Dendritic voltage-gated K+ conductance gradient in pyramidal neurones of neocortical layer 5B from rats

Estimation of persistent sodium-current density in rat hippocampal mossy fibre boutons: Correction of space-clamp errors

We used whole-cell patch clamp to estimate the stationary voltage dependence of persistent sodium-current density (iNaP) in rat hippocampal mossy fibre boutons. Cox's method for correcting space-clamp errors was extended to the case of an isopotential compartment with attached neurites. The method was applied to voltage-ramp experiments, in which iNaP is assumed to gate instantaneously. The raw estimates of iNaP led to predicted clamp currents that were at variance with observation, hence an algorithm was devised to improve these estimates. Optionally, the method also allows an estimate of the membrane specific capacitance, although values of the axial resistivity and seal resistance must be provided. Assuming that membrane specific capacitance and axial resistivity were constant, we conclude that seal resistance continued to fall after adding TTX to the bath. This might have been attributable to a further deterioration of the seal after baseline rather than an unlikely effect of TTX. There was an increase in the membrane specific resistance in TTX. The reason for this is unknown, but it meant that iNaP could not be determined by simple subtraction. Attempts to account for iNaP with a Hodgkin-Huxley model of the transient sodium conductance met with mixed results. One thing to emerge was the importance of voltage shifts. Also, a large variability in previously reported values of transient sodium conductance in mossy fibre boutons made comparisons with our results difficult. Various other possible sources of error are discussed. Simulations suggest a role for iNaP in modulating the axonal attenuation of EPSPs. KEY POINTS: We used whole-cell patch clamp to estimate the stationary voltage dependence of persistent sodium-current density (iNaP) in rat hippocampal mossy fibre boutons, using a KCl-based internal (pipette) solution and correcting for the liquid junction potential (2 mV). Space-clamp errors and deterioration of the patch-clamp seal during the experiment were corrected for by compartmental modelling. Attempts to account for iNaP in terms of the transient sodium conductance met with mixed results. One possibility is that the transient sodium conductance is higher in mossy fibre boutons than in the axon shaft. The analysis illustrates the need to account for various voltage shifts (Donnan potentials, liquid junction potentials and, possibly, other voltage shifts). Simulations suggest a role for iNaP in modulating the axonal attenuation of excitatory postsynaptic potentials, hence analog signalling by dentate granule cells.

Network-neuron interactions underlying sensory responses of layer 5 pyramidal tract neurons in barrel cortex

Neurons in the cerebral cortex receive thousands of synaptic inputs per second from thousands of presynaptic neurons. How the dendritic location of inputs, their timing, strength, and presynaptic origin, in conjunction with complex dendritic physiology, impact the transformation of synaptic input into action potential (AP) output remains generally unknown for in vivo conditions. Here, we introduce a computational approach to reveal which properties of the input causally underlie AP output, and how this neuronal input-output computation is influenced by the morphology and biophysical properties of the dendrites. We demonstrate that this approach allows dissecting of how different input populations drive in vivo observed APs. For this purpose, we focus on fast and broadly tuned responses that pyramidal tract neurons in layer 5 (L5PTs) of the rat barrel cortex elicit upon passive single whisker deflections. By reducing a multi-scale model that we reported previously, we show that three features are sufficient to predict with high accuracy the sensory responses and receptive fields of L5PTs under these specific in vivo conditions: the count of active excitatory versus inhibitory synapses preceding the response, their spatial distribution on the dendrites, and the AP history. Based on these three features, we derive an analytically tractable description of the input-output computation of L5PTs, which enabled us to dissect how synaptic input from thalamus and different cell types in barrel cortex contribute to these responses. We show that the input-output computation is preserved across L5PTs despite morphological and biophysical diversity of their dendrites. We found that trial-to-trial variability in L5PT responses, and cell-to-cell variability in their receptive fields, are sufficiently explained by variability in synaptic input from the network, whereas variability in biophysical and morphological properties have minor contributions. Our approach to derive analytically tractable models of input-output computations in L5PTs provides a roadmap to dissect network-neuron interactions underlying L5PT responses across different in vivo conditions and for other cell types.

A universal workflow for creation, validation, and generalization of detailed neuronal models

Detailed single-neuron modeling is widely used to study neuronal functions. While cellular and functional diversity across the mammalian cortex is vast, most of the available computational tools focus on a limited set of specific features characteristic of a single neuron. Here, we present a generalized automated workflow for the creation of robust electrical models and illustrate its performance by building cell models for the rat somatosensory cortex. Each model is based on a 3D morphological reconstruction and a set of ionic mechanisms. We use an evolutionary algorithm to optimize neuronal parameters to match the electrophysiological features extracted from experimental data. Then we validate the optimized models against additional stimuli and assess their generalizability on a population of similar morphologies. Compared to the state-of-the-art canonical models, our models show 5-fold improved generalizability. This versatile approach can be used to build robust models of any neuronal type.

