Movement Disorders Vol. 6 , No. 3, 1991, pp. 189-204, Q 1991 Movement Disorder Society

Modeling the Functional Organization of the Basal Ganglia A Parallel Distributed Processing Approach I. J. Mitchell, J. M. Brotchie, *G. D. A. Brown, and A. R. Crossman Experimental Neurology Group, Department of Cell and Structural Biology, University of Manchester, Manchester, England, and *Department of Psychology, University College of North Wales, Bangor, Gwynedd, Wales

Summary: Despite recent advances in the understanding of the pathophysiology of movement disorders, little is known about the precise function the basal ganglia play in the control of movement. We review an approach to studying the function of neural systems that is based on the use of a class of computer models known as parallel distributed processors (PDPs) and indicate its potential range of applications to the study of movement disorders. PDPs can be used to construct computational devices that take into account the anatomical and pharmacological properties of real neural systems. They can also provide computational-level insights that can lead to novel hypotheses concerning brain function. We discuss both these approaches and outline a scheme of the functional organization of the basal ganglia, which predicts some of the pathophysiological mechanisms that mediate movement disorders and which can be formally modeled on a computer. Key Words: Basal ganglia-Parallel distributed processor.

CURRENT APPROACHES TO THE STUDY OF THE FUNCTIONAL ORGANIZATION OF THE BASAL GANGLIA Little is known about the precise function the basal ganglia play in the control of movement. The variety of movement disorders that result from different basal ganglia pathologies have been extensively studied and are well characterized. This has resulted in the evolution of a rich clinical vocabulary that can describe and classify abnormal movements. For example, hyperkinetic disorders can be dissociated on the basis of their physical appearance and categorized using terms such as chorea, athetosis, and ballism (1,2). Advances in experimental neurology have enabled statements to be made about the mechanisms that underlie such conditions and have led to the realization that apparently diPTerent disorders may be mediated by common neural mechanisms (3-5).

Dyskinetic movements associated with basal ganglia dysfunction are often considered to be essentially normal patterns of movement that are released inappropriately and repeatedly in the disease state (6). This implies that the basal ganglia contain a store of programs, or pointers to programs, for crude “prototype” movements that are triggered inappropriately in dyskinesia. From this perspective it follows that an understanding of the way in which motor programs are synthesized, stored, and executed is of critical importance in understanding the functional organization of the basal ganglia. More specifically, one would need to know how the programs are represented and what mechanisms control their release. These questions can be thought of in terms of both the anatomical structures involved and the nature of the information computed. Unfortunately, little progress toward answering these questions has been made. Part of the difficulty lies in the inappropriateness of our vocabulary for describing the complex functions that the basal ganglia perform. Much of the terminology used has been borrowed from control theory and has been

Address correspondence and reprint requests to J. M. Brotchie, Experimental Neurology Group, Department of Cell and Structural Biology, University of Manchester, Manchester, M13 9PT, England.

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extensively used by physiological psychologists. For example, the basal ganglia are said to be involved in sensorimotor integration. However, in the context of basal ganglia function, this statement is both true and nonpredictive. Because the structures are situated between the sensory inputs that enter the brain and the motor outputs leaving it, they must in some sense be involved with sensorimotor integration. In addition, the statement fails to make any qualification about the nature of the integration that takes place. Similar criticisms can be leveled at the use of terms such as feedback loop, regulate, gate, and relay, which are used in “black box” descriptions of basal ganglia organization. These terms have little descriptive or predictive value in the absence of data concerning the type of information being processed or the rules that govern that processing. We intend to illustrate how the adopting methodologies from the field of cognitive science and computational neuroscience may begin to enable us to define the transformational rules that convert inputs into outputs in the basal ganglia. Recent advances in computational neuroscience have shown that networks of neural-like elements with simple learning rules can accomplish impressive cognitive feats. This has led to the development of a class of computer models known as parallel distributed processors (PDPs) (7). These networks have many features similar to a biological nervous system, although there are also many differences. In this theoretical article we discuss several ways in which the PDP approach may offer a more constrained and genuinely explanatory approach to basal ganglia function. We also present the background to a more specific network design that could provide a qualitative model of the basal ganglia. In defining this system we have attempted to adhere wherever possible to the known neurobiology of the basal ganglia. The ideas presented are somewhat speculative, but serve to illustrate the potential of a PDP approach to the problem of accounting for information processing in the basal ganglia in normal and disease states. Parallel Distributed Processing It is intuitively obvious that brains and computers process information differently. Computers are good at computational tasks such as arithmetic but are relatively poor at solving problems such as the complex pattern recognition tasks that the human visual system finds trivial. The reason why the

