Control of time-dependent biological processes by temporally patterned input

Interplay between Subthreshold Oscillations and Depressing Synapses in Single Neurons

In this paper we analyze the interplay between the subthreshold oscillations of a single neuron conductance-based model and the short-term plasticity of a dynamic synapse with a depressing mechanism. In previous research, the computational properties of subthreshold oscillations and dynamic synapses have been studied separately. Our results show that dynamic synapses can influence different aspects of the dynamics of neuronal subthreshold oscillations. Factors such as maximum hyperpolarization level, oscillation amplitude and frequency or the resulting firing threshold are modulated by synaptic depression, which can even make subthreshold oscillations disappear. This influence reshapes the postsynaptic neuron’s resonant properties arising from subthreshold oscillations and leads to specific input/output relations. We also study the neuron’s response to another simultaneous input in the context of this modulation, and show a distinct contextual processing as a function of the depression, in particular for detection of signals through weak synapses. Intrinsic oscillations dynamics can be combined with the characteristic time scale of the modulatory input received by a dynamic synapse to build cost-effective cell/channel-specific information discrimination mechanisms, beyond simple resonances. In this regard, we discuss the functional implications of synaptic depression modulation on intrinsic subthreshold dynamics.

Evaluation of gene association methods for coexpression network construction and biological knowledge discovery

BACKGROUND

Constructing coexpression networks and performing network analysis using large-scale gene expression data sets is an effective way to uncover new biological knowledge; however, the methods used for gene association in constructing these coexpression networks have not been thoroughly evaluated. Since different methods lead to structurally different coexpression networks and provide different information, selecting the optimal gene association method is critical.

METHODS AND RESULTS

In this study, we compared eight gene association methods - Spearman rank correlation, Weighted Rank Correlation, Kendall, Hoeffding's D measure, Theil-Sen, Rank Theil-Sen, Distance Covariance, and Pearson - and focused on their true knowledge discovery rates in associating pathway genes and construction coordination networks of regulatory genes. We also examined the behaviors of different methods to microarray data with different properties, and whether the biological processes affect the efficiency of different methods.

CONCLUSIONS

We found that the Spearman, Hoeffding and Kendall methods are effective in identifying coexpressed pathway genes, whereas the Theil-sen, Rank Theil-Sen, Spearman, and Weighted Rank methods perform well in identifying coordinated transcription factors that control the same biological processes and traits. Surprisingly, the widely used Pearson method is generally less efficient, and so is the Distance Covariance method that can find gene pairs of multiple relationships. Some analyses we did clearly show Pearson and Distance Covariance methods have distinct behaviors as compared to all other six methods. The efficiencies of different methods vary with the data properties to some degree and are largely contingent upon the biological processes, which necessitates the pre-analysis to identify the best performing method for gene association and coexpression network construction.

Beyond the wiring diagram: signalling through complex neuromodulator networks

During the computations performed by the nervous system, its 'wiring diagram'--the map of its neurons and synaptic connections--is dynamically modified and supplemented by multiple actions of neuromodulators that can be so complex that they can be thought of as constituting a biochemical network that combines with the neuronal network to perform the computation. Thus, the neuronal wiring diagram alone is not sufficient to specify, and permit us to understand, the computation that underlies behaviour. Here I review how such modulatory networks operate, the problems that their existence poses for the experimental study and conceptual understanding of the computations performed by the nervous system, and how these problems may perhaps be solved and the computations understood by considering the structural and functional 'logic' of the modulatory networks.