Pareto optimality, economy-effectiveness trade-offs and ion channel degeneracy: improving population modelling for single neurons

Neurons encounter unavoidable evolutionary trade-offs between multiple tasks. They must consume as little energy as possible while effectively fulfilling their functions. Cells displaying the best performance for such multi-task trade-offs are said to be Pareto optimal, with their ion channel configurations underpinning their functionality. Ion channel degeneracy, however, implies that multiple ion channel configurations can lead to functionally similar behaviour. Therefore, instead of a single model, neuroscientists often use populations of models with distinct combinations of ionic conductances. This approach is called population (database or ensemble) modelling. It remains unclear, which ion channel parameters in the vast population of functional models are more likely to be found in the brain. Here we argue that Pareto optimality can serve as a guiding principle for addressing this issue by helping to identify the subpopulations of conductance-based models that perform best for the trade-off between economy and functionality. In this way, the high-dimensional parameter space of neuronal models might be reduced to geometrically simple low-dimensional manifolds, potentially explaining experimentally observed ion channel correlations. Conversely, Pareto inference might also help deduce neuronal functions from high-dimensional Patch-seq data. In summary, Pareto optimality is a promising framework for improving population modelling of neurons and their circuits.

A Minimal Biophysical Model of Neocortical Pyramidal Cells: Implications for Frontal Cortex Microcircuitry and Field Potential Generation

Ca²⁺ spikes initiated in the distal trunk of layer 5 pyramidal cells (PCs) underlie nonlinear dynamic changes in the gain of cellular response, critical for top-down control of cortical processing. Detailed models with many compartments and dozens of ionic channels can account for this Ca²⁺ spike-dependent gain and associated critical frequency. However, current models do not account for all known Ca²⁺-dependent features. Previous attempts to include more features have required increasing complexity, limiting their interpretability and utility for studying large population dynamics. We overcome these limitations in a minimal two-compartment biophysical model. In our model, a basal-dendrites/somatic compartment included fast-inactivating Na⁺ and delayed-rectifier K⁺ conductances, while an apical-dendrites/trunk compartment included persistent Na⁺, hyperpolarization-activated cation (I _h ), slow-inactivating K⁺, muscarinic K⁺, and Ca²⁺ L-type. The model replicated the Ca²⁺ spike morphology and its critical frequency plus three other defining features of layer 5 PC synaptic integration: linear frequency-current relationships, back-propagation-activated Ca²⁺ spike firing, and a shift in the critical frequency by blocking I _h Simulating 1000 synchronized layer 5 PCs, we reproduced the current source density patterns evoked by Ca²⁺ spikes and describe resulting medial-frontal EEG on a male macaque monkey. We reproduced changes in the current source density when I _h was blocked. Thus, a two-compartment model with five crucial ionic currents in the apical dendrites reproduces all features of these neurons. We discuss the utility of this minimal model to study the microcircuitry of agranular areas of the frontal lobe involved in cognitive control and responsible for event-related potentials, such as the error-related negativity.SIGNIFICANCE STATEMENT A minimal model of layer 5 pyramidal cells replicates all known features crucial for distal synaptic integration in these neurons. By redistributing voltage-gated and returning transmembrane currents in the model, we establish a theoretical framework for the investigation of cortical microcircuit contribution to intracranial local field potentials and EEG. This tractable model will enable biophysical evaluation of multiscale electrophysiological signatures and computational investigation of cortical processing.

The neurobiology of bipolar disorder: from circuits to cells to molecular regulation

Over the past 15 years, postmortem studies of the corticolimbic system in subjects with bipolar disorder (BPD) have demonstrated a variety of abnormalities affecting the gamma aminobutyric acid (GABA)ergic system. Although some of the changes are similar to those seen in individuals with schizophrenia, there are pronounced differences in the regulation of complex networks of genes involved in the expression of GAD67, a key marker for functionally differentiated GABAergic interneurons. Overall, these changes vary not only according to diagnosis, but also subregion and layer, suggesting that the activity of GABA cells in complex neural circuits are differentially affected by the unique extrinsic and intrinsic inputs that they receive at different points along a circuit like the trisynaptic pathway. Our ability to understand the functional implications in terms of complex molecular changes will ultimately influence our ability to develop novel treatments for BPD.

