ARE THE BASAL GANGLIA THE DIMENSIONALITY
REDUCER OF THE CORTEX?
Abstract
Recent advances in new techniques have resulted in the use of population coding and findings that support the idea that the brain encodes high- or low-dimensional information in populations. The cortex processes multi-modal high-dimensional information, which eventually needs to be reduced to a clear low-dimensional signal for more executive areas. Thus, dependent on the task and brain area, there might be a need for dimensionality reduction in the brain. Here, the basal ganglia (BG) are presented as the perfect candidate to reduce the dimensionality in the brain. The BG consist of several subcortical nuclei that are part of the cortico-basal ganglia-thalamo-cortical loop. Several of its unique properties that might serve the purpose of dimensionality reduction are highlighted and discussed, such as: highly converging subsequent layers with little shared input between neurons. An active decorrelation system including irregularly oscillating neurons and lateral as well as feedforward inhibitory connections that ensure independence of neurons, and aid the independence and formation of flexible attractors or stable architectural nodes that both receive functionally or temporally related information. The unique properties of the basal ganglia seem to be tailored toward recoding or compiling information, finding important features, reducing redundancy, and ensuring independence of processed information. These are also vital for successful and efficient dimensionality reduction methods, such as principal component analysis.
Lizz Fellinger Student (10852034)
MSc Brain & Cognitive Sciences, University of Amsterdam Dr. Ingo Willuhn Supervisor Willuhn group,
Netherlands Inst. for Neuroscience Dr. Birte Forstmann
I.
Introduction
In recent years, the spatial and temporal resolution of neural recording techniques have dramatically improved. Technological advances of recording techniques such as electrophysiology, calcium imaging and optical tools now allow in vivo recording of many neurons, while simultaneously manipulating, at multiple sites in freely behaving animals (for example: Berényi et al., 2014; Billard et al., 2018; Dayan and Abbott, 2001; Dombeck et al., 2007; de Groot et al., 2020; Michon et al., 2016). The massive increase in data generated with these novel
techniques has rendered the previously used single-neuron coding
analyses too time- and resource-consuming. Many neuroscientists
have instead started using population coding analyses. This method of
analysis has advantages in addition to being time- and resource-saving: 1.) Important features of a data set can be distilled through the use of dimensionality reduction, that cannot be identified using traditional single-cell analysis methods. 2.) Single-neuron activity is subject to trial-to-trial variability (i.e. noise in single-neuron coding), while the population code is less affected by this, since it does not separate fast within-trial dynamics from slow-across trial components and thus loses some trial-by-trial resolution but can predict the trial-to-trial variability (Montijn et al., 2016). 3.) The method has more biological plausibility compared to traditional single-cell analyses, since the brain seems to encode information in neuronal populations rather than in single neurons too.
Dimensionality reduction methods try to capture a complex signal in just a few summarizing features, i.e. dimensions. In the case of neuroscientific data, it characterizes how the firing rates of different neurons covary while discarding the spiking variability as noise
(Cunningham and Yu, 2014). Principal component analysis (PCA) is a
specific linear method of dimensionality reduction which tries to capture and sort uncorrelated dimensions that explain the largest amount of variance, i.e. the principal components (PCs). Each dimension captures a common feature (that is related to variance in the data) across the neurons in the population. A weight is ascribed to each individual neuron for each PC, and these weights can then be mapped onto a new geometrical coordinate system defined by the PCs. PCA ensures that the most relevant information or features are captured in the PCs, and that those are orthogonal to each other in the geometric coordinate system, i.e. capture the maximum amount of variance. When a few PCs are able to capture a large amount of variance in the dataset, this is indicative of a low-dimensional structure. A high-dimensional structure has many PCs and usually contains neurons that respond to more than one stimulus or multiple features of a stimulus (Fusi et al., 2016). In PCA, the single neuron activity is less important than the pattern of activation spread over the
Single-neuron coding Based on the assumption that individual neurons are a crucial unit of function in the brain.
Population coding
Based on the idea that populations of neurons are the essential unit of computation in the brain. Aims to represent interesting features/stimuli as a joint activity of a number of neurons.
Dimensionality reduction Represents a complex signal in terms of a few defining or summarizing features. It is applied to multi-neuronal activity in order to transform high-dimensional data into a low-dimensional space while preserving and highlighting meaningful features in the data.
Principal component analysis (PCA). Uses a linear mapping of data into a lower-dimensional space such that the variance is maximized in the low-dimensional space.
entire recorded population, to distill the most important or defining features and map them onto a lower-dimensional space.
The use of dimensionality reduction methods and more specifically PCA in neuroscience has revealed that population activity tends to encode more information than is revealed by the single-neuron analysis (Saxena and Cunningham, 2019). For example, Bagur et al., (2018) found through the use of a linear dimensionality reduction technique that in the primary auditory cortex (A1) of ferrets trained in a go/no-go task, a population-level modulation of the spontaneous activity occurred upon task engagement before stimulus presentation. The modulation of spontaneous activity at task engagement occurred in such a way that the population level suppression caused by the no-go stimulus blended in with spontaneous activity, while the evoked activity related to the go cue stood out. This preparatory modulation of spontaneous activity did not happen when animals were not engaged and would have remained unnoticed with the analysis of traditional single-neuron methods, since the average stimulus-evoked activity (corrected for increased baseline activity) did not differ between target or reference stimuli (Bagur et al., 2018). This is a good illustration of how population coding is more flexible and attuned to the broad spectrum of neuronal encoding compared to single neuron encoding. Other ways in which population coding could contain more information, can be deducted from features that are ignored when looking at single-neuron data, such as: the exact timing of the single-neuronal firing in respect to its previous activation/spike, the synchronicity of activity of one neuron compared to other neurons, or the phasic lack/increase of activity (Yuste, 2015).
Another insight gained from the use of dimensionality reduction methods is that the preferable dimensionality differs per task or brain region. For example, Rigotti et al. (2013) found that high-dimensional processing in the prefrontal cortex (PFC) is necessary for the successful performance of a complex cognitive tasks, while poor performance is characterized by low dimensional processing in this particular region. Other regions that are associated with complex tasks have been found to process high-dimensional information as well. For example, Ni et al. (2018) illustrate that the amount of correlated variability within visual area 4 (V4) of two rhesus monkeys decreased (i.e. higher dimensional processing) as performance in a visual orientation change-detection task improved. Additionally, both the level of attention paid during the task and the progression in learning over a period of time were negatively impacted by correlated variability in V4 (i.e. by low dimensional processing). Both these studies underline the benefit of higher dimensionality processing in order to perform and learn complex tasks.
