Synaptic Time Delay Research Articles

Spiking Neural Membrane Systems with Adaptive Synaptic Time Delay.

Spiking neural membrane systems (or spiking neural P systems, SNP systems) are a new type of computation model which have attracted the attention of plentiful scholars for parallelism, time encoding, interpretability and extensibility. The original SNP systems only consider the time delay caused by the execution of rules within neurons, but not caused by the transmission of spikes via synapses between neurons and its adaptive adjustment. In view of the importance of time delay for SNP systems, which are a time encoding computation model, this study proposes SNP systems with adaptive synaptic time delay (ADSNP systems) based on the dynamic regulation mechanism of synaptic transmission delay in neural systems. In ADSNP systems, besides neurons, astrocytes that can generate adenosine triphosphate (ATP) are introduced. After receiving spikes, astrocytes convert spikes into ATP and send ATP to the synapses controlled by them to change the synaptic time delays. The Turing universality of ADSNP systems in number generating and accepting modes is proved. In addition, a small universal ADSNP system using 93 neurons and astrocytes is given. The superiority of the ADSNP system is demonstrated by comparison with the six variants. Finally, an ADSNP system is constructed for credit card fraud detection, which verifies the feasibility of the ADSNP system for solving real-world problems. By considering the adaptive synaptic delay, ADSNP systems better restore the process of information transmission in biological neural networks, and enhance the adaptability of SNP systems, making the control of time more accurate.

Synchronization in STDP-driven memristive neural networks with time-varying topology

Synchronization is a widespread phenomenon in the brain. Despite numerous studies, the specific parameter configurations of the synaptic network structure and learning rules needed to achieve robust and enduring synchronization in neurons driven by spike-timing-dependent plasticity (STDP) and temporal networks subject to homeostatic structural plasticity (HSP) rules remain unclear. Here, we bridge this gap by determining the configurations required to achieve high and stable degrees of complete synchronization (CS) and phase synchronization (PS) in time-varying small-world and random neural networks driven by STDP and HSP. In particular, we found that decreasing P (which enhances the strengthening effect of STDP on the average synaptic weight) and increasing F (which speeds up the swapping rate of synapses between neurons) always lead to higher and more stable degrees of CS and PS in small-world and random networks, provided that the network parameters such as the synaptic time delay tau _c, the average degree langle k rangle, and the rewiring probability beta have some appropriate values. When tau _c, langle k rangle, and beta are not fixed at these appropriate values, the degree and stability of CS and PS may increase or decrease when F increases, depending on the network topology. It is also found that the time delay tau _c can induce intermittent CS and PS whose occurrence is independent F. Our results could have applications in designing neuromorphic circuits for optimal information processing and transmission via synchronization phenomena.

A change in behavioral state switches the pattern of motor output that underlies rhythmic head and orofacial movements

The breathing rhythm serves as a reference that paces orofacial motor actions and orchestrates active sensing. Past work has reported that pacing occurs solely at a fixed phase relative to sniffing. We re-evaluated this constraint as a function of exploratory behavior. Allocentric and egocentric rotations of the head and the electromyogenic activity of the motoneurons for head and orofacial movements were recorded in free-ranging rats as they searched for food. We found that a change in state from foraging to rearing is accompanied by a large phase shift in muscular activation relative to sniffing, and a concurrent change in the frequency of sniffing, so that pacing now occurs at one of the two phases. Further, head turning is biased such that an animal gathers a novel sample of its environment upon inhalation. In total, the coordination of active sensing has a previously unrealized computational complexity. This can emerge from hindbrain circuits with fixed architecture and credible synaptic time delays.

Combined effects of spike-timing-dependent plasticity and homeostatic structural plasticity on coherence resonance.

