Theta Neuron Research Articles

Improving working memory by electrical stimulation and cross-frequency coupling

Working memory (WM) is essential for the temporary storage and processing of information required for complex cognitive tasks and relies on neuronal theta and gamma oscillations. Given the limited capacity of WM, researchers have investigated various methods to improve it, including transcranial alternating current stimulation (tACS), which modulates brain activity at specific frequencies. One particularly promising approach is theta-gamma peak-coupled-tACS (TGCp-tACS), which simulates the natural interaction between theta and gamma oscillations that occurs during cognitive control in the brain. The aim of this study was to improve WM in healthy young adults with TGCp-tACS, focusing on both behavioral and neurophysiological outcomes. Thirty-one participants completed five WM tasks under both sham and verum stimulation conditions. Electroencephalography (EEG) recordings before and after stimulation showed that TGCp-tACS increased power spectral density (PSD) in the high-gamma region at the stimulation site, while PSD decreased in the theta and delta regions throughout the cortex. From a behavioral perspective, although no significant changes were observed in most tasks, there was a significant improvement in accuracy in the 14-item Sternberg task, indicating an improvement in phonological WM. In conclusion, TGCp-tACS has the potential to promote and improve the phonological component of WM. To fully realize the cognitive benefits, further research is needed to refine the stimulation parameters and account for individual differences, such as baseline cognitive status and hormonal factors.

How synaptic function controls critical transitions in spiking neuron networks: insight from a Kuramoto model reduction.

The dynamics of synaptic interactions within spiking neuron networks play a fundamental role in shaping emergent collective behavior. This paper studies a finite-size network of quadratic integrate-and-fire neurons interconnected via a general synaptic function that accounts for synaptic dynamics and time delays. Through asymptotic analysis, we transform this integrate-and-fire network into the Kuramoto-Sakaguchi model, whose parameters are explicitly expressed via synaptic function characteristics. This reduction yields analytical conditions on synaptic activation rates and time delays determining whether the synaptic coupling is attractive or repulsive. Our analysis reveals alternating stability regions for synchronous and partially synchronous firing, dependent on slow synaptic activation and time delay. We also demonstrate that the reduced microscopic model predicts the emergence of synchronization, weakly stable cyclops states, and non-stationary regimes remarkably well in the original integrate-and-fire network and its theta neuron counterpart. Our reduction approach promises to open the door to rigorous analysis of rhythmogenesis in networks with synaptic adaptation and plasticity.

Exact finite-dimensional description for networks of globally coupled spiking neurons.

We consider large networks of globally coupled spiking neurons and derive an exact low-dimensional description of their collective dynamics in the thermodynamic limit. Individual neurons are described by the Ermentrout-Kopell canonical model that can be excitable or tonically spiking and interact with other neurons via pulses. Utilizing the equivalence of the quadratic integrate-and-fire and the theta-neuron formulations, we first derive the dynamical equationsin terms of the Kuramoto-Daido order parameters (Fourier modes of the phase distribution) and relate them to two biophysically relevant macroscopic observables, the firing rate and the mean voltage. For neurons driven by Cauchy white noise or for Cauchy-Lorentz distributed input currents, we adapt the results by Cestnik and Pikovsky [Chaos 32, 113126 (2022)1054-150010.1063/5.0106171] and show that for arbitrary initial conditions the collective dynamics reduces to six dimensions. We also prove that in this case the dynamics asymptotically converges to a two-dimensional invariant manifold first discovered by Ott and Antonsen. For identical, noise-free neurons, the dynamics reduces to three dimensions, becoming equivalent to the Watanabe-Strogatz description. We illustrate the exact six-dimensional dynamics outside the invariant manifold by calculating nontrivial basins of different asymptotic regimes in a bistable situation.

