The Role of Plasma Membrane ATPase Pumps in the Regulation of Rhythmic Activity in Electrically Excitable Cells

Membrane bound ion pumps have long been studied in a housekeeping role, and it is well known that they play a major part in creating the ionic gradients which determine the electrical excitability in a cell. Recent work has begun to highlight other, more direct roles for ion pumps in rhythm generation and information processing. As many pumps obtain energy for active ion transport from adenosine triphosphate (ATP) hydrolysis, they can exchange ions in an electrically asymmetric manner, generating an outward current, which along with ion channel currents, drives the membrane potential of the cell. Membrane potential is a major determining characteristic for how information is transferred between neurons, and so in persistently active excitable cells, pumps can provide a considerable contribution to neuron dynamics. Specialized networks of neurons and non-neural cells which drive rhythmic behaviors such as breathing and locomotion, must robustly produce useful patterns for the animal under dynamic behavioral goals in a highly variable environment. Here we will focus on two well-studied classes of ATPase pumps (the plasma membrane calcium ATPase pump (PMCA) and the sodium-potassium ATPase pump (Na+/K+ pump)) and investigate the role of these pumps in two rhythm generating biological subsystems with a combination of modeling and experimental approaches. In a model of a leech heartbeat central pattern generator, we demonstrate how the neuromodulator myomodulin can regulate the temporal properties of rhythm generation through effects on the hyperpolarization-activated current and the Na+/K+ pump current, and discuss the benefits of modulators which target multiple currents. With this model, we also show how synaptic inhibition can support a functional pattern when pump current is downregulated. Then, in a model of interstitial cells of Cajal (ICC) in the muscular syncytium of the intestinal walls, we demonstrate that due to the importance of complex intracellular calcium oscillations in the generation of ICC rhythms, the PMCA pump can play a major role in regulating the temporal properties of rhythm generation. We discuss rhythm generation mechanisms in both systems and predict parameter domains of multistability which correspond to both functional and pathological states of rhythm generation

A Role for Compromise: Synaptic Inhibition and Electrical Coupling Interact to Control Phasing in the Leech Heartbeat CPG

How can flexible phasing be generated by a central pattern generator (CPG)? To address this question, we have extended an existing model of the leech heartbeat CPG's timing network to construct a model of the CPG core and explore how appropriate phasing is set up by parameter variation. Within the CPG, the phasing among premotor interneurons switches regularly between two well defined states – synchronous and peristaltic. To reproduce experimentally observed phasing, we varied the strength of inhibitory synaptic and excitatory electrical input from the timing network to follower premotor interneurons. Neither inhibitory nor electrical input alone was sufficient to produce proper phasing on both sides, but instead a balance was required. Our model suggests that the different phasing of the two sides arises because the inhibitory synapses and electrical coupling oppose one another on one side (peristaltic) and reinforce one another on the other (synchronous). Our search of parameter space defined by the strength of inhibitory synaptic and excitatory electrical input strength led to a CPG model that well approximates the experimentally observed phase relations. The strength values derived from this analysis constitute model predictions that we tested by measurements made in the living system. Further, variation of the intrinsic properties of follower interneurons showed that they too systematically influence phasing. We conclude that a combination of inhibitory synaptic and excitatory electrical input interacting with neuronal intrinsic properties can flexibly generate a variety of phase relations so that almost any phasing is possible

Control strategies of 3-cell Central Pattern Generator via global stimuli

The study of the synchronization patterns of small neuron networks that control several biological processes has become an interesting growing discipline. Some of these synchronization patterns of individual neurons are related to some undesirable neurological diseases, and they are believed to play a crucial role in the emergence of pathological rhythmic brain activity in different diseases, like Parkinson''s disease. We show how, with a suitable combination of short and weak global inhibitory and excitatory stimuli over the whole network, we can switch between different stable bursting patterns in small neuron networks (in our case a 3-neuron network). We develop a systematic study showing and explaining the effects of applying the pulses at different moments. Moreover, we compare the technique on a completely symmetric network and on a slightly perturbed one (a much more realistic situation). The present approach of using global stimuli may allow to avoid undesirable synchronization patterns with nonaggressive stimuli

