Spike frequency adaptation affects the synchronization properties of networks of cortical oscillators

Oscillations in many regions of the cortex have common temporal characteristics with dominant frequencies centered around the 40 Hz (gamma) frequency range and the 5–10 Hz (theta) frequency range. Experimental results also reveal spatially synchronous oscillations, which are stimulus dependent (Gray&Singer, 1987;Gray, König, Engel, & Singer, 1989; Engel, König, Kreiter, Schillen, & Singer, 1992). This rhythmic activity suggests that the coherence of neural populations is a crucial feature of cortical dynamics (Gray, 1994). Using both simulations and a theoretical coupled oscillator approach, we demonstrate that the spike frequency adaptation seen in many pyramidal cells plays a subtle but important role in the dynamics of cortical networks. Without adaptation, excitatory connections among model pyramidal cells are desynchronizing. However, the slow processes associated with adaptation encourage stable synchronous behavior

Synchronization and oscillatory dynamics in heterogeneous mutually inhibited neurons

We study some mechanisms responsible for synchronous oscillations and loss of synchrony at physiologically relevant frequencies (10-200 Hz) in a network of heterogeneous inhibitory neurons. We focus on the factors that determine the level of synchrony and frequency of the network response, as well as the effects of mild heterogeneity on network dynamics. With mild heterogeneity, synchrony is never perfect and is relatively fragile. In addition, the effects of inhibition are more complex in mildly heterogeneous networks than in homogeneous ones. In the former, synchrony is broken in two distinct ways, depending on the ratio of the synaptic decay time to the period of repetitive action potentials ($\tau_s/T$), where $T$ can be determined either from the network or from a single, self-inhibiting neuron. With $\tau_s/T > 2$, corresponding to large applied current, small synaptic strength or large synaptic decay time, the effects of inhibition are largely tonic and heterogeneous neurons spike relatively independently. With $\tau_s/T < 1$, synchrony breaks when faster cells begin to suppress their less excitable neighbors; cells that fire remain nearly synchronous. We show numerically that the behavior of mildly heterogeneous networks can be related to the behavior of single, self-inhibiting cells, which can be studied analytically.Comment: 17 pages, 6 figures, Kluwer.sty. Journal of Compuational Neuroscience (in press). Originally submitted to the neuro-sys archive which was never publicly announced (was 9802001

Frequency control in synchronized networks of inhibitory neurons

We analyze the control of frequency for a synchronized inhibitory neuronal network. The analysis is done for a reduced membrane model with a biophysically-based synaptic influence. We argue that such a reduced model can quantitatively capture the frequency behavior of a larger class of neuronal models. We show that in different parameter regimes, the network frequency depends in different ways on the intrinsic and synaptic time constants. Only in one portion of the parameter space, called `phasic', is the network period proportional to the synaptic decay time. These results are discussed in connection with previous work of the authors, which showed that for mildly heterogeneous networks, the synchrony breaks down, but coherence is preserved much more for systems in the phasic regime than in the other regimes. These results imply that for mildly heterogeneous networks, the existence of a coherent rhythm implies a linear dependence of the network period on synaptic decay time, and a much weaker dependence on the drive to the cells. We give experimental evidence for this conclusion.Comment: 18 pages, 3 figures, Kluwer.sty. J. Comp. Neurosci. (in press). Originally submitted to the neuro-sys archive which was never publicly announced (was 9803001

Locally embedded presages of global network bursts

Spontaneous, synchronous bursting of neural population is a widely observed phenomenon in nervous networks, which is considered important for functions and dysfunctions of the brain. However, how the global synchrony across a large number of neurons emerges from an initially non-bursting network state is not fully understood. In this study, we develop a new state-space reconstruction method combined with high-resolution recordings of cultured neurons. This method extracts deterministic signatures of upcoming global bursts in "local" dynamics of individual neurons during non-bursting periods. We find that local information within a single-cell time series can compare with or even outperform the global mean field activity for predicting future global bursts. Moreover, the inter-cell variability in the burst predictability is found to reflect the network structure realized in the non-bursting periods. These findings demonstrate the deterministic mechanisms underlying the locally concentrated early-warnings of the global state transition in self-organized networks

Inhibition Modifies the Effects of Slow Calcium-Activated Potassium Channels on Epileptiform Activity in a Neuronal Network Model

Generation of epileptiform activity typically results from a change in the balance between network excitation and inhibition. Experimental evidence indicates that alterations of either synaptic activity or intrinsic membrane properties can produce increased network excitation. The slow Ca2+-activated K+ currents (sI AHP) are important modulators of neuronal firing rate and excitability and have important established and potential roles in epileptogenesis. While the effects of changes in sI AHP on individual neuronal excitability are readily studied and well established, the effects of such changes on network behavior are less well known. The experiments here utilize a defined small network model of multicompartment pyramidal cells and an inhibitory interneuron to study the effects of changes in sI AHP on network behavior. The benefits of this model system include the ability to observe activity in all cells in a network and the effects of interactions of multiple simultaneous influences. In the model with no inhibitory interneuron, increasing sI AHP results in progressively decreasing burst activity. Adding an inhibitory interneuron changes the observed effects; at modest inhibitory strengths, increasing sI AHP in all network neurons actually results in increased network bursting (except at very high values). The duration of the burst activity is influenced by the length of delay in a feedback loop, with longer loops resulting in more prolonged bursting. These observations illustrate that the study of potential antiepileptogenic membrane effects must be extended to realistic networks. Network inhibition can dramatically alter the observations seen in pure excitatory networks