The steady state and response to a periodic stimulation of the firing rate for a theta neuron with correlated noise

The stochastic activity of neurons is caused by various sources of correlated fluctuations and can be described in terms of simplified, yet biophysically grounded, integrate-and-fire models. One paradigmatic model is the quadratic integrate-and-fire model and its equivalent phase description by the theta neuron. Here we study the theta neuron model driven by a correlated Ornstein-Uhlenbeck noise and by periodic stimuli. We apply the matrix-continued-fraction method to the associated Fokker-Planck equation to develop an efficient numerical scheme to determine the stationary firing rate as well as the stimulus-induced modulation of the instantaneous firing rate. For the stationary case, we identify the conditions under which the firing rate decreases or increases by the effect of the colored noise and compare our results to existing analytical approximations for limit cases. For an additional periodic signal we demonstrate how the linear and nonlinear response terms can be computed and report resonant behavior for some of them. We extend the method to the case of two periodic signals, generally with incommensurable frequencies, and present a particular case for which a strong mixed response to both signals is observed, i.e. where the response to the sum of signals differs significantly from the sum of responses to the single signals. We provide Python code for our computational method: https://github.com/jannikfranzen/theta_neuron.

Theta neuron subject to delayed feedback: a prototypical model for self-sustained pulsing

We consider a single theta neuron with delayed self-feedback in the form of a Dirac delta function in time. Because the dynamics of a theta neuron on its own can be solved explicitly—it is either excitable or shows self-pulsations—we are able to derive algebraic expressions for the existence and stability of the periodic solutions that arise in the presence of feedback. These periodic solutions are characterized by one or more equally spaced pulses per delay interval, and there is an increasing amount of multistability with increasing delay time. We present a complete description of where these self-sustained oscillations can be found in parameter space; in particular, we derive explicit expressions for the loci of their saddle-node bifurcations. We conclude that the theta neuron with delayed self-feedback emerges as a prototypical model: it provides an analytical basis for understanding pulsating dynamics observed in other excitable systems subject to delayed self-coupling.

Causal Evidence for a Role of Cerebellar Lobulus Simplex in Prefrontal-Hippocampal Interaction in Spatial Working Memory Decision-Making.

Spatial working memory (SWM) is a cerebrocerebellar cognitive skill supporting survival-relevant behaviors, such as optimizing foraging behavior by remembering recent routes and visited sites. It is known that SWM decision-making in rodents requires the medial prefrontal cortex (mPFC) and dorsal hippocampus. The decision process in SWM tasks carries a specific electrophysiological signature of a brief, decision-related increase in neuronal communication in the form of an increase in the coherence of neuronal theta oscillations (4-12Hz) between the mPFC and dorsal hippocampus, a finding we replicated here during spontaneous exploration of a plus maze in freely moving mice. We further evaluated SWM decision-related coherence changes within frequency bands above theta. Decision-related coherence increases occurred in seven frequency bands between 4 and 200Hz and decision-outcome-related differences in coherence modulation occurred within the beta and gamma frequency bands and in higher frequency oscillations up to 130Hz. With recent evidence that Purkinje cells in the cerebellar lobulus simplex (LS) represent information about the phase and phase differences of gamma oscillations in the mPFC and dorsal hippocampus, we hypothesized that LS might be involved in the modulation of mPFC-hippocampal gamma coherence. We show that optical stimulation of LS significantly impairs SWM performance and decision-related mPFC-dCA1 coherence modulation, providing causal evidence for an involvement of cerebellar LS in SWM decision-making at the behavioral and neuronal level. Our findings suggest that the cerebellum might contribute to SWM decision-making by optimizing the decision-related modulation of mPFC-dCA1 coherence.

A neuronal theta band signature of error monitoring during integration of facial expression cues.

