Robert C. Elson

Synchronous Behavior of Two Coupled Biological Neurons

We report experimental studies of synchronization phenomena in a pair of biological neurons that interact through naturally occurring, electrical coupling. When these neurons generate irregular bursts of spikes, the natural coupling synchronizes slow oscillations of membrane potential, but not the fast spikes. By adding artificial electrical coupling we studied transitions between synchrony and asynchrony in both slow oscillations and fast spikes. We discuss the dynamics of bursting and synchronization in living neurons with distributed functional morphology. [S0031-9007(98)08008-9] The dynamics of many neural ensembles such as central pattern generators (CPGs) or thalamo-cortical circuits pose questions related to cooperative behavior of neurons. Individual neurons may show irregular behavior [1], while ensembles of different neurons can synchronize in order to process biological information [2] or to produce regular, rhythmical activity [3]. How do the irregular neurons synchronize? How do they inhibit noise and intrinsic fluctuations? What parameters of the ensemble are responsible for such synchronization and regularization? Answers to these and similar questions may be found through experiments that enable one to follow qualitatively the cooperative dynamics of neurons as intrinsic and synaptic parameters are varied. Despite their interest, these problems have not received extensive study. Results of such an experiment for a minimal ensemble of two coupled, living neurons are reported in this communication. The experiment was carried out on two electrically coupled neurons (the pyloric dilators, PD) from the pyloric CPG of the lobster stomatogastric ganglion [3]. Individually, these neurons can generate spiking-bursting activity that is irregular and seemingly chaotic. This activity pattern can be altered by injecting dc current (I1 and I2) into the neurons; see Fig. 1. In parallel to their natural coupling, we added artificial coupling by a dynamic current clamp device [7]. Varying these control parameters (offset current and artificial coupling), we found the following regimes of cooperative behavior. Natural coupling produces state-dependent synchronization; see Fig. 2. (i) When depolarized by positive dc current, both neurons fire a continuous pattern of synchronized spikes (Fig. 2d). (ii) With little or no applied current, the neurons fire spikes in irregular bursts: now the slow oscillations are well synchronized while spikes are not (Fig. 2a). Changing the magnitude and sign of electrical coupling restructures the cooperative dynamics. (iii) Increasing the strength of coupling produces complete synchronization of both irregular slow oscillations and fast spikes (see below). (iv) Compensating the natural coupling leads to the onset

Extended dynamic clamp: controlling up to four neurons using a single desktop computer and interface

The dynamic clamp protocol allows an experimenter to simulate the presence of membrane conductances in, and synaptic connections between, biological neurons. Existing protocols and commercial ADC/DAC boards provide ready control in and between < or =2 neurons. Control at >2 sites is desirable when studying neural circuits with serial or ring connectivity. Here, we describe how to extend dynamic clamp control to four neurons and their associated synaptic interactions, using a single IBM-compatible PC, an ADC/DAC interface with two analog outputs, and an additional demultiplexing circuit. A specific C++ program, DYNCLAMP4, implements these procedures in a Windows environment, allowing one to change parameters while the dynamic clamp is running. Computational efficiency is increased by varying the duration of the input-output cycle. The program simulates < or =8 Hodgkin-Huxley-type conductances and < or =18 (chemical and/or electrical) synapses in < or =4 neurons and runs at a minimum update rate of 5 kHz on a 450 MHz CPU. (Increased speed is possible in a two-neuron version that does not need auxiliary circuitry). Using identified neurons of the crustacean stomatogastric ganglion, we illustrate on-line parameter modification and the construction of three-member synaptic rings.

Reliable circuits from irregular neurons: A dynamical approach to understanding central pattern generators

Central pattern generating neurons from the lobster stomatogastric ganglion were analyzed using new nonlinear methods. The LP neuron was found to have only four or five degrees of freedom in the isolated condition and displayed chaotic behavior. We show that this chaotic behavior could be regularized by periodic pulses of negative current injected into the neuron or by coupling it to another neuron via inhibitory connections. We used both a modified Hindmarsh-Rose model to simulate the neurons behavior phenomenologically and a more realistic conductance-based model so that the modeling could be linked to the experimental observations. Both models were able to capture the dynamics of the neuron behavior better than previous models. We used the Hindmarsh-Rose model as the basis for building electronic neurons which could then be integrated into the biological circuitry. Such neurons were able to rescue patterns which had been disabled by removing key biological neurons from the circuit.

