Pattern formation,contrast control,and oscillations in the short term memory of shunting on-center off-surround networks

The transformation of spatial patterns and their storage in short term memory by shunting neural networks are studied herein. Various mechanisms are described for real-time regulation of the amount of contrast with which a pattern will be stored. Parametric studies are described for the amount of contrast in the network responses to patterns presented at variable background or overall activity levels. Mechanisms for removing spurious peak splits and other disinhibitory responses are described. Furman's (1965) results on processing of patterns by shunting networks are generalized and reanalysed. Periodic responses (stable and unstable) corresponding to the time scale of slow cortical waves can be generated if a tonic input is set between two threshold activity levels. Their frequency as a function of tonic input size is unimodal. Order-preserving limit cycles are never found in STM; hence sustained slow oscillations as a mechanism for storing a pattern in STM are ruled out in favor of steady states (i.e., fast oscillations) with spatially graded activity levels. Such slow oscillations can, nonetheless, continuously retune the network's responsiveness to the patterns that perturb it.     

Oscillations in MAPK cascade triggered by two distinct designs of coupled positive and negative feedback loops

ABSTRACT: BACKGROUND: Feedback loops, both positive and negative are embedded in the Mitogen Activated Protein Kinase (MAPK) cascade. In the three layer MAPK cascade, both feedback loops originate from the terminal layer and their sites of action are either of the two upstream layers. Recent studies have shown that the cascade uses coupled positive and negative feedback loops in generating oscillations. Two plausible designs of coupled positive and negative feedback loops can be elucidated from the literature; in one design the positive feedback precedes the negative feedback in the direction of signal flow and vice-versa in another. But it remains unexplored how the two designs contribute towards triggering oscillations in MAPK cascade. Thus it is also not known how amplitude, frequency, robustness or nature (analogous/digital) of the oscillations would be shaped by these two designs. RESULTS: We built two models of MAPK cascade that exhibited oscillations as function of two underlying designs of coupled positive and negative feedback loops. Frequency, amplitude and nature (digital/analogous) of oscillations were found to be differentially determined by each design. It was observed that the positive feedback emerging from an oscillating MAPK cascade and functional in an external signal processing module can trigger oscillations in the target module, provided that the target module satisfy certain parametric requirements. The augmentation of the two models was done to incorporate the nuclear-cytoplasmic shuttling of cascade components followed by induction of a nuclear phosphatase. It revealed that the fate of oscillations in the MAPK cascade is governed by the feedback designs. Oscillations were unaffected due to nuclear compartmentalization owing to one design but were completely abolished in the other case. CONCLUSION: The MAPK cascade can utilize two distinct designs of coupled positive and negative feedback loops to trigger oscillations. The amplitude, frequency and robustness of the oscillations in presence or absence of nuclear compartmentalization were differentially determined by two designs of coupled positive and negative feedback loops. A positive feedback from an oscillating MAPK cascade was shown to induce oscillations in an external signal processing module, uncovering a novel regulatory aspect of MAPK signal processing.     

Fluctuation-driven rhythmogenesis in an excitatory neuronal network with slow adaptation

We study an excitatory all-to-all coupled network of N spiking neurons with synaptically filtered background noise and slow activity-dependent hyperpolarization currents. Such a system exhibits noise-induced burst oscillations over a range of values of the noise strength (variance) and level of cell excitability. Since both of these quantities depend on the rate of background synaptic inputs, we show how noise can provide a mechanism for increasing the robustness of rhythmic bursting and the range of burst frequencies. By exploiting a separation of time scales we also show how the system dynamics can be reduced to low-dimensional mean field equations in the limit N → ∞. Analysis of the bifurcation structure of the mean field equations provides insights into the dynamical mechanisms for initiating and terminating the bursts.     

Stimulus-induced transitions between spike-wave discharges and spindles with the modulation of thalamic reticular nucleus

