Dendritic and Axonal Propagation Delays Determine Emergent Structures of Neuronal Networks with Plastic Synapses

Simulated dataset on coordinated reset stimulation of homogeneous and inhomogeneous networks of excitatory leaky integrate-and-fire neurons with spike-timing-dependent plasticity

We present simulated data on coordinated reset stimulation (CRS) of plastic neuronal networks. The neuronal network consists of excitatory leaky integrate-and-fire neurons and plasticity is implemented as spike-timing-dependent plasticity (STDP). A synchronized state with strong synaptic connectivity and a desynchronized state with weak synaptic connectivity coexist. CRS may drive the network from the synchronized state into a desynchronized state inducing long-lasting desynchronization effects that persist after cessation of stimulation. This is used to model brain stimulation-induced transitions between a pathological state, with abnormally strong neuronal synchrony, and a physiological state, e.g., in Parkinson's disease. During CRS, a sequence of stimuli is delivered to multiple stimulation sites - called CR sequence. We present simulated data for the analysis of long-lasting desynchronization effects of CRS with shuffled CR sequences versus non-shuffled CR sequences in which the order of stimulus deliveries to the sites remains unchanged throughout the entire stimulation period. Such data are presented for networks with homogeneous synaptic connectivity and networks with inhomogeneous synaptic connectivity. Homogeneous synaptic connectivity refers to a network in which the probability of a synaptic connection does not depend on the pre- and postsynaptic neurons' locations. In contrast, inhomogeneous synaptic connectivity refers to a network in which the probability of a synaptic connection depends on the neurons' locations. The presented neuronal network model was used to analyse the impact of the CR sequences and their shuffling on the long-lasting effects of CRS [1].

Synchronization of delayed coupled neurons with multiple synaptic connections

Synchronization is a key feature of the brain dynamics and is necessary for information transmission across brain regions and in higher brain functions like cognition, learning and memory. Experimental findings demonstrated that in cortical microcircuits there are multiple synapses between pairs of connected neurons. Synchronization of neurons in the presence of multiple synaptic connections may be relevant for optimal learning and memory, however, its effect on the dynamics of the neurons is not adequately studied. Here, we address the question that how changes in the strength of the synaptic connections and transmission delays between neurons impact synchronization in a two-neuron system with multiple synapses. To this end, we analytically and computationally investigated synchronization dynamics by considering both phase oscillator model and conductance-based Hodgkin-Huxley (HH) model. Our results show that symmetry/asymmetry of feedforward and feedback connections crucially determines stability of the phase locking of the system based on the strength of connections and delays. In both models, the two-neuron system with multiple synapses achieves in-phase synchrony in the presence of small and large delays, whereas an anti-phase synchronization state is favored for median delays. Our findings can expand the understanding of the functional role of multisynaptic contacts in neuronal synchronization and may shed light on the dynamical consequences of pathological multisynaptic connectivity in a number of brain disorders.

Controlling neocortical epileptic seizures using forced temporal spike-time stimulation: an in silico computational study

Epileptic seizure is typically characterized by highly synchronized episodes of neural activity. Existing stimulation therapies focus purely on suppressing the pathologically synchronized neuronal firing patterns during the ictal (seizure) period. While these strategies are effective in suppressing seizures when they occur, they fail to prevent the re-emergence of seizures once the stimulation is turned off. Previously, we developed a novel neurostimulation motif, which we refer to as "Forced Temporal Spike-Time Stimulation" (FTSTS) that has shown remarkable promise in long-lasting desynchronization of excessively synchronized neuronal firing patterns by harnessing synaptic plasticity. In this paper, we build upon this prior work by optimizing the parameters of the FTSTS protocol in order to efficiently desynchronize the pathologically synchronous neuronal firing patterns that occur during epileptic seizures using a recently published computational model of neocortical-onset seizures. We show that the FTSTS protocol applied during the ictal period can modify the excitatory-to-inhibitory synaptic weight in order to effectively desynchronize the pathological neuronal firing patterns even after the ictal period. Our investigation opens the door to a possible new neurostimulation therapy for epilepsy.

