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The fluid movement of an arm is controlled by multiple parameters that can be set independently. Recent studies argue that arm movements are generated by the collective dynamics of neurons in motor cortex. But how these collective dynamics simultaneously encode and control multiple parameters of movement is an open question. Using a task where monkeys made sequential, varied arm movements, we show that the direction and urgency of arm movements are simultaneously encoded in the low-dimensional trajectories of population activity: each movement’s direction by a fixed, looped neural trajectory and its urgency by how quickly that trajectory was traversed. Network models showed this latent coding is potentially advantageous as it allows the direction and urgency of arm movement to be independently controlled. Our results suggest how low-dimensional neural dynamics can define multiple parameters of goal-directed movement simultaneously.

The striatum's complex microcircuit is made by connections within and between its D1- and D2-receptor expressing projection neurons and at least five species of interneuron. Precise knowledge of this circuit is likely essential to understanding striatum's functional roles and its dysfunction in a wide range of movement and cognitive disorders. We introduce here a Bayesian approach to mapping neuron connectivity using intracellular recording data, which lets us simultaneously evaluate the probability of connection between neuron types, the strength of evidence for it, and its dependence on distance. Using it to synthesize a complete map of the mouse striatum, we find strong evidence for two asymmetries: a selective asymmetry of projection neuron connections, with D2 neurons connecting twice as densely to other projection neurons than do D1 neurons, but neither subtype preferentially connecting to another; and a length-scale asymmetry, with interneuron connection probabilities remaining non-negligible at more than twice the distance of projection neuron connections. We further show that our Bayesian approach can evaluate evidence for wiring changes, using data from the developing striatum and a mouse model of Huntington's disease. By quantifying the uncertainty in our knowledge of the microcircuit, our approach reveals a wide range of potential striatal wiring diagrams consistent with current data.SIGNIFICANCE STATEMENTTo properly understand a neuronal circuit's function, it is important to have an accurate picture of the rate of connection between individual neurons and how this rate changes with the distance separating pairs of neurons. We present a Bayesian method for extracting this information from experimental data and apply it to the mouse striatum, a subcortical structure involved in learning and decision-making, which is made up of a variety of different projection neurons and interneurons. Our resulting statistical map reveals not just the most robust estimates of the probability of connection between neuron types, but also the strength of evidence for them, and their dependence on distance.

In monogenetic generalized forms of dystonia, in vitro neurophysiological recordings have demonstrated direct evidence for abnormal plasticity at the level of the cortico‐striatal synapse. It is unclear whether similar abnormalities contribute to the pathophysiology of cervical dystonia, the most common type of focal dystonia. We investigated whether abnormal cortico‐striatal synaptic plasticity contributes to abnormal reward‐learning behavior in patients with focal dystonia. Forty patients and 40 controls performed a reward gain and loss avoidance reversal learning task. Participant's behavior was fitted to a computational model of the basal ganglia incorporating detailed cortico‐striatal synaptic learning rules. Model comparisons were performed to assess the ability of four hypothesized receptor specific abnormalities of cortico‐striatal long‐term potentiation (LTP) and long‐term depression (LTD): increased or decreased D1:LTP/LTD and increased or decreased D2: LTP/LTD to explain abnormal behavior in patients. Patients were selectively impaired in the post‐reversal phase of the reward task. Individual learning rates in the reward reversal task correlated with the severity of the patient's motor symptoms. A model of the striatum with decreased D2:LTP/ LTD best explained the patient's behavior, suggesting excessive D2 cortico‐striatal synaptic depotentiation could underpin biased reward‐learning in patients with cervical dystonia. Reversal learning impairment in cervical dystonia may be a behavioral correlate of D2‐specific abnormalities in cortico‐striatal synaptic plasticity. Reinforcement learning tasks with computational modeling could allow the identification of molecular targets for novel treatments based on their ability to restore normal reward‐learning behavior in these patients., Here we demonstrate that reward‐learning in patients with cervical dystonia is abnormal and that this can be directly related to impaired plasticity at the cortico‐striatal synapse. These results support the idea that a common link between focal and generalized forms of dystonia (where animal models have provided direct evidence aberrant of striatal plasticity) is the presence of abnormal cortico‐striatal plasticity. In the future, treatments which target this may be used clinically to alleviate symptoms of this common movement disorder.

