A modeling comparison of projection neuron- and neuromodulator-elicited oscillations in a central pattern generating network

Many central pattern generating networks are influenced by synaptic input from modulatory projection neurons. The network response to a projection neuron is sometimes mimicked by bath applying the neuronally-released modulator, despite the absence of network interactions with the projection neuron. One interesting example occurs in the crab stomatogastric ganglion (STG), where bath applying the neuropeptide pyrokinin (PK) elicits a gastric mill rhythm which is similar to that elicited by the projection neuron modulatory commissural neuron 1 (MCN1), despite the absence of PK in MCN1 and the fact that MCN1 is not active during the PK-elicited rhythm. MCN1 terminals have fast and slow synaptic actions on the gastric mill network and are presynaptically inhibited by this network in the STG. These local connections are inactive in the PK-elicited rhythm, and the mechanism underlying this rhythm is unknown. We use mathematical and biophysically-realistic modeling to propose potential mechanisms by which PK can elicit a gastric mill rhythm that is similar to the MCN1-elicited rhythm. We analyze slow-wave network oscillations using simplified mathematical models and, in parallel, develop biophysically-realistic models that account for fast, action potential-driven oscillations and some spatial structure of the network neurons. Our results illustrate how the actions of bath-applied neuromodulators can mimic those of descending projection neurons through mathematically similar but physiologically distinct mechanisms.     

Maintaining phase of the crustacean tri-phasic pyloric rhythm

We construct and analyze a model network of the pyloric rhythm of the crustacean stomatogastric ganglion consisting of an oscillator neuron that inhibits two reciprocally inhibitory follower neurons. We derive analytic expressions that determine the phase of firing of the follower neurons with respect to the oscillator. An important aspect of the model is the inclusion of synapses that exhibit short-term synaptic depression. We show that these type of synapses allow there to be a complicated relationship between the intrinsic properties of the neurons and the synapses between them in determining phase relationships. Our analysis reveals the circumstances and ranges of cycle periods under which these properties work in concert with or independently from one another. In particular, we show that phase maintenance over a range of oscillator periods can be enhanced through the interplay of the two follower neurons if the synapses between these neurons are depressing. Since our model represents the core of the oscillatory pyloric network, the results of our analysis can be compared to experimental data and used to make predictions about the biological network.     

Timing regulation in a network reduced from voltage-gated equations to a one-dimensional map

 We discuss a method by which the dynamics of a network of neurons, coupled by mutual inhibition, can be reduced to a one-dimensional map. This network consists of a pair of neurons, one of which is an endogenous burster, and the other excitable but not bursting in the absence of phasic input. The latter cell has more than one slow process. The reduction uses the standard separation of slow/fast processes; it also uses information about how the dynamics on the slow manifold evolve after a finite amount of slow time. From this reduction we obtain a one-dimensional map dependent on the parameters of the original biophysical equations. In some parameter regimes, one can deduce that the original equations have solutions in which the active phase of the originally excitable cell is constant from burst to burst, while in other parameter regimes it is not. The existence or absence of this kind of regulation corresponds to qualitatively different dynamics in the one-dimensional map. The computations associated with the reduction and the analysis of the dynamics includes the use of coordinates that parameterize by time along trajectories, and “singular Poincaré maps” that combine information about flows along a slow manifold with information about jumps between branches of the slow manifold. Received: 19 May 1997 / Revised version: 6 April 1998     

A database of computational models of a half-center oscillator for analyzing how neuronal parameters influence network activity

A half-center oscillator (HCO) is a common circuit building block of central pattern generator networks that produce rhythmic motor patterns in animals. Here we constructed an efficient relational database table with the resulting characteristics of the Hill et al.’s (J Comput Neurosci 10:281–302, 2001) HCO simple conductance-based model. The model consists of two reciprocally inhibitory neurons and replicates the electrical activity of the oscillator interneurons of the leech heartbeat central pattern generator under a variety of experimental conditions. Our long-range goal is to understand how this basic circuit building block produces functional activity under a variety of parameter regimes and how different parameter regimes influence stability and modulatability. By using the latest developments in computer technology, we simulated and stored large amounts of data (on the order of terabytes). We systematically explored the parameter space of the HCO and corresponding isolated neuron models using a brute-force approach. We varied a set of selected parameters (maximal conductance of intrinsic and synaptic currents) in all combinations, resulting in about 10 million simulations. We classified these HCO and isolated neuron model simulations by their activity characteristics into identifiable groups and quantified their prevalence. By querying the database, we compared the activity characteristics of the identified groups of our simulated HCO models with those of our simulated isolated neuron models and found that regularly bursting neurons compose only a small minority of functional HCO models; the vast majority was composed of spiking neurons.     

