The role of striatal feedforward inhibition in the maintenance of absence seizures 

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Closed loops in the BG-thalamo-cortical network

There are three named parallel pathways from the cortex to the BG output nuclei: cortex-striatum-GPi/SNr, the direct pathway; cortex-striatum-GPe-STN-GPi/SNr, the indirect pathway; cortex-STN-GPi/SNr, the hyperdirect pathway. The direct and indirect pathways were described rst (Albin, Young, and Penney 1989; Alexander and Crutcher 1990) and later the hyperdirect pathway was described as the route responsible for fast excitation of GPi in monkeys (Nambu, Tokuno, and Takada 2002). These pathways project back to the cortex via thalamus. Thus, we extend standard terminology and call the feedback loops through direct, indirect and hyperdirect pathways the direct, indirect and hyperdirect (feedback) loops, respectively. Furthermore, each loop has ner topographicaly organized feedback loop structure (Alexander, DeLong, and Strick 1986; Nakano et al. 2000; Yin, Knowlton, and Balleine 2006; Utter and Basso 2008; Redgrave et al. 2010) such as sensorimotor, associative and limbic networks. This characteristic is also referred to as \parallel » in the literature but we call it coextensive to avoid confusion and emphasize that we do not mean strictly segregated sub-loops. For example, in our terminology, direct and hyperdirect loops are parallel while sensorimotor and associative loops are coextensive. The corticostriatal projections have rough topographical organization. For example, the somatosensory and motor cortices innervate to the posterior putamen and the prefrontal cortex innervates the anterior caudate. Somatosensory and motor corticostrital projections preserves somatotopy. In rats, corticostrital projections from the barrel cortex have anisotropic pattern in which a small region of the striatum receives inputs mainly from the same row of the barrels (Alloway et al. 2006). STN also receives somatotopic projections from motor cortex in monkeys (Monakow, Akert, and Kunzle 1978; Nambu et al. 1996; Nambu, Tokuno, and Takada 2002) and in rats although not as clear as in monkeys (Afsharpour 1985; Canteras et al. 1990). In non-human primates, GPe and GPi also somatotopically re ect activity in the primary motor cortex (M1) and supplementary motor area (SMA) (Nambu 2011). The SNr also has somatotopic organization representing orofacial, oculomotor and prefrontal regions but not as clearly organized as GPi (Nambu 2011). Using retrograde transneuronal transport of rabies virus Kelly and Strick (2004) showed that di erent regions in the GPe, striatum and STN project to M1 and Area 46 via multisynaptic connections in monkeys. Furthermore, they showed that the regions in the striatum and STN which projects to M1 receive projections from M1 thereby directly proving that the BG-thalamo-cortical network has closed loops.