It is believed that thalamic reticular nucleus (TRN) controls spindles and spike-wave discharges (SWD) in seizure or sleeping processes. The dynamical mechanisms of spatiotemporal evolutions between these two types of activity, however, are not well understood. In light of this, we first use a single-compartment thalamocortical neural field model to investigate the effects of TRN on occurrence of SWD and its transition. Results show that the increasing inhibition from TRN to specific relay nuclei (SRN) can lead to the transition of system from SWD to slow-wave oscillation. Specially, it is shown that stimulations applied in the cortical neuronal populations can also initiate the SWD and slow-wave oscillation from the resting states under the typical inhibitory intensity from TRN to SRN. Then, we expand into a 3-compartment coupled thalamocortical model network in linear and circular structures, respectively, to explore the spatiotemporal evolutions of wave states in different compartments. The main results are: (i) for the open-ended model network, SWD induced by stimulus in the first compartment can be transformed into sleep-like slow UP-DOWN and spindle states as it propagates into the downstream compartments; (ii) for the close-ended model network, weak stimulations performed in the first compartment can result in the consistent experimentally observed spindle oscillations in all three compartments; in contrast, stronger periodic single-pulse stimulations applied in the first compartment can induce periodic transitions between SWD and spindle oscillations. Detailed investigations reveal that multi-attractor coexistence mechanism composed of SWD, spindles and background state underlies these state evolutions. What’s more, in order to demonstrate the state evolution stability with respect to the topological structures of neural network, we further expand the 3-compartment coupled network into 10-compartment coupled one, with linear and circular structures, and nearest-neighbor (NN) coupled network as well as its realization of small-world (SW) topology via random rewiring, respectively. Interestingly, for the cases of linear and circular connetivities, qualitatively similar results were obtained in addition to the more irregularity of firings. However, SWD can be eventually transformed into the consistent low-amplitude oscillations for both NN and SW networks. In particular, SWD evolves into the slow spindling oscillations and background tonic oscillations within the NN and SW network, respectively. Our modeling and simulation studies highlight the effect of network topology in the evolutions of SWD and spindling oscillations, which provides new insights into the mechanisms of cortical seizures development.     

Three roads to islet bursting: emergent oscillations in coupled phantom bursters

Glucose-induced membrane potential and Ca(2+) oscillations in isolated pancreatic beta-cells occur over a wide range of frequencies, from >6/min (fast) to <1/min (slow). However, cells within intact islets generally oscillate with periods of 10-60 s (medium). The phantom bursting concept addresses how beta-cells can generate such a wide range of frequencies. Here, we explore an updated phantom bursting model to determine how heterogeneity in a single parameter can explain both the broad frequency range observed in single cells and the rarity of medium oscillations. We then incorporate the single-cell model into an islet model with parameter heterogeneity. We show that strongly coupled islets must be composed of predominantly medium oscillating single cells or a mixture of fast and slow cells to robustly produce medium oscillations. Surprisingly, we find that this constraint does not hold for moderate coupling, and that robustly medium oscillating islets can arise from populations of single cells that are essentially all slow or all fast. Thus, with coupled phantom bursters, medium oscillating islets can be constructed out of cells that are either all fast, all slow, or a combination of the two.     

Respiratory rhythmicity in the cat.

Brain stem respiratory neuron activity in the cat was studied in relation to efferent outflow (phrenic discharge) under the influence of several forcing inputs: 1) CO2 tension: hypocapnia produces disappearance of firing in some neurons, and conversion of respiratory-modulated to continuous (tonic) firing in others. 2) Lung inflation: during the Bruer-Hering reflex, some neurons have "classical" responses and others have "paradoxical" responses (i.e., opposite in direction to peripheral discharge). 3) Electrical stimulation: stimulus trains to the pneumotaxic center region (rostral lateral pons) produce phase-switching, whose threshold is: a) sharp (indicating action of positive-feedback mechanisms), and b) dependent on timing of stimulus delivery (indicating continuous excitability changes during each respiratory phase). Auto- and crosscorrelation analysis revealed the existence of short-term interactions between: a) medullary inspiratory (I) neurons and phrenic motoneurons; b) pairs of medullary I neurons; c) medullary I neurons and expiratory (E) neurons. A model of the respiratory oscillator is presented, in which the processes of conversion of tonic to phasic activity and switching of the respiratory phases are explained by recurrent excitatory and inhibitory loops.     

Modulation of Oscillatory Synchronization in an Interneuronal Network under the Influence of Tonic GABA-ergic Inhibition: a Model Study

The influence of a tonic GABA-ergic current on the processes of network synchronization was examined using a computer model of the neural network with shunting GABA-ergic synapses and tonic excitation that initiated spiking. The tonic inhibitory current was characterized by two parameters, the reversal potential and the conductance introduced. We found that tonic current with a reversal potential more negative than the threshold for spike generation reduces the network spiking frequency and synchronization. A monotonic decrease in the network synchronization with augmentation of the tonic current conductance was shown. We also found that a particular range of tonic current conductance leads to a bistable character of the network dynamics. Depending on the initial conditions of the network examined, spontaneous synchronous oscillations similar to epileptiform activity could appear.     