Muscle anatomy is a primary determinant of muscle relaxation dynamics in the lobster (Panulirus interruptus) stomatogastric system

We stained sarcomere thin filaments with fluorescently labeled phalloidin, measured sarcomere and muscle length, and calculated sarcomere number in pyloric and gastric mill muscles. A wide range of sarcomere lengths (3.25-12.29 microm), muscle lengths (5.9-21.1 mm), and sarcomere numbers (648-3,036) were observed. Sarcomere number differences occurred both because of changes in sarcomere length and muscle length, and sarcomere and muscle length varied independently. This independence, the wide range of sarcomere numbers present, and the muscles being all 'slow', graded muscles allowed us to use these data to test Huxley and Neidergerke's (1954) hypothesis that muscle dynamics depend on sarcomere number. The time constants of exponential fits to contraction relaxations were used to measure muscle dynamics, and comparison of theoretical predictions and experimental results quantitatively confirm the predicted dependence. The differing dynamics of the various pyloric muscles are likely functionally important, and the dependence of muscle dynamics on sarcomere number implies that sarcomere number is likely closely regulated in these muscles. The stomatogastric system may thus be an excellent model system for studying the mechanisms regulating muscle sarcomere number.

Functional penetration of variability of motor neuron spike timing through a modulated neuromuscular system

Variability of the neuronal spike pattern is usually thought of in terms of the information that the different interspike intervals might be encoding. However, the very presence of the variability can have other kinds of functional significance. Here we consider the example of the B15/B16-ARC neuromuscular system of Aplysia, a model system for the study of neuromuscular modulation and control. We show that variability of motor neuron spike timing at the input to the system penetrates throughout the system, affecting all downstream variables including modulator release, modulator concentrations, modulatory actions, and the contraction of the muscle. Furthermore, not only does the variability penetrate through the system, but it is actually instrumental in maintaining its modulation and contractions at a robust, physiological level.

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

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

A role for ERKII in synaptic pattern selectivity on the time-scale of minutes

Stimulus reinforcement strengthens learning. Intervals between reinforcement affect both the kind of learning that occurs and the amount of learning. Stimuli spaced by a few minutes result in more effective learning than when massed together. There are several synaptic correlates of repeated stimuli, such as different kinds of plasticity and the amplitude of synaptic change. Here we study the role of signalling pathways in the synapse on this selectivity for spaced stimuli. Using the in vitro hippocampal slice technique we monitored long-term potentiation (LTP) amplitude in CA1 for repeated 100-Hz, 1-s tetani. We observe the highest LTP levels when the inter-tetanus interval is 5-10 min. We tested biochemical activity in the slice following the same stimuli, and found that extracellular signal-regulated kinase type II (ERKII) but not CaMKII exhibits a peak at about 10 min. When calcium influx into the slice is buffered using AM-ester calcium dyes, amplitude of the physiological and biochemical response is reduced, but the timing is not shifted. We have previously used computer simulations of synaptic signalling to predict such temporal tuning from signalling pathways. In the current study we consider feedback and feedforward models that exhibit temporal tuning consistent with our experiments. We find that a model incorporating post-stimulus build-up of PKM zeta acting upstream of mitogen-activated protein kinase is sufficient to explain the observed temporal tuning. On the basis of these combined experimental and modelling results we propose that the dynamics of PKM activation and ERKII signalling may provide a mechanism for functionally important forms of synaptic pattern selectivity.

Modeling neuromuscular modulation in Aplysia. III. Interaction of central motor commands and peripheral modulatory state for optimal behavior