Mechanisms of the Coregulation of Multiple Ionic Currents for the Control of Neuronal Activity

An open question in contemporary neuroscience is how neuromodulators coregulate multiple conductances to maintain functional neuronal activity. Neuromodulators enact changes to properties of biophysical characteristics, such as the maximal conductance or voltage of half-activation of an ionic current, which determine the type and properties of neuronal activity. We apply dynamical systems theory to study the changes to neuronal activity that arise from neuromodulation. Neuromulators can act on multiple targets within a cell. The coregulation of mulitple ionic currents extends the scope of dynamic control on neuronal activity. Different aspects of neuronal activity can be independently controlled by different currents. The coregulation of multiple ionic currents provides precise control over the temporal characteristics of neuronal activity. Compensatory changes in multiple ionic currents could be used to avoid dangerous dynamics or maintain some aspect of neuronal activity. The coregulation of multiple ionic currents can be used as bifurcation control to ensure robust dynamics or expand the range of coexisting regimes. Multiple ionic currents could be involved in increasing the range of dynamic control over neuronal activity. The coregulation of multiple ionic currents in neuromodulation expands the range over which biophysical parameters support functional activity

Key Bifurcations of Bursting Polyrhythms in 3-Cell Central Pattern Generators

We identify and describe the key qualitative rhythmic states in various 3-cell network motifs of a multifunctional central pattern generator (CPG). Such CPGs are neural microcircuits of cells whose synergetic interactions produce multiple states with distinct phase-locked patterns of bursting activity. To study biologically plausible CPG models, we develop a suite of computational tools that reduce the problem of stability and existence of rhythmic patterns in networks to the bifurcation analysis of fixed points and invariant curves of a Poincare´ return maps for phase lags between cells. We explore different functional possibilities for motifs involving symmetry breaking and heterogeneity. This is achieved by varying coupling properties of the synapses between the cells and studying the qualitative changes in the structure of the corresponding return maps. Our findings provide a systematic basis for understanding plausible biophysical mechanisms for the regulation of rhythmic patterns generated by various CPGs in the context of motor control such as gait-switching in locomotion. Our analysis does not require knowledge of the equations modeling the system and provides a powerful qualitative approach to studying detailed models of rhythmic behavior. Thus, our approach is applicable to a wide range of biological phenomena beyond motor control

A Codimension-2 Bifurcation Controlling Endogenous Bursting Activity and Pulse-Triggered Responses of a Neuron Model

The dynamics of individual neurons are crucial for producing functional activity in neuronal networks. An open question is how temporal characteristics can be controlled in bursting activity and in transient neuronal responses to synaptic input. Bifurcation theory provides a framework to discover generic mechanisms addressing this question. We present a family of mechanisms organized around a global codimension-2 bifurcation. The cornerstone bifurcation is located at the intersection of the border between bursting and spiking and the border between bursting and silence. These borders correspond to the blue sky catastrophe bifurcation and the saddle-node bifurcation on an invariant circle (SNIC) curves, respectively. The cornerstone bifurcation satisfies the conditions for both the blue sky catastrophe and SNIC. The burst duration and interburst interval increase as the inverse of the square root of the difference between the corresponding bifurcation parameter and its bifurcation value. For a given set of burst duration and interburst interval, one can find the parameter values supporting these temporal characteristics. The cornerstone bifurcation also determines the responses of silent and spiking neurons. In a silent neuron with parameters close to the SNIC, a pulse of current triggers a single burst. In a spiking neuron with parameters close to the blue sky catastrophe, a pulse of current temporarily silences the neuron. These responses are stereotypical: the durations of the transient intervals–the duration of the burst and the duration of latency to spiking–are governed by the inverse-square-root laws. The mechanisms described here could be used to coordinate neuromuscular control in central pattern generators. As proof of principle, we construct small networks that control metachronal-wave motor pattern exhibited in locomotion. This pattern is determined by the phase relations of bursting neurons in a simple central pattern generator modeled by a chain of oscillators

