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1.  Cross-frequency interaction of the eye-movement related LFP signals in V1 of freely viewing monkeys 
Recent studies have emphasized the functional role of neuronal activity underlying oscillatory local field potential (LFP) signals during visual processing in natural conditions. While functionally relevant components in multiple frequency bands have been reported, little is known about whether and how these components interact with each other across the dominant frequency bands. We examined this phenomenon in LFP signals obtained from the primary visual cortex of monkeys performing voluntary saccadic eye movements (EMs) on still images of natural-scenes. We identified saccade-related changes in respect to power and phase in four dominant frequency bands: delta-theta (2–4 Hz), alpha-beta (10–13 Hz), low-gamma (20–40 Hz), and high-gamma (>100 Hz). The phase of the delta-theta band component is found to be entrained to the rhythm of the repetitive saccades, while an increment in the power of the alpha-beta and low-gamma bands were locked to the onset of saccades. The degree of the power modulation in these frequency bands is positively correlated with the degree of the phase-locking of the delta-theta oscillations to EMs. These results suggest the presence of cross-frequency interactions in the form of phase-amplitude coupling (PAC) between slow (delta-theta) and faster (alpha-beta and low gamma) oscillations. As shown previously, spikes evoked by visual fixations during free viewing are phase-locked to the fast oscillations. Thus, signals of different types and at different temporal scales are nested to each other during natural viewing. Such cross-frequency interaction may provide a general mechanism to coordinate sensory processing on a fast time scale and motor behavior on a slower time scale during active sensing.
doi:10.3389/fnsys.2013.00001
PMCID: PMC3572441  PMID: 23420631
local field potential; oscillation; saccade; natural vision; cross-frequency coupling
2.  The Local Field Potential Reflects Surplus Spike Synchrony 
Cerebral Cortex (New York, NY)  2011;21(12):2681-2695.
While oscillations of the local field potential (LFP) are commonly attributed to the synchronization of neuronal firing rate on the same time scale, their relationship to coincident spiking in the millisecond range is unknown. Here, we present experimental evidence to reconcile the notions of synchrony at the level of spiking and at the mesoscopic scale. We demonstrate that only in time intervals of significant spike synchrony that cannot be explained on the basis of firing rates, coincident spikes are better phase locked to the LFP than predicted by the locking of the individual spikes. This effect is enhanced in periods of large LFP amplitudes. A quantitative model explains the LFP dynamics by the orchestrated spiking activity in neuronal groups that contribute the observed surplus synchrony. From the correlation analysis, we infer that neurons participate in different constellations but contribute only a fraction of their spikes to temporally precise spike configurations. This finding provides direct evidence for the hypothesized relation that precise spike synchrony constitutes a major temporally and spatially organized component of the LFP.
doi:10.1093/cercor/bhr040
PMCID: PMC3209854  PMID: 21508303
motor cortex; oscillation; population signals; synchrony
3.  Neuronal Functional Connection Graphs among Multiple Areas of the Rat Somatosensory System during Spontaneous and Evoked Activities 
PLoS Computational Biology  2013;9(6):e1003104.
Small-World Networks (SWNs) represent a fundamental model for the comprehension of many complex man-made and biological networks. In the central nervous system, SWN models have been shown to fit well both anatomical and functional maps at the macroscopic level. However, the functional microscopic level, where the nodes of a network are represented by single neurons, is still poorly understood. At this level, although recent evidences suggest that functional connection graphs exhibit small-world organization, it is not known whether and how these maps, potentially distributed in multiple brain regions, change across different conditions, such as spontaneous and stimulus-evoked activities. We addressed these questions by analyzing the data from simultaneous multi-array extracellular recordings in three brain regions of rats, diversely involved in somatosensory information processing: the ventropostero-lateral thalamic nuclei, the primary somatosensory cortex and the centro-median thalamic nuclei. From both spike and Local Field Potential (LFP) recordings, we estimated the functional connection graphs by using the Normalized Compression Similarity for spikes and the Phase Synchrony for LFPs. Then, by using graph-theoretical statistics, we characterized the functional topology both during spontaneous activity and sensory stimulation. Our main results show that: (i) spikes and LFPs show SWN organization during spontaneous activity; (ii) after stimulation onset, while substantial functional graph reconfigurations occur both in spike and LFPs, small-worldness is nonetheless preserved; (iii) the stimulus triggers a significant increase of inter-area LFP connections without modifying the topology of intra-area functional connections. Finally, investigating computationally the functional substrate that supports the observed phenomena, we found that (iv) the fundamental concept of cell assemblies, transient groups of activating neurons, can be described by small-world networks. Our results suggest that activity of neurons from multiple areas of the rat somatosensory system contributes to the integration of local computations arisen in distributed functional cell assemblies according to the principles of SWNs.
Author Summary
Cell assemblies (sequences of neuronal activations), seem to represent a functional unit of information processing. However, it remains unclear how groups of neurons may organize their activity during information processing, working as a sole functional unit. One prominent principle in complex network theory is covered by small-world networks, in which each node is easily reachable by each other and organized in highly dense clusters. Small-world networks have been already observed on large scales in human and primate brain areas while their presence at the neuronal level remains unclear. The aim of this work was to investigate the possibility that functional, related neural populations, encompassing multiple brain regions, could be organized in small-world networks. We investigated the coherent neuronal activity among multiple rat brain regions involved in somatosensory information processing. We found that the recorded neuronal populations represented small-world networks and that these topologies were maintained during stimulations. Furthermore, by using simulations to explore the hidden substrates supporting the observed topological features, we inferred that small-world networks represent a plausible topology for cell assemblies. This work suggests that the coherent activity of neurons from multiple brain areas promotes the integration of local computations, the functional principle of small-world networks.
doi:10.1371/journal.pcbi.1003104
PMCID: PMC3681651  PMID: 23785273
4.  Impact of Adaptation Currents on Synchronization of Coupled Exponential Integrate-and-Fire Neurons 
PLoS Computational Biology  2012;8(4):e1002478.
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.
