Arkypallidal neurons in the external globus pallidus can mediate inhibitory control by altering competition in the striatum.

Reactive inhibitory control is crucial for survival. Traditionally, this control in mammals was attributed solely to the hyperdirect pathway, with cortical control signals flowing unidirectionally from the subthalamic nucleus (STN) to basal ganglia output regions. Yet recent findings have put this model into question, suggesting that the STN is assisted in stopping actions through ascending control signals to the striatum mediated by the external globus pallidus (GPe). Here we investigate this suggestion by harnessing a biologically-constrained spiking model of the corticobasal ganglia-thalamic (CBGT) circuit that includes pallidostriatal pathways originating from arkypallidal neurons. Through a series of experiments probing the interaction between three critical inhibitory nodes (the STN, arkypallidal cells, and indirect path-way spiny projection neurons), we find that the GPe acts as a critical mediator of both ascending and descending inhibitory signals in the CBGT circuit. In particular, pallidostriatal pathways regulate this process by weakening the direct pathway dominance of the evidence accumulation process driving decisions, which increases the relative suppressive influence of the indirect pathway on basal ganglia output. These findings delineate how pallidostriatal pathways can facilitate action cancellation by managing the bidirectional flow of information within CBGT circuits.

Dopamine depletion weakens direct pathway modulation of SNr neurons.

Neurons in the substantia nigra reticulata (SNr) transmit information about basal ganglia output to dozens of brain regions in thalamocortical and brainstem motor networks. Activity of SNr neurons is regulated by convergent input from upstream basal ganglia nuclei, including GABAergic inputs from the striatum and the external globus pallidus (GPe). GABAergic inputs from the striatum convey information from the direct pathway, while GABAergic inputs from the GPe convey information from the indirect pathway. Chronic loss of dopamine, as occurs in Parkinson's disease, disrupts the balance of direct and indirect pathway neurons at the level of the striatum, but the question of how dopamine loss affects information propagation along these pathways outside of the striatum is less well understood. Using a combination of in vivo and slice electrophysiology, we find that dopamine depletion selectively weakens the direct pathway's influence over neural activity in the SNr due to changes in the decay kinetics of GABA-mediated synaptic currents. GABAergic signaling from GPe neurons in the indirect pathway was not affected, resulting in an inversion of the normal balance of inhibitory control over basal ganglia output through the SNr. These results highlight the contribution of cellular mechanisms outside of the striatum that impact the responses of basal ganglia output neurons to the direct and indirect pathways in disease.

Rethinking the external globus pallidus and information flow in cortico-basal ganglia-thalamic circuits.

For decades, the external globus pallidus (GPe) has been viewed as a passive way-station in the indirect pathway of the cortico-basal ganglia-thalamic (CBGT) circuit, sandwiched between striatal inputs and basal ganglia outputs. According to this model, one-way descending striatal signals in the indirect pathway amplify the suppression of downstream thalamic nuclei by inhibiting GPe activity. Here, we revisit this assumption, in light of new and emerging work on the cellular complexity, connectivity and functional role of the GPe in behaviour. We show how, according to this new circuit-level logic, the GPe is ideally positioned for relaying ascending and descending control signals within the basal ganglia. Focusing on the problem of inhibitory control, we illustrate how this bidirectional flow of information allows for the integration of reactive and proactive control mechanisms during action selection. Taken together, this new evidence points to the GPe as being a central hub in the CBGT circuit, participating in bidirectional information flow and linking multifaceted control signals to regulate behaviour.

Introducing the STReaC (Spike Train Response Classification) toolbox.