Delay-dependent transitions of phase synchronization and coupling symmetry between neurons shaped by spike-timing-dependent plasticity

Synchronization plays a key role in learning and memory by facilitating the communication between neurons promoted by synaptic plasticity. Spike-timing-dependent plasticity (STDP) is a form of synaptic plasticity that modifies the strength of synaptic connections between neurons based on the coincidence of pre- and postsynaptic spikes. In this way, STDP simultaneously shapes the neuronal activity and synaptic connectivity in a feedback loop. However, transmission delays due to the physical distance between neurons affect neuronal synchronization and the symmetry of synaptic coupling. To address the question that how transmission delays and STDP can jointly determine the emergent pairwise activity-connectivity patterns, we studied phase synchronization properties and coupling symmetry between two bidirectionally coupled neurons using both phase oscillator and conductance-based neuron models. We show that depending on the range of transmission delays, the activity of the two-neuron motif can achieve an in-phase/anti-phase synchronized state and its connectivity can attain a symmetric/asymmetric coupling regime. The coevolutionary dynamics of the neuronal system and the synaptic weights due to STDP stabilizes the motif in either one of these states by transitions between in-phase/anti-phase synchronization states and symmetric/asymmetric coupling regimes at particular transmission delays. These transitions crucially depend on the phase response curve (PRC) of the neurons, but they are relatively robust to the heterogeneity of transmission delays and potentiation-depression imbalance of the STDP profile.

Decoupling of interacting neuronal populations by time-shifted stimulation through spike-timing-dependent plasticity

The synaptic organization of the brain is constantly modified by activity-dependent synaptic plasticity. In several neurological disorders, abnormal neuronal activity and pathological synaptic connectivity may significantly impair normal brain function. Reorganization of neuronal circuits by therapeutic stimulation has the potential to restore normal brain dynamics. Increasing evidence suggests that the temporal stimulation pattern crucially determines the long-lasting therapeutic effects of stimulation. Here, we tested whether a specific pattern of brain stimulation can enable the suppression of pathologically strong inter-population synaptic connectivity through spike-timing-dependent plasticity (STDP). More specifically, we tested how introducing a time shift between stimuli delivered to two interacting populations of neurons can effectively decouple them. To that end, we first used a tractable model, i.e., two bidirectionally coupled leaky integrate-and-fire (LIF) neurons, to theoretically analyze the optimal range of stimulation frequency and time shift for decoupling. We then extended our results to two reciprocally connected neuronal populations (modules) where inter-population delayed connections were modified by STDP. As predicted by the theoretical results, appropriately time-shifted stimulation causes a decoupling of the two-module system through STDP, i.e., by unlearning pathologically strong synaptic interactions between the two populations. Based on the overall topology of the connections, the decoupling of the two modules, in turn, causes a desynchronization of the populations that outlasts the cessation of stimulation. Decoupling effects of the time-shifted stimulation can be realized by time-shifted burst stimulation as well as time-shifted continuous simulation. Our results provide insight into the further optimization of a variety of multichannel stimulation protocols aiming at a therapeutic reshaping of diseased brain networks.

Efficient suppression of parkinsonian beta oscillations in a closed-loop model of deep brain stimulation with amplitude modulation

Introduction

Parkinson's disease (PD) is a movement disorder characterized by the pathological beta band (15-30 Hz) neural oscillations within the basal ganglia (BG). It is shown that the suppression of abnormal beta oscillations is correlated with the improvement of PD motor symptoms, which is a goal of standard therapies including deep brain stimulation (DBS). To overcome the stimulation-induced side effects and inefficiencies of conventional DBS (cDBS) and to reduce the administered stimulation current, closed-loop adaptive DBS (aDBS) techniques were developed. In this method, the frequency and/or amplitude of stimulation are modulated based on various disease biomarkers.

Methods

Here, by computational modeling of a cortico-BG-thalamic network in normal and PD conditions, we show that closed-loop aDBS of the subthalamic nucleus (STN) with amplitude modulation leads to a more effective suppression of pathological beta oscillations within the parkinsonian BG.

Results

Our results show that beta band neural oscillations are restored to their normal range and the reliability of the response of the thalamic neurons to motor cortex commands is retained due to aDBS with amplitude modulation. Furthermore, notably less stimulation current is administered during aDBS compared with cDBS due to a closed-loop control of stimulation amplitude based on the STN local field potential (LFP) beta activity.