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brain is so good at such tasks appears to lie not in the speed of processing (brains compute at much slower speeds than computers), but in that brains compute in a massively parallel manner, whereas traditional computers process information sequentially. Recently, there have been dramatic advances in constructing and simulating devices capable of parallel processing. These devices are of great interest to neurobiologists and cognitive psychologists because they offer a potential tool with which to understand how the structure of the brain governs its functioning in both health and disease. PDP models represent such a tool. PDPs or connectionist architectures consist of networks of highly interconnected simple processing elements (8). The individual processing elements are capable of performing only trivial mathematical operations, such as summating the values of inputs or subtracting threshold values. However, the highly interconnected nature of the network enables the system to solve extremely complex problems that traditional computers cannot. The activity of a processing element is determined by the sum of the inputs, and the interconnections provide a means for processing elements to influence each other. The activity in any connection (i.e., the input to a processing element) is generally determined by transforming the activation by a transfer function, which is usually sigmoid or linear. Furthermore, the connections are weighted, such that they can be either positive or negative. An input can therefore either excite or inhibit a processing element depending on the sign of the weight. The functional strengths of the connections are not fixed but can be changed in accordance with certain learning rules. An example of a simple but important learning rule is the Hebb rule, which, in its most general form, states that connectional strengths will be increased whenever the input to an element is activated at the same time as that element (9). Other frequently used learning rules include the delta rule and competitive learning rule (5,7). The functional properties of a PDP are determined in part by its architecture or anatomy and by the type of learning rule, transfer, and summation functions used. There are thus many types of PDPs or networks that can be defined by different combinations of basic architectures and processing rules, each type having its own characteristic problem-solving features. The types of PDPs that will be described here as potentially useful in accounting for the functional organization of the basal ganglia include pattern-

COMPUTER MODELS OF THE BASAL GANGLIA association nets and Jordan nets. These nets are useful for solving specific classes of problems, such as feature extraction, pattern recognition, or temporal sequencing. PDPs have been adopted by psychologists in order to model various cognitive processes. This has enabled the discovery of powerful brainlike algorithms for performing highly specific tasks such as code generation and phoneme recognition (1&12). PDPs are also of interest to neuroscientists, because they may help to explain how biological systems underpin complex cognitive functions. Neuronal systems can be mapped onto a PDP in a variety of ways. One possibility, which we will investigate in some detail, is to assume that the units of PDPs represent neurons, connections represent axons, and the changing weights represent altering synaptic efficiencies. These assumptions allow the construction of connectionist architectures that provide a metaphorical representation of the anatomy that subserves complex cognitive functions. Thus, PDPs can be used to construct explicit models of real neural systems by using the anatomical and neurophysiological information on that system to constrain the architecture (and processing rules), and therefore the functional properties, of the network. This technique has been successfully applied to studies of the hippocampus and has demonstrated the potential mechanisms by which this stores and retrieves information (13). Similarly, the olfactory and visual cortex have been modeled and this has provided insights into how these regions may process information (14,1.5). Important dissimilarities may exist between real and artificial neural networks. For example, the assumption that units of PDPs can be seen as representing neurons is not uncontroversial. Shepherd (16) has argued that the units of PDPs cannot straightforwardly be interpreted as analogous to neurons, because the complexity of real neurons is ignored by such models. Whereas the PDP approach generally assumes summation of activity at a single neuron, the many synapses on the outer parts of the dendritic tree are of computational significance in real biological systems and may represent independent computational units. The principle that real connections in the brain are generally either excitatory or inhibitory, not both, is also ignored by most current PDP approaches. In light of the important differences between real and artificial neural networks, it is important to emphasize the valuable roles that PDP modeling can

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play even in the absence of strict neurobiological plausibility. First, understanding the general computational principles governing the operation of large networks of simple computational elements can be enlightening in itself. For example, it is known that different properties of visual images are processed by separate cortical pathways in primate visual processing. Rueckl et al. (17) have shown through computational modeling how a division like this can be explained. It appears that more efficient representations of identity and location information are formed by a PDP system if resources are split between the two tasks. Another example is provided by studies that have proposed mechanisms at the computational level by which abnormalities of dopamine transmission might lead to the cognitive deficits of schizophrenia (18,19). These examples illustrate how general computational insights, which are applicable to the understanding of real nervous systems, can emerge from models that characterize computation at more abstract levels. Later we will show how this same approach can be used to formulate novel hypotheses concerning the structure and function of the basal ganglia and their role in the control of movement. PDP modeling that is even further removed from known neurobiological constraints can still be useful insofar as it requires the provision of a computationally explicit account of the processes to be understood. Talk of motor programs, for example, can lack explanatory content in the absence of any formally explicit account of the assumed mechanisms. The attempt to formulate one’s hypotheses in the form of a computer program can reveal inadequacies and inconsistencies that were not apparent in the purely verbal formulation of a model. Thus, PDP modeling can be useful on several levels in understanding neural functioning. In this article we are mainly concerned with discussing ways in which PDP models of the basal ganglia could be constructed that take as much account as possible of the known neuroanatomy, but we also provide examples of potential contributions from the PDP approach at other levels. In general, there is a need for a combination of “top-down” and “bottom-up” approaches, combining computational level insights and neurobiological constraints, if the neuroscience of movement disorders is to be understood. The networks in PDP models are capable of learning by changing the strengths of the connectional weights in an appropriate manner. There is evidence to suggest that such procedures underlie

