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Fishberg Department of Neuroscience, Mount Sinai School of Medicine, New York, New York
Submitted 10 May 2005; accepted in final form 6 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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The ARC muscle is one of the muscles of the buccal mass, a complex structure that produces rhythmic, cyclical movements of the animal's food-grasping organ, the radula, in several types of consummatory feeding behavior such as biting, swallowing, and rejection of unsuitable food (Kupfermann 1974
). The structure of the ARC system is summarized in Fig. 1. The muscle is innervated by two motor neurons, B15 and B16, which, when they fire, release their classical transmitter acetylcholine (ACh) to depolarize and contract the muscle (Cohen et al. 1978; Fig. 1, left). In addition, however, the two motor neurons release several families of modulatory peptide cotransmitters that shape the basal ACh-induced contractions (Fig. 1, right; for review and complete references see Brezina et al. 2003a, 2005; Hooper et al. 1999; Kupfermann et al. 1997; Weiss et al. 1993). Most important are the small cardioactive peptides (SCPs), released from motor neuron B15 (e.g., Cropper et al. 1987a; Lloyd et al. 1984; Vilim et al. 1996b), and the myomodulins (MMs), released from motor neuron B16 (Brezina et al. 1995; Cropper et al. 1987b, 1991; Vilim et al. 2000). The SCPs and MMs shape contractions through three main effects on the muscle: 1) they potentiate the contractions by enhancing the muscle's depolarization-activated Ca current that supplies Ca2+ essential for contraction (e.g., Brezina and Weiss 1995; Brezina et al. 1994a, 1995); 2) they depress the contractions by activating in the muscle a K current that opposes the ACh-induced depolarization, activation of the Ca current, and Ca2+ influx (Brezina et al. 1994b, 1995; Orekhova et al. 2003); and 3) they increase the relaxation rate of the contractions probably by modulating the muscle's contractile machinery (Heierhorst et al. 1994, 1995; Probst et al. 1994). The balance of the competing potentiating and depressing effects determines the net modulation of contraction size that, together with the modulation of the relaxation rate, then produces the final shape of the contraction. Similar networks of modulatory effects shape the contractions of the other muscles of the buccal mass (e.g., Church et al. 1993; Evans et al. 1999; Hurwitz et al. 2000; Keating and Lloyd 1999).
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, 2000b, 2003a,b, 2005).
There is, however, a serious potential difficulty with this scenario. Vilim et al. (1996a) found that the release of the modulatory peptide cotransmitters from the motor neurons is extremely sensitive to temperature. Figure 2 replots the data of Vilim et al. (1996a) for the release of the SCPs from the ARC motor neuron B15, measured by direct radioimmunoassay of the amount of released peptide (each point is the mean ± SE, smaller than the mean symbol size, of four preparations). Also plotted is the simultaneous release of the buccalins, peptides of another family that are costored in the same dense-core vesicles with the SCPs in B15 (as with the MMs in B16; "Buc" in Fig. 1) and coreleased by the same release process (Vilim et al. 1996b, 2000). Release of both peptide families declines dramatically with increasing temperature: an increase of 10°C reduces release approximately 20-fold (see Fig. 2 legend).
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). [Other Aplysia species, such as A. fasciata in the Mediterranean Sea or A. dactylomela in the Caribbean, live and feed at up to at least 29°C (Carefoot 1987; Gev et al. 1984), but the modulatory tuning of the feeding musculature has not been studied in these species.] Aplysia are, of course, poikilotherms that cannot maintain an internal temperature that is appreciably different from that of the surrounding water. According to Fig. 2, there is little release of the peptide modulators at, say, 25°C.1 Yet Aplysia live and feed at this temperature. Does this mean that the modulatory tuning is, after all, not important for functional, efficient feeding? In this paper we provide a resolution of this difficulty. Even though the release of the modulators declines dramatically with increasing temperature, the overall strength of the modulatory tuning does not decline. This is because the modulatory system incorporates mechanisms, individual effects with the opposite temperature dependency as well as more general mechanisms that are inherent in the network structure of the system, that maintain its output throughout the entire temperature range.
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METHODS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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PREPARATION.
