Interspike interval correlations in neuron models with adaptation and correlated noise

The generation of neural action potentials (spikes) is random but nevertheless may result in a rich statistical structure of the spike sequence. In particular, contrary to the popular renewal assumption of theoreticians, the intervals between adjacent spikes are often correlated. Experimentally, different patterns of interspike-interval correlations have been observed and computational studies have identified spike-frequency adaptation and correlated noise as the two main mechanisms that can lead to such correlations. Analytical studies have focused on the single cases of either correlated (colored) noise or adaptation currents in combination with uncorrelated (white) noise. For low-pass filtered noise or adaptation, the serial correlation coefficient can be approximated as a single geometric sequence of the lag between the intervals, providing an explanation for some of the experimentally observed patterns. Here we address the problem of interval correlations for a widely used class of models, multidimensional integrate-and-fire neurons subject to a combination of colored and white noise sources and a spike-triggered adaptation current. Assuming weak noise, we derive a simple formula for the serial correlation coefficient, a sum of two geometric sequences, which accounts for a large class of correlation patterns. The theory is confirmed by means of numerical simulations in a number of special cases including the leaky, quadratic, and generalized integrate-and-fire models with colored noise and spike-frequency adaptation. Furthermore we study the case in which the adaptation current and the colored noise share the same time scale, corresponding to a slow stochastic population of adaptation channels; we demonstrate that our theory can account for a nonmonotonic dependence of the correlation coefficient on the channel’s time scale. Another application of the theory is a neuron driven by network-noise-like fluctuations (green noise). We also discuss the range of validity of our weak-noise theory and show that by changing the relative strength of white and colored noise sources, we can change the sign of the correlation coefficient. Finally, we apply our theory to a conductance-based model which demonstrates its broad applicability.

Unusually slow spike frequency adaptation in deep cerebellar nuclei neurons preserves linear transformations on the sub-second time scale

Purkinje cells (PCs) are spontaneously active neurons of the cerebellar cortex that inhibit glutamatergic projection neurons within the deep cerebellar nuclei (DCN) that in turn provide the primary cerebellar output. Brief reductions in PC firing rapidly increase DCN neuron firing. However, prolonged reductions in PC inhibition, as seen in some disease states, certain types of transgenic mice, and in acute slices of the cerebellum, do not evoke large sustained increases in DCN firing. Here we test whether there is a mechanism of spike-frequency adaptation in DCN neurons that could account for these properties. We find that prolonged optogenetic suppression of PC synapses in vivo transiently elevates PC firing that strongly adapts within ten seconds. We perform current-clamp recordings at near physiological temperature in acute brain slices to examine how DCN neurons respond to prolonged depolarizations. Adaptation in DCN neurons is exceptionally slow and bidirectional. A depolarizing current step evokes large initial increases in firing that decay to less than 20% of the initial increase within approximately ten seconds. Such slow adaptation could allow DCN neurons to adapt to prolonged changes in PC firing while maintaining their linear firing frequency-current relationship on subsecond time scales.

Spike frequency adaptation supports network computations on temporally dispersed information

For solving tasks such as recognizing a song, answering a question, or inverting a sequence of symbols, cortical microcircuits need to integrate and manipulate information that was dispersed over time during the preceding seconds. Creating biologically realistic models for the underlying computations, especially with spiking neurons and for behaviorally relevant integration time spans, is notoriously difficult. We examine the role of spike frequency adaptation in such computations and find that it has a surprisingly large impact. The inclusion of this well-known property of a substantial fraction of neurons in the neocortex – especially in higher areas of the human neocortex – moves the performance of spiking neural network models for computations on network inputs that are temporally dispersed from a fairly low level up to the performance level of the human brain.

