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1Department of Physiology and Biophysics and Fishberg Department of Neuroscience, Mount Sinai School of Medicine, New York; and 2Department of Neurobiology and Behavior, Cornell University, Ithaca, New York
Submitted 15 March 2005; accepted in final form 3 June 2005
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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), to be solved by averaging, redundancy, and, more generally, degeneracy in the mapping from one level of the system to the next higher level, to finally achieve a predictable, reproducible behavior. There are, however, other proposals in which the variability is not merely a problem to be eliminated, but plays a positive, active role in the production of functional behavior. We continue here our study of such a role that variability might play in the feeding behavior of Aplysia.
Aplysia consummatory feeding behavior—biting, swallowing, and rejection of unsuitable food—is a cyclical, rhythmic behavior produced by a complex neuromuscular system: the contractions of numerous muscles in the animal's feeding organ, the buccal mass, each controlled by the firing patterns of its individual motor neurons, all driven ultimately by feeding motor programs generated by a multitasking central pattern generator (CPG) in the buccal ganglia (Kupfermann 1974; reviewed by Elliott and Susswein 2002; Kupfermann et al. 1997). Traditionally, the behavior has been thought of as stereotyped. Yet we have recently found that essentially all of the basic parameters of the cycling of the CPG, motor neuron firing, and contractions of the individual muscles (Horn et al. 2004; Zhurov et al. 2004, 2005a), as well as higher-level parameters of the coordination between entire motor neuron–muscle subsystems within the feeding neuromusculature (Zhurov et al. 2005b), are extremely variable from one cycle of the behavior to the next. Remarkably, this is so even when the stimulation that elicits each cycle, or, in functional terms, the functional task or functional goal of the behavior, is the same in each cycle.
There are several possible scenarios of the consequences of this variability for the production of functional behavior (see Horn et al. 2004; Zhurov et al. 2005b). These scenarios can be distinguished, however, by one critical, experimentally testable question. Does the variability that is observed within the neuromuscular system appear in the functional performance of the behavior? In other words, when evaluated in terms of their satisfaction of the functional goal of the behavior, do all cycles of the behavior achieve equally good performance, or are there some cycles that are good, but some that are less good, and some, perhaps, that are not functional at all? It could be that the variability that is observed in the neuromusculature is indeed eliminated already internally, by complementary relationships among the neuromuscular components—by a degeneracy or multiple degrees of freedom (Beer et al. 1999; Bernstein 1967) in the mapping of, for instance, individual muscle contractions to overall movements. Degeneracy at this level may indeed exist in the Aplysia buccal neuromusculature (see, e.g., Drushel et al. 1997, 1998; Neustadter et al. 2002a,b). There could also be degeneracy at the next higher level, in the mapping of the movements to functional performance, so that, even if variable movements are produced, in terms of functional performance they are all equally good. In either case, the same behavior—stereotyped perhaps even in the actual physical movements but, more important, in their functional significance—is produced in each cycle. In either case the scenario is of the traditional kind. If, on the other hand, the variability does emerge in the functional performance of the behavior, then we must think about the organization and operation of the neuromuscular system in an entirely different way. We have proposed that the variability is permitted to exist, and may even be actively generated by the CPG (Horn et al. 2004), because it serves a higher-order functional purpose. When the animal is faced with a new and only imperfectly known feeding task in each cycle, the variability implements a trial-and-error search through the space of possible feeding movements, a strategy that clearly will not be successful in every individual cycle, but on average, over many cycles, may in fact be the animal's optimal strategy in an uncertain and changing feeding environment (Brezina et al. 2005; Horn et al. 2004; Zhurov et al. 2005b; see DISCUSSION).
It is thus necessary to measure, in intact, freely feeding animals, the functional performance of the feeding behavior. The work documenting the neuromuscular variability was either done in vitro (Horn et al. 2004; Zhurov et al. 2004, 2005a,b), with the components of the neuromusculature partially disassembled and stimulated in ways that may not reproduce the full stimulus set experienced by the intact feeding animal, or, when neuromuscular activity was monitored in intact animals with chronically implanted electrodes (Horn et al. 2004), there was no measurement of function. In vitro, it is difficult to measure function because it is not clear how function is to be evaluated for an isolated component of the neuromuscular system such as an individual muscle. In intact animals, however, a reasonably self-evident measure of function offers itself, for an ingestive feeding behavior such as swallowing, for example, in the form of the amount of food actually ingested at any point in time. At least two previous studies (Hurwitz and Susswein 1992; Kabotyanski et al. 2000) have used such a measure of performance, but in each case they reported only the average performance over many cycles, not the performance in each individual cycle. What distinguishes the different scenarios of the organization of the neuromuscular system, however, is not their average performance—they all predict good average performance, as they must do to be plausible at all—but their different predictions of the distribution of the performance over successive cycles. The proposed trial-and-error feeding strategy, too, predicts performance that is good, indeed optimal, on average, but highly variable from cycle to cycle. The trial-and-error strategy, if it is to be considered as a reasonable explanation of how the system operates, in fact requires the variability to emerge in the behavior as an essential part of its mechanism of action. Thus as a critical test of these various theories, in this study we measure and statistically analyze the feeding performance of intact Aplysia on a cycle-by-cycle basis. Because we simultaneously monitor CPG, motor neuron, and muscle activity with implanted electrodes, we can furthermore begin to directly correlate the variability at the two levels, the variability in the activity of the neuromuscular system and its functional consequences.