Neuronal dynamics and synaptic interactions in the basal ganglia

Dynamics of striatal neurons

The output neurons of the striatum are the GABAergic Medium Spiny Neurons (MSN). MSN have a very powerful potassium inwardly rectifying current Ikir (Nisenbaum and Wilson 1995) and thus it is expected that a large number of correlated excitatory input is required for discharge of MSN. Accordingly, in quiet resting rats, majority (72.7%) of striatal cells are silent and the ring rate of active neurons are low (4.85 spikes/sec) which re ects lack of strong excitatory input (Sandstrom and Rebec 2003). Due to this inwardly rectifying current, the resting potential of MSN is low (-80mV) (Nisenbaum and Wilson 1995) which is even below the GABAA receptor reversal potential (-75mV measured in visual cortex of cats and rats; Connors, Malenka, and Silva 1988). It means that GABAergic inputs to MSN which come from MSN and GABAergic interneurons are excitatory at the resting potential. The distribution of the membrane potentials of the MSN in anesthetized rats also peak at similar value (-73mV; Wilson and Kawaguchi 1996). Despite their low ring rate, the striatal neurons re ect cortical activity and it was proposed that the activity of striatal neurons depends on the states of vigilance (Mahon, Deniau, and Charpier 2001; Mahon, Deniau, and Charpier 2003). Under urethane and/or ketamine-xylazine anesthesia in which cortical activity show slow oscillations at 1 Hz, the membrane potentials of MSN are known to have distribution (Wilson and Kawaguchi 1996; Stern, Kincaid, and Wilson 1997; Reynolds and Wickens 2000) re ecting the membrane dynamics which shows plateaus near the threshold (Up state) and the potassium equilibrium potential (Down state). Classically, it has been hypothesized that the potassium inwardly rectifying current of MSN is responsible for stabilizing the Down state (Mahon, Deniau, and Charpier 2003; Wilson 2008). However, under barbiturate anesthesia in which cortical spindle waves are observed in EEG, MSN membrane potentials show unimodal distribution (Mahon, Deniau, and Charpier 2003). Under neurolept-analgesia, cortical EEG activity is irregular and does not show apparent rhythmicity and MSN membrane potential dynamics do not show switching between the Up and Down states. The cross-correlogram between membrane potential of MSN and EEG shows highly oscillatory patterns under ketamine-xylazine or barbiturate anesthesia (Mahon, Deniau, and Charpier 2003) in which cortical population activity is synchronous while it is at under neurolept-analgesia (Mahon, Deniau, and Charpier 2001) in which cortical neurons are not synchronized. These results show that MSN membrane potential is controlled by a population of cortical neurons (Mahon, Deniau, and Charpier 2003).
Even though almost all neurons in the striatum are the MSN (97.7% in rats, Rymar et al. 2004; possibly 23% in primates Graveland, Williams, and Di glia 1985, Tepper and Bolam 2004), the activity of MSN is strongly regulated by the Fast Spiking Interneurons (FSI) (Mallet et al. 2005). The FSI are parvalbumin expressing neurons which consist about 0.7 % of rat neostriatum (Tepper and Bolam 2004). They can re at 200{300 Hz with little or no adaptation when strongly depolarized, are coupled together with other FSI via gap junctions, have perisomatic synapses onto MSN, produce large inhibitory postsynaptic potentials (ISPSs) in MSN, and have converging input from the cortex. As a result, striatal feedforward inhibition (cortex-FSI-MSN) have strong control of MSN activity which is at least as fast as direct cortical excitation (Mallet et al. 2005; Pidoux et al. 2011). In behaving rats, signi cantly more FSI have increase in ring rate related to task choice than MSN while both MSN and FSI populations have subpopulation which increases ring rate related to reward (Gage et al. 2010). The same study shows that nearby MSN and FSI have preference to opposing behavior and the authors proposed that FSI inhibit alternative actions.
The striatal neurons contain signi cantly more dopamine receptors than any other brain region (Dawson et al. 1986; Lidow et al. 1989; Rich eld, Penney, and Young 1989) and depletion of dopamine results in various motor dysfunctions and dopamine is involved in reward-based learning (see below). Thus, dopamine neuromodulation has been known to be crucial for understanding functions and dysfunctions of the striatum. Depending of intracellular signaling, dopamine recep-tors are categorized into at least ve subtypes and two families, namely D1 (D1 and D5 subtypes) and D2 (D2, D3 and D4 subtypes) families (Sibley and Monsma 1992; Niznik and Van Tol 1992). It has been hypothesized that D1 and D2 families are expressed in MSN on direct and indirect pathways, respectively (Albin, Young, and Penney 1989; Gerfen et al. 1990; Surmeier et al. 2007). Although anatomical studies (Hersch et al. 1995; Le Moine and Bloch 1995; Deng, Lei, and Reiner 2006) supported this hypothesis, substantial amount of cells show electrophysiological responses mediated by both D1 and D2 receptors (Uchimura, Higashi, and Nishi 1986; Surmeier et al. 1992; Cepeda, Buchwald, and Levine 1993). This incoherence was resolved with more advance in anatomical and physiological approaches showing that virtually all MSN contain D1 and D2 receptors (Surmeier, Song, and Yan 1996; Aizman et al. 2000). Moreover, majority of MSN are projecting both to GPe and SNr (Bolam et al. 2000; Wu, Richard, and Parent 2000; Levesque and Parent 2005).
Activation of D1 receptor mediates synaptic plasticity by enhancing surface expression of AMPA (Snyder et al. 2000) and NMDA (Hallett et al. 2006) receptors. However, the e ect of D1 receptor at faster timescale on glutamate receptors are less clear. On one hand, excitatory postsynaptic potentials (EPSP) from whole cell current clamp recording of the dorsal striatal neurons are not modulated by D1 receptor (Nicola and Malenka 1998). On the other hand, intracellular current clamp recording using sharp electrodes shows that D1 receptor activation enhances the responses evoked by NMDA (Cepeda, Buchwald, and Levine 1993). These opposing results where shown to be due to indirect e ect of D1 receptor on NMDA response through voltage-gated calcium-dependent currents which was altered in the cells recorded with the whole-cell patch clamp technique due to contamination of intracellular environment (Liu et al. 2004). As D1 receptor agonist reduces sodium current (Surmeier et al. 1992) which is responsible for initiation and propagation of the action potential, threshold of the striatal neurons is found to be increased when D1 agonist is applied (Schi mann, Lledo, and Vincent 1995). Note that the e ects of D1 receptor on MSN activity through enhancement of NMDA response and reduction of sodium current are opposite as the former increases the ring rate while the latter decreases it. It has been hypothesized that one of the function of dopamine modulation is to increase signal-to-noise ratio (O’Donnell 2003; Nicola, Hopf, and Hjelmstad 2004). Indeed, if dopamine e ect through D1 receptor is to amplify the signal by larger corticostriatal gain, it makes sense to scale threshold similarly to lter out the ampli ed noise part.
As in D1 receptor, contribution to synaptic plasticity of D2 receptor is suggested for AMPA receptor (Hakansson et al. 2006) and shown to attenuate NMDA receptor response (Higley and Sabatini 2010). D2 receptor stimulation also diminishes presynaptic release of glutamate (Bamford et al. 2004) which may be due to post- and/or presynaptic mechanisms (Yin, Knowlton, and Balleine 2006). Activation of D2 receptors also immediately attenuate AMPA receptor currents (Cepeda, Buchwald, and Levine 1993; Hernandez-Echeagaray et al. 2004). Excitability of MSN is shown to be diminished by D2 receptor stimulation by reducing opening of voltage-dependent sodium channels (Surmeier et al. 1992), e ectively increasing the potassium inwardly rectifying current (Greif et al. 1995), and reducing L-type calcium currents (Hernandez-Lopez et al. 2000). Unlike D1 receptor, the e ects of D2 receptor through synaptic transmission and intrinsic dynamics are in the same direction to reduce MSN activity.