Discussion

Efficient models of closed-loop stimulation may contribute to the clinical development of optimized aDBS techniques designed to reduce potential stimulation-induced side effects of cDBS in PD patients while leading to a better therapeutic outcome.

Synaptic reshaping of plastic neuronal networks by periodic multichannel stimulation with single-pulse and burst stimuli

Synaptic dysfunction is associated with several brain disorders, including Alzheimer's disease, Parkinson's disease (PD) and obsessive compulsive disorder (OCD). Utilizing synaptic plasticity, brain stimulation is capable of reshaping synaptic connectivity. This may pave the way for novel therapies that specifically counteract pathological synaptic connectivity. For instance, in PD, novel multichannel coordinated reset stimulation (CRS) was designed to counteract neuronal synchrony and down-regulate pathological synaptic connectivity. CRS was shown to entail long-lasting therapeutic aftereffects in PD patients and related animal models. This is in marked contrast to conventional deep brain stimulation (DBS) therapy, where PD symptoms return shortly after stimulation ceases. In the present paper, we study synaptic reshaping by periodic multichannel stimulation (PMCS) in networks of leaky integrate-and-fire (LIF) neurons with spike-timing-dependent plasticity (STDP). During PMCS, phase-shifted periodic stimulus trains are delivered to segregated neuronal subpopulations. Harnessing STDP, PMCS leads to changes of the synaptic network structure. We found that the PMCS-induced changes of the network structure depend on both the phase lags between stimuli and the shape of individual stimuli. Single-pulse stimuli and burst stimuli with low intraburst frequency down-regulate synapses between neurons receiving stimuli simultaneously. In contrast, burst stimuli with high intraburst frequency up-regulate these synapses. We derive theoretical approximations of the stimulation-induced network structure. This enables us to formulate stimulation strategies for inducing a variety of network structures. Our results provide testable hypotheses for future pre-clinical and clinical studies and suggest that periodic multichannel stimulation may be suitable for reshaping plastic neuronal networks to counteract pathological synaptic connectivity. Furthermore, we provide novel insight on how the stimulus type may affect the long-lasting outcome of conventional DBS. This may strongly impact parameter adjustment procedures for clinical DBS, which, so far, primarily focused on acute effects of stimulation.

Inhibitory Spike-Timing-Dependent Plasticity Can Account for Pathological Strengthening of Pallido-Subthalamic Synapses in Parkinson's Disease

Parkinson's disease (PD) is a neurodegenerative brain disorder associated with dysfunction of the basal ganglia (BG) circuitry. Dopamine (DA) depletion in experimental PD models leads to the pathological strengthening of pallido-subthalamic synaptic connections, contributing to the emergence of abnormally synchronized neuronal activity in the external segment of the globus pallidus (GPe) and subthalamic nucleus (STN). Augmented GPe-STN transmission following loss of DA was attributed to heterosynaptic plasticity mechanisms induced by cortico-subthalamic inputs. However, synaptic plasticity may play a role in this process. Here, by employing computational modeling we show that assuming inhibitory spike-timing-dependent plasticity (iSTDP) at pallido-subthalamic synapses can account for pathological strengthening of pallido-subthalamic synapses in PD by further promoting correlated neuronal activity in the GPe-STN network. In addition, we show that GPe-STN transmission delays can shape bistable activity-connectivity states due to iSTDP, characterized by strong connectivity and strong synchronized activity (pathological states) as opposed to weak connectivity and desynchronized activity (physiological states). Our results may shed light on how abnormal reshaping of GPe-STN connectivity by synaptic plasticity during parkinsonism is related to the PD pathophysiology and contribute to the development of therapeutic brain stimulation techniques targeting plasticity-induced rewiring of network connectivity.

