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Item Contribution of synchronized GABAergic neurons to dopaminergic neuron firing and bursting(APS Journals, 2016-10-01) Morozova, Ekaterina O.; Myroshnychenko, Maxym; Zakharov, Denis; di Volo, Matteo; Gutkin, Boris; Lapish, Christopher C.; Kuznetsov, Alexey; Mathematical Sciences, School of SciencePresented herein ventral tegmental area microcircuit model challenges the classical view that GABA neurons exclusively reduce dopamine neuron firing and bursting. Rather, high levels of synchrony amongst GABA neurons can produce increases in firing and bursting of the dopamine neuron. Dopamine bursting can be produced in the absence of bursty excitatory input, if the neuron receives transiently synchronized GABA input. We provide an explanation of the mechanisms whereby GABA neurons could contribute to dopamine neuron burst firing., In the ventral tegmental area (VTA), interactions between dopamine (DA) and γ-aminobutyric acid (GABA) neurons are critical for regulating DA neuron activity and thus DA efflux. To provide a mechanistic explanation of how GABA neurons influence DA neuron firing, we developed a circuit model of the VTA. The model is based on feed-forward inhibition and recreates canonical features of the VTA neurons. Simulations revealed that γ-aminobutyric acid (GABA) receptor (GABAR) stimulation can differentially influence the firing pattern of the DA neuron, depending on the level of synchronization among GABA neurons. Asynchronous activity of GABA neurons provides a constant level of inhibition to the DA neuron and, when removed, produces a classical disinhibition burst. In contrast, when GABA neurons are synchronized by common synaptic input, their influence evokes additional spikes in the DA neuron, resulting in increased measures of firing and bursting. Distinct from previous mechanisms, the increases were not based on lowered firing rate of the GABA neurons or weaker hyperpolarization by the GABAR synaptic current. This phenomenon was induced by GABA-mediated hyperpolarization of the DA neuron that leads to decreases in intracellular calcium (Ca2+) concentration, thus reducing the Ca2+-dependent potassium (K+) current. In this way, the GABA-mediated hyperpolarization replaces Ca2+-dependent K+ current; however, this inhibition is pulsatile, which allows the DA neuron to fire during the rhythmic pauses in inhibition. Our results emphasize the importance of inhibition in the VTA, which has been discussed in many studies, and suggest a novel mechanism whereby computations can occur locally.Item Dynamics of desynchronized episodes in intermittent synchronization(Frontiers, 2014-06) Rubchinsky, Leonid L.; Ahn, Sungwoo; Park, Choongseok; Department of Mathematical Sciences, School of ScienceIntermittent synchronization is observed in a variety of different experimental settings in physics and beyond and is an established research topic in nonlinear dynamics. When coupled oscillators exhibit relatively weak, intermittent synchrony, the trajectory in the phase space spends a substantial fraction of time away from a vicinity of a synchronized state. Thus to describe and understand the observed dynamics one may consider both synchronized episodes and desynchronized episodes (the episodes when oscillators are not synchronous). This mini-review discusses recent developments in this area. We explain how one can consider variation in synchrony on the very short time-scales, provided that there is some degree of overall synchrony. We show how to implement this approach in the case of intermittent phase locking, review several recent examples of the application of these ideas to experimental data and modeling systems, and discuss when and why these methods may be useful.Item Spike-Timing Dependent Plasticity Effect on the Temporal Patterning of Neural Synchronization(Frontiers, 2020-06-12) Zirkle, Joel; Rubchinsky, Leonid L.; Mathematical Sciences, School of ScienceNeural synchrony in the brain at rest is usually variable and intermittent, thus intervals of predominantly synchronized activity are interrupted by intervals of desynchronized activity. Prior studies suggested that this temporal structure of the weakly synchronous activity might be functionally significant: many short desynchronizations may be functionally different from few long desynchronizations even if the average synchrony level is the same. In this study, we used computational neuroscience methods to investigate the effects of spike-timing dependent plasticity (STDP) on the temporal patterns of synchronization in a simple model. We employed a small network of conductance-based model neurons that were connected via excitatory plastic synapses. The dynamics of this network was subjected to the time-series analysis methods used in prior experimental studies. We found that STDP could alter the synchronized dynamics in the network in several ways, depending on the time scale that plasticity acts on. However, in general, the action of STDP in the simple network considered here is to promote dynamics with short desynchronizations (i.e., dynamics reminiscent of that observed in experimental studies). Complex interplay of the cellular and synaptic dynamics may lead to the activity-dependent adjustment of synaptic strength in such a way as to facilitate experimentally observed short desynchronizations in the intermittently synchronized neural activity.Item Synchronization and long-time memory in neural networks with inhibitory hubs and synaptic plasticity(APS, 2017-01) Bertolotti, Elena; Burioni, Raffaella; di Volo, Matteo; Vezzani, Alessandro; Department of Mathematical Sciences, School of ScienceWe investigate the dynamical role of inhibitory and highly connected nodes (hub) in synchronization and input processing of leaky-integrate-and-fire neural networks with short term synaptic plasticity. We take advantage of a heterogeneous mean-field approximation to encode the role of network structure and we tune the fraction of inhibitory neurons f I and their connectivity level to investigate the cooperation between hub features and inhibition. We show that, depending on f I , highly connected inhibitory nodes strongly drive the synchronization properties of the overall network through dynamical transitions from synchronous to asynchronous regimes. Furthermore, a metastable regime with long memory of external inputs emerges for a specific fraction of hub inhibitory neurons, underlining the role of inhibition and connectivity also for input processing in neural networks.Item Using Mathematics to Become in Sync With the Brain(Frontiers, 2022-05-19) Swartz, Micah; Rubchinsky, Leonid L.; Mathematical Sciences, School of ScienceFrom a young age, we are told that being “in sync” is a good thing! From being in sync with the music as we dance to being in sync with teammates on the field, synchronization is celebrated. However, too little or too much synchronization can be bad. In the brain, synchronization allows important information to be sent back and forth between neurons, so that we can make decisions and function in our daily lives. Mathematics can help researchers and doctors understand patterns of abnormal synchronization in the brain and help them to diagnose and potentially treat the symptoms of brain disorders. In this article, we will dive into how mathematics is used to explore and understand the brain—one of our body’s most important organs.