Autapses promote synchronization in neuronal networks

Characterizing the role of autaptic feedback in enhancing precision of neuronal firing times

In a chemical synapse, information flow occurs via the release of neurotransmitters from a presynaptic neuron that triggers an Action potential (AP) in the postsynaptic neuron. At its core, this occurs via the postsynaptic membrane potential integrating neurotransmitter-induced synaptic currents, and AP generation occurs when potential reaches a critical threshold. This manuscript investigates feedback implementation via an autapse, where the axon from the postsynaptic neuron forms an inhibitory synapse onto itself. Using a stochastic model of neuronal synaptic transmission, we formulate AP generation as a first-passage time problem and derive expressions for both the mean and noise of AP-firing times. Our analytical results supported by stochastic simulations identify parameter regimes where autaptic feedback transmission enhances the precision of AP firing times consistent with experimental data. These noise attenuating regimes are intuitively based on two orthogonal mechanisms - either expanding the time window to integrate noisy upstream signals; or by linearizing the mean voltage increase over time. Interestingly, we find regimes for noise amplification that specifically occur when the inhibitory synapse has a low probability of release for synaptic vesicles. In summary, this work explores feedback modulation of the stochastic dynamics of autaptic neurotransmission and reveals its function of creating more regular AP firing patterns.

Synchronization of the neurons coupled with sequential developing electrical and chemical synapses

There is some evidence representing the sequential formation and elimination of electrical and chemical synapses in particular brain regions. Relying on this feature, this paper presents a purely mathematical modeling study on the synchronization among neurons connected by transient electrical synapses transformed to chemical synapses over time. This deletion and development of synapses are considered consecutive. The results represent that the transient synapses lead to burst synchronization of the neurons while the neurons are resting when both synapses exist constantly. The period of the transitions and also the time of presence of electrical synapses to chemical ones are effective on the synchronization. The larger synchronization error is obtained by increasing the transition period and the time of chemical synapses' existence.

Neuronal synchronization in long-range time-varying networks

We study synchronization in neuronal ensembles subject to long-range electrical gap junctions which are time-varying. As a representative example, we consider Hindmarsh-Rose neurons interacting based upon temporal long-range connections through electrical couplings. In particular, we adopt the connections associated with the direct 1-path network to form a small-world network and follow-up with the corresponding long-range network. Further, the underlying direct small-world network is allowed to temporally change; hence, all long-range connections are also temporal, which makes the model much more realistic from the neurological perspective. This time-varying long-range network is formed by rewiring each link of the underlying 1-path network stochastically with a characteristic rewiring probability p_r, and accordingly all indirect k(>1)-path networks become temporal. The critical interaction strength to reach complete neuronal synchrony is much lower when we take up rapidly switching long-range interactions. We employ the master stability function formalism in order to characterize the local stability of the state of synchronization. The analytically derived stability condition for the complete synchrony state agrees well with the numerical results. Our work strengthens the understanding of time-varying long-range interactions in neuronal ensembles.

A dynamical model exploring sensory integration in the insect central complex substructures

It is imperative that an animal has the ability to contextually integrate received sensory information to formulate appropriate behavioral responses. Determining a body heading based on a multitude of ego-motion cues and visual landmarks is an example of such a task that requires this context dependent integration. The work presented here simulates a sensory integrator in the insect brain called the central complex (CX). Based on the architecture of the CX, we assembled a dynamical neural simulation of two structures called the protocerebral bridge (PB) and the ellipsoid body (EB). Using non-spiking neuronal dynamics, our simulation was able to recreate in vivo neuronal behavior such as correlating body rotation direction and speed to activity bumps within the EB as well as updating the believed heading with quick secondary system updates. With this model, we performed sensitivity analysis of certain neuronal parameters as a possible means to control multi-system gains during sensory integration. We found that modulation of synapses in the memory network and EB inhibition are two possible mechanisms in which a sensory system could affect the memory stability and gain of another input, respectively. This model serves as an exploration in network design for integrating simultaneous idiothetic and allothetic cues in the task of body tracking and determining contextually dependent behavioral outputs.

Study of Weak Periodic Signals in the EEG Signals and Their Relationship With Postsynaptic Potentials

In this paper, weak periodic signals detected in the EEG signals were analyzed for each region of the brain, and its relationships with postsynaptic potentials were investigated. For this, EEG signals were collected from 16 different channels according to the international standard channel 10/20 system in the scalp of two patients, one epileptic and one non-epileptic. In our recent work, we have detected weak periodic signals in the EEG signals using a Duffing oscillator system. In this paper, we have used a compact method by combining the Duffing oscillator system with scale index, which is based on a wavelet analysis in order to make the determination of the weak periodic signals more straightforward in practice. A number of weak periodic signals were detected in the range of frequencies 4.7-16 Hz in all channels, and however, these were less observed in epileptic EEG signals than non-epileptic. This methodology illustrates that weak periodic signals can be used to distinguish epileptic EEG signals from non-epileptic EEG signals. We have revealed some findings that the weak periodic signals are the postsynaptic potentials of the brain. Therefore, we can measure some frequencies values of the postsynaptic potentials within the EEG signals with this methodology.