Global structure, robustness, and modulation of neuronal models.

The electrical characteristics of many neurons are remarkably robust in the face of changing internal and external conditions. At the same time, neurons can be highly sensitive to neuromodulators. We find correlates of this dual robustness and sensitivity in a global analysis of the structure of a conductance-based model neuron. We vary the maximal conductance parameters of the model neuron and, for each set of parameters tested, characterize the activity pattern generated by the cell as silent, tonically firing, or bursting. Within the parameter space of the five maximal conductances of the model, we find directions, representing concerted changes in multiple conductances, along which the basic pattern of neural activity does not change. In other directions, relatively small concurrent changes in a few conductances can induce transitions between these activity patterns. The global structure of the conductance-space maps implies that neuromodulators that alter a sensitive set of conductances will have powerful, and possibly state-dependent, effects. Other modulators that may have no direct impact on the activity of the neuron may nevertheless change the effects of such direct modulators via this state dependence. Some of the results and predictions arising from the model studies are replicated and verified in recordings of stomatogastric ganglion neurons using the dynamic clamp.

GABA and responses to GABA in the stomatogastric ganglion of the crab Cancer borealis.

The multifunctional neural circuits in the crustacean stomatogastric ganglion (STG) are influenced by many small-molecule transmitters and neuropeptides that are co-localized in identified projection neurons to the STG. We describe the pattern of gamma-aminobutyric acid (GABA) immunoreactivity in the stomatogastric nervous system of the crab Cancer borealis and demonstrate biochemically the presence of authentic GABA in C. borealis. No STG somata show GABA immunoreactivity but, within the stomatogastric nervous system, GABA immunoreactivity co-localizes with several neuropeptides in two identified projection neurons, the modulatory proctolin neuron (MPN) and modulatory commissural neuron 1 (MCN1). To determine which actions of these neurons are evoked by GABA, it is necessary to determine the physiological actions of GABA on STG neurons. We therefore characterized the response of each type of STG neuron to focally applied GABA. All STG neurons responded to GABA. In some neurons, GABA evoked a picrotoxin-sensitive depolarizing, excitatory response with a reversal potential of approximately -40 mV. This response was also activated by muscimol. In many STG neurons, GABA evoked inhibitory responses with both K(+)- and Cl(-)-dependent components. Muscimol and beta-guanidinopropionic acid weakly activated the inhibitory responses, but many other drugs, including bicuculline and phaclofen, that act on vertebrate GABA receptors were not effective. In summary, GABA is found in projection neurons to the crab STG and can evoke both excitatory and inhibitory actions on STG neurons.

Activity-dependent regulation of potassium currents in an identified neuron of the stomatogastric ganglion of the crab Cancer borealis.

Identified neurons of the stomatogastric ganglion of the crab Cancer borealis were voltage-clamped, and the current densities of three K+ currents were measured. The current densities of each of the three K+ currents varied twofold to fivefold in inferior cardiac (IC) neurons from different animals. Conventionally, this degree of variability has been attributed to experimental artifacts. Instead, we suggest that it reflects a natural variability that may be related to an underlying process of plasticity. First, we found that there is no fixed ratio among the three K+ currents. Second, we found that several hours of stimulation with depolarizing current pulses (0.5 sec duration at 1 Hz) altered the current density of the Ca2+-dependent outward current, IK(Ca), and the transient outward current, IA. This stimulation paradigm mimics the normal pattern of activity for these neurons. The effect of stimulation on the IA current density was eliminated when Ca2+ influx was blocked by extracellular Cd2+. In contrast, the K+ current densities of the lateral pyloric (LP) neuron were unaffected by the same pattern of stimulation, and the currents expressed by both the IC and the LP neurons were insensitive to hyperpolarizing pulses at the same frequency. We conclude that the conductance densities expressed by neurons may vary continually depending on the recent history of electrical activity in the preparation, and that intracellular Ca2+ may play a role in the processes by which activity influences the regulation of current densities in neurons.

Network stability from activity-dependent regulation of neuronal conductances.

Activity-dependent plasticity appears to play an important role in the modification of neurons and neural circuits that occurs during development and learning. Plasticity is also essential for the maintenance of stable patterns of activity in the face of variable environmental and internal conditions. Previous theoretical and experimental results suggest that neurons stabilize their activity by altering the number or characteristics of ion channels to regulate their intrinsic electrical properties. We present both experimental and modeling evidence to show that activity-dependent regulation of conductances, operating at the level of individual neurons, can also stabilize network activity. These results indicate that the stomatogastric ganglion of the crab can generate a characteristic rhythmic pattern of activity in two fundamentally different modes of operation. In one mode, the rhythm is strictly conditional on the presence of neuromodulatory afferents from adjacent ganglia. In the other, it is independent of neuromodulatory input but relies on newly developed intrinsic properties of the component neurons.