Cortical regions are the largest site of neural integration in the entire central nervous system and possess connections to almost all brain regions that serve executive functions. The cortex processes, stores and integrates multimodal information from our complex world and thus unsurprisingly contains high-dimensional information. However, much like data scientists are using dimensionality reduction to try and understand how the brain encodes complex behavior and the environment, there is likely also a need for dimensionality reduction within the brain (Fusi et al., 2016). Low-dimensional information can be found especially in executive brain areas that receive and process clear non-mixed information in order to execute a specific function. For example, during learning of a new motor task, high-dimensional activity is processed in the supplementary motor area (SMA), while the primary motor cortex (M1) activity shows low-dimensional processing. Later, the M1 shows an
followed by a fully proficient skill corresponding with low-dimensional processing in the M1 (Paz et al., 2005). These results suggest that the dimensionality of information processed in the brain is tailored to the job at hand and the brain areas involved. Even though complex novel tasks or environments require high-dimensional information, this information needs to be transformed to low-dimensional information in order for executive brain areas to process and act quickly.
Assuming the brain performs dimensionality reduction to transform high-dimensional information from the cortex into lower-dimensional information, this thesis will argue that the basal ganglia (BG) is well suited to serve as the dimensionality reducer of the brain. Here, the BG will be introduced and some of the arguments will be discussed briefly. The arguments will be elaborated upon in the next chapters. They are based on anatomical, physiological and functional characteristics of the BG, supported by principles of mathematics, findings from artificial neural networks (ANNs), systems neuroscience and several other fields of research. The Basal Ganglia (BG) are a set of nuclei that form a subcortical circuit. This subcortical network is an integral part of the cortico-basal ganglia-thalamo-cortical loop (Parent and Hazrati, 1995). The BG receives input from nearly the entire neocortex, and the output nuclei project back to the cortex as well as to downstream targets, such as pre-motor areas (Dudman and Krakauer, 2016). The BG consists of several nuclei that can be divided into input, intrinsic and output layers through which information progressively flows. Within the BG most projections are inhibitory GABAergic projections. The amount of neurons in each consecutive nucleus reveals a remarkable bottleneck with a final reduction of approximately 3 orders of magnitude (Wilson, 2013). Thus, output nuclei of the BG consist of fewer neurons to contain the information, and likely project a lower dimensional representation of the information back to the cortex and downstream targets (Dudman and Krakauer, 2016).
The BG are a highly conserved structure throughout evolution and are thought to critically support a large variety of functions such as, learning, decision-making, reward-processing and motor control (for example: Balleine et al., 2009; Joel et al., 2002; Mazzoni et al., 2007; Willuhn et al., 2014). These are all functions that could benefit from dimensionality reduction. For example, learning involves a trade-off between exhausting the limited capacity of the system to implement complex and highly detailed input-output functions or to ensure that learning can be generalized. Lower-dimensional models generally increase the capacity to generalize learnings or useful features to different situations and thus are critical for quick adaptation to novel environments, which is critical for the survival of species.
This literature thesis will highlight some of the unique and essential features of the BG that could serve the purpose of dimensionality reduction. In chapter II, the broad anatomical structure of the BG will be laid out with its multiple converging layers, its three-pathway structure, and its mostly inhibitory connections with low synaptic connectivity between layers will be discussed. These properties form the basic anatomical structure of an efficient dimensionality reducer, since they ensure efficient recoding, prevent redundancy of information, and allow variations in recoding. Chapter III will look into the properties of the different nuclei and how these are set up to perform dimensionality reduction computationally. The functional significance of these properties for the entire BG will be addressed in chapter IV, as well as how a functional organization of the BG fits into the cortico-basal ganglia thalamo-cortical loop. In the discussion (chapter V) the features of the BG that aid dimensionality reduction will be laid out once more, and some of the remaining questions, future directions and several considerations will be discussed.
II. Basal Ganglia – Multilayered structure
The basal ganglia consist of a group of subcortical nuclei that can be broadly categorized into three layers: (1) input nuclei, (2) intrinsic nuclei, and (3) output nuclei (Lanciego et al., 2012). The input nucleus of the basal ganglia is the striatum, which is often sub-divided into the dorsal and ventral striatum (DS and VS) and mainly receives information from the cortex and thalamus (Alexander et al., 1986; Parent and Hazrati, 1995). The signal is then relayed to the intrinsic nuclei, consisting of the external segment of the globus pallidus (GPe), subthalamic nucleus (STN), and substantia nigra pars compacta (SNc). Eventually the information ends up in the output nuclei: the internal segment of the globus pallidus (GPi; in humans) or entopeduncular nucleus (EPN; in rodents) and the substantia nigra pars reticulata (SNr), which primarily project back to the thalamus and cerebral cortex. Thus, the nuclei of the BG form a multilayered structure, within the cortico-basal ganglia-thalamo-cortical loop through which information progressively flows (Figure 1; Kelly and Strick, 2004).
Figure 1: A schematic diagram of the cortico-basal ganglia-thalamo-cortical circuit (adapted from Tinaz et al., 2006). The blue boxes represent the input, intrinsic and output layer of the BG, encompassing the nuclei within each layer. Excitatory projections are thick arrows, while inhibitory connections are indicated by thin arrows. The input layer receives excitatory Glutamatergic input from the cortex and dopaminergic input from the SNc. The striatum is the starting point of the direct and indirect pathway marked by the activation of neurons containing respectively D1 receptors or D2 receptors. In the direct (D1) pathway the striatum projects to the GPi/SNr via GABAergic connections. In the indirect pathway the striatum projects to the GPe nucleus of the intrinsic layer. The intrinsic nuclei of the BG, the GPe and STN, form a feedback loop with inhibitory GPe-STN connections and excitatory STN-GPe connections. The STN also receives input directly from the cortex through the hyperdirect pathway. Eventually all pathways end up in the output nuclei: GPi/SNr. SNc: substantia nigra pars compacta; GPe: external segment of the globus pallidus; STN: Subthalamic nucleus; GPi: Internal segment of the globus pallidus (EPN in rodents); SNr: Substantia nigra pars reticulata.
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Layers
The three clearly defined and subsequent layers in the BG
naturally introduce what is termed ‘depth’ in artificial intelligence or
artificial neural networks (ANNs). Depth is known to exponentially decrease the amount of training needed for an ANN to find important functions/features (Goodfellow et al., 2016). Additionally, deeper
ANNs are thought to yield better compression compared to
non-layered or shallow networks (Hinton and Salakhutdinov, 2006). These two benefits of depth in ANNs are essential for efficient dimensionality reduction as well and might be inherently related; imagine the first layer learning a limited number of crude input patterns, feeding it to the subsequent layer, which will then learn larger more refined patterns hereby increasing the efficiency with which information is processed while reducing strain on the computational power by finding larger patterns in smaller subsequent steps. Thus, depth created by the layered structured of the BG can lead to more efficient processing of information, which could aid dimensionality reduction.