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METHODS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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In this work we used Aplysia californica weighing 100–300 g obtained from Marinus Scientific (Garden Grove, CA). Each animal was implanted with two wire electrodes for simultaneous chronic recording from buccal nerve 2 (BN2) and the accessory radula closer (ARC, or I5) muscle, using techniques based on those used in a number of previous studies (e.g., Cropper et al. 1990a,b; Horn and Kupfermann 2002; Horn et al. 2004; Hurwitz et al. 1996; Morton and Chiel 1993a,b). Briefly, the animal was anesthetized by injection of chilled isotonic MgCl2, placed in a bath of chilled seawater on an incline to minimize the escape of hemolymph, and an approximately 1-cm-long access incision was opened in the body wall on the left side of the head. Each wire electrode consisted of a strand of ultrafine Teflon-insulated stainless steel wire (0.002-in. bare, 0.0045-in. insulated; AM Systems, Carlsborg, WA) from which the insulation had been stripped at the very tip. The two wires were pierced separately through the body wall near the access incision and loosely knotted inside the body, leaving free ends of 1–2 cm beyond the knot. An incision was made through the I2 muscle into the buccal mass to expose the ARC muscle. The deinsulated tip of one of the wires was inserted into the ARC muscle and glued in place with Instant Super Glue (ND Industries, Troy, MI). The incision in the I2 muscle was then sutured closed. The tip of the other wire was coiled around one of the buccal nerves 2 and similarly glued in place. The knot on the wires was used as an attachment point for a suture with which the knot was anchored to the body wall, so that the wires would not be pulled out by the movements of the animal. The access incision in the body wall was then sutured closed. The surgery generally lasted 45–60 min.
After surgery, the animals were returned to individual cages inside a large seawater tank maintained at approximately 15°C. The two wires emerging from the body were fastened to a polystyrene float to keep them out of the way of the movements of the animal. Animals generally recovered from the surgery (as determined by their readiness to feed) by the next day.
Experiments
Most recordings analyzed here were obtained from animals 1–3 days after surgery, but in some cases up to 13 days. Animals were selected for recording each day based on their readiness to feed, tested with small samples of seaweed. Each animal was recorded from, as described below, while ingesting standard strips of seaweed, repeatedly until it showed signs of satiation or rejection. It might then be recorded from again on a subsequent day, but not until it had become ready to feed again, usually after one or more interposed days of rest.
For recording, the animal was transferred to an approximately 3-liter rectangular glass or plastic tank filled with seawater. We made no attempt to restrain the animal in any particular position in the tank because during the recording most animals spontaneously assumed a relatively immobile posture with their body extended at the surface of the water (see RESULTS). The recording apparatus was prepared as follows. A standard length transducer (Model 60–3000, Harvard Apparatus, Holliston, MA) was mounted so that its arm, a lightweight 30-cm-long metal rod, extended horizontally. To its end was attached, with a short piece of string, the end of one of the seaweed strips; the strip therefore hung from the arm vertically. A small test piece of seaweed held in forceps, or in some experiments seaweed extract (seaweed soaked in seawater, mashed, and filtered) added to the tank, was used to stimulate the animal to orient itself into the feeding posture, with its mouth upward, and begin rhythmic biting, although not yet able to grasp any food. The freely hanging end of the seaweed strip was then lowered, by moving the entire length transducer unit downward on its mounting rod, until the end of the strip touched the animal's mouth. The animal grasped the strip and began to swallow it. As it progressively pulled the strip into its mouth, this pulled down the transducer arm and recorded the movement. [The same basic approach was used in the previous studies of Hurwitz and Susswein (1992) and Kabotyanski et al. (2000).]