A single pair of interneurons controls motor neuron activity during pre-ecdysis compression behavior in larval Manduca sexta

Manduca sexta molts several times as a larva (caterpillar) before becoming a pupa and then an adult moth. Each molt culminates in ecdysis behavior, during which the old cuticle is shed. Prior to each larval ecdysis, the old cuticle is loosened by pre-ecdysis behavior, which includes rhythmic, synchronous compressions of the abdomen. A previous study indicated that motor neuron activity during pre-ecdysis compression behavior is driven by an ascending neural pathway from the terminal abdominal ganglion. The present study describes a pair of interneurons, designated IN-402, that are located in the terminal ganglion and belong to the ascending pathway. Each IN-402 is synchronously active with pre-ecdysis compression motor bursts, and bilaterally excites compression motor neurons throughout the abdominal nerve cord via apparently monosynaptic connections. The pair of IN-402s appears to be the sole source of rhythmic synaptic drive to the motor neurons during the pre-ecdysis compression motor pattern. These interneurons play a key role in the production of larval pre-ecdysis behavior, and are candidates for contributing to the developmental weakening of pre-ecdysis behavior at pupation.Abbreviations A3, A4... abdominal ganglion 3, abdominal ganglion 4... - AT terminal abdominal ganglion - DN _A anterior branch of the dorsal nerve - EH eclosion hormone - EPSP excitatory postsynaptic potential     

Modulation of the feeding system by a radular mechanosensory neuron in the terrestrial slug,Incilaria fruhstorferi

We investigated the modulatory role of a radular mechanoreceptor (RM) in the feeding system of Incilaria. RM spiking induced by current injection evoked several cycles of rhythmic buccal motor activity in quiescent preparations, and this effect was also observed in preparations lacking the cerebral ganglia. The evoked rhythmic activity included sequential activation of the inframedian radular tensor, the supramedian radular tensor, and the buccal sphincter muscles in that order.In addition to the generation of rhythmic motor activity, RM spiking enhanced tonic activities in buccal nerve 1 as well as in the cerebrobuccal connective, showing a wide excitatory effect on buccal neurons. The excitatory effect was further examined in the supramedian radular tensor motoneuron. RM spiking evoked biphasic depolarization in the tensor motoneuron consisting of fast excitatory postsynaptic potentials and prolonged depolarization lasting after termination of RM spiking. These depolarizations also occurred in high divalent cation saline, suggesting that they were both monosynaptic.When RM spiking was evoked in the fictive rasp phase during food-induced buccal motor rhythm, the activity of the supramedian radular tensor muscle showed the greatest enhancement of the three muscles tested, while the rate of ongoing rhythmic motor activity showed no increase.Abbreviations CPG central pattern generator - EPSP excitatory postsynaptic potential - RBMA rhythmic buccal motor activity - RM radular mechanosensory neuron - SMT supramedian radular tensor neuron     

Qualitative validation of the reduction from two reciprocally coupled neurons to one self-coupled neuron in a respiratory network model

The pre-Bötzinger complex of the mammalian brainstem is a heterogeneous neuronal network, and individual neurons within the network have varying strengths of the persistent sodium and calcium-activated nonspecific cationic currents. Individually, these currents have been the focus of modeling efforts. Previously, Dunmyre et al. (J Comput Neurosci 1–24, 2011) proposed a model and studied the interactions of these currents within one self-coupled neuron. In this work, I consider two identical, reciprocally coupled model neurons and validate the reduction to the self-coupled case. I find that all of the dynamics of the two model neuron network and the regions of parameter space where these distinct dynamics are found are qualitatively preserved in the reduction to the self-coupled case.     

