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

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

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

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

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

Multiscale modeling and simulations in neuroscience is gaining scientific attention due to its growing importance and unexplored capabilities. For instance, it can help to acquire better understanding of biological phenomena that have important features at multiple scales of time and space. This includes synaptic plasticity, memory formation and modulation, homeostasis. There are several ways to organize multiscale simulations depending on the scientific problem and the system to be modeled. One of the possibilities is to simulate different components of a multiscale system simultaneously and exchange data when required. The latter may become a challenging task for several reasons. One of them is that the components of a multiscale system usually span different spatial and temporal scales, such that rigorous analysis of possible coupling solutions is required. For certain classes of problems a number of coupling mechanisms have been proposed and successfully used. However, a strict mathematical theory is missing in many cases. Recent work in the field has not so far investigated artifacts that may arise during coupled integration of different approximation methods. Moreover, the coupling of widely used numerical fixed step size solvers may lead to unexpected inefficiency. In this paper we address the question of possible numerical artifacts that can arise during the integration of a coupled system. We develop an efficient strategy to couple the components of a multiscale test system. We introduce an efficient coupling method based on the second-order backward differentiation formula numerical approximation. The method uses an adaptive step size integration with an error estimation proposed by Skelboe (2000). The method shows a significant advantage over conventional fixed step size solvers used for similar problems. We explore different coupling strategies that define the organization of computations between system components. We study the importance of an appropriate approximation of exchanged variables during the simulation. The analysis shows a substantial impact of these aspects on the solution accuracy in the application to our multiscale test problem. We believe that the ideas presented in the paper may essentially contribute to the development of a robust and efficient framework for multiscale brain modeling and simulations in neuroscience.

The brain enables animals to behaviourally adapt in order to survive in a complex and dynamic environment, but how reward-oriented behaviours are achieved and computed by its underlying neural circuitry is an open question. To address this concern, we have developed a spiking model of the basal ganglia (BG) that learns to dis-inhibit the action leading to a reward despite ongoing changes in the reward schedule. The architecture of the network features the two pathways commonly described in BG, the direct (denoted D1) and the indirect (denoted D2) pathway, as well as a loop involving striatum and the dopaminergic system. The activity of these dopaminergic neurons conveys the reward prediction error (RPE), which determines the magnitude of synaptic plasticity within the different pathways. All plastic connections implement a versatile four-factor learning rule derived from Bayesian inference that depends upon pre- and postsynaptic activity, receptor type and dopamine level. Synaptic weight updates occur in the D1 or D2 pathways depending on the sign of the RPE, and an efference copy informs upstream nuclei about the action selected. We demonstrate successful performance of the system in a multiple-choice learning task with a transiently changing reward schedule. We simulate lesioning of the various pathways and show that a condition without the D2 pathway fares worse than one without D1. Additionally, we simulate the degeneration observed in Parkinson’s disease (PD) by decreasing the number of dopaminergic neurons during learning. The results suggest that the D1 pathway impairment in PD might have been overlooked. Furthermore, an analysis of the alterations in the synaptic weights shows that using the absolute reward value instead of the RPE leads to a larger change in D1.