Surprising Effects of Synaptic Excitation

Typically, excitatory synaptic coupling is thought of as an influence that accelerates and propagates firing in neuronal networks. This paper reviews recent results explaining how, contrary to these expectations, the presence of excitatory synaptic coupling can drastically slow oscillations in a network and how localized, sustained activity can arise in a network with purely excitatory coupling, without sustained inputs. These two effects stem from interactions of excitatory coupling with two different forms of intrinsic neuronal dynamics, and both serve to highlight the fact that the influence of synaptic coupling in a network depends strongly on the intrinsic properties of cells in the network.This work was partially supported by the National Science Foundation, under award DMS-0414023     

Microtubule oscillations. Role of nucleation and microtubule number concentration

Microtubules are capable of performing synchronized oscillations of assembly and disassembly which has been explained by reaction mechanisms involving tubulin subunits, oligomers, microtubules, and GTP. Here we address the question of how microtubule nucleation or their number concentration affects the oscillations. Assembly itself requires a critical protein concentration (Cc), but oscillations require in addition a critical microtubule number concentration (CMT). In spontaneous assembly this can be achieved with protein concentrations Cos well above the critical concentration Cc because this enhances the efficiency of nucleation. Seeding with microtubules can either generate oscillations or suppress them, depending on how the seeds alter the effective microtubule number concentration. The relative influence of microtubule number and total protein concentrations can be varied by the rate at which assembly conditions are induced (e.g. by a temperature rise): Fast T-jumps induce oscillations because of efficient nucleation, slow ones do not. Oscillations become damped for several reasons. One is the consumption of GTP, the second is a decrease in microtubule number, and the third is that the ratio of microtubules in the two phases (growth-competent and shrinkage-competent) approach a steady state value. This ratio can be perturbed, and the oscillations restarted, by a cold shock, addition of seeds, addition of GTP, or fragmentation. Each of these is equivalent to a change in the effective microtubule number concentration.     

Respiratory-related bronchial rhythmic constrictions in the dog with extracorporeal circulation.

Respiratory-related bronchial rhythmic contraction was quantitatively analyzed in eight paralyzed dogs. The caliber of the fifth-generation bronchus was continuously measured as the pressure (Pbr) of a balloon-tipped catheter under the condition of complete immobilization due to extracorporeal oxygenation. Pbr changed rhythmically in synchrony with phrenic nerve activity (PNA) bursts. Rhythmic bronchial constriction started at 1.4 +/- 0.49 (SD) s after onset of PNA, reached a maximum level at 2.8 +/- 1.6 s after termination of PNA, and then decreased exponentially with a time constant of 6.9 +/- 2.5 s. When the respiratory rate of dogs increased at hypercapnia, the various bronchial contractions fused to behave like a tonic contraction. The rhythmic component of this contraction was separated and quantitatively analyzed. Each rhythmic Pbr amplitude linearly increased with increases in PNA amplitude, whereas the end-expiratory Pbr level was not significantly changed. Bilateral efferent nerve transection did not decrease the end-expiratory Pbr level. In response to electric stimulation of efferent nerve fibers, the bronchus did not maintain tonic contraction. We concluded that vagally mediated commands contract bronchial smooth muscle only intermittently and that most of bronchial resting tension may thus be attributed to the summation of rhythmic contractions.     

Membrane and network theta-rhythm generation in hippocampal slices

The hippocampal rhythms observed in vivo are the result of a complex interplay between cellular and synaptic properties within the hippocampus, and extra-hippocampal tonic as well as periodic inputs. For the stable rhythm to occur, the hippocampal circuitry should have the potential to oscillate at the specific frequencies. The in vitro studies revealed multiple mechanisms supporting the generation of the theta rhythm, which is the main operational mode of the hippocampus. In the hippocampus and related structures cellular membranes can oscillate at theta rhythm when they are depolarized to near-threshold membrane potentials; membranes are also adjusted to resonate with the external signal applied at theta frequency. Synaptically connected hippocampal network alone can generate theta rhythm when a necessary tonic excitation is provided. Finally, rhythmic inputs in theta range from the septum and entorhinal cortex have a propensity to synchronize oscillations in the whole hippocampal formation and associated structures to operate in a unified mode of activity. Based on the results obtained in slices and slice cultures, the present review shows this multilevel hierarchy, which serves to guarantee easy occurrence and reliable maintenance of the theta rhythm in the hippocampus.     