Recent work in computational neuroethology has emphasized that "the brain has a body": successful adaptive behavior is not simply commanded by the nervous system, but emerges from interactions of nervous system, body, and environment. Here we continue our study of these issues in the accessory radula closer (ARC) neuromuscular system of Aplysia. The ARC muscle participates in the animal's feeding behaviors, a set of cyclical, rhythmic behaviors driven by a central pattern generator (CPG). Patterned firing of the ARC muscle's two motor neurons, B15 and B16, releases not only ACh to elicit the muscle's contractions but also peptide neuromodulators that then shape the contractions through a complex network of actions on the muscle. These actions are dynamically complex: some are fast, but some are slow, so that they are temporally uncoupled from the motor neuron firing pattern in the current cycle. Under these circumstances, how can the nervous system, through just the narrow channel of the firing patterns of the motor neurons, control the contractions, movements, and behavior in the periphery? In two earlier papers, we developed a realistic mathematical model of the B15/B16-ARC neuromuscular system and its modulation. Here we use this model to study the functional performance of the system in a realistic behavioral task. We run the model with two kinds of inputs: a simple set of regular motor neuron firing patterns that allows us to examine the entire space of patterns, and the real firing patterns of B15 and B16 previously recorded in a 2 1/2-h-long meal of 749 cycles in an intact feeding animal. These real patterns are extremely irregular. Our main conclusions are the following. 1) The modulation in the periphery is necessary for superior functional performance. 2) The components of the modulatory network interact in nonlinear, context- and task-dependent combinations for best performance overall, although not necessarily in any particular cycle. 3) Both the fast and the slow dynamics of the modulatory state make important contributions. 4) The nervous system controls different components of the periphery to different degrees. To some extent the periphery operates semiautonomously. However, the structure of the peripheral modulatory network ensures robust performance under all circumstances, even with the irregular motor neuron firing patterns and even when the parameters of the functional task are randomly varied from cycle to cycle to simulate a variable feeding environment. In the variable environment, regular firing patterns, which are fine-tuned to one particular task, fail to provide robust performance. We propose that the CPG generates the irregular firing patterns, which nevertheless are guaranteed to give robust performance overall through the actions of the peripheral modulatory network, as part of a trial-and-error feeding strategy in a variable, uncertain environment.

Cycle-to-Cycle Variability of Neuromuscular Activity inAplysiaFeeding Behavior

Aplysia consummatory feeding behavior, a rhythmic cycling of biting, swallowing, and rejection movements, is often said to be stereotyped. Yet closer examination shows that cycles of the behavior are very variable. Here we have quantified and analyzed the variability at several complementary levels in the neuromuscular system. In reduced preparations, we recorded the motor programs produced by the central pattern generator, firing of the motor neurons B15 and B16, and contractions of the accessory radula closer (ARC) muscle while repetitive programs were elicited by stimulation of the esophageal nerve. In other similar experiments, we recorded firing of motor neuron B48 and contractions of the radula opener muscle. In intact animals, we implanted electrodes to record nerve or ARC muscle activity while the animals swallowed controlled strips of seaweed or fed freely. In all cases, we found large variability in all parameters examined. Some of this variability reflected systematic, slow, history-dependent changes in the character of the central motor programs. Even when these trends were factored out, however, by focusing only on the differences between successive cycles, considerable variability remained. This variability was apparently random. Nevertheless, it too was the product of central history dependency because regularizing merely the high-level timing of the programs also regularized many of the downstream neuromuscular parameters. Central motor program variability thus appears directly in the behavior. With regard to the production of functional behavior in any one cycle, the large variability may indicate broad tolerances in the operation of the neuromuscular system. Alternatively, some cycles of the behavior may be dysfunctional. Overall, the variability may be part of an optimal strategy of trial, error, and stabilization that the CNS adopts in an uncertain environment.

Neuromuscular modulation in Aplysia. II. Modulation of the neuromuscular transform in behavior

In this work we use mathematical modeling and complementary experiments to study the dynamics of modulation in the accessory radula closer (ARC) neuromuscular system of Aplysia. Here we join a dynamic model of the modulation from the preceding paper to a model of the basal neuromuscular transform (NMT). The resulting complete model of the NMT allows us to predict, test, and analyze the actual modulated contraction shapes in different types of feeding behavior, through entire quasi-realistic meals. The model reproduces a variety of published and new experimental observations. We find that components of the modulatory network act in interdependency and mutual complementarity, one or another playing a key role depending on the behavior and its past history. The history is remembered by slow dynamical components whose persistence prepares the system for future behavior of the same kind. The persistence becomes counterproductive, however, when the behavior suddenly changes. Superposition of fast dynamical components alleviates the problem under most, but not all, circumstances. In the quasi-realistic meals, the modulation improves functional performance on average, but degrades it after certain behavioral switches, when the model predicts sharp contraction transients. These are indeed seen in the real muscle. We propose that the real system does not switch the underlying motor neuron firing patterns abruptly, but relaxes them gradually, matching the relaxation of the peripheral modulatory state, through such behavioral transitions. We model food-induced arousal, a known phenomenon of this kind. The peripheral dynamics of the modulated NMT thus constrain the motor commands of the CNS.