Dynamics of STN neurons

Neurons in STN in a wakefulness condition have irregular spiking activity which shifts to bursting pattern in slow wave sleep with no change of their mean ring rate (Urbain et al. 2000). In vitro STN neurons can re at around 5{15 spikes/sec even without synaptic input, mainly due to the persistent sodium current (Bevan, Atherton, and Baufreton 2006; Charpier, Beurrier, and Paz 2009). STN neurons have calcium and calcium-dependent currents but they do not play a signif-icant role in the single spike ring mode (Charpier, Beurrier, and Paz 2009). Hyperpolarization to 80 mV for > 100 ms de-inactivate calcium channels and following depolarization gener-ates rebound burst action potentials (Bevan, Atherton, and Baufreton 2006). In vitro electrical stimulation to pallidosubthalamic bers activating GABAA and GABAB receptor produces rebound bursts in which GABAA receptor also play an auxiliary role (Hallworth 2005). During movement, wakefulness and slow wave sleep, STN neurons re ect cortical activity rather than generating ac-tivity pattern by their intrinsic dynamics or interaction with GP (Bevan, Atherton, and Baufreton 2006). In monkeys, e ect on cortical stimulation passes through STN rst via NMDA receptors on cortico-subthalamic contacts and then via GABAA receptors on pallido-subthalamic contacts (Nambu et al. 2000). In the basal ganglia slice from mice, brief stimulation of the STN generates a brief monosynaptic AMPA-mediated excitatory postsynaptic current (EPSC) in GP, entopeduncu-lar nucleus and SNr (Ammari et al. 2010). A higher intensity STN stimulation evokes a long-lasting response composed of a barrage of AMPA-mediated EPSCs on top of slow NMDA-mediated cur-rent, possibly generated by the recurrent network in STN.
Majority of GPe neurons in vivo are in single-spike mode in wakefulness and slow wave sleep (Kita and Kitai 1991; Urbain et al. 2000; Ni et al. 2000) although repeated bursts correlated with EEG in slow wave sleep are also reported (Magill, Bolam, and Bevan 2000). In guinea pigs, two major types of neurons (type I: 59%, type II: 37%) are described to have low-threshold calcium conductance. In vitro, the former type is silent and the latter is spontaneously active (Nambu and Llinas 1994). Similar portion (32%) of cells are spontaneously active in GP of rat brain slices but do not exhibit rebound depolarization (Cooper and Stanford 2000). Locally stimulating rat GP neurons in vitro presumably activate local collateral axons and striatal a erent axons and induce slow IPSPs via GABAB receptors (Kaneda and Kita 2005). The same study showed that synap-tically released GABA also activates presynaptic GABAB autoreceptors. In 6-hydroxydopamine (6-OHDA)-treated hemi-parkinsonian rats, reduction of striatal output by muscimol injection to the striatum increased average ring rate and greatly reduced the pauses and bursts in GPe (Kita and Kita 2011). In vitro STN-GPe circuitry was shown to be capable of producing synchronized oscillatory bursts at 0.4, 0.8 and 1.8 Hz (Plenz and Kital 1999).

