The roles of surround inhibition for the intrinsic function of the striatum, analyzed in silico.

The basal ganglia are important for action initiation, selection, and motor learning. The input level, the striatum, receives input preferentially from the cortex and thalamus and is to 95% composed of striatal projection neurons (SPNs) with sparse GABAergic collaterals targeting distal dendrites of neighboring SPNs, in a distance-dependent manner. The remaining 5% are GABAergic and cholinergic interneurons. Our aim here is to investigate the role of surround inhibition for the intrinsic function of the striatum. Large-scale striatal networks of 20 to 40 thousand neurons were simulated with detailed multicompartmental models of different cell types, corresponding to the size of a module of the dorsolateral striatum, like the forelimb area (mouse). The effect of surround inhibition on dendritic computation and network activity was investigated, while groups of SPNs were activated. The SPN-induced surround inhibition in distal dendrites shunted effectively the corticostriatal EPSPs. The size of dendritic plateau-like potentials within the specific dendritic segment was both reduced and enhanced by inhibition, due to the hyperpolarized membrane potential of SPNs and the reversal-potential of GABA. On a population level, the competition between two subpopulations of SPNs was found to depend on the distance between the two units, the size of each unit, the activity level in each subgroup and the dopaminergic modulation of the dSPNs and iSPNs. The SPNs provided the dominating source of inhibition within the striatum, while the fast-spiking interneuron mainly had an initial effect due to short-term synaptic plasticity as shown in with ablation of the synaptic interaction.

Glutamate spillover drives robust all-or-none dendritic plateau potentials-an in silico investigation using models of striatal projection neurons.

Plateau potentials are a critical feature of neuronal excitability, but their all-or-none behavior is not easily captured in modeling. In this study, we investigated models of plateau potentials in multi-compartment neuron models and found that including glutamate spillover provides robust all-or-none behavior. This result arises due to the prolonged duration of extrasynaptic glutamate. When glutamate spillover is not included, the all-or-none behavior is very sensitive to the steepness of the Mg2+ block. These results suggest a potentially significant role of glutamate spillover in plateau potential generation, providing a mechanism for robust all-or-none behavior across a wide range of slopes of the Mg2+ block curve. We also illustrate the importance of the all-or-none plateau potential behavior for nonlinear computation with regard to the nonlinear feature binding problem.

Combining hypothesis- and data-driven neuroscience modeling in FAIR workflows.

Modeling in neuroscience occurs at the intersection of different points of view and approaches. Typically, hypothesis-driven modeling brings a question into focus so that a model is constructed to investigate a specific hypothesis about how the system works or why certain phenomena are observed. Data-driven modeling, on the other hand, follows a more unbiased approach, with model construction informed by the computationally intensive use of data. At the same time, researchers employ models at different biological scales and at different levels of abstraction. Combining these models while validating them against experimental data increases understanding of the multiscale brain. However, a lack of interoperability, transparency, and reusability of both models and the workflows used to construct them creates barriers for the integration of models representing different biological scales and built using different modeling philosophies. We argue that the same imperatives that drive resources and policy for data - such as the FAIR (Findable, Accessible, Interoperable, Reusable) principles - also support the integration of different modeling approaches. The FAIR principles require that data be shared in formats that are Findable, Accessible, Interoperable, and Reusable. Applying these principles to models and modeling workflows, as well as the data used to constrain and validate them, would allow researchers to find, reuse, question, validate, and extend published models, regardless of whether they are implemented phenomenologically or mechanistically, as a few equations or as a multiscale, hierarchical system. To illustrate these ideas, we use a classical synaptic plasticity model, the Bienenstock-Cooper-Munro rule, as an example due to its long history, different levels of abstraction, and implementation at many scales.

Data-Driven Model of Postsynaptic Currents Mediated by NMDA or AMPA Receptors in Striatal Neurons.

