Cold and warmth intensify pain-linked sodium channel gating effects and persistent currents.

Voltage-gated sodium channels (Nav) are key players in excitable tissues with the capability to generate and propagate action potentials. Mutations in the genes encoding Navs can lead to severe inherited diseases, and some of these so-called channelopathies show temperature-sensitive phenotypes, for example, paramyotonia congenita, Brugada syndrome, febrile seizure syndromes, and inherited pain syndromes like erythromelalgia (IEM) and paroxysmal extreme pain disorder (PEPD). Nevertheless, most investigations of mutation-induced gating effects have been conducted at room temperature, and thus the role of cooling or warming in channelopathies remains poorly understood. Here, we investigated the temperature sensitivity of four Nav subtypes: Nav1.3, Nav1.5, Nav1.6, and Nav1.7, and two mutations in Nav1.7 causing IEM (Nav1.7/L823R) and PEPD (Nav1.7/I1461T) expressed in cells of the human embryonic kidney cell line using an automated patch clamp system. Our experiments at 15°C, 25°C, and 35°C revealed a shift of the voltage dependence of activation to more hyperpolarized potentials with increasing temperature for all investigated subtypes. Nav1.3 exhibited strongly slowed inactivation kinetics compared with the other subtypes that resulted in enhanced persistent current, especially at 15°C, indicating a possible role in cold-induced hyperexcitability. Impaired fast inactivation of Nav1.7/I1461T was significantly enhanced by a cooling temperature of 15°C. The subtype-specific modulation as well as the intensified mutation-induced gating changes stress the importance to consider temperature as a regulator for channel gating and its impact on cellular excitability as well as disease phenotypes.

A biophysical and statistical modeling paradigm for connecting neural physiology and function.

To understand single neuron computation, it is necessary to know how specific physiological parameters affect neural spiking patterns that emerge in response to specific stimuli. Here we present a computational pipeline combining biophysical and statistical models that provides a link between variation in functional ion channel expression and changes in single neuron stimulus encoding. More specifically, we create a mapping from biophysical model parameters to stimulus encoding statistical model parameters. Biophysical models provide mechanistic insight, whereas statistical models can identify associations between spiking patterns and the stimuli they encode. We used public biophysical models of two morphologically and functionally distinct projection neuron cell types: mitral cells (MCs) of the main olfactory bulb, and layer V cortical pyramidal cells (PCs). We first simulated sequences of action potentials according to certain stimuli while scaling individual ion channel conductances. We then fitted point process generalized linear models (PP-GLMs), and we constructed a mapping between the parameters in the two types of models. This framework lets us detect effects on stimulus encoding of changing an ion channel conductance. The computational pipeline combines models across scales and can be applied as a screen of channels, in any cell type of interest, to identify ways that channel properties influence single neuron computation.

Kinetic and thermodynamic modeling of a voltage-gated sodium channel.

Like all biological and chemical reactions, ion channel kinetics are highly sensitive to changes in temperature. Therefore, it is prudent to investigate channel dynamics at physiological temperatures. However, most ion channel investigations are performed at room temperature due to practical considerations, such as recording stability and technical limitations. This problem is especially severe for the fast voltage-gated sodium channel, whose activation kinetics are faster than the time constant of the standard patch-clamp amplifier at physiological temperatures. Thus, biologically detailed simulations of the action potential generation evenly scale the kinetic models of voltage-gated channels acquired at room temperature. To quantitatively study voltage-gated sodium channels' temperature sensitivity, we recorded sodium currents from nucleated patches extracted from the rat's layer five neocortical pyramidal neurons at several temperatures from 13.5 to 30 °C. We use these recordings to model the kinetics of the voltage-gated sodium channel as a function of temperature. We show that the temperature dependence of activation differs from that of inactivation. Furthermore, the data indicate that the sustained current has a different temperature dependence than the fast current. Our kinetic and thermodynamic analysis of the current provided a numerical model spanning the entire temperature range. This model reproduced vital features of channel activation and inactivation. Furthermore, the model also reproduced action potential dependence on temperature. Thus, we provide an essential building block for the generation of biologically detailed models of cortical neurons.