At the very beginning, the strip was sometimes slack and not fully transmitting its movement to the transducer. For this and other reasons (see RESULTS), we excluded the first several cycles of swallowing of each strip from our analysis (see following text). After one or more cycles, however, the strip came under full tension. The transducer arm was counterweighted at the other end, with small, known weights fixed at a measured distance from the transducer fulcrum, to maintain the tension at an adequate level, but not so high that the animal would have to pull against an excessive load. Calibration with test weights and calculation of the loads involved showed that the animals were pulling against nominal forces of 0.06–1.7 g, in most experiments at the low end of this range. In several experiments, however, we systematically varied the load up to 1.7 g, to test its effect. Relative to the large variability that we saw in the swallowing of identical, identically loaded strips by different animals or even in succession by the same animal, we saw no obvious systematic effect of the varying load and consequently the results over the entire range of loads have been pooled. [Working with Aplysia oculifera, Hurwitz and Susswein (1992) found an effect already in the range 
1 g, but their animals were 1–2 orders of magnitude smaller than the animals in our study.] Before the animal grasped the strip, the counterweighting of the transducer arm cocked the arm upward, against the stop at the upper end of its range of travel (e.g., in Fig. 1A at "c"; we always quantified the movement of the strip in terms of the length already swallowed, rather than the length remaining, thus inverting our plots of raw strip position or movement). As the animal swallowed the strip, the arm moved down and eventually reached the stop at the lower end of its travel (at "d" in Fig. 1A). At this point the resistance to further ingestion of the strip became effectively infinite and, after a variable period of time, the animal broke or cut the strip (at "e" in Fig. 1A). The dimensions of the apparatus were such that this usually happened after the animal had swallowed 12–14 cm of the standard 15-cm strip. Occasionally the strip broke or was cut by the animal when only partly ingested. After an interval, usually of 1–2 min but in some experiments up to 7 min (no obvious difference was observed), another strip was offered to the animal in the same way (see, e.g., Fig. 9). This continued until the animal showed signs of satiation or rejection, most evident in whole-body turning away from the offered strip. The number of strips ingested by the animal in the recording session ranged from 1 to 11; animals being recorded from for the first time since surgery usually ingested 
6 strips.
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The temperature of the seawater in the recording tank was usually 17.5–19.5°C, but in some experiments as low as 16°C or as high as 24°C. We saw no obvious systematic effect of temperature and the results at all temperatures have been pooled.
Some animals were dissected after the recording session to confirm that the implanted electrodes were still in place. This was almost always the case with recently implanted electrodes. In animals that had gone 2 weeks or longer since the surgery, however, there was often a problem that, in fact, was first evident in the electrical recordings. Normal recordings from BN2 showed several distinct classes of rapid spikes (see following text), but in the older animals the rapid spikes often disappeared and were replaced by slower, smoother waves of activity, like those normally recorded from the ARC muscle (the difference between the rapid spikes and the slow waves is clear, for example, in Fig. 1C), which therefore also were probably a reflection of the adjacent buccal muscle activity. (Even normal recordings with robust rapid spikes often showed some underlying slow-wave activity, which if necessary could be selectively removed by additional high-pass filtering, as it was in Fig. 1, B and C.) Dissection of these animals revealed that, although the animals remained outwardly healthy and continued to feed, BN2 had been damaged or had disintegrated entirely under the glue layer holding the implanted wire in place. Recordings with predominant slow-wave activity in BN2 were therefore discarded and, once this problem was apparent, animals were generally not kept longer than 2 weeks after surgery.
Analysis of electrical and length-transducer signals
The basic unit of analysis was the seaweed strip, which was then divided into the successive individual cycles with which the animal had swallowed it. This division was based, in the first instance, entirely on the electrical record from BN2; the other signals did not enter the analysis until later. The record of BN2 activity was analyzed based on the identification of a certain pattern of electrical activity within it as a marker of the radula-retraction phase of the feeding motor program, a criterion established by Morton and Chiel (1993a,b) and subsequently used in many other studies (e.g., Dembrow et al. 2004; Due et al. 2004; Hurwitz et al. 1996; Kabotyanski et al. 2000; Morgan et al. 2000; Nargeot et al. 1997, 1999; Proekt and Weiss 2003; Proekt et al. 2004; Susswein et al. 1996; Wu et al. 2003).
To recognize this pattern of electrical activity, we followed essentially the same procedure, except implemented in software rather than hardware, as did Morton and Chiel (1993a). First, the threshold event detection module of Clampfit 9 (Axon Instruments) was used to automatically tabulate all spike times and amplitudes in the BN2 record. As found by Morton and Chiel, the record almost always contained three distinct classes of spikes, of small, medium, and large amplitude (labeled "Small," "Medium," and "Large" in Fig. 1B; Morton and Chiel described all three as "large-unit" classes because there were still other classes of truly small spikes, which both Morton and Chiel and we ignored). The few recordings in which the classes were not clearly distinguishable were excluded from the analysis. The threshold amplitudes separating the classes generally differed between recordings from different animals and were determined in each case by inspection. Separately for each class, the 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. This and all further processing was done in Mathematica (Wolfram Research, Champaign, IL).
