Partial phase synchronization of neural populations due to random Poisson inputs

Phase reduction and phase-based optimal control for biological systems: a tutorial

A powerful technique for the analysis of nonlinear oscillators is the rigorous reduction to phase models, with a single variable describing the phase of the oscillation with respect to some reference state. An analog to phase reduction has recently been proposed for systems with a stable fixed point, and phase reduction for periodic orbits has recently been extended to take into account transverse directions and higher-order terms. This tutorial gives a unified treatment of such phase reduction techniques and illustrates their use through mathematical and biological examples. It also covers the use of phase reduction for designing control algorithms which optimally change properties of the system, such as the phase of the oscillation. The control techniques are illustrated for example neural and cardiac systems.

Synchronization properties of coupled chaotic neurons: The role of random shared input

Spike-time correlations of neighbouring neurons depend on their intrinsic firing properties as well as on the inputs they share. Studies have shown that periodically firing neurons, when subjected to random shared input, exhibit asynchronicity. Here, we study the effect of random shared input on the synchronization of weakly coupled chaotic neurons. The cases of so-called electrical and chemical coupling are both considered, and we observe a wide range of synchronization behaviour. When subjected to identical shared random input, there is a decrease in the threshold coupling strength needed for chaotic neurons to synchronize in-phase. The system also supports lag-synchronous states, and for these, we find that shared input can cause desynchronization. We carry out a master stability function analysis for a network of such neurons and show agreement with the numerical simulations. The contrasting role of shared random input for complete and lag synchronized neurons is useful in understanding spike-time correlations observed in many areas of the brain.

Support of a patient-specific therapeutical acoustic stimulation in tinnitus by numerical modeling

The pathogenesis of tinnitus involves multiple hierarchical levels of auditory processing and appraisal of sensory saliency. Early tinnitus onset is most likely attributed to homeostatic plasticity in the periphery, while the chronification and decompensation are tightly linked to brain areas for the allocation of attentional resources, such as e.g., the thalamocortical feedback loops and the limbic system. Increased spontaneous firing after sensory deafferentation might be sufficient to generate a phantom perception, yet the question why not every peripheral hearing loss automatically elicits a tinnitus sensation is still to be addressed. Utilizing quantitative modeling of multiple hierarchical levels in the auditory pathway, we demonstrate the effects of lateral inhibition on increased spontaneous firing and the resulting elevation of firing regularity and synchronization of neural activity. The presented therapeutical approach is based on the idea of disrupting the heightened regularity of the neural population response in the tinnitus frequency range. This neural activity regularity depends on lateral dispersion of common noise and thus is susceptible for edge effects and might be influenced by a change in neural activity in bordering frequency ranges by fitted acoustical stimulation. We propose the use of patient specifically adapted tailor-made notched acoustic stimulation, utilizing modeling results for the optimal adjustment of the stimulation frequencies to archive a therapeutical edge-effect.

Control strategies for underactuated neural ensembles driven by optogenetic stimulation

Motivated by experiments employing optogenetic stimulation of cortical regions, we consider spike control strategies for ensembles of uncoupled integrate and fire neurons with a common conductance input. We construct strategies for control of spike patterns, that is, multineuron trains of action potentials, up to some maximal spike rate determined by the neural biophysics. We emphasize a constructive role for parameter heterogeneity, and find a simple rule for controllability in pairs of neurons. In particular, we determine parameters for which common drive is not limited to inducing synchronous spiking. For large ensembles, we determine how the number of controllable neurons varies with the number of observed (recorded) neurons, and what collateral spiking occurs in the full ensemble during control of the subensemble. While complete control of spiking in every neuron is not possible with a single input, we find that a degree of subensemble control is made possible by exploiting dynamical heterogeneity. As most available technologies for neural stimulation are underactuated, in the sense that the number of target neurons far exceeds the number of independent channels of stimulation, these results suggest partial control strategies that may be important in the development of sensory neuroprosthetics and other neurocontrol applications.

