TABLE without idfile.link as "Related Files",title as "Title",type as "type"FROM "" AND -"Obsidian Assets"WHERE citekey = "guOscillatoryMultiplexingNeural2015" SORT file.cday DESC
Abstract
Interval timing and working memory are critical components of cognition that are supported by neural oscillations in prefrontalâstriatalâhippocampal circuits. In this review, the properties of interval timing and working memory are explored in terms of behavioral, anatomical, pharmacological, and neurophysiological findings. We then describe the various neurobiological theories that have been developed to explain these cognitive processes â largely independent of each other. Following this, a coupled excitatory â inhibitory oscillation (EIO) model of temporal processing is proposed to address the shared oscillatory properties of interval timing and working memory. Using this integrative approach, we describe a hybrid model explaining how interval timing and working memory can originate from the same oscillatory processes, but differ in terms of which dimension of the neural oscillation is utilized for the extraction of item, temporal order, and duration information. This extension of the striatal beat-frequency (SBF) model of interval timing (Matell and Meck, 2000, Matell and Meck, 2004) is based on prefrontalâstriatalâhippocampal circuit dynamics and has direct relevance to the pathophysiological distortions observed in time perception and working memory in a variety of psychiatric and neurological conditions.
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time-based resource-sharing (TBRS) model that explains how forgetting is time related (Barrouillet et al., 2004) as well as the manner in which time plays a crucial role in working memory load (Barrouillet et al., 2007). tp
In addition to the phase locking of spikes to theta oscillations, studies utilizing LFPs or EEG/MEG have reported that phaseamplitude coupling (PAC) between theta-gamma oscillations is involved in working memory (e.g., Axmacher et al., 2010; Jensen and Colgin, 2007; Lisman and Idiart, 1995; Maris et al., 2011; Mizuhara and Yamaguchi, 2011; Sauseng et al., 2009; Schack et al., 2002; van der Meij et al., 2012). PAC, also referred to as ânested oscillationsâ, refers to the phenomenon of coupling between the amplitude of a faster oscillation and the phase of a slower oscillation. Numerous studies have shown evidence of PAC in various species including humans, monkeys, and rats (e.g., Canolty et al., 2006; Chrobak and BuzsĂĄki, 1998; Lakatos et al., 2005, 2008; Sirota et al., 2008; Tort et al., 2009; van der Meij et al., 2012). PAC has been most commonly observed between theta and gamma oscillations; however, recent evidence shows that PAC can occur at multiple frequencies with theta oscillations also being entrained to delta oscillations (e.g., He et al., 2010; Lakatos et al., 2005; Maris et al., 2011; Miller et al., 2010). tp
đ€In addition to the phase locking of spikes to theta oscillations, studies utilizing LFPs or EEG/MEG have reported that phaseamplitude coupling (PAC) between theta-gamma oscillations is involved in working memory (e.g., Axmacher et al., 2010; Jensen and Colgin, 2007; Lisman and Idiart, 1995; Maris et al., 2011; Mizuhara and Yamaguchi, 2011; Sauseng et al., 2009; Schack et al., 2002; van der Meij et al., 2012). PAC, also referred to as ânested oscillationsâ, refers to the phenomenon of coupling between the amplitude of a faster oscillation and the phase of a slower oscillation. Numerous studies have shown evidence of PAC in various species including humans, monkeys, and rats (e.g., Canolty et al., 2006; Chrobak and BuzsĂĄki, 1998; Lakatos et al., 2005, 2008; Sirota et al., 2008; Tort et al., 2009; van der Meij et al., 2012). PAC has been most commonly observed between theta and gamma oscillations; however, recent evidence shows that PAC can occur at multiple frequencies with theta oscillations also being entrained to delta oscillations (e.g., He et al., 2010; Lakatos et al., 2005; Maris et al., 2011; Miller et al., 2010).đ€
The functional role of PAC is thought to involve local neural computations and their communication across large-scale brain networks (Canolty and Knight, 2010). With the extensive evidence of PACs occurring over various frequencies and brain regions, PAC has been shown to be involved in multiple cognitive domains, important for working memory (e.g., Axmacher et al., 2010; Lisman and Idiart, 1995; Maris et al., 2011; Mizuhara and Yamaguchi, 2011; Schack et al., 2002; van der Meij et al., 2012), and also for decision-making, spatial navigation, learning, and perception (Kepecs et al., 2006; Lakatos et al., 2005). Canolty et al. (2006) examined the PAC patterns in different cognitive tasks by recording the electrocorticogram (ECoG) of epilepsy patients, showing that similar tasks evoked similar spatial patterns of theta and gamma PACâsuggesting that âcognitive architecturesâ can be described by these patterns of oscillatory activity. tp