Selective coupling between theta phase and neocortical fast gamma oscillations during REM-sleep in mice

Background

The mammalian brain expresses a wide range of state-dependent network oscillations which vary in frequency and spatial extension. Such rhythms can entrain multiple neurons into coherent patterns of activity, consistent with a role in behaviour, cognition and memory formation. Recent evidence suggests that locally generated fast network oscillations can be systematically aligned to long-range slow oscillations. It is likely that such cross-frequency coupling supports specific tasks including behavioural choice and working memory.

Principal Findings

We analyzed temporal coupling between high-frequency oscillations and EEG theta activity (4–12 Hz) in recordings from mouse parietal neocortex. Theta was exclusively present during active wakefulness and REM-sleep. Fast oscillations occurred in two separate frequency bands: gamma (40–100 Hz) and fast gamma (120–160 Hz). Theta, gamma and fast gamma were more prominent during active wakefulness as compared to REM-sleep. Coupling between theta and the two types of fast oscillations, however, was more pronounced during REM-sleep. This state-dependent cross-frequency coupling was particularly strong for theta-fast gamma interaction which increased 9-fold during REM as compared to active wakefulness. Theta-gamma coupling increased only by 1.5-fold.

Significance

State-dependent cross-frequency-coupling provides a new functional characteristic of REM-sleep and establishes a unique property of neocortical fast gamma oscillations. Interactions between defined patterns of slow and fast network oscillations may serve selective functions in sleep-dependent information processing.     

Impact of adaptation currents on synchronization of coupled exponential integrate-and-fire neurons

The ability of spiking neurons to synchronize their activity in a network depends on the response behavior of these neurons as quantified by the phase response curve (PRC) and on coupling properties. The PRC characterizes the effects of transient inputs on spike timing and can be measured experimentally. Here we use the adaptive exponential integrate-and-fire (aEIF) neuron model to determine how subthreshold and spike-triggered slow adaptation currents shape the PRC. Based on that, we predict how synchrony and phase locked states of coupled neurons change in presence of synaptic delays and unequal coupling strengths. We find that increased subthreshold adaptation currents cause a transition of the PRC from only phase advances to phase advances and delays in response to excitatory perturbations. Increased spike-triggered adaptation currents on the other hand predominantly skew the PRC to the right. Both adaptation induced changes of the PRC are modulated by spike frequency, being more prominent at lower frequencies. Applying phase reduction theory, we show that subthreshold adaptation stabilizes synchrony for pairs of coupled excitatory neurons, while spike-triggered adaptation causes locking with a small phase difference, as long as synaptic heterogeneities are negligible. For inhibitory pairs synchrony is stable and robust against conduction delays, and adaptation can mediate bistability of in-phase and anti-phase locking. We further demonstrate that stable synchrony and bistable in/anti-phase locking of pairs carry over to synchronization and clustering of larger networks. The effects of adaptation in aEIF neurons on PRCs and network dynamics qualitatively reflect those of biophysical adaptation currents in detailed Hodgkin-Huxley-based neurons, which underscores the utility of the aEIF model for investigating the dynamical behavior of networks. Our results suggest neuronal spike frequency adaptation as a mechanism synchronizing low frequency oscillations in local excitatory networks, but indicate that inhibition rather than excitation generates coherent rhythms at higher frequencies.     

藜芦碱和乌头碱在受损背根节神经元诱发不同的放电模式

为了研究钠通道失活门阻断后受损背根节神经元放电模式的变化特征,在大鼠背根节慢性压迫模型上采用单纤维技术记录A类神经元的自发放电。藜芦碱和乌头碱是钠通道失活门的抑制剂,但二者作用于不同的位点,前者结合于D2-S6,后者结合于D3-S6。我们比较了这两种试剂引发的放电模式。结果发现,在同一神经元,藜芦碱(1．5～5．0μmol／L)可以引起放电峰峰间期的慢波振荡,即峰峰间期由大逐渐减小,然后又逐渐增大,形成重复的振荡波形,每个振荡持续约数十秒至数分钟：而乌头碱(10～200μmol／L)则引起强直性放电,即峰峰间期逐渐减小,然后维持在一个稳定的水平。这两种不同的放电模式不因背景放电或试剂浓度的不同而发生明显的改变。实验结果表明,藜芦碱和乌头碱在受损的背根节神经元可以引发不同的放电模式,这可能与它们结合于钠通道上不同位点的抑制作用有关。     

Conditions of activity bubble uniqueness in dynamic neural fields

Dynamic neural fields (DNFs) offer a rich spectrum of dynamic properties like hysteresis, spatiotemporal information integration, and coexistence of multiple attractors. These properties make DNFs more and more popular in implementations of sensorimotor loops for autonomous systems. Applications often imply that DNFs should have only one compact region of firing neurons (activity bubble), whereas the rest of the field should not fire (e.g., if the field represents motor commands). In this article we prove the conditions of activity bubble uniqueness in the case of locally symmetric input bubbles. The qualitative condition on inhomogeneous inputs used in earlier work on DNFs is transfered to a quantitative condition of a balance between the internal dynamics and the input. The mathematical analysis is carried out for the two-dimensional case with methods that can be extended to more than two dimensions. The article concludes with an example of how our theoretical results facilitate the practical use of DNFs.     