Background: This work presents a toolbox that implements methodology for automated classification of diverse neural responses to optogenetic stimulation or other changes in conditions, based on spike train recordings. New Method: The toolbox implements what we call the Spike Train Response Classification algorithm (STReaC), which compares measurements of activity during a baseline period with analogous measurements during a subsequent period to identify various responses that might result from an event such as introduction of a sustained stimulus. The analyzed response types span a variety of patterns involving distinct time courses of increased firing, or excitation, decreased firing, or inhibition, or combinations of these. Excitation (inhibition) is identified from a comparative analysis of the spike density function (interspike interval function) for the baseline period relative to the corresponding function for the response period. Results: The STReaC algorithm as implemented in this toolbox provides a user-friendly, tunable, objective methodology that can detect a variety of neuronal response types and associated subtleties. We demonstrate this with single-unit neural recordings of rodent substantia nigra pars reticulata (SNr) during optogenetic stimulation of the globus pallidus externa (GPe). Comparison with existing methods: In several examples, we illustrate how the toolbox classifies responses in situations in which traditional methods (spike counting and visual inspection) either fail to detect a response or provide a false positive. Conclusions: The STReaC toolbox provides a simple, efficient approach for classifying spike trains into a variety of response types defined relative to a period of baseline spiking.

Subject-specific maximum entropy model of resting state fMRI shows diagnostically distinct patterns of energy state distributions.

Objective: Existing neuroimaging studies of psychotic and mood disorders have reported regional brain activation differences (first-order properties) and alterations in functional connectivity based on pairwise correlations in activation (second-order properties). This study used a generalized Ising model, also called a pairwise maximum entropy model (MEM), to integrate first- and second-order properties to provide a comprehensive picture of BOLD patterns and a system-wide summary measure called energy. This study examines the usefulness of individual level MEMs, attempts to identify image-derived counterparts of the model, and explores potential applications to psychiatry. Method: MEMs are fit to resting state fMRI data of each individual of a sample of 132 participants consisting of schizophrenia/schizoaffective disorder, bipolar disorder, and major depression, and a demographically matched 132 participants without these diagnoses from the UK Biobank to examine the default mode network (DMN). Results: The model explained observed brain state occurrence probabilities well across all participants, and model parameters were highly correlated to image-derived parameters for all groups. Within clinical groups, schizophrenia/schizoaffective disorder and bipolar disorder patients showed significant differences in averaged energy distribution compared to controls for all sub-systems of the DMN except for depression, where differences in the energy distributions were only detected in the DMN of the regions from the right hemisphere. Conclusions: Subject-specific Ising modeling may offer an improved measure of biological functional correlates relative to traditional approaches. The observation of distinct patterns of energy distribution among the three clinical groups compared to controls suggests relative diagnostic specificity and potential for clinical translation.

Energy in functional brain states correlates with cognition in adolescent schizophrenia and healthy persons.

Adolescent-onset schizophrenia (AOS) is a relatively rare and under-studied form of schizophrenia with more severe cognitive impairments and poorer outcome compared to adult-onset schizophrenia. Several neuroimaging studies have reported alterations in regional activations that account for activity in individual regions (first-order model) and functional connectivity that reveals pairwise co-activations (second-order model) in AOS compared to controls. The pairwise maximum entropy model, also called the Ising model, can integrate both first-order and second-order terms to elucidate a comprehensive picture of neural dynamics and captures both individual and pairwise activity measures into a single quantity known as energy, which is inversely related to the probability of state occurrence. We applied the MEM framework to task functional MRI data collected on 23 AOS individuals in comparison with 53 healthy control subjects while performing the Penn Conditional Exclusion Test (PCET), which measures executive function that has been repeatedly shown to be more impaired in AOS compared to adult-onset schizophrenia. Accuracy of PCET performance was significantly reduced among AOS compared to controls as expected. Average cumulative energy achieved for a participant over the course of the fMRI negatively correlated with task performance, and the association was stronger than any first-order associations. The AOS subjects spent more time in higher energy states that represent lower probability of occurrence and were associated with impaired executive function suggesting that the neural dynamics may be less efficient compared to controls who spent more time in lower energy states occurring with higher probability and hence are more stable and efficient. The energy landscapes in both conditions featured attractors that corresponded to two distinct subnetworks, namely fronto-temporal and parieto-motor. Attractor basins were larger in the controls than in AOS; moreover, fronto-temporal basin size was significantly correlated with cognitive performance in controls but not among the AOS. The single trial trajectories for the AOS group also showed higher variability in concordance with shallow attractor basins among AOS. These findings suggest that the neural dynamics of AOS features more frequent occurrence of less probable states with narrower attractors, which lack the relation to executive function associated with attractors in control subjects suggesting a diminished capacity of AOS to generate task-effective brain states.