Synchronization of uncoupled oscillators by common gamma impulses: From phase locking to noise-induced synchronization

Nonlinear oscillators can mutually synchronize when they are driven by common external impulses. Two important scenarios are (i) synchronization resulting from phase locking of each oscillator to regular periodic impulses and (ii) noise-induced synchronization caused by the Poisson random impulses, but their difference has not been fully quantified. Here, we analyze a pair of uncoupled oscillators subject to common random impulses with gamma-distributed intervals, which can be smoothly interpolated between the regular periodic and the random Poisson impulses. Their dynamics are characterized by phase distributions, frequency detuning, Lyapunov exponents, and information-theoretic measures, which clearly reveal the differences between the two synchronization scenarios.

Electrical coupling promotes fidelity of responses in the networks of model neurons

We consider an integrate-and-fire element subject to randomly perturbed synaptic input and an electrically coupled ensemble of such elements. The latter is interpreted as either a model of electrically coupled population of neurons or a multicompartment model of a dendrite. Random fluctuations blur the input signal and cause false responses in the system dynamics. For instance, under the influence of noise, the system may respond with an action potential to a subthreshold stimulus. We show that the responses of the elements within the network are more reliable than the responses of the same elements in isolation. Specifically, we show that the variances of the stochastic processes generated by the coupled model can be made arbitrarily small (i.e., the network responses can be made arbitrarily accurate) by increasing the number of elements in the network and the strength of electrical coupling. Our results suggest that the organization of cells in electrically coupled groups on the network level, or the dendritic morphology on the cellular level, may be involved in the filtering noise and therefore may play an important role in the information processing mechanisms operating on the network or cellular level respectively.

Event-based minimum-time control of oscillatory neuron models: phase randomization, maximal spike rate increase, and desynchronization

We present an event-based feedback control method for randomizing the asymptotic phase of oscillatory neurons. Phase randomization is achieved by driving the neuron's state to its phaseless set, a point at which its phase is undefined and is extremely sensitive to background noise. We consider the biologically relevant case of a fixed magnitude constraint on the stimulus signal, and show how the control objective can be accomplished in minimum time. The control synthesis problem is addressed using the minimum-time-optimal Hamilton-Jacobi-Bellman framework, which is quite general and can be applied to any spiking neuron model in the conductance-based Hodgkin-Huxley formalism. We also use this methodology to compute a feedback control protocol for optimal spike rate increase. This framework provides a straightforward means of visualizing isochrons, without actually calculating them in the traditional way. Finally, we present an extension of the phase randomizing control scheme that is applied at the population level, to a network of globally coupled neurons that are firing in synchrony. The applied control signal desynchronizes the population in a demand-controlled way.

Calcium-activated SK channels influence voltage-gated ion channels to determine the precision of firing in globus pallidus neurons

Globus pallidus (GP) neurons fire rhythmically in the absence of synaptic input, suggesting that they may encode their inputs as changes in the phase of their rhythmic firing. Action potential afterhyperpolarization (AHP) enhances precision of firing by ensuring that the ion channels recover from inactivation by the same amount on each cycle. Voltage-clamp experiments in slices showed that the longest component of the GP neuron's AHP is blocked by apamin, a selective antagonist of calcium-activated SK channels. Application of 100 nm apamin also disrupted the precision of firing in perforated-patch and cell-attached recordings. SK channel blockade caused a small depolarization in spike threshold and made it more variable, but there was no reduction in the maximal rate of rise during an action potential. Thus, the firing irregularity was not caused solely by a reduction in voltage-gated Na(+) channel availability. Subthreshold voltage ramps triggered a large outward current that was sensitive to the initial holding potential and had properties similar to the A-type K(+) current in GP neurons. In numerical simulations, the availability of both Na(+) and A-type K(+) channels during autonomous firing were reduced when SK channels were removed, and a nearly equal reduction in Na(+) and K(+) subthreshold-activated ion channel availability produced a large decrease in the neuron's slope conductance near threshold. This change made the neuron more sensitive to intrinsically generated noise. In vivo, this change would also enhance the sensitivity of GP neurons to small synaptic inputs.