Neuromuscular modulation in Aplysia. I. Dynamic model

Many physiological systems are regulated by complex networks of modulatory actions. Here we use mathematical modeling and complementary experiments to study the dynamic behavior of such a network in the accessory radula closer (ARC) neuromuscular system of Aplysia. The ARC muscle participates in several types of rhythmic consummatory feeding behavior. The muscle's motor neurons release acetylcholine to produce basal contractions, but also modulatory peptide cotransmitters that, through multiple cellular effects, shape the contractions to meet behavioral demands. We construct a dynamic model of the modulatory network and examine its operation as the motor neurons fire in realistic patterns that change gradually over an hour-long meal and abruptly with switches between the different feeding behaviors. The modulatory effects have very disparate dynamical time scales. Some react to the motor neuron firing only over many cycles of the behavior, but one key effect is fast enough to respond to each individual cycle. Switches between the behaviors are therefore followed by rapid relaxations along some modulatory dimensions but not others. The trajectory of the modulatory state is a transient throughout the meal, ranging widely over regions of the modulatory space not accessible in the steady state. There is a pronounced history-dependency: the modulatory state associated with a cycle of a particular behavior depends on when that cycle occurs and what behaviors preceded it. On average, nevertheless, each behavior is associated with a different modulatory state. In the following companion study, we add a model of the neuromuscular transform to reconstruct and evaluate the actual modulated contraction shapes.

Temporal pattern dependence of neuronal peptide transmitter release: models and experiments

In this paper we construct, on the basis of existing experimental data, a mathematical model of firing-elicited release of peptide transmitters from motor neuron B15 in the accessory radula closer neuromuscular system of Aplysia. The model consists of a slow "mobilizing" reaction and the fast release reaction itself. Experimentally, however, it was possible to measure only the mean, heavily averaged release, lacking fast kinetic information. Considered in the conventional way, the data were insufficient to completely specify the details of the model, in particular the relative properties of the slow and the unobservable fast reaction. We illustrate here, with our model and with additional experiments, how to approach such a problem by considering another dimension of release, namely its pattern dependence. The mean release is sensitive to the temporal pattern of firing, even to pattern on time scales much faster than the time scale on which the release is averaged. The mean release varies with the time scale and magnitude of the pattern, relative to the time scale and nonlinearity of the release reactions with which the pattern interacts. The type and magnitude of pattern dependence, especially when correlated systematically over a range of patterns, can therefore yield information about the properties of the release reactions. Thus, temporal pattern can be used as a probe of the release process, even of its fast, directly unobservable components. More generally, the analysis provides insights into the possible ways in which such pattern dependence, widespread especially in neuropeptide- and hormone-releasing systems, might arise from the properties of the underlying cellular reactions.

Temporal pattern dependence of neuronal peptide transmitter release: models and experiments

In this paper we construct, on the basis of existing experimental data, a mathematical model of firing-elicited release of peptide transmitters from motor neuron B15 in the accessory radula closer neuromuscular system of Aplysia. The model consists of a slow "mobilizing" reaction and the fast release reaction itself. Experimentally, however, it was possible to measure only the mean, heavily averaged release, lacking fast kinetic information. Considered in the conventional way, the data were insufficient to completely specify the details of the model, in particular the relative properties of the slow and the unobservable fast reaction. We illustrate here, with our model and with additional experiments, how to approach such a problem by considering another dimension of release, namely its pattern dependence. The mean release is sensitive to the temporal pattern of firing, even to pattern on time scales much faster than the time scale on which the release is averaged. The mean release varies with the time scale and magnitude of the pattern, relative to the time scale and nonlinearity of the release reactions with which the pattern interacts. The type and magnitude of pattern dependence, especially when correlated systematically over a range of patterns, can therefore yield information about the properties of the release reactions. Thus, temporal pattern can be used as a probe of the release process, even of its fast, directly unobservable components. More generally, the analysis provides insights into the possible ways in which such pattern dependence, widespread especially in neuropeptide- and hormone-releasing systems, might arise from the properties of the underlying cellular reactions.