The preparation was the standard preparation used for recording motor neuron-elicited contractions of the ARC muscle (Cohen et al. 1978; Weiss et al. 1978; for recent use see, e.g., Horn et al. 2004; Orekhova et al. 2003). Briefly, the preparation consisted of the bilateral buccal ganglia, the two 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 connected to an intracellular amplifier (Axoclamp 2A/B, Axon Instruments, Union City, CA). Under the control of external timers/stimulators (Pulsemaster A300, World Precision Instruments, Sarasota, FL, and Grass S48/S88, Astro-Med, West Warwick, RI), the motor neurons were stimulated with brief current injections to fire spikes in the desired pattern. All signals were sampled and recorded simultaneously by a computer using Digidata 1322A data-acquisition hardware and pCLAMP 8/9 software (Axon Instruments). When the experiment on the first ARC muscle was finished, the ARC muscle on the opposite side of the preparation was also used, whenever possible, for an independent experiment or a matched pair (see RESULTS).
EXPERIMENTAL DESIGN. Three basic experimental paradigms were used.
1) Single motor neuron self-modulation. Only one of the two ARC motor neurons, either B15 or B16, was fired in a relatively intense bursting pattern, generally at 10–15 Hz for 2 s every 5 s for 3 min, calculated to release the peptide modulators (see Fig. 3).
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; Cropper et al. 1990c; Vilim et al. 1996a). The modulator-releasing neuron was fired for 4 s every 10 s for 60 s, B15 at 20 Hz, and B16 at 20 or 25 Hz.
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7 ml) steadily at 1.25 ml/min, while the reversal of the effects was followed with continuing monitoring contractions (Fig. 9C). When the effects had reversed completely (after 
30 min but sometimes up to 1 h of wash), the application of SCPB was repeated at a different temperature. For additional details see RESULTS and figure legends.
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MEASUREMENT OF CONTRACTION PARAMETERS. The peak amplitude of each contraction was measured relative to the baseline muscle length at the beginning of the motor neuron burst that elicited the contraction, or, in the case of closely spaced bursts that did not allow the muscle to relax fully to the baseline (Fig. 3), the baseline length at the beginning of the first burst. The relaxation rate of each contraction was then evaluated, with a custom-written program in Mathematica (Wolfram Research, Champaign, IL), by fitting a single exponential to the relaxation phase of the contraction from 90 to 33% of the peak amplitude (see Fig. 1, bottom right), or, with the closely spaced contractions, to the beginning of the next motor neuron burst if that came earlier. Over this upper middle portion of the relaxation phase, most contractions were in fact well fitted by single exponentials. The relaxation rate was then the reciprocal of the time constant of the exponential.
Modeling
The dynamic model of the B15/B16–ARC neuromuscular system and its modulation was taken from Brezina et al. (2003a,b) and analytically solved or numerically integrated in Mathematica. Specific changes in parameters, dictated by the experimental results, were made as described in the figure legends. The relaxation rate of the simulated contractions was measured in the same way as that of the real contractions.
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RESULTS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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In the B15/B16–ARC neuromuscular system in vitro, the simplest way to observe the effects of the released modulators is with the single motor neuron self-modulation paradigm, in which just one motor neuron is stimulated both to release the modulators and to elicit the contraction that they modulate. Figure 3 shows a representative experiment of this kind. Motor neuron B16 was stimulated to fire in a repetitive bursting pattern—similar to that which it in fact fires in the intact feeding animal (Cropper et al. 1990a; Horn et al. 2004; see Fig. 12)—that elicited a sequence of contractions. These contractions progressively changed in shape, in amplitude (continuous waveform; axis at left) and in relaxation rate (large black points; axis at right). Previous studies have strongly suggested that much of the change in amplitude and especially relaxation rate arises from the progressive development of the effects of the modulators that such a pattern of firing also releases (e.g., Brezina et al. 2003b; Whim and Lloyd 1990).