The majority of excitatory synapses in the brain uses glutamate as neurotransmitter, and the synaptic transmission is primarily mediated by AMPA and NMDA receptors in postsynaptic neurons. Here, we present data-driven models of the postsynaptic currents of these receptors in excitatory synapses in mouse striatum. It is common to fit two decay time constants to the decay phases of the current profiles but then compute a single weighted mean time constant to describe them. We have shown that this approach does not lead to an improvement in the fitting, and, hence, we present a new model based on the use of both the fast and slow time constants and a numerical calculation of the peak time using Newton's method. Our framework allows for a more accurate description of the current profiles without needing extra data and without overburdening the comptuational costs. The user-friendliness of the method, here implemented in Python, makes it easily applicable to other data sets.

Transient Response of Basal Ganglia Network in Healthy and Low-Dopamine State.

The basal ganglia (BG) are crucial for a variety of motor and cognitive functions. Changes induced by persistent low-dopamine (e.g., in Parkinson's disease; PD) result in aberrant changes in steady-state population activity (ß band oscillations) and the transient response of the BG. Typically, a brief cortical stimulation results in a triphasic response in the substantia nigra pars reticulata (SNr; an output of the BG). The properties of the triphasic responses are shaped by dopamine levels. While mechanisms underlying aberrant steady state activity are well studied, it is still unclear which BG interactions are crucial for the aberrant transient responses in the BG. Moreover, it is also unclear whether mechanisms underlying the aberrant changes in steady-state activity and transient response are the same. Here, we used numerical simulations of a network model of BG to identify the key factors that determine the shape of the transient responses. We show that an aberrant transient response of the SNr in the low-dopamine state involves changes in the direct pathway and the recurrent interactions within the globus pallidus externa (GPe) and between GPe and subthalamic nucleus (STN). However, the connections from D2-type spiny projection neurons (D2-SPN) to GPe are most crucial in shaping the transient response and by restoring them to their healthy level, we could restore the shape of transient response even in low-dopamine state. Finally, we show that the changes in BG that result in aberrant transient response are also sufficient to generate pathologic oscillatory activity in the steady state.

A Modular Workflow for Model Building, Analysis, and Parameter Estimation in Systems Biology and Neuroscience.

Neuroscience incorporates knowledge from a range of scales, from single molecules to brain wide neural networks. Modeling is a valuable tool in understanding processes at a single scale or the interactions between two adjacent scales and researchers use a variety of different software tools in the model building and analysis process. Here we focus on the scale of biochemical pathways, which is one of the main objects of study in systems biology. While systems biology is among the more standardized fields, conversion between different model formats and interoperability between various tools is still somewhat problematic. To offer our take on tackling these shortcomings and by keeping in mind the FAIR (findability, accessibility, interoperability, reusability) data principles, we have developed a workflow for building and analyzing biochemical pathway models, using pre-existing tools that could be utilized for the storage and refinement of models in all phases of development. We have chosen the SBtab format which allows the storage of biochemical models and associated data in a single file and provides a human readable set of syntax rules. Next, we implemented custom-made MATLAB® scripts to perform parameter estimation and global sensitivity analysis used in model refinement. Additionally, we have developed a web-based application for biochemical models that allows simulations with either a network free solver or stochastic solvers and incorporating geometry. Finally, we illustrate convertibility and use of a biochemical model in a biophysically detailed single neuron model by running multiscale simulations in NEURON. Using this workflow, we can simulate the same model in three different simulators, with a smooth conversion between the different model formats, enhancing the characterization of different aspects of the model.

Dopaminergic and Cholinergic Modulation of Large Scale Networks in silico Using Snudda.

