Christian G. Fink

Cellularly-Driven Differences in Network Synchronization Propensity Are Differentially Modulated by Firing Frequency

Spatiotemporal pattern formation in neuronal networks depends on the interplay between cellular and network synchronization properties. The neuronal phase response curve (PRC) is an experimentally obtainable measure that characterizes the cellular response to small perturbations, and can serve as an indicator of cellular propensity for synchronization. Two broad classes of PRCs have been identified for neurons: Type I, in which small excitatory perturbations induce only advances in firing, and Type II, in which small excitatory perturbations can induce both advances and delays in firing. Interestingly, neuronal PRCs are usually attenuated with increased spiking frequency, and Type II PRCs typically exhibit a greater attenuation of the phase delay region than of the phase advance region. We found that this phenomenon arises from an interplay between the time constants of active ionic currents and the interspike interval. As a result, excitatory networks consisting of neurons with Type I PRCs responded very differently to frequency modulation compared to excitatory networks composed of neurons with Type II PRCs. Specifically, increased frequency induced a sharp decrease in synchrony of networks of Type II neurons, while frequency increases only minimally affected synchrony in networks of Type I neurons. These results are demonstrated in networks in which both types of neurons were modeled generically with the Morris-Lecar model, as well as in networks consisting of Hodgkin-Huxley-based model cortical pyramidal cells in which simulated effects of acetylcholine changed PRC type. These results are robust to different network structures, synaptic strengths and modes of driving neuronal activity, and they indicate that Type I and Type II excitatory networks may display two distinct modes of processing information.

A Dynamical Role for Acetylcholine in Synaptic Renormalization

Although sleep is a fundamental behavior observed in virtually all animal species, its functions remain unclear. One leading proposal, known as the synaptic renormalization hypothesis, suggests that sleep is necessary to counteract a global strengthening of synapses that occurs during wakefulness. Evidence for sleep-dependent synaptic downscaling (or synaptic renormalization) has been observed experimentally, but the physiological mechanisms which generate this phenomenon are unknown. In this study, we propose that changes in neuronal membrane excitability induced by acetylcholine may provide a dynamical mechanism for both wake-dependent synaptic upscaling and sleep-dependent downscaling. We show in silico that cholinergically-induced changes in network firing patterns alter overall network synaptic potentiation when synaptic strengths evolve through spike-timing dependent plasticity mechanisms. Specifically, network synaptic potentiation increases dramatically with high cholinergic concentration and decreases dramatically with low levels of acetylcholine. We demonstrate that this phenomenon is robust across variation of many different network parameters.

Network Mechanisms Generating Abnormal and Normal Hippocampal High-Frequency Oscillations: A Computational Analysis.

Abstract High-frequency oscillations (HFOs) are an intriguing potential biomarker for epilepsy, typically categorized according to peak frequency as either ripples (100–250 Hz) or fast ripples (>250 Hz). In the hippocampus, fast ripples were originally thought to be more specific to epileptic tissue, but it is still very difficult to distinguish which HFOs are caused by normal versus pathological brain activity. In this study, we use a computational model of hippocampus to investigate possible network mechanisms underpinning normal ripples, pathological ripples, and fast ripples. Our results unify several prior findings regarding HFO mechanisms, and also make several new predictions regarding abnormal HFOs. We show that HFOs are generic, emergent phenomena whose characteristics reflect a wide range of connectivity and network input. Although produced by different mechanisms, both normal and abnormal HFOs generate similar ripple frequencies, underscoring that peak frequency is unable to distinguish the two. Abnormal ripples are generic phenomena that arise when input to pyramidal cells overcomes network inhibition, resulting in high-frequency, uncoordinated firing. In addition, fast ripples transiently and sporadically arise from the precise conditions that produce abnormal ripples. Lastly, we show that such abnormal conditions do not require any specific network structure to produce coherent HFOs, as even completely asynchronous activity is capable of producing abnormal ripples and fast ripples in this manner. These results provide a generic, network-based explanation for the link between pathological ripples and fast ripples, and a unifying description for the entire spectrum from normal ripples to pathological fast ripples.

Effects of the Frequency Dependence of Phase Response Curves on Network Synchronization

Neuronal phase response curves (PRCs) generally fall into one of two classes. Type I PRCs exhibit exclusively phase advances and lead to decreased propensity for synchronization of excitatory networks, while Type II PRCs show regions of both phase delay and phase advance and better facilitate synchronization of excitatory networks. One little-investigated feature of neuronal PRCs is that they are attenuated as neuronal firing frequency increases. Interestingly, Type II PRCs often experience greater attenuation of their phase delay region compared to their phase advance region, while Type I PRCs typically show uniform attenuation of phase shifts. We simulate large-scale excitatory networks of Morris–Lecar neurons in order to investigate the effects of these phenomena upon network synchrony, and we show that they lead to Type I network synchrony increasing with increased frequency and Type II network synchrony decreasing with increased frequency.