The Origin of Abnormal Beta Oscillations in the Parkinsonian Corticobasal Ganglia Circuits

Parkinson's disease (PD) is a neurodegenerative brain disorder associated with motor and nonmotor symptoms. Exaggerated beta band (15–30 Hz) neuronal oscillations are widely observed in corticobasal ganglia (BG) circuits during parkinsonism. Abnormal beta oscillations have been linked to motor symptoms of PD, but their exact relationship is poorly understood. Nevertheless, reduction of beta oscillations can induce therapeutic effects in PD patients. While it is widely believed that the external globus pallidus (GPe) and subthalamic nucleus (STN) are jointly responsible for abnormal rhythmogenesis in the parkinsonian BG, the role of other cortico-BG circuits cannot be ignored. To shed light on the origin of abnormal beta oscillations in PD, here we review changes of neuronal activity observed in experimental PD models and discuss how the cortex and different BG nuclei cooperate to generate and stabilize abnormal beta oscillations during parkinsonism. This may provide further insights into the complex relationship between abnormal beta oscillations and motor dysfunction in PD, which is crucial for potential target-specific therapeutic interventions in PD patients.

Spike-Timing-Dependent Plasticity Mediated by Dopamine and its Role in Parkinson's Disease Pathophysiology

Parkinson's disease (PD) is a multi-systemic neurodegenerative brain disorder. Motor symptoms of PD are linked to the significant dopamine (DA) loss in substantia nigra pars compacta (SNc) followed by basal ganglia (BG) circuit dysfunction. Increasing experimental and computational evidence indicates that (synaptic) plasticity plays a key role in the emergence of PD-related pathological changes following DA loss. Spike-timing-dependent plasticity (STDP) mediated by DA provides a mechanistic model for synaptic plasticity to modify synaptic connections within the BG according to the neuronal activity. To shed light on how DA-mediated STDP can shape neuronal activity and synaptic connectivity in the PD condition, we reviewed experimental and computational findings addressing the modulatory effect of DA on STDP as well as other plasticity mechanisms and discussed their potential role in PD pathophysiology and related network dynamics and connectivity. In particular, reshaping of STDP profiles together with other plasticity-mediated processes following DA loss may abnormally modify synaptic connections in competing pathways of the BG. The cascade of plasticity-induced maladaptive or compensatory changes can impair the excitation-inhibition balance towards the BG output nuclei, leading to the emergence of pathological activity-connectivity patterns in PD. Pre-clinical, clinical as well as computational studies reviewed here provide an understanding of the impact of synaptic plasticity and other plasticity mechanisms on PD pathophysiology, especially PD-related network activity and connectivity, after DA loss. This review may provide further insights into the abnormal structure-function relationship within the BG contributing to the emergence of pathological states in PD. Specifically, this review is intended to provide detailed information for the development of computational network models for PD, serving as testbeds for the development and optimization of invasive and non-invasive brain stimulation techniques. Computationally derived hypotheses may accelerate the development of therapeutic stimulation techniques and potentially reduce the number of related animal experiments.

Numerical Simulation: Fluctuation in Background Synaptic Activity Regulates Synaptic Plasticity

Synaptic plasticity is vital for learning and memory in the brain. It consists of long-term potentiation (LTP) and long-term depression (LTD). Spike frequency is one of the major components of synaptic plasticity in the brain, a noisy environment. Recently, we mathematically analyzed the frequency-dependent synaptic plasticity (FDP) in vivo and found that LTP is more likely to occur with an increase in the frequency of background synaptic activity. Meanwhile, previous studies suggest statistical fluctuation in the amplitude of background synaptic activity. Little is understood, however, about its contribution to synaptic plasticity. To address this issue, we performed numerical simulations of a calcium-based synapse model. Then, we found attenuation of the tendency to become LTD due to an increase in the fluctuation of background synaptic activity, leading to an enhancement of synaptic weight. Our result suggests that the fluctuation affects synaptic plasticity in the brain.

Voltage-dependent plasticity of spin-polarized conductance in phenyl-based single-molecule magnetic tunnel junctions

