None of the material has been published or is under consideration for pub lication elsewhere. 1A b stra c t T he p u rp o se of th is stu d y w as to o b tain a b e tte r u n d e r stan d in g of neu ro n al responses to co rrelated in p u t, in p a rtic u lar focussing on th e asp ect of sy nchronizatio n of n eu ro n al activity. T h e first aim w as to o b tain an an aly tical expression for th e coherence betw een th e o u tp u t spike tra in an d co rre la te d in p u t and for th e coherence betw een o u tp u t spike tra in s of neu ro n s w ith co rrelated in p u t. For Poisson neurons, we could derive th a t th e p eak of th e coherence betw een th e cor re la te d in p u t and m u lti-u n it activ ity increases p ro p o rtio n ally w ith th e square ro o t of th e n u m b er of neurons in th e m u lti u n it recording. T h e coherence betw een tw o typical m u lti-u n it record in gs (2 to 10 single-units) w ith p a rtia lly co rrelated in p u t increases p ro p o rtio n ally w ith th e n u m b er of u n its in th e m u lti-u n it recordings. T he second aim of th is stu d y w as to investigate to w h at e x ten t th e am p litu d e an d signal-to-noise ra tio of th e coherence betw een in p u t and o u tp u t varied for single versus m u lti-u n it activ ity and how th e y are affected by th e d u ra tio n of th e recording. T h e sam e pro b lem w as a d dressed for th e coherence betw een tw o single-unit spike series an d betw een tw o m u lti-u n it spike series. T he an aly tical re su lts for th e Poisson n eu ro n and nu m erical sim ulations for th e co n d u ctan ce-b ased leaky in teg rate-an d -fire n eu ro n an d for th e co n d u ctan ce-b ased H odgkin-H uxley n eu ro n show th a t th e ex p e c ta tio n value of th e coherence fun ctio n does no t increase for a longer d u ra tio n of th e recording. T h e only effect of a longer d u ra tio n of th e spike record in g is a re d u ctio n of th e noise in th e coherence function. T h e resu lts of an aly tical derivation s and c o m p u ter sim ulations for m odel neurons show th a t th e coher ence for m u lti-u n it activ ity is larg er th a n th a t for single-unit activity. T his is in agreem ent w ith th e resu lts of ex p erim en tal d a ta o b tain ed from m onkey visual co rtex (V 4). Finally, we show th a t m u lti-ta p e r tech niqu es g reatly c o n trib u te to a m ore a c cu ra te estim a te of th e coherence by redu cin g th e bias and variance in th e coherence estim ate.3

Several brain disorders are characterized by abnormally strong neuronal synchrony. Coordinated Reset (CR) stimulation was developed to selectively counteract abnormal neuronal synchrony by desynchronization. For this, phase resetting stimuli are delivered to different subpopulations in a timely coordinated way. In neural networks with spike timing-dependent plasticity CR stimulation may eventually lead to an anti-kindling, i.e., an unlearning of abnormal synaptic connectivity and abnormal synchrony. The spatiotemporal sequence by which all stimulation sites are stimulated exactly once is called the stimulation site sequence, or briefly sequence. So far, in simulations, pre-clinical and clinical applications CR was applied either with fixed sequences or rapidly varying sequences (RVS). In this computational study we show that appropriate repetition of the sequence with occasional random switching to the next sequence may significantly improve the anti-kindling effect of CR. To this end, a sequence is applied many times before randomly switching to the next sequence. This new method is called SVS CR stimulation, i.e., CR with slowly varying sequences. In a neuronal network with strong short-range excitatory and weak long-range inhibitory dynamic couplings SVS CR stimulation turns out to be superior to CR stimulation with fixed sequences or RVS.