A model neuron with activity-dependent conductances regulated by multiple calcium sensors.

Membrane channels are subject to a wide variety of regulatory mechanisms that can be affected by activity. We present a model of a stomatogastric ganglion (STG) neuron in which several Ca2+-dependent pathways are used to regulate the maximal conductances of membrane currents in an activity-dependent manner. Unlike previous models of this type, the regulation and modification of maximal conductances by electrical activity is unconstrained. The model has seven voltage-dependent membrane currents and uses three Ca2+ sensors acting on different time scales. Starting from random initial conditions over a given range, the model sets the maximal conductances for its active membrane currents to values that produce a predefined target pattern of activity approximately 90% of the time. In these models, the same pattern of electrical activity can be produced by a range of maximal conductances, and this range is compared with voltage-clamp data from the lateral pyloric neuron of the STG. If the electrical activity of the model neuron is perturbed, the maximal conductances adjust to restore the original pattern of activity. When the perturbation is removed, the activity pattern is again restored after a transient adjustment period, but the conductances may not return to their initial values. The model suggests that neurons may regulate their conductances to maintain fixed patterns of electrical activity, rather than fixed maximal conductances, and that the regulation process requires feedback systems capable of reacting to changes of electrical activity on a number of different time scales.

D-glucose-sensitive neurosecretory cells of the crab Cancer borealis and negative feedback regulation of blood glucose level.

We studied the effects of glucose on cultured X-organ neurons of the crab Cancer borealis using single-electrode current- and voltage-clamp techniques. A subpopulation of the cells responded to D-glucose with a hyperpolarization. These cells, but not glucose-insensitive cells, showed immunoreactivity to crustacean hyperglycemic hormone (CHH), the hormone responsible for the elevation of blood glucose levels in crustaceans. Glucose-sensitive cells were also inhibited by serotonin and gamma-aminobutyric acid but were not affected by dopamine and Leu-enkephalin. The response was specific for D-glucose, with an EC50 of 0.25 mmoll-1. No response was seen to L-glucose, sucrose, galactose, mannose or fructose. The glucose response persisted in the absence of extracellular Na+ and in low-Ca2+/Mn2+ saline. In voltage-clamp experiments, D-glucose evoked a small current with a reversal potential close to that of voltage-dependent K+ currents. We conclude that D-glucose activates a K+ current in CHH-immunoreactive cells that, in normal saline, induces a hyperpolarization. We propose that this enables glucose to regulate directly the release of CHH into the hemolymph, thus constituting a negative feedback mechanism regulating hemolymph glucose concentration.

Memory from the dynamics of intrinsic membrane currents.

Almost all theoretical and experimental studies of the mechanisms underlying learning and memory focus on synaptic efficacy and make the implicit assumption that changes in synaptic efficacy are both necessary and sufficient to account for learning and memory. However, network dynamics depends on the complex interaction between intrinsic membrane properties and synaptic strengths and time courses. Furthermore, neuronal activity itself modifies not only synaptic efficacy but also the intrinsic membrane properties of neurons. This paper presents examples demonstrating that neurons with complex temporal dynamics can provide short-term "memory" mechanisms that rely solely on intrinsic neuronal properties. Additionally, we discuss the potential role that activity may play in long-term modification of intrinsic neuronal properties. While not replacing synaptic plasticity as a powerful learning mechanism, these examples suggest that memory in networks results from an ongoing interplay between changes in synaptic efficacy and intrinsic membrane properties.

Enhancement by muscarinic agonists of a high voltage-activated Ca2+ current via phosphorylation in a snail neuron.