NeuroGPU: Accelerating multi-compartment, biophysically detailed neuron simulations on GPUs.

BACKGROUND: The membrane potential of individual neurons depends on a large number of interacting biophysical processes operating on spatial-temporal scales spanning several orders of magnitude. The multi-scale nature of these processes dictates that accurate prediction of membrane potentials in specific neurons requires the utilization of detailed simulations. Unfortunately, constraining parameters within biologically detailed neuron models can be difficult, leading to poor model fits. This obstacle can be overcome partially by numerical optimization or detailed exploration of parameter space. However, these processes, which currently rely on central processing unit (CPU) computation, often incur orders of magnitude increases in computing time for marginal improvements in model behavior. As a result, model quality is often compromised to accommodate compute resources. NEW METHOD: Here, we present a simulation environment, NeuroGPU, that takes advantage of the inherent parallelized structure of the graphics processing unit (GPU) to accelerate neuronal simulation. RESULTS & COMPARISON WITH EXISTING METHODS: NeuroGPU can simulate most biologically detailed models 10-200 times faster than NEURON simulation running on a single core and 5 times faster than GPU simulators (CoreNEURON). NeuroGPU is designed for model parameter tuning and best performs when the GPU is fully utilized by running multiple (> 100) instances of the same model with different parameters. When using multiple GPUs, NeuroGPU can reach to a speed-up of 800 fold compared to single core simulations, especially when simulating the same model morphology with different parameters. We demonstrate the power of NeuoGPU through large-scale parameter exploration to reveal the response landscape of a neuron. Finally, we accelerate numerical optimization of biophysically detailed neuron models to achieve highly accurate fitting of models to simulation and experimental data. CONCLUSIONS: Thus, NeuroGPU is the fastest available platform that enables rapid simulation of multi-compartment, biophysically detailed neuron models on commonly used computing systems accessible by many scientists.

Endocannabinoids and Dopamine Balance Basal Ganglia Output.

The entopeduncular nucleus is one of the basal ganglia's output nuclei, thereby controlling basal ganglia information processing. Entopeduncular nucleus neurons integrate GABAergic inputs from the Striatum and the globus pallidus, together with glutamatergic inputs from the subthalamic nucleus. We show that endocannabinoids and dopamine interact to modulate the long-term plasticity of all these primary afferents to the entopeduncular nucleus. Our results suggest that the interplay between dopamine and endocannabinoids determines the balance between direct pathway (striatum) and indirect pathway (globus pallidus) in entopeduncular nucleus output. Furthermore, we demonstrate that, despite the lack of axon collaterals, information is transferred between neighboring neurons in the entopeduncular nucleus via endocannabinoid diffusion. These results transform the prevailing view of the entopeduncular nucleus as a feedforward "relay" nucleus to an intricate control unit, which may play a vital role in the process of action selection.

Electrophysiologic Characterization of Developing Human Embryonic Stem Cell-Derived Photoreceptor Precursors.

Purpose: Photoreceptor precursor cells (PRPs) differentiated from human embryonic stem cells can serve as a source for cell replacement therapy aimed at vision restoration in patients suffering from degenerative diseases of the outer retina, such as retinitis pigmentosa and AMD. In this work, we studied the electrophysiologic maturation of PRPs throughout the differentiation process. Methods: Human embryonic stem cells were differentiated into PRPs and whole-cell recordings were performed for electrophysiologic characterization at days 0, 30, 60, and 90 along with quantitative PCR analysis to characterize the expression level of various ion channels, which shape the electrophysiologic response. Finally, to characterize the electrically induced calcium currents, we employed calcium imaging (rhod4) to visualize intracellular calcium dynamics in response to electrical activation. Results: Our results revealed an early and steady presence (approximately 100% of responsive cells) of the delayed potassium rectifier current. In contrast, the percentage of cells exhibiting voltage-gated sodium currents increased with maturation (from 0% to almost 90% of responsive cells at 90 days). Moreover, calcium imaging revealed the presence of voltage-gated calcium currents, which play a major role in vision formation. These results were further supported by quantitative PCR analysis, which revealed a significant and continuous (3- to 50-fold) increase in the expression of various voltage-gated channels concomitantly with the increase in the expression of the photoreceptor marker CRX. Conclusions: These results can shed light on the electrophysiologic maturation of neurons in general and PRP in particular and can form the basis for devising and optimizing cell replacement-based vision restoration strategies.

