Correction: Elucidation of molecular kinetic schemes from macroscopic traces using system identification.

[This corrects the article DOI: 10.1371/journal.pcbi.1005376.].

Elucidation of molecular kinetic schemes from macroscopic traces using system identification.

Overall cellular responses to biologically-relevant stimuli are mediated by networks of simpler lower-level processes. Although information about some of these processes can now be obtained by visualizing and recording events at the molecular level, this is still possible only in especially favorable cases. Therefore the development of methods to extract the dynamics and relationships between the different lower-level (microscopic) processes from the overall (macroscopic) response remains a crucial challenge in the understanding of many aspects of physiology. Here we have devised a hybrid computational-analytical method to accomplish this task, the SYStems-based MOLecular kinetic scheme Extractor (SYSMOLE). SYSMOLE utilizes system-identification input-output analysis to obtain a transfer function between the stimulus and the overall cellular response in the Laplace-transformed domain. It then derives a Markov-chain state molecular kinetic scheme uniquely associated with the transfer function by means of a classification procedure and an analytical step that imposes general biological constraints. We first tested SYSMOLE with synthetic data and evaluated its performance in terms of its rate of convergence to the correct molecular kinetic scheme and its robustness to noise. We then examined its performance on real experimental traces by analyzing macroscopic calcium-current traces elicited by membrane depolarization. SYSMOLE derived the correct, previously known molecular kinetic scheme describing the activation and inactivation of the underlying calcium channels and correctly identified the accepted mechanism of action of nifedipine, a calcium-channel blocker clinically used in patients with cardiovascular disease. Finally, we applied SYSMOLE to study the pharmacology of a new class of glutamate antipsychotic drugs and their crosstalk mechanism through a heteromeric complex of G protein-coupled receptors. Our results indicate that our methodology can be successfully applied to accurately derive molecular kinetic schemes from experimental macroscopic traces, and we anticipate that it may be useful in the study of a wide variety of biological systems.

Decoding the signaling of a GPCR heteromeric complex reveals a unifying mechanism of action of antipsychotic drugs.

Atypical antipsychotic drugs, such as clozapine and risperidone, have a high affinity for the serotonin 5-HT(2A) G protein-coupled receptor (GPCR), the 2AR, which signals via a G(q) heterotrimeric G protein. The closely related non-antipsychotic drugs, such as ritanserin and methysergide, also block 2AR function, but they lack comparable neuropsychological effects. Why some but not all 2AR inhibitors exhibit antipsychotic properties remains unresolved. We now show that a heteromeric complex between the 2AR and the G(i)-linked GPCR, metabotropic glutamate 2 receptor (mGluR2), integrates ligand input, modulating signaling output and behavioral changes. Serotonergic and glutamatergic drugs bind the mGluR2/2AR heterocomplex, which then balances Gi- and Gq-dependent signaling. We find that the mGluR2/2AR-mediated changes in Gi and Gq activity predict the psychoactive behavioral effects of a variety of pharmocological compounds. These observations provide mechanistic insight into antipsychotic action that may advance therapeutic strategies for disorders including schizophrenia and dementia.

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.

Distinct mechanisms produce functionally complementary actions of neuropeptides that are structurally related but derived from different precursors.

Many bioactive neuropeptides containing RFamide at their C terminus have been described in both invertebrates and vertebrates. To obtain insight into the functional logic of RFamide signaling, we investigate it here in the feeding system of Aplysia. We focus on the expression, localization, and actions of two families of RFamide peptides, the FRFamides and FMRFamide, in the central neuronal circuitry and the peripheral musculature that generate the feeding movements. We describe the cloning of the FRFamide precursor protein and show that the FRFamides and FMRFamide are derived from different precursors. We map the expression of the FRFamide and FMRFamide precursors in the feeding circuitry using in situ hybridization and immunostaining and confirm proteolytic processing of the FRFamide precursor by mass spectrometry. We show that the two precursors are expressed in different populations of sensory neurons in the feeding system. In a representative feeding muscle, we demonstrate the presence of both FRFamides and FMRFamide and their release, probably from the processes of the sensory neurons in the muscle. Both centrally and in the periphery, the FRFamides and FMRFamide act in distinct ways, apparently through distinct mechanisms, and nevertheless, from an overall functional perspective, their actions are complementary. Together, the FRFamides and FMRFamide convert feeding motor programs from ingestive to egestive and depress feeding muscle contractions. We conclude that these structurally related peptides, although derived from different precursors, expressed in different neurons, and acting through different mechanisms, remain related to each other in the functional roles that they play in the system.

