 1 x 10-cm strips of seaweed (Laver). A new strip was held to the lips whenever the previous strip had been entirely ingested, repeatedly until the animal was satiated. The experimenter observed and marked the approximate times of the presentation of each strip, the animal's initial bite-swallow, and the successive swallowing (or, rarely, rejection-like) movements during the ingestion of the strip.
DATA ANALYSIS.
Similar methods were used as for the esophageal motor programs above. The radula nerve and buccal nerve 2 records were divided into blocks corresponding to the ingestion of the individual seaweed strips; each block contained multiple programs, that is, coordinated bursts of electrical activity in the two nerves. After presentation of the strip, the animal sometimes made one or more bites, with associated programs recorded in the nerves, then always a bite-swallow, associated with an unusually strong program. All of these were ignored, so that each block used for analysis ran from the program corresponding to the first observed pure swallow to that corresponding to the last observed swallow of each strip. Observed swallows invariably corresponded to programs recorded in the nerves; however, some blocks contained additional recorded programs during which no obvious swallowing movement was observed (see, e.g., Fig. 8). All programs in each block (including those without movement) were analyzed, or, when toward the end of the experiment the satiated animal showed major signs of rejection, the entire block was discarded. Altogether, 1,388 programs in 153 blocks, each corresponding to an ingested seaweed strip (
9 programs/strip on average), from 3 animals were accepted for further analysis.
|
), and similarly in the radula nerve, where the largest units are likely to be neurons B8 (Morton and Chiel 1993b). In each burst, the times of "events" of all sizes above a minimal threshold were automatically tabulated using the threshold event–detection module of Clampfit 9, then converted to instantaneous frequency functions. Because both nerves contain multiple units and the firing of each unit may produce multiple peaks in the extracellular record, these frequencies must be regarded as measures merely of the aggregate activity of each nerve. In vivo nerve activity during spontaneous feeding
EXPERIMENTS. Chronic electrodes were implanted on the radula nerve and buccal nerve 2 and recordings were made as above. In these experiments continuous recordings were made as the food-deprived animals fed spontaneously on seaweed (Gracilaria) introduced into the tank.
DATA ANALYSIS.
Similar methods were used as above, except that the beginning and end times of the bursts of radula nerve activity (only the radula nerve was analyzed in this data set) were identified automatically. The identification used the multimodal distribution of the interevent intervals of the largest units in the nerve, presumably the neurons B8. Based on this distribution, bursts were defined as continuous sequences of 
5 events with interevent intervals of <1 s. After identification of the bursts, the aggregate activity within them was computed from the times of events of all sizes as above. Altogether 1,449 bursts were identified from one animal.
In vivo ARC muscle activity during spontaneous feeding
EXPERIMENTS.
A chronic electrode was implanted in the ARC muscle and recordings were made as above (see also Cropper et al. 1990; Evans et al. 1996). Continuous recordings were made as the food-deprived animals fed spontaneously on seaweed (Gracilaria) introduced into the tank.
DATA ANALYSIS.
Similar methods were used as above. Bursts of electrical activity in the muscle were identified automatically; bursts were defined as continuous sequences of 10 large events with interevent intervals of <1 s. Altogether, 5,791 bursts were identified from 4 animals.
Motor neuron-elicited ARC muscle contractions in the reduced buccal-ARC preparation
EXPERIMENTS.
These experiments used the standard buccal-ARC neuromuscular preparation without extracellular nerve recording or stimulation. Some of the experiments were new, but a large part of the data set was obtained by reanalysis of control runs from previous studies that used this preparation (e.g., Brezina et al. 1996, 2000a,b ; Orekhova et al. 2003). Either motor neuron B15 or B16 was intracellularly stimulated with repetitive brief current injections to fire bursts of spikes such that each burst elicited an ARC muscle contraction of moderate amplitude. B15 was typically fired at 10–13 Hz, B16 at 15–25 Hz, for 1 or 1.5 s every 20 or 30 s; within each experiment, the pattern of spikes was completely regular and invariant from burst to burst. The results of interest were indistinguishable for the two motor neurons and have been pooled.
