Biomedical subjects
Publications and source records attributed to E Marder.
We present a scheme for systematically reducing the number of differential equations required for biophysically realistic neuron models. The techniques are general, are designed to be applicable to a large set of such models and retain in the reduced system as high a degree of fidelity to the original system as possible. As examples, we provide reductions of the Hodgkin-Huxley system and the A-current model of Connor et al. (1977).
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.
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.
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.
1. We use an electronic circuit to artificially electrically couple neurons. 2. Strengthening the coupling between an oscillating neuron and a hyperpolarized, passive neuron can either increase or decrease the frequency of the oscillator depending on the properties of the oscillator. 3. The result of electrically coupling two neuronal oscillators depends on the membrane potentials, intrinsic properties of the neurons, and the coupling strength. 4. The interplay between chemical inhibitory synapses and electrical synapses can be studied by creating both chemical and electrical synapses between two cultured neurons and by artificially strengthening the electrical synapse between the ventricular dilator and one pyloric dilator neuron of the stomatogastric ganglion.
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.
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.
The lateral gastric (LG) motor neuron of the stomatogastric nervous system of the crab Cancer borealis has a large soma in the stomatogastric ganglion (STG). The LG motor neuron makes inhibitory synaptic connections within the neuropil of the STG, and also projects to the periphery, where it innervates a series of muscles that control the movements of the lateral teeth of the gastric mill. The LG motor neuron has a spike initiation zone close to its neuropilar integrative regions, from which spikes propagate orthodromically to the muscles. Additionally, under certain conditions, the LG neuron can initiate spikes at peripheral axonal sites that can be 0.5-2.0 cm from the STG. Peripherally initiated spikes propagate antidromically into the STG and also propagate to the muscle. The peripheral spike initiation zones are often active in combined preparations in which the muscles are left attached. When the muscles are removed, depolarization of the LG soma together with 5-HT applied to the motor nerve also evokes peripheral spike initiation. At a given 5-HT concentration, the duration of the trains of antidromic spikes can be controlled by current injection into the soma, suggesting the presence of a slow voltage-dependent conductance in the LG axon. The antidromic spikes contribute to lengthening of the duration of contraction in some of the muscles innervated by the LG, but do not evoke IPSPs onto LG follower neurons. Thus, the LG neuron can send different signals to its peripheral and central targets.
Pigment-dispersing hormone (PDH) acts to disperse pigments within the chromatophores of crustaceans. Using an antibody raised against beta-PDH from the fiddler crab Uca pugilator, we characterized the distribution of beta-PDH-like immunoreactivity in the stomatogastric nervous system of five decapod crustaceans: the crabs, Cancer borealis and Cancer antennarius, the lobsters, Panulirus interruptus and Homarus americanus, and the crayfish, Procambarus clarkii. No somata were stained in the stomatogastric ganglion (STG) or the esophageal ganglion in any of these species. Intense PDH-like staining was seen in the neuropil of the STG in P. interruptus only. In all 5 species, cell bodies, processes, and neuropil within the paired circumesophageal ganglia (CGs) showed PDH-like staining; the pattern of this staining was unique for each species. In each CG, the beta-PDH antibody stained: 1 large cell in C. borealis; 3 small to large cells in C. antennarius; 3-8 medium cells in P. clarkii; 1-4 small cells in H. americanus; and 13-17 small cells in P. interruptus. The smallest cell in each CG in C. antennarius sends its axon, via the inferior esophageal nerves, into the opposite CG; this pair of cells, not labeled in the other species studied, may act as bilateral coordinators of sensory or motor function. These diverse staining patterns imply some degree of evolutionary diversity among these crustaceans. A beta-PDH-like peptide may act as a neuromodulator of the rhythms produced by the stomatogastric nervous system of decapod crustaceans.
Rhythmic movements in animals are controlled by neuronal circuits that generate repeating motor patterns. Recent research is providing new insights into the cellular mechanisms by which central pattern generating circuits are reorganized by sensory, central and hormonal inputs to allow the animal to respond flexibly to varying environmental and behavioral demands.
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1. The stomatogastric ganglion (STG) of decapod crustaceans has been characterized by its production of two motor patterns, the gastric mill rhythm and the pyloric rhythm. The period of the gastric rhythm is typically 5-10 s, whereas the period of the pyloric rhythm is approximately 1 s. 2. In the STG of the crab, Cancer borealis, we find routinely that many motor neurons are active in time with both the pyloric and gastric rhythms. We rigorously identified the motor neurons according to the muscles they innervate. Some neurons usually classified as members of the pyloric network can be active in time with the gastric rhythm. All of the gastric motor neurons except the dorsal gastric (DG) neuron can generate pyloric-timed firing patterns. 3. Two motor neurons innervate muscles found in several different regions of the stomach. The inferior cardiac (IC) neuron, usually considered part of the pyloric network, innervates cardiac sac, gastric mill, and pyloric muscles. The lateral posterior gastric (LPG) neurons innervate muscles of both the gastric mill and the pyloric chamber. 4. These data show that the gastric and pyloric networks in the crab are not separate groups of neurons that independently generate two different rhythmic behaviors. Rather, these neurons together provide a synaptically connected pool of neurons from which many different pattern-generating circuits can be assembled, under different physiological conditions.