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learning in real biological systems, many of which are thought to be mediated by excitatory amino acid (EAA) transmission. For example, a structural change in certain synapses accompanies learning in chicks and leads to increased numbers of postsynaptic densities (20). This is accompanied by an increase in the number of postsynaptic EAA receptors (21). There are several other lines of evidence that suggest that this and other changes in connectional strengths are controlled by EAA transmission. Thus, Morris has demonstrated that the ability of a rat to learn the spatial location of objects in a water maze task is blocked by the intraventricular administration of EAA antagonists (22). EAA antagonists are also capable of interfering with the process of competitive learning by which the retinotectal and geniculostriate topographic maps are established in the neonatal visual system (23,24). The latter process may act through an EAA-stimulated inositol triphosphate (IP,) system, which is only activated during the so-called critical period of the neonate (25). It is also well established that Nmethyl-D-aspartate (NMDA) receptors, a subtype of EAA receptors, are capable of mediating changes in synaptic efficiency through the physiologically defined process of long-term potentiation (LTP) (26). In addition to chemically evoked changes in synaptic efficacy, long-lasting alterations in responses at electrically mediated gap junctions have also been reported, but it appears that even these synaptic changes are reliant on activation of an associated chemical synapse where an EAA is a transmitter (27). LTP is defined as a long-lasting increase in the sensitivity of a cell in response to released transmitter, and thus represents a way of changing the connectional weights. This biological process is of great relevance to PDPs, because it suggests a mechanism by which learning rules can be implemented. In particular, it is thought that LTP may represent a way of implementing the Hebb learning rule. The Hebb rule, as mentioned previously, states that the strength of a connection is changed in proportion to the product of the activation of both the input and output neuron; that is, a connection can only be strengthened if the input and output are coactivated (9). This learning rule would enable the immediate matching of two inputs to form associations and is accordingly thought to underlie associative memory. For the rule to be implemented by the brain there must be some sort of mechanism whereby the postsynaptic neuron can communicate with the pre-

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synaptic input to it. Such a “handshaking” mechanism has been described in LTP between pre- and postsynaptic components (26). The Hebb rule also derives biological viability from the local nature of implementation because all the information required for adjusting a synaptic weight is present at that synapse. This is not necessarily the case with other learning rules such as the generalized delta rule implemented in back propagation. Here information is transferred from output units to the input processing elements via hidden units (i.e., units that are neither connected directly to the input or the output), and thus in its biological counterpart would necessitate a means of transferring information retrogradely down axons. However, back propagation can be seen as one way of implementing the learning procedure known as gradient descent, and it is possible that the same algorithm is implemented in real biological hardware, but in some other way. LTP has been studied mainly in the hippocampus, but it is clear that it can be elicited in a wide range of structures, including various cortical areas and the tectum (28-30). All of these structures have high densities of NMDA receptors, which is in keeping with the critical role that these receptors are known to play in the initiation and maintenance of LTP (26,31). From this it could be argued that any brain region that lacks high densities of NMDA receptors may not be capable of LTP, and conversely any brain region that has an abundance of NMDA receptors may be capable of LTP. However, not all forms of EAA-dependent learning processes act via NMDA receptors. As mentioned earlier, transient increases in EAA-induced inositol phosphate metabolism may underlie some learning processes (25). This effect appears to be mediated through a non-NMDA EAA receptor, though little is known about the precise mechanisms involved. Additionally, a form of LTP induced by potassium channel blockers involves actions at non-NMDA receptors (32). We believe that different EAA receptors subtypes may be responsible for mediating different types of plasticity and may therefore reflect the biological implementation of different learning rules. It follows therefore that a detailed knowledge of EAA transmission in the basal ganglia and its associated structures is required in order to construct a PDP model of this system. The next section describes the general layout of a PDP model, which we are developing in order to describe the functional organization of the basal

COMPUTER MODELS OF THE BASAL GANGLIA ganglia. The approach has enabled us to begin constructing a neurobiologically constrained scheme that could account for how cortical afferents arriving in the basal ganglia interact with the inputs from the thalamus and the substantia nigra in order to result in appropriate motor programs that are executed in a correct temporal sequence. We have attempted to use knowledge of the neurobiology of the basal ganglia to constrain the model wherever possible. Eventually, of course, the scheme will need to be made sufficiently explicit to be formally modeled on a computer. At present, we are simply concerned with showing how the PDP modeling approach is potentially a valuable one for investigating basal ganglia function and movement disorders. GENERAL SCHEME OF A FUNCTIONAL MODEL OF THE BASAL GANGLIA A possible general scheme of the functional organization of the basal ganglia envisages the basal ganglia and associated structures as a system of three interconnected networks or PDPs. The three networks are broadly equivalent to the striatum, the globus pallidudsubthalamic nucleus (GPISTN), and the ventral thalamus. The three networks are interconnected such that there is a flow of information between nets. Thus, the output of the striatal net forms the input for the GP/STN net and it in turn provides the input for the thalamic net. The output of the thalamic net is thought of as being a collection of effector commands and so might be considered to be equivalent to rudimentary motor programs, or pointers to such programs, which are selectively activated by correctly associated pallidal inputs. We will describe mechanisms by which the anatomy of the basal ganglia is able to implement a temporal dimension to motor control. Each of the nets has specific functional properties, the properties arising from the nature of its anatomical configuration, its EAA receptor pharmacology, and the so-called learning rules. Delong has suggested that the basal ganglia can be thought of as containing several anatomically distinct loops that operate in parallel (33). For the sake of simplicity we will concentrate on one loop, namely the putaminal part of the striatum and its output to the medial segment of the globus pallidus. We speculate that the same general rules will operate in all of the loops, but the specifics of the information processing will vary according to the precise nature of the anatomical afferents in each pathway.

