A single Markov-type kinetic model accounting for the macroscopic currents of all human voltage-gated sodium channel isoforms

Modelling ionic channels represents a fundamental step towards developing biologically detailed neuron models. Until recently, the voltage-gated ion channels have been mainly modelled according to the formalism introduced by the seminal works of Hodgkin and Huxley (HH). However, following the continuing achievements in the biophysical and molecular comprehension of these pore-forming transmembrane proteins, the HH formalism turned out to carry limitations and inconsistencies in reproducing the ion-channels electrophysiological behaviour. At the same time, Markov-type kinetic models have been increasingly proven to successfully replicate both the electrophysiological and biophysical features of different ion channels. However, in order to model even the finest non-conducting molecular conformational change, they are often equipped with a considerable number of states and related transitions, which make them computationally heavy and less suitable for implementation in conductance-based neurons and large networks of those. In this purely modelling study we develop a Markov-type kinetic model for all human voltage-gated sodium channels (VGSCs). The model framework is detailed, unifying (i.e., it accounts for all ion-channel isoforms) and computationally efficient (i.e. with a minimal set of states and transitions). The electrophysiological data to be modelled are gathered from previously published studies on whole-cell patch-clamp experiments in mammalian cell lines heterologously expressing the human VGSC subtypes (from NaV1.1 to NaV1.9). By adopting a minimum sequence of states, and using the same state diagram for all the distinct isoforms, the model ensures the lightest computational load when used in neuron models and neural networks of increasing complexity. The transitions between the states are described by original ordinary differential equations, which represent the rate of the state transitions as a function of voltage (i.e., membrane potential). The kinetic model, developed in the NEURON simulation environment, appears to be the simplest and most parsimonious way for a detailed phenomenological description of the human VGSCs electrophysiological behaviour

The Arbitration–Extension Hypothesis: A Hierarchical Interpretation of the Functional Organization of the Basal Ganglia

Based on known anatomy and physiology, we present a hypothesis where the basal ganglia motor loop is hierarchically organized in two main subsystems: the arbitration system and the extension system. The arbitration system, comprised of the subthalamic nucleus, globus pallidus, and pedunculopontine nucleus, serves the role of selecting one out of several candidate actions as they are ascending from various brain stem motor regions and aggregated in the centromedian thalamus or descending from the extension system or from the cerebral cortex. This system is an action-input/action-output system whose winner-take-all mechanism finds the strongest response among several candidates to execute. This decision is communicated back to the brain stem by facilitating the desired action via cholinergic/glutamatergic projections and suppressing conflicting alternatives via GABAergic connections. The extension system, comprised of the striatum and, again, globus pallidus, can extend the repertoire of responses by learning to associate novel complex states to certain actions. This system is a state-input/action-output system, whose organization enables it to encode arbitrarily complex Boolean logic rules using striatal neurons that only fire given specific constellations of inputs (Boolean AND) and pallidal neurons that are silenced by any striatal input (Boolean OR). We demonstrate the capabilities of this hierarchical system by a computational model where a simulated generic “animal” interacts with an environment by selecting direction of movement based on combinations of sensory stimuli, some being appetitive, others aversive or neutral. While the arbitration system can autonomously handle conflicting actions proposed by brain stem motor nuclei, the extension system is required to execute learned actions not suggested by external motor centers. Being precise in the functional role of each component of the system, this hypothesis generates several readily testable predictions

Transient Calcium and Dopamine Increase PKA Activity and DARPP-32 Phosphorylation

Reinforcement learning theorizes that strengthening of synaptic connections in medium spiny neurons of the striatum occurs when glutamatergic input (from cortex) and dopaminergic input (from substantia nigra) are received simultaneously. Subsequent to learning, medium spiny neurons with strengthened synapses are more likely to fire in response to cortical input alone. This synaptic plasticity is produced by phosphorylation of AMPA receptors, caused by phosphorylation of various signalling molecules. A key signalling molecule is the phosphoprotein DARPP-32, highly expressed in striatal medium spiny neurons. DARPP-32 is regulated by several neurotransmitters through a complex network of intracellular signalling pathways involving cAMP (increased through dopamine stimulation) and calcium (increased through glutamate stimulation). Since DARPP-32 controls several kinases and phosphatases involved in striatal synaptic plasticity, understanding the interactions between cAMP and calcium, in particular the effect of transient stimuli on DARPP-32 phosphorylation, has major implications for understanding reinforcement learning. We developed a computer model of the biochemical reaction pathways involved in the phosphorylation of DARPP-32 on Thr34 and Thr75. Ordinary differential equations describing the biochemical reactions were implemented in a single compartment model using the software XPPAUT. Reaction rate constants were obtained from the biochemical literature. The first set of simulations using sustained elevations of dopamine and calcium produced phosphorylation levels of DARPP-32 similar to that measured experimentally, thereby validating the model. The second set of simulations, using the validated model, showed that transient dopamine elevations increased the phosphorylation of Thr34 as expected, but transient calcium elevations also increased the phosphorylation of Thr34, contrary to what is believed. When transient calcium and dopamine stimuli were paired, PKA activation and Thr34 phosphorylation increased compared with dopamine alone. This result, which is robust to variation in model parameters, supports reinforcement learning theories in which activity-dependent long-term synaptic plasticity requires paired glutamate and dopamine inputs

Run-Time Interoperability Between Neuronal Network Simulators Based on the MUSIC Framework

MUSIC is a standard API allowing large scale neuron simulators to exchange data within a parallel computer during runtime. A pilot implementation of this API has been released as open source. We provide experiences from the implementation of MUSIC interfaces for two neuronal network simulators of different kinds, NEST and MOOSE. A multi-simulation of a cortico-striatal network model involving both simulators is performed, demonstrating how MUSIC can promote inter-operability between models written for different simulators and how these can be re-used to build a larger model system. Benchmarks show that the MUSIC pilot implementation provides efficient data transfer in a cluster computer with good scaling. We conclude that MUSIC fulfills the design goal that it should be simple to adapt existing simulators to use MUSIC. In addition, since the MUSIC API enforces independence of the applications, the multi-simulation could be built from pluggable component modules without adaptation of the components to each other in terms of simulation time-step or topology of connections between the modules

Cell-type-specific inhibition of the dendritic plateau potential in striatal spiny projection neurons

Striatal spiny projection neurons (SPNs) receive convergent excitatory synaptic inputs from the cortex and thalamus. Activation of spatially clustered and temporally synchronized excitatory inputs at the distal dendrites could trigger plateau potentials in SPNs. Such supralinear synaptic integration is crucial for dendritic computation. However, how plateau potentials interact with subsequent excitatory and inhibitory synaptic inputs remains unknown. By combining computational simulation, two-photon imaging, optogenetics, and dualcolor uncaging of glutamate and GABA, we demonstrate that plateau potentials can broaden the spatiotemporal window for integrating excitatory inputs and promote spiking. The temporal window of spiking can be delicately controlled by GABAergic inhibition in a celltype–specific manner. This subtle inhibitory control of plateau potential depends on the location and kinetics of the GABAergic inputs and is achieved by the balance between relief and reestablishment of NMDA receptor Mg2+ block. These findings represent a mechanism for controlling spatiotemporal synaptic integration in SPNs