How does your brain decide what you will do next? Over the past few decades compelling evidence has emerged that the basal ganglia, a collection of nuclei in the fore- and mid-brain of all vertebrates, are vital to action selection. Gurney, Prescott, and Redgrave published an influential computational account of this idea in Biological Cybernetics in 2001. Here we take a look back at this pair of papers, outlining the "GPR" model contained therein, the context of that model's development, and the influence it has had over the past twenty years. Tracing its lineage into models and theories still emerging now, we are encouraged that the GPR model is that rare thing, a computational model of a brain circuit whose advances were directly built on by others., 6 pages, 2 figures

If spikes are the medium, what is the message? Answering that question is driving the development of large-scale, single neuron resolution recordings from behaving animals, on the scale of thousands of neurons. But these data are inherently high-dimensional, with as many dimensions as neurons - so how do we make sense of them? For many the answer is to reduce the number of dimensions. Here I argue we can distinguish weak and strong principles of neural dimension reduction. The weak principle is that dimension reduction is a convenient tool for making sense of complex neural data. The strong principle is that dimension reduction shows us how neural circuits actually operate and compute. Elucidating these principles is crucial, for which we subscribe to provides radically different interpretations of the same neural activity data. I show how we could make either the weak or strong principles appear to be true based on innocuous looking decisions about how we use dimension reduction on our data. To counteract these confounds, I outline the experimental evidence for the strong principle that do not come from dimension reduction; but also show there are a number of neural phenomena that the strong principle fails to address. To reconcile these conflicting data, I suggest that the brain has both principles at play., 27 pages, 5 figures

Calcium imaging is a powerful tool for capturing the simultaneous activity of large populations of neurons. Here we determine the extent to which our inferences of neural population activity, correlations, and coding depend on our choice of whether and how we deconvolve the calcium time-series into spike-driven events. To this end, we use a range of deconvolution algorithms to create nine versions of the same calcium imaging data obtained from barrel cortex during a pole-detection task. Seeking suitable values for the deconvolution algorithms’ parameters, we optimise them against ground-truth data, and find those parameters both vary by up to two orders of magnitude between neurons and are sensitive to small changes in their values. Applied to the barrel cortex data, we show that a substantial fraction of the processing methods fail to recover simple features of population activity in barrel cortex already established by electrophysiological recordings. Raw calcium time-series contain an order of magnitude more neurons tuned to features of the pole task; yet there is also qualitative disagreement between deconvolution methods on which neurons are tuned to the task. Finally, we show that raw and processed calcium time-series qualitatively disagree on the structure of correlations within the population and the dimensionality of its joint activity. Collectively, our results show that properties of neural activity, correlations, and coding inferred from calcium imaging are sensitive to the choice of if and how spike-evoked events are recovered. We suggest that quantitative results obtained from population calcium-imaging be verified across multiple processed forms of the calcium time-series.

Medial prefrontal cortex (mPfC) activity represents information about the state of the world, including present behaviour, such as decisions, and the immediate past, such as short-term memory. Unknown is whether information about different states of the world are represented in the same mPfC neural population and, if so, how they are kept distinct. To address this, we analyse here mPfC population activity of rats learning rules in a Y-maze, with self-initiated choice trials to an arm-end followed by a self-paced return during the inter-trial interval (ITI). We find that trial and ITI population activity from the same population fall into different low-dimensional subspaces. These subspaces encode different states of the world: multiple features of the task can be decoded from both trial and ITI activity, but the decoding axes for the same feature are roughly orthogonal between the two task phases, and the decodings are predominantly of features of the present during the trial but features of the preceding trial during the ITI. These subspace distinctions are carried forward into sleep, where population activity is preferentially reactivated in post-training sleep, but differently for activity from the trial and ITI subspaces. Our results suggest that the problem of interference when representing different states of the world is solved in mPfC by population activity occupying different subspaces for the world states, which can be independently decoded by downstream targets and independently addressed by upstream inputs.Significance statementActivity in the medial prefrontal cortex plays a roles in representing the current and past states of the world. We show that during a maze task the activity of a single population in medial prefrontal cortex represents at least two different states of the world. These representations were sequential and sufficiently distinct that a downstream population could separately read out either state from that activity. Moreover, the activity representing different states is differently reactivated in sleep. Different world states can thus be represented in the same medial prefrontal cortex population, but in such a way that prevents potentially catastrophic interference between them.