đ€The functional role of PAC is thought to involve local neural computations and their communication across large-scale brain networks (Canolty and Knight, 2010). With the extensive evidence of PACs occurring over various frequencies and brain regions, PAC has been shown to be involved in multiple cognitive domains, important for working memory (e.g., Axmacher et al., 2010; Lisman and Idiart, 1995; Maris et al., 2011; Mizuhara and Yamaguchi, 2011; Schack et al., 2002; van der Meij et al., 2012), and also for decision-making, spatial navigation, learning, and perception (Kepecs et al., 2006; Lakatos et al., 2005). Canolty et al. (2006) examined the PAC patterns in different cognitive tasks by recording the electrocorticogram (ECoG) of epilepsy patients, showing that similar tasks evoked similar spatial patterns of theta and gamma PACâsuggesting that âcognitive architecturesâ can be described by these patterns of oscillatory activity.đ€
In working memory tasks, the amplitude of gamma is modulated by theta phase in multiple brain areas, while PAC strength is modulated in a heterogeneous manner. Maris et al. (2011), for example, showed that working memory tasks are associated with increases in PAC strength in the parietal-temporal and right frontal areas, with an associated decrease in strength in right temporal lobe in humans. Moreover, when the amplitudeand phase-providing oscillations are spatially dissociated using decomposition techniques, the PAC was shown to be widely distributed across the brain, with the spatial extent of the phase-providing (slower) oscillations tending to be more widespread than the amplitudeproviding (faster) oscillations (Maris et al., 2011; van der Meij et al., 2012). The widely distributed PAC networks demonstrated in these human studies, together with the evidence of cross-area couplings from rodents and primates (Liebe et al., 2012; Sirota et al., 2008; Tort et al., 2009), support the functional role of PAC in facilitating communication among brain areas by modulating the synchronous patterns of neural firing. tp
đ€In working memory tasks, the amplitude of gamma is modulated by theta phase in multiple brain areas, while PAC strength is modulated in a heterogeneous manner. Maris et al. (2011), for example, showed that working memory tasks are associated with increases in PAC strength in the parietal-temporal and right frontal areas, with an associated decrease in strength in right temporal lobe in humans. Moreover, when the amplitudeand phase-providing oscillations are spatially dissociated using decomposition techniques, the PAC was shown to be widely distributed across the brain, with the spatial extent of the phase-providing (slower) oscillations tending to be more widespread than the amplitudeproviding (faster) oscillations (Maris et al., 2011; van der Meij et al., 2012). The widely distributed PAC networks demonstrated in these human studies, together with the evidence of cross-area couplings from rodents and primates (Liebe et al., 2012; Sirota et al., 2008; Tort et al., 2009), support the functional role of PAC in facilitating communication among brain areas by modulating the synchronous patterns of neural firing.đ€
state-dependent network (SDN) model proposes that temporal information is locally encoded in an intrinsic spatiotemporal neural network along with representations of other stimulus attributes (e.g., Buonomano, 2000; Buonomano and Laje, 2010; Buonomano and Maass, 2009; Buonomano and Merzenich, 1995; Buonomano et al., 1995, 2009; Karmarkar and Buonomano, 2007); tp
đ€state-dependent network (SDN) model proposes that temporal information is locally encoded in an intrinsic spatiotemporal neural network along with representations of other stimulus attributes (e.g., Buonomano, 2000; Buonomano and Laje, 2010; Buonomano and Maass, 2009; Buonomano and Merzenich, 1995; Buonomano et al., 1995, 2009; Karmarkar and Buonomano, 2007);đ€
stochastic ramp and trigger (SRT) model, which is an integration-based model, proposes that time is encoded as an average firing rate of neural populations and detected with a fixed threshold (Simen et al., 2011); tp
đ€stochastic ramp and trigger (SRT) model, which is an integration-based model, proposes that time is encoded as an average firing rate of neural populations and detected with a fixed threshold (Simen et al., 2011);đ€
integrated timing model of Taatgen et al. (2007) tp
ariance in cognitive performance fluctuates over tens to hundreds of seconds and has largely been considered ânoiseâ; however, the variance of cognition/behavior has shown to increase with time scales, showing 1/f-type power distribution rather than just a random (white noise) distribution in the temporal sequence of errors (Gilden 2001; Gilden et al., 1995, see also Farrell et al., 2006). tp
Extracted Annotations and Comments
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The involvement of beta in working memory as well as in temporal behavior as previously described, in together with the evidence of other frequency bands of neural oscillations, suggests that oscillatory features could be shared between timing and working memory. In addition, beta rhythms are important in basal ganglia disorders and fluctuations in beta oscillations in the basal ganglia and sensorimotor cortex are frequently observed as a function of dopamine levels (Brittain and Brown 2014; Jenkinson and Brown, 2011; Gu et al., 2014), providing an anatomical link between beta rhythms and the cortico-striatal circuits involved in temporal processing and working memory.