Efficient processing and transfer of information in neurons have been linked to noise-induced resonance phenomena such as coherence resonance (CR), and adaptive rules in neural networks have been mostly linked to two prevalent mechanisms: spike-timing-dependent plasticity (STDP) and homeostatic structural plasticity (HSP). Thus this paper investigates CR in small-world and random adaptive networks of Hodgkin-Huxley neurons driven by STDP and HSP. Our numerical study indicates that the degree of CR strongly depends, and in different ways, on the adjusting rate parameter P, which controls STDP, on the characteristic rewiring frequency parameter F, which controls HSP, and on the parameters of the network topology. In particular, we found two robust behaviors. (i) Decreasing P (which enhances the weakening effect of STDP on synaptic weights) and decreasing F (which slows down the swapping rate of synapses between neurons) always leads to higher degrees of CR in small-world and random networks, provided that the synaptic time delay parameter τ_{c} has some appropriate values. (ii) Increasing the synaptic time delay τ_{c} induces multiple CR (MCR)-the occurrence of multiple peaks in the degree of coherence as τ_{c} changes-in small-world and random networks, with MCR becoming more pronounced at smaller values of P and F. Our results imply that STDP and HSP can jointly play an essential role in enhancing the time precision of firing necessary for optimal information processing and transfer in neural systems and could thus have applications in designing networks of noisy artificial neural circuits engineered to use CR to optimize information processing and transfer.

Non-Gaussian noise and autapse-induced inverse stochastic resonance in bistable Izhikevich neural system under electromagnetic induction

Inverse stochastic resonance refers to the phenomenon that the average firing rate of a neuron is inhibited by noise, of which mechanism is widely used in a variety of biological cells and economic phenomena. In this paper, a bistable Izhikevich neural model and triple-neuron feed-forward loop Izhikevich neural network motifs under the effects of electromagnetic induction are constructed to investigate the phenomenon of inverse stochastic resonance induced by Non-Gaussian colored noise and electrical autapse. It is found that there exists a minimum value of the average firing rate curve caused by intensity of non-Gaussian colored noise, which is the phenomenon of inverse stochastic resonance. Obtained results also show that the inverse stochastic resonance induced by electrical autapse shows a decaying oscillation process with respect to synaptic delay time, and further research indicates that average firing rate has several minimums as a function of time delay of electrical autapse, which is called multiple inverse stochastic resonance. Furthermore, the inverse stochastic resonance in triple-neuron feed-forward loop Izhikevich neural network motifs are also examined, and it is confirmed that the responses of single Izhikevich neuron and neural network motifs to different parameters show consistency under same conditions, but also show some differences. Finally, the effects of electromagnetic induction on inverse stochastic resonance are checked both in single Izhikevich neural model and feed-forward loop network motifs. Electromagnetic induction feedback gain coefficient k1 should not be too large under certain conditions, otherwise it may cause FFL network motifs to loss the function of suppressing the discharge activity. No matter how the values of electromagnetic induction parameter k2 and magnetic flux leakage coefficient k3 change, they basically cannot affect the ISR in the feed-forward loop neural network motifs The conclusions of this paper may help researchers understanding how using unique mechanism of inverse stochastic resonance to find advantages and avoid disadvantages in biomedical field and many interdisciplinary research.

Synchronization in a multilayer neuronal network: effect of time delays

Multilayer neuronal networks provide the opportunity of considering multiple types of synaptic connections. In this paper, a two-layer neuronal network with chemical intralayer connections and electrical interlayer connections is investigated, where two layers have different spiking and bursting behaviours. The effects of synaptic time delay and also the self-feedback time delay on the synchronization are studied by calculating a statistical synchronization factor for intralayer synchronization and defining an interlayer synchronization error. It is observed that the interlayer coupling strength changes the spiking behaviour of first-layer neurons toward the chaotic behaviour of the second layer. The intralayer coupling is effective on the collective behaviour of the layers. Computing the synchronization measures for the time delays separately, shows the effects of each time delay on the network’s synchronized behaviour. It also reveals that the lowest interlayer synchronization error and the highest intralayer synchronization factors are attained by using the self-feedback delay.