CBGTPy: An extensible cortico-basal ganglia-thalamic framework for modeling biological decision making.

Here we introduce CBGTPy, a virtual environment for designing and testing goal-directed agents with internal dynamics that are modeled off of the cortico-basal-ganglia-thalamic (CBGT) pathways in the mammalian brain. CBGTPy enables researchers to investigate the internal dynamics of the CBGT system during a variety of tasks, allowing for the formation of testable predictions about animal behavior and neural activity. The framework has been designed around the principle of flexibility, such that many experimental parameters in a decision making paradigm can be easily defined and modified. Here we demonstrate the capabilities of CBGTPy across a range of single and multi-choice tasks, highlighting the ease of set up and the biologically realistic behavior that it produces. We show that CBGTPy is extensible enough to apply to a wide range of experimental protocols and to allow for the implementation of model extensions with minimal developmental effort.

Rigorous Mapping of Data to Qualitative Properties of Parameter Values and Dynamics: A Case Study on a Two-Variable Lotka-Volterra System.

In this work, we describe mostly analytical work related to a novel approach to parameter identification for a two-variable Lotka-Volterra (LV) system. Specifically, this approach is qualitative, in that we aim not to determine precise values of model parameters but rather to establish relationships among these parameter values and properties of the trajectories that they generate, based on a small number of available data points. In this vein, we prove a variety of results about the existence, uniqueness, and signs of model parameters for which the trajectory of the system passes exactly through a set of three given data points, representing the smallest possible data set needed for identification of model parameter values. We find that in most situations such a data set determines these values uniquely; we also thoroughly investigate the alternative cases, which result in nonuniqueness or even nonexistence of model parameter values that fit the data. In addition to results about identifiability, our analysis provides information about the long-term dynamics of solutions of the LV system directly from the data without the necessity of estimating specific parameter values.

Slow negative feedback enhances robustness of square-wave bursting.

Square-wave bursting is an activity pattern common to a variety of neuronal and endocrine cell models that has been linked to central pattern generation for respiration and other physiological functions. Many of the reduced mathematical models that exhibit square-wave bursting yield transitions to an alternative pseudo-plateau bursting pattern with small parameter changes. This susceptibility to activity change could represent a problematic feature in settings where the release events triggered by spike production are necessary for function. In this work, we analyze how model bursting and other activity patterns vary with changes in a timescale associated with the conductance of a fast inward current. Specifically, using numerical simulations and dynamical systems methods, such as fast-slow decomposition and bifurcation and phase-plane analysis, we demonstrate and explain how the presence of a slow negative feedback associated with a gradual reduction of a fast inward current in these models helps to maintain the presence of spikes within the active phases of bursts. Therefore, although such a negative feedback is not necessary for burst production, we find that its presence generates a robustness that may be important for function.

Sensitivity to Control Signals in Triphasic Rhythmic Neural Systems: A Comparative Mechanistic Analysis via Infinitesimal Local Timing Response Curves.

Similar activity patterns may arise from model neural networks with distinct coupling properties and individual unit dynamics. These similar patterns may, however, respond differently to parameter variations and specifically to tuning of inputs that represent control signals. In this work, we analyze the responses resulting from modulation of a localized input in each of three classes of model neural networks that have been recognized in the literature for their capacity to produce robust three-phase rhythms: coupled fast-slow oscillators, near-heteroclinic oscillators, and threshold-linear networks. Triphasic rhythms, in which each phase consists of a prolonged activation of a corresponding subgroup of neurons followed by a fast transition to another phase, represent a fundamental activity pattern observed across a range of central pattern generators underlying behaviors critical to survival, including respiration, locomotion, and feeding. To perform our analysis, we extend the recently developed local timing response curve (lTRC), which allows us to characterize the timing effects due to perturbations, and we complement our lTRC approach with model-specific dynamical systems analysis. Interestingly, we observe disparate effects of similar perturbations across distinct model classes. Thus, this work provides an analytical framework for studying control of oscillations in nonlinear dynamical systems and may help guide model selection in future efforts to study systems exhibiting triphasic rhythmic activity.