Pretty much the thesis
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Moreover, the âphase lockingâ of spikes during the maintenance phase is often exhibited without increases in firing rates (Lee et al., 2005), suggesting that the temporal coordination of spikes with ongoing neural oscillations may be even more important than the firing rates of spikes for the maintenance of information during a retention interval.
đ€Moreover, the âphase lockingâ of spikes during the maintenance phase is often exhibited without increases in firing rates (Lee et al., 2005), suggesting that the temporal coordination of spikes with ongoing neural oscillations may be even more important than the firing rates of spikes for the maintenance of information during a retention interval.đ€
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In the working memory literature, various models also have been proposed in an effort to explain the underlying mechanisms of working memory, such as the TBRS model with emphasis on processing time in the determination of working memory load (e.g., Barrouillet et al., 2004, 2007), the cognitive model of working memory with a central executive (e.g., Baddeley, 1986, 2000; Baddeley and Hitch, 1974; Repovs and Baddeley, 2006), or the model defining working memory as an emergent property of activated neural
đ€In the working memory literature, various models also have been proposed in an effort to explain the underlying mechanisms of working memory, such as the TBRS model with emphasis on processing time in the determination of working memory load (e.g., Barrouillet et al., 2004, 2007), the cognitive model of working memory with a central executive (e.g., Baddeley, 1986, 2000; Baddeley and Hitch, 1974; Repovs and Baddeley, 2006), or the model defining working memory as an emergent property of activated neuralđ€
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systems (DâEsposito, 2007; Postle, 2006). However, given the complexity of working memory, the precise information-processing mechanisms and the underlying neuronal properties have yet to be fully revealed, and there are multiple working memory models currently being debated (Wiley and Jarosz, 2012).
đ€systems (DâEsposito, 2007; Postle, 2006). However, given the complexity of working memory, the precise information-processing mechanisms and the underlying neuronal properties have yet to be fully revealed, and there are multiple working memory models currently being debated (Wiley and Jarosz, 2012).đ€
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As one of the models explaining neuroanatomical localization of working memory, the prefrontal cortex, basal ganglia working memory (PBWM) model (Frank et al., 2001; Hazy et al., 2006, 2007; OâReilly and Frank, 2006) suggests a critical role for cortico-striatal circuits in selecting and maintaining relevant information in working memory. The PBWM model explains that PFC actively maintains task-relevant information that is dynamically gated/updated by the basal ganglia. In addition, the posterior cortex and hippocampus play a role in automatic sensory/motor processing and the rapid learning of arbitrary associations, respectively (e.g., Collins and Franck, 2012).
đ€As one of the models explaining neuroanatomical localization of working memory, the prefrontal cortex, basal ganglia working memory (PBWM) model (Frank et al., 2001; Hazy et al., 2006, 2007; OâReilly and Frank, 2006) suggests a critical role for cortico-striatal circuits in selecting and maintaining relevant information in working memory. The PBWM model explains that PFC actively maintains task-relevant information that is dynamically gated/updated by the basal ganglia. In addition, the posterior cortex and hippocampus play a role in automatic sensory/motor processing and the rapid learning of arbitrary associations, respectively (e.g., Collins and Franck, 2012).đ€
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The proposed neural mechanisms of the PBWM model share some similarities with the SBF model of interval timing. For example, both rely on the posited involvement of the same brain areasâemphasizing a role for the striatum in detecting/gating cortical inputs. Specifically, the role of the striatum has been suggested as detecting the coincident pattern of cortical inputs in the SBF model and as gating/updating information by integration of cortical input and DA signals in PBWM model.
