Regulation of rhythmic activity in the stomatogastric ganglion of decapod crustaceans

Neuronal networks produce reliable functional output throughout the lifespan of an animal despite ceaseless molecular turnover and a constantly changing environment. The cellular and molecular mechanisms underlying the ability of these networks to maintain functional stability remain poorly understood. Central pattern generating circuits produce a stable, predictable rhythm, making them ideal candidates for studying mechanisms of activity maintenance. By identifying and characterizing the regulators of activity in small neuronal circuits, we not only obtain a clearer understanding of how neural activity is generated, but also arm ourselves with knowledge that may eventually be used to improve medical care for patients whose normal nervous system activity has been disrupted through trauma or disease. We utilize the pattern-generating pyloric circuit in the crustacean stomatogastric nervous system to investigate the general scientific question: How are specific aspects of rhythmic activity regulated in a small neuronal network? The first aim of this thesis poses this question in the context of a single neuron. We used a single-compartment model neuron database to investigate whether co-regulation of ionic conductances supports the maintenance of spike phase in rhythmically bursting “pacemaker” neurons. The second aim of the project extends the question to a network context. Through a combination of computational and electrophysiology studies, we investigated how the intrinsic membrane conductances of the pacemaker neuron influence its response to synaptic input within the framework of the Phase Resetting Curve (PRC). The third aim of the project further extends the question to a systems-level context. We examined how ambient temperatures affect the stability of the pyloric rhythm in the intact, behaving animal. The results of this work have furthered our understanding of the principles underlying the long-term stability of neuronal network function.Ph.D

Dynamics of phase locking in neuronal networks in the presence of synaptic plasticity

The behavior generated by neuronal networks depends on the phase relationships of its individual neurons. Observed phases result from the combined effects of individual cells and synaptic connections whose properties change dynamically. The properties of individual cells and synapses can often be characterized by driving the cell or synapse with inputs that arrive at different phases or frequencies, thus producing a feed-forward description of these properties. In this study, a recurrent network of two oscillatory neurons that are coupled with reciprocal synapses is considered. Feed-forward descriptions of the phase response curves of the neurons and the short-term synaptic plasticity properties are used to define Poincar´e maps for the activity of the network. The fixed points of these maps correspond to the phase locked modes of the network. These maps allow analysis of the dependence of the resulting network activity on the properties of network components. Using a combination of analysis and simulations, how various parameters of the model affect the existence and stability of phase-locked solutions is shown. It is also shown that synaptic plasticity provides flexibility and supports phase maintenance in networks. Conditions are found on the synaptic plasticity profiles and the phase response curves of the neurons for the network to be able to maintain a constant firing period, while varying the relative activity phase of the neurons or vice versa. Synaptic plasticity is shown to yield bistable phase locking modes. These results are geometrically demonstrated using a generalization to cobwebbing for two dimensional maps. Type I neurons modeled with Morris-Lecar and Quadratic Integrate-and-Fire are used to estimate the predictive power of the analytical results; however, the results hold in general. The properties of the Negative-Leak model are also studied; a recent conductance-based model which is obtained by replacing a regenerative inward current with a negative-slope-conductance linear current. The map methods are extended to analyze networking properties of Negative-Leak neurons by including burst response curves. Finally, geometric singular perturbation techniques are applied to analyze how a hyperpolarization-activated inward current contributes to the generation of oscillations in this model. This work introduces a general method to determine how changes in the phase response curves or synaptic dynamics affect phase locking in a recurrent network which can be generalized to study larger networks

Mechanisms of Multistability in Neuronal Models

Multistability is a fundamental attribute of the dynamics of neuronal systems under normal and pathological conditions. The mechanism of bistability of bursting and silence is not well understood and to our knowledge has not been experimentally recorded in single neurons. We considered four models. Two of them described the dynamics of a leech heart interneuron: the canonical model and a low-dimensional model. The other two models described mammalian pacemakers from the respiratory center. We investigated the low-dimensional model and identified six different types of multistability of dynamical regimes. We described six generic mechanisms underlying the co-existence of oscillatory and silent regimes. The mechanisms are based either on a saddle equilibrium or a saddle periodic orbit. The stable manifold of the saddle equilibrium or the saddle orbit sets the threshold between the regimes. In the two models of the leech interneuron the range of the controlling parameters supporting the co-existence of bursting and silence is limited by the Andronov-Hopf and homoclinic bifurcations (Malashchenko, Master Thesis 2007). The bistability was found in a narrow range of the leak currents\u27 parameters. Here, we introduced a propensity index to bistability as the width of the range on a bifurcation diagram; we investigated how the propensity index was affected by modifications of the ionic currents, and found that conductances of only two currents substantially affected the index. The increase of the conductance of the hyperpolarization-activated current, Ih, and the reduction of the fast Ca2+ current, ICaF, notably increased the propensity index. These findings define modulatory conditions under which we suggest the bistability of bursting and silence could be experimentally revealed in leech heart interneurons. We hypothesize that this mechanism could be commonly found in a large variety of neuronal models. We applied our techniques to models of vertebrate neurons controlling respiratory rhythm, which represent two types of inspiratory pacemakers of the Pre-Bӧtzinger Complex. We showed that both types of neurons could exhibit bistability of bursting and silence in accordance with the mechanism which we described