As found by Morton and Chiel, the retraction phase of each motor program was identifiable by a distinct, often indeed very intense, burst of firing, that is, a large increase in firing frequency, generally of all three spike classes (see Figs. 1, 7A, and 9). The precise times when each burst began and ended—then taken to be the times when the retraction phase began and ended—were determined by a semiautomated but supervised algorithm implemented in Mathematica. Proceeding along the three instantaneous firing frequency functions, fsmall(t), fmedium(t), and flarge(t), extracted from the BN2 record over the duration of each strip, this algorithm identified each successive burst, first, by flarge(t) rising, from nearly zero between the bursts, above a threshold value, v1, usually set at 1 Hz. The algorithm then worked backward from this time to the last time that the product fsmall(t) x fmedium(t) had been lower than another threshold value, v2, usually 5 Hz2. (The values of v1 and v2 were sometimes adjusted if a particular recording had unusually high or low firing frequencies. Also, if the instantaneous firing frequency functions were very irregular, they were sometimes smoothed for more robust results.) The algorithm also worked forward to the first time at which both flarge(t) had fallen again below v1 and fsmall(t) x fmedium(t) had fallen below v2. In most cases, this algorithm correctly set the beginning of the burst to just after the distinct pause or break in firing, which preceded many bursts (e.g., "Break" in Fig. 1B), that Morton and Chiel identified as a suitable marker of the beginning of the retraction-phase firing, and set the end of the burst to include not merely the burst of large spikes but also most of the following distinctive tail of intense medium- and small-spike firing ("f" in Fig. 1B), but at the same time excluded the low-frequency regular firing of the medium and small spikes that sometimes proceeded throughout the interburst interval ("g" in Fig. 1B). The algorithm thus demarcated the bursts essentially as they are generally demarcated by eye (e.g., in the references at the beginning of this section). Because the bursts were very variable, however, occasionally the algorithm failed completely, especially with bursts that contained only sporadic or no large spikes. More complex algorithms tried in these cases were somewhat more successful, but in the end we preferred to retain the simple algorithm but to supervise it, confirming its suggested demarcation of each burst or, if necessary, manually correcting any obvious mistakes. If excessive correction was required, the entire strip was excluded from the analysis.
This initial analysis yielded a series of retraction phases (e.g., gray rectangles in Fig. 1B)—more exactly, retraction phases as operationally defined just from the electrical activity (see RESULTS)—of the successive motor programs used to ingest each seaweed strip. Each of the intervals between the retraction phases was therefore the sum of the radula-protraction phase of the motor program and the interprogram interval. A "cycle" was taken to be the sum of a retraction phase and the preceding interretraction interval (see Fig. 1B).
Next, we excluded from the analysis any cycle during any part of which the seaweed strip was not under the correct tension, that is, any cycle during which the transducer arm made contact with the stop either at the bottom or at the top of its range of travel. This excluded several cycles at the beginning of many strips; in any case, we always excluded at least the first two cycles (see RESULTS). This criterion also excluded a variable, sometimes quite large (e.g., Fig. 9, 1.5-cm strip), number of cycles at the end of each strip, when the animal had already ingested as much of the strip as it could pull down but before it broke or cut the strip. If there were any cycles that were not themselves excluded by this criterion but were separated by an excluded cycle from the main sequence of included cycles, they too were excluded, so that what was included in the analysis was just a single sequence of contiguous cycles (e.g., in Fig. 1A within the dashed box) constituting the bulk of each strip. Strips that broke when only partly ingested were included in the analysis provided at least five cycles, after those excluded at the beginning, had been recorded. The sequence analyzed from completely ingested strips always had more cycles than this.
Finally, only those strips were included for which there was throughout a clear, uncorrupted, relatively noise-free recording of each of the three channels: the electrical activity in BN2, the electrical activity in the ARC muscle, and the movement of the strip. Altogether, these various criteria yielded a data set of 2,755 cycles from 143 strips ingested by 26 animals for further analysis.
All further analysis operated on retraction- or cycle-length segments of various instantaneous functions derived from the three channels of recording: the instantaneous firing frequency functions of the three spike classes in BN2 or the similarly constructed function of all of the spikes combined; the instantaneous frequency function of all of the peaks, above a certain minimal threshold, in the ARC muscle record (see RESULTS); and the instantaneous position of the seaweed strip. In each cycle as defined by the analysis of the BN2 bursts, the corresponding segments of these functions, either just over the retraction phase or over the entire cycle, were cut, if necessary aligned at the beginning of the BN2 burst, that is, the beginning of retraction, and analyzed either individually or in relation to each other. Several different ways to visualize the variability in the data set were used, as described further in RESULTS and in the relevant figure legends.
Video analysis
In some experiments the feeding animal was continuously videotaped with a Sony DCR-TRV950 Digital Video Camera Recorder mounted on a tripod. Several different camera angles were used, but in one series of experiments the animal was systematically videotaped through the side of the recording tank parallel to the surface of the water, that is, orthogonally to the movement of the seaweed strip (see the second video segment1 and the frame taken from this segment in Fig. 2B ). These side-view videos were then analyzed to compare the movement of the head of the animal to the movement of the seaweed strip recorded with the length transducer. The playing speed of the videos was increased 16-fold—that is, frames were extracted every 533 ms from the original video and assembled into a new video—using Vegas 5 (Sony Pictures Digital). If necessary the light level was adjusted and contrast was enhanced at the same time. Logger Pro 3 (Vernier Software and Technology) was then used to step through the frames of the new video while marking with the mouse cursor the location of some precisely identifiable feature—skin fold or spot—on the animal's head in each frame. If, as occasionally happened, that feature disappeared from view, a new feature was selected and followed. The time series of the vertical coordinates of the feature was then synchronized with the transducer record of the movement of the seaweed strip (see, e.g., Fig. 2C) by aligning the moment at which the strip broke or was cut by the animal, a quasi-instantaneous event that could be precisely located in a particular frame of the video as well as in the transducer record (e.g., at "e" in Fig. 1A). The vertical scale of the video was calibrated by equating the size of the movements of the strip visible in the video to their size in centimeters in the transducer record.
