Dendritic sodium channels regulate network integration in globus pallidus neurons: a modeling study

The microcircuits of striatum in silico

The basal ganglia play an important role in decision making and selection of action primarily based on input from cortex, thalamus, and the dopamine system. Their main input structure, striatum, is central to this process. It consists of two types of projection neurons, together representing 95% of the neurons, and 5% of interneurons, among which are the cholinergic, fast-spiking, and low threshold-spiking subtypes. The membrane properties, soma-dendritic shape, and intrastriatal and extrastriatal synaptic interactions of these neurons are quite well described in the mouse, and therefore they can be simulated in sufficient detail to capture their intrinsic properties, as well as the connectivity. We focus on simulation at the striatal cellular/microcircuit level, in which the molecular/subcellular and systems levels meet. We present a nearly full-scale model of the mouse striatum using available data on synaptic connectivity, cellular morphology, and electrophysiological properties to create a microcircuit mimicking the real network. A striatal volume is populated with reconstructed neuronal morphologies with appropriate cell densities, and then we connect neurons together based on appositions between neurites as possible synapses and constrain them further with available connectivity data. Moreover, we simulate a subset of the striatum involving 10,000 neurons, with input from cortex, thalamus, and the dopamine system, as a proof of principle. Simulation at this biological scale should serve as an invaluable tool to understand the mode of operation of this complex structure. This platform will be updated with new data and expanded to simulate the entire striatum.

A general method to generate artificial spike train populations matching recorded neurons

We developed a general method to generate populations of artificial spike trains (ASTs) that match the statistics of recorded neurons. The method is based on computing a Gaussian local rate function of the recorded spike trains, which results in rate templates from which ASTs are drawn as gamma distributed processes with a refractory period. Multiple instances of spike trains can be sampled from the same rate templates. Importantly, we can manipulate rate-covariances between spike trains by performing simple algorithmic transformations on the rate templates, such as filtering or amplifying specific frequency bands, and adding behavior related rate modulations. The method was examined for accuracy and limitations using surrogate data such as sine wave rate templates, and was then verified for recorded spike trains from cerebellum and cerebral cortex. We found that ASTs generated with this method can closely follow the firing rate and local as well as global spike time variance and power spectrum. The method is primarily intended to generate well-controlled spike train populations as inputs for dynamic clamp studies or biophysically realistic multicompartmental models. Such inputs are essential to study detailed properties of synaptic integration with well-controlled input patterns that mimic the in vivo situation while allowing manipulation of input rate covariances at different time scales.

Motor cortex can directly drive the globus pallidus neurons in a projection neuron type-dependent manner in the rat

The basal ganglia are critical for the control of motor behaviors and for reinforcement learning. Here, we demonstrate in rats that primary and secondary motor areas (M1 and M2) make functional synaptic connections in the globus pallidus (GP), not usually thought of as an input site of the basal ganglia. Morphological observation revealed that the density of axonal boutons from motor cortices in the GP was 47% and 78% of that in the subthalamic nucleus (STN) from M1 and M2, respectively. Cortical excitation of GP neurons was comparable to that of STN neurons in slice preparations. FoxP2-expressing arkypallidal neurons were preferentially innervated by the motor cortex. The connection probability of cortico-pallidal innervation was higher for M2 than M1. These results suggest that cortico-pallidal innervation is an additional excitatory input to the basal ganglia, and that it can affect behaviors via the cortex-basal ganglia-thalamus motor loop.

Distal spike initiation zone location estimation by morphological simulation of ionic current filtering demonstrated in a novel model of an identified Drosophila motoneuron

Studying ion channel currents generated distally from the recording site is difficult because of artifacts caused by poor space clamp and membrane filtering. A computational model can quantify artifact parameters for correction by simulating the currents only if their exact anatomical location is known. We propose that the same artifacts that confound current recordings can help pinpoint the source of those currents by providing a signature of the neuron’s morphology. This method can improve the recording quality of currents initiated at the spike initiation zone (SIZ) that are often distal to the soma in invertebrate neurons. Drosophila being a valuable tool for characterizing ion currents, we estimated the SIZ location and quantified artifacts in an identified motoneuron, aCC/MN1-Ib, by constructing a novel multicompartmental model. Initial simulation of the measured biophysical channel properties in an isopotential Hodgkin-Huxley type neuron model partially replicated firing characteristics. Adding a second distal compartment, which contained spike-generating Na⁺ and K⁺ currents, was sufficient to simulate aCC’s in vivo activity signature. Matching this signature using a reconstructed morphology predicted that the SIZ is on aCC’s primary axon, 70 μm after the most distal dendritic branching point. From SIZ to soma, we observed and quantified selective morphological filtering of fast activating currents. Non-inactivating K⁺ currents are filtered ∼3 times less and despite their large magnitude at the soma they could be as distal as Na⁺ currents. The peak of transient component (NaT) of the voltage-activated Na⁺ current is also filtered more than the magnitude of slower persistent component (NaP), which can contribute to seizures. The corrected NaP/NaT ratio explains the previously observed discrepancy when the same channel is expressed in different cells. In summary, we used an in vivo signature to estimate ion channel location and recording artifacts, which can be applied to other neurons.