Feedback from peripheral musculature to central pattern generator in the neurogenic heart of the crab Callinectes sapidus: role of mechanosensitive dendrites.

The neurogenic heart of decapod crustaceans is a very simple, self-contained, model central pattern generator (CPG)-effector system. The CPG, the nine-neuron cardiac ganglion (CG), is embedded in the myocardium itself; it generates bursts of spikes that are transmitted by the CG's five motor neurons to the periphery of the system, the myocardium, to produce its contractions. Considerable evidence suggests that a CPG-peripheral loop is completed by a return feedback pathway through which the contractions modify, in turn, the CG motor pattern. One likely pathway is provided by dendrites, presumably mechanosensitive, that the CG neurons project into the adjacent myocardial muscle. Here we have tested the role of this pathway in the heart of the blue crab, Callinectes sapidus. We performed "de-efferentation" experiments in which we cut the motor neuron axons to the myocardium and "de-afferentation" experiments in which we cut or ligated the dendrites. In the isolated CG, these manipulations had no effect on the CG motor pattern. When the CG remained embedded in the myocardium, however, these manipulations, interrupting either the efferent or afferent limb of the CPG-peripheral loop, decreased contraction amplitude, increased the frequency of the CG motor neuron spike bursts, and decreased the number of spikes per burst and burst duration. Finally, passive stretches of the myocardium likewise modulated the spike bursts, an effect that disappeared when the dendrites were cut. We conclude that feedback through the dendrites indeed operates in this system and suggest that it completes a loop through which the system self-regulates its activity.

Distinct inhibitory neurons exert temporally specific control over activity of a motoneuron receiving concurrent excitation and inhibition.

Recent work suggests that concurrent excitation and inhibition originating in central pattern generators (CPGs) may be used to control rhythmic motoneuronal activity. The specific roles that the inhibition plays in such cases are not well understood, however, in part because of the lack of identification of presynaptic inhibitory neurons. Here we demonstrate that, in the Aplysia feeding CPG, inhibitory inputs may be critical for flexible control of the activity of motoneurons in different forms of behavior. The feeding CPG generates ingestive and egestive motor programs, differing in the high and low activity, respectively, of the motoneuron B8 during the retraction phase of the programs. We show that, during retraction, B8 receives concurrent excitation and inhibition that produces a high-conductance state. The inhibition originates in two types of CPG neurons, B4/5 and B70, that are more active in egestion than ingestion and play a role in suppressing B8 activity during egestion. In turn, the activities of both B4/5 and B70 are suppressed by the ingestion-promoting descending interneuron CBI-3 (for cerebral-buccal interneuron 3). Thus, concurrent excitation and inhibition may be an effective means of controlling motoneuronal activity in a behavior-dependent manner. More detailed analyses reveal, furthermore, that B4/5 and B70 exert complementary actions by acting preferentially in the early and late part of retraction, respectively. Thus, the use of multiple neurons to generate inhibitory inputs to motoneurons that receive concurrent excitation and inhibition brings an additional level of flexibility that allows a temporally specific control of motoneuronal activity within a single phase of motor programs.

A method for decoding the neurophysiological spike-response transform.

Many physiological responses elicited by neuronal spikes-intracellular calcium transients, synaptic potentials, muscle contractions-are built up of discrete, elementary responses to each spike. However, the spikes occur in trains of arbitrary temporal complexity, and each elementary response not only sums with previous ones, but can itself be modified by the previous history of the activity. A basic goal in system identification is to characterize the spike-response transform in terms of a small number of functions-the elementary response kernel and additional kernels or functions that describe the dependence on previous history-that will predict the response to any arbitrary spike train. Here we do this by developing further and generalizing the "synaptic decoding" approach of Sen et al. (1996). Given the spike times in a train and the observed overall response, we use least-squares minimization to construct the best estimated response and at the same time best estimates of the elementary response kernel and the other functions that characterize the spike-response transform. We avoid the need for any specific initial assumptions about these functions by using techniques of mathematical analysis and linear algebra that allow us to solve simultaneously for all of the numerical function values treated as independent parameters. The functions are such that they may be interpreted mechanistically. We examine the performance of the method as applied to synthetic data. We then use the method to decode real synaptic and muscle contraction transforms.