Error monitoring is the metacognitive process by which we are able to detect and signal our errors once a response has been made. Monitoring when the outcome of our actions deviates from the intended goal is crucial for behavior, learning, and the development of higher-order social skills. Here, we explored the neuronal substrates of error monitoring during the integration of facial expression cues using electroencephalography (EEG). Our goal was to investigate the signatures of error monitoring before and after a response execution dependent on the integration of facial cues. We followed the hypothesis of midfrontal theta as a robust neuronal marker of error monitoring since it has been consistently described as a mechanism to signal the need for cognitive control. Also, we hypothesized that EEG frequency-domain components might bring advantage to study error monitoring in complex scenarios as it carries information from locked and non-phase-locked signals. A challenging go/no-go saccadic paradigm was applied to elicit errors: integration of facial emotional signals and gaze direction was required to solve it. EEG data were acquired from twenty healthy participants and analyzed at the level of theta band activity during response preparation and execution. Although theta modulation has been consistently demonstrated during error monitoring, it is still unclear how early it starts to occur. We found theta power differences at midfrontal channels between correct and error trials. Theta was higher immediately after erroneous responses. Moreover, before response initiation we observed the opposite: lower theta preceding errors. These results suggest theta band activity not only as an index of error monitoring, which is needed to enhance cognitive control, but also as a requisite for success. This study adds to previous evidence for the role of theta band in error monitoring processes by revealing error-related patterns even before response execution in complex tasks, and using a paradigm requiring the integration of facial expression cues.

Histamine 3 receptor inverse agonist Samelisant (SUVN-G3031): Pharmacological characterization of an investigational agent for the treatment of cognitive disorders.

Central histamine H3 receptors are a family of presynaptic auto and heteroreceptors. Blockade of the presynaptic H3 receptors activates the downstream pathway(s) involved in the processes of learning and memory, making it a potential therapeutic option for ameliorating cognitive dysfunction. Samelisant (SUVN-G3031) is a potent and selective inverse agonist at the H3 receptors. The aim of this research is to study the effects of Samelisant in diverse animal models of cognitive functions. The effects of Samelisant on cognitive functions were studied using social recognition, object recognition and Morris water maze tasks. Neurochemical and electrophysiological effects of Samelisant were monitored using microdialysis and electroencephalography techniques. Samelisant showed procognitive effects in diverse animal models of cognition at doses ranging from 0.3 to 3 mg/kg, per os (p.o.) (social recognition and object recognition task). Samelisant significantly increased the brain acetylcholine levels in the cortex at doses of 10 and 20 mg/kg, p.o. In the Morris water maze task, combined administration of suboptimal doses of Samelisant and donepezil resulted in procognitive effects significantly larger than the either treatment. Similarly, Samelisant significantly potentiated the effects of donepezil on pharmacodynamic biomarkers of cognition i.e. acetylcholine levels in brain and neuronal theta oscillations. Samelisant may have potential utility in the treatment of cognitive deficits associated with hypocholinergic state.

Auditory detection is modulated by theta phase of silent lip movements.

Audiovisual speech perception relies, among other things, on our expertise to map a speaker's lip movements with speech sounds. This multimodal matching is facilitated by salient syllable features that align lip movements and acoustic envelope signals in the 4–8 ​Hz theta band. Although non-exclusive, the predominance of theta rhythms in speech processing has been firmly established by studies showing that neural oscillations track the acoustic envelope in the primary auditory cortex. Equivalently, theta oscillations in the visual cortex entrain to lip movements, and the auditory cortex is recruited during silent speech perception. These findings suggest that neuronal theta oscillations may play a functional role in organising information flow across visual and auditory sensory areas. We presented silent speech movies while participants performed a pure tone detection task to test whether entrainment to lip movements directs the auditory system and drives behavioural outcomes. We showed that auditory detection varied depending on the ongoing theta phase conveyed by lip movements in the movies. In a complementary experiment presenting the same movies while recording participants' electro-encephalogram (EEG), we found that silent lip movements entrained neural oscillations in the visual and auditory cortices with the visual phase leading the auditory phase. These results support the idea that the visual cortex entrained by lip movements filtered the sensitivity of the auditory cortex via theta phase synchronization.

Moving bumps in theta neuron networks

We consider large networks of theta neurons on a ring, synaptically coupled with an asymmetric kernel. Such networks support stable "bumps" of activity, which move along the ring if the coupling kernel is asymmetric. We investigate the effects of the kernel asymmetry on the existence, stability, and speed of these moving bumps using continuum equations formally describing infinite networks. Depending on the level of heterogeneity within the network, we find complex sequences of bifurcations as the amount of asymmetry is varied, in strong contrast to the behavior of a classical neural field model.

