Kevin N. Gurney

The basal ganglia : a vertebrate solution to the selection problem?

A selection problem arises whenever two or more competing systems seek simultaneous access to a restricted resource. Consideration of several selection architectures suggests there are significant advantages for systems which incorporate a central switching mechanism. We propose that the vertebrate basal ganglia have evolved as a centralized selection device, specialized to resolve conflicts over access to limited motor and cognitive resources. Analysis of basal ganglia functional architecture and its position within a wider anatomical framework suggests it can satisfy many of the requirements expected of an efficient selection mechanism.

Network 'small-world-ness': A quantitative method for determining canonical network equivalence

Background Many technological, biological, social, and information networks fall into the broad class of ‘small-world’ networks: they have tightly interconnected clusters of nodes, and a shortest mean path length that is similar to a matched random graph (same number of nodes and edges). This semi-quantitative definition leads to a categorical distinction (‘small/not-small’) rather than a quantitative, continuous grading of networks, and can lead to uncertainty about a networks small-world status. Moreover, systems described by small-world networks are often studied using an equivalent canonical network model – the Watts-Strogatz (WS) model. However, the process of establishing an equivalent WS model is imprecise and there is a pressing need to discover ways in which this equivalence may be quantified. Methodology/Principal Findings We defined a precise measure of ‘small-world-ness’ S based on the trade off between high local clustering and short path length. A network is now deemed a ‘small-world’ if S>1 - an assertion which may be tested statistically. We then examined the behavior of S on a large data-set of real-world systems. We found that all these systems were linked by a linear relationship between their S values and the network size n. Moreover, we show a method for assigning a unique Watts-Strogatz (WS) model to any real-world network, and show analytically that the WS models associated with our sample of networks also show linearity between S and n. Linearity between S and n is not, however, inevitable, and neither is S maximal for an arbitrary network of given size. Linearity may, however, be explained by a common limiting growth process. Conclusions/Significance We have shown how the notion of a small-world network may be quantified. Several key properties of the metric are described and the use of WS canonical models is placed on a more secure footing.

The brainstem reticular formation is a small-world, not scale-free, network

Recently, it has been demonstrated that several complex systems may have simple graph-theoretic characterizations as so-called ‘small-world’ and ‘scale-free’ networks. These networks have also been applied to the gross neural connectivity between primate cortical areas and the nervous system of Caenorhabditis elegans. Here, we extend this work to a specific neural circuit of the vertebrate brain—the medial reticular formation (RF) of the brainstem—and, in doing so, we have made three key contributions. First, this work constitutes the first model (and quantitative review) of this important brain structure for over three decades. Second, we have developed the first graph-theoretic analysis of vertebrate brain connectivity at the neural network level. Third, we propose simple metrics to quantitatively assess the extent to which the networks studied are small-world or scale-free. We conclude that the medial RF is configured to create small-world (implying coherent rapid-processing capabilities), but not scale-free, type networks under assumptions which are amenable to quantitative measurement.

The Basal Ganglia and Cortex Implement Optimal Decision Making Between Alternative Actions

Neurophysiological studies have identified a number of brain regions critically involved in solving the problem of action selection or decision making. In the case of highly practiced tasks, these regions include cortical areas hypothesized to integrate evidence supporting alternative actions and the basal ganglia, hypothesized to act as a central switch in gating behavioral requests. However, despite our relatively detailed knowledge of basal ganglia biology and its connectivity with the cortex and numerical simulation studies demonstrating selective function, no formal theoretical framework exists that supplies an algorithmic description of these circuits. This article shows how many aspects of the anatomy and physiology of the circuit involving the cortex and basal ganglia are exactly those required to implement the computation defined by an asymptotically optimal statistical test for decision making: the multihypothesis sequential probability ratio test (MSPRT). The resulting model of basal ganglia provides a new framework for understanding the computation in the basal ganglia during decision making in highly practiced tasks. The predictions of the theory concerning the properties of particular neuronal populations are validated in existing experimental data. Further, we show that this neurobiologically grounded implementation of MSPRT outperforms other candidates for neural decision making, that it is structurally and parametrically robust, and that it can accommodate cortical mechanisms for decision making in a way that complements those in basal ganglia.

A physiologically plausible model of action selection and oscillatory activity in the basal ganglia

The basal ganglia (BG) have long been implicated in both motor function and dysfunction. It has been proposed that the BG form a centralized action selection circuit, resolving conflict between multiple neural systems competing for access to the final common motor pathway. We present a new spiking neuron model of the BG circuitry to test this proposal, incorporating all major features and many physiologically plausible details. We include the following: effects of dopamine in the subthalamic nucleus (STN) and globus pallidus (GP), transmission delays between neurons, and specific distributions of synaptic inputs over dendrites. All main parameters were derived from experimental studies. We find that the BG circuitry supports motor program selection and switching, which deteriorates under dopamine-depleted and dopamine-excessive conditions in a manner consistent with some pathologies associated with those dopamine states. We also validated the model against data describing oscillatory properties of BG. We find that the same model displayed detailed features of both γ-band (30–80 Hz) and slow (∼1 Hz) oscillatory phenomena reported by Brown et al. (2002) and Magill et al. (2001), respectively. Only the parameters required to mimic experimental conditions (e.g., anesthetic) or manipulations (e.g., lesions) were changed. From the results, we derive the following novel predictions about the STN–GP feedback loop: (1) the loop is functionally decoupled by tonic dopamine under normal conditions and recoupled by dopamine depletion; (2) the loop does not show pacemaking activity under normal conditions in vivo (but does after combined dopamine depletion and cortical lesion); (3) the loop has a resonant frequency in the γ-band.

