Capturing dopaminergic modulation and bimodal membrane behaviour of striatal medium spiny neurons in accurate, reduced models

Incorporating slow NMDA-type receptors with nonlinear voltage-dependent magnesium block in a next generation neural mass model: derivation and dynamics

We derive a next generation neural mass model of a population of quadratic-integrate-and-fire neurons, with slow adaptation, and conductance-based AMPAR, GABAR and nonlinear NMDAR synapses. We show that the Lorentzian ansatz assumption can be satisfied by introducing a piece-wise polynomial approximation of the nonlinear voltage-dependent magnesium block of NMDAR current. We study the dynamics of the resulting system for two example cases of excitatory cortical neurons and inhibitory striatal neurons. Bifurcation diagrams are presented comparing the different dynamical regimes as compared to the case of linear NMDAR currents, along with sample comparison simulation time series demonstrating different possible oscillatory solutions. The omission of the nonlinearity of NMDAR currents results in a shift in the range (and possible disappearance) of the constant high firing rate regime, along with a modulation in the amplitude and frequency power spectrum of oscillations. Moreover, nonlinear NMDAR action is seen to be state-dependent and can have opposite effects depending on the type of neurons involved and the level of input firing rate received. The presented model can serve as a computationally efficient building block in whole brain network models for investigating the differential modulation of different types of synapses under neuromodulatory influence or receptor specific malfunction.

Extreme value statistics of nerve transmission delay

Delays in nerve transmission are an important topic in the field of neuroscience. Spike signals fired or received by the dendrites of a neuron travel from the axon to a presynaptic cell. The spike signal then triggers a chemical reaction at the synapse, wherein a presynaptic cell transfers neurotransmitters to the postsynaptic cell, regenerates electrical signals via a chemical reaction through ion channels, and transmits them to neighboring neurons. In the context of describing the complex physiological reaction process as a stochastic process, this study aimed to show that the distribution of the maximum time interval of spike signals follows extreme-order statistics. By considering the statistical variance in the time constant of the leaky Integrate-and-Fire model, a deterministic time evolution model for spike signals, we enabled randomness in the time interval of the spike signals. When the time constant follows an exponential distribution function, the time interval of the spike signal also follows an exponential distribution. In this case, our theory and simulations confirmed that the histogram of the maximum time interval follows the Gumbel distribution, one of the three forms of extreme-value statistics. We further confirmed that the histogram of the maximum time interval followed a Fréchet distribution when the time interval of the spike signal followed a Pareto distribution. These findings confirm that nerve transmission delay can be described using extreme value statistics and can therefore be used as a new indicator of transmission delay.

Anti-Hebbian plasticity drives sequence learning in striatum

Spatio-temporal activity patterns have been observed in a variety of brain areas in spontaneous activity, prior to or during action, or in response to stimuli. Biological mechanisms endowing neurons with the ability to distinguish between different sequences remain largely unknown. Learning sequences of spikes raises multiple challenges, such as maintaining in memory spike history and discriminating partially overlapping sequences. Here, we show that anti-Hebbian spike-timing dependent plasticity (STDP), as observed at cortico-striatal synapses, can naturally lead to learning spike sequences. We design a spiking model of the striatal output neuron receiving spike patterns defined as sequential input from a fixed set of cortical neurons. We use a simple synaptic plasticity rule that combines anti-Hebbian STDP and non-associative potentiation for a subset of the presented patterns called rewarded patterns. We study the ability of striatal output neurons to discriminate rewarded from non-rewarded patterns by firing only after the presentation of a rewarded pattern. In particular, we show that two biological properties of striatal networks, spiking latency and collateral inhibition, contribute to an increase in accuracy, by allowing a better discrimination of partially overlapping sequences. These results suggest that anti-Hebbian STDP may serve as a biological substrate for learning sequences of spikes.

Simulated Dopamine Modulation of a Neurorobotic Model of the Basal Ganglia

The vertebrate basal ganglia play an important role in action selection-the resolution of conflicts between alternative motor programs. The effective operation of basal ganglia circuitry is also known to rely on appropriate levels of the neurotransmitter dopamine. We investigated reducing or increasing the tonic level of simulated dopamine in a prior model of the basal ganglia integrated into a robot control architecture engaged in a foraging task inspired by animal behaviour. The main findings were that progressive reductions in the levels of simulated dopamine caused slowed behaviour and, at low levels, an inability to initiate movement. These states were partially relieved by increased salience levels (stronger sensory/motivational input). Conversely, increased simulated dopamine caused distortion of the robot's motor acts through partially expressed motor activity relating to losing actions. This could also lead to an increased frequency of behaviour switching. Levels of simulated dopamine that were either significantly lower or higher than baseline could cause a loss of behavioural integration, sometimes leaving the robot in a 'behavioral trap'. That some analogous traits are observed in animals and humans affected by dopamine dysregulation suggests that robotic models could prove useful in understanding the role of dopamine neurotransmission in basal ganglia function and dysfunction.

A Multi-Scale Computational Model of Levodopa-Induced Toxicity in Parkinson's Disease

Parkinson's disease (PD) is caused by the progressive loss of dopaminergic cells in substantia nigra pars compacta (SNc). The root cause of this cell loss in PD is still not decisively elucidated. A recent line of thinking has traced the cause of PD neurodegeneration to metabolic deficiency. Levodopa (L-DOPA), a precursor of dopamine, used as a symptom-relieving treatment for PD, leads to positive and negative outcomes. Several researchers inferred that L-DOPA might be harmful to SNc cells due to oxidative stress. The role of L-DOPA in the course of the PD pathogenesis is still debatable. We hypothesize that energy deficiency can lead to L-DOPA-induced toxicity in two ways: by promoting dopamine-induced oxidative stress and by exacerbating excitotoxicity in SNc. We present a systems-level computational model of SNc-striatum, which will help us understand the mechanism behind neurodegeneration postulated above and provide insights into developing disease-modifying therapeutics. It was observed that SNc terminals are more vulnerable to energy deficiency than SNc somas. During L-DOPA therapy, it was observed that higher L-DOPA dosage results in increased loss of terminals in SNc. It was also observed that co-administration of L-DOPA and glutathione (antioxidant) evades L-DOPA-induced toxicity in SNc neurons. Our proposed model of the SNc-striatum system is the first of its kind, where SNc neurons were modeled at a biophysical level, and striatal neurons were modeled at a spiking level. We show that our proposed model was able to capture L-DOPA-induced toxicity in SNc, caused by energy deficiency.