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Striatal Net The anatomy of the striatum is well documented and can be used to constrain the architecture of the striatal net (34). The most striking feature is the massive topographically organized convergence of afferents from all areas of the cortex onto the striatum. In addition, the striatum receives major inputs from the substantia nigra pars compacta and from the centromedian and parafascicular nuclei of the thalamus. The synapses of the major inputs to the striatum are located in specific regions on the dendrite (35). Cortical afferents are known to synapse onto the heads of the dendritic spines on the striatal output neurons. In contrast, the dopaminergic inputs from the substantia nigra pars compacta synapse on the necks of the spines and thus are in a strategic position to regulate the cortical input. The position of the thalamic inputs is currently unknown but preliminary observations suggest that it may be on the necks of the dendritic spines (Fig. 1). The transmitter used in the corticostriatal projection is known to be an EAA, probably glutamate (36). In keeping with this idea, several subtypes of EAA receptors have been visualized in the striatum, NMDA receptors being found in particularly high densities (26,31). These anatomical and pharmacological properties can be used to begin to construct a PDP model of the striatum. The architecture suggested by these properties resembles that which underlies many devices that act as pattern associators. Pattern associator models Pattern associators represent one of the basic types of network architectures and have been extensively used in conjunction with distributed memory problems (37). They are based on arrays of intersecting elements such that elements in one plane represent inputs, whereas elements in another plane represent outputs. The network is of an essentially simple design, containing no hidden units but consisting of just one layer of units that is capable of making associations. The activity of each output element is determined by the action of the inputs interacting with the connectional strengths on it. The general properties of these nets and their ability to make associative memories of patterns of activity can be seen easily if we study a simple case. Imagine that the inputs and outputs are given in the form of simple binary vectors 1 and 0. The weights of all the connections will initially be set at

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\

t\t\t\/ \ FIG. 1. Diagram illustrating the relative positions of terminals from different inputs on striatal dendrites. Note how the dopamine input from the substantia nigra pars compacta synapses onto the neck of the striatal dendrite, which places it in a strategic position to regulate the activity of the cortical and thalamic inputs to the cell. SNC, substantia nigra pars compacta; CM, centromedian nucleus.

Cortical neuron

-

Striatal output neuron

zero and incremented by the most simple form of Hebb learning rule (Eq. 1) during the learning stage. The summation rule for computing the activation is a simple arithmetic sum acting on a threshold (Eq. 2). The activation is transferred to the output by a simple linear transfer function whereby the output equals the activation. A threshold (0) can then be set, which determines whether or not the output neuron gives an output. Let wij be the connection weight between the input unit j and the output unit i, and A w be ~ the change to be made in the strength of the connection between the input unit j and the output unit i. Aw.. = a. * II 1

0. J’

(1)

where a, is the activation of the output unit and oj is the output of the input unit; ai =

(ZOj

*

WJ

- 0,

(2)

where 0 is the threshold value for activation of the output unit. The network can be “trained” to learn to associate a variety of patterns of inputs with a specific output by using the rules outlined above. Thus, when the network initially receives its inputs (i.e., in a learning phase), the connection weights are altered in accordance with the simple rules. Later, that is, in a recall phase, the weights are clamped and the activation of the units is calculated without any reference to the learning rules. This procedure

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enables the network to learn to associate many input vectors with a specific output extremely quickly; in fact, the associations can be made with just one presentation of the initial input pattern (37) (Fig. 2). The trained network possesses many properties that are common to all PDPs and the brain. One such property is termed graceful degradation (7). This refers to the phenomenon whereby disruption of a network or brain does not render it completely useless, but instead, results in a gradual breakdown in function. Thus, a network will still give the correct output for a specific input even after a large number of synapses have been removed from it (Fig. 3). The network is also capable of making limited generalizations. The correct response can thus be given to an input that deviates from the ideal or expected one. For example, if a similar input vector is given, say (0.8, 0.1, 0.8, 0.1, 0.1) instead of (1, 0, 1, 0, 0) then the correct output will be given. The network is also capable of “completion,” whereby a correct output can be given even when part of the input is corrupted. Thus, the network may still be able to give the correct output vector if parts of the input vector are either missing or incorrect. For example, a network might be able to give the desired output in response to an erroneous input pattern of (01011) instead of the correct input pattern of (01001). In this manner the networks serve to filter out noise from an input.

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FIG. 2. Diagram of a simple pattern associator. The horizontal lines can be thought of as representing axons of processing elements in the input layer and the vertical lines as dendrites of output units. Each of the circles at intersections of input axons and output dendrites represents a connection weight, Note how the intersecting axons and dendrites can implement a local learning rule such as a Hebb rule. They can be trained to give specific output patterns in response to an input pattern. Processing elements are either on or off (1 or 0). The net has been trained to associate three pairs of inputioutput patterns (the input patterns are 0101 1, 11100, and 10101; their respective output patterns are 00110, 10011, and OlOOO). Filled circles indicate connections that have been strengthened during the training stage. The effect of stimulation on the dendrite of each output element is summated. If the sum exceeds the threshold value (in this instance 0 = 2) then the output neuron is activated as signified by an activation score of 1.

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4 II(

4 4 H SUM

3

e=2

I IIIIIII

ACTIVATION OUTPUT

The striatum as a pattern associator

It is conceptually easy to map the anatomy of the striatum onto a PDP capable of pattern association. The output elements of the pattern associator can be thought of as the striatal output neurons (Figs. 2 and 3). The input elements can be thought of in terms of the corticostriate fibers that synapse onto

2 IIIIIIIIIII

d

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the striatal dendrites. Each striatal cell would be expected to receive an input from many cortical cells in view of the convergence of the cortical output on to the striatum. The changing connectional strengths could be subserved by NMDA receptors that, as we have already noted, are both particularly abundant in the striatum and suitable for implementing a Hebbian learning rule. Such a system

FIG. 3. Diagram of a simple pattern-associating net to illustrate the principle of graceful degradation. The diagram represents the trained net described in Fig. 2, which has been “lesioned.” The net can function entirely normally and give the correct outputs for the three given input patterns, even though 24% of the synapses in this net have been removed.