Perceptual decision making is an active process where animals move their sense organs to extract task-relevant information. To investigate how the brain translates sensory input into decisions during active sensation, we developed a mouse active touch task where the mechanosensory input can be precisely measured and that challenges animals to use multiple mechanosensory cues. Mice were trained to localise a pole using a single whisker and to report their decision by selecting one of three choices. Using high-speed imaging and machine vision we estimated whisker-object mechanical forces at millisecond resolution. Mice solved the task by a sensory-motor strategy where both the strength and direction of whisker bending were informative cues to pole location. We found competing influences of immediate sensory input and choice memory on mouse choice. On correct trials, choice could be predicted from the direction and strength of whisker bending, but not from previous choice. In contrast, on error trials, choice could be predicted from previous choice but not from whisker bending. This study shows that animal choices during active tactile decision making can be predicted from mechanosenory and choice-memory signals; and provides a new task, well-suited for future study of the neural basis of active perceptual decisions.SIGNIFICANCE STATEMENTDue to the difficulty of measuring the sensory input to moving sense organs, active perceptual decision making remains poorly understood. The whisker system provides a way forward since it is now possible to measure the mechanical forces due to whisker-object contact during behaviour. Here we train mice in a novel behavioural task that challenges them to use rich mechanosensory cues, but can be performed using one whisker and enables task-relevant mechanical forces to be precisely estimated. This approach enables rigorous study of how sensory cues translate into action during active, perceptual decision making. Our findings provide new insight into active touch and how sensory/internal signals interact to determine behavioural choices.

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.

The joint activity of neural populations is high dimensional and complex. One strategy for reaching a tractable understanding of circuit function is to seek the simplest dynamical system that can account for the population activity. By imaging Aplysia’s pedal ganglion during fictive locomotion, here we show that its population-wide activity arises from a low-dimensional spiral attractor. Evoking locomotion moved the population into a low-dimensional, periodic, decaying orbit - a spiral - in which it behaved as a true attractor, converging to the same orbit when evoked, and returning to that orbit after transient perturbation. We found the same attractor in every preparation, and could predict motor output directly from its orbit, yet individual neurons’ participation changed across consecutive locomotion bouts. From these results, we propose that only the low-dimensional dynamics for movement control, and not the high-dimensional population activity, are consistent within and between nervous systems. DOI: http://dx.doi.org/10.7554/eLife.27342.001, eLife digest In all animals, neurons in the brain work together to generate movement. From a slug’s ability to crawl, to your ability to move your hand, movement is dependent on hundreds or thousands of neurons being active at the same time. Rhythmic movements such as crawling or swimming show this clearly: groups of neurons fire together and remain silent together in a repeating sequence, producing waves of muscle contraction. But do we need to understand the activity of each of the hundreds or thousands of individual neurons to know how they generate these movements? Bruno et al. argue that we do not, and propose instead that brain circuits that generate movement show a few set patterns of activity. By recording the activity of a population of neurons, we can identify the pattern of activity that generates a particular movement. To illustrate this point, Bruno et al. examined the network of neurons that drives the rhythmic crawling movement of the sea slug Aplysia. The results show that the network of neurons seems to contain many different patterns of activity during crawling. Yet collectively these different patterns are reflections of a simpler hidden system, a spiral of ever-decreasing, oscillating activity. This pattern is referred to as a spiral attractor because whenever the network is activated, the overall pattern of activity is always pulled into this spiral regardless of its starting point. The same applies whenever the network is disturbed. The key thing to note, however, is that individual neurons within the network do not show the same activity each time the network is active. This means that only the spiral attractor itself, and not the contribution of the individual neurons, is constant every time the sea slug crawls. What do we need to know to understand the brain? The results presented by Bruno et al. suggests that identifying the hidden systems that underlie seemingly complex and varying neural activity is the key to understanding how brains generate movement. This may also be true for how brains form memories, make decisions, and give rise to sight, hearing and touch. DOI: http://dx.doi.org/10.7554/eLife.27342.002

Deep brain stimulation (DBS) is a remarkably successful treatment for the motor symptoms of Parkinson's disease. High-frequency stimulation of the subthalamic nucleus (STN) within the basal ganglia is a main clinical target, but the physiological mechanisms of therapeutic STN DBS at the cellular and network level are unclear. We set out to begin to address the hypothesis that a mixture of responses in the basal ganglia output nuclei, combining regularized firing and inhibition, is a key contributor to the effectiveness of STN DBS. We used our computational model of the complete basal ganglia circuit to show how such a mixture of responses in basal ganglia output naturally arises from the network effects of STN DBS. We replicated the diversification of responses recorded in a primate STN DBS study to show that the model's predicted mixture of responses is consistent with therapeutic STN DBS. We then showed how this 'mixture of response' perspective suggests new ideas for DBS mechanisms: first, that the therapeutic frequency of STN DBS is above 100�€ƒHz because the diversification of responses exhibits a step change above this frequency; and second, that optogenetic models of direct STN stimulation during DBS have proven therapeutically ineffective because they do not replicate the mixture of basal ganglia output responses evoked by electrical DBS.