Duty Cycle Maintenance in an Artificial Neuron

Neuroprosthetics is at the intersection of neuroscience, biomedical engineering, and physics. A biocompatible neuroprosthesis contains artificial neurons exhibiting biophysically plausible dynamics. Hybrid systems analysis could be used to prototype such artificial neurons. Biohybrid systems are composed of artificial and living neurons coupled via real-time computing and dynamic clamp. Model neurons must be thoroughly tested before coupled with a living cell. We use bifurcation theory to identify hazardous regimes of activity that may compromise biocompatibility and to identify control strategies for regimes of activity desirable for functional behavior. We construct real-time artificial neurons for the analysis of hybrid systems and demonstrate a mechanism through which an artificial neuron could maintain duty cycle independent of variations in period

Homeostatic compensation and neuromodulation maintain synchronized motor neuron activity in the crustacean cardiac ganglion

Dissertation supervisor: Dr. David J. Schulz.Includes vita.Animals rely on the nervous system to produce appropriate behavior throughout their lives. In sending commands to the musculature for rhythmic motor behaviors such as breathing or walking, neural networks must be stable enough to send a reliable level of drive with the proper temporal coordination. Networks must also be flexible enough to meet changing environmental demands. A network's output ultimately arises from the intrinsic excitability of its constituent neurons and the synaptic connections between them. Interestingly, neurons and networks are able to produce highly conserved output from highly variable underlying intrinsic and synaptic properties. To explore the consequences of this variability, we have used the crustacean cardiac ganglion (CG) which consists of 9 neurons: 4 pacemaker cells that give excitatory input to 5 Large Cell motor neurons (LCs) which are responsible for driving the simultaneous contraction of the musculature that makes up the walls of the animal's single-chambered heart (Alexandrowicz, 1934; Hartline, 1967; Anderson and Cooke, 1971). The intact network can be dissected from the animal in physiological saline and it continues to produce robust, reliable, and rhythmic output (Welsh and Maynard, 1951; Cooke, 2002). LCs have virtually identical synchronized activity, but their intrinsic ionic conductances can be highly variable (Ransdell et al., 2013a). In Chapter 1, we exploit this variability by pharmacologically blocking a subset of their conductances to make LCs hyperexcitable and desynchronize their activity. We find that homeostatic compensation restores synchronized activity and excitability within one hour. This happens via two synergistic mechanisms: the membrane properties of each cell are re-tuned to converge on similar voltage activity, and increased conductance of the gap junctions between the cells helps to buffer away differences in their voltage activity. A separate but related study asked whether naturalistic perturbations of network activity would also result in desynchronization. Neuromodulation provides flexibility in the output of neural networks by altering a subset of their conductances. We hypothesized that this could also cause desynchronization. We found that modulation with serotonin and dopamine both increased the excitability of the CG. Interestingly, serotonin desynchronized the CG, but dopamine did not. We found that dopaminergic modulation directly increases gap junctional conductance. By co-applying these modulators, we found dopamine was able to prevent serotonin from desynchronizing the network without occluding its effects. It was also able to prevent the desynchronization caused by ion channel blockers. Finally, to fully understand the output of LCs, we must recognize that their activity arises not only from their intrinsic properties, but also from their synaptic drive from pacemaker cells. To address how variable this can be from one animal to the next, we analyze the activity of 131 animals taken over the course of approximately 5 years. We use this to address the fundamental question of how variable networks underlying a particular behavior can be across animals. We recognize two distinct classes of pacemaker inputs to LCs, and characterize bursting patterns for both types of pacemaker spike and LC output. We conclude that LCs from different animals receive different temporal patterns of pacemaker drive, which may have important functional implications. We also compare animals from winter and summer months, and find that temperature-independent seasonal effects may explain some of the variance in our data.Includes bibliographical references