Elevated temperature alters the ionic dependence of amine-induced pacemaker activity in a conditional burster neuron

Summary The anterior burster neuron of the lobster (Panulirus interruptus) stomatogastric ganglion is a conditional burster that functions as the primary pacemaker for the pyloric motor network. When modulatory inputs to this cell are blocked, it loses its bursting properties and becomes quiescent. Applications of the monoamines, dopamine, octopamine or serotonin restore rhythmic bursting in this cell (Flamm and Harris-Warrick 1986). At 15 °C, serotonin- and octopamine-induced oscillations depend critically upon sodium entry (blocked by low sodium saline or tetrodotoxin); dopamine-induced oscillations depend upon calcium entry (blocked by reduced extracellular calcium; Harris-Warrick and Flamm 1987). We show here that the ionic dependence of amine-induced oscillations in the anterior burster cell differs at 15 and 21 °C. At 21 °C, all amines have the potential to induce rhythmic oscillations in saline containing tetrodotoxin. At the elevated temperature and in tetrodotoxin, both calcium and sodium currents are essential for the maintenance of dopamine-induced oscillaions; serotonin-induced oscillations do not depend upon either calcium or sodium alone; octopamine-induced oscillations do not depend upon calcium and show a variable dependence upon sodium. Thus, multiple ionic mechanisms, which vary with both the modulator and the ambient temperature, can be recruited to support rhythmic activity in a conditional burster neuron.Abbreviations AB anterior burster - PD pyloric dilator - PY pyloric constrictor - DA dopamine - 5HT serotonin - Oct octopamine - STG stomatogastric ganglion - TTX tetrodotoxin - GSP graded synaptic potential     

Neuroanatomy and neurophysiology of the locust hypocerebral ganglion

The insect stomatogastric ganglia control foregut movements. Most previous work on the system has concentrated on the frontal ganglion (FG), including research into the role of the FG in feeding as well as molting-related behavior, mostly in locusts, but also in other insect species. The stomatogastric system exerts its physiological actions by way of careful interaction and coordination between its different neural centers and pattern-generating circuits. One such hitherto unstudied neural center is the hypocerebral ganglion (HG), which is connected to the FG via the recurrent nerve. It sends two pairs of nerves along the esophagus and to the posterior region of the crop, terminating in the paired ingluvial ganglia. Very little is known about the neuroanatomy and neurophysiology of the insect HG. Here we investigate, for the first time, the neuronal composition of the locust HG, as well as its motor output. We identify rhythmic patterns endogenous to the isolated HG, demonstrating the presence of a central pattern-generating network. Our findings suggest interactions between the HG and FG rhythm-generating circuits leading to complex physiological actions of both ganglia. This work will serve as a basis for future investigation into the physiology of the HG and its role in insect behavior.     

The brain can eat: Establishing the existence of a central pattern generator for feeding in third instar larvae of Drosophila virilis and Drosophila melanogaster

To establish the existence of a central pattern generator for feeding in the larval central nervous system of two Drosophila species, the gross anatomy of feeding related muscles and their innervation is described, the motor units of the muscles identified and rhythmic motor output recorded from the isolated CNS. The cibarial dilator muscles that mediate food ingestion are innervated by the frontal nerve. Their motor pathway projects from the brain through the antennal nerves, the frontal connectives and the frontal nerve junction. The mouth hook elevator and depressor system is innervated by side branches of the maxillary nerve. The motor units of the two muscle groups differ in amplitude: the elevator is always activated by a small unit, the depressor by a large one. The dorsal protractors span the cephalopharyngeal skeleton and the body wall hence mediating an extension of the CPS. These muscles are innervated by the prothoracic accessory nerve. Rhythmic motor output produced by the isolated central nervous system can simultaneously be recorded from all three nerves. The temporal pattern of the identified motor units resembles the sequence of muscle contractions deduced from natural feeding behavior and is therefore considered as fictive feeding. Phase diagrams show an almost identical fictive feeding pattern is in both species.     

