Publications

Neurons in the substantia nigra reticulata (SNr) transmit information about basal ganglia output to dozens of brain regions in thalamocortical and brainstem motor networks. Activity of SNr neurons is regulated by convergent input from upstream basal ganglia nuclei, including GABAergic inputs from the striatum and the external globus pallidus (GPe). GABAergic inputs from the striatum convey information from the direct pathway, while GABAergic inputs from the GPe convey information from the indirect pathway. Chronic loss of dopamine, as occurs in Parkinson's disease, disrupts the balance of direct and indirect pathway neurons at the level of the striatum, but the question of how dopamine loss affects information propagation along these pathways outside of the striatum is less well understood. Using a combination of in vivo and slice electrophysiology, we find that dopamine depletion selectively weakens the direct pathway's influence over neural activity in the SNr due to changes in the decay kinetics of GABA-mediated synaptic currents. GABAergic signaling from GPe neurons in the indirect pathway was not affected, resulting in an inversion of the normal balance of inhibitory control over basal ganglia output through the SNr. These results highlight the contribution of cellular mechanisms outside of the striatum that impact the responses of basal ganglia output neurons to the direct and indirect pathways in disease.

Background: This work presents a toolbox that implements methodology for automated classification of diverse neural responses to optogenetic stimulation or other changes in conditions, based on spike train recordings. New Method: The toolbox implements what we call the Spike Train Response Classification algorithm (STReaC), which compares measurements of activity during a baseline period with analogous measurements during a subsequent period to identify various responses that might result from an event such as introduction of a sustained stimulus. The analyzed response types span a variety of patterns involving distinct time courses of increased firing, or excitation, decreased firing, or inhibition, or combinations of these. Excitation (inhibition) is identified from a comparative analysis of the spike density function (interspike interval function) for the baseline period relative to the corresponding function for the response period. Results: The STReaC algorithm as implemented in this toolbox provides a user-friendly, tunable, objective methodology that can detect a variety of neuronal response types and associated subtleties. We demonstrate this with single-unit neural recordings of rodent substantia nigra pars reticulata (SNr) during optogenetic stimulation of the globus pallidus externa (GPe). Comparison with existing methods: In several examples, we illustrate how the toolbox classifies responses in situations in which traditional methods (spike counting and visual inspection) either fail to detect a response or provide a false positive. Conclusions: The STReaC toolbox provides a simple, efficient approach for classifying spike trains into a variety of response types defined relative to a period of baseline spiking.

Parkinson’s disease (PD) and animal models of PD feature enhanced oscillations in several frequency bands in the basal ganglia (BG). Past research has emphasized the enhancement of 13-30 Hz beta oscillations. Recently, however, oscillations in the delta band (0.5-4 Hz) have been identified as a robust predictor of dopamine loss and motor dysfunction in several BG regions in mouse models of PD. In particular, delta oscillations in the substantia nigra pars reticulata (SNr) were shown to lead oscillations in motor cortex (M1) and persist under M1 lesion, but it is not clear where these oscillations are initially generated. In this paper, we use a computational model to study how delta oscillations may arise in the SNr due to projections from the globus pallidus externa (GPe). We propose a network architecture that incorporates inhibition in SNr from oscillat- ing GPe neurons and other SNr neurons. In our simulations, this configuration yields firing patterns in model SNr neurons that match those measured in vivo. In particular, we see the spontaneous emergence of near-antiphase active-predicting and inactive-predicting neural populations in the SNr, which persist under the inclusion of STN inputs based on experimental recordings. These results demonstrate how delta oscillations can propagate through BG nuclei despite imperfect oscillatory synchrony in the source site, narrowing down potential targets for the source of delta oscillations in PD models and giving new insight into the dynamics of SNr oscillations.

Recent work has highlighted the vast array of dynamics possible within both neuronal networks and individual neural models. In this work, we demonstrate the capability of interacting chaotic Hindmarsh–Rose neurons to communicate and transition into periodic dynamics through specific interactions which we call mutual stabilization, despite individual units existing in chaotic parameter regimes. Mutual stabilization has been seen before in other chaotic systems but has yet to be reported in interacting neural models. The process of chaotic stabilization is similar to related previous work, where a control scheme which provides small perturbations on carefully chosen Poincaré surfaces that act as control planes stabilized a chaotic trajectory onto a cupolet. For mutual stabilization to occur, the symbolic dynamics of a cupolet are passed through an interaction function such that the output acts as a control on a second chaotic system. If chosen correctly, the second system stabilizes onto another cupolet. This process can send feedback to the first system, replacing the original control, so that in some cases the two systems are locked into persistent periodic behavior as long as the interaction continues. Here, we demonstrate how this process works in a two-cell network and then extend the results to four cells with potential generalizations to larger networks. We conclude that stabilization of different states may be linked to a type of information storage or memory.