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We did not analyze these results in any detail because, although the single motor neuron paradigm is simple, its results are difficult to interpret. As the motor neuron firing continues, all of the system components shown in Fig. 1—modulator release, modulator concentrations, the various modulator effects, as well as processes that shape the basal contraction such as presynaptic facilitation and potentiation of ACh release (Cohen et al. 1978) and postsynaptic summation of the contraction waveform itself—continue to evolve at different rates (Brezina et al. 2003a), in continuing interaction with each other. Each feature of the contraction shape thus has multiple interpretations.
Two motor neuron cross-modulation is not weaker at higher temperature
More readily interpretable are the results of the two motor neuron cross-modulation paradigm, first introduced in this system by Whim and Lloyd (1990). One motor neuron is stimulated to fire brief bursts at regular infrequent intervals, which release little or no modulator themselves (Brezina et al. 2003b; Cropper et al. 1990c; Vilim et al. 1996a) but elicit regular "monitoring" contractions. The other motor neuron is then fired in a relatively short, intense bursting pattern to release the modulators. This pattern inevitably elicits a contraction, too, but afterward the contraction rapidly relaxes while the effects of the released modulators, some of which are very long lasting (Brezina et al. 2003a; see following text), persist to modulate the continuing monitoring contractions.2 Figure 4A1 shows a representative experiment. After the modulator-releasing firing of motor neuron B16, the monitoring contractions elicited by motor neuron B15 were increased in both amplitude (continuous waveform; axis at left) and relaxation rate (large black points; axis at right), and remained so for many minutes. From what is known about the system (see INTRODUCTION), both effects were presumably caused by the MMs released from motor neuron B16. When, in other experiments, the roles of the monitoring and modulator-releasing motor neurons were reversed, similar increases in contraction amplitude and relaxation rate were observed, in that case presumably caused by the SCPs released from motor neuron B15. Previous work has shown that the SCPs and MMs increase the relaxation rate in an identical fashion and have identical potentiating effects on contraction amplitude (Fig. 1; Brezina et al. 1996, 2003a).
Figure 4, A and B shows the same experiment repeated, in the two ARC muscles of the same preparation, at 15 and 25°C. Figure 4, A2 and B2 compares in detail three contractions expanded from A1 and B1, in particular a control contraction before the modulator-releasing firing (contraction 1) with the modulated contraction about 2 min after the end of the modulator-releasing firing (contraction 2), at each temperature. Clearly, the observed modulation was not weaker at the higher temperature. The modulation of the relaxation rate, especially, was significantly stronger.
Quantification of the modulation of relaxation rate
In our analysis of the results of the two motor neuron cross-modulation experiments, we focused primarily on the modulation of the relaxation rate and only secondarily on that of contraction amplitude. Even in the cross-modulation paradigm, the modulation of contraction amplitude is still a composite process with multiple interpretations. On the potentiating effect of the SCPs and MMs, mediated by enhancement of Ca current in the muscle, is superimposed a simultaneous depressing effect, mediated by activation of a K current (INTRODUCTION, Fig. 1). Furthermore, together with the SCPs and MMs both motor neurons B15 and B16 corelease the buccalins, which depress contractions (Cropper et al. 1988, 1990b; Orekhova et al. 2003; Vilim et al. 1994). Thus no net change in contraction amplitude, for example, could mean no modulator release, or conversely robust modulator release with the potentiating effect of the released SCPs, or MMs, balanced by an equally strong depressing effect of the SCPs or MMs, or of the coreleased buccalins.3 To fully understand how the modulation of contraction amplitude is affected by temperature, these various effects would have to be studied in isolation, each with its own paradigm in a different type of reduced preparation (see, e.g., Brezina et al. 1994a,b, 1995, 2003a; Orekhova et al. 2003).
In contrast, the modulation of the relaxation rate is, as far as is known, a unitary process, which furthermore is activated, in an identical fashion, just by the SCPs and MMs: the buccalins do not modulate the relaxation rate (Cropper et al. 1988; Vilim et al. 1994). Analysis of the relaxation rate, however, has its own difficulty. In different preparations, the initial, "unmodulated" relaxation rate of the ARC muscle—the control relaxation rate against which the modulation is then evaluated—can be very different (Brezina et al. 1995; see following text and Figs. 5 and 8). We attempted to manipulate the control relaxation rate by altering the load on the muscle, with limited success. Where possible we also made matched pairs of measurements, at 15 and 25°C, in the two muscles of the same preparation or successively in the same muscle. This reduced the variability somewhat, but considerable variability still remained.