đ€The proposed neural mechanisms of the PBWM model share some similarities with the SBF model of interval timing. For example, both rely on the posited involvement of the same brain areasâemphasizing a role for the striatum in detecting/gating cortical inputs. Specifically, the role of the striatum has been suggested as detecting the coincident pattern of cortical inputs in the SBF model and as gating/updating information by integration of cortical input and DA signals in PBWM model.đ€
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The selected (gated) signals are hypothesized to pass through the thalamus to the cortex in both models and to be modulated by DA (see Hazy et al., 2006, 2007; Matell and Meck, 2004). Also, both models accommodate a role for DA signaling in learning so that the synapses of MSNs in the striatum can be weighted appropriately. In the SBF model, feedback and/or the delivery of reward for responses occurring just after the target duration induces phasic DA input to the striatum which can strengthen the synapses of MSN receiving inputs from the relevant subset of cortical oscillating neurons in order for them to serve as âdetectorsâ for specific target durations (Ullsperger et al., 2014; van Rijn et al., 2014). Similarly, the PBWM model explains that phasic DA input modulates the MSN synapses so that the relevant cortical inputs can trigger the gating/updating of the relevant information. Given these similarities, it has been suggested that interval timing and working memory rely not only on the same gross anatomical structures, but also on the same neural representations (Buhusi and Meck, 2009; Lewis and Miall, 2006; Lustig and Meck, 2005; Lustig et al., 2005).
đ€The selected (gated) signals are hypothesized to pass through the thalamus to the cortex in both models and to be modulated by DA (see Hazy et al., 2006, 2007; Matell and Meck, 2004). Also, both models accommodate a role for DA signaling in learning so that the synapses of MSNs in the striatum can be weighted appropriately. In the SBF model, feedback and/or the delivery of reward for responses occurring just after the target duration induces phasic DA input to the striatum which can strengthen the synapses of MSN receiving inputs from the relevant subset of cortical oscillating neurons in order for them to serve as âdetectorsâ for specific target durations (Ullsperger et al., 2014; van Rijn et al., 2014). Similarly, the PBWM model explains that phasic DA input modulates the MSN synapses so that the relevant cortical inputs can trigger the gating/updating of the relevant information. Given these similarities, it has been suggested that interval timing and working memory rely not only on the same gross anatomical structures, but also on the same neural representations (Buhusi and Meck, 2009; Lewis and Miall, 2006; Lustig and Meck, 2005; Lustig et al., 2005).đ€
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Specifically, the SBF model suggests that each cortical neuron oscillates at a preferred oscillatory frequency covering, for example, the alpha and theta frequency bands. With the onset of a stimulus to-be-timed, the phases of multiple oscillators are reset by a burst of dopaminergic input from the ventral tegmental area (VTA).
đ€Specifically, the SBF model suggests that each cortical neuron oscillates at a preferred oscillatory frequency covering, for example, the alpha and theta frequency bands. With the onset of a stimulus to-be-timed, the phases of multiple oscillators are reset by a burst of dopaminergic input from the ventral tegmental area (VTA).đ€
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Then, these cortical neurons continue to oscillate according to their endogenous oscillatory periods, and their coincident activation pattern can be detected by striatal MSNs during the course of the to-be-timed signal as illustrated in Fig. 2.
đ€Then, these cortical neurons continue to oscillate according to their endogenous oscillatory periods, and their coincident activation pattern can be detected by striatal MSNs during the course of the to-be-timed signal as illustrated in Fig. 2.đ€
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MSNâs have the potential to serve as coincidence detectors because one MSN receives tens of thousands of inputs from divergent cortical and thalamic neurons and needs simultaneous input to be activated (Groves et al., 1995; Wilson, 1995, 1998).
đ€MSNâs have the potential to serve as coincidence detectors because one MSN receives tens of thousands of inputs from divergent cortical and thalamic neurons and needs simultaneous input to be activated (Groves et al., 1995; Wilson, 1995, 1998).đ€
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The synaptic weights between a MSN and cortical neurons with different endogenous oscillatory periods determine for which duration this MSN encodes. Even with drift in the oscillatory periods over time, the synchrony provided by the resetting at the start of a signal is sufficient to maintain a stable encoding of duration.
đ€The synaptic weights between a MSN and cortical neurons with different endogenous oscillatory periods determine for which duration this MSN encodes. Even with drift in the oscillatory periods over time, the synchrony provided by the resetting at the start of a signal is sufficient to maintain a stable encoding of duration.đ€
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The combination of drift on the one hand, and the reliance on slower oscillating cortical neurons for MSNs that encode for longer durations provide a constant coefficient of variation across signal durations in the seconds-to-minutes range and match the level of sensitivity to time observed in humans and other animals (Gibbon et al., 1984, 1997; Matell and Meck, 2004; Penney et al., 2008).