This paper reports the first finding of cupolets in a chaotic Hindmarsh–Rose neural model. Cupolets (chaotic, unstable, periodic, orbit-lets) are unstable periodic orbits that have been stabilized through a particular control scheme by applying a binary control sequence. We demonstrate different neural dynamics (periodic or chaotic) of the Hindmarsh–Rose model through a bifurcation diagram where the external input current, I, is the bifurcation parameter. We select a region in the chaotic parameter space and provide the results of numerical simulations. In this chosen parameter space, a control scheme is applied when the trajectory intersects with either of the two control planes. The type of the control is determined by a bit in a binary control sequence. The control is either a small microcontrol (0) or a large macrocontrol (1) that adjusts the future dynamics of the trajectory by a perturbation determined by the coding function r_N(x). We report the discovery of many cupolets with corresponding control sequences and comment on the differences with previously reported cupolets in the double scroll system. We provide some examples of the generated cupolets and conclude by discussing potential implications for biological neurons.

Recent work has demonstrated that interacting chaotic systems can establish persistent, periodic behavior, called mutual stabilization, when certain information is passed through interaction functions. In particular, this was first shown with two interacting cupolets (Chaotic Unstable Periodic Orbit-lets) of the double scroll oscillator. Cupolets are highly accurate approximations of unstable periodic orbits of a chaotic attractor that can be generated through a control scheme that repeatedly applies perturbations along Poincaré sections. The decision to perturb or not to perturb the trajectory is determined by a bit in a binary control sequence. One interaction function used in the original cupolet research was based on integrate-and-fire dynamics that are often seen in neural and laser systems and was used to demonstrate mutual stabilization between two double scroll oscillators. This result provided the motivation for this thesis where the stabilization of chaos in mathematical models of communicating neurons is investigated. This thesis begins by introducing mathematical models of neurons and discusses the biological realism of the models. Then, we consider the two-dimensional FitzHugh-Nagumo (FHN) neural model and we show how two FHN neurons can exhibit chaotic behavior when communication is mediated by a coupling constant, g, representative of the synaptic strength between the neurons. Through a bifurcation analysis, where the synaptic strength is the bifurcation parameter, we analyze the space of possible long-term behaviors of this model. After identifying regions of periodic and chaotic behavior, we show how a synaptic sigmoidal learning rule transitions the chaotic dynamics of the system to periodic dynamics in the presence of an external signal. After the signal passes through the synapse, synaptic learning alters the synaptic strength and the two neurons remain in a persistent, mutually stabilized periodic state even after the signal is removed. This result provides a proof-of-concept for chaotic stabilization in communicating neurons. Next, we focus on the 3-dimensional Hindmarsh-Rose (HR) neural model that is known to exhibit chaotic behavior and bursting neural firing. Using this model, we create a control scheme using two Poincaré sections in a manner similar to the control scheme for the double scroll system. Using the control scheme we establish that it is possible to generate cupolets in the HR model. We use the HR model to create neural networks where the communication between neurons is mediated by an integrate-and-fire interaction function. With this interaction, we show how a signal can propagate down a unidirectional chain of chaotic neurons. We further show how mutual stabilization can occur if two neurons communicate through this interaction function. Lastly, we expand the investigation to more complicated networks including a feedback network and a chain of neurons that ends in a feedback loop between the two terminal neurons. Mutual stabilization is found to exist in all cases. At each stage, we comment on the potential biological implications and extensions of these results.

This paper investigates the interaction between two coupled neurons at the terminal end of a long chain of neurons. Specifically, we examine a bidirectional, two-cell FitzHugh–Nagumo neural model capable of exhibiting chaotic dynamics. Analysis of this model shows how mutual stabilization of the chaotic dynamics can occur through sigmoidal synaptic learning. Initially, this paper begins with a bifurcation analysis of an adapted version of a previously studied FitzHugh–Nagumo model that indicates regions of periodic and chaotic behaviors. Through allowing the synaptic properties to change dynamically via neural learning, it is shown how the system can evolve from chaotic to stable periodic behavior. The driving factor between this transition is representative of a stimulus coming down a long neural pathway. The result that two chaotic neurons can mutually stabilize via a synaptic learning implies that this may be a mechanism whereby neurons can transition from a disordered, chaotic state to a stable, ordered periodic state that persists. This approach shows that even at the simplest level of two terminal neurons, chaotic behavior can become stable, sustained periodic behavior. This is achieved without the need for a large network of neurons.