1. In previous work we have shown that in the snail Helix aspersa neuron F1 carbamylcholine (CCh) and other muscarinic agonists enhance the inward current carried through high voltage-activated Ca2+ channels by Ba2+ (HVA-ICa). It was also found that cyclic nucleotides, inositol trisphosphate or arachidonic acid are not involved in this modulation. Moreover, despite the effect of CCh being blocked by intracellular injection of EGTA, neither protein kinase C nor Ca(2+)-calmodulin-dependent protein kinase II appeared to play a role. 2. In the present paper, the intracellular mechanism of this muscarinic modulation was investigated further by studying the effects of inhibitors of Ser-Thr protein phosphatases (PP) on both the HVA-ICa of neuron F1 and its enhancement by CCh. 3. Intracellular injections in the F1 neuron of either microcystin LR or okadaic acid, both inhibitors of PP1 and PP2A, mimic the action of CCh on the HVA-ICa and occlude the effects of CCh on this current. In contrast, cyclosporin A, an inhibitor of PP2B (calcineurin), affects neither the HVA Ca2+ current itself nor its modulation by CCh. 4. The efficacy of PP inhibitors was tested in F1 neurons in which serotonin (5-HT) induces an inward current involving intracellular increases in cAMP and a protein kinase A-dependent closing of K+ channels. We found that intracellular injection of either microcystin LR or okadaic acid mimicked the 5-HT-induced inward current and occluded the effect of further application of 5-HT.(ABSTRACT TRUNCATED AT 250 WORDS)

Presynaptic control of modulatory fibers by their neural network targets.

Numerous modulatory fibers control the output of the pyloric and gastric mill neural networks in the crustacean stomatogastric ganglion (STG). We now describe the first results of intracellular recordings from the axon of one of these input neurons, stomatogastric nerve axon 1 (SNAX 1), close to where it enters the STG. SNAX 1 excites both the pyloric and gastric mill rhythms and is identified on the basis of its synaptic interactions with identified STG neurons. SNAX 1 receives synaptic input from several sources within the STG. As a result of these synaptic inputs, SNAX 1 fires bursts of action potentials that are time-locked to both the pyloric and gastric mill rhythms. The synaptic connections made onto the SNAX axon terminals are likely to play important roles in shaping the impulse activity patterns in these modulatory inputs. Thus, the fibers that modulate the pattern-generating networks in the STG are themselves influenced by elements in these networks, and modulation is a dynamic interaction between input fibers and STG neurons.

Proctolin activates an inward current whose voltage dependence is modified by extracellular Ca2+.

The pentapeptide proctolin modulates the activity of the rhythmic pattern generators in the crustacean stomatogastric nervous system. Proctolin strongly excites the lateral pyloric and the inferior cardiac neurons of the stomatogastric ganglion (STG), causing them to fire extended high-frequency bursts of action potentials (Hooper and Marder, 1987; Nusbaum and Marder, 1989a,b). We now report that proctolin depolarizes these cells maximally at membrane potentials close to the threshold for action potential generation. In voltage clamp, proctolin evokes an inward current, carried at least partially by Na+, that shows strong outward rectification. Removal of extracellular Ca2+ markedly increases the amplitude of the proctolin-evoked current and linearizes its current-voltage curve. The properties of the proctolin current make it ideally suited to contribute to the activity-dependent modulation of the pyloric network of the STG.

Ionic currents of the lateral pyloric neuron of the stomatogastric ganglion of the crab.

1. The lateral pyloric (LP) neuron is an important component of the network that generates the pyloric rhythm of the stomatogastric ganglion (STG) and is a direct target of many modulatory inputs to the STG. Our aim in this and the subsequent two papers is to describe the conductances present in this cell and to understand the role these conductances play in shaping the activity of the neuron. 2. LP neurons were studied in two-electrode voltage clamp (TEVC) in a saline solution containing tetrodotoxin (TTX) and picrotoxin (PTX) to isolate them pharmacologically from presynaptic inputs. 3. We identified six voltage-dependent ionic conductances. These include three outward currents that resemble a delayed rectifier current, a Ca(2+)-activated K+ current and an A-current similar to those seen in many other preparations. LP neurons show three inward currents, a fast TTX-sensitive current, a hyperpolarization-activated inward current, and a Ca2+ current.

Mathematical model of an identified stomatogastric ganglion neuron.

1. The ionic currents in the lateral pyloric (LP) cell of the stomatogastric ganglion (STG) described in the preceding paper of the rock crab Cancer borealis were fit with a set of differential equations that describe their voltage, time, and Ca2+ dependence. The voltage-dependent currents modeled are a delayed rectifier-like current, id; a Ca(2+)-activated outward current, io(Ca); a transient A-like current, iA; a Ca2+ current, iCa; an inwardly rectifying current, ih; and a fast tetrodotoxin (TTX)-sensitive Na+ current, iNa. 2. A single-compartment, isopotential model of the LP cell was constructed from the six voltage-dependent currents, a voltage-independent leak current il, a Ca2+ buffering system, and the membrane capacitance. 3. The behavior of the model LP neuron was compared with that of the biological neuron by simulating physiological experiments carried out in both voltage-clamp and current-clamp modes. The model and biological neurons show similar action-potential shapes, durations, steady-state current-voltage (I-V) curves, and respond to injected current in a comparable way.