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would be able to construct immediate associative representations of cortical activity. The striatal output neurons in such a system would only be activated by specific complex spatial patterns of cortical activity. The dopaminergic input from the nigra could play an important role in such a system. As stated earlier, the dopaminergic afferents synapse onto the necks of the dendrites (35). Furthermore, the ascending dopaminergic pathway has a much more diffuse topography than the corticostriatal pathway (38). Cohen and Servan-Schreiber (18,19) have argued that the effects of catecholamines can be modeled in terms of changes in the input-output functions of particular units. Here we assume that the dopaminergic pathway could serve to set the threshold value that the output neurons would have to exceed in order for the cell to fire, which can be expressed mathematically as 0 (see Eq. 2). The threshold would have the action of stopping unwanted firings in recall stage. In order to model the striatum, the inputs to each unit will not be represented by binary notation but by graded levels of activation. The activations will be transformed by a nonlinear transfer function, that is, a thresholded sigmoid function. This is necessary to allow for the fact that neurons have a maximum firing rate and do not increase firing rate as a linear function of soma1 activation. This simple Hebbian learning rule described above is not entirely appropriate for modeling striatal function. This follows from the fact that if the system experiences a certain input more than once during a learning stage the synaptic weights will be further strengthened and with time (in a nondecaying system) will tend to infinity. To overcome this problem we have used a learning rule known as the delta rule (39). With this rule, the change in the weights of the synapses is driven by the difference between the observed output and the desired output. The delta rule is not normally implemented in biologically constrained systems because in most nets it requires the back propagation of information from the output layer to units that do not synapse directly onto them. This would require mechanisms, such as the retrograde transport of information, which are generally considered to be biologically implausible. In a single-layer network, however, this is not the case. In a system that implements the delta rule, the change in weights is driven by the difference in the value of the actual output from the value of the target output. This ensures that no further changes

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of weights will occur once the system has learned successfully. This may be important for the striatal model, as NMDA receptors are present throughout life and the striatum will presumably be capable of changing synaptic efficacy and thereby making new associations throughout life. Implications for pathophysiology of movement disorders The model striatum outlined would be consistent with some of the pathophysiological properties seen in the parkinsonian striatum. Evidence from 2deoxyglucose, in situ hybridization, and electrophysiological studies have demonstrated that striatal output cells increase their activity in the parkinsonian primate (40-43). This effect is also a property of the model. We argued above that the activation threshold (0) is set by dopamine. Thus, we speculate that if the dopaminergic input is removed, as is the case in parkinsonism, the threshold would fall and the probability of a given striatal output cell firing in response to a specific pattern of cortical activity would increase (Fig. 4). The model would also predict that the response specificity of the striatal output cells would alter. Decreasing the threshold gain on the striatal output cells will effectively increase the number of cortical input patterns that can make the cell fire, that is, reduce the specificity of the cell. Thus, if the response properties of the striatal cell reflect the cortical representation that is inputing onto it, the cell will fire to a wider range of stimuli. In the example given previously (Fig. Z), the input vector 11100 resulted in the output vector 10011. When the threshold 8 is decreased to 1, the same input gives the output vector of 11011. An output element is now activated on presentation of an input vector to which it was previously unresponsive (Fig. 4). Evidence for a similar process has been seen in unit recording studies in MPTP-induced parkinsonian primates. Filion has demonstrated that individual striatal cells in the normal brain are known to respond to passive movement of a specific joint (38). Equivalent cells in parkinsonian striatum show decreased response selectivity such that the cell responds to the movement of several joints. The nature of the dopaminergic input to the striatum, however, is not clear. Dopamine can have apparently different effects on the direct and indirect pathways from the striatum as a whole (44). The mechanisms underlying these functional effects have not been elucidated and may reflect different actions of

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FIG.4. Computational-level effects of altering activation thresholds in the simple pattern-associator network described in Fig. 2. By decreasing the threshold (0 now equals l), the output units respond to a wider range of input patterns. This can be mapped onto the functional anatomy of the striatum. As discussed in the text, dopamine could serve to set 0 in a pattern-associator model of the striatum. The output neurons in the parkinsonian striatum might accordingly discharge to a wider range of cortical stimuli.

dopamine at the two populations of striatal output cells. Alternative explanations may reflect a computational-level property derived from differences in the fine anatomy of the output pathways, for example, due to differences in recurrent collateralization or other interneuronal connections. PDP modeling techniques have already provided useful insights into the ways in which topographic maps, of the type found in the striatum and elsewhere, can emerge as a natural consequence of the computational properties of networks of simple neuronlike elements (45). This provides another example of ways in which the PDP approach can aid in understanding observed neurobiological phenomena from a computational point of view. The output of the striatal net will be used as the input for the GP/STN net which will now be described.

