Emergent gamma synchrony in all-to-all interneuronal networks.

We investigate the emergence of in-phase synchronization in a heterogeneous network of coupled inhibitory interneurons in the presence of spike timing dependent plasticity (STDP). Using a simple network of two mutually coupled interneurons (2-MCI), we first study the effects of STDP on in-phase synchronization. We demonstrate that, with STDP, the 2-MCI network can evolve to either a state of stable 1:1 in-phase synchronization or exhibit multiple regimes of higher order synchronization states. We show that the emergence of synchronization induces a structural asymmetry in the 2-MCI network such that the synapses onto the high frequency firing neurons are potentiated, while those onto the low frequency firing neurons are de-potentiated, resulting in the directed flow of information from low frequency firing neurons to high frequency firing neurons. Finally, we demonstrate that the principal findings from our analysis of the 2-MCI network contribute to the emergence of robust synchronization in the Wang-Buzsaki network (Wang and Buzsáki, 1996) of all-to-all coupled inhibitory interneurons (100-MCI) for a significantly larger range of heterogeneity in the intrinsic firing rate of the neurons in the network. We conclude that STDP of inhibitory synapses provide a viable mechanism for robust neural synchronization.

Genesis of interictal spikes in the CA1: a computational investigation.

Interictal spikes (IISs) are spontaneous high amplitude, short time duration <400 ms events often observed in electroencephalographs (EEG) of epileptic patients. In vitro analysis of resected mesial temporal lobe tissue from patients with refractory temporal lobe epilepsy has revealed the presence of IIS in the CA1 subfield. In this paper, we develop a biophysically relevant network model of the CA1 subfield and investigate how changes in the network properties influence the susceptibility of CA1 to exhibit an IIS. We present a novel template based approach to identify conditions under which synchronization of paroxysmal depolarization shift (PDS) events evoked in CA1 pyramidal (Py) cells can trigger an IIS. The results from this analysis are used to identify the synaptic parameters of a minimal network model that is capable of generating PDS in response to afferent synaptic input. The minimal network model parameters are then incorporated into a detailed network model of the CA1 subfield in order to address the following questions: (1) How does the formation of an IIS in the CA1 depend on the degree of sprouting (recurrent connections) between the CA1 Py cells and the fraction of CA3 Shaffer collateral (SC) connections onto the CA1 Py cells? and (2) Is synchronous afferent input from the SC essential for the CA1 to exhibit IIS? Our results suggest that the CA1 subfield with low recurrent connectivity (absence of sprouting), mimicking the topology of a normal brain, has a very low probability of producing an IIS except when a large fraction of CA1 neurons (>80%) receives a barrage of quasi-synchronous afferent input (input occurring within a temporal window of ≤24 ms) via the SC. However, as we increase the recurrent connectivity of the CA1 (P sprout > 40); mimicking sprouting in a pathological CA1 network, the CA1 can exhibit IIS even in the absence of a barrage of quasi-synchronous afferents from the SC (input occurring within temporal window >80 ms) and a low fraction of CA1 Py cells (≈30%) receiving SC input. Furthermore, we find that in the presence of Poisson distributed random input via SC, the CA1 network is able to generate spontaneous periodic IISs (≈3 Hz) for high degrees of recurrent Py connectivity (P sprout > 70). We investigate the conditions necessary for this phenomenon and find that spontaneous IISs closely depend on the degree of the network's intrinsic excitability.

Computational modeling of channelrhodopsin-2 photocurrent characteristics in relation to neural signaling.

Channelrhodopsins-2 (ChR2) are a class of light sensitive proteins that offer the ability to use light stimulation to regulate neural activity with millisecond precision. In order to address the limitations in the efficacy of the wild-type ChR2 (ChRwt) to achieve this objective, new variants of ChR2 that exhibit fast mon-exponential photocurrent decay characteristics have been recently developed and validated. In this paper, we investigate whether the framework of transition rate model with 4 states, primarily developed to mimic the biexponential photocurrent decay kinetics of ChRwt, as opposed to the low complexity 3 state model, is warranted to mimic the mono-exponential photocurrent decay kinetics of the newly developed fast ChR2 variants: ChETA (Gunaydin et al., Nature Neurosci. 13:387-392, 2010) and ChRET/TC (Berndt et al., Proc. Natl. Acad. Sci. 108:7595-7600, 2011). We begin by estimating the parameters of the 3-state and 4-state models from experimental data on the photocurrent kinetics of ChRwt, ChETA, and ChRET/TC. We then incorporate these models into a fast-spiking interneuron model (Wang and Buzsaki, J. Neurosci. 16:6402-6413, 1996) and a hippocampal pyramidal cell model (Golomb et al., J. Neurophysiol. 96:1912-1926, 2006) and investigate the extent to which the experimentally observed neural response to various optostimulation protocols can be captured by these models. We demonstrate that for all ChR2 variants investigated, the 4 state model implementation is better able to capture neural response consistent with experiments across wide range of optostimulation protocol. We conclude by analytically investigating the conditions under which the characteristic specific to the 3-state model, namely the monoexponential photocurrent decay of the newly developed variants of ChR2, can occur in the framework of the 4-state model.