đ€The combination of drift on the one hand, and the reliance on slower oscillating cortical neurons for MSNs that encode for longer durations provide a constant coefficient of variation across signal durations in the seconds-to-minutes range and match the level of sensitivity to time observed in humans and other animals (Gibbon et al., 1984, 1997; Matell and Meck, 2004; Penney et al., 2008).đ€
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According to this account, the learning of a new target duration can be explained within the same cortico-striatal circuit by modulating synaptic weights among MSNs and subsets of cortical neurons. For example, if the learning of a 6-s target duration has induced a MSN to be highly connected with a subset of cortical neurons whose firing rates are maximal 6 s after signal onset, the learning of a 10-s target duration will induce a different set of synaptic weights to a MSN as a result of stronger connections with a subset of cortical neurons that fire more frequently around 10 s.
đ€According to this account, the learning of a new target duration can be explained within the same cortico-striatal circuit by modulating synaptic weights among MSNs and subsets of cortical neurons. For example, if the learning of a 6-s target duration has induced a MSN to be highly connected with a subset of cortical neurons whose firing rates are maximal 6 s after signal onset, the learning of a 10-s target duration will induce a different set of synaptic weights to a MSN as a result of stronger connections with a subset of cortical neurons that fire more frequently around 10 s.đ€
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Phasic DA release into the striatum from the SNc is hypothesized to serve as the reinforcement signal for learning of new target durations, thus allowing modulation of the MSN synaptic weights and new learning (Agostino et al., 2011; MacDonald et al., 2012; Matell and Meck, 2004).
đ€Phasic DA release into the striatum from the SNc is hypothesized to serve as the reinforcement signal for learning of new target durations, thus allowing modulation of the MSN synaptic weights and new learning (Agostino et al., 2011; MacDonald et al., 2012; Matell and Meck, 2004).đ€
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The strength of the SBF model lies in its specification of known neural mechanisms, as well as its consistency with the available anatomical, behavioral, and pharmacological evidence (Allman and Meck, 2012; Coull et al., 2011; Merchant et al., 2013a). MSNs in the striatum have the appropriate characteristics to serve as a largescale coincidence-detector system because they receive a great deal of convergent, multi-modal input from the cortex (Wilson, 1995, 1998) and such coincident excitatory input from the cortex can drive the MSNs into the âUp stateâ (OâDonnell and Grace, 1995; Wilson, 1993).
đ€The strength of the SBF model lies in its specification of known neural mechanisms, as well as its consistency with the available anatomical, behavioral, and pharmacological evidence (Allman and Meck, 2012; Coull et al., 2011; Merchant et al., 2013a). MSNs in the striatum have the appropriate characteristics to serve as a largescale coincidence-detector system because they receive a great deal of convergent, multi-modal input from the cortex (Wilson, 1995, 1998) and such coincident excitatory input from the cortex can drive the MSNs into the âUp stateâ (OâDonnell and Grace, 1995; Wilson, 1993).đ€
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It has been suggested, however, that this model can be susceptible to the variance of the oscillation periods. If the cortical oscillators are independent of each other so that they have different variations in their oscillation period, the ability of representing detectable coincident patterns will be significantly impaired even with a small amount of variance if they arenât reset properly. The variance in oscillation period (i.e., variability in clock speed) that the model allows under this condition are quite small, i.e., less than 3% of the period, and considering that the variance can accumulate with time, the detection of longer durations in the minutes range could be much more debilitated. However, if the variance is introduced globally (e.g., all oscillation periods are increased by 4%), the modelsâ detection ability is not affected, but only the overall clock speed will be changed (see Oprisan and Buhusi, 2011, 2013, 2014).
đ€It has been suggested, however, that this model can be susceptible to the variance of the oscillation periods. If the cortical oscillators are independent of each other so that they have different variations in their oscillation period, the ability of representing detectable coincident patterns will be significantly impaired even with a small amount of variance if they arenât reset properly. The variance in oscillation period (i.e., variability in clock speed) that the model allows under this condition are quite small, i.e., less than 3% of the period, and considering that the variance can accumulate with time, the detection of longer durations in the minutes range could be much more debilitated. However, if the variance is introduced globally (e.g., all oscillation periods are increased by 4%), the modelsâ detection ability is not affected, but only the overall clock speed will be changed (see Oprisan and Buhusi, 2011, 2013, 2014).đ€
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Therefore, additional coupling mechanisms for cortical oscillators that can reduce the independence of oscillating neurons with different frequencies be investigated in order to incorporate a more biologically plausible level of variance into the system while still allowing for independence of multiple timing processes (Buhusi and Meck, 2009b)
đ€Therefore, additional coupling mechanisms for cortical oscillators that can reduce the independence of oscillating neurons with different frequencies be investigated in order to incorporate a more biologically plausible level of variance into the system while still allowing for independence of multiple timing processes (Buhusi and Meck, 2009b)đ€
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In relation to the importance of theta and gamma oscillations for working memory, Lisman and colleagues (e.g., Lisman, 2005, 2010; Lisman and Idiart, 1995) proposed an oscillatory model of working memory. According to this model, gamma oscillations entrained within theta could represent maintained memory by repetitively activating relevant neuronal groups with temporal precision, and multiple items can be maintained in working memory by the multiple cycles of sequential gamma oscillations entrained within a theta oscillation (Jensen, 2006; Jensen and Lisman, 1998; Lisman, 2010; Lisman and Idiart, 1995âFig. 3).