Predicting adaptive behavior in the environment from central nervous system dynamics.

To generate adaptive behavior, the nervous system is coupled to the environment. The coupling constrains the dynamical properties that the nervous system and the environment must have relative to each other if adaptive behavior is to be produced. In previous computational studies, such constraints have been used to evolve controllers or artificial agents to perform a behavioral task in a given environment. Often, however, we already know the controller, the real nervous system, and its dynamics. Here we propose that the constraints can also be used to solve the inverse problem--to predict from the dynamics of the nervous system the environment to which they are adapted, and so reconstruct the production of the adaptive behavior by the entire coupled system. We illustrate how this can be done in the feeding system of the sea slug Aplysia. At the core of this system is a central pattern generator (CPG) that, with dynamics on both fast and slow time scales, integrates incoming sensory stimuli to produce ingestive and egestive motor programs. We run models embodying these CPG dynamics--in effect, autonomous Aplysia agents--in various feeding environments and analyze the performance of the entire system in a realistic feeding task. We find that the dynamics of the system are tuned for optimal performance in a narrow range of environments that correspond well to those that Aplysia encounter in the wild. In these environments, the slow CPG dynamics implement efficient ingestion of edible seaweed strips with minimal sensory information about them. The fast dynamics then implement a switch to a different behavioral mode in which the system ignores the sensory information completely and follows an internal "goal," emergent from the dynamics, to egest again a strip that proves to be inedible. Key predictions of this reconstruction are confirmed in real feeding animals.

State dependence of network output: modeling and experiments.

Emerging experimental evidence suggests that both networks and their component neurons respond to similar inputs differently, depending on the state of network activity. The network state is determined by the intrinsic dynamical structure of the network and may change as a function of neuromodulation, the balance or stochasticity of synaptic inputs to the network, and the history of network activity. Much of the knowledge on state-dependent effects comes from comparisons of awake and sleep states of the mammalian brain. Yet, the mechanisms underlying these states are difficult to unravel. Several vertebrate and invertebrate studies have elucidated cellular and synaptic mechanisms of state dependence resulting from neuromodulation, sensory input, and experience. Recent studies have combined modeling and experiments to examine the computational principles that emerge when network state is taken into account; these studies are highlighted in this article. We discuss these principles in a variety of systems (mammalian, crustacean, and mollusk) to demonstrate the unifying theme of state dependence of network output.

Regulation of the crab heartbeat by FMRFamide-like peptides: multiple interacting effects on center and periphery.

We are studying the functional "logic" of neuromodulatory actions in a simple central pattern generator (CPG)-effector system, the heart of the blue crab Callinectes sapidus. The rhythmic contractions of this heart are neurogenic, driven by rhythmic motor patterns generated by the cardiac ganglion (CG). Here we used anatomical and physiological methods to examine the sources and actions on the system of the FMRFamide-like peptides (FLPs) TNRNFLRFamide (F(1)), SDRNFLRFamide (F(2)), and GYNRSFLRFamide, an authentic Callinectes FLP. Immunohistochemical localization revealed a plexus of FLP-immunoreactive fibers in the pericardial organs (POs), from which modulators are released to reach the heart as circulating neurohormones. Combined backfill and immunohistochemical experiments indicated that the FLPs in the POs originated in the CNS, from large neurosecretory cells in the B cluster of the first thoracic neuromere. In physiological experiments, we examined the actions of the FLPs on the intact working heart, on the semi-intact heart in which we could record the motor patterns as well as the muscle contractions, on the isolated CG, and in a preparation developed to assess direct actions on the muscle with controlled patterns of motor neuron spikes. The FLPs had strong positive chronotropic and inotropic effects. Dissection of these effects suggested that they were produced through at least two primary actions of the FLPs exerted both on the heart muscle and on the CG. These primary actions elicited numerous secondary consequences mediated by the feedforward and feedback interactions that integrate the activity of the complete, coupled CPG-effector system.

Regulation of the crab heartbeat by crustacean cardioactive peptide (CCAP): central and peripheral actions.