A computational model of action selection in the basal ganglia. II. Analysis and simulation of behaviour

Abstract. In a companion paper a new functional architecture was proposed for the basal ganglia based on the premise that these brain structures play a central role in behavioural action selection. The current paper quantitatively describes the properties of the model using analysis and simulation. The decomposition of the basal ganglia into selection and control pathways is supported in several ways. First, several elegant features are exposed – capacity scaling, enhanced selectivity and synergistic dopamine modulation – which might be expected to exist in a well designed action selection mechanism. The discovery of these features also lends support to the computational premise of selection that underpins our model. Second, good matches between model globus pallidus external segment output and globus pallidus internal segment and substantia nigra reticulata area output, and neurophysiological data, have been found which are indicative of common architectural features in the model and biological basal ganglia. Third, the behaviour of the model as a signal selection mechanism has parallels with some kinds of action selection observed in animals under various levels of dopaminergic modulation.

Computational models of the basal ganglia: from robots to membranes

With the rapid accumulation of neuroscientific data comes a pressing need to develop models that can explain the computational processes performed by the basal ganglia. Relevant biological information spans a range of structural levels, from the activity of neuronal membranes to the role of the basal ganglia in overt behavioural control. This viewpoint presents a framework for understanding the aims, limitations and methods for testing of computational models across all structural levels. We identify distinct modelling strategies that can deliver important and complementary insights into the nature of problems the basal ganglia have evolved to solve, and describe methods that are used to solve them.

Implementing Spiking Neural Networks for Real-Time Signal-Processing and Control Applications: A Model-Validated FPGA Approach

In this paper, we present two versions of a hardware processing architecture for modeling large networks of leaky-integrate-and-flre (LIF) neurons; the second version provides performance enhancing features relative to the first. Both versions of the architecture use fixed-point arithmetic and have been implemented using a single field-programmable gate array (FPGA). They have successfully simulated networks of over 1000 neurons configured using biologically plausible models of mammalian neural systems. The neuroprocessor has been designed to be employed primarily for use on mobile robotic vehicles, allowing bio-inspired neural processing models to be integrated directly into real-world control environments. When a neuroprocessor has been designed to act as part of the closed-loop system of a feedback controller, it is imperative to maintain strict real-time performance at all times, in order to maintain integrity of the control system. This resulted in the reevaluation of some of the architectural features of existing hardware for biologically plausible neural networks (NNs). In addition, we describe a development system for rapidly porting an underlying model (based on floating-point arithmetic) to the fixed-point representation of the FPGA-based neuroprocessor, thereby allowing validation of the hardware architecture. The developmental system environment facilitates the cooperation of computational neuroscientists and engineers working on embodied (robotic) systems with neural controllers, as demonstrated by our own experience on the Whiskerbot project, in which we developed models of the rodent whisker sensory system.

2009 Special Issue: Dopamine-modulated dynamic cell assemblies generated by the GABAergic striatal microcircuit

The striatum, the principal input structure of the basal ganglia, is crucial to both motor control and learning. It receives convergent input from all over the neocortex, hippocampal formation, amygdala and thalamus, and is the primary recipient of dopamine in the brain. Within the striatum is a GABAergic microcircuit that acts upon these inputs, formed by the dominant medium-spiny projection neurons (MSNs) and fast-spiking interneurons (FSIs). There has been little progress in understanding the computations it performs, hampered by the non-laminar structure that prevents identification of a repeating canonical microcircuit. We here begin the identification of potential dynamically-defined computational elements within the striatum. We construct a new three-dimensional model of the striatal microcircuits connectivity, and instantiate this with our dopamine-modulated neuron models of the MSNs and FSIs. A new model of gap junctions between the FSIs is introduced and tuned to experimental data. We introduce a novel multiple spike-train analysis method, and apply this to the outputs of the model to find groups of synchronised neurons at multiple time-scales. We find that, with realistic in vivo background input, small assemblies of synchronised MSNs spontaneously appear, consistent with experimental observations, and that the number of assemblies and the time-scale of synchronisation is strongly dependent on the simulated concentration of dopamine. We also show that feed-forward inhibition from the FSIs counter-intuitively increases the firing rate of the MSNs. Such small cell assemblies forming spontaneously only in the absence of dopamine may contribute to motor control problems seen in humans and animals following a loss of dopamine cells.

The role of intra-thalamic and thalamocortical circuits in action selection

We previously proposed that the basal ganglia (BG) play a crucial role in action selection. Quantitative analysis and simulation of a computational model of the intrinsic BG demonstrated that its output was consistent with this proposition. Here we build on that model by embedding it into a wider circuit containing the motor thalamocortical loop and thalamic reticular nucleus (TRN). Simulation of this extended model showed that the additions gave five main results which are desirable in a selection/switching mechanism. First, low salience actions (i.e. those with low urgency) could be selected. Second, the range of salience values over which actions could be switched between was increased. Third, the contrast between the selected and non-selected actions was enhanced via improved differentiation of outputs from the BG. Fourth, transient increases in the salience of a non-selected action were prevented from interrupting the ongoing action, unless the transient was of sufficient magnitude. Finally, the selection of the ongoing action persisted when a new closely matched salience action became active. The first result was facilitated by the thalamocortical loop; the rest were dependent on the presence of the TRN. Thus, we conclude that the results are consistent with these structures having clearly defined functions in action selection.