The prefrontal cortex is thought to learn the relationships between actions and their outcomes. But little is known about what changes to population activity in prefrontal cortex are specific to learning these relationships. Here we characterise the plasticity of population activity in the medial prefrontal cortex of male rats learning rules on a Y-maze. First, we show that the population always changes its patterns of joint activity between the periods of sleep either side of a training session on the maze, irrespective of successful rule learning during training. Next, by comparing the structure of population activity in sleep and training, we show that this population plasticity differs between learning and non-learning sessions. In learning sessions, the changes in population activity in posttraining sleep incorporate the changes to the population activity during training on the maze. In non-learning sessions, the changes in sleep and training are unrelated. Finally, we show evidence that the non-learning and learning forms of population plasticity are driven by different neuron-level changes, with the non-learning form entirely accounted for by independent changes to the excitability of individual neurons, and the learning form also including changes to firing rate couplings between neurons. Collectively, our results suggest two different forms of population plasticity in prefrontal cortex during the learning of action-outcome relationships, one a persistent change in population activity structure decoupled from overt rule-learning, the other a directional change driven by feedback during behaviour.Significance statementThe prefrontal cortex is thought to represent our knowledge about what action is worth doing in which context. But we do not know how the activity of neurons in prefrontal cortex collectively changes when learning which actions are relevant. Here we show in a trial-and-error task that population activity in prefrontal cortex is persistently changing, irrespective of learning. Only during episodes of clear learning of relevant actions are the accompanying changes to population activity carried forward into sleep, suggesting a long-lasting form of neural plasticity. Our results suggest that representations of relevant actions in prefrontal cortex are acquired by reward imposing a direction onto ongoing population plasticity.

Optical recording with fast voltage sensitive dyes makes it possible, in suitable preparations, to simultaneously monitor the action potentials of large numbers of individual neurons. Here we describe methods for doing this, including considerations of different dyes and imaging systems, methods for correlating the optical signals with their source neurons, procedures for getting good signals, and the use of Independent Component Analysis for spike-sorting raw optical data into single neuron traces. These combined tools represent a powerful approach for large-scale recording of neural networks with high temporal and spatial resolution.

The existence of multiple parallel loops connecting sensorimotor systems to the basal ganglia has given rise to proposals that these nuclei serve as a selection mechanism resolving competitions between the alternative actions available in a given context. A strong test of this hypothesis is to require a computational model of the basal ganglia to generate integrated selection sequences in an autonomous agent, we therefore describe a robot architecture into which such a model is embedded, and require it to control action selection in a robotic task inspired by animal observations. Our results demonstrate effective action selection by the embedded model under a wide range of sensory and motivational conditions. When confronted with multiple, high salience alternatives, the robot also exhibits forms of behavioral disintegration that show similarities to animal behavior in conflict situations. The model is shown to cast light on recent neurobiological findings concerning behavioral switching and sequencing.

Neurobehavioral data from intact, decerebrate, and neonatal rats suggests that the reticular formation provides a brainstem substrate for action selection in the vertebrate central nervous system. In this article, Kilmer, McCulloch and Blum’s (1969) landmark reticular formation model (see also Kilmer, 1997) is described and re-evaluated, both in simulation and, for the first time, as a mobile robot con troller. Particular model configurations are found to provide effective action selection mechanisms in a robot survival task using either simulated or physical robots. The model’s competence is dependent on the organization of afferents from model sensory systems, and a genetic algorithm search identi fied a class of afferent configurations which have long survival times. The results support our proposal that the reticular formation evolved to provide effective arbitration between innate behaviors and, with the forebrain basal ganglia, may constitute the integrative, “centrencephalic” core of vertebrate brain architecture. Additionally, the results demonstrate that the Kilmer et al. model provides an alternative form of robot controller to those usually considered in the adaptive behavior literature.

SummaryThe neural substrates of motor programs are only well understood for small, dedicated circuits. Here we investigate how a motor program is constructed within a large network. We imaged populations of neurons in the Aplysia pedal ganglion during execution of a locomotion motor program. We found that the program was built from a very small number of dynamical building blocks, including both neural ensembles and low-dimensional rotational dynamics. These map onto physically discrete regions of the ganglion, so that the motor program has a corresponding modular organization in both dynamical and physical space. Using this dynamic map, we identify the population potentially implementing the rhythmic pattern generator and find that its activity physically traces a looped trajectory, recapitulating its low-dimensional rotational dynamics. Our results suggest that, even in simple invertebrates, neural motor programs are implemented by large, distributed networks containing multiple dynamical systems.