In the past decades, many studies have focussed on the relation between the input and output of neurons with the aim to understand information processing by neurons. A particular aspect of neuronal information, which has not received much attention so far, concerns the problem of information transfer when a neuron or a population of neurons receives input from two or more (populations of) neurons, in particular when these (populations of) neurons carry different types of information. The aim of the present study is to investigate the responses of neurons to multiple inputs modulated in the gamma frequency range. By a combination of theoretical approaches and computer simulations, we test the hypothesis that enhanced modulation of synchronized excitatory neuronal activity in the gamma frequency range provides an advantage over a less synchronized input for various types of neurons. The results of this study show that the spike output of various types of neurons [i.e. the leaky integrate and fire neuron, the quadratic integrate and fire neuron and the Hodgkin-Huxley (HH) neuron] and that of excitatory-inhibitory coupled pairs of neurons, like the Pyramidal Interneuronal Network Gamma (PING) model, is highly phase-locked to the larger of two gamma-modulated input signals. This implies that the neuron selectively responds to the input with the larger gamma modulation if the amplitude of the gamma modulation exceeds that of the other signals by a certain amount. In that case, the output of the neuron is entrained by one of multiple inputs and that other inputs are not represented in the output. This mechanism for selective information transmission is enhanced for short membrane time constants of the neuron.

Several brain diseases are characterized by abnormally strong neuronal synchrony. Coordinated Reset (CR) stimulation was computationally designed to specifically counteract abnormal neuronal synchronization processes by desynchronization. In the presence of spike-timing-dependent plasticity (STDP) this may lead to a decrease of synaptic excitatory weights and ultimately to an anti-kindling, i.e. unlearning of abnormal synaptic connectivity and abnormal neuronal synchrony. The long-lasting desynchronizing impact of CR stimulation has been verified in pre-clinical and clinical proof of concept studies. However, as yet it is unclear how to optimally choose the CR stimulation frequency, i.e. the repetition rate at which the CR stimuli are delivered. This work presents the first computational study on the dependence of the acute and long-term outcome on the CR stimulation frequency in neuronal networks with STDP. For this purpose, CR stimulation was applied with Rapidly Varying Sequences (RVS) as well as with Slowly Varying Sequences (SVS) in a wide range of stimulation frequencies and intensities. Our findings demonstrate that acute desynchronization, achieved during stimulation, does not necessarily lead to long-term desynchronization after cessation of stimulation. By comparing the long-term effects of the two different CR protocols, the RVS CR stimulation turned out to be more robust against variations of the stimulation frequency. However, SVS CR stimulation can obtain stronger anti-kindling effects. We revealed specific parameter ranges that are favorable for long-term desynchronization. For instance, RVS CR stimulation at weak intensities and with stimulation frequencies in the range of the neuronal firing rates turned out to be effective and robust, in particular, if no closed loop adaptation of stimulation parameters is (technically) available. From a clinical standpoint, this may be relevant in the context of both invasive as well as non-invasive CR stimulation.

Many studies have reported long-range synchronization of neuronal activity between brain areas, in particular in the beta and gamma bands with frequencies in the range of 14–30 and 40–80 Hz, respectively. Several studies have reported synchrony with zero phase lag, which is remarkable considering the synaptic and conduction delays inherent in the connections between distant brain areas. This result has led to many speculations about the possible functional role of zero-lag synchrony, such as for neuronal communication, attention, memory, and feature binding. However, recent studies using recordings of single-unit activity and local field potentials report that neuronal synchronization may occur with non-zero phase lags. This raises the questions whether zero-lag synchrony can occur in the brain and, if so, under which conditions. We used analytical methods and computer simulations to investigate which connectivity between neuronal populations allows or prohibits zero-lag synchrony. We did so for a model where two oscillators interact via a relay oscillator. Analytical results and computer simulations were obtained for both type I Mirollo–Strogatz neurons and type II Hodgkin–Huxley neurons. We have investigated the dynamics of the model for various types of synaptic coupling and importantly considered the potential impact of Spike-Timing Dependent Plasticity (STDP) and its learning window. We confirm previous results that zero-lag synchrony can be achieved in this configuration. This is much easier to achieve with Hodgkin–Huxley neurons, which have a biphasic phase response curve, than for type I neurons. STDP facilitates zero-lag synchrony as it adjusts the synaptic strengths such that zero-lag synchrony is feasible for a much larger range of parameters than without STDP.

Experiments in visual cortex have shown that the firing rate of a neuron in response to the simultaneous presentation of a preferred and non-preferred stimulus within the receptive field is intermediate between that for the two stimuli alone (stimulus competition). Attention directed to one of the stimuli drives the response towards the response induced by the attended stimulus alone (selective attention). This study shows that a simple feedforward model with fixed synaptic conductance values can reproduce these two phenomena using synchronization in the gamma-frequency range to increase the effective synaptic gain for the responses to the attended stimulus. The performance of the model is robust to changes in the parameter values. The model predicts that the phase locking between presynaptic input and output spikes increases with attention.