Synaptic strengths between neurons in brain networks are highly adaptive due to synaptic plasticity. Spike-timing-dependent plasticity (STDP) is a form of synaptic plasticity induced by temporal correlations between the firing activity of neurons. The development of experimental techniques in recent years enabled the realization of brain-inspired neuromorphic devices. Particularly, magnetic tunnel junctions (MTJs) provide a suitable means for the implementation of learning processes in molecular junctions. Here, we first considered a two-neuron motif subjected to STDP. By employing theoretical analysis and computer simulations we showed that the dynamics and emergent structure of the motif can be predicted by introducing an effective two-neuron synaptic conductance. Then, we considered a phenyl-based single-molecule MTJ connected to two ferromagnetic (FM) cobalt electrodes and investigated its electrical properties using the non-equilibrium Green’s function (NEGF) formalism. Similar to the two-neuron motif, we introduced an effective spin-polarized conductance in the MTJ. Depending on the polarity, frequency and strength of the bias voltage applied to the MTJ, the system can learn input signals by adaptive changes of the effective conductance. Interestingly, this voltage-dependent plasticity is an intrinsic property of the MTJ where its behavior is reminiscent of the classical temporally asymmetric STDP. Furthermore, the shape of voltage-dependent plasticity in the MTJ is determined by the molecule-electrode coupling strength or the length of the molecule. Our results may be relevant for the development of single-molecule devices that capture the adaptive properties of synapses in the brain.

Comparing feedforward and recurrent neural network architectures with human behavior in artificial grammar learning

In recent years artificial neural networks achieved performance close to or better than humans in several domains: tasks that were previously human prerogatives, such as language processing, have witnessed remarkable improvements in state of the art models. One advantage of this technological boost is to facilitate comparison between different neural networks and human performance, in order to deepen our understanding of human cognition. Here, we investigate which neural network architecture (feedforward vs. recurrent) matches human behavior in artificial grammar learning, a crucial aspect of language acquisition. Prior experimental studies proved that artificial grammars can be learnt by human subjects after little exposure and often without explicit knowledge of the underlying rules. We tested four grammars with different complexity levels both in humans and in feedforward and recurrent networks. Our results show that both architectures can "learn" (via error back-propagation) the grammars after the same number of training sequences as humans do, but recurrent networks perform closer to humans than feedforward ones, irrespective of the grammar complexity level. Moreover, similar to visual processing, in which feedforward and recurrent architectures have been related to unconscious and conscious processes, the difference in performance between architectures over ten regular grammars shows that simpler and more explicit grammars are better learnt by recurrent architectures, supporting the hypothesis that explicit learning is best modeled by recurrent networks, whereas feedforward networks supposedly capture the dynamics involved in implicit learning.

Multicoding in neural information transfer suggested by mathematical analysis of the frequency-dependent synaptic plasticity in vivo

Two elements of neural information processing have primarily been proposed: firing rate and spike timing of neurons. In the case of synaptic plasticity, although spike-timing-dependent plasticity (STDP) depending on presynaptic and postsynaptic spike times had been considered the most common rule, recent studies have shown the inhibitory nature of the brain in vivo for precise spike timing, which is key to the STDP. Thus, the importance of the firing frequency in synaptic plasticity in vivo has been recognized again. However, little is understood about how the frequency-dependent synaptic plasticity (FDP) is regulated in vivo. Here, we focused on the presynaptic input pattern, the intracellular calcium decay time constants, and the background synaptic activity, which vary depending on neuron types and the anatomical and physiological environment in the brain. By analyzing a calcium-based model, we found that the synaptic weight differs depending on these factors characteristic in vivo, even if neurons receive the same input rate. This finding suggests the involvement of multifaceted factors other than input frequency in FDP and even neural coding in vivo.

Spike-Timing-Dependent Plasticity With Axonal Delay Tunes Networks of Izhikevich Neurons to the Edge of Synchronization Transition With Scale-Free Avalanches

Critical brain hypothesis has been intensively studied both in experimental and theoretical neuroscience over the past two decades. However, some important questions still remain: (i) What is the critical point the brain operates at? (ii) What is the regulatory mechanism that brings about and maintains such a critical state? (iii) The critical state is characterized by scale-invariant behavior which is seemingly at odds with definitive brain oscillations? In this work we consider a biologically motivated model of Izhikevich neuronal network with chemical synapses interacting via spike-timing-dependent plasticity (STDP) as well as axonal time delay. Under generic and physiologically relevant conditions we show that the system is organized and maintained around a synchronization transition point as opposed to an activity transition point associated with an absorbing state phase transition. However, such a state exhibits experimentally relevant signs of critical dynamics including scale-free avalanches with finite-size scaling as well as critical branching ratios. While the system displays stochastic oscillations with highly correlated fluctuations, it also displays dominant frequency modes seen as sharp peaks in the power spectrum. The role of STDP as well as time delay is crucial in achieving and maintaining such critical dynamics, while the role of inhibition is not as crucial. In this way we provide possible answers to all three questions posed above. We also show that one can achieve supercritical or subcritical dynamics if one changes the average time delay associated with axonal conduction.