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Statistical analysis was performed in Mathematica or SigmaPlot (Systat Software, Point Richmond, CA).
MULTIPLE LINEAR REGRESSION.
To evaluate the correlation of one or more "independent" data parameters x1, x2, ... , xk with a "dependent" parameter y, we used multiple linear regression to find the least-squares fit of a regression model that included each independent parameter up to the third power. With just one independent parameter x (Figs. 2D, 5, 6, and 8A), the regression model was thus
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0...3 are the regression coefficients, 
is the residual error, and i = 1, 2, ... , n is the index of the successive points in the data set. The best fit was then given by
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0...3 and 
i that minimized the error sum of squares, SS(Error), or equivalently maximized the model sum of squares, SS(Model), in the relation
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is the mean y.
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1 = 2 = 3 = 0 by computing the statistic
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, we used the simple Bonferroni correction for multiple comparisons (Shaffer 1995), reducing the criterion for each individual correlation to /N (thus in Fig. 6 to 0.05/90 = 0.00056).
As a measure of the strength of the correlation with one independent parameter, we used the coefficient of determination adjusted for positive bias
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; Olejnik and Algina 2000), we used the formula (Friedman 1968)
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To evaluate the correlation of k independent parameters with the dependent parameter, the regression model in Eq. 1 was expanded to
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CONTRAST BETWEEN GROUPS.
To evaluate the statistical significance of a contrast between a group of n values x1, x2, ... , xn, with mean 
and SD 
x, and a group of m values y1, y2, ... , ym, with mean and SD y, we used a standard two-tailed t-test with df = n + m – 2. In Figs. 7, B and C, and 8, "***" indicates P < 0.001 and "n.s." indicates P > 0.05. To evaluate the magnitude of the contrast, we computed Cohen's d using the formula (Olejnik and Algina 2000)
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RESULTS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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All experiments reported in this paper were done with animals that had been chronically implanted with two wire electrodes to record electrical activity. One wire was implanted on buccal nerve 2 (BN2), a nerve whose spike pattern is widely used to identify the radula-retraction phase of the feeding motor programs (Morton and Chiel 1993a; see METHODS). The other wire was implanted in the accessory radula closer (ARC) muscle (Cohen et al. 1978), an extensively studied, representative buccal-mass muscle. Animals generally recovered from the brief surgery to implant the wires by the next day, when they were ready to feed. They remained apparently healthy and were used in experiments over many days in some cases. The feeding behavior and all other behaviors observed appeared quite normal.
To measure the performance of the feeding behavior, we hung vertically down from above the animal a strip of seaweed, of a type that the animals consumed readily, from a length transducer counterweighted with a light load. As the animal pulled down and swallowed, spaghetti-like in progressive small increments, the strip of seaweed, the transducer continuously recorded the position, and thus the movement, of the strip (see two short video segments of these movements in the Supplementary Material; one frame from each segment is shown in Fig. 2, A and B). The three simultaneous recordings, of the electrical activity in BN2, the electrical activity in the ARC muscle, and the movement of the strip, obtained during the swallowing of a typical strip are shown in Fig. 1.
Although the animal was perfectly free to decide when and how to take each successive swallow, in some important respects this was not a completely unstructured free-feeding situation. In particular, the seaweed strip was of a controlled, regular size and shape. The standard strips that we used in most experiments were 15 cm long and 1 cm wide, and only these strips are analyzed throughout this paper. We also tested strips of other widths, as described below, but these were not systematically analyzed.
With a strip of constant thickness and width, presented to the animal at a constant angle and under constant tension, it was arguably the case that, in each of the many cycles that it generally took to swallow the entire length of the strip, the animal was experiencing the same stimulus—facing the same feeding task.2 We took care to ensure this constancy of stimulus or task by excluding from our analysis all cycles at the beginning and end of the strip in which the strip was not able to move freely, and in any case the first two cycles of each strip—so that, in general, we analyzed from each strip only a single continuous sequence of "internal" cycles, each having as its predecessor (and usually also successor) another cycle exactly like it in stimulus or task, although not necessarily response. The sequence of cycles analyzed from the strip in Fig. 1, for example, is that enclosed in the dashed box in Fig. 1A. We also ignored the numerous cycles of biting behavior—clearly different from swallowing—that occurred before and after the ingestion of each strip (for example, at "a" and "b" in Fig. 1A), and excluded any strip during which the animal showed overt signs of rejection behavior. This is therefore an analysis purely of swallowing behavior, in response to a constant feeding stimulus or task.
From the distinctive, structured burst of the three main classes of spikes in the BN2 record in each cycle (Fig. 1, B and C), we defined, using standard criteria based on those of Morton and Chiel (1993a) (see METHODS), the beginning and end of the radula-retraction phase of the feeding motor program (that is, the retraction phase as defined electrically: see further below). In Fig. 1B, for example, these retraction phases are indicated by the gray rectangles. Immediately before each radula-retraction phase, there was presumably a radula-protraction phase, but we had no way to define its beginning so as to demarcate it from the preceding interprogram interval. The intervals between the retraction phases in Fig. 1B are therefore the sum of both protraction and interprogram interval. In our analysis, we took a "cycle" to be the sum of a retraction phase and its preceding protraction and interprogram interval.