Animal-to-animal variability in the phasing of the crustacean cardiac motor pattern: An experimental and computational analysis

The cardiac ganglion (CG) of Homarus americanus is a central pattern generator that consists of two oscillatory groups of neurons: small cells (SCs) and large cells (LCs). We have shown that SCs and LCs begin their bursts nearly simultaneously but end their bursts at variable phases. This variability contrasts with many other central pattern generator systems in which phase is well maintained. To determine both the consequences of this variability and how CG phasing is controlled, we modeled the CG as a pair of Morris-Lecar oscillators coupled by electrical and excitatory synapses and constructed a database of 15,000 simulated networks using random parameter sets. These simulations, like our experimental results, displayed variable phase relationships, with the bursts beginning together but ending at variable phases. The model suggests that the variable phasing of the pattern has important implications for the functional role of the excitatory synapses. In networks in which the two oscillators had similar duty cycles, the excitatory coupling functioned to increase cycle frequency. In networks with disparate duty cycles, it functioned to decrease network frequency. Overall, we suggest that the phasing of the CG may vary without compromising appropriate motor output and that this variability may critically determine how the network behaves in response to manipulations. © 2013 the American Physiological Society

The Utility of Phase Models in Studying Neural Synchronization

Synchronized neural spiking is associated with many cognitive functions and thus, merits study for its own sake. The analysis of neural synchronization naturally leads to the study of repetitive spiking and consequently to the analysis of coupled neural oscillators. Coupled oscillator theory thus informs the synchronization of spiking neuronal networks. A crucial aspect of coupled oscillator theory is the phase response curve (PRC), which describes the impact of a perturbation to the phase of an oscillator. In neural terms, the perturbation represents an incoming synaptic potential which may either advance or retard the timing of the next spike. The phase response curves and the form of coupling between reciprocally coupled oscillators defines the phase interaction function, which in turn predicts the synchronization outcome (in-phase versus anti-phase) and the rate of convergence. We review the two classes of PRC and demonstrate the utility of the phase model in predicting synchronization in reciprocally coupled neural models. In addition, we compare the rate of convergence for all combinations of reciprocally coupled Class I and Class II oscillators. These findings predict the general synchronization outcomes of broad classes of neurons under both inhibitory and excitatory reciprocal coupling.Comment: 18 pages, 5 figure

Stochastic Neural Oscillators

We seek to understand collective neural phenomena such as synchronization, correlation transfer and information propagation in the presence of additive broadband noise. Our findings contribute to a growing scientific literature that has shown that uncoupled type II neural oscillators synchronize more readily under the influence of noisy input currents than do type I oscillators. We use stochastic phase reduction and regular perturbations to show that the type II phase response curve (PRC) minimizes the Lyapunov exponent. We also derived expressions for the correlation between output spike trains using the steady state probability distribution of the phase difference between oscillators. Over short time scales we find that, for a given level of input correlation, spike trains from type II membranes show greater output correlation than from type I. However, we find the reverse is true for oscillators observed over long time scales, in agreement with recent results. Previous investigations of specific ion channels have generated insights into mechanisms by which neuromodulators can switch the bifurcation structure of an oscillator. In a similar vein, we undertake an exploratory and qualitative study of the influence of the A-type potassium current on spike train synchrony, correlation transfer and information content in a reduced 3-dimensional neuron model that exhibits both type I and type II oscillations, as well as a bifurcation to bursting dynamics. Using the local Lyapunov exponent in place of the PRC as a measure of sensitivity to perturbation, we find that the region of bursting dynamics shows prolonged elevated sensitivity during the inter-burst interval. In the oscillatory regime, a similar phenomenon occurs near the bifurcation to bursting, and we see that the magnitude of the PRC grows markedly as this border is approached. Furthermore, we find that the highly sensitive dynamics result in a combination of spike time reliability and increased ISI variability that produces greater mutual information between a spike train and a broadband input signal. These findings suggest that there may be an optimal balance of dynamical sensitivity and stability that maximizes the computationally relevant statistical dependence between input signals and output spike trains

A Mechanism of Co-Existence of Bursting and Silent Regimes of Activities of a Neuron

The co-existence of bursting activity and silence is a common property of various neuronal models. We describe a novel mechanism explaining the co-existence of and the transition between these two regimes. It is based on the specific homoclinic and Andronov-Hopf bifurcations of the hyper- and depolarized steady states that determine the co-existence domain in the parameter space of the leech heart interneuron models: canonical and simplified. We found that a sub-critical Andronov-Hopf bifurcation of the hyperpolarized steady state gives rise to small amplitude sub-threshold oscillations terminating through the secondary homoclinic bifurcation. Near the corresponding boundary the system can exhibit long transition from bursting oscillations into silence, as well as the bi-stability where the observed regime is determined by the initial state of the neuron. The mechanism found is shown to be generic for the simplified 4D and the original 14D leech heart interneuron models