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 (β 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 dynamical model for the basal ganglia-thalamo-cortical oscillatory activity and its implications in Parkinson's disease

We propose to investigate brain electrophysiological alterations associated with Parkinson’s disease through a novel adaptive dynamical model of the network of the basal ganglia, the cortex and the thalamus. The model uniquely unifies the influence of dopamine in the regulation of the activity of all basal ganglia nuclei, the self-organised neuronal interdependent activity of basal ganglia-thalamo-cortical circuits and the generation of subcortical background oscillations. Variations in the amount of dopamine produced in the neurons of the substantia nigra pars compacta are key both in the onset of Parkinson’s disease and in the basal ganglia action selection. We model these dopamine-induced relationships, and Parkinsonian states are interpreted as spontaneous emergent behaviours associated with different rhythms of oscillatory activity patterns of the basal ganglia-thalamo-cortical network. These results are significant because: (1) the neural populations are built upon single-neuron models that have been robustly designed to have eletrophysiologically-realistic responses, and (2) our model distinctively links changes in the oscillatory activity in subcortical structures, dopamine levels in the basal ganglia and pathological synchronisation neuronal patterns compatible with Parkinsonian states, this still remains an open problem and is crucial to better understand the progression of the disease.

A Multi-Scale Computational Model of Excitotoxic Loss of Dopaminergic Cells in Parkinson's Disease

Parkinson's disease (PD) is a neurodegenerative disorder caused by loss of dopaminergic neurons in substantia nigra pars compacta (SNc). Although the exact cause of cell death is not clear, the hypothesis that metabolic deficiency is a key factor has been gaining attention in recent years. In the present study, we investigated this hypothesis using a multi-scale computational model of the subsystem of the basal ganglia comprising the subthalamic nucleus (STN), globus pallidus externa (GPe), and SNc. The proposed model is a multiscale model in that interaction among the three nuclei are simulated using more abstract Izhikevich neuron models, while the molecular pathways involved in cell death of SNc neurons are simulated in terms of detailed chemical kinetics. Simulation results obtained from the proposed model showed that energy deficiencies occurring at cellular and network levels could precipitate the excitotoxic loss of SNc neurons in PD. At the subcellular level, the models show how calcium elevation leads to apoptosis of SNc neurons. The therapeutic effects of several neuroprotective interventions are also simulated in the model. From neuroprotective studies, it was clear that glutamate inhibition and apoptotic signal blocker therapies were able to halt the progression of SNc cell loss when compared to other therapeutic interventions, which only slowed down the progression of SNc cell loss.

A Basal Ganglia Computational Model to Explain the Paradoxical Sensorial Improvement in the Presence of Huntington's Disease

The basal ganglia (BG) represent a critical center of the nervous system for sensorial discrimination. Although it is known that Huntington's disease (HD) affects this brain area, it still remains unclear how HD patients achieve paradoxical improvement in sensorial discrimination tasks. This paper presents a computational model of the BG including the main nuclei and the typical firing properties of their neurons. The BG model has been embedded within an auditory signal detection task. We have emulated the effect that the altered levels of dopamine and the degree of HD affectation have in information processing at different layers of the BG, and how these aspects shape transient and steady states differently throughout the selection task. By extracting the independent components of the BG activity at different populations, it is evidenced that early and medium stages of HD affectation may enhance transient activity in the striatum and the substantia nigra pars reticulata. These results represent a possible explanation for the paradoxical improvement that HD patients present in discrimination task performance. Thus, this paper provides a novel understanding on how the fast dynamics of the BG network at different layers interact and enable transient states to emerge throughout the successive neuron populations.

Basal ganglia role in learning rewarded actions and executing previously learned choices: Healthy and diseased states

The basal ganglia (BG) is a collection of nuclei located deep beneath the cerebral cortex that is involved in learning and selection of rewarded actions. Here, we analyzed BG mechanisms that enable these functions. We implemented a rate model of a BG-thalamo-cortical loop and simulated its performance in a standard action selection task. We have shown that potentiation of corticostriatal synapses enables learning of a rewarded option. However, these synapses became redundant later as direct connections between prefrontal and premotor cortices (PFC-PMC) were potentiated by Hebbian learning. After we switched the reward to the previously unrewarded option (reversal), the BG was again responsible for switching to the new option. Due to the potentiated direct cortical connections, the system was biased to the previously rewarded choice, and establishing the new choice required a greater number of trials. Guided by physiological research, we then modified our model to reproduce pathological states of mild Parkinson's and Huntington's diseases. We found that in the Parkinsonian state PMC activity levels become extremely variable, which is caused by oscillations arising in the BG-thalamo-cortical loop. The model reproduced severe impairment of learning and predicted that this is caused by these oscillations as well as a reduced reward prediction signal. In the Huntington state, the potentiation of the PFC-PMC connections produced better learning, but altered BG output disrupted expression of the rewarded choices. This resulted in random switching between rewarded and unrewarded choices resembling an exploratory phase that never ended. Along with other computational studies, our results further reconcile the apparent contradiction between the critical involvement of the BG in execution of previously learned actions and yet no impairment of these actions after BG output is ablated by lesions or deep brain stimulation. We predict that the cortico-BG-thalamo-cortical loop conforms to previously learned choice in healthy conditions, but impedes those choices in disease states.

Phosphodiesterase 10A levels are related to striatal function in schizophrenia: a combined positron emission tomography and functional magnetic resonance imaging study

Pharmacological inhibition of phosphodiesterase 10A (PDE10A) is being investigated as a treatment option in schizophrenia. PDE10A acts postsynaptically on striatal dopamine signaling by regulating neuronal excitability through its inhibition of cyclic adenosine monophosphate (cAMP), and we recently found it to be reduced in schizophrenia compared to controls. Here, this finding of reduced PDE10A in schizophrenia was followed up in the same sample to investigate the effect of reduced striatal PDE10A on the neural and behavioral function of striatal and downstream basal ganglia regions. A positron emission tomography (PET) scan with the PDE10A ligand [¹¹C]Lu AE92686 was performed, followed by a 6 min resting-state magnetic resonance imaging (MRI) scan in ten patients with schizophrenia. To assess the relationship between striatal function and neurophysiological and behavioral functioning, salience processing was assessed using a mismatch negativity paradigm, an auditory event-related electroencephalographic measure, episodic memory was assessed using the Rey auditory verbal learning test (RAVLT) and executive functioning using trail-making test B. Reduced striatal PDE10A was associated with increased amplitude of low-frequency fluctuations (ALFF) within the putamen and substantia nigra, respectively. Higher ALFF in the substantia nigra, in turn, was associated with lower episodic memory performance. The findings are in line with a role for PDE10A in striatal functioning, and suggest that reduced striatal PDE10A may contribute to cognitive symptoms in schizophrenia.