Author Summary
Synchronization of neuronal spiking in the brain is related to cognitive functions, such as perception, attention, and memory. It is therefore important to determine which properties of neurons influence their collective behavior in a network and to understand how. A prominent feature of many cortical neurons is spike frequency adaptation, which is caused by slow transmembrane currents. We investigated how these adaptation currents affect the synchronization tendency of coupled model neurons. Using the efficient adaptive exponential integrate-and-fire (aEIF) model and a biophysically detailed neuron model for validation, we found that increased adaptation currents promote synchronization of coupled excitatory neurons at lower spike frequencies, as long as the conduction delays between the neurons are negligible. Inhibitory neurons on the other hand synchronize in presence of conduction delays, with or without adaptation currents. Our results emphasize the utility of the aEIF model for computational studies of neuronal network dynamics. We conclude that adaptation currents provide a mechanism to generate low frequency oscillations in local populations of excitatory neurons, while faster rhythms seem to be caused by inhibition rather than excitation.
doi:10.1371/journal.pcbi.1002478
PMCID: PMC3325187  PMID: 22511861
5.  Timing of Single-Neuron and Local Field Potential Responses in the Human Medial Temporal Lobe 
Current Biology  2014;24(3):299-304.
Summary
The relationship between the firing of single cells and local field potentials (LFPs) has received increasing attention, with studies in animals [1–11] and humans [12–14]. Recordings in the human medial temporal lobe (MTL) have demonstrated the existence of neurons with selective and invariant responses [15], with a relatively late but precise response onset around 300 ms after stimulus presentation [16–18] and firing only upon conscious recognition of the stimulus [19]. This represents a much later onset than expected from direct projections from inferotemporal cortex [16, 18]. The neural mechanisms underlying this onset remain unclear. To address this issue, we performed a joint analysis of single-cell and LFP responses during a visual recognition task. Single-neuron responses were preceded by a global LFP deflection in the theta range. In addition, there was a local and stimulus-specific increase in the single-trial gamma power. These LFP responses correlated with conscious recognition. The timing of the neurons’ firing was phase locked to these LFP responses. We propose that whereas the gamma phase locking reflects the activation of local networks encoding particular recognized stimuli, the theta phase locking reflects a global activation that provides a temporal window for processing consciously perceived stimuli in the MTL.
Highlights
•Global theta LFP increases immediately precede MTL single-cell responses•Gamma power reflects activations of local networks encoding specific stimuli•The timing of the neurons’ firing is phase locked to LFP responses•LFP responses give a temporal window for processing consciously perceived stimuli
Rey et al. show that, in human medial temporal lobe (MTL), single-cell responses triggered by consciously perceived stimuli are locked to global theta and local gamma LFP responses; the latter reflects local activations, but the former shortly precedes the spike responses and may provide a window for stimulus processing in the MTL.
doi:10.1016/j.cub.2013.12.004
PMCID: PMC3963414  PMID: 24462002
6.  Specific Entrainment of Mitral Cells during Gamma Oscillation in the Rat Olfactory Bulb 
PLoS Computational Biology  2009;5(10):e1000551.
Local field potential (LFP) oscillations are often accompanied by synchronization of activity within a widespread cerebral area. Thus, the LFP and neuronal coherence appear to be the result of a common mechanism that underlies neuronal assembly formation. We used the olfactory bulb as a model to investigate: (1) the extent to which unitary dynamics and LFP oscillations can be correlated and (2) the precision with which a model of the hypothesized underlying mechanisms can accurately explain the experimental data. For this purpose, we analyzed simultaneous recordings of mitral cell (MC) activity and LFPs in anesthetized and freely breathing rats in response to odorant stimulation. Spike trains were found to be phase-locked to the gamma oscillation at specific firing rates and to form odor-specific temporal patterns. The use of a conductance-based MC model driven by an approximately balanced excitatory-inhibitory input conductance and a relatively small inhibitory conductance that oscillated at the gamma frequency allowed us to provide one explanation of the experimental data via a mode-locking mechanism. This work sheds light on the way network and intrinsic MC properties participate in the locking of MCs to the gamma oscillation in a realistic physiological context and may result in a particular time-locked assembly. Finally, we discuss how a self-synchronization process with such entrainment properties can explain, under experimental conditions: (1) why the gamma bursts emerge transiently with a maximal amplitude position relative to the stimulus time course; (2) why the oscillations are prominent at a specific gamma frequency; and (3) why the oscillation amplitude depends on specific stimulus properties. We also discuss information processing and functional consequences derived from this mechanism.
Author Summary
Olfactory function relies on a chain of neural relays that extends from the periphery to the central nervous system and implies neural activity with various timescales. A central question in neuroscience is how information is encoded by the neural activity. In the mammalian olfactory bulb, local neural activity oscillations in the 40–80 Hz range (gamma) may influence the timing of individual neuron activities such that olfactory information may be encoded in this way. In this study, we first characterize in vivo the detailed activity of individual neurons relative to the oscillation and find that, depending on their state, neurons can exhibit periodic activity patterns. We also find, at least qualitatively, a relation between this activity and a particular odor. This is reminiscent of general physical phenomena—the entrainment by an oscillation—and to verify this hypothesis, in a second phase, we build a biologically realistic model mimicking these in vivo conditions. Our model confirms quantitatively this hypothesis and reveals that entrainment is maximal in the gamma range. Taken together, our results suggest that the neuronal activity may be specifically formatted in time during the gamma oscillation in such a way that it could, at this stage, encode the odor.
doi:10.1371/journal.pcbi.1000551
PMCID: PMC2760751  PMID: 19876377
7.  Predicting Spike Occurrence and Neuronal Responsiveness from LFPs in Primary Somatosensory Cortex 
PLoS ONE  2012;7(5):e35850.