Neuromodulation is present throughout the nervous system and serves a critical role for circuit function and dynamics. The computational investigations of neuromodulation in large scale networks require supportive software platforms. Snudda is a software for the creation and simulation of large scale networks of detailed microcircuits consisting of multicompartmental neuron models. We have developed an extension to Snudda to incorporate neuromodulation in large scale simulations. The extended Snudda framework implements neuromodulation at the level of single cells incorporated into large-scale microcircuits. We also developed Neuromodcell, a software for optimizing neuromodulation in detailed multicompartmental neuron models. The software adds parameters within the models modulating the conductances of ion channels and ionotropic receptors. Bath application of neuromodulators is simulated and models which reproduce the experimentally measured effects are selected. In Snudda, we developed an extension to accommodate large scale simulations of neuromodulation. The simulator has two modes of simulation - denoted replay and adaptive. In the replay mode, transient levels of neuromodulators can be defined as a time-varying function which modulates the receptors and ion channels within the network in a cell-type specific manner. In the adaptive mode, spiking neuromodulatory neurons are connected via integrative modulating mechanisms to ion channels and receptors. Both modes of simulating neuromodulation allow for simultaneous modulation by several neuromodulators that can interact dynamically with each other. Here, we used the Neuromodcell software to simulate dopaminergic and muscarinic modulation of neurons from the striatum. We also demonstrate how to simulate different neuromodulatory states with dopamine and acetylcholine using Snudda. All software is freely available on Github, including tutorials on Neuromodcell and Snudda-neuromodulation.

AKAP79 enables calcineurin to directly suppress protein kinase A activity.

Interplay between the second messengers cAMP and Ca2+ is a hallmark of dynamic cellular processes. A common motif is the opposition of the Ca2+-sensitive phosphatase calcineurin and the major cAMP receptor, protein kinase A (PKA). Calcineurin dephosphorylates sites primed by PKA to bring about changes including synaptic long-term depression (LTD). AKAP79 supports signaling of this type by anchoring PKA and calcineurin in tandem. In this study, we discovered that AKAP79 increases the rate of calcineurin dephosphorylation of type II PKA regulatory subunits by an order of magnitude. Fluorescent PKA activity reporter assays, supported by kinetic modeling, show how AKAP79-enhanced calcineurin activity enables suppression of PKA without altering cAMP levels by increasing PKA catalytic subunit capture rate. Experiments with hippocampal neurons indicate that this mechanism contributes toward LTD. This non-canonical mode of PKA regulation may underlie many other cellular processes.

Predicting Synaptic Connectivity for Large-Scale Microcircuit Simulations Using Snudda.

Simulation of large-scale networks of neurons is an important approach to understanding and interpreting experimental data from healthy and diseased brains. Owing to the rapid development of simulation software and the accumulation of quantitative data of different neuronal types, it is possible to predict both computational and dynamical properties of local microcircuits in a 'bottom-up' manner. Simulated data from these models can be compared with experiments and 'top-down' modelling approaches, successively bridging the scales. Here we describe an open source pipeline, using the software Snudda, for predicting microcircuit connectivity and for setting up simulations using the NEURON simulation environment in a reproducible way. We also illustrate how to further 'curate' data on single neuron morphologies acquired from public databases. This model building pipeline was used to set up a first version of a full-scale cellular level model of mouse dorsal striatum. Model components from that work are here used to illustrate the different steps that are needed when modelling subcortical nuclei, such as the basal ganglia.

Predicting complex spikes in striatal projection neurons of the direct pathway following neuromodulation by acetylcholine and dopamine.

The input structure of the basal ganglia, striatum, receives dense neuromodulatory input in the form of dopamine and acetylcholine. The two systems are tightly connected, for example, synchronized activity of cholinergic interneurons, leading to increased acetylcholine release, has been shown to directly trigger dopamine release from dopaminergic terminals in striatum. Both signals are further needed for induction of locomotion. High dopamine concentration leads to increased excitability of the direct pathway striatal projection neurons. High cholinergic tone inhibits various potassium channels further increasing the excitability of striatal projection neurons. Here, we investigate the combined effect of concurrent high acetylcholine and dopamine using biophysically detailed models based on rodent data. The aim of the study is to investigate how neuromodulation affects dendritic integration. The result shows that neuromodulation paired with synaptic activation of dendrites can give rise to complex spiking patterns, resembling spike shapes seen in the hippocampus. In the hippocampus, these complex spikes are associated with behavioral time scale plasticity and place cell tuning. We further investigate the mechanisms behind the complex spikes and find that there are two components, one axo-somatic and one dendritic in origin.