Bipolar oscillations between positive and negative mood states in a computational model of Basal Ganglia

Bipolar disorder is characterized by mood swings-oscillations between manic and depressive states. The swings (oscillations) mark the length of an episode in a patient's mood cycle (period), and can vary from hours to years. The proposed modeling study uses decision making framework to investigate the role of basal ganglia network in generating bipolar oscillations. In this model, the basal ganglia system performs a two-arm bandit task in which one of the arms (action responses) leads to a positive outcome, while the other leads to a negative outcome. We explore the dynamics of key reward and risk related parameters in the system while the model agent receives various outcomes. Particularly, we study the system using a model that represents the fast dynamics of decision making, and a module to capture the slow dynamics that describe the variation of some meta-parameters of fast dynamics over long time scales. The model is cast at three levels of abstraction: (1) a two-dimensional dynamical system model, that is a simple two variable model capable of showing bistability for rewarding and punitive outcomes; (2) a phenomenological basal ganglia model, to extend the implications from the reduced model to a cortico-basal ganglia setup; (3) a detailed network model of basal ganglia, that incorporates detailed cellular level models for a more realistic understanding. In healthy conditions, the model chooses positive action and avoids negative one, whereas under bipolar conditions, the model exhibits slow oscillations in its choice of positive or negative outcomes, reminiscent of bipolar oscillations. Phase-plane analyses on the simple reduced dynamical system with two variables reveal the essential parameters that generate pathological 'bipolar-like' oscillations. Phenomenological and network models of the basal ganglia extend that logic, and interpret bipolar oscillations in terms of the activity of dopaminergic and serotonergic projections on the cortico-basal ganglia network dynamics. The network's dysfunction, specifically in terms of reward and risk sensitivity, is shown to be responsible for the pathological bipolar oscillations. The study proposes a computational model that explores the effects of impaired serotonergic neuromodulation on the dynamics of the cortico basal ganglia network, and relates this impairment to abstract mood states (manic and depressive episodes) and oscillations of bipolar disorder.

Learning the payoffs and costs of actions

A set of sub-cortical nuclei called basal ganglia is critical for learning the values of actions. The basal ganglia include two pathways, which have been associated with approach and avoid behavior respectively and are differentially modulated by dopamine projections from the midbrain. Inspired by the influential opponent actor learning model, we demonstrate that, under certain circumstances, these pathways may represent learned estimates of the positive and negative consequences (payoffs and costs) of individual actions. In the model, the level of dopamine activity encodes the motivational state and controls to what extent payoffs and costs enter the overall evaluation of actions. We show that a set of previously proposed plasticity rules is suitable to extract payoffs and costs from a prediction error signal if they occur at different moments in time. For those plasticity rules, successful learning requires differential effects of positive and negative outcome prediction errors on the two pathways and a weak decay of synaptic weights over trials. We also confirm through simulations that the model reproduces drug-induced changes of willingness to work, as observed in classical experiments with the D2-antagonist haloperidol.

The basal ganglia are structures underneath the surface of the vertebrate brain, associated with error-driven learning. Much is known about the anatomical and biological features of the basal ganglia; scientists now try to understand the algorithms implemented by these structures. Numerous models aspire to capture the learning functionality, but many of them only cover some specific aspect of the algorithm. Instead of further adding to that pool of partial models, we unify two existing ones—one which captures what the basal ganglia learn, and one that describes the learning mechanism itself. The first model suggests that the basal ganglia weigh positive against negative consequences of actions according to the motivational state. It hints how payoff and cost might be represented, but does not explain how those representations arise. The other model consists of biologically plausible plasticity rules, which describe how learning takes place, but not how the brain makes use of what is learned. We show that the two theories are compatible. Together, they form a model of learning and decision making that integrates the motivational state as well as the learned payoffs and costs of opportunities.

Insights into Parkinson's disease from computational models of the basal ganglia

Movement disorders arise from the complex interplay of multiple changes to neural circuits. Successful treatments for these disorders could interact with these complex changes in myriad ways, and as a consequence their mechanisms of action and their amelioration of symptoms are incompletely understood. Using Parkinson's disease as a case study, we review here how computational models are a crucial tool for taming this complexity, across causative mechanisms, consequent neural dynamics and treatments. For mechanisms, we review models that capture the effects of losing dopamine on basal ganglia function; for dynamics, we discuss models that have transformed our understanding of how beta-band (15-30 Hz) oscillations arise in the parkinsonian basal ganglia. For treatments, we touch on the breadth of computational modelling work trying to understand the therapeutic actions of deep brain stimulation. Collectively, models from across all levels of description are providing a compelling account of the causes, symptoms and treatments for Parkinson's disease.

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.

SpineCreator: a Graphical User Interface for the Creation of Layered Neural Models

There is a growing requirement in computational neuroscience for tools that permit collaborative model building, model sharing, combining existing models into a larger system (multi-scale model integration), and are able to simulate models using a variety of simulation engines and hardware platforms. Layered XML model specification formats solve many of these problems, however they are difficult to write and visualise without tools. Here we describe a new graphical software tool, SpineCreator, which facilitates the creation and visualisation of layered models of point spiking neurons or rate coded neurons without requiring the need for programming. We demonstrate the tool through the reproduction and visualisation of published models and show simulation results using code generation interfaced directly into SpineCreator. As a unique application for the graphical creation of neural networks, SpineCreator represents an important step forward for neuronal modelling.

Generation of low-gamma oscillations in a GABAergic network model of the striatum

Striatal oscillations in the low-gamma frequency range have been consistently recorded in a number of experimental studies. However, whether these rhythms are locally generated in the striatum circuit, which is mainly composed of GABAergic neurons, remains an open question. GABAergic medium spiny projection neurons represent the great majority of striatal neurons, but they fire at very low rates. GABAergic fast-spiking interneurons typically show firing rates that are approximately 10 times higher than those of principal neurons, but they are a very small minority of the total neuronal population. In this study, based on physiological constraints we developed a computational network model of these neurons and dissected the oscillations. Simulations showed that the population of medium spiny projection neurons, and not the GABAergic fast-spiking interneurons, determines the frequency range of the oscillations. D2-type dopamine receptor-expressing neurons dominate the generation of low-gamma rhythms. Feedforward inputs from GABAergic fast-spiking interneurons promote the oscillations by strengthening the inhibitory interactions between medium spiny projection neurons. The promotion effect is independent of the degree of synchronization in the fast-spiking interneuron population but affected by the strength of their feedforward inputs to medium spiny projection neurons. Our results provide a theoretical explanation for how firing properties and connections of the three types of GABAergic neurons, which are susceptible to on-going behaviors, experience, and dopamine disruptions, sculpt striatal oscillations.