The BN2 record thus indicated the overall cycling and phasing of the CPG. The ARC muscle record, on the other hand, reflected motor neuron firing and muscle contraction.3 Each peak of the slow waves of electrical activity that we recorded in the muscle (Fig. 1, B and C) is believed to correspond to an excitatory junctional potential (EJC) elicited in the muscle by a spike fired by one of the muscle's two motor neurons, B15 or B16 (Cropper et al. 1990a,b). The bursts of this activity were in most cycles intense enough to have produced a muscle contraction, with a size and shape reflecting the pattern of the burst but delayed with respect to it by as much as several hundred milliseconds in this slow muscle (see, e.g., Brezina et al. 2000a; Cohen et al. 1978; Zhurov et al. 2004).4 Altogether, then, we had from the two electrical records at least some degree of information about each of the levels of the neuromuscular system: the CPG, motor neurons, and muscle. Simultaneously, of course, we had the record of the movement of the seaweed strip. For further analysis, we collected together a data set of 2,755 cycles from 143 strips (a mean of approximately 19 cycles/strip) ingested by 26 animals.
Strip movements are movements of the buccal mass, not of the whole body
The animals were not restrained in any way. We were therefore concerned that to some degree the movements of the seaweed strip that were registered by the length transducer might have reflected movements of the animal's head or whole body, rather than the movements of the buccal feeding apparatus inside the head that were our primary interest. To find out whether this was a problem, we compared the movements of the strip recorded with the length transducer with the movements of the animal's head in the video record of the experiment.
For this purpose we videotaped the animal through the side of the recording tank parallel to the surface of the water, that is, orthogonally to the movement of the seaweed strip, as shown in the second video segment and in Fig. 2B. In the video we then tracked the position of some particular identifiable feature on the animal's head—a skin fold or spot—in frames approximately 0.5 s apart (see METHODS). Figure 2C shows, for one typical strip, the simultaneous records of the strip position registered by the length transducer and of the vertical position of the animal's head.5 Clearly, even when the strip moved rapidly, the head moved hardly at all. Figure 2D shows group data, 2,984 pairs of simultaneous measurements of strip and head movement computed approximately 0.5 s apart (thus spanning more than 26 min) over 241 cycles of swallowing of five strips by three animals (a subset of the larger data set analyzed in the rest of this study). The head movements are much smaller than, and furthermore are completely uncorrelated with, the movements of the strip.
This confirms our visual impression in observing these experiments, which can also be gained from watching the two video segments. Within one or two cycles (excluded from our analysis) after first grasping the seaweed strip, the animal ceased the head-waving movements that characterize the appetitive (food-orienting) phase of the feeding behavior (Kupfermann 1974), and settled into a typical posture, extending the front half of its body at the surface of the water with the mouth upward (see particularly the first video segment). In this posture the animal remained relatively immobile while ingesting the strip. Frequent twitches and ripples could be observed in the skin, the tentacles, and the oral veil, but these movements were small and bore no obvious relation to the movements of the strip, especially the large periodic movements in which the strip was pulled quickly in through the mouth apparently by something inside (see the video segments). Presumably this was the buccal-mass apparatus. We conclude therefore that the strip movements recorded in these experiments can be attributed almost entirely to the action of the buccal neuromusculature.
The swallowing cycles are very variable in all parameters including functional performance
Even though the seaweed strip stimulus was perfectly constant and regular in each cycle, the animal's response to it was not at all regular. There was great variability from one cycle to the next in the records of BN2 and ARC muscle electrical activity—variability in the cycling and phasing of the CPG, the firing of the ARC motor neurons, and, presumably, the contractions of the muscle. This was as expected from the work of Horn et al. (2004). Furthermore, as can be appreciated already in Figs. 1A and 2C, the movement of the seaweed strip—the functional performance of the feeding task—was likewise very variable from cycle to cycle.
Following Horn et al. (2004), we quantified and analyzed this variability in several complementary ways.
VARIABILITY OF TEMPORAL PROFILES.