In Parkinson’s disease (PD), cortical networks show enhanced synchronized activity but whether this precedes motor signs is unknown. We investigated this question in PINK1−/− mice, a genetic rodent model of the PARK6 variant of familial PD which shows impaired spontaneous locomotion at 16 months. We used two-photon calcium imaging and whole-cell patch clamp in slices from juvenile (P14–P21) wild-type or PINK1−/− mice. We designed a horizontal tilted cortico-subthalamic slice where the only connection between cortex and subthalamic nucleus (STN) is the hyperdirect cortico-subthalamic pathway. We report excessive correlation and synchronization in PINK1−/− M1 cortical networks 15 months before motor impairment. The percentage of correlated pairs of neurons and their strength of correlation were higher in the PINK1−/− M1 than in the wild type network and the synchronized network events involved a higher percentage of neurons. Both features were independent of thalamo-cortical pathways, insensitive to chronic levodopa treatment of pups, but totally reversed by antidromic invasion of M1 pyramidal neurons by axonal spikes evoked by high frequency stimulation (HFS) of the STN. Our study describes an early excess of synchronization in the PINK1−/− cortex and suggests a potential role of antidromic activation of cortical interneurons in network desynchronization. Such backward effect on interneurons activity may be of importance for HFS-induced network desynchronization., The study was financed by Inserm, Association France-Parkinson (Constance Hammond), ERA-Net Neuron (Constance Hammond), MRC Senior non-Clinical Fellowship (Mark D. Humphries and Abhinav Singh) and Medtronic. We thank the Gispert/Auburger team at the University Frankfurt am Main for providing the PINK1-KO mice.

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.

International audience; Cortical activity involves large populations of neurons, even when it is limited to functionally coherent areas. Electrophysiological recordings, on the other hand, involve comparatively small neural ensembles, even when modern-day techniques are used. Here we review results which have started to fill the gap between these two scales of inquiry, by shedding light on the statistical distributions of activity in large populations of cells. We put our main focus on data recorded in awake animals that perform simple decision-making tasks and consider statistical distributions of activity throughout cortex, across sensory, associative, and motor areas. We transversally review the complexity of these distributions, from distributions of firing rates and metrics of spike-train structure, through distributions of tuning to stimuli or actions and of choice signals, and finally the dynamical evolution of neural population activity and the distributions of (pairwise) neural interactions. This approach reveals shared patterns of statistical organization across cortex, including: (i) long-tailed distributions of activity, where quasi-silence seems to be the rule for a majority of neurons; that are barely distinguishable between spontaneous and active states; (ii) distributions of tuning parameters for sensory (and motor) variables, which show an extensive extrapolation and fragmentation of their representations in the periphery; and (iii) population-wide dynamics that reveal rotations of internal representations over time, whose traces can be found both in stimulus-driven and internally generated activity. We discuss how these insights are leading us away from the notion of discrete classes of cells, and are acting as powerful constraints on theories and models of cortical organization and population coding.

International audience; 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 favours exploiting knowledge to maximise gains; volatility favours 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 the tonic dopamine in the striatum, the basal ganglia's input nucleus, sets the current exploration-exploitation tradeoff. We first advanced 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 favour 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 ho 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.

Adult motor coordination requires strong coincident cortical excitatory input to hyperpolarized Medium Spiny Neurons (MSNs), the dominant neuronal population of the striatum. However, cortical and subcortical neurons generate during development large ongoing patterns required for activity-dependent construction of networks. This raises the question of whether immature MSNs have adult features from early stages or whether they generate immature patterns that are timely silenced to enable locomotion. Using a wide range of techniques including dynamic two photon imaging, whole-cell or single channel patch clamp recording in slices from Nkx2.1-GFP mice, we now report a silencing of MSNs that timely coincides with locomotion. At embryonic stage (as early as E16) and during early postnatal days, genetically identified MSNs have a depolarized resting membrane potential, a high input resistance and lack both inward rectifying (IKIR) and early slowly decaying (ID) potassium currents. They generate intrinsic voltage-gated clustered calcium activity without synaptic components. From postnatal days 5 to 7, the striatal network transiently generates synapse-driven giant depolarizing potentials (GDPs) when activation of cortical inputs evokes long lasting EPSCs in MSNs. Both are mediated by NR2C/D-receptors. These immature features are abruptly replaced by adult ones before P10: MSNs express IKIR and ID and generate short lasting, time-locked corticostriatal AMPA/NMDA EPSCs with no NR2C/D component. This shift parallels the onset of quadruped motion by the pup. Therefore, MSNs generate immature patterns that are timely shut off to enable the coordination of motor programs.