Octopamine and tyramine influence the behavioral profile of locomotor activity in the honey bee (Apis mellifera)

The biogenic amines octopamine and tyramine are believed to play a number of important roles in the behavior of invertebrates including the regulation of motor function. To investigate the role of octopamine and tyramine in locomotor behavior in honey bees, subjects were injected with a range of concentrations of octopamine, tyramine, mianserin or yohimbine. Continuous observation of freely moving worker bees was used to examine the effects of these treatments on the amount of time honey bees spent engaged in different locomotor behaviors such as walking, grooming, fanning and flying. All treatments produced significant shifts in behavior. Decreases in time spent walking and increases in grooming or stopped behavior were observed for every drug. However, the pattern of the shift depended on drug, time after injection and concentration. Flying behavior was differentially affected with increases in flying seen in octopamine treated bees, whereas those receiving tyramine showed a decrease in flying. Taken together, these data provide evidence that octopamine and tyramine modulate motor function in the honey bee perhaps via interaction with central pattern generators or through effects on sensory perception.     

Organization of the larval pre-ecdysis motor pattern in the tobacco hornworm,Manduca sexta

The tobacco hornworm, Manduca sexta, undergoes several larval molts before transforming into a pupa and then an adult moth. Each molt culminates in ecdysis, when the old cuticle is shed. Prior to each larval ecdysis, the old cuticle is loosened by pre-ecdysis behavior, which consists of rhythmic compressions that are synchronous along the abdomen and on both body sides, and rhythmic retractions of the abdominal prolegs. Both pre-ecdysis and ecdysis behaviors are triggered by a peptide, eclosion hormone. The aim of the present study was to investigate the neural circuitry underlying larval preecdysis behavior. The pre-ecdysis motor pattern was recorded in isolated nerve cords from eclosion hormone-treated larvae, and the effects of connective transections and ionic manipulations were tested. Our results suggest that the larval pre-ecdysis compression motor pattern is coordinated and maintained by interneurons in the terminal abdominal ganglion that ascend the nerve cord without chemical synaptic relays; these interneurons make bilateral, probably monosynaptic, excitatory connections with identified pre-ecdysis motor neurons throughout the abdominal nerve cord. This model of the organization of the larval pre-ecdysis motor pattern should facilitate identification of the relevant interneurons, allowing future investigation of the neural basis of the developmental weakening of the pre-ecdysis motor pattern that accompanies the larval-pupal transformation.Abbreviations A3, A4... abdominal ganglia 3, 4... - AT terminal abdominal ganglion - ALE anterior lateral external muscle - DN dorsal nerve - DN_A anterior branch of the dorsal nerve - DN_L lateral branch of the dorsal nerve - DN_P posterior branch of the dorsal nerve - EH eclosion hormone - TP tergopleural muscle - VN ventral nerve - VN_A anterior branch of the ventral nerve - VN_L lateral branch of the ventral nerve - VN_P posterior branch of the ventral nerve     

Modular functional organisation of the axial locomotor system in salamanders

Most investigations on tetrapod locomotion have been concerned with limb movements. However, there is compelling evidence that the axial musculoskeletal system contributes to important functions during locomotion. Adult salamanders offer a remarkable opportunity to examine these functions because these amphibians use axial undulations to propel themselves in both aquatic and terrestrial environments. In this article, we review the currently available biological data on axial functions during various locomotor modes in salamanders. We also present data showing the modular organisation of the neural networks that generate axial synergies during locomotion. The functional implication of this modular organisation is discussed.     

Dominant ionic mechanisms explored in spiking and bursting using local low-dimensional reductions of a biophysically realistic model neuron

The large number of variables involved in many biophysical models can conceal potentially simple dynamical mechanisms governing the properties of its solutions and the transitions between them as parameters are varied. To address this issue, we extend a novel model reduction method, based on “scales of dominance,” to multi-compartment models. We use this method to systematically reduce the dimension of a two-compartment conductance-based model of a crustacean pyloric dilator (PD) neuron that exhibits distinct modes of oscillation—tonic spiking, intermediate bursting and strong bursting. We divide trajectories into intervals dominated by a smaller number of variables, resulting in a locally reduced hybrid model whose dimension varies between two and six in different temporal regimes. The reduced model exhibits the same modes of oscillation as the 16 dimensional model over a comparable parameter range, and requires fewer ad hoc simplifications than a more traditional reduction to a single, globally valid model. The hybrid model highlights low-dimensional organizing structure in the dynamics of the PD neuron, and the dependence of its oscillations on parameters such as the maximal conductances of calcium currents. Our technique could be used to build hybrid low-dimensional models from any large multi-compartment conductance-based model in order to analyze the interactions between different modes of activity.     