First, we examined the variability of entire waveforms. We collected together the waveforms of the instantaneous frequencies of each of the three separate classes of spikes in BN2, of all of these spikes combined, and of the peaks or spikes in the ARC muscle record,6 over the duration of the cycle from all 2,755 cycles in the data set, aligned at the beginning of retraction. In Fig. 3 (plots 1–5), we have then plotted, at each time point relative to this boundary (vertical line at time = 0), 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 profiles seen. The time at which each percentile profile first rises above zero marks the corresponding percentile of the distribution of the durations of protraction and the preceding interprogram interval; where it eventually falls below zero, of retraction (these percentiles are explicitly indicated by the gray bar at the bottom). Clearly, there is a manyfold difference, about as large as that found by Horn et al. (2004), in each of the dimensions of cycle timing and spike frequency represented in these profiles between the smallest and largest cycles in the data set.7
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Examining the profiles in more detail, we see that, although there was usually some activity in BN2 throughout the interprogram interval and protraction (in an individual cycle, these spikes can be seen, for example, at "g" in Fig. 1B), before the distinct dip in activity that characteristically occurred just before the beginning of retraction ("Break" in Fig. 1B; see METHODS), most of the activity in BN2 was in retraction. This is indeed to be expected because that activity was used to define retraction. More interestingly, the ARC activity also occurred largely in retraction. The ARC muscle participates in closing together the two halves of the radula, the handlike structure at the core of the buccal mass, to grasp the seaweed so that it can be moved (Cohen et al. 1978). Thus the ARC electrical activity—presumably resulting in contraction of the muscle—in retraction, when the radula is retracted and rotated backward so as to pull the seaweed into the mouth, conforms with our picture of how the feeding apparatus operates during ingestive cycles. In a minority of the cycles, however, the ARC spikes clearly began well before the beginning of retraction (arrow in plot 5 of Fig. 3; a tendency to this can be seen even in the individual cycles of Fig. 1B).
This situation is reminiscent of the findings of Morton and Chiel (1993a,b) with another radula closer muscle and its motor neurons, the neurons B8. The spikes of B8, like those of B15 and B16 that we monitored here in the ARC muscle, come during retraction—defined by Morton and Chiel, as here, by the electrical activity in BN2—in the majority of ingestive cycles, and indeed the degree of temporal overlap between the burst of B8 firing and the retraction-defining burst in BN2 was proposed by Morton and Chiel as a convenient (and thereafter widely used) electrical criterion of the type of motor program produced by the CPG. Substantial overlap between the B8 firing and the BN2 burst indicates an ingestive program; relatively little overlap, with most of the B8 firing coming before the BN2 burst, would on the other hand indicate an egestive (rejection) program, in which the phasing of the movements would be reversed, closing the radula during protraction rather than retraction so as to expel inedible material out of the mouth. In the recordings of Morton and Chiel, too, there was, however, a significant minority of cycles in which there was little overlap—like the ARC spikes in some cycles here, the B8 spikes began well before the BN2 burst—yet the cycle was still ingestive behaviorally, as judged by the inward movement of the seaweed that the animal was swallowing. (Morton and Chiel did not quantify the movement, however: they merely observed it.) Conversely, there were cycles in which there was substantial overlap, yet the seaweed moved outward. There were also numerous cycles, with or without overlap, in which there was no seaweed movement at all.
As with B8, several possibilities, or some combination of them, may explain the early firing of the ARC motor neurons in some cycles. 1) The large variability and irregularity of the BN2 bursts may have caused the beginning of retraction to be misidentified in some cycles: retraction actually began somewhat earlier. 2) Although we discarded recordings and discontinued experiments whenever animals showed signs of overt behavioral rejection, some cycles, even within otherwise ingestive sequences, may nevertheless have been egestive, or, more precisely, may have been more egestive than others along a smooth ingestive–egestive continuum (see DISCUSSION). 3) Finally, it is clear that behavioral retraction does not correspond exactly to the retraction defined by the electrical activity in BN2. Examination of the profiles in Fig. 3, as well as individual retraction phases such as those marked by the gray rectangles in Fig. 1B, shows that there was some interval of time after the beginning of the BN2 burst during which the firing of the ARC and other radula closer motor neurons had probably already closed the radula around the seaweed strip because the strip moved, but it moved outward. The radula must therefore still have been protracting at this time, and began retracting only later, some considerable time (0.5 s or longer) after the beginning of the the BN2 burst. (At the end of retraction, there was a disparity, too: overt behavioral retraction ended some time before the end of the BN2 burst.) This initial outward movement was evident in most individual cycles in our data set here, in the form of the obvious downward dip preceding each upward ratcheting of the seaweed in Figs. 1, A and B, 2C, 7A, and 9, for example, and clearly visible in the average profiles in Fig. 3. (Even though in physical reality the animal was pulling the seaweed strip downward, in the figures this is plotted inverted, as the length of seaweed already swallowed.) The initial outward movement is clear in each of the video segments. Closure of the radula some time before the peak of protraction was previously reported by Friedman et al. (2002; and SC Rosen, personal communication). A substantial initial outward movement of the food being swallowed before its inward movement in each cycle thus seems to be a systematic feature of Aplysia swallowing.
Much of this was indeed noted by Morton and Chiel (1993a,b). In their summary timing diagram for swallowing (Fig. 8B of Morton and Chiel 1993a), behavioral retraction begins 0.5–0.7 s after the beginning of the BN2 burst, while the firing of B8, like the ARC firing here, begins a fraction of a second before the BN2 burst. In these respects, our results here thus confirm and extend the findings of Morton and Chiel.