Another striking feature of the BG is its funnel structure, which can be observed when looking at the number of neurons along each layer. The high rate of convergence between nuclei should aid the process of finding useful features in information; every subsequent layer of the BG is substantially smaller than the previous layer, hereby structurally forcing each nucleus to compound information. Within the layers of
the BG, a final reduction in the output nuclei of 104 for the GPi/EPN and
103 for SNr compared to the cortico-striatal input is achieved (Zheng
and Wilson, 2002). In rats specifically, about 17 million cortical neurons innervate the striatum, while about 2.8 million striatal neurons project to 46,000 neurons in the GPe (Oorschot, 1998). In turn, about half of the neurons of the GPe innervate approximately 3,200 neurons of the EPN and 26,300 neurons of the SNr (Oorschot, 1998). In humans, the striatum contains about 100 million neurons, while the GPe only contains about 500,000 neurons, and the GPi even less with 160,000 neurons. The dramatic convergence from each layer onto the next suggests that the BG must recode the information in order to maintain useful or important features: For example, the striatum simply cannot perform loss-free encoding, since the same number of neurons would be needed in the BG to match the cortico-striatal input patterns exactly, unless the cortico-striatal input to the BG is extremely redundant. Since the cortico-striatal cells outnumber the striatal neurons by a factor of 10, this would mean that 9 out of 10 combinations of cortico-striatal input should be redundant in order for the striatum to exactly represent it (Zheng and Wilson, 2002). To stress this point even further, the extreme convergence throughout the entire BG would increase the amount of redundancy in the cortex to staggering and very unlikely amounts. Thus, the BG must perform some kind of dimensionality reduction in each layer to prevent loss of vast amounts of information coming in from the cortex. In ANNs high
Depth
A characteristic of a neural network that has one or multiple layers between the input and output layer. Artificial Neural Network (ANN). A computing system that is inspired by a specific biological neural network and is often used to simulate the functioning of the brain. Compression
A process that recodes information aiming to use less units than needed by the original representation. Autoencoder
A type of ANN that consists of a side for reduction and one for reconstruction. It can perform dimensionality reduction and is used to learn representations of input data and to ignore signal noise.
rates of convergence in layered networks (such as autoencoders) are often used to force each layer to compress the input information and project useful (abstract) features onto the next layer. Additionally, high rates of convergence allow each neuron in consecutive layers to gain access to an increasing portion of essential information, hereby reducing the number of dimensions from each layer onto the next. A dramatic convergence in capacity from each layer onto the next is observed across species (see Bar-Gad et al., 2003), so it seems likely that the convergence in the BG serves an important function. The large convergence per layer reduces the computational cost of processing substantial amounts of information and enforces the compilation of data resulting in a decreasing dimensionality of data within each layer.
Additionally, the synaptic connectivity between layers is relatively low. Meaning that even though the projection of the top layer onto the lower layer is vast, the individual axons make sparse innervations onto dendritic trees of the latter. Most axonal branches of cortico-striatal neurons do not come into each other’s vicinity, so there is little shared input between the neurons that are closely located to each other within a nucleus i.e. the presynaptic pool is rarely shared by the postsynaptic neurons. Estimates of the overlapping connectivity of cortico-striatal axons is 1.2-1.4% (Kincaid et al., 1998; Zheng and Wilson, 2002). The striatum does contain some denser hotspots with higher innervation rates and where axons do approach each other more closely. However, the boutons of these more proximal axons never exceed 250 resulting in a maximum possible innervation of 9% of neurons within the dendritic field of the specific axon and thus slim chances of overlapping innervation between proximal neurons (Zheng and Wilson, 2002). Additionally, the cortico-striatal connectivity ensures a lack of redundancy in neighboring neurons, since striatal neurons with overlapping dendritic volumes have very few common presynaptic cortical axons, while overlapping cortical cells have few common striatal targets (Kincaid et al., 1998). In other regions of the BG average connectivity has been estimated to be similarly low: striatum-GPe 0.8% (in monkeys), GPe-STN 2%, GPe-STN-GPe 1.2% (Kincaid et al., 1998; Yelnik et al., 1996). However, these studies assume random connectivity and do not take into consideration that pre- and postsynaptic targets might be clustered into denser hotspots, just like in the striatum (Sadek et al., 2007; Wilson, 2013). In support of this assumption, GPe-STN terminals have been found to be sparsely distributed across large expanses of the STN dendrites, so close STN neurons are unlikely to be innervated by the same GPe neuron (Baufreton et al., 2009). Even so, non-random connectivity such as reciprocal connections between the GPe and STN is possible, and this will significantly heighten the shared input to 32% shared STN-GPe projections and 52% of GPe-STN projections (Wilson, 2013). However, such a tightly controlled reciprocity between the GPe and STN is unlikely, and the chances of neurons receiving the exact same information are slim due to the wide distribution and low density of innervation across the BG. Interestingly, the need for shared input in dimensionality reduction is greatly reduced by the introduction of depth (Bar-Gad et al., 2003), possibly due to an increase in the portion of original input each neuron receives in each subsequent layer, or combining smaller into larger patterns within each layer; the parallel that can be drawn with the BG with its deep structure and sparse connectivity is undeniable.
Pathways
Structurally the BG harbors another interesting feature: it consists of at least three separate pathways: the direct, indirect and hyperdirect pathway. Each of these pathways flow through a different set of nuclei within the BG. A different type of processing with a different outcome could be performed depending on the connections between layers and/or on the properties of that specific layer (the latter will be discussed in more detail in chapter III).