DATA ANALYSIS. Similar methods were used as above. Because the muscle contraction lagged considerably behind and outlasted the motor neuron burst, the mean contraction amplitude was evaluated over a standard 5-s interval starting with the first spike of the burst. This interval included segments of the contraction baseline, but this did not matter because we focused primarily on the cycle-to-cycle variability. The mean contraction amplitude was normalized by the maximal amplitude reached in that particular preparation. In total 2,762 contractions were analyzed from 28 preparations.
|
RESULTS |
|---|
|
TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
|---|
The reduced preparations used in this work consisted of the buccal ganglia, which contain the feeding CPG, still connected to parts of the buccal mass, the complex muscular organ that moves the food-grasping structure, the radula (see Elliott and Susswein 2002; Kupfermann 1974). The CPG generates cyclical, rhythmic motor programs that can be recorded intracellularly in the firing of many individual CPG interneurons and buccal motor neurons as well as extracellularly in the activity of nerves that project to the buccal-mass musculature (Fig. 1). In this work, following established practice (e.g., Hurwitz et al. 1996; Jing and Weiss 2001; Morgan et al. 2002; Morton and Chiel 1993a), we used the activity of two nerves, the I2 nerve and buccal nerve 2, respectively as markers of the two major phases of each program that, in the intact animal, produce protraction and then immediately retraction of the radula. We define a "motor program" as one unit of these two phases, and a complete "cycle" as a motor program together with the preceding interprogram interval (see Fig. 1). Simultaneously, in the buccal-ARC preparation, we recorded the firing of two buccal motor neurons, B15 and B16, and contractions of the muscle that these neurons innervate, the accessory radula closer (ARC, or I5) muscle (Cohen et al. 1978). The ARC is routinely studied as a representative buccal-mass muscle (Brezina et al. 2003a; Hooper et al. 1999).
To elicit the programs, again following previous work (e.g., Chiel et al. 1986; Morgan et al. 2002), we electrically stimulated another of the buccal nerves, the esophageal nerve. In our standard "continuous" protocol (see METHODS), we stimulated the nerve with brief shocks delivered at a moderate frequency (2–3 Hz) continuously for 3 min. Figure 1 shows one such "block" of stimulation. As can be seen, multiple motor programs were typically elicited. After a rest period of 7 min, another block was recorded. Altogether, we collected 1,076 programs in 166 blocks (6.5 programs/block on average), satisfying our criteria (see METHODS) for further analysis.
Variability of the esophageal motor programs
Although the esophageal nerve stimulation was perfectly regular and continuous throughout the 3-min block, the elicited motor programs were not at all regular. As Fig. 1 shows, they varied in all respects—in their timing, their intensities of nerve activity, their motor neuron firing frequencies and patterns, and the sizes and shapes of their muscle contractions. We used several complementary approaches to quantify and analyze this variability.
The downstream levels of the neuromuscular system, the muscle contractions and, ultimately, functional movement, integrate in a complex way multiple upstream parameters (Brezina et al. 1997, 2000a). The contractions of the ARC muscle, for example, depend on the overall firing frequencies of both motor neurons B15 and B16, on the detailed pattern of the firing of each neuron and the mutual relationship of the two patterns, and on the duration of the firing, determined by the duration of the protraction and retraction phases generated by the CPG. To simultaneously visualize the variability in all these parameters, we examined the variability of entire waveforms. We collected together the waveforms of the instantaneous firing frequencies of B15 and B16 and of the ARC contraction amplitude over the duration of the protraction and retraction phases of all 1,076 programs in the data set, aligned at their protraction–retraction boundaries. In Fig. 2, left column, we have then plotted, at each time point relative to this boundary (vertical line), the 10th, 25th, 50th (median), 75th, and 90th percentile values across the entire ensemble of waveforms. The corresponding values at successive time points constitute the 10th, 25th, 50th, 75th, and 90th percentile waveforms seen. The time at which each percentile waveform first rises above zero marks the corresponding percentile of the distribution of protraction durations; where it eventually falls below zero, of retraction durations (the phase duration percentiles are explicitly indicated by the gray bar at the bottom). Clearly, there is a many-fold difference in the motor neuron firing frequencies and muscle contraction amplitude, at any particular time and overall, as well as in the protraction and retraction durations, between the smallest and the largest programs in the data set.
|
The plots in Fig. 2 show well the simultaneous multidimensional variability of entire waveforms, but they do not lend themselves easily to further statistical treatment. A different quantification of the variability in the data set is therefore presented in Fig. 3. Here we have simply plotted, one by one, the distributions of values of 11 principal parameters of the overall cycling and phasing of the programs (Fig. 3A) and the firing of the motor neurons B15 and B16 and contractions of the ARC muscle (Fig. 3B) measured from all 1,076 programs in the data set. We will refer to such values measured from individual programs as "absolute" values, in contrast to the relative cycle-to-cycle differences between programs introduced below. The 10th, 25th, 50th (median), 75th, and 90th percentiles of each distribution are marked by the thin vertical lines. Again, the bulk of each distribution is very broad, and there is furthermore in most cases a long right-hand tail, extending even offscale, in which the values are many times those at the left-hand end of the distribution.