Striatal Neuropeptides Enhance Selection and Rejection of Sequential Actions

The striatum is the primary input nucleus for the basal ganglia, and receives glutamatergic afferents from the cortex. Under the hypothesis that basal ganglia perform action selection, these cortical afferents encode potential “action requests.” Previous studies have suggested the striatum may utilize a mutually inhibitory network of medium spiny neurons (MSNs) to filter these requests so that only those of high salience are selected. However, the mechanisms enabling the striatum to perform clean, rapid switching between distinct actions that form part of a learned action sequence are still poorly understood. Substance P (SP) and enkephalin are neuropeptides co-released with GABA in MSNs preferentially expressing D₁ or D₂ dopamine receptors respectively. SP has a facilitatory effect on subsequent glutamatergic inputs to target MSNs, while enkephalin has an inhibitory effect. Blocking the action of SP in the striatum is also known to affect behavioral transitions. We constructed phenomenological models of the effects of SP and enkephalin, and integrated these into a hybrid model of basal ganglia comprising a spiking striatal microcircuit and rate–coded populations representing other major structures. We demonstrated that diffuse neuropeptide connectivity enhanced the selection of unordered action requests, and that for true action sequences, where action semantics define a fixed structure, a patterning of the SP connectivity reflecting this ordering enhanced selection of actions presented in the correct sequential order and suppressed incorrect ordering. We also showed that selective pruning of SP connections allowed context–sensitive inhibition of specific undesirable requests that otherwise interfered with selection of an action group. Our model suggests that the interaction of SP and enkephalin enhances the contrast between selection and rejection of action requests, and that patterned SP connectivity in the striatum allows the “chunking” of actions and improves selection of sequences. Efficient execution of action sequences may therefore result from a combination of ordered cortical inputs and patterned neuropeptide connectivity within striatum.

Frequency and function in the basal ganglia: the origins of beta and gamma band activity

KEY POINTS

Neuronal oscillations in the basal ganglia have been observed to correlate with behaviours, although the causal mechanisms and functional significance of these oscillations remain unknown. We present a novel computational model of the healthy basal ganglia, constrained by single unit recordings from non-human primates. When the model is run using inputs that might be expected during performance of a motor task, the network shows emergent phenomena: it functions as a selection mechanism and shows spectral properties that match those seen in vivo. Beta frequency oscillations are shown to require pallido-striatal feedback, and occur with behaviourally relevant cortical input. Gamma oscillations arise in the subthalamic-globus pallidus feedback loop, and occur during movement. The model provides a coherent framework for the study of spectral, temporal and functional analyses of the basal ganglia and lays the foundation for an integrated approach to study basal ganglia pathologies such as Parkinson's disease in silico.

ABSTRACT

Neural oscillations in the basal ganglia (BG) are well studied yet remain poorly understood. Behavioural correlates of spectral activity are well described, yet a quantitative hypothesis linking time domain dynamics and spectral properties to BG function has been lacking. We show, for the first time, that a unified description is possible by interpreting previously ignored structure in data describing globus pallidus interna responses to cortical stimulation. These data were used to expose a pair of distinctive neuronal responses to the stimulation. This observation formed the basis for a new mathematical model of the BG, quantitatively fitted to the data, which describes the dynamics in the data, and is validated against other stimulus protocol experiments. A key new result is that when the model is run using inputs hypothesised to occur during the performance of a motor task, beta and gamma frequency oscillations emerge naturally during static-force and movement, respectively, consistent with experimental local field potentials. This new model predicts that the pallido-striatum connection has a key role in the generation of beta band activity, and that the gamma band activity associated with motor task performance has its origins in the pallido-subthalamic feedback loop. The network's functionality as a selection mechanism also occurs as an emergent property, and closer fits to the data gave better selection properties. The model provides a coherent framework for the study of spectral, temporal and functional analyses of the BG and therefore lays the foundation for an integrated approach to study BG pathologies such as Parkinson's disease in silico.

Feedback for reinforcement learning based brain-machine interfaces using confidence metrics

OBJECTIVE

For brain-machine interfaces (BMI) to be used in activities of daily living by paralyzed individuals, the BMI should be as autonomous as possible. One of the challenges is how the feedback is extracted and utilized in the BMI. Our long-term goal is to create autonomous BMIs that can utilize an evaluative feedback from the brain to update the decoding algorithm and use it intelligently in order to adapt the decoder. In this study, we show how to extract the necessary evaluative feedback from a biologically realistic (synthetic) source, use both the quantity and the quality of the feedback, and how that feedback information can be incorporated into a reinforcement learning (RL) controller architecture to maximize its performance.

APPROACH

Motivated by the perception-action-reward cycle (PARC) in the brain which links reward for cognitive decision making and goal-directed behavior, we used a reward-based RL architecture named Actor-Critic RL as the model. Instead of using an error signal towards building an autonomous BMI, we envision to use a reward signal from the nucleus accumbens (NAcc) which plays a key role in the linking of reward to motor behaviors. To deal with the complexity and non-stationarity of biological reward signals, we used a confidence metric which was used to indicate the degree of feedback accuracy. This confidence was added to the Actor's weight update equation in the RL controller architecture. If the confidence was high (>0.2), the BMI decoder used this feedback to update its parameters. However, when the confidence was low, the BMI decoder ignored the feedback and did not update its parameters. The range between high confidence and low confidence was termed as the 'ambiguous' region. When the feedback was within this region, the BMI decoder updated its weight at a lower rate than when fully confident, which was decided by the confidence. We used two biologically realistic models to generate synthetic data for MI (Izhikevich model) and NAcc (Humphries model) to validate proposed controller architecture.

MAIN RESULTS

In this work, we show how the overall performance of the BMI was improved by using a threshold close to the decision boundary to reject erroneous feedback. Additionally, we show the stability of the system improved when the feedback was used with a threshold.