GPlSTN Net The majority of the striatal output ultimately makes contact with the medial segment of the globus pallidus. This is achieved via two major routes, either directly via the striatomedial pallidal pathway, or indirectly via the projection from the striaturn to the lateral pallidal segment, which projects in turn to the medial pallidal segment via the intermediary of the subthalamic nucleus (46). In addition to projecting to the medial pallidal segment, the

subthalamic nucleus also projects back onto the lateral segment. There is also some evidence to suggest that the lateral pallidal segment projects to the medial palIidal segment (47). The nuclei involved in this system are anatomically relatively simple. Bbth segments of the globus pallidus and the subthalamic nucleus contain only one cell type and few, if any, interneurons are found in these structures (48,49). In contrast to the striatum, the GP and STN contain many NMDA receptors, even though the major transmitter used by the STN is known to be an EAA (26,31,50,51-53). The pattern of interconnections between the globus pallidus and the subthalamic nucleus may impose interesting computational properties on this anatomical system. An indication of these properties can be seen by looking at simple simulations using nonbiologically constrained nets. Reciprocal connections of the type made between the lateral pallidal segment and the subthalamic nucleus are particularly useful when processing tasks that involve the use of internal “hidden” representations. Minsky and Papert (53) showed that simple neuronlike computing elements (perceptrons) could not compute certain elementary problems, such as exclusive/or- (XOR-) type decisions. XOR tasks involve making a response on the basis of the similarity of inputs. An example of a simple XOR problem would be to compare two inputs and to make a

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given response if the two inputs are the same but to give an alternative response if they are different. This can be illustrated using the following simple example based on a set of vectors of binary numbers (0,O; 0,l; 1,O; 1,l). The problem would entail giving an output of 1 if the inputs are 1 , 1 or 0,O but giving an output of 0 if the inputs are 1,0 or 0,l (i.e., give an output of 1 if the two numbers are the same but 0 if the numbers are different). This is a nontrivial problem because the input representations are not easily mapped onto an output representation, that is, the inputs and the outputs can look completely different; indeed the inputs with least overlap (i.e., 1,l and 0,O) lead to the same output. Part of the resurgence in PDP modeling over the last decade has arisen as a result of the observation that suitable neural network architectures can in fact solve problems of this type (39). A simple net loosely relating to the anatomical arrangement of the globus pallidus and the subthalamic nucleus can easily learn to solve an XOR problem. This network consists of five interconnected nodes. Two of the nodes can be used to represent two different striatal outputs, the other nodes representing the medial and lateral segments of the globus pallidus (GPM, GPL) and STN. The nodes can then be connected up in an arrangement based loosely on the projection anatomy of the basal ganglia (Fig. 5). [Note, in this highly simplified example, that we have assumed that each striatal cell sends collateral projections to both pallidal segments. However, in primates, it is thought that the degree of collateralization is small (46).] The network can then be trained to solve an XOR problem by feeding in the set of training data (binary numbers) and comparing the actual output of the system with the desired output. The delta rule can be used as the learning rule such that an error signal can be calculated and used to alter the connectional strengths. Its connectional weights are initially assigned randomly. The network is given presentations of sets of training data to which it applies the delta rule. This simple network soon reaches an equilibrium state, where its connectional strengths no longer change and it always gives the correct output for any pair of inputs. In its own right, this is not a surprising finding because problems of this type can be solved by many PDPs, provided they have a layer of hidden units that connect an input layer of units with an output layer (39). However, the network does have two surprising features. First, for a net to solve a

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FIG. 5. The basic inputautput connections of the GP/STN net. A simple PDP circuit was constructed where the arrangement of processing elements and their connections was similar to the basic organization of the af€erents and efferents of the pallidal complex. This arrangementof processing elements appears to be particularly suited to solving XOR problems. In solving these problems the synaptic weights must be in keeping with known biological data; i.e., all connections are inhibitory except those from the node analagous to the subthalamic nucleus, which have positive weights (i.e., are excitatory). STN, subthalamic nucleus; GPI, lateral segment of the globus pallidus; GPm, medial segment of the globus pallidus.

simple XOR problem it is usually necessary to incorporate a bias element that has the effect of making a neuron always active unless it is turned off. In the simple GP/STN network described here there is no need for the inclusion of a bias element. We were unable to find any other arrangement of five interconnected processing elements that could solve the XOR problem in the absence of a bias element. We believe this is due to the presence of the excitatory STN loop in the circuit. Indeed, any significant deviation from this pattern of connections results in an inability to learn. This is of particular interest as we consider a bias element to be biologically implausible. Second, the network solves the XOR problem by choosing synaptic weights that are in keeping with known biological data. Thus, all the synapses in the network are inhibitory with the exception of the outputs of the node, which is analogous to the

COMPUTER MODELS OF THE BASAL GANGLIA subthalamic nucleus. All outputs from this processing element have weights that are positive (equivalent to an excitatory transmitter). The significance of this finding is hard to gauge, but it is interesting to note that the probability of all the signs of synaptic weights occurring correctly by chance alone is very low. Clearly, this network is not biologically constrained, but it does indicate how the GPlSTN may be ideally constructed, in terms of connections and transmitters, to solve problems that contain a complex XOR comparison of the output of the striatal net. Note that the XOR task here is simply being used to represent a general class of computational problem that can be problematic for some neural net architectures; no claim is being made about the particular computation that is being performed by this part of the basal ganglia. Autoradiographic studies of both rat and human GP have demonstrated that EAA receptors appear transiently in the neonate and disappear in the adult (5435). The observation finds parallels with work on the organization of the visual cortex during the so-called critical period for synaptic modification in the kitten. During the critical period, an IP, system is active which is regulated by EAA transmission (25). The close temporal correlation of developmental profile of EAA-stimulated IP, and the postnatal changes in cortical susceptibility to visual deprivation implies that this system plays a critical role in developmental plasticity. The EAA receptors expressed transiently in the neonatal GP have a pharmacological profile consistent with those related to inositol phosphate metabolism. We suggest that these receptors are concerned with some critical role in the developmental organization of the basal ganglia and hence the development of motor control. The precise developmental role of such a system is unclear, although it is tempting to speculate that it may have a role in training the GP/STN net such that it can correctly execute associations with similar computational properties to XOR-type tasks. This net has the useful property of being able to give the same output vectors in response to vastly different input vectors from the striatum. This may provide a means by which the GPM can elicit similar motor commands in different situations (56-58). Thalamic Net The main output of the medial segment of the globus pallidus is known to terminate in the ventral anterior (VA) and ventral lateral (VL) nuclei of the