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First, it can be seen that the modulator-releasing firing always brought about an increase—never any significant decrease—in the relaxation rate. Essentially all points in Fig. 5A lie above the 0% diagonal line; the lines joining the corresponding control and modulated values in Fig. 5B all slant upward. In individual experiments the increase could be small (e.g., experiment a in Fig. 5A, lying close to the 0% diagonal line) or large (experiment b, with >3,000% increase in the relaxation rate). The mean increase, however, was statistically highly significant at both 15 and 25°C (see Fig. 5 legend).
Previous work has suggested that a major factor that determines the size of the increase in relaxation rate in this kind of experiment is the control relaxation rate that the modulation acts on (Brezina et al. 1995). If the control relaxation rate is small, the absolute increase (the change in units of s–1), and still more the relative increase (the change in %), is large. If the control relaxation rate is already large, the absolute and the relative increases are small. In either case, the modulation tends to bring the relaxation rate to about the same absolute level. A natural explanation is that there is some upper limit, some maximal rate, beyond which the muscle cannot be made to relax any faster by the modulation under those conditions. To demonstrate this again here, we performed six experiments with the two motor neuron cross-modulation paradigm, firing motor neuron B15 to release the SCPs, at 15°C, but in the presence of a saturating concentration of one of the SCPs, 10–5 M SCPB (see Brezina et al. 1996; Lloyd et al. 1984). These experiments are shown by the open blue circles in Fig. 5, A and B. The exogenous SCP increased—essentially tripled—the relaxation rate to >1.5 s–1, whereupon the modulator-releasing firing had little further effect. All of these experiments lie close to the 0% diagonal line in Fig. 5A; there was no statistically significant difference between their control and modulated means in Fig. 5B (see legend). We can reasonably take the mean modulated relaxation rate in these experiments, about 1.8 s–1, to be the presumed maximal relaxation rate at 15°C. This upper limit is indicated by the horizontal dashed line across Fig. 5, A and B. Note that all of the other experiments at 15°C fall below the line.
Consider now the experiments at 25°C (red symbols) in Fig. 5, A and B. Clearly, these often had modulated relaxation rates considerably larger than any experiment at 15°C, exceeding by a substantial margin the limit just discussed. The green lines in Fig. 5A indicate matched pairs of experiments, at 15 and 25°C, in the two muscles of the same preparation. In some cases at least, the two muscles had similar control relaxation rates—for example, the pair c–d—and in each of these cases the modulated relaxation rate was larger at 25 than at 15°C. Finally, although in Fig. 5B the mean control relaxation rate was somewhat larger at 25 than at 15°C (see also Figs. 7–9), statistical analysis (see legend) showed that the difference was not statistically significant. The mean modulated relaxation rate, however, was substantially larger at 25 than at 15°C, and this difference was highly significant.
It thus appears that in the two motor neuron cross-modulation experiments the modulation of the relaxation rate was not only not weaker at the higher temperature, but on the contrary was significantly stronger.
The modulation of relaxation rate reverses more rapidly at higher temperature
In Fig. 4 it appears that, although the modulation of the relaxation rate was stronger at 25 than at 15°C, it reversed more rapidly after the end of the modulator-releasing firing (as, apparently, did the modulation of contraction amplitude). The group data in Fig. 6, averaging together the time courses of the modulation of the relaxation rate in all of the experiments (without exogenous SCP) in Fig. 5, bear this out. The faster reversal of the modulation at 25 than at 15°C was statistically highly significant (see Fig. 6 legend).