Chimera states in a multilayer network of coupled and uncoupled neurons.

We study the emergence of chimera states in a multilayer neuronal network, where one layer is composed of coupled and the other layer of uncoupled neurons. Through the multilayer structure, the layer with coupled neurons acts as the medium by means of which neurons in the uncoupled layer share information in spite of the absence of physical connections among them. Neurons in the coupled layer are connected with electrical synapses, while across the two layers, neurons are connected through chemical synapses. In both layers, the dynamics of each neuron is described by the Hindmarsh-Rose square wave bursting dynamics. We show that the presence of two different types of connecting synapses within and between the two layers, together with the multilayer network structure, plays a key role in the emergence of between-layer synchronous chimera states and patterns of synchronous clusters. In particular, we find that these chimera states can emerge in the coupled layer regardless of the range of electrical synapses. Even in all-to-all and nearest-neighbor coupling within the coupled layer, we observe qualitatively identical between-layer chimera states. Moreover, we show that the role of information transmission delay between the two layers must not be neglected, and we obtain precise parameter bounds at which chimera states can be observed. The expansion of the chimera region and annihilation of cluster and fully coherent states in the parameter plane for increasing values of inter-layer chemical synaptic time delay are illustrated using effective range measurements. These results are discussed in the light of neuronal evolution, where the coexistence of coherent and incoherent dynamics during the developmental stage is particularly likely.

Modeling influences of dopamine on synchronization behavior of striatum

ABSTRACTA network model of striatum that comprises medium spiny neurons (MSNs) and fast spiking interneurons (FSIs) is constructed following the work of Humphries et al. (2009). The dynamic behavior of striatum microcircuit is investigated using a dopamine-modulated modified Izhikevich neuron model. The influences of dopamine on the synchronization behavior of the striatal microcircuit and the dependence on receptor type are investigated with and without time delay. To investigate the role of two types of dopamine receptors, D1 and D2, on the overall activity of the striatum microcircuit, the activities of two groups are considered as disconnected and connected. When the connection exists between D1 and D2 sub-networks with zero dopamine and time delay, neuronal activity decreases because of an inhibitory effect of the connected neurons of the other sub-network. In the presence of dopamine, an increase in the activity of D1 type MSNs and quiescent behavior of D2 type MSNs are observed when the time delay is zero. However, the diversity in synchronization of D1 and D2 type MSNs is observed for different synaptic time delays and synaptic strengths in the case that dopamine is present.

Physiologically motivated multiplex Kuramoto model describes phase diagram of cortical activity.

We derive a two-layer multiplex Kuramoto model from Wilson-Cowan type physiological equations that describe neural activity on a network of interconnected cortical regions. This is mathematically possible due to the existence of a unique, stable limit cycle, weak coupling, and inhibitory synaptic time delays. We study the phase diagram of this model numerically as a function of the inter-regional connection strength that is related to cerebral blood flow, and a phase shift parameter that is associated with synaptic GABA concentrations. We find three macroscopic phases of cortical activity: background activity (unsynchronized oscillations), epileptiform activity (highly synchronized oscillations) and resting-state activity (synchronized clusters/chaotic behaviour). Previous network models could hitherto not explain the existence of all three phases. We further observe a shift of the average oscillation frequency towards lower values together with the appearance of coherent slow oscillations at the transition from resting-state to epileptiform activity. This observation is fully in line with experimental data and could explain the influence of GABAergic drugs both on gamma oscillations and epileptic states. Compared to previous models for gamma oscillations and resting-state activity, the multiplex Kuramoto model not only provides a unifying framework, but also has a direct connection to measurable physiological parameters.

Synchronization of map-based neurons with memory and synaptic delay

Abstract Synchronization of two synaptically coupled neurons with memory and synaptic delay is studied using the Rulkov map, one of the simplest neuron models which displays specific features inherent to bursting dynamics. We demonstrate a transition from lag to anticipated synchronization as the relationship between the memory duration and the synaptic delay time changes. The neuron maps synchronize either with anticipation, if the memory is longer than the synaptic delay time, or with lag otherwise. The mean anticipation time is equal to the difference between the memory and synaptic delay independently of the coupling strength. Frequency entrainment and phase-locking phenomena as well as a transition from regular spikes to chaos are demonstrated with respect to the coupling strength.