Contribution of individual ionic currents to activity of a model stomatogastric ganglion neuron.

1. The behavior of the mathematical model for the lateral pyloric (LP) neuron of the crustacean stomatogastric ganglion (STG) developed in the previous paper was further studied. 2. The action of proctolin, a neuromodulatory peptide that acts directly on the LP neuron, was modeled. The effect of the proctolin-activated current (iproc) on the model neuron mimics the effects of proctolin on the isolated biological LP neuron. The depolarization and increased frequency of firing seen when iproc is activated are associated with changes in the relative contributions of the delayed rectifier (id) and the Ca(2+)-activated outward current (io(Ca] to the repolarization phase of the action potential. 3. The effects of turning off the A-current (iA) in the model were compared with those obtained by pharmacologically blocking iA in the biological neuron. iA appears to regulate action-potential frequency as well as postinhibitory rebound activity. 4. The role of iA on the rhythmic activity of the cell was studied by modifying several of its parameters while periodically activating a simulated synaptically activated conductance, isyn. 5. The effects of manipulations of the maximal conductances (g) for id and io(Ca) were studied. id strongly influences action-potential frequency, whereas io(Ca) strongly influences action-potential duration. 6. Modifications of the maximal conductance of the inward Ca2+ current (iCa) were compared with the effects of blocking iCa in the real cell. 7. The role of the hyperpolarization-activated inward current (ih) during ongoing rhythmic activity was assessed by periodically activating isyn while modifying ih.

Allosteric effects of Mg2+ on the gating of Ca2+-activated K+ channels from mammalian skeletal muscle.

Ca2+-activated K+ channels from rat muscle transverse tubule membranes were inserted into planar phospholipid bilayers, and the activation of these channels by Ca2+ was studied. On the cytoplasmic side of the channel, calcium ions (in the range 10-100 mumol l-1) increase the opening probability of the channel in a graded way. This 'activation curve' is sigmoid, with an average Hill coefficient of about 2. Magnesium ions, in the range 1-10 mmol l-1, increase the apparent affinity of the channel for Ca2+ and greatly enhance the sigmoidicity of the Ca2+ activation curve. In the presence of 10 mmol l-1 Mg2+, the Hill coefficient for Ca2+ activation is about 4.5. This effect depends upon Mg2+ concentration but not upon applied voltage. Mg2+ is effective only when added to the cytoplasmic side of the channel. The results argue that this high-conductance, Ca2+-activated K+ channel contains at least six Ca2+-binding sites involved in the activation process.

The innervation of the pyloric region of the crab, Cancer borealis: homologous muscles in decapod species are differently innervated.

The muscles of the pyloric region of the stomach of the crab, Cancer borealis, are innervated by motorneurons found in the stomatogastric ganglion (STG). Electrophysiological recording and stimulating techniques were used to study the detailed pattern of innervation of the pyloric region muscles. Although there are two Pyloric Dilator (PD) motorneurons in lobsters, previous work reported four PD motorneurons in the crab STG (Dando et al. 1974; Hermann 1979a, b). We now find that only two of the crab PD neurons innervate muscles homologous to those innervated by the PD neurons in the lobster, Panulirus interruptus. The remaining two PD neurons innervate muscles that are innervated by pyloric (PY) neurons in P. interruptus. The innervation patterns of the Lateral Pyloric (LP), Ventricular Dilator (VD), Inferior Cardiac (IC), and PY neurons were also determined and compared with those previously reported in lobsters. Responses of the muscles of the pyloric region to the neurotransmitters, acetylcholine (ACh) and glutamate, were determined by application of exogenous cholinergic agonists and glutamate. The effect of the cholinergic antagonist, curare, on the amplitude of the excitatory junctional potentials (EJPs) evoked by stimulation of the pyloric motor nerves was measured. These experiments suggest that the differences in innervation pattern of the pyloric muscles seen in crab and lobsters are also associated with a change in the neurotransmitter active on these muscles. Possible implications of these findings for phylogenetic relations of decapod crustaceans and for the evolution of neural circuits are discussed.