Existence and stability criteria for phase-locked modes in ring neural networks based on the spike time resetting curve method

We developed a systematic and consistent mathematical approach to predicting 1:1 phase-locked modes in ring neural networks of spiking neurons based on the open loop spike time resetting curve (STRC) and its almost equivalent counterpart—the phase resetting curve (PRC). The open loop STRCs/PRCs were obtained by injecting into an isolated model neuron a triangular shaped time-dependent stimulus current closely resembling an actual synaptic input. Among other advantages, the STRC eliminates the confusion regarding the undefined phase for stimuli driving the neuron outside of the unperturbed limit cycle. We derived both open loop PRC and STRC-based existence and stability criteria for 1:1 phase-locked modes developed in ring networks of spiking neurons. Our predictions were in good agreement with the closed loop numerical simulations. Intuitive graphical methods for predicting phase-locked modes were also developed both for half-centers and for larger ring networks.     

Neural mechanism for generating and switching motor patterns of rhythmic movements of ovipositor valves in the cricket

In adult female crickets (Gryllus bimaculatus), rhythmic movements of ovipositor valves are produced by contractions of a set of ovipositor muscles that mediate egg-laying behavior. Recordings from implanted wire electrodes in the ovipositor muscles of freely moving crickets revealed sequential changes in the temporal pattern of motor activity that corresponded to shifts between behavioral steps: penetration of the ovipositor into a substrate, deposition of eggs, and withdrawal of the ovipositor from the substrate. We aimed in this study to illustrate the neuronal organization producing these motor patterns and the pattern-switching mechanism during the behavioral sequence. Firstly, we obtained intracellular recordings in tethered preparations, and identified 12 types of interneurons that were involved in the rhythmic activity of the ovipositor muscles. These interneurons fell into two classes: ‘initiator interneurons’ in which excitation preceded the rhythmic contractions of ovipositor muscles, and ‘oscillator interneurons’ in which the rhythmic oscillation and spike bursting occurred in sync with the oviposition motor rhythm. One of the oscillator interneurons exhibited different depolarization patterns in the penetration and deposition motor rhythms. It is likely that some of the oscillator interneurons are involved in producing different oviposition motor patterns. Secondly, we analyzed oviposition motor patterns when the mecahnosensory hairs located on the inside surface of the dorsal ovipositor valves were removed. In deafferented preparations, the sequential change from deposition to withdrawal did not occur. Therefore, the switching from deposition pattern to withdrawal pattern is signaled by the hair sensilla that detect the passage of an egg just before it is expelled.     

Multivariable harmonic balance analysis of the neuronal oscillator for leech swimming

Biological systems, and particularly neuronal circuits, embody a very high level of complexity. Mathematical modeling is therefore essential for understanding how large sets of neurons with complex multiple interconnections work as a functional system. With the increase in computing power, it is now possible to numerically integrate a model with many variables to simulate behavior. However, such analysis can be time-consuming and may not reveal the mechanisms underlying the observed phenomena. An alternative, complementary approach is mathematical analysis, which can demonstrate direct and explicit relationships between a property of interest and system parameters. This paper introduces a mathematical tool for analyzing neuronal oscillator circuits based on multivariable harmonic balance (MHB). The tool is applied to a model of the central pattern generator (CPG) for leech swimming, which comprises a chain of weakly coupled segmental oscillators. The results demonstrate the effectiveness of the MHB method and provide analytical explanations for some CPG properties. In particular, the intersegmental phase lag is estimated to be the sum of a nominal value and a perturbation, where the former depends on the structure and span of the neuronal connections and the latter is roughly proportional to the period gradient, communication delay, and the reciprocal of the intersegmental coupling strength.