SIGNIFICANCE

The result of this study is a step towards making BMIs autonomous. While our method is not fully autonomous, the results demonstrate that extensive training times necessary at the beginning of each BMI session can be significantly decreased. In our approach, decoder training time was only limited to 10 trials in the first BMI session. Subsequent sessions used previous session weights to initialize the decoder. We also present a method where the use of a threshold can be applied to any decoder with a feedback signal that is less than perfect so that erroneous feedback can be avoided and the stability of the system can be increased.

Untangling Basal Ganglia Network Dynamics and Function: Role of Dopamine Depletion and Inhibition Investigated in a Spiking Network Model

The basal ganglia are a crucial brain system for behavioral selection, and their function is disturbed in Parkinson's disease (PD), where neurons exhibit inappropriate synchronization and oscillations. We present a spiking neural model of basal ganglia including plausible details on synaptic dynamics, connectivity patterns, neuron behavior, and dopamine effects. Recordings of neuronal activity in the subthalamic nucleus and Type A (TA; arkypallidal) and Type I (TI; prototypical) neurons in globus pallidus externa were used to validate the model. Simulation experiments predict that both local inhibition in striatum and the existence of an indirect pathway are important for basal ganglia to function properly over a large range of cortical drives. The dopamine depletion-induced increase of AMPA efficacy in corticostriatal synapses to medium spiny neurons (MSNs) with dopamine receptor D2 synapses (CTX-MSN D2) and the reduction of MSN lateral connectivity (MSN-MSN) were found to contribute significantly to the enhanced synchrony and oscillations seen in PD. Additionally, reversing the dopamine depletion-induced changes to CTX-MSN D1, CTX-MSN D2, TA-MSN, and MSN-MSN couplings could improve or restore basal ganglia action selection ability. In summary, we found multiple changes of parameters for synaptic efficacy and neural excitability that could improve action selection ability and at the same time reduce oscillations. Identification of such targets could potentially generate ideas for treatments of PD and increase our understanding of the relation between network dynamics and network function.

Learning touch preferences with a tactile robot using dopamine modulated STDP in a model of insular cortex

Neurorobots enable researchers to study how behaviors are produced by neural mechanisms in an uncertain, noisy, real-world environment. To investigate how the somatosensory system processes noisy, real-world touch inputs, we introduce a neurorobot called CARL-SJR, which has a full-body tactile sensory area. The design of CARL-SJR is such that it encourages people to communicate with it through gentle touch. CARL-SJR provides feedback to users by displaying bright colors on its surface. In the present study, we show that CARL-SJR is capable of learning associations between conditioned stimuli (CS; a color pattern on its surface) and unconditioned stimuli (US; a preferred touch pattern) by applying a spiking neural network (SNN) with neurobiologically inspired plasticity. Specifically, we modeled the primary somatosensory cortex, prefrontal cortex, striatum, and the insular cortex, which is important for hedonic touch, to process noisy data generated directly from CARL-SJR's tactile sensory area. To facilitate learning, we applied dopamine-modulated Spike Timing Dependent Plasticity (STDP) to our simulated prefrontal cortex, striatum, and insular cortex. To cope with noisy, varying inputs, the SNN was tuned to produce traveling waves of activity that carried spatiotemporal information. Despite the noisy tactile sensors, spike trains, and variations in subject hand swipes, the learning was quite robust. Further, insular cortex activities in the incremental pathway of dopaminergic reward system allowed us to control CARL-SJR's preference for touch direction without heavily pre-processed inputs. The emerged behaviors we found in this model match animal's behaviors wherein they prefer touch in particular areas and directions. Thus, the results in this paper could serve as an explanation on the underlying neural mechanisms for developing tactile preferences and hedonic touch.

Identifying the Basal Ganglia network model markers for medication-induced impulsivity in Parkinson's disease patients

Impulsivity, i.e. irresistibility in the execution of actions, may be prominent in Parkinson's disease (PD) patients who are treated with dopamine precursors or dopamine receptor agonists. In this study, we combine clinical investigations with computational modeling to explore whether impulsivity in PD patients on medication may arise as a result of abnormalities in risk, reward and punishment learning. In order to empirically assess learning outcomes involving risk, reward and punishment, four subject groups were examined: healthy controls, ON medication PD patients with impulse control disorder (PD-ON ICD) or without ICD (PD-ON non-ICD), and OFF medication PD patients (PD-OFF). A neural network model of the Basal Ganglia (BG) that has the capacity to predict the dysfunction of both the dopaminergic (DA) and the serotonergic (5HT) neuromodulator systems was developed and used to facilitate the interpretation of experimental results. In the model, the BG action selection dynamics were mimicked using a utility function based decision making framework, with DA controlling reward prediction and 5HT controlling punishment and risk predictions. The striatal model included three pools of Medium Spiny Neurons (MSNs), with D1 receptor (R) alone, D2R alone and co-expressing D1R-D2R. Empirical studies showed that reward optimality was increased in PD-ON ICD patients while punishment optimality was increased in PD-OFF patients. Empirical studies also revealed that PD-ON ICD subjects had lower reaction times (RT) compared to that of the PD-ON non-ICD patients. Computational modeling suggested that PD-OFF patients have higher punishment sensitivity, while healthy controls showed comparatively higher risk sensitivity. A significant decrease in sensitivity to punishment and risk was crucial for explaining behavioral changes observed in PD-ON ICD patients. Our results highlight the power of computational modelling for identifying neuronal circuitry implicated in learning, and its impairment in PD. The results presented here not only show that computational modelling can be used as a valuable tool for understanding and interpreting clinical data, but they also show that computational modeling has the potential to become an invaluable tool to predict the onset of behavioral changes during disease progression.

A spiking Basal Ganglia model of synchrony, exploration and decision making

To make an optimal decision we need to weigh all the available options, compare them with the current goal, and choose the most rewarding one. Depending on the situation an optimal decision could be to either “explore” or “exploit” or “not to take any action” for which the Basal Ganglia (BG) is considered to be a key neural substrate. In an attempt to expand this classical picture of BG function, we had earlier hypothesized that the Indirect Pathway (IP) of the BG could be the subcortical substrate for exploration. In this study we build a spiking network model to relate exploration to synchrony levels in the BG (which are a neural marker for tremor in Parkinson's disease). Key BG nuclei such as the Sub Thalamic Nucleus (STN), Globus Pallidus externus (GPe) and Globus Pallidus internus (GPi) were modeled as Izhikevich spiking neurons whereas the Striatal output was modeled as Poisson spikes. The model is cast in reinforcement learning framework with the dopamine signal representing reward prediction error. We apply the model to two decision making tasks: a binary action selection task (similar to one used by Humphries et al., 2006) and an n-armed bandit task (Bourdaud et al., 2008). The model shows that exploration levels could be controlled by STN's lateral connection strength which also influenced the synchrony levels in the STN-GPe circuit. An increase in STN's lateral strength led to a decrease in exploration which can be thought as the possible explanation for reduced exploratory levels in Parkinson's patients. Our simulations also show that on complete removal of IP, the model exhibits only Go and No-Go behaviors, thereby demonstrating the crucial role of IP in exploration. Our model provides a unified account for synchronization, action section, and explorative behavior.