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So far, with both of our motor neuron stimulation paradigms, we have studied the modulation, that of the relaxation rate in particular, as one overall input–output process, Motor neuron firing 
Relaxation rate modulation, and determined what we will call its cumulative temperature dependency. The overall process is composed of a sequence of more elementary steps: Motor neuron firing Modulator release Modulator concentration Relaxation rate modulation (Fig. 1). Each of these steps will have its own intrinsic temperature dependency, which will then combine with that of the other steps to give the cumulative temperature dependency of the overall process. To understand the origin of the cumulative temperature dependency, we must therefore know the intrinsic temperature dependency of the individual steps. We already know that of the first step, Motor neuron firing Modulator release (Fig. 2). What about the intrinsic temperature dependency of the subsequent steps, in particular the last step, Modulator concentration Relaxation rate modulation, the actual modulatory effect itself?4
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On contraction amplitude, previous work has shown that the potentiating (Ca-current) and depressing (K-current) effects of the modulators combine asymmetrically so as to give net potentiation at low modulator concentrations and net depression at high concentrations (see Brezina et al. 1995, 1996, 2003a). It appears from Fig. 7, A and B, that both the net potentiation at low SCPB concentrations and the net depression at high SCPB concentrations—and therefore presumably, both of the underlying potentiating and depressing effects—were larger at 25 than at 15°C. Indeed, high SCPB concentrations often produced at 25°C a very substantial net depression (Fig. 7A), such as is only rarely seen at lower temperatures with the SCPs—although it is seen with the MMs, which activate a much larger amplitude of the K current in the muscle (Brezina et al. 1995, 1996).5
The modulation of the relaxation rate, too, was larger at 25 than at 15°C (Fig. 7C). Indeed, it was much larger: as Fig. 7C shows, it was necessary to scale the 15°C dose–response relation up approximately fivefold before it reproduced, quite well at all concentrations, the magnitude of the dose–response relation obtained at 25°C.6
In another series of these experiments, we applied just a single steady concentration of the modulator, 10–7 M SCPB, and followed systematically the time course of the development of the modulation, and in some experiments also that of its reversal on washout of the SCPB, at both 15 and 25°C. From these experiments, Fig. 8 first presents, in the same way as did Fig. 5, the magnitude of the fully developed modulation of the relaxation rate. Figure 8A plots the modulated relaxation rate against the control relaxation rate in each experiment at 15°C (blue circles) and 25°C (red circles). The green lines join matched pairs of measurements. (In this series of experiments the matched measurements were made not just in the same preparation, but in the very same muscle with two applications of SCPB separated by wash.) Figure 8B then plots the same measurements, and their means, for statistical comparison. Again, the modulated relaxation rate was always much larger at 25 than at 15°C. At 15°C the modulated relaxation rate was smaller, but at 25°C considerably larger, than the presumed maximal relaxation rate attainable at 15°C (horizontal dashed line, taken from Fig. 5). In Fig. 8B, the difference between the mean modulated relaxation rates at the two temperatures was statistically highly significant (see Fig. 8 legend). (In this series of experiments, unlike in Fig. 5, the difference between the mean control relaxation rates—larger at 25 than at 15°C—was also significant.)
Figure 9 summarizes the time course of the modulation of the relaxation rate in these experiments. Figure 9A shows simply the averaged absolute relaxation rates at each time point during the development of the modulation in all of the experiments at 15°C (blue) and at 25°C (red). Figure 9B shows the same data first normalized within each experiment, as in Fig. 6, to discard magnitude differences and allow comparison just of the time course shapes at the two temperatures. Figure 9C shows, similarly normalized, the time courses of the reversal of the modulation on washout of the SCPB. To characterize the time courses quantitatively, we fitted the experimental data with best single-exponential fits (solid black curves) as follows. First, statistical analysis (see Fig. 9 legend) showed that the normalized time courses of the development of the modulation in Fig. 9B were not significantly different at 15 and 25°C. We therefore fitted all of the data in Fig. 9B simultaneously with the same exponential, with time constant 
= 179 s. With this time constant, fitting the unnormalized data in Fig. 9A then yielded the magnitudes of the fully developed modulation at 15 and 25°C. In this series of experiments, the modulation was about 3.2-fold larger at 25 than at 15°C. (This result was already implicit in Fig. 8, which used the same data.) Finally, statistical analysis—and just simple inspection—showed that the time courses of the reversal of the modulation in Fig. 9C were very significantly different at 15 and 25°C. We therefore fitted the data in Fig. 9C, over the range of times shown, with two different exponentials at the two temperatures, yielding = 3,995 s at 15°C and = 462 s at 25°C. Thus the modulation of the relaxation rate by the exogenous modulator was not only intrinsically larger at the higher temperature, but, just like the modulation by the endogenously released modulator in Figs. 4 and 6, it reversed more rapidly when the modulator was removed.