Spontaneous electromagnetic induction promotes the formation of economical neuronal network structure via self-organization process

Developed through evolution, brain neural system self-organizes into an economical and dynamic network structure with the modulation of repetitive neuronal firing activities through synaptic plasticity. These highly variable electric activities inevitably produce a spontaneous magnetic field, which also significantly modulates the dynamic neuronal behaviors in the brain. However, how this spontaneous electromagnetic induction affects the self-organization process and what is its role in the formation of an economical neuronal network still have not been reported. Here, we investigate the effects of spontaneous electromagnetic induction on the self-organization process and the topological properties of the self-organized neuronal network. We first find that spontaneous electromagnetic induction slows down the self-organization process of the neuronal network by decreasing the neuronal excitability. In addition, spontaneous electromagnetic induction can result in a more homogeneous directed-weighted network structure with lower causal relationship and less modularity which supports weaker neuronal synchronization. Furthermore, we show that spontaneous electromagnetic induction can reconfigure synaptic connections to optimize the economical connectivity pattern of self-organized neuronal networks, endowing it with enhanced local and global efficiency from the perspective of graph theory. Our results reveal the critical role of spontaneous electromagnetic induction in the formation of an economical self-organized neuronal network and are also helpful for understanding the evolution of the brain neural system.

Encoding information into autonomously bursting neural network with pairs of time-delayed pulses

Biological neural networks with many plastic synaptic connections can store external input information in the map of synaptic weights as a form of unsupervised learning. However, the same neural network often produces dramatic reverberating events in which many neurons fire almost simultaneously – a phenomenon coined as ‘population burst.’ The autonomous bursting activity is a consequence of the delicate balance between recurrent excitation and self-inhibition; as such, any periodic sequences of burst-generating stimuli delivered even at a low frequency (~1 Hz) can easily suppress the entire network connectivity. Here we demonstrate that ‘Δt paired-pulse stimulation’, can be a novel way for encoding spatially-distributed high-frequency (~10 Hz) information into such a system without causing a complete suppression. The encoded memory can be probed simply by delivering multiple probing pulses and then estimating the precision of the arrival times of the subsequent evoked recurrent bursts.

Dopaminergic Modulation of Synaptic Plasticity, Its Role in Neuropsychiatric Disorders, and Its Computational Modeling

Neuromodulators modify intrinsic characteristics of the nervous system in order to reconfigure the functional properties of neural circuits. This reconfiguration is crucial for the flexibility of the nervous system to respond on an input-modulated basis. Such a functional rearrangement is realized by modification of intrinsic properties of the neural circuits including synaptic interactions. Dopamine is an important neuromodulator involved in motivation and stimulus-reward learning process, and adjusts synaptic dynamics in multiple time scales through different pathways. The modification of synaptic plasticity by dopamine underlies the change in synaptic transmission and integration mechanisms, which affects intrinsic properties of the neural system including membrane excitability, probability of neurotransmitters release, receptors’ response to neurotransmitters, protein trafficking, and gene transcription. Dopamine also plays a central role in behavioral control, whereas its malfunction can cause cognitive disorders. Impaired dopamine signaling is implicated in several neuropsychiatric disorders such as Parkinson’s disease, drug addiction, schizophrenia, attention-deficit/hyperactivity disorder, obsessive-compulsive disorder and Tourette’s syndrome. Therefore, dopamine plays a crucial role in the nervous system, where its proper modulation of neural circuits may enhance plasticity-related procedures, but disturbances in dopamine signaling might be involved in numerous neuropsychiatric disorders. In recent years, several computational models are proposed to formulate the involvement of dopamine in synaptic plasticity or neuropsychiatric disorders and address their connection based on the experimental findings.