In regulating neurophysiological systems, neuromodulators exert multiple actions at multiple sites in such a way as to control the activity in an integrated manner. We are studying how this happens in a simple central pattern generator (CPG)-effector system, the heart of the blue crab Callinectes sapidus. The rhythmic contractions of this heart are neurogenic, driven by rhythmic motor patterns generated by the cardiac ganglion (CG). In this study, we used anatomical and physiological methods to examine the sources and actions on the system of crustacean cardioactive peptide (CCAP). Immunohistochemical localization revealed a plexus of CCAP-immunoreactive fibers in the pericardial organs (POs), neurohemal structures from which blood-borne neurohormones reach the heart. Combined backfill and immunohistochemical experiments indicated that the CCAP in the POs originated from a large contralateral neuron in each thoracic neuromere. In physiological experiments, we examined the actions of exogenous CCAP on the intact working heart, on the semi-intact heart in which we could record the motor patterns as well as the muscle contractions, and on the isolated CG. CCAP had strong positive inotropic and chronotropic effects. Dissection of these effects in terms of dose dependency, time course, and the preparation type in which they occurred suggested that they were produced by the interaction of three primary actions of CCAP exerted both on the heart muscle and on the CG. We conclude that CCAP released from the POs as a neurohormone regulates the crab heart by multiple actions on both the central and peripheral components of this model CPG-effector system.

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.

Decoding modulation of the neuromuscular transform.

When modulators of neuromuscular function alter the motor neuron spike patterns that elicit muscle contractions, it is predicted that they will also retune correspondingly the connecting processes of the neuromuscular transform. Here we confirm this prediction by analyzing data from the cardiac neuromuscular system of the blue crab. We apply a method that decodes the contraction response to the spike pattern in terms of three elementary building-block functions that completely characterize the neuromuscular transform. This method allows us to dissociate modulator-induced changes in the neuromuscular transform from changes in the spike pattern in the normally operating, essentially unperturbed neuromuscular system.

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.

Cycle-to-cycle variability as an optimal behavioral strategy.

Aplysia feeding behavior is highly variable from cycle to cycle. In some cycles, when the variability causes a mismatch between the animal's movements and the requirements of the feeding task, the variability makes the behavior unsuccessful. We propose that the behavior is variable nevertheless because the variability 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. Over many cycles, this may be the animal's optimal strategy in an uncertain and changing feeding environment.

Identification of a new neuropeptide precursor reveals a novel source of extrinsic modulation in the feeding system of Aplysia.

The Aplysia feeding system is advantageous for investigating the role of neuropeptides in behavioral plasticity. One family of Aplysia neuropeptides is the myomodulins (MMs), originally purified from one of the feeding muscles, the accessory radula closer (ARC). However, two MMs, MMc and MMe, are not encoded on the only known MM gene. Here, we identify MM gene 2 (MMG2), which encodes MMc and MMe and four new neuropeptides. We use matrix-assisted laser desorption/ionization time-of-flight mass spectrometry to verify that these novel MMG2-derived peptides (MMG2-DPs), as well as MMc and MMe, are synthesized from the precursor. Using antibodies against the MMG2-DPs, we demonstrate that neuronal processes that stain for MMG2-DPs are found in the buccal ganglion, which contains the feeding network, and in the buccal musculature including the ARC muscle. Surprisingly, however, no immunostaining is observed in buccal neurons including the ARC motoneurons. In situ hybridization reveals only few MMG2-expressing neurons that are mostly located in the pedal ganglion. Using immunohistochemical and electrophysiological techniques, we demonstrate that some of these pedal neurons project to the buccal ganglion and are the likely source of the MMG2-DP innervation of the feeding network and musculature. We show that the MMG2-DPs are bioactive both centrally and peripherally: they bias egestive feeding programs toward ingestive ones, and they modulate ARC muscle contractions. The multiple actions of the MMG2-DPs suggest that these peptides play a broad role in behavioral plasticity and that the pedal-buccal projection neurons that express them are a novel source of extrinsic modulation of the feeding system of Aplysia.

Temperature compensation of neuromuscular modulation in aplysia.