Dynamic input-dependent encoding of individual basal ganglia neurons.

Computational models are crucial to studying the encoding of individual neurons. Static models are composed of a fixed set of parameters, thus resulting in static encoding properties that do not change under different inputs. Here, we challenge this basic concept which underlies these models. Using generalized linear models, we quantify the encoding and information processing properties of basal ganglia neurons recorded in-vitro. These properties are highly sensitive to the internal state of the neuron due to factors such as dependency on the baseline firing rate. Verification of these experimental results with simulations provides insights into the mechanisms underlying this input-dependent encoding. Thus, static models, which are not context dependent, represent only part of the neuronal encoding capabilities, and are not sufficient to represent the dynamics of a neuron over varying inputs. Input-dependent encoding is crucial for expanding our understanding of neuronal behavior in health and disease and underscores the need for a new generation of dynamic neuronal models.

Short-term depression shapes information transmission in a constitutively active GABAergic synapse.

Short-term depression is a low-pass filter of synaptic information, reducing synaptic information transfer at high presynaptic firing frequencies. Consequently, during elevated presynaptic firing, little information passes to the postsynaptic neuron. However, many neurons fire at relatively high frequencies all the time. Does depression silence their synapses? We tested this apparent contradiction in the indirect pathway of the basal ganglia. Using numerical modeling and whole-cell recordings from single entopeduncular nucleus (EP) neurons in rat brain slices, we investigated how different firing rates of globus pallidus (GP) neurons affect information transmission to the EP. Whole-cell recordings showed significant variability in steady-state depression, which decreased as stimulation frequency increased. Modeling predicted that this variability would translate into different postsynaptic noise levels during constitutive presynaptic activity. Our simulations further predicted that individual GP-EP synapses mediate gain control. However, when we consider the integration of multiple inputs, the broad range of GP firing rates would enable different modes of information transmission. Finally, we predict that changes in dopamine levels can shift the action of GP neurons from rate coding to gain modulation. Our results thus demonstrate how short-term depression shapes information transmission in the basal ganglia in particular and via GABAergic synapses in general.

Proliferation of Inhibitory Input to the Substantia Nigra in Experimental Parkinsonism.

The substantia nigra pars reticulata (SNr) is one of the output nuclei of the basal ganglia (BG) and plays a vital role in movement execution. Death of dopaminergic neurons in the neighboring nucleus, the substantia nigra pars compacta (SNc), leads to Parkinson's disease. The ensuing dopamine depletion affects all BG nuclei. However, the long-term effects of dopamine depletion on BG output are less characterized. In this in vitro study, we applied electrophysiological and immunohistochemical techniques to investigate the long-term effects of dopamine depletion on GABAergic transmission to the SNr. The findings showed a reduction in firing rate and regularity in SNr neurons after unilateral dopamine depletion with 6-OHDA, which we associate with homeostatic mechanisms. The strength of the GABAergic synapses between the globus pallidus (GP) and the SNr increased but not their short-term dynamics. Consistent with this observation, there was an increase in the frequency and amplitude of spontaneous inhibitory synaptic events to SNr neurons. Immunohistochemistry revealed an increase in the density of vGAT-labeled puncta in dopamine depleted animals. Overall, these results may suggest that synaptic proliferation can explain how dopamine depletion augments GABAergic transmission in the SNr.