Detecting effective connectivity in networks of coupled neuronal oscillators.

The application of data-driven time series analysis techniques such as Granger causality, partial directed coherence and phase dynamics modeling to estimate effective connectivity in brain networks has recently gained significant prominence in the neuroscience community. While these techniques have been useful in determining causal interactions among different regions of brain networks, a thorough analysis of the comparative accuracy and robustness of these methods in identifying patterns of effective connectivity among brain networks is still lacking. In this paper, we systematically address this issue within the context of simple networks of coupled spiking neurons. Specifically, we develop a method to assess the ability of various effective connectivity measures to accurately determine the true effective connectivity of a given neuronal network. Our method is based on decision tree classifiers which are trained using several time series features that can be observed solely from experimentally recorded data. We show that the classifiers constructed in this work provide a general framework for determining whether a particular effective connectivity measure is likely to produce incorrect results when applied to a dataset.

Control of neural synchrony using channelrhodopsin-2: a computational study.

In this paper, we present an optical stimulation based approach to induce 1:1 in-phase synchrony in a network of coupled interneurons wherein each interneuron expresses the light sensitive protein channelrhodopsin-2 (ChR2). We begin with a transition rate model for the channel kinetics of ChR2 in response to light stimulation. We then define "functional optical time response curve (fOTRC)" as a measure of the response of a periodically firing interneuron (transfected with ChR2 ion channel) to a periodic light pulse stimulation. We specifically consider the case of unidirectionally coupled (UCI) network and propose an open loop control architecture that uses light as an actuation signal to induce 1:1 in-phase synchrony in the UCI network. Using general properties of the spike time response curves (STRCs) for Type-1 neuron model (Ermentrout, Neural Comput 8:979-1001, 1996) and fOTRC, we estimate the (open loop) optimal actuation signal parameters required to induce 1:1 in-phase synchrony. We then propose a closed loop controller architecture and a controller algorithm to robustly sustain stable 1:1 in-phase synchrony in the presence of unknown deviations in the network parameters. Finally, we test the performance of this closed-loop controller in a network of mutually coupled (MCI) interneurons.

Analysis of video-based microscopic particle trajectories using Kalman filtering.

The fidelity of the trajectories obtained from video-based particle tracking determines the success of a variety of biophysical techniques, including in situ single cell particle tracking and in vitro motility assays. However, the image acquisition process is complicated by system noise, which causes positioning error in the trajectories derived from image analysis. Here, we explore the possibility of reducing the positioning error by the application of a Kalman filter, a powerful algorithm to estimate the state of a linear dynamic system from noisy measurements. We show that the optimal Kalman filter parameters can be determined in an appropriate experimental setting, and that the Kalman filter can markedly reduce the positioning error while retaining the intrinsic fluctuations of the dynamic process. We believe the Kalman filter can potentially serve as a powerful tool to infer a trajectory of ultra-high fidelity from noisy images, revealing the details of dynamic cellular processes.

Support vector machines for seizure detection in an animal model of chronic epilepsy.

We compare the performance of three support vector machine (SVM) types: weighted SVM, one-class SVM and support vector data description (SVDD) for the application of seizure detection in an animal model of chronic epilepsy. Large EEG datasets (273 h and 91 h respectively, with a sampling rate of 1 kHz) from two groups of rats with chronic epilepsy were used in this study. For each of these EEG datasets, we extracted three energy-based seizure detection features: mean energy, mean curve length and wavelet energy. Using these features we performed twofold cross-validation to obtain the performance statistics: sensitivity (S), specificity (K) and detection latency (tau) as a function of control parameters for the given SVM. Optimal control parameters for each SVM type that produced the best seizure detection statistics were then identified using two independent strategies. Performance of each SVM type is ranked based on the overall seizure detection performance through an optimality index metric (O). We found that SVDD not only performed better than the other SVM types in terms of highest value of the mean optimality index metric (O⁻) but also gave a more reliable performance across the two EEG datasets.