A theta rhythm in macaque visual cortex and its attentional modulation

Theta rhythms govern rodent sniffing and whisking, and human language processing. Human psychophysics suggests a role for theta also in visual attention. However, little is known about theta in visual areas and its attentional modulation. We used electrocorticography (ECoG) to record local field potentials (LFPs) simultaneously from areas V1, V2, V4, and TEO of two macaque monkeys performing a selective visual attention task. We found a ≈4-Hz theta rhythm within both the V1-V2 and the V4-TEO region, and theta synchronization between them, with a predominantly feedforward directed influence. ECoG coverage of large parts of these regions revealed a surprising spatial correspondence between theta and visually induced gamma. Furthermore, gamma power was modulated with theta phase. Selective attention to the respective visual stimulus strongly reduced these theta-rhythmic processes, leading to an unusually strong attention effect for V1. Microsaccades (MSs) were partly locked to theta. However, neuronal theta rhythms tended to be even more pronounced for epochs devoid of MSs. Thus, we find an MS-independent theta rhythm specific to visually driven parts of V1-V2, which rhythmically modulates local gamma and entrains V4-TEO, and which is strongly reduced by attention. We propose that the less theta-rhythmic and thereby more continuous processing of the attended stimulus serves the exploitation of this behaviorally most relevant information. The theta-rhythmic and thereby intermittent processing of the unattended stimulus likely reflects the ecologically important exploration of less relevant sources of information.

Relationship between the mechanisms of gamma rhythm generation and the magnitude of the macroscopic phase response function in a population of excitatory and inhibitory modified quadratic integrate-and-fire neurons.

Gamma oscillations are thought to play an important role in brain function. Interneuron gamma (ING) and pyramidal interneuron gamma (PING) mechanisms have been proposed as generation mechanisms for these oscillations. However, the relation between the generation mechanisms and the dynamical properties of the gamma oscillation are still unclear. Among the dynamical properties of the gamma oscillation, the phase response function (PRF) is important because it encodes the response of the oscillation to inputs. Recently, the PRF for an inhibitory population of modified theta neurons that generate an ING rhythm was computed by the adjoint method applied to the associated Fokker-Planck equation (FPE) for the model. The modified theta model incorporates conductance-based synapses as well as the voltage and current dynamics. Here, we extended this previous work by creating an excitatory-inhibitory (E-I) network using the modified theta model and described the population dynamics with the corresponding FPE. We conducted a bifurcation analysis of the FPE to find parameter regions which generate gamma oscillations. In order to label the oscillatory parameter regions by their generation mechanisms, we defined ING- and PING-type gamma oscillation in a mathematically plausible way based on the driver of the inhibitory population. We labeled the oscillatory parameter regions by these generation mechanisms and derived PRFs via the adjoint method on the FPE in order to investigate the differences in the responses of each type of oscillation to inputs. PRFs for PING and ING mechanisms are derived and compared. We found the amplitude of the PRF for the excitatory population is larger in the PING case than in the ING case. Finally, the E-I population of the modified theta neuron enabled us to analyze the PRFs of PING-type gamma oscillation and the entrainment ability of E and I populations. We found a parameter region in which PRFs of E and I are both purely positive in the case of PING oscillations. The different entrainment abilities of E and I stimulation as governed by the respective PRFs was compared to direct simulations of finite populations of model neurons. We find that it is easier to entrain the gamma rhythm by stimulating the inhibitory population than by stimulating the excitatory population as has been found experimentally.

Developmental Changes in Hippocampal CA1 Single Neuron Firing and Theta Activity during Associative Learning.

Hippocampal development is thought to play a crucial role in the emergence of many forms of learning and memory, but ontogenetic changes in hippocampal activity during learning have not been examined thoroughly. We examined the ontogeny of hippocampal function by recording theta and single neuron activity from the dorsal hippocampal CA1 area while rat pups were trained in associative learning. Three different age groups [postnatal days (P)17-19, P21-23, and P24-26] were trained over six sessions using a tone conditioned stimulus (CS) and a periorbital stimulation unconditioned stimulus (US). Learning increased as a function of age, with the P21-23 and P24-26 groups learning faster than the P17-19 group. Age- and learning-related changes in both theta and single neuron activity were observed. CA1 pyramidal cells in the older age groups showed greater task-related activity than the P17-19 group during CS-US paired sessions. The proportion of trials with a significant theta (4–10 Hz) power change, the theta/delta ratio, and theta peak frequency also increased in an age-dependent manner. Finally, spike/theta phase-locking during the CS showed an age-related increase. The findings indicate substantial developmental changes in dorsal hippocampal function that may play a role in the ontogeny of learning and memory.