The study of ion channels is essential both for understanding normal brain function and for finding drug targets to treat neurological disease. Traditional experimental techniques remain challenging for recording ion channel currents accurately because of their locations in the neuron. Computer modeling of the three dimensional structure of neurons can provide a correction estimate for the measurement error introduced by neuronal membranes. To achieve this, we developed a modeling approach to localize, and correct for, distant ion channels. We demonstrated this approach by constructing novel computer models of an identified insect motor neuron, which provides a powerful model for studying the central nervous system. Through the study of electrical activity and genetic manipulations, it has been found that the persistent sodium current contributes to seizure. By modeling three dimensional structure, we were able to predict the location of these currents in the neuron, which were more distal than expected. Localizing sodium channels allowed us to predict their properties at origin, which favorably matched isolated recordings of these channels in more compact cells. This result is important in validating the use of heterologous compact cells to study insect sodium channels, and also demonstrates the usefulness of the presented modeling approach for studying channel physiology more generally.

Using multi-compartment ensemble modeling as an investigative tool of spatially distributed biophysical balances: application to hippocampal oriens-lacunosum/moleculare (O-LM) cells

Multi-compartmental models of neurons provide insight into the complex, integrative properties of dendrites. Because it is not feasible to experimentally determine the exact density and kinetics of each channel type in every neuronal compartment, an essential goal in developing models is to help characterize these properties. To address biological variability inherent in a given neuronal type, there has been a shift away from using hand-tuned models towards using ensembles or populations of models. In collectively capturing a neuron's output, ensemble modeling approaches uncover important conductance balances that control neuronal dynamics. However, conductances are never entirely known for a given neuron class in terms of its types, densities, kinetics and distributions. Thus, any multi-compartment model will always be incomplete. In this work, our main goal is to use ensemble modeling as an investigative tool of a neuron's biophysical balances, where the cycling between experiment and model is a design criterion from the start. We consider oriens-lacunosum/moleculare (O-LM) interneurons, a prominent interneuron subtype that plays an essential gating role of information flow in hippocampus. O-LM cells express the hyperpolarization-activated current (Ih). Although dendritic Ih could have a major influence on the integrative properties of O-LM cells, the compartmental distribution of Ih on O-LM dendrites is not known. Using a high-performance computing cluster, we generated a database of models that included those with or without dendritic Ih. A range of conductance values for nine different conductance types were used, and different morphologies explored. Models were quantified and ranked based on minimal error compared to a dataset of O-LM cell electrophysiological properties. Co-regulatory balances between conductances were revealed, two of which were dependent on the presence of dendritic Ih. These findings inform future experiments that differentiate between somatic and dendritic Ih, thereby continuing a cycle between model and experiment.

Synchronized firing of fast-spiking interneurons is critical to maintain balanced firing between direct and indirect pathway neurons of the striatum

The inhibitory circuits of the striatum are known to be critical for motor function, yet their contributions to Parkinsonian motor deficits are not clear. Altered firing in the globus pallidus suggests that striatal medium spiny neurons (MSN) of the direct (D1 MSN) and indirect pathway (D2 MSN) are imbalanced during dopamine depletion. Both MSN classes receive inhibitory input from each other and from inhibitory interneurons within the striatum, specifically the fast-spiking interneurons (FSI). To investigate the role of inhibition in maintaining striatal balance, we developed a biologically-realistic striatal network model consisting of multicompartmental neuron models: 500 D1 MSNs, 500 D2 MSNs and 49 FSIs. The D1 and D2 MSN models are differentiated based on published experiments of individual channel modulations by dopamine, with D2 MSNs being more excitable than D1 MSNs. Despite this difference in response to current injection, in the network D1 and D2 MSNs fire at similar frequencies in response to excitatory synaptic input. Simulations further reveal that inhibition from FSIs connected by gap junctions is critical to produce balanced firing. Although gap junctions produce only a small increase in synchronization between FSIs, removing these connections resulted in significant firing differences between D1 and D2 MSNs, and balanced firing was restored by providing synchronized cortical input to the FSIs. Together these findings suggest that desynchronization of FSI firing is sufficient to alter balanced firing between D1 and D2 MSNs.