Synaptotagmin Has an Essential Function in Synaptic Vesicle Positioning for Synchronous Release in Addition to Its Role as a Calcium Sensor

A multitude of synaptic proteins interact at the active zones of nerve terminals to achieve the high temporal precision of neurotransmitter release in synchrony with action potentials. Though synaptotagmin has been recognized as the Ca2+ sensor for synchronous release, it may have additional roles of action. We address this question at the calyx of Held, a giant presynaptic terminal, that allows biophysical dissection of multiple roles of molecules in synaptic transmission. Using high-level expression recombinant adenoviruses, in conjunction with a stereotactic surgery in postnatal day 1 rats, we overcame the previous inability to molecular perturb the calyx by overexpression of a mutated synaptotagmin. We report that this mutation leaves intrinsic Ca2+ sensitivity of vesicles intact while it destabilizes the readily releasable pool of vesicles and loosens the tight coupling between Ca2+ influx and release, most likely by interfering with the correct positioning of vesicles with respect to Ca2+ channels.

Just-in-Time Connectivity for Large Spiking Networks

The scale of large neuronal network simulations is memory limited due to the need to store connectivity information: connectivity storage grows as the square of neuron number up to anatomically relevant limits. Using the NEURON simulator as a discrete-event simulator (no integration), we explored the consequences of avoiding the space costs of connectivity through regenerating connectivity parameters when needed: just in time after a presynaptic cell fires. We explored various strategies for automated generation of one or more of the basic static connectivity parameters: delays, postsynaptic cell identities, and weights, as well as run-time connectivity state: the event queue. Comparison of the JitCon implementation to NEURON's standard NetCon connectivity method showed substantial space savings, with associated run-time penalty. Although JitCon saved space by eliminating connectivity parameters, larger simulations were still memory limited due to growth of the synaptic event queue. We therefore designed a JitEvent algorithm that added items to the queue only when required: instead of alerting multiple postsynaptic cells, a spiking presynaptic cell posted a callback event at the shortest synaptic delay time. At the time of the callback, this same presynaptic cell directly notified the first postsynaptic cell and generated another self-callback for the next delay time. The JitEvent implementation yielded substantial additional time and space savings. We conclude that just-in-time strategies are necessary for very large network simulations but that a variety of alternative strategies should be considered whose optimality will depend on the characteristics of the simulation to be run.

Synchrony and Antiphase State in Coupled Stochastic Neural Oscillators

Synchrony and antiphase phase locking in synaptically coupled neurons have been studied by employing numerical simulations. By using a Morris–Lecar (ML) model of two coupled stochastic neural oscillators, the effect of noise on the phase dynamics is extensively investigated in two different synaptic-coupling schemes; reciprocal excitatory and excitatory–inhibitory synapses. All possible dynamical features are presented in the parameter space of two important branching parameters, the coupling strength gsyn and the synaptic time delay τd. In this work, antiphase states are observed and analyzed as the breaking dynamics of synchrony. As a transition state from synchrony to antiphase phase locking in the stochastic system, intermittent antiphase states are also reported.

Learning-induced synchronization of a globally coupled excitable map system.

We propose a pulse-coupled neural network model in which one-dimensional excitable maps connected in a time-delayed network serve as the neural processing units. Although the individual processing unit has simple dynamical properties, the network exhibits collective chaos in the active states. Introducing a Hebbian learning algorithm for synaptic connections enhances the synchronization of excitation timing of the units within a subpopulation. The synchronizing clusters approximately exhibit a power-law size distribution, suggesting a hierarchy of synchronization. After applying a stationary signal to a subpopulation of the units with learning, the network then reproduces the signal. The learnable time range is much longer than the inherent time scale of the processing units, i.e., the synaptic delay time. Also, the network can reproduce periodic signals with time resolution finer than the delay time. Our present network model can be considered as a temporal association device which operates in chaotic states.