A new framework for cortico-striatal plasticity: behavioural theory meets in vitro data at the reinforcement-action interface

A computational model yields new insights into the bewildering complexity of cortico-striatal plasticity and its rationale for supporting operant learning.

Operant learning requires that reinforcement signals interact with action representations at a suitable neural interface. Much evidence suggests that this occurs when phasic dopamine, acting as a reinforcement prediction error, gates plasticity at cortico-striatal synapses, and thereby changes the future likelihood of selecting the action(s) coded by striatal neurons. But this hypothesis faces serious challenges. First, cortico-striatal plasticity is inexplicably complex, depending on spike timing, dopamine level, and dopamine receptor type. Second, there is a credit assignment problem—action selection signals occur long before the consequent dopamine reinforcement signal. Third, the two types of striatal output neuron have apparently opposite effects on action selection. Whether these factors rule out the interface hypothesis and how they interact to produce reinforcement learning is unknown. We present a computational framework that addresses these challenges. We first predict the expected activity changes over an operant task for both types of action-coding striatal neuron, and show they co-operate to promote action selection in learning and compete to promote action suppression in extinction. Separately, we derive a complete model of dopamine and spike-timing dependent cortico-striatal plasticity from in vitro data. We then show this model produces the predicted activity changes necessary for learning and extinction in an operant task, a remarkable convergence of a bottom-up data-driven plasticity model with the top-down behavioural requirements of learning theory. Moreover, we show the complex dependencies of cortico-striatal plasticity are not only sufficient but necessary for learning and extinction. Validating the model, we show it can account for behavioural data describing extinction, renewal, and reacquisition, and replicate in vitro experimental data on cortico-striatal plasticity. By bridging the levels between the single synapse and behaviour, our model shows how striatum acts as the action-reinforcement interface.

A key component of survival is the ability to learn which actions, in what contexts, yield useful and rewarding outcomes. Actions are encoded in the brain in the cortex but, as many actions are possible at any one time, there needs to be a mechanism to select which one is to be performed. This problem of action selection is mediated by a set of nuclei known as the basal ganglia, which receive convergent “action requests” from all over the cortex and select the one that is currently most important. Working out which is most important is determined by the strength of the input from each action request: the stronger the connection, the more important that action. Understanding learning thus requires understanding how that strength is changed by the outcome of each action. We built a computational model that demonstrates how the brain's internal signal for outcome (carried by the neurotransmitter dopamine) changes the strength of these cortical connections to learn the selection of rewarded actions, and the suppression of unrewarded ones. Our model shows how several known signals in the brain work together to shape the influence of cortical inputs to the basal ganglia at the interface between our actions and their outcomes.

From model specification to simulation of biologically constrained networks of spiking neurons

A declarative extensible markup language (SpineML) for describing the dynamics, network and experiments of large-scale spiking neural network simulations is described which builds upon the NineML standard. It utilises a level of abstraction which targets point neuron representation but addresses the limitations of existing tools by allowing arbitrary dynamics to be expressed. The use of XML promotes model sharing, is human readable and allows collaborative working. The syntax uses a high-level self explanatory format which allows straight forward code generation or translation of a model description to a native simulator format. This paper demonstrates the use of code generation in order to translate, simulate and reproduce the results of a benchmark model across a range of simulators. The flexibility of the SpineML syntax is highlighted by reproducing a pre-existing, biologically constrained model of a neural microcircuit (the striatum). The SpineML code is open source and is available at http://bimpa.group.shef.ac.uk/SpineML .

An extended reinforcement learning model of basal ganglia to understand the contributions of serotonin and dopamine in risk-based decision making, reward prediction, and punishment learning

Although empirical and neural studies show that serotonin (5HT) plays many functional roles in the brain, prior computational models mostly focus on its role in behavioral inhibition. In this study, we present a model of risk based decision making in a modified Reinforcement Learning (RL)-framework. The model depicts the roles of dopamine (DA) and serotonin (5HT) in Basal Ganglia (BG). In this model, the DA signal is represented by the temporal difference error (δ), while the 5HT signal is represented by a parameter (α) that controls risk prediction error. This formulation that accommodates both 5HT and DA reconciles some of the diverse roles of 5HT particularly in connection with the BG system. We apply the model to different experimental paradigms used to study the role of 5HT: (1) Risk-sensitive decision making, where 5HT controls risk assessment, (2) Temporal reward prediction, where 5HT controls time-scale of reward prediction, and (3) Reward/Punishment sensitivity, in which the punishment prediction error depends on 5HT levels. Thus the proposed integrated RL model reconciles several existing theories of 5HT and DA in the BG.

Striatal disorders dissociate mechanisms of enhanced and impaired response selection - Evidence from cognitive neurophysiology and computational modelling

Paradoxically enhanced cognitive processes in neurological disorders provide vital clues to understanding neural function. However, what determines whether the neurological damage is impairing or enhancing is unclear. Here we use the performance of patients with two disorders of the striatum to dissociate mechanisms underlying cognitive enhancement and impairment resulting from damage to the same system. In a two-choice decision task, Huntington's disease patients were faster and less error prone than controls, yet a patient with the rare condition of benign hereditary chorea (BHC) was both slower and more error prone. EEG recordings confirmed significant differences in neural processing between the groups. Analysis of a computational model revealed that the common loss of connectivity between striatal neurons in BHC and Huntington's disease impairs response selection, but the increased sensitivity of NMDA receptors in Huntington's disease potentially enhances response selection. Crucially the model shows that there is a critical threshold for increased sensitivity: below that threshold, impaired response selection results. Our data and model thus predict that specific striatal malfunctions can contribute to either impaired or enhanced selection, and provide clues to solving the paradox of how Huntington's disease can lead to both impaired and enhanced cognitive processes.

