On the Role of Arkypallidal and Prototypical Neurons for Phase Transitions in the External Pallidum

Neurophysiological avenues to better conceptualizing adaptive cognition

We delve into the human brain's remarkable capacity for adaptability and sustained cognitive functioning, phenomena traditionally encompassed as executive functions or cognitive control. The neural underpinnings that enable the seamless navigation between transient thoughts without detracting from overarching goals form the core of our article. We discuss the concept of "metacontrol," which builds upon conventional cognitive control theories by proposing a dynamic balancing of processes depending on situational demands. We critically discuss the role of oscillatory processes in electrophysiological activity at different scales and the importance of desynchronization and partial phase synchronization in supporting adaptive behavior including neural noise accounts, transient dynamics, phase-based measures (coordination dynamics) and neural mass modelling. The cognitive processes focused and neurophysiological avenues outlined are integral to understanding diverse psychiatric disorders thereby contributing to a more nuanced comprehension of cognitive control and its neural bases in both health and 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.

Synaptic Changes in Pallidostriatal Circuits Observed in the Parkinsonian Model Triggers Abnormal Beta Synchrony with Accurate Spatio-temporal Properties across the Basal Ganglia

Excessive oscillatory activity across basal ganglia (BG) nuclei in the β frequencies (12-30 Hz) is a hallmark of Parkinson's disease (PD). While the link between oscillations and symptoms remains debated, exaggerated β oscillations constitute an important biomarker for therapeutic effectiveness in PD. The neuronal mechanisms of β-oscillation generation however remain unknown. Many existing models rely on a central role of the subthalamic nucleus (STN) or cortical inputs to BG. Contrarily, neural recordings and optogenetic manipulations in normal and parkinsonian rats recently highlighted the central role of the external pallidum (GPe) in abnormal β oscillations, while showing that the integrity of STN or motor cortex is not required. Here, we evaluate the mechanisms for the generation of abnormal β oscillations in a BG network model where neuronal and synaptic time constants, connectivity, and firing rate distributions are strongly constrained by experimental data. Guided by a mean-field approach, we show in a spiking neural network that several BG sub-circuits can drive oscillations. Strong recurrent STN-GPe connections or collateral intra-GPe connections drive γ oscillations (>40 Hz), whereas strong pallidostriatal loops drive low-β (10-15 Hz) oscillations. We show that pathophysiological strengthening of striatal and pallidal synapses following dopamine depletion leads to the emergence of synchronized oscillatory activity in the mid-β range with spike-phase relationships between BG neuronal populations in-line with experiments. Furthermore, inhibition of GPe, contrary to STN, abolishes oscillations. Our modeling study uncovers the neural mechanisms underlying PD β oscillations and may thereby guide the future development of therapeutic strategies.

Neural heterogeneity controls computations in spiking neural networks

The brain is composed of complex networks of interacting neurons that express considerable heterogeneity in their physiology and spiking characteristics. How does this neural heterogeneity influence macroscopic neural dynamics, and how might it contribute to neural computation? In this work, we use a mean-field model to investigate computation in heterogeneous neural networks, by studying how the heterogeneity of cell spiking thresholds affects three key computational functions of a neural population: the gating, encoding, and decoding of neural signals. Our results suggest that heterogeneity serves different computational functions in different cell types. In inhibitory interneurons, varying the degree of spike threshold heterogeneity allows them to gate the propagation of neural signals in a reciprocally coupled excitatory population. Whereas homogeneous interneurons impose synchronized dynamics that narrow the dynamic repertoire of the excitatory neurons, heterogeneous interneurons act as an inhibitory offset while preserving excitatory neuron function. Spike threshold heterogeneity also controls the entrainment properties of neural networks to periodic input, thus affecting the temporal gating of synaptic inputs. Among excitatory neurons, heterogeneity increases the dimensionality of neural dynamics, improving the network's capacity to perform decoding tasks. Conversely, homogeneous networks suffer in their capacity for function generation, but excel at encoding signals via multistable dynamic regimes. Drawing from these findings, we propose intra-cell-type heterogeneity as a mechanism for sculpting the computational properties of local circuits of excitatory and inhibitory spiking neurons, permitting the same canonical microcircuit to be tuned for diverse computational tasks.