Reproduction of the observed temperature dependency in a mathematical model of the system
A dynamic model of the B15/B16–ARC neuromuscular system, including the basal ACh-induced contraction and the major components of the modulation—all of the variables X(t) in Fig. 1—was previously constructed from a variety of experimental data by Brezina et al. (2003a,b). We now modified the model to incorporate into it temperature dependency for the two steps that we have focused on in this paper. From the experimental data in Fig. 2, we modeled the intrinsic temperature dependency of the release of the modulators (for details see Fig. 2 legend). The continuous curves in Fig. 2 show the modeled release, decreasing, like the experimentally measured release, about 20-fold for a 10°C increase in temperature. From the experimental data in Figs. 7– 9, we then modeled the intrinsic temperature dependency of the modulation of the relaxation rate (for details see Fig. 10 legend). Figure 7C suggests that the magnitude of the modulation might increase about fivefold, whereas Fig. 9A suggests about 3.2-fold, for a 10°C increase in temperature. Conservatively, we modeled it as increasing threefold. We also modeled a fivefold increase in the rate constants of the modulation, so that the reversal of the modulation, in particular, would proceed faster at higher tem-perature as observed in Fig. 9C. Again, the fivefold increase was conservative: Fig. 9C suggests a greater than eightfold increase.
With the incorporation of the intrinsic temperature dependencies of these two steps, the model was then well able to reproduce the cumulative temperature dependency that we observed, in particular, in our two motor neuron cross-modulation experiments. Figure 10 shows a simulation of an experiment like that in Fig. 4. After the firing of the modulator-releasing motor neuron, the modeled relaxation rate in Fig. 10, just like the experimentally measured rate in Fig. 4, increases considerably more at 25 than at 15°C, but then falls back to the basal rate much faster.
The modulation of contraction amplitude in the simulation in Fig. 10—not only the net modulation but each of its component effects, which can be inspected in the model—is smaller at 25 than at 15°C, whereas in the real experiment in Fig. 4 it is not smaller, and may even be somewhat larger. Because we did not characterize separately the intrinsic temperature dependencies of each of the component effects, we could not incorporate them into the model as we did that of the modulation of the relaxation rate, but presumably the modeling of such increases of the effects with temperature as were observed in Fig. 7, A and B, would largely correct the deficiency seen in Fig. 10. Even without this correction, nevertheless, it is remarkable in Fig. 10 that the modulation of contraction amplitude is not grossly incorrect. Even though the modulator release decreases 20-fold as the temperature increases from 15 to 25°C, the modulation of contraction amplitude decreasesonly moderately. This is because the system incorporates a second type of temperature-compensating mechanism, quite distinct from the intrinsic temperature dependencies of the various steps, as the following analysis of the model reveals.
Second, structural mechanism of temperature compensation: saturating curvature of dose–response relations
For consistency we will discuss the second mechanism as it operates, once again, in the particular case of the modulation of the relaxation rate, but from its principles it will be seen that the mechanism will operate similarly for all of the modulatory effects, all those that contribute to the modulation of contraction amplitude as well. In the case of the relaxation rate, that there must be an additional mechanism becomes clear when we consider the magnitudes of the intrinsic temperature dependencies that we modeled above. Modulator release decreases 20-fold for a 10°C increase in temperature, whereas the modulation of the relaxation rate increases, intrinsically, only threefold. Cumulatively, when the modulation is caused by the released modulator, we should therefore expect the modulation still to decrease, to a first approximation, approximately 20/threefold—more than sixfold—when the temperature is raised from 15 to 25°C. Instead, we see in Fig. 10 that the modulation does not decrease, and even increases. An additional temperature-compensating mechanism must therefore be operating in the model and, presumably, in the real system. Furthermore, it is not a mechanism that we ourselves have explicitly incorporated into the model. It must be implicit in the structure of the model network—present, for example, even in the previous model of Brezina et al. (2003a,b), which had no explicit temperature dependency at all.