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For example, different items in memory are represented by different neuronal groups (e.g., spatial pattern of cells), and each neuronal group is activated during each gamma cycle. Because multiple gamma cycles of 30â80 Hz are present within each theta cycle of 4â10 Hz, multiple item information/memory represented by multiple gamma cycles is activated every theta cycle so that they can be maintained as separated from each other within a specific temporal sequence.
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the firing of place cells shows theta-phase precession during spatial navigation (Fig. 4A). For example, as a subject reaches its target area, the place-cell firing occurs at earlier phases of the theta oscillation of the LFP so that the firing phase of the cell reflects the relative distance that the subject has traveled through the cellâs place field (e.g., firing at late phases of theta indicates that the subject has just entered the place fieldâBurgess et al., 1994; Skaggs et al., 1996).
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n the EIO model, excitatory inputs to individual neurons are assumed to be various in oscillating frequencies (e.g. normal distribution, Fig. 5E) due to differences in the degree of dendritic inputs or conductance level of individual neurons. In addition, the population of these neurons is hypothesized to oscillate in a slightly slower frequency than the mean of oscillating individual neurons, and the inhibitory inputs are assumed to oscillate at a similar frequency to the oscillation of neural population as a consequence of the information outlined below.
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Previous findings have shown that typical neural firing oscillates faster than the theta frequency of the LFP (Burgess et al., 2007; Geisler et al., 2007; Harvey et al., 2009; OâKeefe and Recce, 1993). Geisler et al. (2010) attempted to explain this discrepancy between the mean oscillation frequency of individual neurons and the frequency of a neural population using a mathematical model. According to this model, the experimentally obtained parameters for the oscillation frequencies of individual neurons (mean frequency = 8.61 Hz) can produce the slower oscillatory frequency of the neural population output (7.97 Hz), which is similar to the experimentally measured LFP frequency (8.09 Hz) due to temporal shifts in cell assemblies.
What does âtemporal shifts in cell assembliesâ mean?
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If we can bring this findings from hippocampus to the cortical network, then, via the recurrent connections between excitatory and inhibitory neurons and the extensive connections between inhibitory interneurons, the slower oscillation frequency of the population would drive the synchronized inhibitory oscillation at a frequency slower than the mean of the individual excitatory neurons.
What kind of recurrent connections?
Still trying to decipher this
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In other words, excitatory neurons would oscillate with difference frequencies from each other while inhibitory interneurons would show synchronized oscillation at the frequency of the population oscillation (similar to the LFP oscillation), which is slower than the mean of the excitatory oscillation frequencies.
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Depending on the assumption of frequency bands for EO and IO, various ranges of PAC can be generated, and even the relation among these frequency bands can be fractal. For example, given the assumption of a gamma range for EO and IO that will generate gamma entrained within the theta oscillation (as illustrated in Fig. 5A and B), this generated theta oscillation will in turn produce theta entrained within the delta oscillation by way of interaction with the theta range of IO as illustrated in Fig. 5C and D. The hierarchical organization of these frequency bands is one of the prominent features of our neural oscillation model and corresponds to the harmonics observed in the SBF model of interval timing (Gu et al., 2011; Matell and Meck, 2004). Penttonen and BuzsĂĄki (2003) showed the natural logarithmic relationship in the periods of delta, theta, gamma, and ultra-fast oscillations.
Super interesting, potentially related to criticality as they mention fractal hierarchy
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This new EIO model assumes that the frequency of EO varies across neurons, but this varying frequency across neurons is relatively constant given a particular stimulus. The underlying mechanisms of various EO frequencies (and the synchronized IO) should receive further consideration; however, different amounts of recurrent excitatory inputs to each cell or different effects of DA at each neuron or different conductance ratios of neurons could be major factors contributing to the variation in oscillation frequencies (e.g., Gasparini and Magee, 2006; Magee, 2001).