Dynamics of SNr/GPi neurons

Neurons in SNr and GPi are tonically active with high ring rate even in vitro without excitatory drive (Atherton and Bevan, 2005; Rick and Lacey, 1994; Yuan et al., 2004). Glutamatergic input to SNr is virtually ine ective in awake rats (Windels 2004) while GABAergic input to SNr can control SNr activity in freely moving rats although it is less e ective compared to anesthetized rats (Windels and Kiyatkin 2006). In monkeys, it was shown that activation of motor and so-matosensory cortex shapes response in GPi activity with early excitation and inhibition followed by late excitation mediated by hyperdirect, direct and indirect pathways, respectively (Nambu et al. 2000). Electrically stimulating SNr in awake rats increases extra-cellar level of GABA that is of an exocytotic origin. This increase is compensated after rst 3-min interval upon stimulation possibly because of GABAA autoreceptor of nigrothalamic neurons (Timmerman and Westerink 1997).

Functions of the basal ganglia

The topographically organized coextensive feedback networks through the BG can be divided to three coextensive loops in terms of function: limbic (motivational and emotional), associative (cognitive; e.g., goal-directed control of behavior) and sensorimotor (e.g., habitual control of behavior) networks (Yin, Knowlton, and Balleine 2006; Utter and Basso 2008; Redgrave et al. 2010).

Habitual control

The functions of the sensorimotor network are understood well compared to those of the other two networks. In the striatum and motor cortex, trial-to-trial variability decreases as the skill is consolidated through motor learning (Brainard and Doupe 2002; Tchernichovski et al. 2001; Hikosaka et al. 1999; Miyachi et al. 1997; Jin and Costa 2010; Sakai, Kitaguchi, and Hikosaka 2003). Thus, it is suggested that a particular cortico-BG sub-network is chosen as skills are crystallized and provides a functionality analogous to re exive stimulus-response which promotes motor performance by \chunking » sequence of actions (Jin and Costa 2015). Indeed, NMDA-receptor dependent corticostriatal long-term potentiation (Calabresi et al. 1992; Shen et al. 2008) is required to learn to perform motor sequence faster, although the ability to learn the task is una ected (Jin and Costa 2010). Knockout or knockdown of genes known to impair corticostriatal long-term depression (Gerdeman, Ronesi, and Lovinger 2002; Groszer et al. 2008) also have shown to disrupt habit and skill learning in mice and song learning in songbirds (Hilario et al. 2007; Groszer et al. 2008; French et al. 2012; Haesler et al. 2007).
How are these learned behaviors are coded in the BG? There are striatal neurons which increase activity at the initiation, termination or both timings of a particular behavioral sequence (Miyachi, Hikosaka, and Lu 2002; Jin, Tecuapetla, and Costa 2014). Similar neurons are found in SNr and GPe (Jin and Costa 2010). Comparing to MSN and GP, FSI re at the initiation of chosen action in particular (Gage et al. 2010). In addition these types of neurons with phasic response during action, comparable amount of neurons in striatum, SNr and GPe increase or decrease activity during whole action sequence of a particular behavior (Jin, Tecuapetla, and Costa 2014). D1 receptor expressing MSN tend to elevate activity during the task while D2 receptor expressing MSN tend to suppressed during the task (Jin, Tecuapetla, and Costa 2014). These phasic, inhibited and sustained neural responses throughout the BG may underlie representation of \chunked » actions (Jin and Costa 2015).

Goal-directed control

The BG are also involved in goal-directed control of behavior for which the associative sub-network in the BG is responsible. Showing such involvement and dissociating it from habitual control required development of assays for behavioral learning experiment which can detect whether the animal operates habitually or intentionally (Yin and Knowlton 2006). A common class of such assays is the control of outcome value. For example, exposing the animal to the food reinforcer before a probe test decreases the value of food used as a reward. If the behavior is goal-directed, it has to be sensitive to such control. Another common class of assays is manipulation of action{ outcome contingency. If the probability of reward does not depend on whether or not a particular action is taken, the contingency is said to be completely degraded. Again, the behavior is expected to be sensitive to such manipulation if it is goal-directed.
Using such set of assays, it was shown that goal-directed control is blocked by inactivation of the rat posterior dorsomedial (associative) striatum with excitotoxic lesions or GABA agonist (muscimol) (Yin et al. 2005) or by suppression of long term plasticity by NMDA antagonist (2-amino-5-phosphonopentanoic acid) (Yin, Knowlton, and Balleine 2005). If the dorsolateral (sensorimotor) striatum of rats were lesioned before training, they adjusted behavior upon outcome devaluation (Yin, Knowlton, and Balleine 2004) and contingency degradation (Yin, Knowlton, and Balleine 2006) even with the amount of training after which non-lesioned rats shows habitual response and insensitivity to such manipulations.