|
To quantify the "random" variability of type 4 alone, we examined pairwise cycle-to-cycle differences between successive programs in the same block. In Fig. 4 we have plotted the distributions of these differences for the same 11 parameters as in Fig. 3. The differences were computed from the block-normalized parameter values, so that –1 and 1 on the horizontal scale indicate decreases and increases, respectively, from one program to the next that are equal in magnitude to the mean of the parameter. The distributions are roughly symmetrical around zero, showing that any systematic trends of type 3 have been for the most part eliminated. Each distribution has a distinct central peak, but this peak is still quite broad, and there are still long tails indicating some very large differences between successive programs. The plots in Fig. 4 also give the SD (
) of each distribution. With the block-normalized values used, is a dimensionless measure similar to the coefficient of variation that is often used to quantify variability (see, e.g., Shadlen and Newsome 1998; Stevens and Zador 1998; Zoccolan et al. 2002). As can be seen, is of the order of 0.3–0.6 for many of the parameters, but 1 or more for some parameters, in particular those of the ARC muscle contraction.
|
Having thus isolated the "random" variability of type 4, we could return to the variability of type 3—systematic trends over successive programs in the same block. One indication that such trends existed was that the cycle-to-cycle differences inFig. 4 were distributed differently than expected if they had originated by purely random assortment of the absolute parameter values in Fig. 3. Figure 5 A shows this formally for two representative parameters: the interprogram interval and the mean firing frequency of motor neuron B16 in protraction. We performed, essentially, a Monte Carlo simulation to construct the distributions of cycle-to-cycle differences expected from pairs of values resampled at random from the absolute-value distributions in Fig. 3 (thin continuous curves in Fig. 5A) or, more important, from the block-normalized versions of those distributions (thick continuous curves). The actual distributions of cycle-to-cycle differences, reproduced from Fig. 4, are shown by the gray histograms. The actual distributions clearly have a narrower central peak than the random expected distributions, reflected in a generally smaller value of . Yet in some cases—for instance, that of the interprogram interval—the actual distribution also had longer tails, leaving unchanged. The single-dimensional parameter was thus inadequate to capture the more complex differences in the shapes of the distributions.
|
; Press et al. 2002). The Kolmogorov–Smirnov test found a significant difference (P < 10–10) between the actual distribution and either random expected distribution for each of the two parameters. Then, to determine which parts of the distribution were different, we constructed and compared binwise 95% confidence intervals around each distribution (thin vertical lines in Fig. 5A; see legend for details). The asterisks (*) at the top of each plot in Fig. 5A mark where the actual distribution is significantly greater than the block-normalized random expected distribution, the plus signs (+) the converse. The generally narrower shape of the actual distributions indicated that successive programs were more similar than if they had been completely independent of one another. Although other explanations are possible, this could be if on average—under the overlay of the large "random" variability—the programs progressively evolved throughout the block. To visualize these trends directly, for each of the 11 parameters, we examined the location of the distribution of the subset of all first, second, third, and so forth, programs from each block, within the entire distribution of the block-normalized absolute values from all programs. Plotted in Fig. 5B are the medians of the program subdistributions expressed as percentiles of the entire distribution. If the subdistributions were randomly sampled from the entire distribution, the program medians should be centered around the median of the entire distribution, the line marked "Random sampling." Instead, the medians of most of the parameters, including the two studied in Fig. 5A ("4—interprogram interval" and "8—B16 in protraction"), clearly trend systematically from smaller to larger values as the programs proceed. Others, conversely, trend from larger to smaller values ("9—B16 in retraction").
Structure of the variability of the esophageal motor programs
Figure 5B reveals coherent structure in the parameter space of the motor programs. Yet this structure is not informative in the way we would wish, because there are reasons to believe that the trends that give rise to the structure represent evolution of the type of program, from a relatively ingestive (biting- or swallowing-like) to a more egestive (rejection-like) type (see DISCUSSION). In the intact animal, such trends would be thought of as reflecting a progressive change in functional goal, rather than different ways of reaching the same goal. Can we find structure even when the goal remains the same—when the progressive trends are eliminated, in the "random" variability of the cycle-to-cycle differences?