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In our simulated model the distribution of EO frequencies is defined as a normal distribution with a mean of 6.5 Hz and a standard deviation of 0.2 Hz as illustrated in Fig. 6C. The IO frequency was fixed at 6 Hz for a particular neuronal population, based upon evidence from the previous reports (Geisler et al., 2010; Matell and Meck, 2004).
Simulation parameters
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the EIO account does not require a separate accumulator for temporal information, nor does it require a specialized pacemaker providing the temporal information, but it instead derives temporal information from the dynamics of other cognitive components such as the encoding and storage of new information in memory
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all problem-specific memory representations are eventually stored in the declarative memory stores
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However, the number of multiple theta oscillations that are possible will restrict the number of items in working memory. In this way, the model can account for both decay and interference features of forgetting.
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Simultaneous maintenance of different frequencies of theta oscillations (representing multiple items) would be easily disrupted by the interactions from other neuronal groups, especially when the two neuronal groups are tightly connected to each otherâa result consistent with interference theory.
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Consistent with this view, explorations with a recurrent spiking network showed that some persistent activity of neural populations fades out or merges together as the working memory load increases, representing the decay and interference features of working memory (Wei et al., 2012).
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recent focus on the temporal/oscillatory properties of brain and behavior has opened up another dimension for understanding the cognitive architecture of the brain (e.g., Cohen, 2011). Interval timing and working memory in particular share the characteristic that some internal process must continue over the course of time regardless of the existence of an external stimulus.
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spatio-temporal patterns of activation supporting these cognitive functions are sustained in neural networks over a time and these neural networks can be managed through the oscillatory fluctuations that reside in the recurrent networks. Because of the importance of these neural dynamics, the temporal/oscillatory properties of the brain should be emphasized in future studies of interval timing, attention, and working memory (see, for example, Cohen, 2011;Henry and Herrmann, 2014; Lake et al., 2014; Rohenkohl and Nobre, 2011; Rohenkohl et al., 2012).
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In particular, the default network has been shown to âanti-correlateâ with cognitive effort, thus leading to speculation on its role and relation to infra-slow fluctuations. In concert with this, the measurement of infra-slow fluctuations in BOLD signals has been highly controversial and the underlying mechanism remains a mystery. Recent evidence, however, shows a relationship between electrophysiological signals and large-scale brain networks revealed by BOLD signals (He et al., 2008; Liu et al., 2010; Palva and Palva, 2012). Consequently, the coupled EIO model of PAC proposed in this review could also be applied to these infraslow fluctuations in large-scale brain networksâespecially when the natural logarithmic relations among different frequency bands are considered (Penttonen and BuzsĂĄki, 2003).
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n the same manner that interaction between theta ranges of oscillation can produce a delta oscillation, the interaction between delta ranges of oscillations could produce the slow oscillations shown in functional connectivity studies (see BuzsĂĄki, 2006; BuzsĂĄki et al., 2012; Palva and Palva, 2012). In this way, the different frequency ranges of oscillations are hierarchically interrelated to each other through the PACâthus allowing slow and fast oscillations, as well as multiple ranges of oscillation to be present at the same time in a network of brain regions (Akam and Kullmann, 2010, 2014; BuzsĂĄki, 2006; BuzsĂĄki and Draguhn, 2004; Lakatos et al., 2005).
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One thing to speculate about is the possibility that this hierarchical organization across oscillation frequencies would also include a hierarchical spatial organization, so that the slowerfrequency oscillations are synchronized over larger brain areas. In
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relation to this, it has been hypothesized that the slower-frequency oscillations are involved in long-range communication in the brain (e.g., BuzsĂĄki, 2006; BuzsĂĄki and Draguhn, 2004; BuzsĂĄki et al., 2012; Murray et al., 2014).
Figures (blue)
Figure
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Figure 2
Fig. 2. Striatal-beat frequency (SBF) model. At the beginning of an interval, dopaminergic input synchronize the oscillatory neurons in the cortex, and the cortical neurons begin oscillating at their endogenous frequencies. Upper panel shows the different frequencies of oscillation of individual cortical neurons and the sum of those oscillations. Through the connections between specific cortical neurons and a striatal medium spiny neuron, the coincident pattern of cortical neuron firing can be detected at the specific point of time, and those connections can be strengthened by the delivery of reinforcement at the target time (dopaminergic inputs). Glutamatergic (green), GABAergic (red) and dopaminergic (blue) connections are indicated separately. Adapted from Matell and Meck (2004). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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Figure
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Figure 3
Fig. 3. Working memory of multiple items by temporal segmentation. Each item is represented by the synchronous firing pattern of selected neurons, and the different items are reactivated at different gamma cycles. In this way, the multiple item representations are sequentially reactivated in gamma (30â80 Hz) cycles, and up to seven gamma cycles can be entrained in each theta cycle (4â10 Hz). The limited number of gamma cycles in each theta cycle corresponds to the limited number of different items that can be maintained. Adapted from Lisman and Idiart (1995) and Lisman (2010).