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Common function

Are di erent functions of the BG sub-networks subserved by di erent physiological properties in them? Qualitative similarity of these networks suggests there is a general computational mechanism underlying such di erent functions such as a generic \selection » function (Redgrave, Prescott, and Gurney 1999; Mink 1996; Hikosaka, Takikawa, and Kawagoe 2000; Redgrave, Gur-ney, and Reynolds 2008; Yin and Knowlton 2006; Redgrave et al. 2010). The selection may take place within a sub-network (e.g., choosing a particular behavior from habitual repertoire) or between sub-networks (e.g., suppressing habitual control and use goal-directed control). Thus, the BG circuits representing such behavioral options may need to communicate each other over or within their functional domains (Redgrave, Prescott, and Gurney 1999; Redgrave, Gurney, and Reynolds 2008; Redgrave et al. 2010).

Reinforcement learning

Hinted by biological researches on stimulus-response reinforcement, so-called reinforcement learn-ing algorithms are developed in the eld of machine learning by computer scientists (Sutton and Barto 1998). These algorithms are in turn brought back to neuroscience to explain BG functions (Doya 1999; Doya 2000; Ito and Doya 2011) although the initial idea of simple stimulus-response reinforcement is generalized and does not literally hold. For example, the Q-leaning algorithm does not learn the actions directly but instead it learns so-called Q function, a mapping from a state/action pair to the corresponding value (or utility; expected sum of the future rewards) (Sut-ton and Barto 1998). The Q-leaning algorithm combined with so-called deep learning (LeCun, Bengio, and Hinton 2015) techniques developed in machine learning shows human-level scores in video games (Mnih et al. 2015) demonstrating that this algorithm is scalable to the tasks demand-ing even to humans. An optimal action argmaxaQ(s; a) can be computed from learned Q function by maximizing it with respect to actions with the given state s. Such exploitation of knowledge of task at hand may be appropriate to explain goal-directed side of BG function. The value of Q function in neuroscience literature is called action value (Tanaka et al. 2004; Samejima et al. 2005; Ito and Doya 2009; Kim et al. 2009) perhaps because only a single class of actions (e.g., choose left vs right) is typically analyzed rather than a sequence of actions and state transitions. Although \(action, state)-value » re ects the de nition more correctly, we follow the conventional terminology. The value of Q function evaluated with chosen action (and the state at which the action is taken) is called chosen value. Computation of this value is required for calculating error of the Q function hence for the Q-learning.
Another representative example of reinforcement learning algorithm is the actor-critic method composed of two modules: a critic which represents the mapping from a state to the value and an actor which represents the conditional probability distribution (policy) of an action given a state (Sutton and Barto 1998). In the actor-critic method, once the policy is su ciently learned it can operate without the critic and without explicit maximization operation which is needed for the Q-learning. This feature resembles the habit learning in the BG. The state-value mapping function learned by the critic is related to the Q function since the state value can be obtained by averaging Q function over actions using the probability distribution of learned by the actor (provided that the actor is optimal). Further assuming that the probability of choosing each action is uniform, the state value function can be calculated by just summing the action value function over possible actions (typically two actions such as choose left or right). The action value is similar to chosen value since they are action-independent although the action value is obtained via averaging and the chosen value via maximization plus random exploration. Thus, the e ect presented as chosen value may actually represents the action value (Ito and Doya 2011) and vice versa.
The action value coding neurons are found in the dorsal striatum (Samejima et al. 2005; Pasquereau et al. 2007; Wunderlich, Rangel, and O’Doherty 2009; Hori, Minamimoto, and Kimura 2009; Lau and Glimcher 2008), the GPi (Pasquereau et al. 2007) and the supplemental motor area (Wunderlich, Rangel, and O’Doherty 2009) of primates and in the small population of the dorsal and ventral striatum of rodents (Ito and Doya 2009; Kim et al. 2009; Roesch et al. 2009). The action-independent value which may represent chosen or action value is shown to be coded in a substantial but small population of neurons in the dorsal striatum of monkeys (Samejima et al. 2005; Lau and Glimcher 2008) and in the dorsal and ventral striatum of rats (Ito and Doya 2009; Kim et al. 2009). Human fMRI data suggests that the ventral striatum implements the critic module (i.e., codes state value) (O’Doherty et al. 2004). The neurons coding forthcoming action command are found in the dorsal striatum (Samejima et al. 2005; Pasquereau et al. 2007; Kim et al. 2009; Pasupathy and Miller 2005) but majority of the studies (except for Roesch et al. 2009) report lack of action command coding in the ventral striatum (Ito and Doya 2009; Kim et al. 2009; Kim et al. 2007). Action command-coding neurons are also found in the presupplementary motor (Hoshi and Tanji 2004), the prefrontal (Pasupathy and Miller 2005) and the parietal (Roitman and Shadlen 2002) areas of monkey cortex.
Ito and Doya (2011) suggested an explanation of the nding that only small amount action value and action command coding neurons are found (except in Roesch et al. 2009), based on hierarchical reinforcement learning. In the hierarchical reinforcement learning framework, the higher level module learns to control the lower level module by regarding the action command of the higher level as the state for the lower level providing the task context at the lower level. They proposed a hierarchy along the dorsolateral axis: the dorsolateral, the dorsomedial and the ventral striatum take care of the tasks at increasing spatial and temporal scales. Their idea is that the dorsolateral striatum learns lowest and more e ector speci c control while the dorsomedial striatum learns higher order control such as \turn left », \turn right » and \go straight ». The ventral striatum learns to switch the context of lower levels such as \do a task » and \take a rest ». Their proposal is based on the aforementioned recent results on the dissociation of habitual (dorsolateral) and goal-directed (dorsomedial) control in the BG (Yin and Knowlton 2006; Redgrave et al. 2010).