To demonstrate the second mechanism more formally, in Fig. 11A we have analytically solved the model equations to plot the cumulative steady-state temperature dependency from the level of motor neuron firing to each of the subsequent levels in the sequence leading to the modulation of the relaxation rate. In other words, for the same representative pattern of motor neuron firing throughout (see Fig. 11 legend), Fig. 11A plots the temperature dependency of modulator release (i.e., of the step Motor neuron firing Modulator release; light gray curve), modulator concentration (Motor neuron firing Modulator concentration; light gray curve again, identical to that for modulator release), and finally the modulation of the relaxation rate (Motor neuron firing Relaxation rate modulation), either without (dark gray curve) or with (black curve) the incorporation of the intrinsic temperature dependency of the step Modulator concentration Relaxation rate modulation that we modeled above. The light gray curve of the temperature dependency of modulator release is simply the curve already seen in Fig. 2, along which modulator release decreases 20-fold for a 10°C increase in temperature. Because modulator concentration is, in this model, simply a linear reflection of modulator release (see Eq. 8 in Fig. 11 legend), its cumulative temperature dependency is identical. However, the next level of the model, the modulation of the relaxation rate, does not at all follow this dramatic decrease with temperature. Even without any intrinsic temperature dependency of its own (dark gray curve), the modulation of the relaxation rate decreases only very moderately. The incorporation of the intrinsic temperaturedependency of the modulatory effect then converts the moderate decrease into a positive increase (black curve). Foldwise, however, it is the second mechanism, revealed in the large difference between the cumulative temperature dependency of the modulator concentration and that of the modulation of the relaxation rate, even without its own intrinsic temperature dependency, that is most significant under these circumstances.
What precisely is the nature of this second mechanism? Consider Fig. 11B, which shows simply the intrinsic steady-state dose–response relation of the modulatory effect, the step Modulator concentration Relaxation rate modulation. This quasi-hyperbolic relation is everywhere curved concave-down.7 Consequently any change in the input modulator concentration will result in a smaller relative change in the output relaxation rate modulation. For example, the point labeled "Actual at 15°C" is the steady-state point reached with the motor neuron firing used in Fig. 11A at 15°C. When the temperature is now increased to 25°C, there is a 20-fold decrease in modulator concentration and, if the modulation of the relaxation rate simply reflected the modulator concentration linearly, we would also expect a 20-fold decrease in the modulation of the relaxation rate, to the point labeled "Expected at 25°C with linear dose–response relation." Instead, along the curved dose–response relation, the modulation of the relaxation rate decreases much less, to the point labeled "Actual at 25°C."
The inset of Fig. 11A extends the main plot to higher temperatures. Even at much higher temperatures, together the two temperature-compensating mechanisms operating in the system—the "first" mechanism of compensating intrinsic temperature dependency and the second, structural mechanism—do a remarkably good job of maintaining the overal
= 
f
kp+/kp– and 
= D1–y is the pattern dependency of the release, D = dintra/(dintra + dinter) is the duty cycle of the firing pattern, and 
1/20), S0,SCP = 628 fmol, and S0,Buc = 245 fmol, and the curves shown. [Value of S0,SCP found here is 16% larger, and the value of S0,Buc is 24% larger, than the consensus values of 541 and 198 fmol that were determined by Brezina et al. (2000a), presumably again because the different preparations used released different absolute amounts of peptides.]
R (see Eq. 1h of Brezina et al. 2003b; here 
is the concentration of SCP, CSCP, modified by the Hill coefficient hR = 0.7, kR+ and kR– are rate constants, and t is time. After a step at t = 0 to a new, maintained CSCP(t 
kR–/kR+, and time constant 
of Brezina et al. (2003a) must be preserved at all temperatures. This restricts the choice of kR+ and kR– and requires both to have the same temperature coefficient, Q10,kR. When CSCP(t 
as well as, through the relationship KR = kR–/kR+ = 3.64 x 10–6 
, kR–(15°C) = 5.55 x 10–4 s–1 (so that, still, KR = 3.64 x 10–6 
. 