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Comparative study on well-defined neurological disorders

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Striatal disorders dissociate mechanisms of enhanced and impaired cognition.

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Neurophysiological data in patients is combined with computational modelling.

Timing and expectation of reward: a neuro-computational model of the afferents to the ventral tegmental area

Neural activity in dopaminergic areas such as the ventral tegmental area is influenced by timing processes, in particular by the temporal expectation of rewards during Pavlovian conditioning. Receipt of a reward at the expected time allows to compute reward-prediction errors which can drive learning in motor or cognitive structures. Reciprocally, dopamine plays an important role in the timing of external events. Several models of the dopaminergic system exist, but the substrate of temporal learning is rather unclear. In this article, we propose a neuro-computational model of the afferent network to the ventral tegmental area, including the lateral hypothalamus, the pedunculopontine nucleus, the amygdala, the ventromedial prefrontal cortex, the ventral basal ganglia (including the nucleus accumbens and the ventral pallidum), as well as the lateral habenula and the rostromedial tegmental nucleus. Based on a plausible connectivity and realistic learning rules, this neuro-computational model reproduces several experimental observations, such as the progressive cancelation of dopaminergic bursts at reward delivery, the appearance of bursts at the onset of reward-predicting cues or the influence of reward magnitude on activity in the amygdala and ventral tegmental area. While associative learning occurs primarily in the amygdala, learning of the temporal relationship between the cue and the associated reward is implemented as a dopamine-modulated coincidence detection mechanism in the nucleus accumbens.

Transient and steady-state selection in the striatal microcircuit

Although the basal ganglia have been widely studied and implicated in signal processing and action selection, little information is known about the active role the striatal microcircuit plays in action selection in the basal ganglia-thalamo-cortical loops. To address this knowledge gap we use a large scale three dimensional spiking model of the striatum, combined with a rate coded model of the basal ganglia-thalamo-cortical loop, to asses the computational role the striatum plays in action selection. We identify a robust transient phenomena generated by the striatal microcircuit, which temporarily enhances the difference between two competing cortical inputs. We show that this transient is sufficient to modulate decision making in the basal ganglia-thalamo-cortical circuit. We also find that the transient selection originates from a novel adaptation effect in single striatal projection neurons, which is amenable to experimental testing. Finally, we compared transient selection with models implementing classical steady-state selection. We challenged both forms of model to account for recent reports of paradoxically enhanced response selection in Huntington's disease patients. We found that steady-state selection was uniformly impaired under all simulated Huntington's conditions, but transient selection was enhanced given a sufficient Huntington's-like increase in NMDA receptor sensitivity. Thus our models provide an intriguing hypothesis for the mechanisms underlying the paradoxical cognitive improvements in manifest Huntington's patients.

Computational models of basal-ganglia pathway functions: focus on functional neuroanatomy

Over the past 15 years, computational models have had a considerable impact on basal-ganglia research. Most of these models implement multiple distinct basal-ganglia pathways and assume them to fulfill different functions. As there is now a multitude of different models, it has become complex to keep track of their various, sometimes just marginally different assumptions on pathway functions. Moreover, it has become a challenge to oversee to what extent individual assumptions are corroborated or challenged by empirical data. Focusing on computational, but also considering non-computational models, we review influential concepts of pathway functions and show to what extent they are compatible with or contradict each other. Moreover, we outline how empirical evidence favors or challenges specific model assumptions and propose experiments that allow testing assumptions against each other.

Using a hybrid neuron in physiologically inspired models of the basal ganglia

Our current understanding of the basal ganglia (BG) has facilitated the creation of computational models that have contributed novel theories, explored new functional anatomy and demonstrated results complementing physiological experiments. However, the utility of these models extends beyond these applications. Particularly in neuromorphic engineering, where the basal ganglia's role in computation is important for applications such as power efficient autonomous agents and model-based control strategies. The neurons used in existing computational models of the BG, however, are not amenable for many low-power hardware implementations. Motivated by a need for more hardware accessible networks, we replicate four published models of the BG, spanning single neuron and small networks, replacing the more computationally expensive neuron models with an Izhikevich hybrid neuron. This begins with a network modeling action-selection, where the basal activity levels and the ability to appropriately select the most salient input is reproduced. A Parkinson's disease model is then explored under normal conditions, Parkinsonian conditions and during subthalamic nucleus deep brain stimulation (DBS). The resulting network is capable of replicating the loss of thalamic relay capabilities in the Parkinsonian state and its return under DBS. This is also demonstrated using a network capable of action-selection. Finally, a study of correlation transfer under different patterns of Parkinsonian activity is presented. These networks successfully captured the significant results of the originals studies. This not only creates a foundation for neuromorphic hardware implementations but may also support the development of large-scale biophysical models. The former potentially providing a way of improving the efficacy of DBS and the latter allowing for the efficient simulation of larger more comprehensive networks.

Dopaminergic Control of the Exploration-Exploitation Trade-Off via the Basal Ganglia

We continuously face the dilemma of choosing between actions that gather new information or actions that exploit existing knowledge. This "exploration-exploitation" trade-off depends on the environment: stability favors exploiting knowledge to maximize gains; volatility favors exploring new options and discovering new outcomes. Here we set out to reconcile recent evidence for dopamine's involvement in the exploration-exploitation trade-off with the existing evidence for basal ganglia control of action selection, by testing the hypothesis that tonic dopamine in the striatum, the basal ganglia's input nucleus, sets the current exploration-exploitation trade-off. We first advance the idea of interpreting the basal ganglia output as a probability distribution function for action selection. Using computational models of the full basal ganglia circuit, we showed that, under this interpretation, the actions of dopamine within the striatum change the basal ganglia's output to favor the level of exploration or exploitation encoded in the probability distribution. We also found that our models predict striatal dopamine controls the exploration-exploitation trade-off if we instead read-out the probability distribution from the target nuclei of the basal ganglia, where their inhibitory input shapes the cortical input to these nuclei. Finally, by integrating the basal ganglia within a reinforcement learning model, we showed how dopamine's effect on the exploration-exploitation trade-off could be measurable in a forced two-choice task. These simulations also showed how tonic dopamine can appear to affect learning while only directly altering the trade-off. Thus, our models support the hypothesis that changes in tonic dopamine within the striatum can alter the exploration-exploitation trade-off by modulating the output of the basal ganglia.