Local Field Potentials (LFPs) integrate multiple neuronal events like synaptic inputs and intracellular potentials. LFP spatiotemporal features are particularly relevant in view of their applications both in research (e.g. for understanding brain rhythms, inter-areal neural communication and neronal coding) and in the clinics (e.g. for improving invasive Brain-Machine Interface devices). However the relation between LFPs and spikes is complex and not fully understood. As spikes represent the fundamental currency of neuronal communication this gap in knowledge strongly limits our comprehension of neuronal phenomena underlying LFPs. We investigated the LFP-spike relation during tactile stimulation in primary somatosensory (S-I) cortex in the rat. First we quantified how reliably LFPs and spikes code for a stimulus occurrence. Then we used the information obtained from our analyses to design a predictive model for spike occurrence based on LFP inputs. The model was endowed with a flexible meta-structure whose exact form, both in parameters and structure, was estimated by using a multi-objective optimization strategy. Our method provided a set of nonlinear simple equations that maximized the match between models and true neurons in terms of spike timings and Peri Stimulus Time Histograms. We found that both LFPs and spikes can code for stimulus occurrence with millisecond precision, showing, however, high variability. Spike patterns were predicted significantly above chance for 75% of the neurons analysed. Crucially, the level of prediction accuracy depended on the reliability in coding for the stimulus occurrence. The best predictions were obtained when both spikes and LFPs were highly responsive to the stimuli. Spike reliability is known to depend on neuron intrinsic properties (i.e. on channel noise) and on spontaneous local network fluctuations. Our results suggest that the latter, measured through the LFP response variability, play a dominant role.
doi:10.1371/journal.pone.0035850
PMCID: PMC3346760  PMID: 22586452
8.  State-Space Analysis of Time-Varying Higher-Order Spike Correlation for Multiple Neural Spike Train Data 
PLoS Computational Biology  2012;8(3):e1002385.
Precise spike coordination between the spiking activities of multiple neurons is suggested as an indication of coordinated network activity in active cell assemblies. Spike correlation analysis aims to identify such cooperative network activity by detecting excess spike synchrony in simultaneously recorded multiple neural spike sequences. Cooperative activity is expected to organize dynamically during behavior and cognition; therefore currently available analysis techniques must be extended to enable the estimation of multiple time-varying spike interactions between neurons simultaneously. In particular, new methods must take advantage of the simultaneous observations of multiple neurons by addressing their higher-order dependencies, which cannot be revealed by pairwise analyses alone. In this paper, we develop a method for estimating time-varying spike interactions by means of a state-space analysis. Discretized parallel spike sequences are modeled as multi-variate binary processes using a log-linear model that provides a well-defined measure of higher-order spike correlation in an information geometry framework. We construct a recursive Bayesian filter/smoother for the extraction of spike interaction parameters. This method can simultaneously estimate the dynamic pairwise spike interactions of multiple single neurons, thereby extending the Ising/spin-glass model analysis of multiple neural spike train data to a nonstationary analysis. Furthermore, the method can estimate dynamic higher-order spike interactions. To validate the inclusion of the higher-order terms in the model, we construct an approximation method to assess the goodness-of-fit to spike data. In addition, we formulate a test method for the presence of higher-order spike correlation even in nonstationary spike data, e.g., data from awake behaving animals. The utility of the proposed methods is tested using simulated spike data with known underlying correlation dynamics. Finally, we apply the methods to neural spike data simultaneously recorded from the motor cortex of an awake monkey and demonstrate that the higher-order spike correlation organizes dynamically in relation to a behavioral demand.
Author Summary
Nearly half a century ago, the Canadian psychologist D. O. Hebb postulated the formation of assemblies of tightly connected cells in cortical recurrent networks because of changes in synaptic weight (Hebb's learning rule) by repetitive sensory stimulation of the network. Consequently, the activation of such an assembly for processing sensory or behavioral information is likely to be expressed by precisely coordinated spiking activities of the participating neurons. However, the available analysis techniques for multiple parallel neural spike data do not allow us to reveal the detailed structure of transiently active assemblies as indicated by their dynamical pairwise and higher-order spike correlations. Here, we construct a state-space model of dynamic spike interactions, and present a recursive Bayesian method that makes it possible to trace multiple neurons exhibiting such precisely coordinated spiking activities in a time-varying manner. We also formulate a hypothesis test of the underlying dynamic spike correlation, which enables us to detect the assemblies activated in association with behavioral events. Therefore, the proposed method can serve as a useful tool to test Hebb's cell assembly hypothesis.
doi:10.1371/journal.pcbi.1002385
PMCID: PMC3297562  PMID: 22412358
9.  Spike-Timing Precision and Neuronal Synchrony Are Enhanced by an Interaction between Synaptic Inhibition and Membrane Oscillations in the Amygdala 
PLoS ONE  2012;7(4):e35320.
The basolateral complex of the amygdala (BLA) is a critical component of the neural circuit regulating fear learning. During fear learning and recall, the amygdala and other brain regions, including the hippocampus and prefrontal cortex, exhibit phase-locked oscillations in the high delta/low theta frequency band (∼2–6 Hz) that have been shown to contribute to the learning process. Network oscillations are commonly generated by inhibitory synaptic input that coordinates action potentials in groups of neurons. In the rat BLA, principal neurons spontaneously receive synchronized, inhibitory input in the form of compound, rhythmic, inhibitory postsynaptic potentials (IPSPs), likely originating from burst-firing parvalbumin interneurons. Here we investigated the role of compound IPSPs in the rat and rhesus macaque BLA in regulating action potential synchrony and spike-timing precision. Furthermore, because principal neurons exhibit intrinsic oscillatory properties and resonance between 4 and 5 Hz, in the same frequency band observed during fear, we investigated whether compound IPSPs and intrinsic oscillations interact to promote rhythmic activity in the BLA at this frequency. Using whole-cell patch clamp in brain slices, we demonstrate that compound IPSPs, which occur spontaneously and are synchronized across principal neurons in both the rat and primate BLA, significantly improve spike-timing precision in BLA principal neurons for a window of ∼300 ms following each IPSP. We also show that compound IPSPs coordinate the firing of pairs of BLA principal neurons, and significantly improve spike synchrony for a window of ∼130 ms. Compound IPSPs enhance a 5 Hz calcium-dependent membrane potential oscillation (MPO) in these neurons, likely contributing to the improvement in spike-timing precision and synchronization of spiking. Activation of the cAMP-PKA signaling cascade enhanced the MPO, and inhibition of this cascade blocked the MPO. We discuss these results in the context of spike-timing dependent plasticity and modulation by neurotransmitters important for fear learning, such as dopamine.
doi:10.1371/journal.pone.0035320
PMCID: PMC3338510  PMID: 22563382
10.  The Effects of Visual Stimulation and Selective Visual Attention on Rhythmic Neuronal Synchronization in Macaque Area V4 
The Journal of Neuroscience  2008;28(18):4823-4835.