Exact Neural Fields Incorporating Gap Junctions

We consider networks of quadratic integrate-and-fire neurons coupled via both chemical synapses and gap junctions. After transforming to “theta neuron” coordinates, a network's governing equations are of a form amenable to the use of the Ott--Antonsen ansatz. This ansatz allows us to derive an exact description of a network's dynamics in the limit of an infinite number of neurons. For an all-to-all connected network we derive a single (complex) ordinary differential equation, while for spatially extended networks we derive neural field equations (nonlocal partial differential equations). We perform extensive numerical analysis of the resulting equations, showing how the presence of gap junctional coupling can destroy certain spatiotemporal patterns, such as stationary “bump” solutions, and create others, such as traveling waves and spatiotemporal chaos. Our results provide significant insight into the effects of gap junctions on the dynamics of networks of Type I neurons.

Fastest strategy to achieve given number of neuronal firing in theta model

We investigate the constrained optimization of excitatory synaptic input patterns to fastest generate given number of spikes in theta neuron model. Optimal input timings and strengths are identified by using phase plane arguments for discrete input kicks with a given total magnitude. Furthermore, analytical results are conducted to estimate the firing time of given number of spikes resulting from a given input train. We obtain the fastest strategy as the total input size increases. In particular, when the parameter −b is large and total input size G is not so large, there are two candidate strategies to fastest achieve given number of spikes, which depend on the considered parameters. The fastest strategy for some cases of G≫−b to fire m spikes should partition m spikes into m−n+1 spikes for the highest band, with largest g, and one spike for each subsequent n−1 band. When G is sufficiently large, big kick is the fastest strategy. In addition, we establish an optimal value for the dependent variable, θ, where each input should be delivered in a non-threshold-based strategy to fastest achieve given output of subsequent spikes. Moreover, we find that reset and kick strategy is the fastest when G is small and G≫−b. The obtained results can lead to a better understanding of how the period of nonlinear oscillators are affected by different input timings and strengths.

Emergent Dynamics from Spiking Neuron Networks through Symmetry Breaking of Connectivity

Low-dimensional attractive manifolds with flows prescribing the evolution of state variables are commonly used to capture the lawful behavior of behavioral and cognitive variables. Neural network dynamics underlie many of the mechanistic explanations of function and demonstrate the existence of such low-dimensional attractive manifolds. In this study, we focus on exploring the network mechanisms due to asymmetric couplings giving rise to the emergence of arbitrary flows in low dimensional spaces. Here we use a spiking neural network model, specifically the theta neuron model and simple synaptic dynamics, to show how a qualitatively identical set of basic behaviors arises from different combinations of couplings with broken symmetry, in fluctuations of both firing rate and spike timing. We further demonstrate how such network dynamics can be combined to create more complex processes. These results suggest that 1) asymmetric coupling is not always a variance to be averaged over, 2) different networks may produce the same dynamics by different dynamical routes and 3) complex dynamics may be formed by simpler dynamics through a combination of couplings.

Bilateral frontal theta-waves in EEG of 7–8-year-old children with learning difficulties: Qualitative and quantitative analysis

We analyzed EEG recorded in the rest condition (eye closed) in 22 children aged from 7 to 8 years old who experienced learning difficulties and whose EEG recordings were characterized by sporadic short-term appearance of bilateral synchronous slow waves over the frontal and/or central cortices--frontal theta-waves (FTW). The vector autoregressive modeling was used in order to assess the strength of directed cortico-cortical functional connectivity pattern for FTW and for surrounding EEG. The comparison of the two patterns showed that FTW is characterized by diffuse strengthening of the functional links connecting frontal, central and (to some extent) temporal cortices as well as the links directed to the above regions from the other cortical areas. The results of the study suggest that FTW is most probably caused by the common for the fronto-central cortices neuronal theta activity synchronized via cortico-subcortical links. This suggestion is in a good agreement with the view that FTW reflects the alterations in functioning of fronto-thalamic system.