Reciprocal interaction between striatal cholinergic and low-threshold spiking interneurons - A computational study.

The striatum is the main input stage of the basal ganglia receiving extrinsic input from cortex and thalamus. The striatal projection neurons (SPN) constitute 95% of the neurons in the striatum in mice while the remaining 5% are cholinergic and GABAergic interneurons. The cholinergic (ChIN) and low-threshold spiking interneurons (LTS) are spontaneously active and form a striatal subnetwork involved in salience detection and goal-directed learning. Activation of ChINs has been shown to inhibit LTS via muscarinic receptor type 4 (M4R) and LTS in turn can modulate ChINs via nitric oxide (NO) causing a prolonged depolarization. Thalamic input prefentially excites ChINs, whereas input from motor cortex favours LTS, but can also excite ChINs. This varying extrinsic input with intrinsic reciprocal, yet opposing, effects raises the possibility of a slow input-dependent modulatory subnetwork. Here, we simulate this subnetwork using multicompartmental neuron models that incorporate data regarding known ion channels and detailed morphological reconstructions. The modelled connections replicate the experimental data on muscarinic (M4R) and nitric oxide modulation onto LTS and ChIN, respectively, and capture their physiological interaction. Finally, we show that the cortical and thalamic inputs triggering the opposing modulation within the network induce periods of increased and decreased spiking activity in ChINs and LTS. This could provide different temporal windows for selective modulation by acetylcholine and nitric oxide, and the possibility of interaction with the wider striatal microcircuit.

The microcircuits of striatum in silico.

The basal ganglia play an important role in decision making and selection of action primarily based on input from cortex, thalamus, and the dopamine system. Their main input structure, striatum, is central to this process. It consists of two types of projection neurons, together representing 95% of the neurons, and 5% of interneurons, among which are the cholinergic, fast-spiking, and low threshold-spiking subtypes. The membrane properties, soma-dendritic shape, and intrastriatal and extrastriatal synaptic interactions of these neurons are quite well described in the mouse, and therefore they can be simulated in sufficient detail to capture their intrinsic properties, as well as the connectivity. We focus on simulation at the striatal cellular/microcircuit level, in which the molecular/subcellular and systems levels meet. We present a nearly full-scale model of the mouse striatum using available data on synaptic connectivity, cellular morphology, and electrophysiological properties to create a microcircuit mimicking the real network. A striatal volume is populated with reconstructed neuronal morphologies with appropriate cell densities, and then we connect neurons together based on appositions between neurites as possible synapses and constrain them further with available connectivity data. Moreover, we simulate a subset of the striatum involving 10,000 neurons, with input from cortex, thalamus, and the dopamine system, as a proof of principle. Simulation at this biological scale should serve as an invaluable tool to understand the mode of operation of this complex structure. This platform will be updated with new data and expanded to simulate the entire striatum.

Regulation of adenylyl cyclase 5 in striatal neurons confers the ability to detect coincident neuromodulatory signals.