Physiological systems that must operate over a range of temperatures often incorporate temperature-compensatory mechanisms to maintain their output within a relatively narrow, functional range of values. We analyze here an example in the accessory radula closer (ARC) neuromuscular system, a representative part of the feeding neuromusculature of the sea slug Aplysia. The ARC muscle's two motor neurons, B15 and B16, release, in addition to ACh that contracts the muscle, modulatory peptide cotransmitters that, through a complex network of effects in the muscle, shape the ACh-induced contractions. It is believed that this modulation is critical in optimizing the performance of the muscle for successful, efficient feeding behavior. However, previous work has shown that the release of the modulatory peptides from the motor neurons decreases dramatically with increasing temperature. From 15 to 25 degrees C, for example, release decreases 20-fold. Yet Aplysia live and feed successfully not only at 15 degrees C, but at 25 degrees C and probably at higher temperatures. Here, working with reduced B15/B16-ARC preparations in vitro as well as a mathematical model of the system, we have found a resolution of this apparent paradox. Although modulator release decreases 20-fold when the temperature is raised from 15 to 25 degrees C, the observed modulation of contraction shape does not decrease at all. Two mechanisms are responsible. First, further downstream within the modulatory network, the modulatory effects themselves-experimentally dissected by exogenous modulator application-have temperature dependencies opposite to that of modulator release, increasing with temperature. Second, the saturating curvature of the dose-response relations within the network diminishes the downstream impact of the decrease of modulator release. Thus two quite distinct mechanisms, one depending on the characteristics of the individual components of the network and the other emerging from the network's structure, combine to compensate for temperature changes to maintain the output of this physiological system.

Variability of swallowing performance in intact, freely feeding aplysia.

Variability in nervous systems is often taken to be merely "noise." Yet in some cases it may play a positive, active role in the production of behavior. The central pattern generator (CPG) that drives the consummatory feeding behaviors of Aplysia generates large, quasi-random variability in the parameters of the feeding motor programs from one cycle to the next; the variability then propagates through the firing patterns of the motor neurons to the contractions of the feeding muscles. We have proposed that, when the animal is faced with a new, imperfectly known feeding task in each cycle, the variability implements a trial-and-error search through the space of possible feeding movements. Although this strategy will not be successful in every cycle, over many cycles it may be the optimal strategy for feeding in an uncertain and changing environment. To play this role, however, the variability must actually appear in the feeding movements and, presumably, in the functional performance of the feeding behavior. Here we have tested this critical prediction. We have developed a technique to measure, in intact, freely feeding animals, the performance of Aplysia swallowing behavior, by continuously recording with a length transducer the movement of the seaweed strip being swallowed. Simultaneously, we have recorded with implanted electrodes activity at each of the internal levels, the CPG, motor neurons, and muscles, of the feeding neuromusculature. Statistical analysis of a large data set of these recordings suggests that functional performance is not determined strongly by one or a few parameters of the internal activity, but weakly by many. Most important, the internal variability does emerge in the behavior and its functional performance. Even when the animal is swallowing a long, perfectly regular seaweed strip, remarkably, the length swallowed from cycle to cycle is extremely variable, as variable as the parameters of the activity of the CPG, motor neurons, and muscles.

Tight or loose coupling between components of the feeding neuromusculature of Aplysia?

Like other complex behaviors, the cyclical, rhythmic consummatory feeding behaviors of Aplysia-biting, swallowing, and rejection of unsuitable food-are produced by a complex neuromuscular system: the animal's buccal mass, with numerous pairs of antagonistic muscles, controlled by the firing of numerous motor neurons, all driven by the motor programs of a central pattern generator (CPG) in the buccal ganglia. In such a complex neuromuscular system, it has always been assumed that the activities of the various components must necessarily be tightly coupled and coordinated if successful functional behavior is to be produced. However, we have recently found that the CPG generates extremely variable motor programs from one cycle to the next, and so very variable motor neuron firing patterns and contractions of individual muscles. Here we show that this variability extends even to higher-level parameters of the operation of the neuromuscular system such as the coordination between entire antagonistic subsystems within the buccal neuromusculature. In motor programs elicited by stimulation of the esophageal nerve, we have studied the relationship between the contractions of the accessory radula closer (ARC) muscle, and the firing patterns of its motor neurons B15 and B16, with those of its antagonist, the radula opener (I7) muscle, and its motor neuron B48. There are two separate B15/B16-ARC subsystems, one on each side of the animal, and these are indeed very tightly coupled. Tight coupling can, therefore, be achieved in this neuromuscular system where required. Yet there is essentially no coupling at all between the contractions of the ARC muscles and those of the antagonistic radula opener muscle. We interpret this result in terms of a hypothesis that ascribes a higher-order benefit to such loose coupling in the neuromusculature. The variability, emerging in the successive feeding movements made by the animal, diversifies the range of movements and thereby implements a trial-and-error search through the space of movements that might be successful, an optimal strategy for the animal in an unknown, rapidly changing feeding environment.