Synchrony and Clustering in Two and Three Synaptically Coupled Hodgkin–Huxley Neurons with a Time Delay

Synchrony and clustering in phase dynamics of two and three Hodgkin–Huxley neurons coupled globally by excitatory synapses with a time delay have been studied by numerical simulations and bifurcation analysis. In particular, we have obtained phase diagrams for the synchronous state and various cluster states in the parameter space of the synaptic coupling strength, G syn , and the synaptic time delay, τd, by computing the phase shifts of action potential spikes. In the weak coupling limit the computed phase diagrams are found to be consistent with the results of phase model analysis. The bifurcation analysis shows the phase model predictions break down at G syn ~ 0.3 and new complex phase dynamics appear. For all numbers of neurons explored, the critical time delay at which the nature of synaptic coupling changes completely is found to be typically about 2–4 msec, which may have some implications in modeling cortical dynamics.

Inhibition synchronizes sparsely connected cortical neurons within and between columns in realistic network models.

Networks of compartmental model neurons were used to investigate the biophysical basis of the synchronization observed between sparsely-connected neurons in neocortex. A model of a single column in layer 5 consisted of 100 model neurons: 80 pyramidal and 20 inhibitory. The pyramidal cells had conductances that caused intrinsic repetitive bursting at different frequencies when driven with the same input. When connected randomly with a connection density of 10%, a single model column displayed synchronous oscillatory action potentials in response to stationary, uncorrelated Poisson spike-train inputs. Synchrony required a high ratio of inhibitory to excitatory synaptic strength; the optimal ratio was 4 : 1, within the range observed in cortex. The synchrony was insensitive to variation in amplitudes of postsynaptic potentials and synaptic delay times, even when the mean synaptic delay times were varied over the range 1 to 7 ms. Synchrony was found to be sensitive to the strength of reciprocal inhibition between the inhibitory neurons in one column: Too weak or too strong reciprocal inhibition degraded intra-columnar synchrony. The only parameter that affected the oscillation frequency of the network was the strength of the external driving input which could shift the frequency between 35 to 60 Hz. The same results were obtained using a model column of 1000 neurons with a connection density of 5%, except that the oscillation became more regular. Synchronization between cortical columns was studied in a model consisting of two columns with 100 model neurons each. When connections were made with a density of 3% between the pyramidal cells of each column there was no inter-columnar synchrony and in some cases the columns oscillated 180 degrees out of phase with each other. Only when connections from the pyramidal cells in each column to the inhibitory cells in the other column were added was synchrony between the columns observed. This synchrony was established within one or two cycles of the oscillation and there was on average less than 1 ms phase difference between the two columns. Unlike the intra-columnar synchronization, the inter-columnar synchronization was found to be sensitive to the synaptic delay: A mean delay of greater than 5 ms virtually abolished synchronization between columns.

Responses of pigeon horizontal semicircular canal afferent fibers. II. High-frequency mechanical stimulation.