In the classical BG model only the direct and indirect pathway were included. These two pathways are thought to have an opposing effect on the BG output due to their connections. The direct pathway consists of GABAergic inhibitory connections starting from the striatum onto the output nuclei GPi/EPN and SNr, resulting in an inhibition of the output nuclei when this pathway is activated. While activation of the indirect pathway disinhibits the GPi/EPN and SNr through an inhibitory GABAergic connection from the striatum to GPe, GABAergic projection from GPe to STN, essentially disinhibiting the STN which projects to the GPi/EPN and SNr through an excitatory glutamatergic projection. Therefore, the net effect of striatal activation of this pathway is opposite from the direct pathway. Kravitz et al. (2010) elegantly demonstrated the effect of optogenetic stimulation of the direct or indirect pathway in the dorsomedial striatum (DMS) on SNr neurons, respectively resulting in behavioral inhibition or activation. Behaviorally, the activation of the direct or indirect pathway in the DMS on motor control led to respectively reduced freezing and increased and longer locomotion or in increased and longer bouts of freezing and less frequent and shorter locomotor. In another study, Kravitz et al. (2012) demonstrated the role of the pathways in reinforcement learning by optogenetically stimulating either pathway in the DMS in behaving mice during a place preference and operant tasks. Stimulation of the direct pathway improved reinforcement and installed place preference, while stimulation of the indirect pathway led to place avoidance or transient punishment. So, the direct pathway seems to serve a facilitating role and the indirect pathway a suppressing role within the different behavioral functions of the BG. It is important to note that the final output of the BG is not dependent on activation of a single pathway per se, but on the relative activation of the pathways compared to each other (Wiecki and Frank, 2013). For example, motor symptoms in Parkinson’s disease are proposed to be caused by an imbalanced BG due to an overactive indirect pathway and an underactive direct pathway (Mallet et al., 2006). The differential combinations of nuclei that are incorporated in each pathway and the connections between these nuclei allows the BG to efficiently select and implement behaviors through reducing complex information with a minimal amount of anatomical structures.
The hyperdirect pathway was discovered later and added to the classical model: In this pathway excitatory input from the cortex is received by the STN which mainly sends inhibitory projections to the GPi/EPN (Chesselet and Delfs, 1996; Wichmann and Delong, 1996). The function of the hyperdirect pathway is a little less clear, however it seems to rapidly inhibit the output neurons of the BG when there is a conflict between stimuli and to reflect a kind of salience property (Cavanagh et al. 2011). These functional properties of the hyperdirect pathway point to an additional advantage of having several pathways: temporal processing differences. As described in the ‘race model’, which states that Go and No-Go cues elicit Go and No-Go processes that each race toward completion. Whichever process finishes first wins and the action is initiated or suppressed dependent on the outcome (Logan and Cowan, 1984).
Many adaptations have been made to this model over the years, but the ‘racing’ aspect between the pathways has remained (for example: Aron, 2011; Schmidt and Berke, 2017).
For example, even though the hyperdirect pathway might process information more crudely due to its limited number of nuclei, it can serve a preparatory role and adjust decision thresholds in the output nuclei due to a faster processing time (Jahfari et al., 2012; Schmidt et al., 2013). Thus, the three pathways seem to have different timelines for processing the information and can allow different features to be highlighted due to inclusion of different nuclei in each pathway, which can be advantageous for dimensionality reduction. The properties of these nuclei will be discussed in more detail in the next chapter.
III. Basal Ganglia – Layers & Connected Nodes
Each nucleus in the input, intrinsic, or output layer of the BG has certain unique identifying properties. Those properties that might serve dimensionality reduction can be divided up into two main categories: independent nodes and active decorrelation. Here, the properties within each layer will be discussed per category to provide an overview of how the combination of layers and properties are perfectly set up for and serve the purpose of dimensionality reduction.Independent nodes
The main input nucleus of the basal ganglia, the striatum, is a heterogeneous structure that consist of 90% medium-sized spiny neurons (MSNs) and 10% interneurons (O’Donnell and Grace, 1993). The striatal neurons and their afferent terminals are spatially distributed into distinct compartments that are referred to as the
striosomes and matrix (Graybiel and Ragsdale, 1978). The two can be
distinguished from each other through their input-output organization and expression of molecular markers (Fujiyama et al., 2011). Striosomes are nodes of cells that are embedded in the matrix. The matrix also contains nodes of cells (matrisomes) that are closely linked to the neighboring striosomes and receive input from related cortical regions (Kincaid et al., 1998). The compartmental segregation within the striatum restricts the shape and extent of dendrites according to its boundaries; MSN dendrites in the striosome never enter the matrix, and the other way around for matrix dendrites (Fujiyama et al., 2011). Interestingly, the cholinergic and GABAergic parvalbumin containing interneurons seem to originate in the matrix but their dendrites can cross the matrix/striosome boundaries, unlike MSN dendrites (Graybiel et al., 1986; Humphries et al., 2006; Mallet et al., 2006). These interneurons seem to help bridge between striatal ‘nodes’.
The striatal nodes, albeit striosomes or matrisomes, consist mainly of MSNs that receive a large number of individually weak and mostly non-correlated distal dendritic inputs from the cortex (Kincaid et al., 1998; Zheng and Wilson, 2002). The MSNs maintain a relatively negative membrane potential when in rest, have a high resistance to depolarization and due to small uncorrelated excitatory input require a consorted effort of many cortical neurons to become increasingly active (Kincaid and Wilson, 1996; Yim et al., 2011). Those MSNs that
are located within the same node are connected to each other by local
lateral inhibition. Lateral inhibition is thought to facilitate ensemble synchronization through depolarizing connected neurons to a potential nearer to the reversal potential, hereby enabling synchronization of larger ensembles of MSNs when they are innervated within a certain timeframe (Moyer et al., 2014; Tunstall et al., 2002). Due to the functional nature of cortical projections to striatal regions, each single MSN output can be thought of as a representation
Local lateral inhibition Provides independence of neurons by suppressing the activity of the neighboring neurons.
Feedforward inhibition Dampens the effects of afferent excitation on the principal neuron, through independent activation of an inhibitory interneuron. Feedback inhibition Regulates the principal neuron activation by altering the discharge frequency of a connected inhibitory interneuron leading to reduced activation of the principal neuron.
Ensemble
A group of neurons that show spatiotemporal co-activation. Attractor
A stable or semi-stable point, which ‘attracts’ the activity in a neuronal population. Several attractors can exist simultaneously within a population, separated by attractor ‘basins’ that converge network activity patterns to the attractors. Anti-hebbian rule
A learning rule that dictates a reduction in synaptic strength between neurons that fire together.
of the activation of a distributed ensemble of cortical neurons. While MSNs that are located in the same area of the striatum are less likely to share their cortical inputs, they tend to receive weakly correlated inputs and thus are likely to be included in the ensemble via lateral inhibition. This could result in a group of MSNs representing functionally related but slightly varied information from multiple related populations in the cortex, which is similar to how data points can be projected onto principal components, with each data point strengthening the explanatory power of the PC, but slightly varying in their fit.