A Mirror-Symmetric Excitatory Link Coordinates Odor Maps across Olfactory Bulbs and Enables Odor Perceptual Unity.

Sensory input reaching the brain from bilateral and offset channels is nonetheless perceived as unified. This unity could be explained by simultaneous projections to both hemispheres, or inter-hemispheric information transfer between sensory cortical maps. Odor input, however, is not topographically organized, nor does it project bilaterally, making olfactory perceptual unity enigmatic. Here we report a circuit that interconnects mirror-symmetric isofunctional mitral/tufted cells between the mouse olfactory bulbs. Connected neurons respond to similar odors from ipsi- and contra-nostrils, whereas unconnected neurons do not respond to odors from the contralateral nostril. This connectivity is likely mediated through a one-to-one mapping from mitral/tufted neurons to the ipsilateral anterior olfactory nucleus pars externa, which activates the mirror-symmetric isofunctional mitral/tufted neurons glutamatergically. This circuit enables sharing of odor information across hemispheres in the absence of a cortical topographical organization, suggesting that olfactory glomerular maps are the equivalent of cortical sensory maps found in other senses.

Long-term plasticity of glutamatergic input from the subthalamic nucleus to the entopeduncular nucleus.

The hyperdirect pathway of the basal ganglia bypasses the striatum, and delivers cortical information directly to the subthalamic nucleus (STN). In rodents, the STN excites the two output nuclei of the basal ganglia, the entopeduncular nucleus (EP) and the substantia nigra reticulata (SNr). Thus, during hyperdirect pathway activation, the STN drives EP firing inhibiting the thalamus. We hypothesized that STN activity could induce long-term changes to the STN->EP synapse. To test this hypothesis, we recorded in the whole-cell mode from neurons in the EP in acute brain slices from rats while electrically stimulating the STN. Repetitive pre-synaptic stimulation generated modest long-term depression (LTD) in the STN->EP synapse. However, pairing EP firing with STN stimulation generated robust LTD that manifested for pre-before post-as well as for post- before pre-synaptic pairing. This LTD was highly sensitive to the time difference and was not detected at a time delay of 10 ms. To investigate whether post-synaptic calcium levels were important for LTD induction, we made dendritic recordings from EP neurons that revealed action potential back-propagation and dendritic calcium transients. Buffering the dendritic calcium concentration in the EP neurons with EGTA generated long term potentiation instead of LTD. Finally, mild LTD could be induced by post-synaptic activity alone that was blocked by an endocannabinoid 1 (CB1) receptor blocker. These results thus suggest there may be an adaptive mechanism for buffering the impact of the hyperdirect pathway on basal ganglia output which could contribute to the de-correlation of STN and EP firing.

Voltage-Gated Sodium Channels in Neocortical Pyramidal Neurons Display Cole-Moore Activation Kinetics.

Exploring the properties of action potentials is a crucial step toward a better understanding of the computational properties of single neurons and neural networks. The voltage-gated sodium channel is a key player in action potential generation. A comprehensive grasp of the gating mechanism of this channel can shed light on the biophysics of action potential generation. However, most models of voltage-gated sodium channels assume a concerted Hodgkin and Huxley kinetic gating scheme. However, it is not clear if Hodgkin and Huxley models are suitable for use in action potential simulations of central nervous system neurons. To resolve this, we investigated the activation kinetics of voltage-gated sodium channels. Here we performed high resolution voltage-clamp experiments from nucleated patches extracted from the soma of layer 5 (L5) cortical pyramidal neurons in rat brain slices. We show that the gating mechanism does not follow traditional Hodgkin and Huxley kinetics and that much of the channel voltage-dependence is probably due to rapid closed-closed transitions that lead to substantial onset latency reminiscent of the Cole-Moore effect observed in voltage-gated potassium conductances. Thus, the classical Hodgkin and Huxley description of sodium channel kinetics may be unsuitable for modeling the physiological role of this channel. Furthermore, our results reconcile between apparently contradicting studies sodium channel activation. Our findings may have key implications for the role of sodium channels in synaptic integration and action potential generation.