Long-term potentiation and depression of synaptic activity in response to stimuli is a key factor in reinforcement learning. Strengthening of the corticostriatal synapses depends on the second messenger cAMP, whose synthesis is catalysed by the enzyme adenylyl cyclase 5 (AC5), which is itself regulated by the stimulatory Gαolf and inhibitory Gαi proteins. AC isoforms have been suggested to act as coincidence detectors, promoting cellular responses only when convergent regulatory signals occur close in time. However, the mechanism for this is currently unclear, and seems to lie in their diverse regulation patterns. Despite attempts to isolate the ternary complex, it is not known if Gαolf and Gαi can bind to AC5 simultaneously, nor what activity the complex would have. Using protein structure-based molecular dynamics simulations, we show that this complex is stable and inactive. These simulations, along with Brownian dynamics simulations to estimate protein association rates constants, constrain a kinetic model that shows that the presence of this ternary inactive complex is crucial for AC5's ability to detect coincident signals, producing a synergistic increase in cAMP. These results reveal some of the prerequisites for corticostriatal synaptic plasticity, and explain recent experimental data on cAMP concentrations following receptor activation. Moreover, they provide insights into the regulatory mechanisms that control signal processing by different AC isoforms.

Molecular mechanisms underlying striatal synaptic plasticity: relevance to chronic alcohol consumption and seeking.

The striatum, the input structure of the basal ganglia, is a major site of learning and memory for goal-directed actions and habit formation. Spiny projection neurons of the striatum integrate cortical, thalamic, and nigral inputs to learn associations, with cortico-striatal synaptic plasticity as a learning mechanism. Signaling molecules implicated in synaptic plasticity are altered in alcohol withdrawal, which may contribute to overly strong learning and increased alcohol seeking and consumption. To understand how interactions among signaling molecules produce synaptic plasticity, we implemented a mechanistic model of signaling pathways activated by dopamine D1 receptors, acetylcholine receptors, and glutamate. We use our novel, computationally efficient simulator, NeuroRD, to simulate stochastic interactions both within and between dendritic spines. Dopamine release during theta burst and 20-Hz stimulation was extrapolated from fast-scan cyclic voltammetry data collected in mouse striatal slices. Our results show that the combined activity of several key plasticity molecules correctly predicts the occurrence of either LTP, LTD, or no plasticity for numerous experimental protocols. To investigate spatial interactions, we stimulate two spines, either adjacent or separated on a 20-µm dendritic segment. Our results show that molecules underlying LTP exhibit spatial specificity, whereas 2-arachidonoylglycerol exhibits a spatially diffuse elevation. We also implement changes in NMDA receptors, adenylyl cyclase, and G protein signaling that have been measured following chronic alcohol treatment. Simulations under these conditions suggest that the molecular changes can predict changes in synaptic plasticity, thereby accounting for some aspects of alcohol use disorder.

Roles for globus pallidus externa revealed in a computational model of action selection in the basal ganglia.

The basal ganglia are considered vital to action selection - a hypothesis supported by several biologically plausible computational models. Of the several subnuclei of the basal ganglia, the globus pallidus externa (GPe) has been thought of largely as a relay nucleus, and its intrinsic connectivity has not been incorporated in significant detail, in any model thus far. Here, we incorporate newly revealed subgroups of neurons within the GPe into an existing computational model of the basal ganglia, and investigate their role in action selection. Three main results ensued. First, using previously used metrics for selection, the new extended connectivity improved the action selection performance of the model. Second, low frequency theta oscillations were observed in the subpopulation of the GPe (the TA or 'arkypallidal' neurons) which project exclusively to the striatum. These oscillations were suppressed by increased dopamine activity - revealing a possible link with symptoms of Parkinson's disease. Third, a new phenomenon was observed in which the usual monotonic relationship between input to the basal ganglia and its output within an action 'channel' was, under some circumstances, reversed. Thus, at high levels of input, further increase of this input to the channel could cause an increase of the corresponding output rather than the more usually observed decrease. Moreover, this phenomenon was associated with the prevention of multiple channel selection, thereby assisting in optimal action selection. Examination of the mechanistic origin of our results showed the so-called 'prototypical' GPe neurons to be the principal subpopulation influencing action selection. They control the striatum via the arkypallidal neurons and are also able to regulate the output nuclei directly. Taken together, our results highlight the role of the GPe as a major control hub of the basal ganglia, and provide a mechanistic account for its control function.

Uncertainty quantification, propagation and characterization by Bayesian analysis combined with global sensitivity analysis applied to dynamical intracellular pathway models.