Even though the MSNs are connected through local lateral inhibitions within their
compartment, the primary source of inhibition in the striatum is feedforward inhibition
(inhibition from interneurons to MSNs) coming from GABAergic parvalbumin containing interneurons (Owen et al., 2018; Tepper et al., 2004; Tunstall et al., 2002). They are referred to as fast spiking interneurons (FSIs) due to their brief action potentials followed by large and rapidly peaking spike afterhyperpolarizations. Only 3-5% of striatal neurons are FSIs, but they are extremely potent (Kita and Kitai, 1988; Tepper et al., 2004); a single action potential can delay or block the occurrence of spikes in MSNs, while synchronous activation of FSIs collectively can cause long-lasting changes in synaptic plasticity (Bonsi et al., 2011; Moyer et
al., 2014). Also, striatal interneurons can facilitate ensembles of MSNs, while simultaneously
inhibiting other ensembles of MSNs (Czubayko and Plenz, 2002; Lanciego et al., 2012). Acutely silencing FSIs with in vivo optogenetics disinhibited MSN spiking and altered the pattern of MSN spiking to enhance bursting and calcium signaling throughout the network (Owen et al., 2018). Further stressing the importance of FSIs for striatal functioning is the fact that they have unique properties in the striatum; striatal FSIs only deliver feedforward inhibition, while FSIs in the cortex and hippocampus deliver both feedforward and feedback inhibition (Owen et al., 2018). Additionally, disrupting FSIs affected learning, but not performance of well-trained animals on an action selection task and a dysfunction of interneurons in the striatum is observed in many disorders (for example: Gittis et al., 2011; Mallet et al., 2006; or for review see: Crittenden and Graybiel, 2011). Thus, the striatal FSIs are essential for learning by means of a well-functioning striatal activity; they can activate and inhibit MSNs, can alter calcium signaling and can adapt MSN synaptic plasticity.
The set-up and function of interneurons in the matrix and striosome compartments
closely resembles the following ANN that was set up to perform PCA with an anti-Hebbian
rule: the output neurons were connected through inhibitory connections that became
stronger (more negative) when the firing of the two output neurons was correlated resulting in a weakening of the input-output connection or enhanced the input-output connection when the two output neurons fired in an opposite direction (Foldiak, 1989, 1990). The output neurons in this ANN contained the information, while the lateral inhibitory connections between the output neurons forced them to encode different components of the input and
adapt synaptic strength of the input-output connection. Even though we cannot assume that
simplified ANNs resemble complex biological systems (for example in some cases interneurons seem to encode information opposite from MSNs: Martiros et al., 2018), this specific ANN does provide an idea of what the important function of these interneurons might be. The striatal compartments seem to form low-dimensional building blocks for cortical information to flow into that are known to function with little FSI interference in an acquired task (Owen et al., 2018); after all according to this model the synaptic strengths, input-output connection and active nodes have been set up during acquisition. While during learning, the
striatal and cortical neuron. In this way, the striatal matrix and striosomes could represent a flexible system in which the statistical dependency of the nodes is reduced, just like the principal components in dimensionality reduction.
Local collateral inhibitory connections are also prevalent in the GPe and SNr, in respectively the intrinsic and output layer of the BG. These connections are known to aid the
creation of ensembles in these nuclei. Ensembles can be viewed as a more spatially and
temporally flexible form of building-blocks and could therefore be a continuation of the representation from the striosomes and matrisomes. In fact, in primates anterograde tracers showed the existence of distinguishable bands of neurons in the GPe with projections from
adjacent areas of the striatum (Parent and Hazrati, 1995). The feedback connections between
ensembles enable the network to generate intrinsic activity. Chan et al., (2004) have shown
in vivo that coordinated dStr-GPe input (e.g. from striosomes or matrisomes) can temporarily
promote synchronization of the intrinsic activity despite the usual strong autonomous pacemaking of GPe neurons (pacemaking will be addressed below). When the intrinsic activity
is stable at specific timepoints, attractors are formed. Attractors in ANNs are used as temporal
and spatial building blocks that ‘attract’ activity, while neighboring neurons redirect their activity towards the attractor point. These attractors are therefore a more flexible way for nuclei to attract and compress information, decrease variability and recode the incoming related information. Attractors have been shown to implement associative and spatial memories in the hippocampus (Wills, 2005), decision-making in ANNs, and have provided solutions to computational problems (Yuste, 2015), so these could definitely be employed by the intrinsic and output nuclei of the BG during learning to recode and increase efficiency. However, much more research is needed to provide a definitive answer on whether (and if so how) temporary attractors or ensembles come into existence in the intrinsic and output layer of the BG and also into how the information in the nodes in intrinsic and output layers relates to the information in the striatal matrisomes and striosomes of the input layer.
Active decorrelation
The BG employs an active decorrelation mechanism to prevent synchronous firing and network patterns and to promote diversity within the population (Wilson, 2014). The intrinsic and output nuclei of the BG harbor spontaneous oscillating neurons, meaning that even in the absence of input these neurons will fire continuously at rates of 1 to 100 spikes per second. The autonomous oscillatory pattern of these neurons is perturbed by synaptic input, so spontaneous irregular firing is sustained by both inhibitory and excitatory input. These active decorrelation mechanisms are specific to the BG since in almost all other brain regions oscillating neurons lead to phase-locked or synchronous firing and network patterns. A loss of pacemaking in the BG results in the development of highly synchronous oscillatory patterns
of activity in Parkinson’s disease that correlate with some of their symptoms(Nini et al., 1995;
Wilson, 2013).
Neurons in the GPe, GPi/EPN, STN and SNr fire rapidly even though they receive almost no excitatory input, because they are intrinsic pacemakers, also referred to as spontaneous
oscillating neurons. The pacemaker neurons are not easily perturbed by synaptic input. For
example, the in vivo blocking of either all glutamate or all GABA receptors of a GPe neuron with an antagonist injection in its vicinity, only led to a moderate change in the irregular firing rate. The neurons displayed rhythmic near-baseline levels of firing when both receptor types were blocked in vivo in monkeys (Kita et al., 2004), but also in slice (Mercer et al., 2007). So, the oscillating character of these neurons is inherent and not related to input, but irregularity
in the pattern of each individual neuron is introduced by input. The mechanism behind spontaneous firing are nearly the same for neurons in the GPe, GPi/EPN, SNr and STN nuclei (Atherton and Bevan, 2005; Bevan and Wilson, 1999; Mercer et al., 2007). They are all based on ion channels similar to those that generate action potentials, but in which the activation of specific sodium current channels is much more persistent and occurs at voltages far below the threshold for action potentials. Almost immediately after the occurrence of an action potential, depolarization is restarted since the sodium current in these neurons overtakes the size of the potassium current at about -65mV. High frequency firing is achieved through the activation of specific high-voltage activated potassium channels that rapidly repolarize the cell membrane during the action potential. The fast recovery after an action potential is sped up by the activation of a hyperpolarization-activated cation channel (HCN) when hyperpolarization occurs, resulting in a depolarizing current. The HCN is also responsible for the rhythmicity of firing and ensures that these cells have no membrane potential and thus oscillate rapidly.