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.

Biological computational modellers are becoming increasingly interested in building large, eclectic models, including components on many different computational substrates, both biological and non-biological. At the same time, the rise of the philosophy of embodied modelling is generating a need to deploy biological models as controllers for robots in real-world environments. Finally, robotics engineers are beginning to find value in seconding biomimetic control strategies for use on practical robots. Together with the ubiquitous desire to make good on past software development effort, these trends are throwing up new challenges of intellectual and technological integration (for example across scales, across disciplines, and even across time) - challenges that are unmet by existing software frameworks. Here, we outline these challenges in detail, and go on to describe a newly developed software framework, BRAHMS. that meets them. BRAHMS is a tool for integrating computational process modules into a viable, computable system: its generality and flexibility facilitate integration across barriers, such as those described above, in a coherent and effective way. We go on to describe several cases where BRAHMS has been successfully deployed in practical situations. We also show excellent performance in comparison with a monolithic development approach. Additional benefits of developing in the framework include source code self-documentation, automatic coarse-grained parallelisation, cross-language integration, data logging, performance monitoring, and will include dynamic load-balancing and 'pause and continue' execution. BRAHMS is built on the nascent, and similarly general purpose, model markup language, SystemML. This will, in future, also facilitate repeatability and accountability (same answers ten years from now), transparent automatic software distribution, and interfacing with other SystemML tools. (C) 2009 Elsevier Ltd. All rights reserved.

We recently proposed that short-latency, sensory-evoked dopamine release is critical for learning action-outcome causality [1]. If an action causes an unexpected outcome associated with a phasic visual event, there will be a phasic burst of dopamine in the striatum. Subsequent reinforcement of the striatal response to the cortical representation of the action then makes the selection of the action (and its outcome) more likely; i.e. there is "repetition biasing" of action selection. This, in turn, facilitates associative learning of the action-outcome pairing elsewhere in the brain. Here, we present a model of cortico-striatal plasticity in medium spiny neurons (MSNs) that could form the basis for a quantitative account of action-outcome learning in basal ganglia.

Loss of dopamine cells in Parkinson's Disease and its ani-mal models leads to profound motor deficits. An intactdopamine system also seems to be critical for many formsof learning [1]. Much work on understanding these rolesof dopamine has focused on the striatum, the main inputnucleus of the basal ganglia, as the striatum is the mainlocus of dopamine's action in the verterbrate brain [2].Damage to the striatum itself also impairs both motoraction and learning [3]. Thus, the twin problems of under-standing the computational roles of dopamine and thestriatum are inseparably intertwined.Understanding dopamine's effects on the complex striatalmicrocircuit ideally requires large-scale models that repli-cate the neuron types, numbers, and connectivity at one-to-one scale. To build at such scales, we require individualneuron models that are simple enough to be computa-tionally tractable, but sufficiently complex to capture keymembrane properties that contribute to the characteristicbehavior of a neuron species. Our neuron model of choiceis the recent canonical spiking model of Izhikevich [4].However, it has not yet been extended to account for theaction of neuromodulators.We extend the striatal medium spiny (MSN) and fast-spik-ing (FS) interneuron models of [5] to account fordopaminergic modulation of intrinsic ion channels andsynaptic inputs. We use data from a recent 189 compart-ment model of the MSN [3] to tune our simple model ofthat neuron under both current injection and spikinginput regimes with varying activation of dopamine D1-and D2-type receptors. The reduced models capture theinput-output relationships for both current injection andspiking input with remarkable accuracy. We derive a fullset of stability properties for the original and dopaminemodulated forms of the MSN model. We use these toestablish that the dopamine models do not change thestability properties and hence the models predict that theMSN is not bistable in either baseline or dopamine-satu-rated conditions. Our extensions to the simple model ofthe FS interneuron are consistent with the existing data,but tuning the new parameters is made difficult by thelack of quantitative results from experimental work. Ourwork thus establishes reduced yet accurate dopamine-modulated forms of MSN and FS interneuron models,suitable for use in large-scale models of the striatum.Moreover, these also provide a tractable framework forfurther study of dopamine's effects on individual neuroncomputation.