Determining how stable network oscillations arise from neuronal and synaptic mechanisms

Many animal behaviors involve the generation of rhythmic patterns and movements. These rhythmic patterns are commonly mediated by neural networks that produce an oscillatory activity pattern, where different neurons maintain a relative phase relationship. This thesis examines the relationships between the cellular and synaptic properties that give rise to stable activity in the form of phase maintenance, across different frequencies in a well-suited model system, the pyloric network of the crab Cancer borealis. The pyloric network has endogenously oscillating ‘pacemaker’ neurons that inhibit ‘follower’ neurons, which in turn feed back onto the pacemaker neurons. The focus of this thesis was to determine the methods by which phase maintenance is achieved in an oscillatory network. This thesis examines the idea that phase maintenance occurs through the actions of intrinsic properties of isolated neurons or through the dynamics of their synaptic connections or both. A combination of pharmacological and electrophysiological techniques a used to show how identified membrane properties and short-term synaptic plasticity are involved with phase maintenance over a range of biologically relevant oscillation frequencies. To examine whether network stability is due to the characteristic stable activity of the identified pyloric neuron types, the hypothesis that phase maintenance is an inherent property of synaptically-isolated individual neurons in the pyloric network was first tested. A set of parameters were determined (frequency-dependent activity profile) to define the response of each isolated pyloric neuron to sinusoidal input at different frequencies. The parameters that define the activity profile are: burst onset phase, burst end phase, resonance frequency and intra-burst spike frequency. Each pyloric neuron type was found to possess a unique activity profile, indicating that the individual neuron types are tuned to produce a particular activity pattern at different frequencies depending on their role in the network. To elucidate the biophysical properties underlying the frequency-dependent activity profiles of the neurons, the hyperpolarization activated current (Ih) was measured and found to possess frequency-dependent properties. This implies that Ih has a different influence on the activity phase of pyloric neurons at different frequencies. Additionally, it was found that the Ih contribution to the burst onset phase depends on the neuron type: in the pacemaker group neurons (PD) it had no influence on the burst onset phase at any frequency whereas in follower neurons it acted to advance the onset phase in one neuron type (LP) and, paradoxically, to delay it in a different neuron type (PY). The results from this part of the study provided evidence that stability is due in part to the intrinsic neuronal properties but that these intrinsic properties do not fully explain network stability. To address the contribution of pyloric synapses to network stability, the mechanisms by which synapses promote phase maintenance were investigated. An artificial synapse that mimicked the feedforward PD to LP synapse, was used so that the synaptic parameters could be varied in a controlled manner in order to examine the influence of the properties of this synapse on the postsynaptic LP neuron. It was found that a static synapse with fixed parameters (such as strength and peak phase) across frequencies cannot result in a constant activity phase in the LP neuron. However, if the synaptic strength decreases and the peak phase is delayed as a function of frequency, the LP neuron can maintain a constant activity phase across a large range of frequencies. These dynamic changes in the strength and peak phase of the PD to LP synapse are consistent with the short-term plasticity properties previously reported for this synapse. In the pyloric network, the follower neuron LP provides the sole transmitter-mediated feedback to the pacemaker neurons. To understand the role of this synapse in network stability, this synapse was blocked and replaced by an artificial synapse using the dynamic clamp technique. Different parameters of the artificial synapse, including strength, peak phase, duration and onset phase were found to affect the pyloric cycle period. The most effective parameters that influence cycle period were the synaptic duration and its onset phase. Overall this study demonstrated that both the intrinsic properties of individual neurons and the dynamic properties of the synapses are essential in producing stable activity phases in this oscillatory network. The insight obtained from this thesis can provide a general understanding of the contribution of intrinsic properties to neuronal activity phase and how short-term synaptic dynamics can act to promote phase maintenance in oscillatory networks