Selective attention lends relevant sensory input priority access to higher-level brain areas and ultimately to behavior. Recent studies have suggested that those neurons in visual areas that are activated by an attended stimulus engage in enhanced gamma-band (30–70 Hz) synchronization compared with neurons activated by a distracter. Such precise synchronization could enhance the postsynaptic impact of cells carrying behaviorally relevant information. Previous studies have used the local field potential (LFP) power spectrum or spike-LFP coherence (SFC) to indirectly estimate spike synchronization. Here, we directly demonstrate zero-phase gamma-band coherence among spike trains of V4 neurons. This synchronization was particularly evident during visual stimulation and enhanced by selective attention, thus confirming the pattern inferred from LFP power and SFC. We therefore investigated the time course of LFP gamma-band power and found rapid dynamics consistent with interactions of top-down spatial and feature attention with bottom-up saliency. In addition to the modulation of synchronization during visual stimulation, selective attention significantly changed the prestimulus pattern of synchronization. Attention inside the receptive field of the recorded neuronal population enhanced gamma-band synchronization and strongly reduced α-band (9–11 Hz) synchronization in the prestimulus period. These results lend further support for a functional role of rhythmic neuronal synchronization in attentional stimulus selection.
doi:10.1523/JNEUROSCI.4499-07.2008
PMCID: PMC3844818  PMID: 18448659
synchronization; oscillation; coherence; gamma; α; attention
11.  Temporal Correlation Mechanisms and Their Role in Feature Selection: A Single-Unit Study in Primate Somatosensory Cortex 
PLoS Biology  2014;12(11):e1002004.
How neurons pay attention Top-down selective attention mediates feature selection by reducing the noise correlations in neural populations and enhancing the synchronized activity across subpopulations that encode the relevant features of sensory stimuli.
Studies in vision show that attention enhances the firing rates of cells when it is directed towards their preferred stimulus feature. However, it is unknown whether other sensory systems employ this mechanism to mediate feature selection within their modalities. Moreover, whether feature-based attention modulates the correlated activity of a population is unclear. Indeed, temporal correlation codes such as spike-synchrony and spike-count correlations (rsc) are believed to play a role in stimulus selection by increasing the signal and reducing the noise in a population, respectively. Here, we investigate (1) whether feature-based attention biases the correlated activity between neurons when attention is directed towards their common preferred feature, (2) the interplay between spike-synchrony and rsc during feature selection, and (3) whether feature attention effects are common across the visual and tactile systems. Single-unit recordings were made in secondary somatosensory cortex of three non-human primates while animals engaged in tactile feature (orientation and frequency) and visual discrimination tasks. We found that both firing rate and spike-synchrony between neurons with similar feature selectivity were enhanced when attention was directed towards their preferred feature. However, attention effects on spike-synchrony were twice as large as those on firing rate, and had a tighter relationship with behavioral performance. Further, we observed increased rsc when attention was directed towards the visual modality (i.e., away from touch). These data suggest that similar feature selection mechanisms are employed in vision and touch, and that temporal correlation codes such as spike-synchrony play a role in mediating feature selection. We posit that feature-based selection operates by implementing multiple mechanisms that reduce the overall noise levels in the neural population and synchronize activity across subpopulations that encode the relevant features of sensory stimuli.
Author Summary
Attention can select stimuli in space based on the stimulus features most relevant for a task. Attention effects have been linked to several important phenomena such as modulations in neuronal spiking rate (i.e., the average number of spikes per unit time) and spike-spike synchrony between neurons. Attention has also been associated with spike count correlations, a measure that is thought to reflect correlated noise in the population of neurons. Here, we studied whether feature-based attention biases the correlated activity between neurons when attention is directed towards their common preferred feature. Simultaneous single-unit recordings were obtained from multiple neurons in secondary somatosensory cortex in non-human primates performing feature-attention tasks. Both firing rate and spike-synchrony were enhanced when attention was directed towards the preferred feature of cells. However, attention effects on spike-synchrony had a tighter relationship with behavior. Further, attention decreased spike-count correlations when it was directed towards the receptive field of cells. Our data indicate that temporal correlation codes play a role in mediating feature selection, and are consistent with a feature-based selection model that operates by reducing the overall noise in a population and synchronizing activity across subpopulations that encode the relevant features of sensory stimuli.
doi:10.1371/journal.pbio.1002004
PMCID: PMC4244037  PMID: 25423284
12.  Effects of nicotine stimulation on spikes, theta frequency oscillations, and spike-theta oscillation relationship in rat medial septum diagonal band Broca slices 
Acta Pharmacologica Sinica  2013;34(4):464-472.
Aim:
Spiking activities and neuronal network oscillations in the theta frequency range have been found in many cortical areas during information processing. The aim of this study is to determine whether nicotinic acetylcholine receptors (nAChRs) mediate neuronal network activity in rat medial septum diagonal band Broca (MSDB) slices.
Methods:
Extracellular field potentials were recorded in the slices using an Axoprobe 1A amplifier. Data analysis was performed off-line. Spike sorting and local field potential (LFP) analyses were performed using Spike2 software. The role of spiking activity in the generation of LFP oscillations in the slices was determined by analyzing the phase-time relationship between the spikes and LFP oscillations. Circular statistic analysis based on the Rayleigh test was used to determine the significance of phase relationships between the spikes and LFP oscillations. The timing relationship was examined by quantifying the spike-field coherence (SFC).
Results:
Application of nicotine (250 nmol/L) induced prominent LFP oscillations in the theta frequency band and both small- and large-amplitude population spiking activity in the slices. These spikes were phase-locked to theta oscillations at specific phases. The Rayleigh test showed a statistically significant relationship in phase-locking between the spikes and theta oscillations. Larger changes in the SFC were observed for large-amplitude spikes, indicating an accurate timing relationship between this type of spike and LFP oscillations. The nicotine-induced spiking activity (large-amplitude population spikes) was suppressed by the nAChR antagonist dihydro-β-erythroidine (0.3 μmol/L).