Absence of Pannexin 1 Stabilizes Hippocampal Excitability After Intracerebral Treatment With Aβ (1-42) and Prevents LTP Deficits in Middle-Aged Mice

Beta-amyloid protein [Aβ(1-42)] plays an important role in the disease progress and pathophysiology of Alzheimer's disease (AD). Membrane properties and neuronal excitability are altered in the hippocampus of transgenic AD mouse models that overexpress amyloid precursor protein. Although gap junction hemichannels have been implicated in the early pathogenesis of AD, to what extent Pannexin channels contribute to Aβ(1-42)-mediated brain changes is not yet known. In this study we, therefore, investigated the involvement of Pannexin1 (Panx1) channels in Aβ-mediated changes of neuronal membrane properties and long-term potentiation (LTP) in an animal model of AD. We conducted whole-cell patch-clamp recordings in CA1 pyramidal neurons 1 week after intracerebroventricular treatments of adult wildtype (wt) and Panx1 knockout (Panx1-ko) mice with either oligomeric Aβ(1-42), or control peptide. Panx1-ko hippocampi treated with control peptide exhibited increased neuronal excitability compared to wt. In addition, action potential (AP) firing frequency was higher in control Panx1-ko slices compared to wt. Aβ-treatment reduced AP firing frequency in both cohorts. But in Aβ-treated wt mice, spike frequency adaptation was significantly enhanced, when compared to control wt and to Aβ-treated Panx1-ko mice. Assessment of hippocampal LTP revealed deficits in Aβ-treated wt compared to control wt. By contrast, Panx1-ko exhibited LTP that was equivalent to LTP in control ko hippocampi. Taken together, our data show that in the absence of Pannexin1, hippocampi are more resistant to the debilitating effects of oligomeric Aβ. Both Aβ-mediated impairments in spike frequency adaptation and in LTP that occur in wt animals, are ameliorated in Panx1-ko mice. These results suggest that Panx1 contributes to early changes in hippocampal neuronal and synaptic function that are triggered by oligomeric Aβ.

A novel density-based neural mass model for simulating neuronal network dynamics with conductance-based synapses and membrane current adaptation

Nowadays, building low-dimensional mean-field models of neuronal populations is still a critical issue in the computational neuroscience community, because their derivation is difficult for realistic networks of neurons with conductance-based interactions and spike-frequency adaptation that generate nonlinear properties of neurons. Here, based on a colored-noise population density method, we derived a novel neural mass model, termed density-based neural mass model (dNMM), as the mean-field description of network dynamics of adaptive exponential integrate-and-fire neurons. Our results showed that the dNMM was capable of correctly estimating firing rate responses under both steady- and dynamic-input conditions. Finally, it was also able to quantitatively describe the effect of spike-frequency adaptation on the generation of asynchronous irregular activity of excitatory-inhibitory cortical networks. We conclude that in terms of its biological reality and calculation efficiency, the dNMM is a suitable candidate to build very large-scale network models involving multiple brain areas.

Impacted Spike Frequency Adaptation Associated with Reduction of KCNQ2/3 Promotes Seizure Activity in Temporal Lobe Epilepsy

ABSTRACTAlthough numerous epilepsy-related genes have been identified by unbiased genome-wide screening based on samples from both animal models and patients, the druggable targets for temporal lobe epilepsy (TLE) are still limited. Meanwhile, a large number of candidate genes that might promote or inhibit seizure activities are waiting for further validation. In this study, we first analyzed two public databases and determined the significant down-regulations of two M-type potassium channel genes (KCNQ2/3) expressions in hippocampus samples from TLE patients. Then we reproduced the similar pathological changes in the pilocarpine mouse model of TLE and further detected the decrease of spike frequency adaptation driven by impacted M-currents on dentate gyrus granule neurons. Finally, we employed a small-scale simulation of dentate gyrus network to investigate potential functional consequences of disrupted neuronal excitability. We demonstrated that the impacted spike frequency adaptation of granule cells facilitated the epileptiform activity among the entire network, including prolonged seizure duration and reduced interictal intervals. Our results identify a new mechanism contributing to ictogenesis in TLE and suggest a novel target for the anti-epileptic drug discovery.