Muscles express motor patterns of non-innervating neural networks by filtering broad-band input

We describe three slow muscles that responded to low-frequency modulation of a high-frequency neuronal input and, consequently, could express the motor patterns of neural networks whose neurons did not directly innervate the muscles. Two of these muscles responded to different frequency components present in the same input, and as a result each muscle expressed the motor pattern of a different, non-innervating, neural network. In an analogous manner, the distinct dynamics of the multiple intracellular processes that most cells possess may allow each process to respond to, and hence differentiate among, specific frequency ranges present in broad-band input.

The neuromuscular transform: the dynamic, nonlinear link between motor neuron firing patterns and muscle contraction in rhythmic behaviors

The nervous system issues motor commands to muscles to generate behavior. All such commands must, however, pass through a filter that we call here the neuromuscular transform (NMT). The NMT transforms patterns of motor neuron firing to muscle contractions. This work is motivated by the fact that the NMT is far from being a straightforward, transparent link between motor neuron and muscle. The NMT is a dynamic, nonlinear, and modifiable filter. Consequently motor neuron firing translates to muscle contraction in a complex way. This complexity must be taken into account by the nervous system when issuing its motor commands, as well as by us when assessing their significance. This is the first of three papers in which we consider the properties and the functional role of the NMT. Physiologically, the motor neuron-muscle link comprises multiple steps of presynaptic and postsynaptic Ca(2+) elevation, transmitter release, and activation of the contractile machinery. The NMT formalizes all these into an overall input-output relation between patterns of motor neuron firing and shapes of muscle contractions. We develop here an analytic framework, essentially an elementary dynamical systems approach, with which we can study the global properties of the transformation. We analyze the principles that determine how different firing patterns are transformed to contractions, and different parameters of the former to parameters of the latter. The key properties of the NMT are its nonlinearity and its time dependence, relative to the time scale of the firing pattern. We then discuss issues of neuromuscular prediction, control, and coding. Does the firing pattern contain a code by means of which particular parameters of motor neuron firing control particular parameters of muscle contraction? What information must the motor neuron, and the nervous system generally, have about the periphery to be able to control it effectively? We focus here particularly on cyclical, rhythmic contractions which reveal the principles particularly clearly. Where possible, we illustrate the principles in an experimentally advantageous model system, the accessory radula closer (ARC)-opener neuromuscular system of Aplysia. In the following papers, we use the framework developed here to examine how the properties of the NMT govern functional performance in different rhythmic behaviors that the nervous system may command.

Optimization of rhythmic behaviors by modulation of the neuromuscular transform

We conclude our study of the properties and the functional role of the neuromuscular transform (NMT). The NMT is an input-output relation that formalizes the processes by which patterns of motor neuron firing are transformed to muscle contractions. Because the NMT acts as a dynamic, nonlinear, and modifiable filter, the transformation is complex. In the two preceding papers we developed a framework for analysis of the NMT and identified with it principles by which the NMT transforms different firing patterns to contractions. We then saw that, with fixed properties, the NMT significantly constrains the production of functional behavior. Many desirable behaviors are not possible with any firing pattern. Here we examine, theoretically as well as experimentally in the accessory radula closer (ARC) neuromuscular system of Aplysia, how this constraint is alleviated by making the properties of the NMT variable by neuromuscular plasticity and modulation. These processes dynamically tune the properties of the NMT to match the desired behavior, expanding the range of behaviors that can be produced. For specific illustration, we continue to focus on the relation between the speed of the NMT and the speed of cyclical, rhythmic behavior. Our analytic framework emphasizes the functional distinction between intrinsic plasticity or modulation of the NMT, dependent, like the contraction itself, on the motor neuron firing pattern, and extrinsic modulation, independent of it. The former is well suited to automatically optimizing the performance of a single behavior; the latter, to multiplying contraction shapes for multiple behaviors. In any case, to alleviate the constraint of the NMT, the plasticity and modulation must be peripheral. Such processes are likely to play a critical role wherever the nervous system must command, through the constraint of the NMT, a broad range of functional behaviors.