Conclusion:
The results demonstrate that large-amplitude spikes are phase-locked to theta oscillations and have a high spike-timing accuracy, which are likely a main contributor to the theta oscillations generated in MSDB during nicotine receptor activation.
doi:10.1038/aps.2012.180
PMCID: PMC4002786  PMID: 23474704
medial septum diagonal band of Broca; theta oscillations; spike; LFP; nicotinic acetylcholine receptor; nicotine; dihydro-β-erythroidine; brain slice; electrophysiology
13.  Brain-control of movement execution onset using LFPs in posterior parietal cortex 
The precise control of movement execution onset is essential for safe and autonomous cortical motor prosthetics. A recent study from the parietal reach region (PRR) suggested that the local field potentials (LFPs) in this area might be useful for decoding execution time information because of the striking difference in the LFP spectrum between the plan and execution states (Scherberger et al. 2005). More specifically, the LFP power in the 0-10 Hz band sharply rises while the power in the 20-40 Hz band falls as the state transitions from plan to execution. However, a change of visual stimulus immediately preceded reach onset, raising the possibility that the observed spectral change reflected the visual event instead of the reach onset. Here, we tested this possibility and found that the LFP spectrum change was still time-locked to the movement onset in the absence of a visual event in self-paced reaches. Furthermore, we successfully trained the macaque subjects to utilize the LFP spectrum change as a “go” signal in a closed-loop brain-control task in which the animals only modulated the LFP and did not execute a reach. The execution onset was signaled by the change in the LFP spectrum while the target position of the cursor was controlled by the spike firing rates recorded from the same site. The results corroborate that the LFP spectrum change in PRR is a robust indicator for the movement onset and can be used for control of execution onset in a cortical prosthesis.
doi:10.1523/JNEUROSCI.2081-09.2009
PMCID: PMC2805702  PMID: 19906983
neural prosthesis; BMI; PRR; behavioral state decoding; self-paced reach; motor plan; movement execution
14.  Spike-field activity in parietal area LIP during coordinated reach and saccade movements 
Journal of Neurophysiology  2011;107(5):1275-1290.
The posterior parietal cortex is situated between visual and motor areas and supports coordinated visually guided behavior. Area LIP in the intraparietal sulcus contains representations of visual space and has been extensively studied in the context of saccades. However, area LIP has not been studied during coordinated movements, so it is not known whether saccadic representations in area LIP are influenced by coordinated behavior. Here, we studied spiking and local field potential (LFP) activity in area LIP while subjects performed coordinated reaches and saccades or saccades alone to remembered target locations to test whether activity in area LIP is influenced by the presence of a coordinated reach. We find that coordination significantly changes the activity of individual neurons in area LIP, increasing or decreasing the firing rate when a reach is made with a saccade compared with when a saccade is made alone. Analyzing spike-field coherence demonstrates that area LIP neurons whose firing rate is suppressed during the coordinated task have activity temporally correlated with nearby LFP activity, which reflects the synaptic activity of populations of neurons. Area LIP neurons whose firing rate increases during the coordinated task do not show significant spike-field coherence. Furthermore, LFP power in area LIP is suppressed and does not increase when a coordinated reach is made with a saccade. These results demonstrate that area LIP neurons display different responses to coordinated reach and saccade movements, and that different spike rate responses are associated with different patterns of correlated activity. The population of neurons whose firing rate is suppressed is coherently active with local populations of LIP neurons. Overall, these results suggest that area LIP plays a role in coordinating visually guided actions through suppression of coherent patterns of saccade-related activity.
doi:10.1152/jn.00867.2011
PMCID: PMC3311693  PMID: 22157119
hand-eye coordination; macaque; sensory-motor; coherence
15.  Estimating the contribution of assembly activity to cortical dynamics from spike and population measures 
The hypothesis that cortical networks employ the coordinated activity of groups of neurons, termed assemblies, to process information is debated. Results from multiple single-unit recordings are not conclusive because of the dramatic undersampling of the system. However, the local field potential (LFP) is a mesoscopic signal reflecting synchronized network activity. This raises the question whether the LFP can be employed to overcome the problem of undersampling. In a recent study in the motor cortex of the awake behaving monkey based on the locking of coincidences to the LFP we determined a lower bound for the fraction of spike coincidences originating from assembly activation. This quantity together with the locking of single spikes leads to a lower bound for the fraction of spikes originating from any assembly activity. Here we derive a statistical method to estimate the fraction of spike synchrony caused by assemblies—not its lower bound—from the spike data alone. A joint spike and LFP surrogate data model demonstrates consistency of results and the sensitivity of the method. Combining spike and LFP signals, we obtain an estimate of the fraction of spikes resulting from assemblies in the experimental data.
doi:10.1007/s10827-010-0241-8
PMCID: PMC2978895  PMID: 20480218
LFP; Synchrony; Oscillations; Network dynamics; Motor cortex
16.  Conversion of Phase Information into a Spike-Count Code by Bursting Neurons 
PLoS ONE  2010;5(3):e9669.
Single neurons in the cerebral cortex are immersed in a fluctuating electric field, the local field potential (LFP), which mainly originates from synchronous synaptic input into the local neural neighborhood. As shown by recent studies in visual and auditory cortices, the angular phase of the LFP at the time of spike generation adds significant extra information about the external world, beyond the one contained in the firing rate alone. However, no biologically plausible mechanism has yet been suggested that allows downstream neurons to infer the phase of the LFP at the soma of their pre-synaptic afferents. Therefore, so far there is no evidence that the nervous system can process phase information. Here we study a model of a bursting pyramidal neuron, driven by a time-dependent stimulus. We show that the number of spikes per burst varies systematically with the phase of the fluctuating input at the time of burst onset. The mapping between input phase and number of spikes per burst is a robust response feature for a broad range of stimulus statistics. Our results suggest that cortical bursting neurons could play a crucial role in translating LFP phase information into an easily decodable spike count code.
doi:10.1371/journal.pone.0009669
PMCID: PMC2837377  PMID: 20300632
17.  Context Matters: The Illusive Simplicity of Macaque V1 Receptive Fields 
PLoS ONE  2012;7(7):e39699.