Dysfunctions of the basal ganglia

It is well known that the basal ganglia (BG) have a key role in abnormal neural oscillations, e.g., in Parkinson’s disease or dystonia (Boraud et al. 2002; Hutchison et al. 2004; Gatev, Darbin, and Wichmann 2006; Leblois et al. 2006; Hammond, Bergman, and Brown 2007; Wichmann and Dostrovsky 2011).
Parkinson’s disease is a neurodegenerative disorder whose patients experience motor de cits such as slowness of movement, rigidity, a low frequency rest tremor, and di culty with balance and also non-motor de cits such as depression, constipation, pain, genitourinary problems, and sleep disorders. The motor de cits are due to degeneration of dopamine containing neurons in the SNc and consequent loss of dopamine in the striatum. Such changes are not uniform within the striatum. Positron emission tomography imaging shows decreased striatal [18F] orodopa uptake, which re ects reduction of number of cells per volume in SNr and striatal DA level (Fearnley and Lees 1991; Pate et al. 1993; Snow et al. 1993), especially in putamen (Morrish, Sawle, and Brooks 1995). Postmortem study of Parkinsonian patients found near-complete depletion of dopamine in the putamen (Kish, Shannak, and Hornykiewicz 1988). This dysfunction of the putamen hence of the sensorimotor network in the BG should then impair stimulus-response habitual control (Redgrave et al. 2010). Consistently, it has been known that Parkinsonian patients have di culty of executing (Schwab 1954; Hoshiyama et al. 1994) and learning (Knowlton, Mangels, and Squire 1996) habitual control of behavior. Furthermore, similar to rats with lesions in the sensorimotor striatum (Yin, Knowlton, and Balleine 2004; Yin, Knowlton, and Balleine 2006), 6-OHDA-treated parkinsonian rats also does not show habit learning under over-training (Faure 2005). Neurons in Parkinsonian BG show abnormal patterns of synchronized oscillations (Boraud et al. 2005; Gatev, Darbin, and Wichmann 2006; Pavlides, Hogan, and Bogacz 2015). Thus, neurons in motor systems downstream to the BG likely to receive normal activity from the goal-directed system and abnormal oscillations from the habitual system (Redgrave, Prescott, and Gurney 1999). This hypothesis that the habitual system in particular have abnormal oscillations is compatible with a fMRI study of Parkinsonian patients showing increased activity in the regions associated with automaticity (Wu, Chan, and Hallett 2010). Reduced e ective connectivity in the same brain regions shown in the same study is consistent with Parkinsonian symptoms such as slowness of movement (bradykinesia) and paucity of movement (akinesia). Patients with Parkinson’s disease have been treated by lesions in the BG which in general do not aggravate or induce motor problems when lesions are unilateral (Marsden and Obeso 1994). This has been noticed paradoxical (Brown and Eusebio 2008) because of the involvement of the BG in movements and particularly the observation that GPi lesions producing the signs of Parkinson’s disease ( exed posture, slow movement, rigidity) in normal monkeys reduces such signs in parkinsonian monkeys (Mink 2008). Redgrave et al. (2010) suggested the reason is that \it may be better to have no output from stimulusresponse habitual control circuits than a ‘noisy’ one. » In rats, lesions or suppression of the associative striatum blocks learning of goal-directed behavior (Yin et al. 2005; Yin, Knowlton, and Balleine 2005) whereas similar manipulation on the sensorimotor striatum blocks habitual learning (Yin, Knowlton, and Balleine 2004; Yin, Knowlton, and Balleine 2006). The latter manipulation and behavioral consequence is akin to the pathophysiological change and behavioral de cits in Parkinson’s disease whereas the same things can be said to the former experiments on the associative striatum and cognitive abulia. Abulia, one of the major syndromes of disorders of diminished motivation, is characterized by poverty of behavior and speech output, lack of initiative, loss of emotional responses, psychomotor slowing, and prolonged speech latency (Marin and Wilkosz 2005) with preservation of ability to perform wide range of tasks upon instruction (Redgrave et al. 2010). Focal lesions associated with abulia may be taken place in associative and mesolimbic territories of the BG (Redgrave et al. 2010). If this is the case, patients with Parkinson’s disease and patients with abulia show double dissociation as in striatum-lesioned rats with lack of habitual and goal-directed behaviors.
The BG are also involved in other neurological pathologies. Huntington’s disease is a neurode-generative genetic disorder whose symptoms include abnormal movements, cognitive and emo-tional di culties (Mink 2008; Obeso et al. 2014). The abnormal movements include involuntary movements termed chorea and motor incoordination. The striatum degenerates at the early stage and loss of MSN can be up to 95% in advanced cases. Dystonia is a neurological movement disorder characterized by sustained abnormal postures (Wichmann and Dostrovsky 2011). In patients and animal models, increased neuronal synchrony resembling Parkinson’s disease is ob-served. For example, increase in 4{10 Hz frequency band of LFP signal is observed in the BG of patients, especially in GPe (Gatev, Darbin, and Wichmann 2006). Tourette syndrome is an in-herited neuropsychiatric disorder whose patients exhibit \tics » which are sudden, rapid, recurrent, nonrhythmic, stereotyped involuntary movements and vocalizations (Obeso et al. 2014). Limited evidence suggests pathologies in cortico-BG network. Mechanistic relations of these motor dis-eases including Parkinson’s disease and how BG can account for such di erent symptoms remain unclear.