A spiking computational model for striatal cholinergic interneurons.

Cholinergic interneurons in the striatum, also known as tonically active interneurons or TANs, are thought to have a strong effect on corticostriatal plasticity and on striatal activity and outputs, which in turn play a critical role in modulating downstream basal ganglia activity and movement. Striatal TANs can exhibit a variety of firing patterns and responses to synaptic inputs; furthermore, they have been found to display various surges and pauses in activity associated with sensory cues and reward delivery in learning as well as with motor tic production. To help explain the factors that contribute to TAN activity patterns and to provide a resource for future studies, we present a novel conductance-based computational model of a striatal TAN. We show that this model produces the various characteristic firing patterns observed in recordings of TANs. With a single baseline tuning associated with tonic firing, the model also captures a wide range of TAN behaviors found in previous experiments involving a variety of manipulations. In addition to demonstrating these results, we explain how various ionic currents in the model contribute to them. Finally, we use this model to explore the contributions of the acetylcholine released by TANs to the production of surges and pauses in TAN activity in response to strong excitatory inputs. These results provide predictions for future experimental testing that may help with efforts to advance our understanding of the role of TANs in reinforcement learning and in motor disorders such as Tourette's syndrome.

Rethinking the external globus pallidus and information flow in cortico-basal ganglia-thalamic circuits.

For decades the external globus pallidus (GPe) has been viewed as a passive way-station in the indirect pathway of the cortico-basal ganglia-thalamic (CBGT) circuit, sandwiched between striatal inputs and basal ganglia outputs. According to this model, one-way descending striatal signals in the indirect pathway amplify the suppression of downstream thalamic nuclei by inhibiting GPe activity. Here we revisit this assumption, in light of new and emerging work on the cellular complexity, connectivity, and functional role of the GPe in behavior. We show how, according to this new circuit-level logic, the GPe is ideally positioned for relaying ascending and descending control signals within the basal ganglia. Focusing on the problem of inhibitory control, we illustrate how this bidirectional flow of information allows for the integration of reactive and proactive control mechanisms during action selection. Taken together, this new evidence points to the GPe as being a central hub in the CBGT circuit, participating in bidirectional information flow and linking multifaceted control signals to regulate behavior.

A model for the collective synchronization of flashing in Photinus carolinus.

Recent empirical investigations have characterized the synchronized flashing behaviours of male Photinus carolinus fireflies in their natural habitat in Great Smoky Mountain National Park as well as in controlled environments. We develop a model for the flash dynamics of an individual firefly based on a canonical elliptic burster, a slow-fast dynamical system that produces a repeating pattern of multiple flashes followed by a quiescent period. We show that a small amount of noise renders that oscillation very irregular, but when multiple model fireflies interact through their flashes, the behaviour becomes much more periodic. We show that the aggregate behaviour is qualitatively similar to the experimental findings. We next distribute the fireflies in a two-dimensional spatial domain and vary the interaction range. In addition to synchronization, various spatio-temporal patterns involving propagation of activity emerge spontaneously. Finally, we allow a certain number of fireflies to move and demonstrate how their speed affects the rate and degree of synchronization.

Predictions and experimental tests of a new biophysical model of the mammalian respiratory oscillator.