Dopamine receptors in the rat entopeduncular nucleus.

Dopamine is critical for the normal functioning of the basal ganglia, modulating both input and output nuclei of this system. The distribution and function of each of the five dopamine receptor subtypes have been studied extensively in the striatum. However, the role of extrastriatal dopamine receptors in basal ganglia information processing is less clear. Here, we studied the anatomical distribution of dopamine receptors in one of the output nuclei of the rodent basal ganglia, the entopeduncular nucleus (EP). The presence of all dopamine receptor subtypes was verified in the EP using immunostaining. We detected co-localization of dopamine receptors with VGAT, which suggests presynaptic expression on GABAergic terminals. D1R and D2R were strongly colocalized with VGAT, whereas DR3-5 showed only sparse co-localization. We further labeled striatal or pallidal neurons with GFP and showed that only D1 receptors were co-localized with striatal terminals, while only D2R and D3R were co-localized with pallidal terminals. Dopamine receptors were also strongly co-localized with MAP2, indicating postsynaptic expression. Overall, these findings suggest that the dopaminergic system modulates activity in the EP both directly via postsynaptic receptors, and indirectly via GABAergic synapses stemming from the direct and indirect pathways.

Dopaminergic Modulation of Synaptic Integration and Firing Patterns in the Rat Entopeduncular Nucleus.

Dopamine is known to differentially modulate the impact of cortical input to the striatum between the direct and indirect pathways of the basal ganglia (BG). However, the role of extrastriatal dopamine receptors (DRs) in BG information processing is less clear. To investigate the role of extrastriatal DRs, we studied their distribution and function in one of the output nuclei of the BG of the rodent, the entopeduncular nucleus (EP). qRT-PCR indicated that all DR subtypes were expressed by EP neurons, suggesting that both D1-like receptors (D1LRs) and D2-like receptors (D2LRs) were likely to affect information processing in the EP. Whole-cell recordings revealed that striatal inputs to the EP were potentiated by D1LRs whereas pallidal inputs to the EP were depressed by D2LRs. Changes to the paired-pulse ratio of inputs to the EP suggested that dopaminergic modulation of striatal inputs is mediated by postsynaptic receptors, and that of globus pallidus-evoked inputs is mediated by presynaptic receptors. We show that these changes in synaptic efficacy changed the information content of EP neuron firing. Overall, the findings suggest that the dopaminergic system affects the passage of feedforward information through the BG by modulating input divergence in the striatum and output convergence in the EP.SIGNIFICANCE STATEMENT The entopeduncular nucleus (EP), one of the basal ganglia (BG) output nuclei, is an important station in information processing in BG. However, it remains unclear how EP neurons encode information and how dopamine affects this process. This contrasts with the well established role of dopamine in the striatum, which is known to redistribute cortical input between the direct and indirect pathways. Here we show that, in symmetry with the striatum, dopamine controls the rebalancing of information flow between the two pathways in the EP. Specifically, we demonstrate that dopamine regulates EP activity by differentially modulating striatal and pallidal GABAergic inputs. These results call for a reassessment of current perspectives on BG information processing by highlighting the functional role of extrastriatal dopamine receptors.

Is realistic neuronal modeling realistic?

Scientific models are abstractions that aim to explain natural phenomena. A successful model shows how a complex phenomenon arises from relatively simple principles while preserving major physical or biological rules and predicting novel experiments. A model should not be a facsimile of reality; it is an aid for understanding it. Contrary to this basic premise, with the 21st century has come a surge in computational efforts to model biological processes in great detail. Here we discuss the oxymoronic, realistic modeling of single neurons. This rapidly advancing field is driven by the discovery that some neurons don't merely sum their inputs and fire if the sum exceeds some threshold. Thus researchers have asked what are the computational abilities of single neurons and attempted to give answers using realistic models. We briefly review the state of the art of compartmental modeling highlighting recent progress and intrinsic flaws. We then attempt to address two fundamental questions. Practically, can we realistically model single neurons? Philosophically, should we realistically model single neurons? We use layer 5 neocortical pyramidal neurons as a test case to examine these issues. We subject three publically available models of layer 5 pyramidal neurons to three simple computational challenges. Based on their performance and a partial survey of published models, we conclude that current compartmental models are ad hoc, unrealistic models functioning poorly once they are stretched beyond the specific problems for which they were designed. We then attempt to plot possible paths for generating realistic single neuron models.