Collective dynamics in basal ganglia-thalamo-cortical net-work

Oscillations in Parkinson’s disease

There are two prominent frequency bands in oscillations of Parkinson’s disease, one peaked within 3{8 Hz (\tremor frequency ») and another within 8{15 Hz (alpha/low-beta), observed as LFP and ring rate oscillations in GPe, GPi and STN of MPTP-treated monkeys (Bergman et al. 1994; Wichmann, Bergman, and DeLong 1994; Raz, Vaadia, and Bergman 2000; Bergman et al. 1998; Wichmann et al. 1999; Dostrovsky and Bergman 2004) and human patients (Levy et al. 2000; Hutchison et al. 1997; Hayase et al. 1998; Hurtado et al. 1999; Magnin, Morel, and Jeanmonod 2000; Levy et al. 2002b). The lower frequency varies almost proportionally to the frequency of tremor (Hutchison et al. 1997) and intermittently synchronized with upper limb tremor (Hurtado et al. 1999). Existence of two frequency components strongly suggests that there are at least two di erent (but possibly over wrapping) neural networks with di erent characteristic time constants. Indeed, STN lesioning selectively suppress only the higher frequency component (Wichmann, Bergman, and DeLong 1994). Levodopa and apomorphine administration reduces low-beta frequency band and increases tremor frequency band of LFP in STN while orphenadrine enhances beta frequency band (Priori et al. 2004; see also Brown, Oliviero, and Mazzone 2001; Levy et al. 2002a). Furthermore, the tremor oscillations of di erent limbs have low coherence and thus it was suggested these oscillatory patterns are generated in di erent circuits (Ben-Pazi et al. 2001). Therefore, it is expected that there are not only two di erent networks with di erent characteristic time constants but also at least the network responsible for the lower frequency (tremor frequency) has multiple subnetworks underlying decoupled tremor oscillations. Topographicaly organized coextensive feedback loop structure in the BG may be responsible for such decoupled subnetworks.