A simple method for characterizing passive and active neuronal properties: application to striatal neurons

The study of active and passive neuronal dynamics usually relies on a sophisticated array of electrophysiological, staining and pharmacological techniques. We describe here a simple complementary method that recovers many findings of these more complex methods but relies only on a basic patch-clamp recording approach. Somatic short and long current pulses were applied in vitro to striatal medium spiny (MS) and fast spiking (FS) neurons from juvenile rats. The passive dynamics were quantified by fitting two-compartment models to the short current pulse data. Lumped conductances for the active dynamics were then found by compensating this fitted passive dynamics within the current-voltage relationship from the long current pulse data. These estimated passive and active properties were consistent with previous more complex estimations of the neuron properties, supporting the approach. Relationships within the MS and FS neuron types were also evident, including a graduation of MS neuron properties consistent with recent findings about D1 and D2 dopamine receptor expression. Application of the method to simulated neuron data supported the hypothesis that it gives reasonable estimates of membrane properties and gross morphology. Therefore detailed information about the biophysics can be gained from this simple approach, which is useful for both classification of neuron type and biophysical modelling. Furthermore, because these methods rely upon no manipulations to the cell other than patch clamping, they are ideally suited to in vivo electrophysiology.

Pathophysiological distortions in time perception and timed performance

Distortions in time perception and timed performance are presented by a number of different neurological and psychiatric conditions (e.g. Parkinson's disease, schizophrenia, attention deficit hyperactivity disorder and autism). As a consequence, the primary focus of this review is on factors that define or produce systematic changes in the attention, clock, memory and decision stages of temporal processing as originally defined by Scalar Expectancy Theory. These findings are used to evaluate the Striatal Beat Frequency Theory, which is a neurobiological model of interval timing based upon the coincidence detection of oscillatory processes in corticostriatal circuits that can be mapped onto the stages of information processing proposed by Scalar Timing Theory.

Dopamine-signaled reward predictions generated by competitive excitation and inhibition in a spiking neural network model

Dopaminergic neurons in the mammalian substantia nigra display characteristic phasic responses to stimuli which reliably predict the receipt of primary rewards. These responses have been suggested to encode reward prediction-errors similar to those used in reinforcement learning. Here, we propose a model of dopaminergic activity in which prediction-error signals are generated by the joint action of short-latency excitation and long-latency inhibition, in a network undergoing dopaminergic neuromodulation of both spike-timing dependent synaptic plasticity and neuronal excitability. In contrast to previous models, sensitivity to recent events is maintained by the selective modification of specific striatal synapses, efferent to cortical neurons exhibiting stimulus-specific, temporally extended activity patterns. Our model shows, in the presence of significant background activity, (i) a shift in dopaminergic response from reward to reward-predicting stimuli, (ii) preservation of a response to unexpected rewards, and (iii) a precisely timed below-baseline dip in activity observed when expected rewards are omitted.

Spike-train communities: finding groups of similar spike trains

Identifying similar spike-train patterns is a key element in understanding neural coding and computation. For single neurons, similar spike patterns evoked by stimuli are evidence of common coding. Across multiple neurons, similar spike trains indicate potential cell assemblies. As recording technology advances, so does the urgent need for grouping methods to make sense of large-scale datasets of spike trains. Existing methods require specifying the number of groups in advance, limiting their use in exploratory analyses. I derive a new method from network theory that solves this key difficulty: it self-determines the maximum number of groups in any set of spike trains, and groups them to maximize intragroup similarity. This method brings us revealing new insights into the encoding of aversive stimuli by dopaminergic neurons, and the organization of spontaneous neural activity in cortex. I show that the characteristic pause response of a rat's dopaminergic neuron depends on the state of the superior colliculus: when it is inactive, aversive stimuli invoke a single pattern of dopaminergic neuron spiking; when active, multiple patterns occur, yet the spike timing in each is reliable. In spontaneous multineuron activity from the cortex of anesthetized cat, I show the existence of neural ensembles that evolve in membership and characteristic timescale of organization during global slow oscillations. I validate these findings by showing that the method both is remarkably reliable at detecting known groups and can detect large-scale organization of dynamics in a model of the striatum.

Reconstructing the three-dimensional GABAergic microcircuit of the striatum

A system's wiring constrains its dynamics, yet modelling of neural structures often overlooks the specific networks formed by their neurons. We developed an approach for constructing anatomically realistic networks and reconstructed the GABAergic microcircuit formed by the medium spiny neurons (MSNs) and fast-spiking interneurons (FSIs) of the adult rat striatum. We grew dendrite and axon models for these neurons and extracted probabilities for the presence of these neurites as a function of distance from the soma. From these, we found the probabilities of intersection between the neurites of two neurons given their inter-somatic distance, and used these to construct three-dimensional striatal networks. The MSN dendrite models predicted that half of all dendritic spines are within 100µm of the soma. The constructed networks predict distributions of gap junctions between FSI dendrites, synaptic contacts between MSNs, and synaptic inputs from FSIs to MSNs that are consistent with current estimates. The models predict that to achieve this, FSIs should be at most 1% of the striatal population. They also show that the striatum is sparsely connected: FSI-MSN and MSN-MSN contacts respectively form 7% and 1.7% of all possible connections. The models predict two striking network properties: the dominant GABAergic input to a MSN arises from neurons with somas at the edge of its dendritic field; and FSIs are inter-connected on two different spatial scales: locally by gap junctions and distally by synapses. We show that both properties influence striatal dynamics: the most potent inhibition of a MSN arises from a region of striatum at the edge of its dendritic field; and the combination of local gap junction and distal synaptic networks between FSIs sets a robust input-output regime for the MSN population. Our models thus intimately link striatal micro-anatomy to its dynamics, providing a biologically grounded platform for further study.

The brain has an immensely complex wiring diagram, but few computational models of brain regions attempt accurate renditions of the wiring between neurons. Consequently, these models' dynamics may not accurately reflect those of the region. Key barriers here are the difficulty of reconstructing such networks and the paucity of critical data on neuron morphology. We demonstrate an approach that gets around these problems by using the available data to construct prototype neuron morphologies, and uses these to estimate how the probability of a connection between two neurons changes as we change the distance between them. With these in hand, we constructed artificial three-dimensional networks of the rat striatum and find that the connection distributions agree well with current estimates from anatomical studies. Our networks show features and dynamical implications of striatal wiring that would be difficult to intuit: the dominant input to the striatal projection neuron arises from other neurons just at the edge of its dendrites, and the main inhibitory interneurons are coupled locally by electrical connections and more distally by chemical synapses. Together, these properties set a unique state for the input-output computations of the striatum.