The neuromuscular transform constrains the production of functional rhythmic behaviors

We continue our study of the properties and the functional role of the neuromuscular transform (NMT). The NMT is an input-output relation that formalizes the processes by which patterns of motor neuron firing are transformed to muscle contractions. Because the NMT acts as a dynamic, nonlinear, and modifiable filter, the transformation is complex. In the preceding paper we developed a framework for analysis of the NMT and identified with it principles by which the NMT transforms different firing patterns to contractions. The ultimate question is functional, however. In sending different firing patterns through the NMT, the nervous system is seeking to command different functional behaviors, with specific contraction requirements. To what extent do the contractions that emerge from the NMT actually satisfy those requirements? In this paper we extend our analysis to address this issue. We define representative behavioral tasks and corresponding measures of performance, for a single neuromuscular unit, for two antagonistic units, and, in a real illustration, for the accessory radula closer (ARC)-opener neuromuscular system of Aplysia. We focus on cyclical, rhythmic behaviors which reveal the underlying principles particularly clearly. We find that, although every pattern of motor neuron firing produces some state of muscle contraction, only a few patterns produce functional behavior, and even fewer produce efficient functional behavior. The functional requirements thus dictate certain patterns to the nervous system. But many desirable functional behaviors are not possible with any pattern. We examine, in particular, how rhythmic behaviors degrade and disintegrate as the nervous system attempts to speed up their cycle frequency. This happens because, with fixed properties, the NMT produces only a limited range of contraction shapes that are kinetically well matched to the firing pattern only on certain time scales. Thus the properties of the NMT constrain and restrict the production of functional behaviors. In the following paper, we see how the constraint may be alleviated and the range of functional behaviors expanded by appropriately tuning the properties of the NMT through neuromuscular plasticity and modulation.

Pattern generation in the buccal system of freely behaving Lymnaea stagnalis

Central pattern generators (CPGs) are neuronal circuits that drive active repeated movements such as walking or swimming. Although CPGs are, by definition, active in isolated central nervous systems, sensory input is thought play an important role in adjusting the output of the CPGs to meet specific behavioral requirements of intact animals. We investigated, in freely behaving snails (Lymnaea stagnalis), how the buccal CPG is used during two different behaviors, feeding and egg laying. Analysis of the relationship between unit activity recorded from buccal nerves and the movements of the buccal mass showed that electrical activity in laterobuccal/ventrobuccal (LB/VB) nerves was as predicted from in vitro data, but electrical activity in the posterior jugalis nerve was not. Autodensity and interval histograms showed that during feeding the CPG produces a much stronger rhythm than during egg laying. The phase relationship between electrical activity and buccal movement changed little between the two behaviors. Fitting the spike trains recorded during the two behaviors with a simple model revealed differences in the patterns of electrical activity produced by the buccal system during the two behaviors investigated. During egg laying the bursts contained less spikes, and the number of spikes per burst was significantly more variable than during feeding. The time between two bursts of in a spike train was longer during egg laying than during feeding. The data show what the qualitative and quantitative differences are between two motor patterns produced by the buccal system of freely behaving Lymnaea stagnalis.