Stomatogastric nervous systems of the shrimp, Palaemon serratus, were stained with antisera raised against the peptide FMRFamide. FMRFamide-like immunoreactivity was found in fibers in the input nerve to the stomatogastric ganglion (STG), in several STG somata, in dense neuropil in the STG, in the motor nerves that innervate the dilator muscles of the pyloric region, but not in the pyloric dilator (PD) motor neurons. FMRFamide and several FMRFamide-like peptides elicited sequences of rhythmic depolarizations and contractions of the pyloric dilator muscle. As peptide concentrations were increased, a discrete threshold for contraction was found, above which contractions were initiated with a decreasing latency in an all-or-none fashion. Muscles stopped rhythmically contracting after many seconds to several minutes of activity; the duration of spontaneous oscillatory activity in peptide was proportional to the concentration of applied peptide. In the absence of peptide, each motor neuron discharge evoked small graded muscle contractions. During peptide-induced oscillations, motor neuron activity did not always entrain muscle oscillations. After spontaneous oscillations had stopped, when the motor neurons were stimulated in the presence of the peptide, each motor neuron burst evoked large amplitude contractions as a result of the peptide-induced regenerative properties of the muscle membrane.
Neurons with oscillatory properties are a common feature of the nervous system, but little is known about how neural oscillators shape the behavior of neuronal networks or how network interactions influence the properties of neural oscillators. Mathematical models are used to examine the effect of electrically coupling an oscillatory neuron to a second neuron that is either silent or tonically firing. Models of oscillatory neurons with varying degrees of complexity show that this coupling can either increase or decrease the frequency of an oscillator, depending on its membrane potential wave form, the state of the neuron to which it is coupled, and the strength of the coupling. Thus, electrical coupling provides a flexible mechanism for modifying the behavior of an oscillatory neural network.
Animals make many different movements as circumstances dictate. These movements often involve the coordination of several neural networks, the output of which can be changed by modulatory substances. Here we report that the neuropeptide red pigment concentrating hormone modulates the interactions between two rhythmic pattern-generating networks in the lobster stomatogastric nervous system. Red pigment concentrating hormone markedly enhances the amplitude of synaptic interactions between elements of two pattern-generating networks--the cardiac sac and the gastric mill. Consequently, two networks operating under some circumstances virtually independently can be fused into one functional unit operating differently from either of the two original networks. These results show how a neuropeptide can alter the functional configuration of a neural network so that widely disparate outputs can be produced by the same neurons.
We present a model for a conditional bursting neuron consisting of five conductances: Hodgkin-Huxley type time- and voltage-dependent Na+ and K+ conductances, a calcium activated voltage-dependent K+ conductance, a calcium-inhibited time- and voltage-dependent Ca++ conductance, and a leakage Cl- conductance. With an initial set of parameters (version S), the model shows a hyperpolarized steady-state membrane potential at which the neuron is silent. Increasing gNa and decreasing gCl, where gi is the maximal conductance for species i, produces bursts of action potentials (Burster N). Alternatively, an increase in gCa produces a different bursting state (Burster C). The two bursting states differ in the periods and amplitudes of their bursting pacemaker potentials. They show different steady-state I-V curves under simulated voltage-clamp conditions; in simulations that mimic a steady-state I-V curve taken under experimental conditions only Burster N shows a negative slope resistance region. Model C continues to burst in the presence of TTX, while bursting in Model N is suppressed in TTX. Hybrid models show a smooth transition between the two states.
A current model proposes that memory consists of two functionally separate systems that have different neurological substrates. Declarative memory appears to be dependent on the diencephalic medial temporal lobe system whereas some speculate that the basal ganglia may be a neurological substrate for procedural memory. This study tested the role of the basal ganglia in regulating different types of procedural skills by comparing performance on a motor and a visuoperceptual skill learning task. Twenty Parkinson's (PD) patients and 20 normal control subjects performed two procedural learning tasks (rotary pursuit and mirror reading) and one declarative learning task (paired associates) over 3 days. The results showed that PD patients were not impaired on mirror reading or paired associate learning. On rotary pursuit, performance levels on day 1 were similar between groups, but the PD group showed less improvement across days than controls. However, only patients with more advanced symptoms of PD showed impaired rotary pursuit learning, and this could not be attributed directly to deficits in primary motor or general cognitive function. These findings suggest that the underlying processes/procedures for procedural learning are specific to the task, and are supported by different neuroanatomical systems.