Parkinson's disease (PD) is associated with abnormal beta oscillations (13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30) in the basal ganglia and motor cortex (M1). Recent reports show that M1 beta-high gamma Hz) phase-amplitude coupling (PAC) is exaggerated in PD and is reduced following acute deep brain stimulation (DBS). Here we analyze invasive M1 electrocorticography recordings in PD patients on and off DBS, and in isolated cervical dystonia patients, and show that M1 beta oscillations are nonsinusoidal, having sharp and asymmetric features. These sharp oscillatory beta features underlie the previously reported PAC, providing an alternative to the standard interpretation of PAC as an interaction between two distinct frequency components. Specifically, the ratio between peak and trough sharpness is nearly perfectly correlated with beta-high gamma PAC (r = 0.96) and predicts PD-related motor deficit. Using a simulation of the local field potential, we demonstrate that sharp oscillatory waves can arise from synchronous synaptic activity. We propose that exaggerated beta-high gamma PAC may actually reflect such synchronous synaptic activity, manifesting as sharp beta oscillations that are "smoothed out" with DBS. These results support the "desynchronization" hypothesis of DBS wherein DBS counteracts pathological synchronization throughout the basal ganglia-thalamocortical loop. We argue that PAC can be influenced by more than one mechanism. In this case synaptic synchrony, rather than the often assumed spike-field coherence, may underlie exaggerated PAC. These often overlooked temporal features of the oscillatory waveform carry critical physiological information about neural processes and dynamics that may lead to better understanding of underlying neuropathology. IntroductionParkinson's disease (PD) is characterized by neuronal degeneration in multiple systems, including midbrain dopaminergic neurons. Though beta (13-30 Hz) oscillations are a normal feature of the basal ganglia-thalamocortical loop, PD is associated with excessive neuronal synchronization in the beta band (1, 2). Despite an established relationship between beta band neuronal synchronization and PD, the physiological mechanism causing motor dysfunction has been unclear. Excessive phase-amplitude coupling (PAC) between beta phase and high gamma amplitude (50-200 Hz) may offer an explanation (3)(4)(5). PAC between distant neural populations has been linked to enhanced neural information flow (6-8), long-term potentiation (9), and improved behavioral performance (10). However PAC strength is greater in M1 of PD patients compared to patients with isolated cervical dystonia or epilepsy (3), leading to the hypothesis that beyond its facilitative role, PAC may play a role in neural pathology (3,4,11).Analyses of PAC implicitly presuppose two separate, interacting physiological processes: a low-frequency component associated with an oscillation in the synaptic currents and a separate high-frequency component associated with local...

Oscillations can improve neural coding by grouping action potentials into synchronous windows, but this same effect harms coding when action potentials become over-synchronized. Diseases ranging from Parkinson's to epilepsy suggest that over-synchronization can lead to pathology, but the precise boundary separating healthy from pathological synchrony remains an open theoretical problem. We address this in series of numerical experiments. We study a simple model that shows how error in individual cells' computations is traded for population-level synchronization. In this model we conceive of a "voltage budget" where instantaneous moments of membrane voltage can be partitioned into oscillatory and computational terms. In comparing these budget terms we suggest a new set of biologically measurable inequalities that separate healthy from pathological synchrony. Finally, we derive an optimal non-biological algorithm for exchanging computational error with population synchrony. Rhythmic entrainment is a common feature of biological systems, but complete synchronization is often undesirable. This can be conceptually illustrated in the case of neural oscillations, where a totally unsynchronized neuronal population might lack communication capacity whereas a perfectly synchronized population might lack computation capacity (1). The biological reality lies in between, where moderate oscillations coordinate the firing of many individual neurons, creating synchronous windows of population communication (2). Temporally grouping action potentials in this manner improves signal to noise (3) and increases the number of coincident firing events (4, 5), driving learning at individual synapses (6-8).Complete independence between neurons dramatically reduces these temporal coincidences, whereas complete synchronization eliminates each neuron's individual firing characteristics, negating any possible computational contribution (9).To understand this problem more intuitively we imagine a population where each neuron receives the same spiking input but otherwise is independent from its neighbors. In this model each cell's response depends only on its immediate synaptic weight and its long-term membrane dynamics. Even in this simple situation the membrane response of each neuron can be complex, spanning chaotic irregular activity, bursting, accelerating, and a decay in rate driven by adaptation (10, 11). Even in the simplest case of regular-firing, with uniform sampling of synaptic weights, a population can exhibit substantial in response variability (as shown in Figure 1a).From a theoretical perspective, the high-dimensional nature of an independent neural response is a powerful potential computational resource (12, 13). However if there are many populations, all trying to communicate at once, we can again imagine how individually useful high-dimensional responses begin to feedback onto each other-with variability amplifying variability. Allowing a population to fall under the sway of a oscillator is one way to stabilize communication...