The irregularity of firing of oscillating neurons is thought to be caused by three different mechanisms that are specific to the BG. Firstly, the oscillating neurons in the GPe show rate heterogeneity among the population. These GPe neurons can vary their firing rate from 1 to 70 spikes per second, and are thought to drift among the entire range of rates (Deister et al., 2013). GPi/EPN neurons display a higher frequency discharge pattern varying anywhere between 60-80 spikes per second (DeLong, 1972). Secondly, (subthreshold) synaptic inputs to oscillating neurons alter the phase of the neuron, affecting the timing of the next spontaneous action potential instead of changing the firing probability (e.g. Gutkin et al., 2005). Independent of the inhibitory or excitatory nature of the input, only input is incorporated into the neurons’ autonomous oscillatory pattern and will affect each neuron differently dependent on its phase. For example, when two independent repetitively firing neurons receive the same input, the input will alter each of their phases, and they may emerge from the encounter with no change in relative phase, closer in phase, or in phases further apart to each other. Thirdly, the existence of local collateral arborizations in the GPe (and SNr) could lead to synchronicity between connected neurons, but have been shown to actively oppose synchronous activity between neurons in the GPe (Sims et al., 2008). In vivo, the cross-correlograms of both GPe and GPi neurons are flat, which indicates that the neuronal pairs are also functionally and statistically independent (Heimer et al., 2002). The STN and GPi/EPN have no or very sparse local axonal collaterals (Kita, 2007; Kita and Kita, 2012). The effect of rate heterogeneity, no or anti-phasic local collateral arborization, and sparse shared inputs, all contribute to an active decorrelation and statistical independence of the individual oscillating neurons.
The spiking variability of each neuron has little to do with the spiking variability of the other and therefore ensure independence of the neurons, the spontaneous firing-rate fluctuations are shared among the whole population and thus can exert influence on the formation of nodes or attractors (Churchland and Abbott, 2012). The result of the unique active decorrelation mechanisms of the BG discussed here is a decorrelation of activity in the BG output nuclei that maximizes the potential information capacity and can ensure statistical independence of neurons and the formation of independent nodes within the layers. Statistical independence and a separation of information in the nodes can also be useful for the separation the functional territories within the cortico-basal
ganglia-thalamo-IV. Basal Ganglia – Functional Units
The BG input nucleus receives input from virtually all cortical regions, processes this information and projects back to the cortex forming a partially closed loop. Throughout the last few decades there has been disagreement about whether the information from all these cortices is combined within or remains separated throughout the cortico-basal ganglia-thalamo-cortical loop. The two most extreme theories state that the BG are either a converging funnel that integrates all the cortical information, or a parallel segregated loop structure that keeps the information segregated throughout. However, most theories integrate pieces of both and state that the BG are a structure of open interconnected loops (Joel and Weiner, 1994). The number of different loops within the BG is still heavily debated. The original idea was that the BG contained two loops: the motor and the associative loop (DeLong and Georgopoulos, 1981). This was later extended to five functionally distinct loops, and later even further to contain subchannels within functionally distinct loops (Alexander et al., 1986; Hoover and Strick, 1993). The division into separate sub-channels within the loops was based on topographical projections from the cortex to the input nucleus of the BG. Although the numbers of reported segregated loops still vary (currently up to ten separate loops have been reported (Middleton and Strick, 2000)), most theories do agree on the existence of a division between limbic, associative and sensorimotor loops.
The striatum, the input nucleus of the BG, receives projections from more or less all cortical regions. The input from the cortex imposes a functional organization upon the striatum in such a way that non-adjacent but functionally related cortical areas project to the same or adjacent striatal areas (Selemon and Goldman-Rakic, 1985). Generally, the input can be divided into three categories which all project to different regions in the striatum: (1) The associative regions in the frontal, temporal and parietal cortices, densely project to the portion of the putamen rostral to the anterior commissure and caudate nucleus. (2) The sensorimotor regions and the primary motor cortex project to dorsolateral section of the putamen and the dorsolateral rim of the head of the caudate nucleus. (3) The limbic and paralimbic regions, including the amygdala and hippocampus, project to the nucleus accumbens, olfactory tubercle and ventral part of the caudate nucleus and putamen. The subchannels within these loops are based on topographical lay out, for example, the motor and somatosensory cortical representation of an individual body part (in this case a digit) are located far apart in the cortex, but project to the same area in the striatum (Brown et al., 1998). These functional topographic territories are also reflected by a distinction between cortico-striatal and thalamo-striatal projections. The thalamo-striatal projections seem to project to the same striatal regions as the cortico-striatal projections,
Converging funnels Based on the fact that the neurons in the BG and especially in the output nuclei of the BG receive highly convergent information leading to funneling. Parallel segregated loops Describes the basal ganglia as segregated circuits that process information in parallel and do not interact with each other.
stressing the functional topography of the projections. Though they have been suggested to reflect and encode complementary information (but also see Corbit et al., 2003). For example, the auditory cortico-striatal projection conveys different but complementary features of a sound compared to the thalamo-striatal projection (Ponvert and Jaramillo, 2019). Thus, at least in the striatum, a topographical segregation between the loops based on their functionality seems to exist.
Additionally, the cortical projections seem to prefer projecting to either striosomes or matrices based on their functionality. The matrix seems to partake in the sensorimotor and associative cortices, while the striosomal MSNs are preferentially targeted by the limbic cortices and the amygdala and hippocampus (Crittenden and Graybiel, 2011; Kincaid and Wilson, 1996). Striosomes influence local activity, as well as global activity within the striatum through interneurons and are therefore suggested to exert control over the sensorimotor and associative information in the matrix (Crittenden and Graybiel, 2011). This suggestion is strengthened by the early striosomal degradation in Huntington’s disease (HD) patients that also displayed early signs of mood disorders, and a disbalance in striosomes in addicts and suicide victims (Graybiel, 2008). Additionally, limbic control over the sensorimotor loop through striosomes could be the mechanism behind the following finding of Aoki et al. (2019). They found that the limbic system can unidirectionally modulate M1 activity, i.e. the limbic loop somehow has access to the motor loop. No evidence was found of modulation from the motor loop onto the limbic loop, suggesting that the partially open structure between the loops is unidirectional. Though this research focused on the limbic and motor loops and therefore does not rule out the existence of more uni- or bidirectional modulations between the (partially) segregated units, it stresses that a separation of loops exists and that information can be shared between the functional units.