VARIABILITY OF ABSOLUTE VALUES OF REPRESENTATIVE PARAMETERS. The profiles in Fig. 3 reveal the simultaneous multidimensional variability of the entire waveforms, but they do not lend themselves readily to further statistical treatment. A different quantification of the variability in the data set is therefore presented in Fig. 4A. Here we have simply plotted the distributions of values of five representative parameters of the BN2 and ARC electrical activity and movement of the seaweed strip, measured from all 2,755 cycles in the data set. We will refer to such values measured from individual cycles as "absolute" values, in contrast to the relative cycle-to-cycle differences described below. The five parameters plotted are (Fig. 4, A1–A5) the retraction duration, the cycle period, the mean frequency of all BN2 spikes in retraction, the mean frequency of all ARC spikes in retraction, and the length of seaweed swallowed in the cycle. Measurement of one single overall value of each parameter from each cycle discards detailed timing information; by the same token, it is relatively robust against such problems as the possible misidentification of the precise beginning and end of the retraction phase. The 10th, 25th, 50th, 75th, and 90th percentiles of each distribution are marked by thin vertical lines. Clearly, each distribution is very broad; the values at the upper end are manyfold larger than those at the lower end. Note again, in Fig. 4A5, the number of cycles in which there was no seaweed movement at all or even negative movement, a net movement of the seaweed strip out of the mouth.
VARIABILITY OF CYCLE-TO-CYCLE DIFFERENCES OF REPRESENTATIVE PARAMETERS.
The absolute-value distributions lump together all types of variability, including global components, relatively uninteresting to us here, such as those arising from differences between animals and in the general state of the animal at different points in the experiment (see Horn et al. 2004). The absolute-value distributions will also reflect slow, progressive changes in the average values of the parameters of the motor programs, muscle contractions, and the behavior (Proekt et al. 2004; Zhurov et al. 2005a) that, although functionally very relevant, are to a first approximation independent of the fast cycle-to-cycle variability that is of interest in this study: the fast variability appears essentially to be superimposed on the slow changes in average parameter values. To exclude these other components of variability, we examined a purely local measure of variability, pairwise cycle-to-cycle differences between the values of a parameter in successive cycles in the same strip. In Fig. 4B we have plotted the distributions of these differences for the same five parameters as in Fig. 4A. The differences in each strip were normalized by the mean of the absolute values of the parameter in that strip, so that –1 and +1 on the horizontal axis indicate decreases and increases, respectively, from one cycle to the next that are equal in magnitude to the mean of the parameter. In addition to the percentile lines, the SD () of each distribution is given. With the normalized values used, is a dimensionless measure similar to the coefficient of variation (see Horn et al. 2004). Again, the distributions are broad: there are numerous differences that are almost as large as, or in some parameters such as the cycle period even larger than, the mean. Moreover, it is the functional performance, the length of seaweed swallowed, that shows the most extreme variability. The distribution in Fig. 4B5 is much broader still (note that it is plotted over a more extended range) than the other cycle-to-cycle distributions. For comparison, the outline of the distribution of the seaweed swallowed from Fig. 4B5 is superimposed (black outline) over each of the other distributions in Fig. 4, B1–B4.
Functional performance is not explained by any single parameter of CPG or neuromuscular activity
From examination of raw records such as those in Fig. 1 (and Figs. 7A and 9), it seems that there should be some parameter of the cycle timing or neuromuscular activity that would predict—and that would therefore be a good candidate to investigate as the causal determinant of—the length of seaweed swallowed in each cycle. For example, it often seemed (e.g., in Fig. 7A) that more seaweed was swallowed whenever the bursts of BN2 and ARC activity were stronger.
To see whether we could identify any such parameter, in Fig. 5 we examined correlations between the parameters. Using multiple linear regression techniques (for details see METHODS), we computed mutual pairwise correlations between ten parameters: the five basic parameters from Fig. 4 and additionally the duration of the interprogram interval and protraction in each cycle; the mean frequencies of the three separate classes of spikes, with small, medium, and large amplitudes, in BN2 in retraction; and the length of seaweed swallowed in retraction. One representative correlation plot, between the retraction duration and the seaweed swallowed in retraction, is shown in Fig. 5A. Each point represents one of the 2,755 cycles in the data set. The best cubic polynomial fit is shown (gray curve) and the value of the coefficient of determination (R2) is given. Figure 5B then shows the strengths of the correlations—the values of R2, represented by the thickness of each line—between the absolute values of all pairwise combinations of the ten parameters, and Fig. 5C between the corresponding cycle-to-cycle differences. The two diagrams are quite similar, apart from a general strengthening of the correlations in Fig. 5C stemming from elimination of the global components of the variability, the systematic differences between strips and animals.8
The coefficient of determination R2—the fraction of the variance of the "dependent" parameter explained by the "independent" parameter—is a good single indicator of the strength of the correlation, bearing a close relationship both to the statistical significance of the correlation and to its magnitude or practical significance (see, e.g., Cohen 1992; Kirk 1996; and METHODS). To make each of these two quantities explicit, however, Fig. 6 provides a table of numerical results expanding the more informative of the two diagrams in Fig. 5, that of the correlations between the cycle-to-cycle differences in Fig. 5C. Each cell in Fig. 6 represents one pairwise correlation and gives the numerical value of R2 (top number), the P value expressing the statistical significance of the correlation (middle number), and Cohen's