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Figure
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Figure 4
Fig. 4. (A) Place cell phase precession shown in the rodent hippocampus. Place cell fires in correlation to the specific position, and the spike firing occurs in higher frequency than the theta of local field potentials (LFPs). Therefore, the spike firings (red ticks) precess to the earlier phases of LFP theta (black). Adapted from Huxter et al. (2003). (B) Dual oscillator interference model of phase precession, showing the sum of an oscillatory somatic (red) and dendritic (blue) inputs produce an interference pattern. The sum shows a high frequency âcarrierâ oscillation (black) entrained in a low frequency âenvelopeâ oscillation (green). The spikes (red ticks) fire at the peak of the interference sum, and this produces the phase precession of spikes to the somatic input oscillations. Adapted from OâKeefe and Recce (1993) and Burgess et al. (2007). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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Fig. 5. (A) Gamma range of excitatory oscillation (EO) and inhibitory oscillation (IO) inputs into a neuron. EO (47 Hz) in individual neuron is in larger frequency than the IO (40 Hz) which is synchronized over a small neuronal population. (B) Interaction of the EO and IO produces phase-amplitude coupling (PAC) between gamma and theta in the membrane potential oscillation (MPO). The gamma (carrier) amplitude is modulated by the 7-Hz theta (envelope) oscillation, whose frequency is determined by the frequency difference between the gamma EO (47 Hz) and IO (40 Hz). (C) The produced theta (7-Hz) oscillation interacts with theta IO (6-Hz). Theta IO is synchronized over a larger neuronal population than the gamma IO. The diagram shows EO and IO filtered in theta frequency bands for a simplification. (D) Interaction between theta EO (7 Hz) and IO (6 Hz), in turn, produces PAC between theta and delta. The delta envelope (delta EO) oscillates in 1 Hz and the delta IO is also modeled as in a lower frequency (0.8 Hz) than the EO. (E) Distribution of gamma EO frequencies of individual neurons (N = 1000) is modeled as a mean of 47 Hz and SD of 2 Hz. (F) A simulation of total IO including gamma (40 Hz), theta (6 Hz) and delta (0.8 Hz) ranges of IOs. The simulated IO is hypothesized to assimilate LFPs. (G) Simulated firing rates of a neuronal population whose gamma EO frequencies are distributed as in panel E and receiving IO inputs as depicted in panel F. Population spikes plotted as a function of 100-ms time bins 10-ms sliding window show a pattern of theta oscillation entrained in delta.
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Figure 5
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Figure 6
(A) Theta range of EO (blue) and IO (red) inputs to each cortical neuron are balanced before a triggering event (e.g., dopamine input). The timing onset drives the EO inputs to individual cortical neurons oscillate in the faster and various frequencies while IO inputs are synchronized such as in 6 Hz. (B) Summation of EO and IO inputs in each neuron generates MPO in theta entrained in delta oscillation. The envelope delta frequency differs by the theta frequency of each individual neuron. For example, larger theta frequency of Neuron 4 produces the faster delta frequencies. Neurons 1 and 3 (Orange) exhibit a peak around 3 s, but not at 4 s; Neurons 2 and 4 (Cyan) exhibit a peak at 4 s, but not at 3 s. Detection of coincident firing of the relevant neuronal groups such as Neurons 2 and 4 will produce the timing of the 4-s target duration. (C) Simulation of theta EO frequencies of 1000 cortical neurons is modeled with a mean of 6.5 Hz and SD of 0.2 Hz while IO frequency is fixed at 6 Hz. (D) Simulation of total spike inputs from the cortex to the striatum. It shows relatively little spiking between 0 and 0.5 s after the DA input and shows a peak at 0.5â1 s. (E) Spikes to each MSN neuron from the cortex show a peak at the target time of each MSN, but also exhibit fluctuating patterns across time. For example, 3 s MSN receives peak inputs at 3 s, however, the inputs fluctuate and oscillate in time. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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