Motivation: Dynamical models describing intracellular phenomena are increasing in size and complexity as more information is obtained from experiments. These models are often over-parameterized with respect to the quantitative data used for parameter estimation, resulting in uncertainty in the individual parameter estimates as well as in the predictions made from the model. Here we combine Bayesian analysis with global sensitivity analysis (GSA) in order to give better informed predictions; to point out weaker parts of the model that are important targets for further experiments, as well as to give guidance on parameters that are essential in distinguishing different qualitative output behaviours. Results: We used approximate Bayesian computation (ABC) to estimate the model parameters from experimental data, as well as to quantify the uncertainty in this estimation (inverse uncertainty quantification), resulting in a posterior distribution for the parameters. This parameter uncertainty was next propagated to a corresponding uncertainty in the predictions (forward uncertainty propagation), and a GSA was performed on the predictions using the posterior distribution as the possible values for the parameters. This methodology was applied on a relatively large model relevant for synaptic plasticity, using experimental data from several sources. We could hereby point out those parameters that by themselves have the largest contribution to the uncertainty of the prediction as well as identify parameters important to separate between qualitatively different predictions. This approach is useful both for experimental design as well as model building. Availability and implementation: Source code is freely available at https://github.com/alexjau/uqsa. Supplementary information: Supplementary data are available at Bioinformatics online.

The high efficacy of muscarinic M4 receptor in D1 medium spiny neurons reverses striatal hyperdopaminergia.

The opposing action of dopamine and acetylcholine has long been known to play an important role in basal ganglia physiology. However, the quantitative analysis of dopamine and acetylcholine signal interaction has been difficult to perform in the native context because the striatum comprises mainly two subtypes of medium-sized spiny neurons (MSNs) on which these neuromodulators exert different actions. We used biosensor imaging in live brain slices of dorsomedial striatum to monitor changes in intracellular cAMP at the level of individual MSNs. We observed that the muscarinic agonist oxotremorine decreases cAMP selectively in the MSN subpopulation that also expresses D1 dopamine receptors, an action mediated by the M4 muscarinic receptor. This receptor has a high efficacy on cAMP signaling and can shut down the positive cAMP response induced by dopamine, at acetylcholine concentrations which are consistent with physiological levels. This supports our prediction based on theoretical modeling that acetylcholine could exert a tonic inhibition on striatal cAMP signaling, thus supporting the possibility that a pause in acetylcholine release is required for phasic dopamine to transduce a cAMP signal in D1 MSNs. In vivo experiments with acetylcholinesterase inhibitors donepezil and tacrine, as well as with the positive allosteric modulators of M4 receptor VU0152100 and VU0010010 show that this effect is sufficient to reverse the increased locomotor activity of DAT-knockout mice. This suggests that M4 receptors could be a novel therapeutic target to treat hyperactivity disorders.

Switch-like PKA responses in the nucleus of striatal neurons.

Although it is known that protein kinase A (PKA) in the nucleus regulates gene expression, the specificities of nuclear PKA signaling remain poorly understood. Here, we combined computational modeling and live-cell imaging of PKA-dependent phosphorylation in mouse brain slices to investigate how transient dopamine signals are translated into nuclear PKA activity in cortical pyramidal neurons and striatal medium spiny neurons. We observed that the nuclear PKA signal in striatal neurons featured an ultrasensitive responsiveness, associated with fast all-or-none responses, which is not consistent with the commonly accepted theory of a slow and passive diffusion of catalytic PKA in the nucleus. Our numerical model suggests that a positive feed-forward mechanism inhibiting nuclear phosphatase activity - possibly mediated by DARPP-32 (also known as PPP1R1B) - could be responsible for this non-linear pattern of nuclear PKA response, allowing for a better detection of the transient dopamine signals that are often associated with reward-mediated learning.