In order for the BG to be considered a part of the segregated loop structure, the segregation should not only be apparent in the striatum but should be maintained throughout the intrinsic nuclei of the BG and be reflected in its output. Anterograde tracing and immunohistochemistry have shown that the GPe contains functional territories similar to those of the striatum (Karachi et al., 2002; Kita and Kita, 2001). Afferents from each functional territory in the striatum project to two narrow bands each in the GPe (Kita and Kita, 2001). Additionally, matrix MSNs have been shown to innervate the GPe, GPi/EPN and SNr, but not the SNc (Fujiyama et al., 2011), while the striosomes prefer to project to the SNc and target the GPe, GPi/EPN and SNr through collaterals (Fujiyama et al., 2011; Kawaguchi, 1993; Lanciego et al., 2012). The preferential targeting of the limbic pathway of the SNc through striosomes provides the limbic system with another way to influence the other loops through the SNc back to the striatum. The other output nucleus of the striatum, the GPi/EPN also seems to adhere to a topographic subdivision between the functionalities with motor located in the ventral part, associative in the dorsal part, and limbic located in the medial tip (Nambu, 2007). The STN does not show any anatomical and histological borders, but shows a much more complex internal structure (Alkemade et al., 2019). Anatomical or histological borders between functional territories were expected based on the idea that neurons move apart during development when they specialize in different functions. However, some tracing studies and in vivo imaging studies do provide support for some functional separation in the STN (Haynes and Haber, 2013; Temel et al., 2005). This suggests that the STN might not show an anatomical separation, but might show a functional separation imposed by topographically
adhere to a functional separation. These findings in the STN, but also in the other nuclei, should be interpreted with care, since the outcomes of these studies vary greatly on the methods used and even show large discrepancies when applying the same methods. Also, the notion of task related flexibility should be kept in mind when studying functional organization, since the BG might utilize flexible nodes to process its information. Overall, the functional organization seems to be maintained throughout most nuclei of the BG.
For the proposition of segregated functional loops to be true, the loops have to project back to the initial input area. Information flowing through the BG influences the cortical areas, as many studies have found (for example: Aoki et al., 2019; Kelly and Strick, 2004; Morcos and Harvey, 2016). However, for the loops to adhere to the open interconnected loops theory, the loop should at least project back to its input regions but also expects the information to return to additional areas. For example, Kelly and Strick (2004) injected a retrograde rabies tracer into the M1 and area 46 and found that virus ended up in functionally segregated regions in the intrinsic nuclei of the BG, the GPe and STN. Then an anterograde tracer was injected in the M1 and the infected neurons in the GPe and STN were compared between viruses. The researchers found that the M1 input ends up in correspond to the neurons that project back to the M1, and in an additional dense group of neurons that is suspected to be part of the limbic system in the dorsal striatum. Another example of a loop structure comes from Aoki et al., (2019) who studied the motor system as well as the limbic system. They used tracing techniques, ex vivo slice recordings and in vivo electrophysiological techniques to confirm cortico-basal ganglia–thalomo-cortical loops for the limbic and motor system and reveal a one-way modulation of the limbic system onto the motor system. Thus, the input cortices seem to receive a version of their input back after it has been processed by the BG.
The function of these partially segregated loops is not known yet, and should be extensively researched to really comprehend the functioning of the BG. However, when combining the two essential functions of the BG, i.e. movement and reward prediction, with its transient but easily modified sustained activity, with the nature of the cortex with sustained cortical activity after input and the returning BG output, some suggestions can be made. Such as, that the loops might be essential for learning task responses: Several cortical regions receive a vast amount of information and project this to the BG. The BG processes this information and reduces its dimensionality, so only the important features remain. The important features are fed back into the cortical input regions to ensure that the right decision is made or action is performed and to improve task performance in the long run. The segregation of different functionalities aided by attractors and/or ensembles, will ensure that the information processing ends up in the same position where the initial processing occurred. For example, the parietal cortex (PPC) is thought to sustain and update its activation for several seconds during learning, after which certain activity patterns are strengthened and correlated to one another (Morcos and Harvey, 2016). They suggest that the weights of the pattern connections are modified by a low-dimensional readout network, such as the BG. Another research recorded population activity during the decision making process, found that during the accumulation of evidence the prefrontal cortex activity reflected the choices and constantly updated the preferred choice, while the PPC encoded and constantly updated the value of the accumulated evidence (Hanks et al., 2015). Kupferschmidt et al. (2017) compared the task-engagement of the mPFC-DMS and M1-DLS inputs to the BG, forming the start of the associative and sensorimotor loops respectively, during the acquisition of a rotarod task. They observed sustained movement related activity in the mPFC, M1 and related areas in the BG
throughout the entire task. However, they found that the associative loop was weakly engaged during the initial (naïve) stages of learning but increased task engagement throughout the first day (early) and that it decreased again later (late), while the sensorimotor loop was engaged during the naïve and early stage and task engagement decreased during the late stages. Thus, the cortico-basal ganglia-thalamo-cortical loop is involved during learning and the associative and sensorimotor loops are engaged in parallel, but their task engagement is temporally and functionally dissociable, since the decrease in engagement of the associative loop was correlated with the rate and extent of learning. Several other studies have also found dissociable task engagement between the loops, such as in action selection, planning and preparation (Monchi et al., 2006). Whether or not this is truly the function of dimensionality reduction in the BG within the cortico-basal ganglia-thalamo-cortical loop can be questioned, but these examples do illustrate the effectiveness of a flexible but structurally set up loop structure that incorporates sustained activity in the cortex and more transient dimensionality reduction, for functions such as learning, movement and decision-making.
V. Discussion
This literature thesis has explored the possibility that the basal ganglia are the dimensionality reducer of the brain. It is by no means complete or conclusive, but has highlighted the unique features of the BG that could support dimensionality reduction.
Starting off, the BG are a part of the cortico-basal ganglia-thalamo-cortical loop through which information progressively flow. The BG with its multiple layers form a funnel due to the decreasing amount of neurons in each layer, hereby forcing the BG compression of information in every subsequent nucleus.
The synaptic connectivity between all the layers is relatively low. Though the weak mostly uncorrelated excitatory input of the cortex to the striatum is vast, the relatively negative membrane potential and high resistance of MSNs requires a coordinated of many neurons, to lead to an action potential. Low synaptic connectivity reduces redundancy in the input and efficiently allows each neuron in a subsequent ‘deeper’ layer to access additional information and combine this into larger patterns.
The three pathways encompass different combination of nuclei and number of layers, allowing for differences in processing, but also for variations in the timeline of processing. This could support functions like preparatory modulation of baseline activity in output nuclei.
The modulation of spontaneous activity is facilitated in the intrinsic and output nuclei by the type of neurons: spontaneous oscillating neurons. The fast oscillation pattern of the neuron incorporated each input through a phase shift, independent of the input size or its excitatory or inhibitory nature. The lack of shared input into spontaneously oscillating neurons leads to irregularity of firing and statistical independence of each neurons’ activity.