Corticomuscular Transmission of Tremor Signals by Propriospinal Neurons in Parkinson's Disease

Cortical oscillatory signals of single and double tremor frequencies act together to cause tremor in the peripheral limbs of patients with Parkinson''s disease (PD). But the corticospinal pathway that transmits the tremor signals has not been clarified, and how alternating bursts of antagonistic muscle activations are generated from the cortical oscillatory signals is not well understood. This paper investigates the plausible role of propriospinal neurons (PN) in C3–C4 in transmitting the cortical oscillatory signals to peripheral muscles. Kinematics data and surface electromyogram (EMG) of tremor in forearm were collected from PD patients. A PN network model was constructed based on known neurophysiological connections of PN. The cortical efferent signal of double tremor frequencies were integrated at the PN network, whose outputs drove the muscles of a virtual arm (VA) model to simulate tremor behaviors. The cortical efferent signal of single tremor frequency actuated muscle spindles. By comparing tremor data of PD patients and the results of model simulation, we examined two hypotheses regarding the corticospinal transmission of oscillatory signals in Parkinsonian tremor. Hypothesis I stated that the oscillatory cortical signals were transmitted via the mono-synaptic corticospinal pathways bypassing the PN network. The alternative hypothesis II stated that they were transmitted by way of PN multi-synaptic corticospinal pathway. Simulations indicated that without the PN network, the alternating burst patterns of antagonistic muscle EMGs could not be reliably generated, rejecting the first hypothesis. However, with the PN network, the alternating burst patterns of antagonist EMGs were naturally reproduced under all conditions of cortical oscillations. The results suggest that cortical commands of single and double tremor frequencies are further processed at PN to compute the alternating burst patterns in flexor and extensor muscles, and the neuromuscular dynamics demonstrated a frequency dependent damping on tremor, which may prevent tremor above 8 Hz to occur.     

Glomerulus-specific synchronization of mitral cells in the olfactory bulb.

Odor elicits a well-organized pattern of glomerular activation in the olfactory bulb. However, the mechanisms by which this spatial map is transformed into an odor code remain unclear. We examined this question in rat olfactory bulb slices in recordings from output mitral cells. Electrical stimulation of incoming afferents elicited slow ( approximately 2 Hz) oscillations that originated in glomeruli and were highly synchronized for mitral cells projecting to the same glomerulus. Cyclical depolarizations were generated by glutamate activation of dendritic autoreceptors, while the slow frequency was determined primarily by the duration of regenerative glutamate release. Patterned stimuli elicited stimulus-entrained oscillations that amplified weak and variable inputs. We suggest that these oscillations maintain the fidelity of the spatial map by ensuring that all mitral cells within a glomerulus-specific network respond to odor as a functional unit.     

New roles for the gamma rhythm: population tuning and preprocessing for the Beta rhythm

Gamma (30–80 Hz) and beta (12–30 Hz) oscillations such as those displayed by in vitro hippocampal (CA1) slice preparations and by in vivo neocortical EEGs often occur successively, with a spontaneous transition between them. In the gamma rhythm, pyramidal cells fire together with the interneurons, while in the beta rhythm, pyramidal cells fire on a subset of cycles of the interneurons. It is shown that gamma and beta rhythms have different properties with respect to creation of cell assemblies. In the presence of heterogeneous inputs to the pyramidal cells, the gamma rhythm creates an assembly of firing pyramidal cells from cells whose drive exceeds a threshold. During the gamma to beta transition, a slow outward potassium current is activated, and as a result the cell assembly vanishes. The slow currents make each of the pyramidal cells fire with a beta rhythm, but the field potential of the network still displays a gamma rhythm. Hebbian changes of connections among the pyramidal cells give rise to a beta rhythm, and the cell assemblies are recovered with a temporal separation between cells firing in different cycles. We present experimental evidence showing that such a separation can occur in hippocampal slices.