Modulation of radula opener muscles in Aplysia

We observed fibers immunoreactive (IR) to serotonin (5-HT), the myomodulins (MMs), and FMRFamide on the I7-I10 complex in the marine mollusk Aplysia californica. The I7-I10 muscle complex, which produces radula opening, is innervated primarily by one motor neuron, B48. B48 is MM-IR and synthesizes authentic MM(A). When B48 is stimulated in a physiological manner, cAMP levels are increased in opener muscles. cAMP increases also are seen when the MMs are applied to opener muscles but are not seen with application of the B48 primary neurotransmitter acetylcholine (ACh). Possible physiological sources of 5-HT and FMRFamide are discussed. When modulators are applied to resting opener muscles, changes in membrane potential are observed. Specifically, 5-HT, MM(B), and low concentrations of MM(A) all depolarize muscle fibers. This depolarization is generally not sufficient to elicit myogenic activity in the absence of neural activity under "rest" conditions. However, if opener muscles are stretched beyond rest length, stretch- and modulator-induced depolarizations can summate and elicit contractions. This only occurs, however, if "depolarizing" modulators are applied alone. Thus other modulators (i.e., FMRFamide and high concentrations of MM(A)) hyperpolarize opener muscle fibers and can prevent depolarizing modulators from eliciting myogenic activity. All modulators tested affected parameters of motor neuron-elicited contractions of opener muscles. MM(B) and 5-HT increased contraction size over the range of concentrations tested, whereas MM(A) potentiated contractions when it was applied at lower concentrations but decreased contraction size at higher concentrations. FMRFamide decreased contraction size at all concentrations and did not affect relaxation rate. Additionally, the MMs and 5-HT increased muscle relaxation rate, decreased contraction latency, and decreased the rate at which tension was developed during motor neuron-elicited muscle contractions. Thus these modulators dramatically affect the ability of opener muscles to follow activity in the opener motor neuron B48. The possible physiological significance of these findings is discussed.

Muscle response to changing neuronal input in the lobster (Panulirus interruptus) stomatogastric system: slow muscle properties can transform rhythmic input into tonic output

Slow, non-twitch muscles are widespread in lower vertebrates and invertebrates and are often assumed to be primarily involved in posture or slow motor patterns. However, in several preparations, including some well known invertebrate "model" preparations, slow muscles are driven by rapid, rhythmic inputs. The response of slow muscles to such inputs is little understood. We are investigating this issue with a slow stomatogastric muscle (cpv1b) driven by a relatively rapid, rhythmic neural pattern. A simple model suggests that as cycle period decreases, slow muscle contractions show increasing intercontraction temporal summation and at steady state consist of phasic contractions overlying a tonic contracture. We identify five components of these contractions: total, average, tonic, and phasic amplitudes, and percent phasic (phasic amplitude divided by total amplitude). cpv1b muscle contractions induced by spontaneous rhythmic neural input in vitro consist of phasic and tonic components. Nerve stimulation at varying cycle periods and constant duty cycle shows that a tonic component is always present, and at short periods the muscle transforms rhythmic input into almost completely tonic output. Varying spike frequency, spike number, and cycle period show that frequency codes total, average, and tonic amplitudes, number codes phasic amplitude, and period codes percent phasic. These data suggest that tonic contraction may be a property of slow muscles driven by rapid, rhythmic input, and in these cases it is necessary to identify the various contraction components and their neural coding. Furthermore, the parameters that code these components are interdependent, and control of slow muscle contraction is thus likely complex.

Muscle response to changing neuronal input in the lobster (Panulirus interruptus) stomatogastric system: slow muscle properties can transform rhythmic input into tonic output

Slow, non-twitch muscles are widespread in lower vertebrates and invertebrates and are often assumed to be primarily involved in posture or slow motor patterns. However, in several preparations, including some well known invertebrate "model" preparations, slow muscles are driven by rapid, rhythmic inputs. The response of slow muscles to such inputs is little understood. We are investigating this issue with a slow stomatogastric muscle (cpv1b) driven by a relatively rapid, rhythmic neural pattern. A simple model suggests that as cycle period decreases, slow muscle contractions show increasing intercontraction temporal summation and at steady state consist of phasic contractions overlying a tonic contracture. We identify five components of these contractions: total, average, tonic, and phasic amplitudes, and percent phasic (phasic amplitude divided by total amplitude). cpv1b muscle contractions induced by spontaneous rhythmic neural input in vitro consist of phasic and tonic components. Nerve stimulation at varying cycle periods and constant duty cycle shows that a tonic component is always present, and at short periods the muscle transforms rhythmic input into almost completely tonic output. Varying spike frequency, spike number, and cycle period show that frequency codes total, average, and tonic amplitudes, number codes phasic amplitude, and period codes percent phasic. These data suggest that tonic contraction may be a property of slow muscles driven by rapid, rhythmic input, and in these cases it is necessary to identify the various contraction components and their neural coding. Furthermore, the parameters that code these components are interdependent, and control of slow muscle contraction is thus likely complex.