Even in V1, where neurons have well characterized classical receptive fields (CRFs), it has been difficult to deduce which features of natural scenes stimuli they actually respond to. Forward models based upon CRF stimuli have had limited success in predicting the response of V1 neurons to natural scenes. As natural scenes exhibit complex spatial and temporal correlations, this could be due to surround effects that modulate the sensitivity of the CRF. Here, instead of attempting a forward model, we quantify the importance of the natural scenes surround for awake macaque monkeys by modeling it non-parametrically. We also quantify the influence of two forms of trial to trial variability. The first is related to the neuron’s own spike history. The second is related to ongoing mean field population activity reflected by the local field potential (LFP). We find that the surround produces strong temporal modulations in the firing rate that can be both suppressive and facilitative. Further, the LFP is found to induce a precise timing in spikes, which tend to be temporally localized on sharp LFP transients in the gamma frequency range. Using the pseudo R2 as a measure of model fit, we find that during natural scene viewing the CRF dominates, accounting for 60% of the fit, but that taken collectively the surround, spike history and LFP are almost as important, accounting for 40%. However, overall only a small proportion of V1 spiking statistics could be explained (R2∼5%), even when the full stimulus, spike history and LFP were taken into account. This suggests that under natural scene conditions, the dominant influence on V1 neurons is not the stimulus, nor the mean field dynamics of the LFP, but the complex, incoherent dynamics of the network in which neurons are embedded.
doi:10.1371/journal.pone.0039699
PMCID: PMC3389039  PMID: 22802940
18.  Different Origins of Gamma Rhythm and High-Gamma Activity in Macaque Visual Cortex 
PLoS Biology  2011;9(4):e1000610.
High-gamma (80–200 Hz) activity can be dissociated from gamma rhythms in the monkey cortex, and appears largely to reflect spiking activity in the vicinity of the electrode.
During cognitive tasks electrical activity in the brain shows changes in power in specific frequency ranges, such as the alpha (8–12 Hz) or gamma (30–80 Hz) bands, as well as in a broad range above ∼80 Hz, called the high-gamma band. The role or significance of this broadband high-gamma activity is unclear. One hypothesis states that high-gamma oscillations serve just like gamma oscillations, operating at a higher frequency and consequently at a faster timescale. Another hypothesis states that high-gamma power is related to spiking activity. Because gamma power and spiking activity tend to co-vary during most stimulus manipulations (such as contrast modulations) or cognitive tasks (such as attentional modulation), it is difficult to dissociate these two hypotheses. We studied the relationship between high-gamma power, gamma rhythm, and spiking activity in the primary visual cortex (V1) of awake monkeys while varying the stimulus size, which increased the gamma power but decreased the firing rate, permitting a dissociation. We found that gamma power became anti-correlated with the high-gamma power, suggesting that the two phenomena are distinct and have different origins. On the other hand, high-gamma power remained tightly correlated with spiking activity under a wide range of stimulus manipulations. We studied this relationship using a signal processing technique called Matching Pursuit and found that action potentials are associated with sharp transients in the LFP with broadband power, which is visible at frequencies as low as ∼50 Hz. These results distinguish broadband high-gamma activity from gamma rhythms as an easily obtained and reliable electrophysiological index of neuronal firing near the microelectrode. Further, they highlight the importance of making a careful dissociation between gamma rhythms and spike-related transients that could be incorrectly decomposed as rhythms using traditional signal processing methods.
Author Summary
Electrical activity in the brain often shows oscillations at distinct frequencies, such as the alpha (8–12 Hz) or gamma (30–80 Hz) bands, which have been linked with distinct cognitive states. In addition, changes in power are seen in a broad range above ∼80 Hz, called the “high-gamma” band. High-gamma power could arise either from sustained oscillations (similar to gamma rhythms but operating at higher frequencies) or from brief bursts of power associated with spikes generated near the electrode (“spike bleed-through”). It is difficult to dissociate these two hypotheses because gamma oscillations and spiking are correlated during most stimulus or cognitive manipulations. Further, most signal processing techniques decompose any signal into a set of oscillatory functions, making it difficult to represent any transient power fluctuations that occur at the time of spikes. We address the first issue by using a stimulus manipulation for which gamma oscillations and spiking activity are anti-correlated, permitting dissociation. To address the second issue, we use a signal processing technique called Matching Pursuit, which is well suited to capture transient activity. We show that gamma and high-gamma power become anti-correlated, suggesting different biophysical origins. Spikes and high-gamma power, however, remain tightly correlated. Broadband high-gamma activity could therefore be an easily obtained and reliable electrophysiological index of neuronal firing in the vicinity of an electrode.
doi:10.1371/journal.pbio.1000610
PMCID: PMC3075230  PMID: 21532743
19.  Detailed Characterization of Local Field Potential Oscillations and Their Relationship to Spike Timing in the Antennal Lobe of the Moth Manduca sexta 
The transient oscillatory model of odor identity encoding seeks to explain how odorants with spatially overlapped patterns of input into primary olfactory networks can be discriminated. This model provides several testable predictions about the distributed nature of network oscillations and how they control spike timing. To test these predictions, 16 channel electrode arrays were placed within the antennal lobe (AL) of the moth Manduca sexta. Unitary spiking and multi site local field potential (LFP) recordings were made during spontaneous activity and in response to repeated presentations of an odor panel. We quantified oscillatory frequency, cross correlations between LFP recording sites, and spike–LFP phase relationships. We show that odor-driven AL oscillations in Manduca are frequency modulating (FM) from ∼100 to 30 Hz; this was odorant and stimulus duration dependent. FM oscillatory responses were localized to one or two recording sites suggesting a localized (perhaps glomerular) not distributed source. LFP cross correlations further demonstrated that only a small (r < 0.05) distributed and oscillatory component was present. Cross spectral density analysis demonstrated the frequency of these weakly distributed oscillations was state dependent (spontaneous activity = 25–55 Hz; odor-driven = 55–85 Hz). Surprisingly, vector strength analysis indicated that unitary phase locking of spikes to the LFP was strongest during spontaneous activity and dropped significantly during responses. Application of bicuculline, a GABAA receptor antagonist, significantly lowered the frequency content of odor-driven distributed oscillatory activity. Bicuculline significantly reduced spike phase locking generally, but the ubiquitous pattern of increased phase locking during spontaneous activity persisted. Collectively, these results indicate that oscillations perform poorly as a stimulus-mediated spike synchronizing mechanism for Manduca and hence are incongruent with the transient oscillatory model.