Previously our computational modeling studies (Phillips et al., 2019) proposed that neuronal persistent sodium current (INaP) and calcium-activated non-selective cation current (ICAN) are key biophysical factors that, respectively, generate inspiratory rhythm and burst pattern in the mammalian preBötzinger complex (preBötC) respiratory oscillator isolated in vitro. Here, we experimentally tested and confirmed three predictions of the model from new simulations concerning the roles of INaP and ICAN: (1) INaP and ICAN blockade have opposite effects on the relationship between network excitability and preBötC rhythmic activity; (2) INaP is essential for preBötC rhythmogenesis; and (3) ICAN is essential for generating the amplitude of rhythmic output but not rhythm generation. These predictions were confirmed via optogenetic manipulations of preBötC network excitability during graded INaP or ICAN blockade by pharmacological manipulations in slices in vitro containing the rhythmically active preBötC from the medulla oblongata of neonatal mice. Our results support and advance the hypothesis that INaP and ICAN mechanistically underlie rhythm and inspiratory burst pattern generation, respectively, in the isolated preBötC.

Identifying control ensembles for information processing within the cortico-basal ganglia-thalamic circuit.

In situations featuring uncertainty about action-reward contingencies, mammals can flexibly adopt strategies for decision-making that are tuned in response to environmental changes. Although the cortico-basal ganglia thalamic (CBGT) network has been identified as contributing to the decision-making process, it features a complex synaptic architecture, comprised of multiple feed-forward, reciprocal, and feedback pathways, that complicate efforts to elucidate the roles of specific CBGT populations in the process by which evidence is accumulated and influences behavior. In this paper we apply a strategic sampling approach, based on Latin hypercube sampling, to explore how variations in CBGT network properties, including subpopulation firing rates and synaptic weights, map to variability of parameters in a normative drift diffusion model (DDM), representing algorithmic aspects of information processing during decision-making. Through the application of canonical correlation analysis, we find that this relationship can be characterized in terms of three low-dimensional control ensembles within the CBGT network that impact specific qualities of the emergent decision policy: responsiveness (a measure of how quickly evidence evaluation gets underway, associated with overall activity in corticothalamic and direct pathways), pliancy (a measure of the standard of evidence needed to commit to a decision, associated largely with overall activity in components of the indirect pathway of the basal ganglia), and choice (a measure of commitment toward one available option, associated with differences in direct and indirect pathways across action channels). These analyses provide mechanistic predictions about the roles of specific CBGT network elements in tuning the way that information is accumulated and translated into decision-related behavior.

Putting the theory into 'burstlet theory' with a biophysical model of burstlets and bursts in the respiratory preBötzinger complex.

Inspiratory breathing rhythms arise from synchronized neuronal activity in a bilaterally distributed brainstem structure known as the preBötzinger complex (preBötC). In in vitro slice preparations containing the preBötC, extracellular potassium must be elevated above physiological levels (to 7-9 mM) to observe regular rhythmic respiratory motor output in the hypoglossal nerve to which the preBötC projects. Reexamination of how extracellular K+ affects preBötC neuronal activity has revealed that low-amplitude oscillations persist at physiological levels. These oscillatory events are subthreshold from the standpoint of transmission to motor output and are dubbed burstlets. Burstlets arise from synchronized neural activity in a rhythmogenic neuronal subpopulation within the preBötC that in some instances may fail to recruit the larger network events, or bursts, required to generate motor output. The fraction of subthreshold preBötC oscillatory events (burstlet fraction) decreases sigmoidally with increasing extracellular potassium. These observations underlie the burstlet theory of respiratory rhythm generation. Experimental and computational studies have suggested that recruitment of the non-rhythmogenic component of the preBötC population requires intracellular Ca2+ dynamics and activation of a calcium-activated nonselective cationic current. In this computational study, we show how intracellular calcium dynamics driven by synaptically triggered Ca2+ influx as well as Ca2+ release/uptake by the endoplasmic reticulum in conjunction with a calcium-activated nonselective cationic current can reproduce and offer an explanation for many of the key properties associated with the burstlet theory of respiratory rhythm generation. Altogether, our modeling work provides a mechanistic basis that can unify a wide range of experimental findings on rhythm generation and motor output recruitment in the preBötC.

Dynamics of ramping bursts in a respiratory neuron model.

