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Autism spectrum disorder is increasingly understood to be based on atypical signal transfer among multiple interconnected networks in the brain. Relative temporal patterns of neural activity have been shown to underlie both the altered neurophysiology and the altered behaviors in a variety of neurogenic disorders. We assessed brain network dynamics variability in autism spectrum disorders (ASD) using measures of synchronization (phase‐locking) strength, and timing of synchronization and desynchronization of neural activity (desynchronization ratio) across frequency bands of resting‐state electroencephalography (EEG). Our analysis indicated that frontoparietal synchronization is higher in ASD but with more short periods of desynchronization. It also indicates that the relationship between the properties of neural synchronization and behavior is different in ASD and typically developing populations. Recent theoretical studies suggest that neural networks with a high desynchronization ratio have increased sensitivity to inputs. Our results point to the potential significance of this phenomenon to the autistic brain. This sensitivity may disrupt the production of an appropriate neural and behavioral responses to external stimuli. Cognitive processes dependent on the integration of activity from multiple networks maybe, as a result, particularly vulnerable to disruption.Autism Res2020, 13: 24–31. © 2019 International Society for Autism Research, Wiley Periodicals, Inc. Lay SummaryParts of the brain can work together by synchronizing the activity of the neurons. We recorded the electrical activity of the brain in adolescents with autism spectrum disorder and then compared the recording to that of their peers without the diagnosis. We found that in participants with autism, there were a lot of very short time periods of non‐synchronized activity between frontal and parietal parts of the brain. Mathematical models show that the brain system with this kind of activity is very sensitive to external events. 

From 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. 

The subthalamic nucleus (STN) has an important role in the pathophysiology of the basal ganglia in Parkinson's disease. The ability of STN cells to generate bursting rhythms under either transient or sustained hyperpolarization may underlie the excessively synchronous beta rhythms observed in Parkinson's disease. In this study, we developed a conductance-based single compartment model of an STN neuron, which is able to generate characteristic activity patterns observed in experiments including hyperpolarization-induced bursts and post-inhibitory rebound bursts. This study focused on the role of three currents in rhythm generation: T-type calcium (CaT) current, L-type calcium (CaL) current, and hyperpolarization-activated cyclic nucleotide-gated (HCN) current. To investigate the effects of these currents in rhythm generation, we performed a bifurcation analysis using slow variables in these currents. Bifurcation analysis showed that the HCN current promotes single-spike activity patterns rather than bursting in agreement with experimental results. It also showed that the CaT current is necessary for characteristic bursting activity patterns. In particular, the CaT current enables STN neurons to generate these activity patterns under hyperpolarizing stimuli. The CaL current enriches and reinforces these characteristic activity patterns. In hyperpolarization-induced bursts or post-inhibitory rebound bursts, the CaL current allows STN neurons to generate long bursting patterns. Thus, the bifurcation analysis explained the synergistic interaction of the CaT and CaL currents, which enables STN neurons to respond to hyperpolarizing stimuli in a salient way. The results of this study implicate the importance of CaT and CaL currents in the pathophysiology of the basal ganglia in Parkinson's disease.