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.

PyRates-A code-generation tool for modeling dynamical systems in biology and beyond

The mathematical study of real-world dynamical systems relies on models composed of differential equations. Numerical methods for solving and analyzing differential equation systems are essential when complex biological problems have to be studied, such as the spreading of a virus, the evolution of competing species in an ecosystem, or the dynamics of neurons in the brain. Here we present PyRates, a Python-based software for modeling and analyzing differential equation systems via numerical methods. PyRates is specifically designed to account for the inherent complexity of biological systems. It provides a new language for defining models that mirrors the modular organization of real-world dynamical systems and thus simplifies the implementation of complex networks of interacting dynamic entities. Furthermore, PyRates provides extensive support for the various forms of interaction delays that can be observed in biological systems. The core of PyRates is a versatile code-generation system that translates user-defined models into "backend" implementations in various languages, including Python, Fortran, Matlab, and Julia. This allows users to apply a wide range of analysis methods for dynamical systems, eliminating the need for manual translation between code bases. PyRates may also be used as a model definition interface for the creation of custom dynamical systems tools. To demonstrate this, we developed two extensions of PyRates for common analyses of dynamic models of biological systems: PyCoBi for bifurcation analysis and RectiPy for parameter fitting. We demonstrate in a series of example models how PyRates can be used in combination with PyCoBi and RectiPy for model analysis and fitting. Together, these tools offer a versatile framework for applying computational modeling and numerical analysis methods to dynamical systems in biology and beyond.

Synaptic network structure shapes cortically evoked spatio-temporal responses of STN and GPe neurons in a computational model

Introduction

The basal ganglia (BG) are involved in motor control and play an essential role in movement disorders such as hemiballismus, dystonia, and Parkinson's disease. Neurons in the motor part of the BG respond to passive movement or stimulation of different body parts and to stimulation of corresponding cortical regions. Experimental evidence suggests that the BG are organized somatotopically, i.e., specific areas of the body are associated with specific regions in the BG nuclei. Signals related to the same body part that propagate along different pathways converge onto the same BG neurons, leading to characteristic shapes of cortically evoked responses. This suggests the existence of functional channels that allow for the processing of different motor commands or information related to different body parts in parallel. Neurological disorders such as Parkinson's disease are associated with pathological activity in the BG and impaired synaptic connectivity, together with reorganization of somatotopic maps. One hypothesis is that motor symptoms are, at least partly, caused by an impairment of network structure perturbing the organization of functional channels.

Methods

We developed a computational model of the STN-GPe circuit, a central part of the BG. By removing individual synaptic connections, we analyzed the contribution of signals propagating along different pathways to cortically evoked responses. We studied how evoked responses are affected by systematic changes in the network structure. To quantify the BG's organization in the form of functional channels, we suggested a two-site stimulation protocol.

Results

Our model reproduced the cortically evoked responses of STN and GPe neurons and the contributions of different pathways suggested by experimental studies. Cortical stimulation evokes spatio-temporal response patterns that are linked to the underlying synaptic network structure. Our two-site stimulation protocol yielded an approximate functional channel width.

Discussion/conclusion

The presented results provide insight into the organization of BG synaptic connectivity, which is important for the development of computational models. The synaptic network structure strongly affects the processing of cortical signals and may impact the generation of pathological rhythms. Our work may motivate further experiments to analyze the network structure of BG nuclei and their organization in functional channels.