1. The horizontal semicircular canals of anesthetized (barbiturate/ketamine) pigeons were mechanically stimulated by the use of a piezoelectric micropusher that provided controlled indentation of the surgically exposed membranous horizontal semicircular duct. 2. Extracellular action potentials from single horizontal semicircular canal afferent (HCA) fibers were recorded during sinusoidal mechanical stimulation. This method of stimulation was shown in the companion paper to produce equivalent responses to those produced by rotation for frequencies ranging from 0.01 to 10 Hz. 3. Sinusoidal mechanical stimulation produced clearly entrained action potentials in some HCA fibers up to a frequency of 400 Hz (highest stimulus frequency tested), with stimulus probe displacements of +/- 1.0 and +/- 2.5 microns. Thirty-four HCA fibers were thoroughly studied. 4. For most HCA fibers, the number of action potentials per stimulus cycle decreased as stimulus frequency increased, until only one action potential per stimulus cycle was elicited. The point at which only one spike per stimulus cycle was observed was dependent on both the fiber's resting mean discharge rate (MDR) and the fiber's coefficient of variation (CV) obtained during the MDR. 5. Dynamic response properties of individual HCA fibers were found to be correlated with the fiber's CV and the resting level MDR. Neurons with lower CV values had less adaptation, higher short time constants, and lower high corner frequencies than did neurons with high CV values. For a given CV class of HCA fibers, neurons with higher MDRs had more enhanced gains and more advanced phase shifts at high stimulus frequencies than did neurons with lower MDRs. 6. Transfer function parameters affecting the dynamics of the high-frequency response were derived from the mean gain and phase shift values of regular-, intermediate-, and irregular-firing HCA fibers. Best-fit short time constant (tau S) values of 4.6, 1.9, and 2.0 ms; hair cell membrane time constant (tau M) values of 10.3, 13, and 7 ms; excitatory postsynaptic membrane time constant (tau E) values of 0.8, 0.4, and 0.5 ms; and synaptic delay time constant (tau D) values of 0.5, 0.5, and 1.4 ms were determined for regular, intermediate, and irregular classes of HCA fibers, respectively. 7. The values of 4.6, 1.9, and 2.0 ms derived for the regular, intermediate, and irregular afferents would suggest upper-corner frequencies of 35, 84, and 80 Hz for these classes of HCA fibers, respectively.

Computer simulation of the generation of the electroencephalogram

We have used a computer program for modeling some features of the scalp electroencephalogram (EEG) in terms of the time- and space-dependent interactions of populations of neurons in different hypothetical brain configurations of increasing levels of complexity. The input of the model consists of: (1) geometric and anatomic data characterizing the brain configuration, including interconnecting fiber pathways between neuronal groups; (2) physiologic characteristics of neurons, such as thresholds, driving potentials and conductances of excitatory and inhibitory synapses, synaptic delay times, and rise and fall times of postsynaptic potentials; and (3) functions describing the time-dependent afferent impulses to the brain configuration under study. The output of the model consists of plots of selected intracellular and extracellular potentials, including electrical potentials measured by an array of electrodes on the surface of the head, as a function of time. The objective was to assess how the characteristic frequencies seen in scalp EEG recordings might be determined by characteristics of local neuronal circuits (such as thalamic ‘pacemakers’) and by global circuit characteristics (such as cortico-cortical and thalamo-cortical interactions). We find that in our model the basic requirement for rhythmic behavior is the existence of local feedback circuits containing inhibitory neurons and that, when parameters of the model are chosen so that sustained rhythmic oscillations in the alpha frequency range are generated, the characteristic frequencies of these oscillations are primarily determined by the local circuit parameters, especially the duration of the inhibitory postsynaptic potentials, and are relatively independent of global circuit parameters such as the ranges of the long interconnecting axons and the propagation velocity of action potentials in these axons.

Synaptic interaction between the giant interneuron and the giant motorneuron in the hermit crab, Pagurus pollicarus

1. 1. An anatomical and physiological investigation was made of several components in the withdrawal escape response of the hermit crab, Pagurus pollicarus. 2. 2. In the fused last thoracic-first abdominal ganglion, the giant axon (GA) synapses with the giant motor (GM) neuron which innervates the abdominal flexor muscles. 3. 3. The synapse is unidirectional, conducting impulses only from the GA to the GM. 4. 4. The synaptic delay time is less than 0.4 msec. 5. 5. Concentrations of MgCl 2 and MnCl 2 which normally block chemical synapses were ineffective in interfering with GA-GM transmission. 6. 6. The GA-GM synapse was reversibly blocked by 0.5 mM DNP. 7. 7. It is concluded that GA-GM connection is a rectifying electrical synapse.