We examined, as a first attempt at the problem, simply pairwise correlations between different parameters. These correlations fell into three classes, examples of which are shown in Fig. 6, A, B, and C, respectively. As expected, there were strong correlations, both in the absolute values and in the cycle-to-cycle differences, where one parameter was an intrinsic part of the other, as for example the interprogram interval was part of the cycle period (Fig. 6A). More interestingly, there were correlations, albeit considerably weaker ones, between the absolute values of some parameters that were not intrinsically linked, such as the two studied in Fig. 5, the interprogram interval and the firing of B16 in protraction (Fig. 6B, left). These correlations were a reflection of the trends found in Fig. 5B. When the trends were eliminated by focusing on the cycle-to-cycle differences, the correlations disappeared (Fig. 6B, right). Finally, there were no correlations at all, either in the absolute values or in the cycle-to-cycle differences, between still other parameters, such as the protraction duration and the retraction duration (Fig. 6C).
|
), might yet find some structure in the cycle-to-cycle variability. However, the strong suggestion of these results is that, when the next program is to be generated by the system, the "choice" of any one of its parameters does not depend on the choice of any other parameter. In this sense the variability is truly random. Variability of esophageal motor programs in a reduced buccal-opener preparation
The ARC muscle closes the radula (Cohen et al. 1978; Orekhova et al. 2001), but it is not the only muscle that does this. The radula is also closed by the firing of motor neurons B8, probably through contraction of the I4 muscles (Morton and Chiel 1993b; Orekhova et al. 2001). There is therefore a degree of degeneracy in the mapping of muscle contractions to movements (see, e.g., Beer et al. 1999; and DISCUSSION): potentially similar closing movements of the radula can be accomplished by contractions of the ARC muscle, the I4 muscle, or combinations of both. The constraint on the ARC muscle to contract in the same way in each cycle may consequently be reduced. Could this account for the particularly large variability seen in the ARC contractions in Figs. 3 and 4?
To help address this question, we performed another set of experiments, essentially identical to those described so far but, instead of B15 and B16 and the ARC muscle, recording the firing of motor neuron B48 and the contractions of the radula opener muscle complex I7–I10 (Evans et al. 1996). The I7–I10 complex is a key muscle that opens the radula and thus would definitely be expected to participate in each functional cycle. The results are shown in Fig. 7. Figure 7A shows part of a typical 3-min block of esophageal motor programs, and Fig. 7B shows the distributions of the cycle-to-cycle variability of the firing frequency of B48 and the contractions of the opener muscle, drawn from the 741 cycles analyzed from these experiments and presented as in Fig. 4. Because B48 fired and the opener muscle contracted strongly in the interprogram interval and in protraction, but not in retraction (Fig. 7A), the cycle-to-cycle distributions are shown for the interprogram interval and protraction. As can be seen, the variability in Fig. 7B is large, essentially no different from what it was in Fig. 4B for the firing of B15 and B16 and contractions of the ARC muscle.
|
The large variability described so far was found in reduced preparations lacking some control mechanisms, such as sensory feedback loops, that might increase variability, but might also conceivably reduce variability. Is there large variability also in intact animals, during normal feeding behavior? To answer this question, we performed three sets of in vivo experiments in which we used chronically implanted electrodes to record the activity of buccal nerve 2 and of the radula nerve (another of the buccal nerves), or the electrical activity of the ARC muscle, while the animals were fed in a semicontrolled manner or engaged in spontaneous feeding.
First, we fed the animals with standard strips of seaweed, each 10 cm long, long enough that the animal, having grasped one end, required multiple swallowing cycles to ingest the entire strip. Figure 8 shows a typical recording from buccal nerve 2 and the radula nerve during the ingestion of one complete strip. The small black rectangles at the top mark the times when actual functional swallowing—inward movement of the strip—was observed. For analysis, we collected complete recordings from 153 strips, comprising 1,388 cycles; thus on average, the animals required approximately 9 cycles to swallow each 10-cm strip.
It can plausibly be argued that, after the initial bite-swallow (which was excluded from the analysis; see METHODS), each swallow during the ingestion of a strip was performed under identical conditions: as in the case of the esophageal nerve stimulation, the half-swallowed strip represented a continuous, regular stimulus. Yet, as Fig. 8 shows, the cycles were again very variable. In Fig. 9 we have quantified this variability in similar ways as for the esophageal motor programs. Figure 9A shows the 10th, 25th, 50th (median), 75th, and 90th percentile waveforms of the ensemble of all program waveforms—in this case, of the bursts of buccal nerve 2 and radula nerve activity—in the data set. Figure 9B shows the absolute-value distribution of the cycle periods, and Fig. 9C the distributions of the cycle-to-cycle differences of the cycle period as well as of the total activity during the burst in each nerve. Overall, the variability is about as large as it was for the esophageal motor programs.