Modeling observed chaotic oscillations in bursting neurons: the role of calcium dynamics and IP 3

Abstract. Chaotic bursting has been recorded in synaptically isolated neurons of the pyloric central pattern generating (CPG) circuit in the lobster stomatogastric ganglion. Conductance-based models of pyloric neurons typically fail to reproduce the observed irregular behavior in either voltage time series or state-space trajectories. Recent suggestions of Chay [Biol Cybern 75: 419–431] indicate that chaotic bursting patterns can be generated by model neurons that couple membrane currents to the nonlinear dynamics of intracellular calcium storage and release. Accordingly, we have built a two-compartment model of a pyloric CPG neuron incorporating previously described membrane conductances together with intracellular Ca2+ dynamics involving the endoplasmic reticulum and the inositol 1,4,5-trisphosphate receptor IP3R. As judged by qualitative inspection and quantitative, nonlinear analysis, the irregular voltage oscillations of the model neuron resemble those seen in the biological neurons. Chaotic bursting arises from the interaction of fast membrane voltage dynamics with slower intracellular Ca2+ dynamics and, hence, depends on the concentration of IP3. Despite the presence of 12 independent dynamical variables, the model neuron bursts chaotically in a subspace characterized by 3–4 active degrees of freedom. The critical aspect of this model is that chaotic oscillations arise when membrane voltage processes are coupled to another slow dynamic. Here we suggest this slow dynamic to be intracellular Ca2+ handling.

State-Dependent Effects of Na Channel Noise on Neuronal Burst Generation

We explore the effects of stochastic sodium (Na) channel activation on the variability and dynamics of spiking and bursting in a model neuron. The complete model segregates Hodgin-Huxley-type currents into two compartments, and undergoes applied current-dependent bifurcations between regimes of periodic bursting, chaotic bursting, and tonic spiking. Noise is added to simulate variable, finite sizes of the population of Na channels in the fast spiking compartment.During tonic firing, Na channel noise causes variability in interspike intervals (ISIs). The variance, as well as the sensitivity to noise, depend on the models biophysical complexity. They are smallest in an isolated spiking compartment; increase significantly upon coupling to a passive compartment; and increase again when the second compartment also includes slow-acting currents. In this full model, sufficient noise can convert tonic firing into bursting.During bursting, the actions of Na channel noise are state-dependent. The higher the noise level, the greater the jitter in spike timing within bursts. The noise makes the burst durations of periodic regimes variable, while decreasing burst length duration and variance in a chaotic regime. Na channel noise blurs the sharp transitions of spike time and burst length seen at the bifurcations of the noise-free model. Close to such a bifurcation, the burst behaviors of previously periodic and chaotic regimes become essentially indistinguishable.We discuss biophysical mechanisms, dynamical interpretations and physiological implications. We suggest that noise associated with finite populations of Na channels could evoke very different effects on the intrinsic variability of spiking and bursting discharges, depending on a biological neurons complexity and applied current-dependent state. We find that simulated channel noise in the model neuron qualitatively replicates the observed variability in burst length and interburst interval in an isolated biological bursting neuron.

Dynamics of two electrically coupled chaotic neurons: Experimental observations and model analysis

Abstract. Conductance-based models of neurons from the lobster stomatogastric ganglion (STG) have been developed to understand the observed chaotic behavior of individual STG neurons. These models identify an additional slow dynamical process – calcium exchange and storage in the endoplasmic reticulum – as a biologically plausible source for the observed chaos in the oscillations of these cells. In this paper we test these ideas further by exploring the dynamical behavior when two model neurons are coupled by electrical or gap junction connections. We compare in detail the model results to the laboratory measurements of electrically-coupled neurons that we reported earlier. The experiments on the biological neurons varied the strength of the effective coupling by applying a parallel, artificial synapse, which changed both the magnitude and polarity of the conductance between the neurons. We observed a sequence of bifurcations that took the neurons from strongly synchronized in-phase behavior, through uncorrelated chaotic oscillations to strongly synchronized – and now regular – out-of-phase behavior. The model calculations reproduce these observations quantitatively, indicating that slow subcellular processes could account for the mechanisms involved in the synchronization and regularization of the otherwise individual chaotic activities.