doi:10.3389/fneng.2011.00012
PMCID: PMC3200547  PMID: 22046161
olfaction; odor coding; oscillations; synchrony; GABAA; olfactory bulb; antennal lobe
20.  Visual encoding and fixation target selection in free viewing: presaccadic brain potentials 
In scrutinizing a scene, the eyes alternate between fixations and saccades. During a fixation, two component processes can be distinguished: visual encoding and selection of the next fixation target. We aimed to distinguish the neural correlates of these processes in the electrical brain activity prior to a saccade onset. Participants viewed color photographs of natural scenes, in preparation for a change detection task. Then, for each participant and each scene we computed an image heat map, with temperature representing the duration and density of fixations. The temperature difference between the start and end points of saccades was taken as a measure of the expected task-relevance of the information concentrated in specific regions of a scene. Visual encoding was evaluated according to whether subsequent change was correctly detected. Saccades with larger temperature difference were more likely to be followed by correct detection than ones with smaller temperature differences. The amplitude of presaccadic activity over anterior brain areas was larger for correct detection than for detection failure. This difference was observed for short “scrutinizing” but not for long “explorative” saccades, suggesting that presaccadic activity reflects top-down saccade guidance. Thus, successful encoding requires local scanning of scene regions which are expected to be task-relevant. Next, we evaluated fixation target selection. Saccades “moving up” in temperature were preceded by presaccadic activity of higher amplitude than those “moving down”. This finding suggests that presaccadic activity reflects attention deployed to the following fixation location. Our findings illustrate how presaccadic activity can elucidate concurrent brain processes related to the immediate goal of planning the next saccade and the larger-scale goal of constructing a robust representation of the visual scene.
doi:10.3389/fnsys.2013.00026
PMCID: PMC3694272  PMID: 23818877
saccades; EEG; presaccadic interval; attention; visual encoding; saccade guidance; change detection; heat maps
21.  Communication through Resonance in Spiking Neuronal Networks 
PLoS Computational Biology  2014;10(8):e1003811.
The cortex processes stimuli through a distributed network of specialized brain areas. This processing requires mechanisms that can route neuronal activity across weakly connected cortical regions. Routing models proposed thus far are either limited to propagation of spiking activity across strongly connected networks or require distinct mechanisms that create local oscillations and establish their coherence between distant cortical areas. Here, we propose a novel mechanism which explains how synchronous spiking activity propagates across weakly connected brain areas supported by oscillations. In our model, oscillatory activity unleashes network resonance that amplifies feeble synchronous signals and promotes their propagation along weak connections (“communication through resonance”). The emergence of coherent oscillations is a natural consequence of synchronous activity propagation and therefore the assumption of different mechanisms that create oscillations and provide coherence is not necessary. Moreover, the phase-locking of oscillations is a side effect of communication rather than its requirement. Finally, we show how the state of ongoing activity could affect the communication through resonance and propose that modulations of the ongoing activity state could influence information processing in distributed cortical networks.
Author Summary
The cortex is a highly modular structure with a large number of functionally specialized areas that communicate with each other through long-range cortical connections. It is has been suggested that communication between spiking neuronal networks (SNNs) requires synchronization of spiking activity which is either provided by the flow of neuronal activity across divergent/convergent connections, as suggested by computational models of SNNs, or by local oscillations in the gamma frequency band (30–100 Hz). However, such communication requires unphysiologically dense/strong connectivity, and the mechanisms required to synchronize separated local oscillators remain poorly understood. Here, we present a novel mechanism that alleviates these shortcomings and enables the propagation synchrony across weakly connected SNNs by locally amplifying feeble synchronization through resonance that naturally occurs in oscillating networks of excitatory and inhibitory neurons. We show that oscillatory stimuli at the network resonance frequencies generate a slowly propagating oscillation that is synchronized across the distributed networks. Moreover, communication with such oscillations depends on the dynamical state of the background activity in the SNN. Our results suggest that the emergence of synchronized oscillations can be viewed as a consequence of spiking activity propagation in weakly connected networks that is supported by resonance and modulated by the dynamics of the ongoing activity.
doi:10.1371/journal.pcbi.1003811
PMCID: PMC4148205  PMID: 25165853
22.  Spectral Analysis of Input Spike Trains by Spike-Timing-Dependent Plasticity 
PLoS Computational Biology  2012;8(7):e1002584.
Spike-timing-dependent plasticity (STDP) has been observed in many brain areas such as sensory cortices, where it is hypothesized to structure synaptic connections between neurons. Previous studies have demonstrated how STDP can capture spiking information at short timescales using specific input configurations, such as coincident spiking, spike patterns and oscillatory spike trains. However, the corresponding computation in the case of arbitrary input signals is still unclear. This paper provides an overarching picture of the algorithm inherent to STDP, tying together many previous results for commonly used models of pairwise STDP. For a single neuron with plastic excitatory synapses, we show how STDP performs a spectral analysis on the temporal cross-correlograms between its afferent spike trains. The postsynaptic responses and STDP learning window determine kernel functions that specify how the neuron “sees” the input correlations. We thus denote this unsupervised learning scheme as ‘kernel spectral component analysis’ (kSCA). In particular, the whole input correlation structure must be considered since all plastic synapses compete with each other. We find that kSCA is enhanced when weight-dependent STDP induces gradual synaptic competition. For a spiking neuron with a “linear” response and pairwise STDP alone, we find that kSCA resembles principal component analysis (PCA). However, plain STDP does not isolate correlation sources in general, e.g., when they are mixed among the input spike trains. In other words, it does not perform independent component analysis (ICA). Tuning the neuron to a single correlation source can be achieved when STDP is paired with a homeostatic mechanism that reinforces the competition between synaptic inputs. Our results suggest that neuronal networks equipped with STDP can process signals encoded in the transient spiking activity at the timescales of tens of milliseconds for usual STDP.
Author Summary
Tuning feature extraction of sensory stimuli is an important function for synaptic plasticity models. A widely studied example is the development of orientation preference in the primary visual cortex, which can emerge using moving bars in the visual field. A crucial point is the decomposition of stimuli into basic information tokens, e.g., selecting individual bars even though they are presented in overlapping pairs (vertical and horizontal). Among classical unsupervised learning models, independent component analysis (ICA) is capable of isolating basic tokens, whereas principal component analysis (PCA) cannot. This paper focuses on spike-timing-dependent plasticity (STDP), whose functional implications for neural information processing have been intensively studied both theoretically and experimentally in the last decade. Following recent studies demonstrating that STDP can perform ICA for specific cases, we show how STDP relates to PCA or ICA, and in particular explains the conditions under which it switches between them. Here information at the neuronal level is assumed to be encoded in temporal cross-correlograms of spike trains. We find that a linear spiking neuron equipped with pairwise STDP requires additional mechanisms, such as a homeostatic regulation of its output firing, in order to separate mixed correlation sources and thus perform ICA.
doi:10.1371/journal.pcbi.1002584
PMCID: PMC3390410  PMID: 22792056
23.  STDP Allows Fast Rate-Modulated Coding with Poisson-Like Spike Trains 
PLoS Computational Biology  2011;7(10):e1002231.