Single cell dynamics determine strength of chaos in collective network dynamics

Cortical neurons have been found to exhibit a much higher action potential (AP) onset rapidness than expected from standard biophysical neuron models [1]. This has raised fundamental physiological questions about the origin of this phenomenon [1,2]. An important issue for the understanding of information processing in the cortex is the impact of rapid AP initiation on the collective dynamics of cortical networks. Here, we report that it in fact strongly reduces the information loss in chaotic cortical networks. As a model of cortical networks, we analyzed spiking neuron networks in the balanced state [3]. The balanced state provides an explanation of the temporally irregular activity of cortical networks observed in vivo[4]. In this state neurons are driven by large input fluctuations, resulting from a dynamical balance of excitation and inhibition. Networks of theta neurons in the balanced state exhibit strongly chaotic dynamics [5]. We recently performed an exact analysis of the full spectra of Lyapunov exponents in such networks, revealing that deterministic chaos is extensive and information is lost at strikingly high rates of up to 1 bit per spike per neuron. The theta neuron model, however, shares the relatively low AP onset rapidness of other biophysical standard neuron models. Here we show that increasing the AP onset rapidness of single neurons strongly reduces the intensity of chaos in balanced networks. Based on the theta neuron model, we developed a new neuron model with variable AP onset rapidness, called the rapid theta neuron model. Parametrically increasing the AP onset rapidness in the neurons reduced the information loss in the chaotic network dynamics and could even induce a transition to stable irregular dynamics (Fig. 1). These results reveal that the action potential rapidness of single neurons plays an important role in the

Changes in the Power Levels of Cortical EEG Rhythms in Cats during Training Using Acoustic Feedback Signals

Chronic experiments on two conscious cats were performed to study the dynamics of the ratios of spectral power levels of beta and theta rhythms and neuron activity in the dopaminergic system of the ventral tegmentum during EEG feedback sessions. Training was performed using a model in which the level of sound signals presented to the animals decreased as the spectral power ratios of the EEG beta and theta rhythms recorded in the frontal leads increased. In a control series, the changes in the sound signal level were independent of the ongoing EEG. These experiments showed that the ratio of the spectral power levels of the beta and theta rhythms changed during feedback sessions, with increases in the spectral power of the beta rhythm and decreases in the spectral power of the theta rhythm. These changes were accompanied by increases in the activity of presumptive dopaminergic neurons in the ventral tegmentum.

Theta Oscillations and Reactivity of Hippocampal Stratum Oriens Neurons

The supposition was advanced that the neuronal theta rhythmicity is the key mode of signal selection at the hippocampal level. To address this hypothesis, the experimental data on the responses of putative hippocampal interneurons of the stratum oriens CA1-CA3 to stimulation during enhanced theta rhythm and after its blockade are reviewed. Both a strong increase and a decrease of the natural theta rhythm disturbed the reactions of hippocampal neurons; during theta augmentation, the responses were masked or disappeared, and after theta blockade, they lost the ability to habituate. In both cases, two important events were broken: the resetting of the background activity and the phase-locking of theta cycles to stimulus. These data allow one to suppose that only important stimuli are normally capable to evoke these events and these stimuli are selected for recording. When the response to a significant stimulus occurs, the following theta prevents the responses to other stimuli. This probably protects the hippocampal activity from interference from irrelevant signals. Presumably, the absence of the theta deprives the hippocampus of this protection. During enhanced and persistent theta oscillations, the reset disappeared and theta bursts were generated without stimulus locking. In this state, the system is probably closed and the information cannot be recorded. During the theta blockade, the reset was too long and did not habituate. In this case, the system is open for any signals and the hippocampus loses the ability to select signal. This analysis suggests that information selection in the hippocampus may be performed with the participation of nonpyramidal neurons.