Neurons encode information in their spike trains. In a range of neural systems, every spike train and potentially each spike is supremely important [1], so important that, given appropriate input, many neurons can reliably repeat their spike timing with startling accuracy [2]. Yet a target neuron sees many such spike trains in its afferent input. And the statistics of such a group of spike-trains are well described by simple models that pay no heed to the single spike or even the single spike train. How then do we reconcile the success of these simple models with the complexity of encoding within and decoding of spike trains [1,3]? First, we set out to understand just how accurate these simple models are. They are often used for qualitative understanding of problems [1] and that is certainly an approach used here. But we show that these simple models can be pushed hard before they break down and thereby can give quantitative insight. We build a framework that directly generates the set of spike-events that occur across all the target neuron's inputs and that encapsulate many simple models of the individual spike trains. Nonetheless, these spike-event generators are sufficiently simple for us to gain analytical insight into exactly how the structure of the input to a neuron is dependent on the number, rate and correlation of the individual spike trains. As an example, we use this to model the global properties that arise from weak pair-wise correlations between spike trains [4]. The framework's most interesting prediction is that the global statistics of the afferent input to a single neuron converge for a wide range of properties of the individual afferent spike trains, thus obscuring potentially important properties of those spike trains. How then does information carried by individual spike trains become decoded into the output of a neuron? This questions stands in contrast to much previous work that has focused on decoding the spike train correlates of continuous stimuli [1,3]. We show, because of the obscuring effects on individual trains, our framework predicts that strongly asymmetric distributions of synaptic conductances are necessary for reliable reproduction of output spike trains in response to common components of different sets of inputs [2]. Thus, we posit this as the reason for such distributions in the vertebrate brain, recently described in many neural circuits [5].

Computational neuroscience is increasingly moving beyond modeling individual neurons or neural systems to consider the integration of multiple models, often constructed by different research groups. We report on our preliminary technical integration of recent hippocampal formation, basal ganglia and physical environment models, together with visualisation tools, as a case study in the use of Python across the modelling tool-chain. We do not present new modeling results here. The architecture incorporates leaky-integrator and rate-coded neurons, a 3D environment with collision detection and tactile sensors, 3D graphics and 2D plots. We found Python to be a flexible platform, offering a significant reduction in development time, without a corresponding significant increase in execution time. We illustrate this by implementing a part of the model in various alternative languages and coding styles, and comparing their execution times. For very large scale system integration, communication with other languages and parallel execution may be required, which we demonstrate using the BRAHMS framework's Python bindings.

The striatum, the principal input structure of the basal ganglia, is crucial to both motor control and learning. It receives convergent input from all over the neocortex, hippocampal formation, amygdala and thalamus, and is the primary recipient of dopamine in the brain. Within the striatum is a GABAergic microcircuit that acts upon these inputs, formed by the dominant medium-spiny projection neurons (MSNs) and fast-spiking interneurons (FSIs). There has been little progress in understanding the computations it performs, hampered by the non-laminar structure that prevents identification of a repeating canonical microcircuit. We here begin the identification of potential dynamically-defined computational elements within the striatum. We construct a new three-dimensional model of the striatal microcircuit's connectivity, and instantiate this with our dopamine-modulated neuron models of the MSNs and FSIs. A new model of gap junctions between the FSIs is introduced and tuned to experimental data. We introduce a novel multiple spike-train analysis method, and apply this to the outputs of the model to find groups of synchronised neurons at multiple time-scales. We find that, with realistic in vivo background input, small assemblies of synchronised MSNs spontaneously appear, consistent with experimental observations, and that the number of assemblies and the time-scale of synchronisation is strongly dependent on the simulated concentration of dopamine. We also show that feed-forward inhibition from the FSIs counter-intuitively increases the firing rate of the MSNs. Such small cell assemblies forming spontaneously only in the absence of dopamine may contribute to motor control problems seen in humans and animals following a loss of dopamine cells. (C) 2009 Elsevier Ltd. All rights reserved.

Loss of dopamine from the striatum can cause both profound motor deficits, as in Parkinsons's disease, and disrupt learning. Yet the effect of dopamine on striatal neurons remains a complex and controversial topic, and is in need of a comprehensive framework. We extend a reduced model of the striatal medium spiny neuron (MSN) to account for dopaminergic modulation of its intrinsic ion channels and synaptic inputs. We tune our D1 and D2 receptor MSN models using data from a recent large-scale compartmental model. The new models capture the input-output relationships for both current injection and spiking input with remarkable accuracy, despite the order of magnitude decrease in system size. They also capture the paired pulse facilitation shown by MSNs. Our dopamine models predict that synaptic effects dominate intrinsic effects for all levels of D1 and D2 receptor activation. We analytically derive a full set of equilibrium points and their stability for the original and dopamine modulated forms of the MSN model. We find that the stability types are not changed by dopamine activation, and our models predict that the MSN is never bistable. Nonetheless, the MSN models can produce a spontaneously bimodal membrane potential similar to that recently observed in vitro following application of NMDA agonists. We demonstrate that this bimodality is created by modelling the agonist effects as slow, irregular and massive jumps in NMDA conductance and, rather than a form of bistability, is due to the voltage-dependent blockade of NMDA receptors. Our models also predict a more pronounced membrane potential bimodality following D1 receptor activation. This work thus establishes reduced yet accurate dopamine-modulated models of MSNs, suitable for use in large-scale models of the striatum. More importantly, these provide a tractable framework for further study of dopamine's effects on computation by individual neurons.