A model description of beta oscillations in the external globus pallidus

The external globus pallidus (GPe), a subcortical nucleus located in the indirect pathway of the basal ganglia, is widely considered to have tight associations with abnormal beta oscillations (13-30 Hz) observed in Parkinson's disease (PD). Despite that many mechanisms have been put forward to explain the emergence of these beta oscillations, however, it is still unclear the functional contributions of the GPe, especially, whether the GPe itself can generate beta oscillations. To investigate the role played by the GPe in producing beta oscillations, we employ a well described firing rate model of the GPe neural population. Through extensive simulations, we find that the transmission delay within the GPe-GPe pathway contributes significantly to inducing beta oscillations, and the impacts of the time constant and connection strength of the GPe-GPe pathway on generating beta oscillations are non-negligible. Moreover, the GPe firing patterns can be significantly modulated by the time constant and connection strength of the GPe-GPe pathway, as well as the transmission delay within the GPe-GPe pathway. Interestingly, both increasing and decreasing the transmission delay can push the GPe firing pattern from beta oscillations to other firing patterns, including oscillation and non-oscillation firing patterns. These findings suggest that if the transmission delays within the GPe are at least 9.8 ms, beta oscillations can be produced originally in the GPe neural population, which also may be the origin of PD-related beta oscillations and should be regarded as a promising target for treatments for PD.

Local inhibition in a model of the indirect pathway globus pallidus network slows and deregularizes background firing, but sharpens and synchronizes responses to striatal input

The external segment of globus pallidus (GPe) is a network of oscillatory neurons connected by inhibitory synapses. We studied the intrinsic dynamic and the response to a shared brief inhibitory stimulus in a model GPe network. Individual neurons were simulated using a phase resetting model based on measurements from mouse GPe neurons studied in slices. The neurons showed a broad heterogeneity in their firing rates and in the shapes and sizes of their phase resetting curves. Connectivity in the network was set to match experimental measurements. We generated statistically equivalent neuron heterogeneity in a small-world model, in which 99% of connections were made with near neighbors and 1% at random, and in a model with entirely random connectivity. In both networks, the resting activity was slowed and made more irregular by the local inhibition, but it did not show any periodic pattern. Cross-correlations among neuron pairs were limited to directly connected neurons. When stimulated by a shared inhibitory input, the individual neuron responses separated into two groups: one with a short and stereotyped period of inhibition followed by a transient increase in firing probability, and the other responding with a sustained inhibition. Despite differences in firing rate, the responses of the first group of neurons were of fixed duration and were synchronized across cells.

Mean-field approximations of networks of spiking neurons with short-term synaptic plasticity

Low-dimensional descriptions of spiking neural network dynamics are an effective tool for bridging different scales of organization of brain structure and function. Recent advances in deriving mean-field descriptions for networks of coupled oscillators have sparked the development of a new generation of neural mass models. Of notable interest are mean-field descriptions of all-to-all coupled quadratic integrate-and-fire (QIF) neurons, which have already seen numerous extensions and applications. These extensions include different forms of short-term adaptation considered to play an important role in generating and sustaining dynamic regimes of interest in the brain. It is an open question, however, whether the incorporation of presynaptic forms of synaptic plasticity driven by single neuron activity would still permit the derivation of mean-field equations using the same method. Here we discuss this problem using an established model of short-term synaptic plasticity at the single neuron level, for which we present two different approaches for the derivation of the mean-field equations. We compare these models with a recently proposed mean-field approximation that assumes stochastic spike timings. In general, the latter fails to accurately reproduce the macroscopic activity in networks of deterministic QIF neurons with distributed parameters. We show that the mean-field models we propose provide a more accurate description of the network dynamics, although they are mathematically more involved. Using bifurcation analysis, we find that QIF networks with presynaptic short-term plasticity can express regimes of periodic bursting activity as well as bistable regimes. Together, we provide novel insight into the macroscopic effects of short-term synaptic plasticity in spiking neural networks, as well as two different mean-field descriptions for future investigations of such networks.