Basal Ganglia Neuromodulation Over Multiple Temporal and Structural Scales-Simulations of Direct Pathway MSNs Investigate the Fast Onset of Dopaminergic Effects and Predict the Role of Kv4.2.

The basal ganglia are involved in the motivational and habitual control of motor and cognitive behaviors. Striatum, the largest basal ganglia input stage, integrates cortical and thalamic inputs in functionally segregated cortico-basal ganglia-thalamic loops, and in addition the basal ganglia output nuclei control targets in the brainstem. Striatal function depends on the balance between the direct pathway medium spiny neurons (D1-MSNs) that express D1 dopamine receptors and the indirect pathway MSNs that express D2 dopamine receptors. The striatal microstructure is also divided into striosomes and matrix compartments, based on the differential expression of several proteins. Dopaminergic afferents from the midbrain and local cholinergic interneurons play crucial roles for basal ganglia function, and striatal signaling via the striosomes in turn regulates the midbrain dopaminergic system directly and via the lateral habenula. Consequently, abnormal functions of the basal ganglia neuromodulatory system underlie many neurological and psychiatric disorders. Neuromodulation acts on multiple structural levels, ranging from the subcellular level to behavior, both in health and disease. For example, neuromodulation affects membrane excitability and controls synaptic plasticity and thus learning in the basal ganglia. However, it is not clear on what time scales these different effects are implemented. Phosphorylation of ion channels and the resulting membrane effects are typically studied over minutes while it has been shown that neuromodulation can affect behavior within a few hundred milliseconds. So how do these seemingly contradictory effects fit together? Here we first briefly review neuromodulation of the basal ganglia, with a focus on dopamine. We furthermore use biophysically detailed multi-compartmental models to integrate experimental data regarding dopaminergic effects on individual membrane conductances with the aim to explain the resulting cellular level dopaminergic effects. In particular we predict dopaminergic effects on Kv4.2 in D1-MSNs. Finally, we also explore dynamical aspects of the onset of neuromodulation effects in multi-scale computational models combining biochemical signaling cascades and multi-compartmental neuron models.

Homologous Basal Ganglia Network Models in Physiological and Parkinsonian Conditions.

The classical model of basal ganglia has been refined in recent years with discoveries of subpopulations within a nucleus and previously unknown projections. One such discovery is the presence of subpopulations of arkypallidal and prototypical neurons in external globus pallidus, which was previously considered to be a primarily homogeneous nucleus. Developing a computational model of these multiple interconnected nuclei is challenging, because the strengths of the connections are largely unknown. We therefore use a genetic algorithm to search for the unknown connectivity parameters in a firing rate model. We apply a binary cost function derived from empirical firing rate and phase relationship data for the physiological and Parkinsonian conditions. Our approach generates ensembles of over 1,000 configurations, or homologies, for each condition, with broad distributions for many of the parameter values and overlap between the two conditions. However, the resulting effective weights of connections from or to prototypical and arkypallidal neurons are consistent with the experimental data. We investigate the significance of the weight variability by manipulating the parameters individually and cumulatively, and conclude that the correlation observed between the parameters is necessary for generating the dynamics of the two conditions. We then investigate the response of the networks to a transient cortical stimulus, and demonstrate that networks classified as physiological effectively suppress activity in the internal globus pallidus, and are not susceptible to oscillations, whereas parkinsonian networks show the opposite tendency. Thus, we conclude that the rates and phase relationships observed in the globus pallidus are predictive of experimentally observed higher level dynamical features of the physiological and parkinsonian basal ganglia, and that the multiplicity of solutions generated by our method may well be indicative of a natural diversity in basal ganglia networks. We propose that our approach of generating and analyzing an ensemble of multiple solutions to an underdetermined network model provides greater confidence in its predictions than those derived from a unique solution, and that projecting such homologous networks on a lower dimensional space of sensibly chosen dynamical features gives a better chance than a purely structural analysis at understanding complex pathologies such as Parkinson's disease.