Spike timing-dependent plasticity (STDP) has been shown to enable single neurons to detect repeatedly presented spatiotemporal spike patterns. This holds even when such patterns are embedded in equally dense random spiking activity, that is, in the absence of external reference times such as a stimulus onset. Here we demonstrate, both analytically and numerically, that STDP can also learn repeating rate-modulated patterns, which have received more experimental evidence, for example, through post-stimulus time histograms (PSTHs). Each input spike train is generated from a rate function using a stochastic sampling mechanism, chosen to be an inhomogeneous Poisson process here. Learning is feasible provided significant covarying rate modulations occur within the typical timescale of STDP (∼10–20 ms) for sufficiently many inputs (∼100 among 1000 in our simulations), a condition that is met by many experimental PSTHs. Repeated pattern presentations induce spike-time correlations that are captured by STDP. Despite imprecise input spike times and even variable spike counts, a single trained neuron robustly detects the pattern just a few milliseconds after its presentation. Therefore, temporal imprecision and Poisson-like firing variability are not an obstacle to fast temporal coding. STDP provides an appealing mechanism to learn such rate patterns, which, beyond sensory processing, may also be involved in many cognitive tasks.
Author Summary
In vivo neural responses to stimuli are known to have a lot of variability across trials. If the same number of spikes is emitted from trial to trial, the neuron is said to be reliable. If the timing of such spikes is roughly preserved across trials, the neuron is said to be precise. Here we demonstrate both analytically and numerically that the well-established Hebbian learning rule of spike-timing-dependent plasticity (STDP) can learn response patterns despite relatively low reliability (Poisson-like variability) and low temporal precision (10–20 ms). These features are in line with many experimental observations, in which a poststimulus time histogram (PSTH) is evaluated over multiple trials. In our model, however, information is extracted from the relative spike times between afferents without the need of an absolute reference time, such as a stimulus onset. Relevantly, recent experiments show that relative timing is often more informative than the absolute timing. Furthermore, the scope of application for our study is not restricted to sensory systems. Taken together, our results suggest a fine temporal resolution for the neural code, and that STDP is an appropriate candidate for encoding and decoding such activity.
doi:10.1371/journal.pcbi.1002231
PMCID: PMC3203056  PMID: 22046113
24.  Sensory information in local field potentials and spikes from visual and auditory cortices: time scales and frequency bands 
Studies analyzing sensory cortical processing or trying to decode brain activity often rely on a combination of different electrophysiological signals, such as local field potentials (LFPs) and spiking activity. Understanding the relation between these signals and sensory stimuli and between different components of these signals is hence of great interest. We here provide an analysis of LFPs and spiking activity recorded from visual and auditory cortex during stimulation with natural stimuli. In particular, we focus on the time scales on which different components of these signals are informative about the stimulus, and on the dependencies between different components of these signals. Addressing the first question, we find that stimulus information in low frequency bands (<12 Hz) is high, regardless of whether their energy is computed at the scale of milliseconds or seconds. Stimulus information in higher bands (>50 Hz), in contrast, is scale dependent, and is larger when the energy is averaged over several hundreds of milliseconds. Indeed, combined analysis of signal reliability and information revealed that the energy of slow LFP fluctuations is well related to the stimulus even when considering individual or few cycles, while the energy of fast LFP oscillations carries information only when averaged over many cycles. Addressing the second question, we find that stimulus information in different LFP bands, and in different LFP bands and spiking activity, is largely independent regardless of time scale or sensory system. Taken together, these findings suggest that different LFP bands represent dynamic natural stimuli on distinct time scales and together provide a potentially rich source of information for sensory processing or decoding brain activity.
Electronic supplementary material
The online version of this article (doi:10.1007/s10827-010-0230-y) contains supplementary material, which is available to authorized users.
doi:10.1007/s10827-010-0230-y
PMCID: PMC2978898  PMID: 20232128
Information theory; Vision; Audition; Population coding; Oscillations; Firing rates
25.  Spike-Timing Dependent Plasticity and Feed-Forward Input Oscillations Produce Precise and Invariant Spike Phase-Locking 
In the hippocampus and the neocortex, the coupling between local field potential (LFP) oscillations and the spiking of single neurons can be highly precise, across neuronal populations and cell types. Spike phase (i.e., the spike time with respect to a reference oscillation) is known to carry reliable information, both with phase-locking behavior and with more complex phase relationships, such as phase precession. How this precision is achieved by neuronal populations, whose membrane properties and total input may be quite heterogeneous, is nevertheless unknown. In this note, we investigate a simple mechanism for learning precise LFP-to-spike coupling in feed-forward networks – the reliable, periodic modulation of presynaptic firing rates during oscillations, coupled with spike-timing dependent plasticity. When oscillations are within the biological range (2–150 Hz), firing rates of the inputs change on a timescale highly relevant to spike-timing dependent plasticity (STDP). Through analytic and computational methods, we find points of stable phase-locking for a neuron with plastic input synapses. These points correspond to precise phase-locking behavior in the feed-forward network. The location of these points depends on the oscillation frequency of the inputs, the STDP time constants, and the balance of potentiation and de-potentiation in the STDP rule. For a given input oscillation, the balance of potentiation and de-potentiation in the STDP rule is the critical parameter that determines the phase at which an output neuron will learn to spike. These findings are robust to changes in intrinsic post-synaptic properties. Finally, we discuss implications of this mechanism for stable learning of spike-timing in the hippocampus.
doi:10.3389/fncom.2011.00045
PMCID: PMC3216007  PMID: 22110429
spike-timing dependent plasticity; oscillations; phase-locking; stable learning; stability of neuronal plasticity; place fields

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