Dendritic and Axonal Propagation Delays May Shape Neuronal Networks With Plastic Synapses

Biological neuronal networks are highly adaptive and plastic. For instance, spike-timing-dependent plasticity (STDP) is a core mechanism which adapts the synaptic strengths based on the relative timing of pre- and postsynaptic spikes. In various fields of physiology, time delays cause a plethora of biologically relevant dynamical phenomena. However, time delays increase the complexity of model systems together with the computational and theoretical analysis burden. Accordingly, in computational neuronal network studies propagation delays were often neglected. As a downside, a classic STDP rule in oscillatory neurons without propagation delays is unable to give rise to bidirectional synaptic couplings, i.e., loops or uncoupled states. This is at variance with basic experimental results. In this mini review, we focus on recent theoretical studies focusing on how things change in the presence of propagation delays. Realistic propagation delays may lead to the emergence of neuronal activity and synaptic connectivity patterns, which cannot be captured by classic STDP models. In fact, propagation delays determine the inventory of attractor states and shape their basins of attractions. The results reviewed here enable to overcome fundamental discrepancies between theory and experiments. Furthermore, these findings are relevant for the development of therapeutic brain stimulation techniques aiming at shifting the diseased brain to more favorable attractor states.

Propagation delays determine neuronal activity and synaptic connectivity patterns emerging in plastic neuronal networks

In plastic neuronal networks, the synaptic strengths are adapted to the neuronal activity. Specifically, spike-timing-dependent plasticity (STDP) is a fundamental mechanism that modifies the synaptic strengths based on the relative timing of pre- and postsynaptic spikes, taking into account the spikes' temporal order. In many studies, propagation delays were neglected to avoid additional dynamic complexity or computational costs. So far, networks equipped with a classic STDP rule typically rule out bidirectional couplings (i.e., either loops or uncoupled states) and are, hence, not able to reproduce fundamental experimental findings. In this review paper, we consider additional features, e.g., extensions of the classic STDP rule or additional aspects like noise, in order to overcome the contradictions between theory and experiment. In addition, we review in detail recent studies showing that a classic STDP rule combined with realistic propagation patterns is able to capture relevant experimental findings. In two coupled oscillatory neurons with propagation delays, bidirectional synapses can be preserved and potentiated. This result also holds for large networks of type-II phase oscillators. In addition, not only the mean of the initial distribution of synaptic weights, but also its standard deviation crucially determines the emergent structural connectivity, i.e., the mean final synaptic weight, the number of two-neuron loops, and the symmetry of the final connectivity pattern. The latter is affected by the firing rates, where more symmetric synaptic configurations emerge at higher firing rates. Finally, we discuss these findings in the context of the computational neuroscience-based development of desynchronizing brain stimulation techniques.

Modeling Pitch Perception With an Active Auditory Model Extended by Octopus Cells

Pitch is an essential category for musical sensations. Models of pitch perception are vividly discussed up to date. Most of them rely on definitions of mathematical methods in the spectral or temporal domain. Our proposed pitch perception model is composed of an active auditory model extended by octopus cells. The active auditory model is the same as used in the Stimulation based on Auditory Modeling (SAM), a successful cochlear implant sound processing strategy extended here by modeling the functional behavior of the octopus cells in the ventral cochlear nucleus and by modeling their connections to the auditory nerve fibers (ANFs). The neurophysiological parameterization of the extended model is fully described in the time domain. The model is based on latency-phase en- and decoding as octopus cells are latency-phase rectifiers in their local receptive fields. Pitch is ubiquitously represented by cascaded firing sweeps of octopus cells. Based on the firing patterns of octopus cells, inter-spike interval histograms can be aggregated, in which the place of the global maximum is assumed to encode the pitch.

Rhythmogenesis evolves as a consequence of long-term plasticity of inhibitory synapses

Brain rhythms are widely believed to reflect numerous cognitive processes. Changes in rhythmicity have been associated with pathological states. However, the mechanism underlying these rhythms remains unknown. Here, we present a theoretical analysis of the evolvement of rhythm generating capabilities in neuronal circuits. We tested the hypothesis that brain rhythms can be acquired via an intrinsic unsupervised learning process of activity dependent plasticity. Specifically, we focused on spike timing dependent plasticity (STDP) of inhibitory synapses. We detail how rhythmicity can develop via STDP under certain conditions that serve as a natural prediction of the hypothesis. We show how global features of the STDP rule govern and stabilize the resultant rhythmic activity. Finally, we demonstrate how rhythmicity is retained even in the face of synaptic variability. This study suggests a role for inhibitory plasticity that is beyond homeostatic processes.