Intensive computational and theoretical work has led to the development of multiple mathematical models for bursting in respiratory neurons in the pre-Bötzinger Complex (pre-BötC) of the mammalian brainstem. Nonetheless, these previous models have not captured the pre-inspiratory ramping aspects of these neurons' activity patterns, in which relatively slow tonic spiking gradually progresses to faster spiking and a full-blown burst, with a corresponding gradual development of an underlying plateau potential. In this work, we show that the incorporation of the dynamics of the extracellular potassium ion concentration into an existing model for pre-BötC neuron bursting, along with some parameter adjustments, suffices to induce this ramping behavior. Using fast-slow decomposition, we show that this activity can be considered as a form of parabolic bursting, but with burst termination at a homoclinic bifurcation rather than as a SNIC bifurcation. We also investigate the parameter-dependence of these solutions and show that the proposed model yields a greater dynamic range of burst frequencies, durations, and duty cycles than those produced by other models in the literature.

A data-driven model of the role of energy in sepsis.

Exposure to pathogens elicits a complex immune response involving multiple interdependent pathways. This response may mitigate detrimental effects and restore health but, if imbalanced, can lead to negative outcomes including sepsis. This complexity and need for balance pose a challenge for clinicians and have attracted attention from modelers seeking to apply computational tools to guide therapeutic approaches. In this work, we address a shortcoming of such past efforts by incorporating the dynamics of energy production and consumption into a computational model of the acute immune response. With this addition, we performed fits of model dynamics to data obtained from non-human primates exposed to Escherichia coli. Our analysis identifies parameters that may be crucial in determining survival outcomes and also highlights energy-related factors that modulate the immune response across baseline and altered glucose conditions.

Transmission of delta band (0.5-4 Hz) oscillations from the globus pallidus to the substantia nigra pars reticulata in dopamine depletion.

Parkinson's disease (PD) and animal models of PD feature enhanced oscillations in several frequency bands in the basal ganglia (BG). Past research has emphasized the enhancement of 13-30 Hz beta oscillations. Recently, however, oscillations in the delta band (0.5-4 Hz) have been identified as a robust predictor of dopamine loss and motor dysfunction in several BG regions in mouse models of PD. In particular, delta oscillations in the substantia nigra pars reticulata (SNr) were shown to lead oscillations in motor cortex (M1) and persist under M1 lesion, but it is not clear where these oscillations are initially generated. In this paper, we use a computational model to study how delta oscillations may arise in the SNr due to projections from the globus pallidus externa (GPe). We propose a network architecture that incorporates inhibition in SNr from oscillating GPe neurons and other SNr neurons. In our simulations, this configuration yields firing patterns in model SNr neurons that match those measured in vivo. In particular, we see the spontaneous emergence of near-antiphase active-predicting and inactive-predicting neural populations in the SNr, which persist under the inclusion of STN inputs based on experimental recordings. These results demonstrate how delta oscillations can propagate through BG nuclei despite imperfect oscillatory synchrony in the source site, narrowing down potential targets for the source of delta oscillations in PD models and giving new insight into the dynamics of SNr oscillations.

Dynamic decision policy reconfiguration under outcome uncertainty.

In uncertain or unstable environments, sometimes the best decision is to change your mind. To shed light on this flexibility, we evaluated how the underlying decision policy adapts when the most rewarding action changes. Human participants performed a dynamic two-armed bandit task that manipulated the certainty in relative reward (conflict) and the reliability of action-outcomes (volatility). Continuous estimates of conflict and volatility contributed to shifts in exploratory states by changing both the rate of evidence accumulation (drift rate) and the amount of evidence needed to make a decision (boundary height), respectively. At the trialwise level, following a switch in the optimal choice, the drift rate plummets and the boundary height weakly spikes, leading to a slow exploratory state. We find that the drift rate drives most of this response, with an unreliable contribution of boundary height across experiments. Surprisingly, we find no evidence that pupillary responses associated with decision policy changes. We conclude that humans show a stereotypical shift in their decision policies in response to environmental changes.