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.

Anatomy and physiology of the thick-tufted layer 5 pyramidal neuron

The thick-tufted layer 5 (TTL5) pyramidal neuron is one of the most extensively studied neuron types in the mammalian neocortex and has become a benchmark for understanding information processing in excitatory neurons. By virtue of having the widest local axonal and dendritic arborization, the TTL5 neuron encompasses various local neocortical neurons and thereby defines the dimensions of neocortical microcircuitry. The TTL5 neuron integrates input across all neocortical layers and is the principal output pathway funneling information flow to subcortical structures. Several studies over the past decades have investigated the anatomy, physiology, synaptology, and pathophysiology of the TTL5 neuron. This review summarizes key discoveries and identifies potential avenues of research to facilitate an integrated and unifying understanding on the role of a central neuron in the neocortex.

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.

Subcellular localization of K+ channels in mammalian brain neurons: remarkable precision in the midst of extraordinary complexity

Potassium channels (KChs) are the most diverse ion channels, in part due to extensive combinatorial assembly of a large number of principal and auxiliary subunits into an assortment of KCh complexes. Their structural and functional diversity allows KChs to play diverse roles in neuronal function. Localization of KChs within specialized neuronal compartments defines their physiological role and also fundamentally impacts their activity, due to localized exposure to diverse cellular determinants of channel function. Recent studies in mammalian brain reveal an exquisite refinement of KCh subcellular localization. This includes axonal KChs at the initial segment, and near/within nodes of Ranvier and presynaptic terminals, dendritic KChs found at sites reflecting specific synaptic input, and KChs defining novel neuronal compartments. Painting the remarkable diversity of KChs onto the complex architecture of mammalian neurons creates an elegant picture of electrical signal processing underlying the sophisticated function of individual neuronal compartments, and ultimately neurotransmission and behavior.

Synaptic Conductance Estimates of the Connection Between Local Inhibitor Interneurons and Pyramidal Neurons in Layer 2/3 of a Cortical Column

Stimulation of a principal whisker yields sparse action potential (AP) spiking in layer 2/3 (L2/3) pyramidal neurons in a cortical column of rat barrel cortex. The low AP rates in pyramidal neurons could be explained by activation of interneurons in L2/3 providing inhibition onto L2/3 pyramidal neurons. L2/3 interneurons classified as local inhibitors based on their axonal projection in the same column were reported to receive strong excitatory input from spiny neurons in L4, which are also the main source of the excitatory input to L2/3 pyramidal neurons. Here, we investigated the remaining synaptic connection in this intracolumnar microcircuit. We found strong and reliable inhibitory synaptic transmission between intracolumnar L2/3 local-inhibitor-to-L2/3 pyramidal neuron pairs [inhibitory postsynaptic potential (IPSP) amplitude −0.88 ± 0.67 mV]. On average, 6.2 ± 2 synaptic contacts were made by L2/3 local inhibitors onto L2/3 pyramidal neurons at 107 ± 64 µm path distance from the pyramidal neuron soma, thus overlapping with the distribution of synaptic contacts from L4 spiny neurons onto L2/3 pyramidal neurons (67 ± 34 µm). Finally, using compartmental simulations, we determined the synaptic conductance per synaptic contact to be 0.77 ± 0.4 nS. We conclude that the synaptic circuit from L4 to L2/3 can provide efficient shunting inhibition that is temporally and spatially aligned with the excitatory input from L4 to L2/3.

A simulation study on the effects of dendritic morphology on layer V prefrontal pyramidal cell firing behavior

Pyramidal cells, the most abundant neurons in neocortex, exhibit significant structural variability across different brain areas and layers in different species. Moreover, in response to a somatic step current, these cells display a range of firing behaviors, the most common being (1) repetitive action potentials (Regular Spiking-RS), and (2) an initial cluster of 2-5 action potentials with short interspike interval (ISIs) followed by single spikes (Intrinsic Bursting-IB). A correlation between firing behavior and dendritic morphology has recently been reported. In this work we use computational modeling to investigate quantitatively the effects of the basal dendritic tree morphology on the firing behavior of 112 three-dimensional reconstructions of layer V PFC rat pyramidal cells. Particularly, we focus on how different morphological (diameter, total length, volume, and branch number) and passive [Mean Electrotonic Path length (MEP)] features of basal dendritic trees shape somatic firing when the spatial distribution of ionic mechanisms in the basal dendritic trees is uniform or non-uniform. Our results suggest that total length, volume and branch number are the best morphological parameters to discriminate the cells as RS or IB, regardless of the distribution of ionic mechanisms in basal trees. The discriminatory power of total length, volume, and branch number remains high in the presence of different apical dendrites. These results suggest that morphological variations in the basal dendritic trees of layer V pyramidal neurons in the PFC influence their firing patterns in a predictive manner and may in turn influence the information processing capabilities of these neurons.