Task-related oscillations

The oscillations in the basal ganglia are also observed in non-pathological condition. In macaque monkeys, 10{25 Hz oscillations are observed in LFP of the striatum and these oscillations are ampli ed during the period of a saccade task (Courtemanche, Fujii, and Graybiel 2003). In rats, similar task-dependent increase in oscillations are observed in theta frequency band (7{14 Hz) during the T-maze task (DeCoteau et al. 2007). It remains unclear why the dominant frequencies in rats and monkeys are di erent (Boraud et al. 2005). However, note that low frequency oscillations < 5 Hz were observed in Courtemanche, Fujii, and Graybiel (2003) but not analyzed to avoid possible artifact from cardiovascular rhythmicity ( 2 Hz) and the delta (< 5 Hz), beta (14{22 Hz) and gamma (30{50 Hz) bands were also observed in DeCoteau et al. (2007). Focal zones in the oculomotor region of the striatum found to temporary increase and decrease synchrony during saccadic eye movements (Courtemanche, Fujii, and Graybiel 2003). Brief (90{115 ms) bursts of the beta band (13{30 Hz) activity is observed at task end, after reward and post-performance period in monkeys performing movement tasks (Feingold et al. 2015). Similar bursts of the beta oscillations occur in the motor cortex but it occur after the last movement (Feingold et al. 2015).
In rats performing cued choice task, brief beta ( 20 Hz) oscillations are observed just after signal informative to make behavioral choice but not necessary during movement (Leventhal et al. 2012). The common feature of non-pathological oscillations are that they are transient in time and more focal compared to pathological oscillations (Boraud et al. 2005).

Table of contents :

1 Introduction 
1.1 Basal ganglia-thalamo-cortical network
1.1.1 Anatomy of basal ganglia-thalamo-cortical network
1.1.2 Closed loops in the BG-thalamo-cortical network
1.1.3 Neuronal dynamics and synaptic interactions in the basal ganglia
1.1.4 Functions of the basal ganglia
1.1.5 Dysfunctions of the basal ganglia
1.2 Collective dynamics in basal ganglia-thalamo-cortical network
1.2.1 Oscillations in Parkinson’s disease
1.2.2 Task-related oscillations
1.2.3 Infraslow oscillations and resting state network
1.2.4 Mathematical concepts for understanding the resting state networks
1.3 Absence seizure
1.3.1 Involvement of the basal ganglia in absence seizure
2 The role of striatal feedforward inhibition in the maintenance of absence seizures 
2.1 Introduction
2.2 Results
2.2.1 The BG-thalamo-cortical network model
2.2.2 Strong striatal feedforward inhibition promotes bistability of the BG-thalamocortical network dynamics
2.2.3 The competition between feedback loops in the BG-thalamo-cortical network
2.2.4 Strong striatal feedforward inhibition promotes bistability
2.2.5 The mechanisms for bistability and suppression of MSN activity
2.2.6 Asynchronous ring and synchronous oscillations in the BG-thalamo-cortical spiking network
2.2.7 Appropriately timed excitatory stimulation of the cortex terminates seizures
2.2.8 Bistable dynamics in the network model with the GPe included
2.3 Discussion
2.3.1 Consistency of our theory with previous experimental results
2.3.2 Comparison to the thalamocortical theory
2.3.3 Perspectives and predictions
2.4 Materials and Methods
2.4.1 The rate model
2.4.2 The spiking model
2.4.3 Analysis of the rate model
2.4.4 Simulations
3 Preliminary evidence for bistable characteristics of absence seizures 
3.1 Introduction
3.2 Results
3.3 Discussion
3.4 Materials and Methods
3.4.1 In vivo experiments from epileptic animals
4 Complex dynamics of basal ganglia-thalamo-cortical loops 
4.1 Introduction
4.2 Discrete-time approximation of basal ganglia-thalamo-cortical network
4.2.1 Reduction to one dimensional discrete system
4.2.2 Analysis of the discrete model dynamics
4.2.3 Eects of synaptic dynamics
4.2.4 Degenerate and non-degenerate rate models
4.2.5 Slow feedback in the direct pathway
4.2.6 How the striatal feedforward inhibition enhances bistability
4.2.7 How the bistability depends on other network parameters
4.3 Complex dynamics
4.4 Discussion
4.4.1 Local and global bifurcation analysis
4.4.2 How to incorporate thalamocortical bursting in the discrete model
4.4.3 Incorporating topographic organization as coupled map systems
5 Discussion 
5.1 Relation to pathological oscillations
5.1.1 Scaling of pathological oscillation frequencies
5.1.2 Scenario 1: hyperdirect feedback drives B-oscillations
5.1.3 Scenario 2: hyperdirect feedback drives SWD
5.1.4 Comparison of the two scenarios
5.1.5 Inter-species scaling of alpha and beta frequency bands
5.1.6 Are Parkinsonian oscillations multi-stable?
5.2 How to determine the oscillation driver experimentally
5.3 Functional implication of the complex dynamics
Appendix

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