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

The search for the neural substrate of vertebrate action selection has focused on structures in the forebrain and midbrain, and particularly on the group of sub-cortical nuclei known as the basal ganglia. Yet, the behavioural repertoire of decerebrate and neonatal animals suggests the existence of a relatively self-contained neural substrate for action selection in the brainstem. We propose that the medial reticular formation (mRF) is the substrate's main component and review evidence showing that the mRF's inputs, outputs and intrinsic organization are consistent with the requirements of an action-selection system. The internal architecture of the mRF is composed of interconnected neuron clusters. We present an anatomical model which suggests that the mRF's intrinsic circuitry constitutes a small-world network and extend this result to show that it may have evolved to reduce axonal wiring. Potential configurations of action representation within the internal circuitry of the mRF are then assessed by computational modelling. We present new results demonstrating that each cluster's output is most likely to represent activation of a component action; thus, coactivation of a set of these clusters would lead to the coordinated behavioural response observed in the animal. Finally, we consider the potential integration of the basal ganglia and mRF substrates for selection and suggest that they may collectively form a layered/hierarchical control system.

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

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

Subcortical substrates for behavioural integration include the fore/midbrain nuclei of the basal ganglia and the hindbrain medial reticular formation. The midbrain superior colliculus requires basal ganglia disinhibition in order to generate orienting movements. The colliculus should therefore be seen as one of many competitors vying for control of the body's effector systems with the basal ganglia acting as the key arbiter.

Local supra-linear summation of excitatory inputs occurring in pyramidal cell dendrites, the so-called dendritic spikes, results in independent spiking dendritic sub-units, which turn pyramidal neurons into two-layer neural networks capable of computing linearly non-separable functions, such as the exclusive OR. Other neuron classes, such as interneurons, may possess only a few independent dendritic sub-units, or only passive dendrites where input summation is purely sub-linear, and where dendritic sub-units are only saturating. To determine if such neurons can also compute linearly non-separable functions, we enumerate, for a given parameter range, the Boolean functions implementable by a binary neuron model with a linear sub-unit and either a single spiking or a saturating dendritic sub-unit. We then analytically generalize these numerical results to an arbitrary number of non-linear sub-units. First, we show that a single non-linear dendritic sub-unit, in addition to the somatic non-linearity, is sufficient to compute linearly non-separable functions. Second, we analytically prove that, with a sufficient number of saturating dendritic sub-units, a neuron can compute all functions computable with purely excitatory inputs. Third, we show that these linearly non-separable functions can be implemented with at least two strategies: one where a dendritic sub-unit is sufficient to trigger a somatic spike; another where somatic spiking requires the cooperation of multiple dendritic sub-units. We formally prove that implementing the latter architecture is possible with both types of dendritic sub-units whereas the former is only possible with spiking dendrites. Finally, we show how linearly non-separable functions can be computed by a generic two-compartment biophysical model and a realistic neuron model of the cerebellar stellate cell interneuron. Taken together our results demonstrate that passive dendrites are sufficient to enable neurons to compute linearly non-separable functions., Author Summary Classical views on single neuron computation treat dendrites as mere collectors of inputs, that is forwarded to the soma for linear summation and causes a spike output if it is sufficiently large. Such a single neuron model can only compute linearly separable input-output functions, representing a small fraction of all possible functions. Recent experimental findings show that in certain pyramidal cells excitatory inputs can be supra-linearly integrated within a dendritic branch, turning this branch into a spiking dendritic sub-unit. Neurons containing many of these dendritic sub-units can compute both linearly separable and linearly non-separable functions. Nevertheless, other neuron types have dendrites which do not spike because the required voltage gated channels are absent. However, these dendrites sub-linearly sum excitatory inputs turning branches into saturating sub-units. We wanted to test if this last type of non-linear summation is sufficient for a single neuron to compute linearly non-separable functions. Using a combination of Boolean algebra and biophysical modeling, we show that a neuron with a single non-linear dendritic sub-unit whether spiking or saturating is able to compute linearly non-separable functions. Thus, in principle, any neuron with a dendritic tree, even passive, can compute linearly non-separable functions.

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., Author Summary 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.