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thalamus (59). The medial pallidal segment also sends fibers to the intralaminar thalamic nuclei, particularly the centromedian nucleus. The output of the GP/STN net will accordingly be used as the input for the thalamic net. The VNVL thalamic nuclei also receive major inputs from the motor cortex. These inputs are topographically organized such that the primary motor cortex projects to the cerebellar territory of the VA/VL thalamus, the supplementary motor cortex to the pallidal territory, and frontal eye fields to the nigral territory (59). The VA/VL thalamus could be represented by a pattern-associating net in much the same way as we have represented the striatum. Thus, the neurons of the medial pallidal segment can be thought of as terminating on the dendrites of the thalamic output cells, which in turn project to the motor (mainly supplementary) cortex. The precise relationship between the cortical input and the pallidal input on these dendrites is unclear. It is known, however, that the transmitter used by the pallidum is GABA whereas that used by the cortex is glutamate (60,6 1). Given that the VNVL gets a large cortical input, the presence of large numbers of EAA receptors in the adult of many species is hard to demonstrate (26,31). This may imply that the ventral thalamus may not be able to engage in many of the EAAmediated forms of plasticity. As such, the thalamic net in the adult might be considered to be a pattern associator, which is incapable of forming new associations. The net would thus be stuck in a recall mode. The output of the thalamic net will be governed by the interaction of the cortical and pallidal inputs terminating on the thalamic dendrites. As stated above, the output of the thalamic net is assumed to be equivalent to a series of motor commands directed at the cortex (rudimentary motor programs or pointers to such programs), which are selectively activated by correctly associated pallidal inputs. The thalamic net can thus be thought of as acting as a pattern associator of primitive motor commands. Because the strengths of the synaptic weights may be thought of as being invariant, the interaction will be governed solely by the pattern of the input activity and the unchanging connectional weights. If there are no thalamic cells activated, then no pattern will be modulated by the ventral thalamiccortical loop. This may be the case in parkinsonism where bradykinesia results from excessive thalamic

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inhibition due to the overactivity of the GABAergic pallidothalamic pathway.

TEMPORAL SEQUENCING AND JORDAN NETS Motor control obviously involves temporal sequencing of effector (motor) commands in response to a particular sensory input (world state). In PDP models it has been shown that it is possible to obtain temporal sequencing of output vectors in response to a static input vector by means of a recurrent loop from the output to the input layer (62). The issue of how dynamic behavior can emerge in simple networks of neuron-like computing elements is of great current interest in connectionist theorizing (63,64). One approach to the representation of time in PDP networks is to make the inputs to a network sensitive to the history of recent outputs. This was the approach adopted by Jordan (63). Figure 6 illustrates the basic architecture of a Jordan net. A static, unchanging input is represented as a pattern of 0s and 1s over the plan units. On each time cycle a corresponding pattern is computed on the output units as in a standard network. After each output is produced, it is copied over to the state units in such a way that the state units always represent a decaying average of recent outputs. This representation acts as part of the input on subsequent time cycles, thus providing a temporal context and permitting the output of the network to cycle through a sequence of different outputs. Networks with this general architecture have been used to model sequential processes such as spoken word production (64) and human short-term memory (65). For present purposes, the key insight that arises from this approach concerns the possible role of recurrent connections in enabling dynamic behavior to emerge. The basal ganglia are rich in such recurrent loops. In particular, the essentially reciprocal connections between the V N V L thalamus and the motor cortex will impose interesting properties on the net. As discussed above, the pallidal input to the thalamus is derived from the striatum and thus represents the output of the whole of the neocortex. This input can be thought of as being derived, via the striatal and GPlSTN nets, from the total sensory perceptions of the external world, as well as a representation of the internal state and motivational states of the person/animal. In contrast, the input from the motor cortex will simply represent the motor information. The supplementary motor cortex input to the thalamus would convey information

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Sequential output from network

Unchanging input to network FIG. 6. The basic design of a Jordan net. This network is capable of providing sequential output in response to a static input. This property of the network is dependent on recurrent connections from the output units to state units that provide part of the input to hidden layers of the model. Arrows reflect the direction of flow of information throughout the network.

about the instruction that had just been sent to the primary motor cortex. This recurrent loop would thereby give an input to the thalamus that describes the motor commands that had just been sent to the motor cortex. The cortical input in effect represents a feedback loop from the output layer of the thalamic pattern associator back to the input layer. Hence, we are left with a situation that is analogous to a Jordan net and is therefore ideal for eliciting a temporally spaced pattern from a specific input from the GPM. This would clearly be invaluable when trying to sequence movements in a correct temporal sequence. A specific sensory input would therefore be able to elicit a series of temporally sequenced movement commands that would constitute collectively a motor program. As stated earlier, part of the pallidal output projects to the centromedian nucleus, which in turns projects to the putamen. The identity of the trans-