Emergence of Narrowband High Frequency Oscillations from Asynchronous, Uncoupled Neural Firing

Previous experimental studies have demonstrated the emergence of narrowband local field potential oscillations during epileptic seizures in which the underlying neural activity appears to be completely asynchronous. We derive a mathematical model explaining how this counterintuitive phenomenon may occur, showing that a population of independent, completely asynchronous neurons may produce narrowband oscillations if each neuron fires quasi-periodically, without requiring any intrinsic oscillatory cells or feedback inhibition. This quasi-periodicity can occur through cells with similar frequency-current ([Formula: see text]-[Formula: see text]) curves receiving a similar, high amount of uncorrelated synaptic noise. Thus, this source of oscillatory behavior is distinct from the usual cases (pacemaker cells entraining a network, or oscillations being an inherent property of the network structure), as it requires no oscillatory drive nor any specific network or cellular properties other than cells that repetitively fire with continual stimulus. We also deduce bounds on the degree of variability in neural spike-timing which will permit the emergence of such oscillations, both for action potential- and postsynaptic potential-dominated LFPs. These results suggest that even an uncoupled network may generate collective rhythms, implying that the breakdown of inhibition and high synaptic input often observed during epileptic seizures may generate narrowband oscillations. We propose that this mechanism may explain why so many disparate epileptic and normal brain mechanisms can produce similar high frequency oscillations.

Neural network modulation, dynamics, and plasticity

Brain networks are unique in their capacity to modify synaptic structure while at the same time modulating neuronal firing properties. We investigated the interaction of these plastic network properties with overall network dynamics in large, biophysical neuronal network models. We modulated firing properties of individual neurons by simulating changing levels of acetylcholine (ACh), a key neurotransmitter whose level varies across waking and sleep states. When synaptic connection strengths were allowed to evolve according to a spike timing-dependent plasticity rule, results showed that ACh-induced changes in cellular properties led to different network activity patterns that resulted in either overall synaptic strengthening or weakening. These results suggest that the effect of ACh on neuron firing could contribute to hypothesized sleep-related synaptic renormalization in the brain.

Network heterogeneity and seizure generation

It has been shown that seizures occur more frequently at the transition from wake to sleep, or from one stage of sleep to another. Acetylcholine (ACh) is a neuromodulator that controls wake and sleep stages, and is present at high levels during waking and is absent in slow wave sleep (SWS). ACh has also been shown to switch the excitability as measured with Phase response curves (PRC) of pyramidal cells from Type 2 to Type 1. In general, Type 1 neurons are integrating type with high-excitability while Type 2 have lower excitability but higher capacity for synchronization. We investigate the effect of non-uniform cholinergic modulation, such as might occur at sleep/wake transitions, on the propensity for neuronal synchronization in large-scale networks of Hodgkin-Huxley models for cortical pyramidal cells. The interplay between the cellular properties and network connectivity in a heterogeneous network of Type 1 and Type 2 neurons can strongly affect network spatio-temporal dynamics. The focus of this research is to detect conditions that promote synchrony and seizure like activity in a mixed network of Type 1 and Type 2 neurons. Here we investigate inhomogeneous networks built of neurons that have non-identical connectivity properties. Namely every cell has an individual ratio of local and long distance synaptic connections. We show that even if the structure of the network is identical (i.e. identical adjacency matrix) there is a differential network-wide synchronization propensity depending on which neurons have Type II cellular properties.

Acetylcholine and synaptic homeostasis

The synaptic renormalization hypothesis posits that a primary function of sleep is to maintain synaptic homeostasis [1]. According to this theory, the flood of sensory signals processed by the brain during waking results in global potentiation of cortical synapses, a process which consumes energy and space and therefore cannot continue unabated. Sleep is therefore a period of global synaptic downscaling that maintains homeostasis, thereby conserving energy and cortical space. Specifically, it is slow-wave activity (SWA) during NREM sleep that is thought to induce this depotentiation. While evidence in support of both global potentiation of synapses during waking [2] and SWA-mediated downscaling of synapses during sleep [3] continues to mount, there is still much uncertainty about the biophysical mechanisms which may contribute to either synaptic upscaling or downscaling [4]. Waking and sleep states are promoted by the activity of brainstem and hypothalamic neuronal nuclei that express key neurotransmitters in thalamic and cortical