Inhibitory short-term plasticity modulates neuronal activity in the rat entopeduncular nucleus in vitro.

The entopeduncular nucleus (EP) is one of the basal ganglia output nuclei integrating synaptic information from several pathways within the basal ganglia. The firing of EP neurons is modulated by two streams of inhibitory synaptic transmission, the direct pathway from the striatum and the indirect pathway from the globus pallidus. These two inhibitory pathways continuously modulate the firing of EP neurons. However, the link between these synaptic inputs to neuronal firing in the EP is unclear. To investigate this input-output transformation we performed whole-cell and perforated-patch recordings from single neurons in the entopeduncular nucleus in rat brain slices during repetitive stimulation of the striatum and the globus pallidus at frequencies within the in vivo activity range of these neurons. These recordings, supplemented by compartmental modelling, showed that GABAergic synapses from the striatum, converging on EP dendrites, display short-term facilitation and that somatic or proximal GABAergic synapses from the globus pallidus show short-term depression. Activation of striatal synapses during low presynaptic activity decreased postsynaptic firing rate by continuously increasing the inter-spike interval. Conversely, activation of pallidal synapses significantly affected postsynaptic firing during high presynaptic activity. Our data thus suggest that low-frequency striatal output may be encoded as progressive phase shifts in downstream nuclei of the basal ganglia while high-frequency pallidal output may continuously modulate EP firing.

Patch-clamp recordings of rat neurons from acute brain slices of the somatosensory cortex during magnetic stimulation.

Although transcranial magnetic stimulation (TMS) is a popular tool for both basic research and clinical applications, its actions on nerve cells are only partially understood. We have previously predicted, using compartmental modeling, that magnetic stimulation of central nervous system neurons depolarized the soma followed by initiation of an action potential in the initial segment of the axon. The simulations also predict that neurons with low current threshold are more susceptible to magnetic stimulation. Here we tested these theoretical predictions by combining in vitro patch-clamp recordings from rat brain slices with magnetic stimulation and compartmental modeling. In agreement with the modeling, our recordings demonstrate the dependence of magnetic stimulation-triggered action potentials on the type and state of the neuron and its orientation within the magnetic field. Our results suggest that the observed effects of TMS are deeply rooted in the biophysical properties of single neurons in the central nervous system and provide a framework both for interpreting existing TMS data and developing new simulation-based tools and therapies.

Markov modeling of ion channels: implications for understanding disease.

Ion channels are the bridge between the biochemical and electrical domains of our life. These membrane crossing proteins use the electric energy stored in transmembrane ion gradients, which are produced by biochemical activity to generate ionic currents. Each ion channel can be imagined as a small power plant similar to a hydroelectric power station, in which potential energy is converted into electric current. This current drives basically all physiological mechanisms of our body. It is clear that a functional blueprint of these amazing cellular power plants is essential for understanding the principle of all aspects of physiology, particularly neurophysiology. The golden path toward this blueprint starts with the biophysical investigation of ion channel activity and continues through detailed numerical modeling of these channels that will eventually lead to a full system-level description of cellular and organ physiology. Here, we discuss the first two stages of this process focusing on voltage-gated channels, particularly the voltage-gated sodium channel which is neurologically and pathologically important. We first detail the correlations between the known structure of the channel and its activity and describe some pathologies. We then provide a hands-on description of Markov modeling for voltage-gated channels. These two sections of the chapter highlight the dichotomy between the vast amounts of electrophysiological data available on voltage-gated channels and the relatively meager number of physiologically relevant models for these channels.