COMPUTER MODELS OF THE BASAL GANGLIA

mitter in this pathway is unknown, but there is some evidence that it is glutamatergic (66).The precise position of the thalamic terminals on the striatodendritic spines is also unclear, but there is evidence to suggest that it does not compete with the cortical input for the head of the spine. This pathway may also play a role in the temporal organization of the basal ganglia by providing the striatum with an input detailing the activity of the output of the GPM/STN net which is initially derived from the corticostriatal representations. Again, this is analogous to a Jordan net and is most useful for getting the GP/STN loop to respond to a particular corticostriatal input vector with a set of temporally spaced output vectors. Hence it is possible, by virtue of the two recurrent loop systems, to elicit a sequence of motor commands from a single atemporal sensory input to the striatum. The GPM, by means of this loop, could provide the V N V L with a sequence of input vectors that would elicit a temporally sequenced string of simple motor commands, which constitutes a motor program. These loops are nested, so the range of complexity of temporal sequencing is immense. As described earlier, the corticothalamic loop does not appear to be associated with a highly plastic NMDA or EAA-activated IP, system in the adult (26,31). We feel that this implies that the loop would be unable to change the sequence of patterns the thalamic pattern associator controls. In contrast, the centromedian-striatal pathway appears to be intimately involved with an active NMDA pathway. This would allow the striatal net to elicit new sequences of simple motor programs in response to a given input. The output of the striatal “Jordanized” pattern associator will therefore provide a means of linking simple motor programs elicited by the thalamic pattern associator. These simple motor programs will themselves be temporally controlled due to the recurrent loop from the cortex VMVL thalamus. The computational properties of recurrent loops have been demonstrated in PDP networks of the type described by Jordan (62) and Elman (64). However, it is also appropriate to discuss ways in which an even more top-down approach could lead to novel hypotheses concerning basal ganglia function in a more global sense. Work on motor control within a neural network framework has focused on the cerebellum and has addressed issues such as robotic control and sensory-motor coordination. Computational level insights into the processes in-

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volved in motor control have also emerged. Attempts to solve nonlinear control problems, such as limb movement sequencing or reversing an articulated truck (67), have led to insights concerning the way such tasks must be divided up to maximize computational tractability. These problems are interesting and computationally difficult. Their unconstrained nature leads to the involvement of many degrees of freedom. Neural network research (62) has converged on the idea that a forward model must be constructed as a separate and earlier task from that of learning how to give the right instructions to effectors on the basis of network input (plans). In the case of Jordan’s example of controlling a robot arm, learning the forward model means learning which movements of the arm will result when effectors (i.e., muscles) are activated in a particular way. The forward model is acquired separately from learning which sequences of effector commands must be sent out to elicit desired movements of the arm in response to changes in the environment, that is, sensory input to the network. An advantage of this approach is that smoothness constraints can be incorporated into the control of movement. The richly recurrent structure of the basal ganglia suggests a role in encoding temporal dimensions in the same way as has been found necessary in artificial neural networks computing nonlinear movement control. Specifically, the complete Jordan architecture with a separate forward model requires time-delayed feedback from the forward model’s output units to (a) effector command units and to (b) state units that encode the network’s current estimates of the arm’s position in the world. There is also a requirement for recurrent connection between effector command units and further state units. In the basal ganglia, there are recurrent connections at least from (a) STN to GPL, (b) cortex to ventral thalamus, and (c) ventral thalamus to striatum (68). It would clearly be naive at present to attempt direct mapping between such recurrent links in the natural and artificial systems. It is tempting, however, to relate the process of forward model construction to EAA developmental plasticity in the basal ganglia, and to argue that early plasticity is due to the need to construct a forward model of the environment before subsequent motor learning can occur. An interesting parallei can be seen in the motor behavior of the human neonate. Apparently random limb movements are generally seen in the human

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newborn and have been described as physiological chorea (69). These choreiform movements overlap temporally with the transient expression of EAA receptors in the globus pallidus (55) and may represent the biological correlate of the construction of a forward model. This kind of consideration provides a rich source of hypotheses concerning possible basal ganglia function.

IMPLICATIONS In this paper we have aimed to show how PDP modeling can provide a powerful method for the study of movement disorders and the relationship between basal ganglia structure and function. The schemes laid out in this paper were intended to give some examples of how the functional organization of the basal ganglia could be understood in terms of PDPs. Even in its current (largely unimplemented) form, the scheme we have outlined is capable of offering new explanations to account for some of the clinical/experimental observations associated with dysfunction of the basal ganglia. However, the real appeal of what we propose lies in the feasibility of taking the various possibilities and modifying them such that they will be explicit enough to be formally modeled on a computer. The models will be sufficiently complex to have hidden properties that will emerge when a simulation is actually run on a computer. These emergent properties may give rise to hypotheses about the anatomy and physiology of the basal ganglia that can be tested experimentally. In addition, the validity of parts of the model, when implemented on a computer, can be tested by corrupting parts of the network in order to simulate different pathological conditions. The approach suggested by this paper may help to bridge the gap between theoretical studies on the control of movement and experimental work on the neurobiology of the basal ganglia and their role in disorders of movement. Hitherto, the functional/ psychological level theorizing has proceeded remarkably unconstrained by the known neuroscience-level microstructural constraints, and the low-level investigations have been equally uninformed by a knowledge of the functions to be computed. Acknowledgment: We gratefully acknowledge support from The Wellcome Trust; the Dystonia Medical Research Foundation, Beverly Hills, California; and the Medical Research Council.

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