Robustness, variability, phase dependence, and longevity of individual synaptic input effects on spike timing during fluctuating synaptic backgrounds: a modeling study of globus pallidus neuron phase response properties

A neuron's phase response curve (PRC) shows how inputs arriving at different times during the spike cycle differentially affect the timing of subsequent spikes. Using a full morphological model of a globus pallidus (GP) neuron, we previously demonstrated that dendritic conductances shape the PRC in a spike frequency-dependent manner, suggesting different functional roles of perisomatic and distal dendritic synapses in the control of patterned network activity. In the present study we extend this analysis to examine the impact of physiologically realistic high conductance states on somatic and dendritic PRCs and the time course of spike train perturbations. First, we found that average somatic and dendritic PRCs preserved their shapes and spike frequency dependence when the model was driven by spatially-distributed, stochastic conductance inputs rather than tonic somatic current. However, responses to inputs during specific synaptic backgrounds often deviated substantially from the average PRC. Therefore, we analyzed the interactions of PRC stimuli with transient fluctuations in the synaptic background on a trial-by-trial basis. We found that the variability in responses to PRC stimuli and the incidence of stimulus-evoked added or skipped spikes were stimulus-phase-dependent and reflected the profile of the average PRC, suggesting commonality in the underlying mechanisms. Clear differences in the relation between the phase of input and variability of spike response between dendritic and somatic inputs indicate that these regions generally represent distinct dynamical subsystems of synaptic integration with respect to influencing the stability of spike time attractors generated by the overall synaptic conductance.

Dendritic sodium channels promote active decorrelation and reduce phase locking to parkinsonian input oscillations in model globus pallidus neurons

Correlated firing among populations of neurons is present throughout the brain and is often rhythmic in nature, observable as an oscillatory fluctuation in the local field potential. Although rhythmic population activity is believed to be critical for normal function in many brain areas, synchronized neural oscillations are associated with disease states in other cases. In the globus pallidus (GP in rodents, homolog of the primate GPe), pairs of neurons generally have uncorrelated firing in normal animals despite an anatomical organization suggesting that they should receive substantial common input. In contrast, correlated and rhythmic GP firing is observed in animal models of Parkinson's disease (PD). Based in part on these findings, it has been proposed that an important part of basal ganglia function is active decorrelation, whereby redundant information is compressed. Mechanisms that implement active decorrelation, and changes that cause it to fail in PD, are subjects of great interest. Rat GP neurons express fast, transient voltage-dependent sodium channels (NaF channels) in their dendrites, with the expression level being highest near asymmetric synapses. We recently showed that the dendritic NaF density strongly influences the responsiveness of model GP neurons to synchronous excitatory inputs. In the present study, we use rat GP neuron models to show that dendritic NaF channel expression is a potential cellular mechanism of active decorrelation. We further show that model neurons with lower dendritic NaF channel expression have a greater tendency to phase lock with oscillatory synaptic input patterns like those observed in PD.

Functional connectivity and integrative properties of globus pallidus neurons

The globus pallidus consists of the external (GPe) and the internal (GPi) segments. The GPe and GPi have different functional roles. The GPe is located centrally within multiple basal ganglia feedforward and feedback connections. The GPi is an output nucleus of the basal ganglia. A complex interplay between intrinsic pacemaking conductances and the balance of glutamatergic and GABAergic input largely determines the rate and pattern of firing of pallidal neurons. The initial part of this article introduces recent findings made in vivo that are related to the roles of glutamatergic and GABAergic inputs in the control of pallidal activity. The latter part describes the roles of intrinsic mechanisms of GPe neurons in the integration of the synaptic inputs. The presence of dendritic voltage-gated sodium channels may allow the initiation of dendritic spikes, giving distal inputs on the long and thin GPe dendrites an opportunity to strongly shape spiking activity. Basal ganglia disorders including Parkinson's disease, hemiballismus, and dystonias are accompanied by increased irregularity and synchronized bursts of pallidal activity. These changes may be in part due to changes in the GABA release in the GPe and GPi, but also involve intrinsic cellular changes in pallidal neurons.