Self-regularization of chaos in neural systems: experimental and theoretical results

The results of neurobiological studies in both vertebrates and invertebrates lead to the general question: How is a population of neurons, whose individual activity is chaotic and uncorrelated able to form functional circuits with regular and stable behavior? What are the circumstances which support these regular oscillations? What are the mechanisms that promote this transition? We address these questions using our experimental and modeling studies describing the behavior of groups of spiking-bursting neurons. We show that the role of inhibitory synaptic coupling between neurons is crucial in the self-control of chaos.

Basic Principles for Generating Motor Output in the Stomatogastric Ganglion

Abstract: The lobster stomatogastric ganglion contains 30 neurons and when modulated can produce two distinct rhythmic motor patterns‐the gastric mill and the pyloric. The complete neural circuitry underlying both patterns is well known. Without modulatory input no patterns are produced, and the neurons fire tonically or are silent. When neuromodulators are released into the ganglion from specific neurons or are delivered as hormones, the properties of the neurons and synapses change dramatically and modulator‐specific gastric mill and pyloric patterns are produced. In general the rhythmicity derives from the induced burstiness of the neurons, and the pattern from the strengths of the electrical and chemical synapses. The organized activity can be traced to a marked reduction of chaotic activity in individual neurons when they shift from the unmodulated to the modulated state.

Neuroanatomy of a crayfish thoracic ganglion: Sensory and motor roots of the walking-leg nerves and possible homologies with insects

The internal organization of the third and fourth thoracic ganglia of the crayfish, Pacifastacus leniusculus, was studied in serial sections stained with osmium ethyl gallate. The aims were 1) to provide an anatomical framework for studies of sensorimotor integration in the walking system and 2) to explore possible homologies with abdominal ganglia in crayfish and with the thoracic ganglia of insects. Crayfish thoracic ganglia show several intersegmental homologies with the unfused ganglia of the abdominal nervous system: 1) Longitudinal tracts and dorsal commissures are arranged similarly, allowing use of the same nomenclature. 2) Paired lateral neuropils are located dorsolaterally and contain many large neurites including those of leg motor neurons and of nonspiking, proprioceptive afferents from the basal limb joints. They resemble the lateral neuropils of abdominal ganglia. 3) Neuropil lying more ventrally is fine textured and receives projections from other leg afferents. This ventral neuropil resembles the “horseshoe neuropil” of abdominal ganglia. The functional implications of this organization are discussed.

Noise, transient dynamics, and the generation of realistic interspike interval variation in square-wave burster neurons.

First return maps of interspike intervals for biological neurons that generate repetitive bursts of impulses can display stereotyped structures (neuronal signatures). Such structures have been linked to the possibility of multicoding and multifunctionality in neural networks that produce and control rhythmical motor patterns. In some cases, isolating the neurons from their synaptic network reveals irregular, complex signatures that have been regarded as evidence of intrinsic, chaotic behavior. We show that incorporation of dynamical noise into minimal neuron models of square-wave bursting (either conductance-based or abstract) produces signatures akin to those observed in biological examples, without the need for fine tuning of parameters or ad hoc constructions for inducing chaotic activity. The form of the stochastic term is not strongly constrained and can approximate several possible sources of noise, e.g., random channel gating or synaptic bombardment. The cornerstone of this signature generation mechanism is the rich, transient, but deterministic dynamics inherent in the square-wave (saddle-node and homoclinic) mode of neuronal bursting. We show that noise causes the dynamics to populate a complex transient scaffolding or skeleton in state space, even for models that (without added noise) generate only periodic activity (whether in bursting or tonic spiking mode).