Delay-Induced Multistability and Loop Formation in Neuronal Networks with Spike-Timing-Dependent Plasticity

Spike-timing-dependent plasticity (STDP) adjusts synaptic strengths according to the precise timing of pre- and postsynaptic spike pairs. Theoretical and computational studies have revealed that STDP may contribute to the emergence of a variety of structural and dynamical states in plastic neuronal populations. In this manuscript, we show that by incorporating dendritic and axonal propagation delays in recurrent networks of oscillatory neurons, the asymptotic connectivity displays multistability, where different structures emerge depending on the initial distribution of the synaptic strengths. In particular, we show that the standard deviation of the initial distribution of synaptic weights, besides its mean, determines the main properties of the emergent structural connectivity such as the mean final synaptic weight, the number of two-neuron loops and the symmetry of the final structure. We also show that the firing rates of the neurons affect the evolution of the network, and a more symmetric configuration of the synapses emerges at higher firing rates. We justify the network results based on a two-neuron framework and show how the results translate to large recurrent networks.

Robustness of STDP to spike timing jitter

In Hebbian plasticity, neural circuits adjust their synaptic weights depending on patterned firing. Spike-timing-dependent plasticity (STDP), a synaptic Hebbian learning rule, relies on the order and timing of the paired activities in pre- and postsynaptic neurons. Classically, in ex vivo experiments, STDP is assessed with deterministic (constant) spike timings and time intervals between successive pairings, thus exhibiting a regularity that differs from biological variability. Hence, STDP emergence from noisy inputs as occurring in in vivo-like firing remains unresolved. Here, we used noisy STDP pairings where the spike timing and/or interval between pairings were jittered. We explored with electrophysiology and mathematical modeling, the impact of jitter on three forms of STDP at corticostriatal synapses: NMDAR-LTP, endocannabinoid-LTD and endocannabinoid-LTP. We found that NMDAR-LTP was highly fragile to jitter, whereas endocannabinoid-plasticity appeared more resistant. When the frequency or number of pairings was increased, NMDAR-LTP became more robust and could be expressed despite strong jittering. Our results identify endocannabinoid-plasticity as a robust form of STDP, whereas the sensitivity to jitter of NMDAR-LTP varies with activity frequency. This provides new insights into the mechanisms at play during the different phases of learning and memory and the emergence of Hebbian plasticity in in vivo-like activity.

Computationally Developed Sham Stimulation Protocol for Multichannel Desynchronizing Stimulation

A characteristic pattern of abnormal brain activity is abnormally strong neuronal synchronization, as found in several brain disorders, such as tinnitus, Parkinson's disease, and epilepsy. As observed in several diseases, different therapeutic interventions may induce a placebo effect that may be strong and hinder reliable clinical evaluations. Hence, to distinguish between specific, neuromodulation-induced effects and unspecific, placebo effects, it is important to mimic the therapeutic procedure as precisely as possibly, thereby providing controls that actually lack specific effects. Coordinated Reset (CR) stimulation has been developed to specifically counteract abnormally strong synchronization by desynchronization. CR is a spatio-temporally patterned multichannel stimulation which reduces the extent of coincident neuronal activity and aims at an anti-kindling, i.e., an unlearning of both synaptic connectivity and neuronal synchrony. Apart from acute desynchronizing effects, CR may cause sustained, long-lasting desynchronizing effects, as already demonstrated in pre-clinical and clinical proof of concept studies. In this computational study, we set out to computationally develop a sham stimulation protocol for multichannel desynchronizing stimulation. To this end, we compare acute effects and long-lasting effects of six different spatio-temporally patterned stimulation protocols, including three variants of CR, using a no-stimulation condition as additional control. This is to provide an inventory of different stimulation algorithms with similar fundamental stimulation parameters (e.g., mean stimulation rates) but qualitatively different acute and/or long-lasting effects. Stimulation protocols sharing basic parameters, but inducing nevertheless completely different or even no acute effects and/or after-effects, might serve as controls to validate the specific effects of particular desynchronizing protocols such as CR. In particular, based on our computational findings we propose a multichannel sham (i.e., inactive) stimulation protocol as control condition for phase 2 and phase 3 studies with desynchronizing multichannel stimulation techniques.