|
) of these subdistributions as a function of program number. The subdistributions become noticeably narrower with increasing program number: their central peak grows while their tails diminish; the vertical lines marking the 10th, 25th, 50th, 75th, and 90th percentiles come closer together, and progressively decreases. For each of the two parameters, the final subdistribution of programs 16–18 differs significantly (P < 10–9 by the Kolmogorov–Smirnov test) from the starting subdistribution of programs 1–3 (the black histogram outlines repeat the latter at the bottom of Fig. 10A for comparison). Note that, because we have here analyzed cycle-to-cycle differences rather than absolute values, the trend seen here reflects not a progressive migration of the location of the average parameter value as in Fig. 5B, but rather a progressive tightening of the spread of its variability.
|
total) of 1.92 (Fig. 11D, left). Removing just the largest 10% and the smallest 10% of the distribution—presumably removing selectively the interbout intervals—leaves a SD (central) of 0.33, similar to the values in the previous data sets.
|
|
|
Broadly, two kinds of mechanisms might explain the large cycle-to-cycle variability found in the system. The variability appears to be random across the parameters of a particular cycle (Fig. 6), and it might be random—after the systematic trends in Fig. 5B have been eliminated—in any one parameter across successive cycles as well. It would then amount to truly random, spontaneous, uncontrollable noise in the system. Alternatively, like the systematic trends, the cycle-to-cycle variability might depend, although perhaps in a much more complex way, on the previous history of activity in the system.
To test for the second mechanism, we should alter the history of the system. In intact animals we cannot do so because we have no control over the production of the motor programs. In a reduced preparation, however, we can exert a considerable degree of control over their timing. We carried out a second series of experiments in the reduced buccal-ARC preparation, identical to the first series except using "discontinuous" esophageal nerve stimulation (see METHODS), essentially more intense but brief bursts of stimulation, each of which reliably elicited one, and only one, motor program. By repeating the bursts of stimulation at regular intervals we were able to elicit the programs at quite regular intervals (not completely regular because the latency from the stimulation to the beginning of the program, as well as the duration of the program, still varied somewhat). Figure 14 shows 4 typical programs from such an experiment; altogether, we collected 856 programs. In Fig. 15 we have quantified the cycle-to-cycle variability of the 11 principal parameters of these regular programs [gray histograms, black percentile lines, SDs () in black], compared to the variability of the irregular programs reproduced from Fig. 4 (red histogram outlines, in red).
|
, and note the symbols at the top of each plot, indicating statistically significant differences between the distributions; furthermore P < 10–10 in each case by the Kolmogorov–Smirnov test). The regular programs are, of course, much less variable in parameters such as the cycle period, which we most directly control. However, they are also considerably less variable in timing parameters that we do not directly control, such as the protraction and retraction phase durations, and even, remarkably, in parameters that intrinsically have little to do with timing, such as the firing frequencies of the motor neurons B15 and B16. Perhaps least regularized, interestingly, are the contractions of the ARC muscle, but even here P < 10–10 by the Kolmogorov–Smirnov test. The neuromuscular transform has little intrinsic cycle-to-cycle variability
One possible explanation for the persistent large variability of the muscle contractions is that the neuromuscular transform—the sum total of the peripheral processes that transform the motor neuron spike patterns into contractions (Brezina et al. 2000a)—itself has large intrinsic variability. That is, even completely identical, regular spike patterns might produce irregular, variable contractions, as has been found in other systems (e.g., Zoccolan et al. 2002). To examine this possibility, we regularized the firing of the motor neurons B15 and B16, stimulating either one by DC injection to fire in completely regular, repetitive bursts, each of which produced a contraction of the ARC muscle. Figure 16 A shows a typical segment from such an experiment. In Fig. 16B we have quantified the cycle-to-cycle variability of the mean amplitude of 2,762 such contractions [gray histogram, black percentile lines, SD () in black], contrasting it with the variability of the mean contraction amplitude in retraction during the irregular (red) and regular (blue) esophageal motor programs from Figs. 4 and 15. As can be seen, the directly elicited contractions have much less variability—indeed, essentially no variability: completely regular firing of the motor neurons produces completely regular contractions of the muscle. The ARC neuromuscular transform thus appears to have very little intrinsic variability.
|
|
DISCUSSION |
|---|
|
TOP |
|---|
that, as the sample size n increases, approaches the true population probability p. What range of p, plow < p < phigh, is 
0.025 and phigh such that F(X = n