We studied the dynamics of synchronization in asymmetrically coupled neural oscillators with time delay. Stability analysis revealed that symmetric excitatory coupling results in synchrony at multiple phase relations. Asymmetry yields two saddle-node bifurcations of the stable states when coupling is asymmetric. By contrast, with inhibitory coupling only in phase or antiphase is stable as long as coupling is symmetric. Otherwise, these stable states shift or even vanish. The reduced bistability range suggests the beneficial role of asymmetric coupling for reliable neural information transfer. DOI: 10.1103/PhysRevE.79.065203 PACS number͑s͒: 05.45.Xt, 87.19.lj, 89.20.Ϫa Entrainment of weakly coupled nonlinear oscillators is well known for many years ͓1,2͔. More recently, the synchronization dynamics in realistic settings received considerable interest, e.g., in nanomechanical oscillators ͓3͔, dynamic gene expression ͓4,5͔, and in neuronal networks ͓6-8͔, to mention a few. Interestingly, entrainment is believed to support information transfer in biological networks ͓9-12͔. In this study, we discuss the emergence of and changes in synchronization between realistic neuronal systems described by nonlinear pulse-coupled oscillators ͓13,14͔. Interaction between neurons is realized via changes in the membrane potential of a neuron due to the arrival of action potentials from another neuron at corresponding synapses. In several studies, neural systems were investigated in the case of symmetric coupling. Mirollo and Strogatz ͓14͔ provided a rigorous discussion of two pulse-coupled oscillators with symmetric excitatory connections and showed that they synchronize at zero phase difference. Ernst et al. ͓15,16͔ extended this study by introducing a time delay in the coupling due to finite conduction velocities of action potentials. The analytically derived return map of their model revealed that neurons with symmetric excitatory coupling synchronize at a phase lag equal to the delay, whereas in agreement with ͓17͔ inhibitory coupling results in stable in-phase synchronization, irrespective of the delay.For two mutually connected neurons, the coupling strength from neuron 1 to neuron 2 can differ significantly from that from 2 to 1. Symmetrical coupling between neurons is indeed the exception rather than the rule. A previous study ͓18͔ has shown that a network of excitatory all-to-all pulse-coupled oscillators without delay but with slightly different coupling strengths always synchronizes, similar to the fully symmetric case in ͓14͔. If time delays are introduced in a population of excitatory neurons with symmetric coupling, the network reveals emerging and decaying synchronized clusters ͓15͔. For inhibitory coupling with time delays, the activity reveals synchronization in multistable clusters of common phases. A network with mainly inhibitory pulsecoupled oscillators with time delays and sparse coupling, which synchronizes for symmetric coupling strengths, desynchronizes when coupling strengths become asymmetric ͓19͔. Fo...

Abnormal neuronal synchrony plays an important role in a number of brain diseases. To specifically counteract abnormal neuronal synchrony by desynchronization, Coordinated Reset (CR) stimulation, a spatiotemporally patterned stimulation technique, was designed with computational means. In neuronal networks with spike timing–dependent plasticity CR stimulation causes a decrease of synaptic weights and finally anti-kindling, i.e., unlearning of abnormally strong synaptic connectivity and abnormal neuronal synchrony. Long-lasting desynchronizing aftereffects of CR stimulation have been verified in pre-clinical and clinical proof of concept studies. In general, for different neuromodulation approaches, both invasive and non-invasive, it is desirable to enable effective stimulation at reduced stimulation intensities, thereby avoiding side effects. For the first time, we here present a two-stage CR stimulation protocol, where two qualitatively different types of CR stimulation are delivered one after another, and the first stage comes at a particularly weak stimulation intensity. Numerical simulations show that a two-stage CR stimulation can induce the same degree of anti-kindling as a single-stage CR stimulation with intermediate stimulation intensity. This stimulation approach might be clinically beneficial in patients suffering from brain diseases characterized by abnormal neuronal synchrony where a first treatment stage should be performed at particularly weak stimulation intensities in order to avoid side effects. This might, e.g., be relevant in the context of acoustic CR stimulation in tinnitus patients with hyperacusis or in the case of electrical deep brain CR stimulation with sub-optimally positioned leads or side effects caused by stimulation of the target itself. We discuss how to apply our method in first in man and proof of concept studies.