Diversity in the population is further supported by lateral inhibitory connections between the neurons. Though, lateral inhibition can also induce temporary synchronicity in an ensemble or ‘attractor’ of neurons, whenever the node is highly innervated within a specific timeframe, leading to a reset of the oscillating patterns of the neurons within the node. This coordinated innervation of nodes is imposed on the intrinsic and output layer of the BG through the functional topography of the cortico-striatal and thalamo-striatal projections into neuroanatomically instated building blocks in the input layer, i.e. striosomes and matrisomes in the striatum. Feedforward inhibition between the striosomes and matrisomes in the striatum by interneurons, such as FSIs, modulate synaptic connectivity and facilitate synchronicity within ensembles, while simultaneously suppressing other ensembles. Hereby, the building blocks in the form of striosomes and matrisomes ensure the strength and statistical independence of their activity and through its projections also the independence of the ensembles or attractors in intrinsic and output layers.
The projection of the cortex and thalamus to the striatum, imposes a functionally topographical distribution onto the entire striatum and displays a preference of limbic cortices onto striosomes and sensorimotor or associative cortices onto matrisomes. This topographical distribution of the functional territories seems to be largely maintained in the intrinsic layer BG nuclei (GPe, STN, and SNc) and in the output nuclei (GPi/EPN and SNr). This could ensure that the lower-dimensional output projection of the BG onto the thalamus and the cortex, ends up in the cortical input area of the loop and potentially in additional functionally related cortical areas.
Thus, the cortico-basal ganglia-thalamo-cortical loop forms the perfect architecture for learning and action monitoring through its sustained high-dimensional multimodal activity in cortical areas, the extraction of important features by dimensionality reduction in the BG, and
the resulting transient projection of a lower-dimensional version of the original input information back onto the original and possibly other functionally related cortical areas.
Remaining questions
In order to conclusively state that the BG are the dimensionality reducer of the brain, the following questions (and many more) should be addressed:
o Is the dimensionality/variability higher in the striatum than in the output nuclei? What is the dimensionality of the information that is projected back to the cortex, and does it change the dimensionality of the cortex’s preparatory/sustained activation?
o Do the matrisomes or striosomes represent different features? How do the matrisomes relate to their neighboring striosomes? Does silencing of FSIs in the striatum lead to statistical dependence of matrisomes and striosomes and if so, does it hamper acquisition of new complex tasks?
o Do the intrinsic and output nuclei of the BG in healthy subjects support the formation of and projection to attractors?
o What is the function of the direct, indirect and hyperdirect pathways on dimensionality reduction? More specifically: Do the pathways have different outcomes in terms of dimensionality or represented features? And, is this related to temporal differences in their processing or something else?
o Do the functional loops process information differently in the same nucleus, or is the same process in each nucleus applied to each functional territory?
These questions show that a lot remains to be investigated before a conclusion can be drawn about whether or not the BG is the dimensionality reducer of the brain.
Future directions
The above questions also reveal that there is a need for multi-site in vivo long-term recording with high spatial and temporal resolutions. Novel techniques can be employed for recording, such as long-term calcium imaging with the NINscope (de Groot et al., 2020; Montijn et al., 2016), multielectrode arrays (for example: Ni et al., 2018), or silicone probes (for review see: Kipke et al., 2008). Additionally, the molecular or histological differences between populations of neurons can be utilized through viral targeting techniques to further explore the role of a specific (functional) pathway, the striosomes/matrisomes, or particular neurons when combined with recording techniques. Optogenetic stimulation and inhibition can be used to manipulate the dimensionality of information and/or the outcome of dimensionality reduction and draw out the necessity of certain (temporal) properties for dimensionality reduction (for example: Rikhye et al., 2018). Another interesting possibility is recording with any of the above techniques and combining the recorded data with decoders in order to validate hypotheses. For example, Ni et al., (2018) first recorded activity from the V4 and then built a choice decoder on their first PC that performed just as well as on the entire data set. These are just a few of the possible techniques or methods that could be used to investigate the dynamics and dimensionality of the brain and specifically the BG.
Experiments designed to estimate the dimensionality of information and to investigate dimensionality reduction, should keep the following things in mind that are known to influence the (recorded) dimensionality of information: (1) The number of recorded neurons should be
the complexity of the task, e.g. if the task is too simple, lower dimensionality will be recorded which would not reflect the potential dimensionality of processing dynamics (for example: Gao and Ganguli, 2015; Gao et al., 2017; Rigotti et al., 2013) . (3) The dimensionality could be influenced by the novelty of a task or stimuli, e.g. dimensionality fluctuates between performance of a task during acquisition and when it is acquired or when it is habitual (for example: Kim and Hikosaka, 2015; Kupferschmidt et al., 2017; Paz et al., 2005; Raposo et al., 2014).
Considerations
In this thesis, the functioning and set-up of the BG has been compared to an often-used linear dimensionality reduction method: PCA. Even though many of the used concepts like statistic independence are important for any dimensionality reduction method, albeit linear or non-linear, it is good to keep in mind that the brain might not be linear in its encoding, and recoding. There are clear cues that the brain might not be linear. For example, the output responses of striatal MSNs are non-linear, due to their clear up state with a high firing rate and a clear down state with zero or very low firing rate and a limited dynamic range in between the up and down state. Contrastingly, the responses of the intrinsic and output layers are more continuous due to their oscillating nature, through which input is reflected in phasic shifts, and thus might adhere better to the concept of linearity. Though, linearity might be possible when considering entire populations of non-linear neurons, the probability of a non-linear brain and/or BG is high, so non-linear ways of dimensionality reduction should also be considered.
Furthermore, many features of the BG have not been addressed in this literature thesis that are unique to or essential for the functioning of the BG, such as dopaminergic input from SNc and VTA, cholinergic input and other interneurons in striatum, complexities of intrinsic BG feedback and feedforward loops etc. For example, the striatum contains more sources of GABAergic signaling, such as low-threshold spiking interneurons, cholinergic interneurons and many more interneurons (Bonsi et al., 2011; Straub et al., 2016; Zhang and Cragg, 2017). The striatum also receives external input from the amygdala, hippocampus, globus pallidus, thalamus and many more regions (Kelly and Strick, 2004; Parent and Hazrati, 1995). The projections from the thalamus indirectly make up as much as 50% of striatal input, due to direct thalamic feedback projections to the striatum and indirect influence on the cortical projections from the prefrontal, premotor and supplementary motor cortex (McFarland and Haber, 2000). Even though the complexity of the BG and the cortico-basal ganglia-thalamo-cortical loop should definitely be further explored and incorporated, the most prominent features for dimensionality reduction have been addressed here.