A quantitative description of dendritic conductances and its application to dendritic excitation in layer 5 pyramidal neurons

Postsynaptic integration is a complex function of passive membrane properties and nonlinear activation of voltage-gated channels. Some cortical neurons express many voltage-gated channels, with each displaying heterogeneous dendritic conductance gradients. This complexity has hindered the construction of experimentally based mechanistic models of cortical neurons. Here we show that it is possible to overcome this obstacle. We recorded the membrane potential from the soma and apical dendrite of layer 5 (L5) pyramidal neurons of the rat somatosensory cortex. A combined experimental and numerical parameter peeling procedure was implemented to optimize a detailed ionic mechanism for the generation and propagation of dendritic spikes in neocortical L5 pyramidal neurons. In the optimized model, the density of voltage-gated Ca(2+) channels decreased linearly from the soma, and leveled at the distal apical dendrite. The density of the small-conductance Ca(2+)-activated channel decreased along the apical dendrite, whereas the density of the large-conductance Ca(2+)-gated K(+) channel was uniform throughout the apical dendrite. The model predicted an ionic mechanism for the generation of a dendritic spike, the interaction of this spike with the backpropagating action potential, the mechanism responsible for the ability of the proximal apical dendrite to control the coupling between the axon and the dendrite, and the generation of NMDA spikes in the distal apical tuft. Moreover, in addition to faithfully predicting many experimental results recorded from the apical dendrite of L5 pyramidal neurons, the model validates a new methodology for mechanistic modeling of neurons in the CNS.

Potassium channels control the interaction between active dendritic integration compartments in layer 5 cortical pyramidal neurons

Active dendritic synaptic integration enhances the computational power of neurons. Such nonlinear processing generates an object-localization signal in the apical dendritic tuft of layer 5B cortical pyramidal neurons during sensory-motor behavior. Here, we employ electrophysiological and optical approaches in brain slices and behaving animals to investigate how excitatory synaptic input to this distal dendritic compartment influences neuronal output. We find that active dendritic integration throughout the apical dendritic tuft is highly compartmentalized by voltage-gated potassium (KV) channels. A high density of both transient and sustained KV channels was observed in all apical dendritic compartments. These channels potently regulated the interaction between apical dendritic tuft, trunk, and axosomatic integration zones to control neuronal output in vitro as well as the engagement of dendritic nonlinear processing in vivo during sensory-motor behavior. Thus, KV channels dynamically tune the interaction between active dendritic integration compartments in layer 5B pyramidal neurons to shape behaviorally relevant neuronal computations.

The Role of Extracellular Conductivity Profiles in Compartmental Models for Neurons: Particulars for Layer 5 Pyramidal Cells

With the rapid increase in the number of technologies aimed at observing electric activity inside the brain, scientists have felt the urge to create proper links between intracellular- and extracellular-based experimental approaches. Biophysical models at both physical scales have been formalized under assumptions that impede the creation of such links. In this work, we address this issue by proposing a multicompartment model that allows the introduction of complex extracellular and intracellular resistivity profiles. This model accounts for the geometrical and electrotonic properties of any type of neuron through the combination of four devices: the integrator, the propagator, the 3D connector, and the collector. In particular, we applied this framework to model the tufted pyramidal cells of layer 5 (PCL5) in the neocortex. Our model was able to reproduce the decay and delay curves of backpropagating action potentials (APs) in this type of cell with better agreement with experimental data. We used the voltage drops of the extracellular resistances at each compartment to approximate the local field potentials generated by a PCL5 located in close proximity to linear microelectrode arrays. Based on the voltage drops produced by backpropagating APs, we were able to estimate the current multipolar moments generated by a PCL5. By adding external current sources in parallel to the extracellular resistances, we were able to create a sensitivity profile of PCL5 to electric current injections from nearby microelectrodes. In our model for PCL5, the kinetics and spatial profile of each ionic current were determined based on a literature survey, and the geometrical properties of these cells were evaluated experimentally. We concluded that the inclusion of the extracellular space in the compartmental models of neurons as an extra electrotonic medium is crucial for the accurate simulation of both the propagation of the electric potentials along the neuronal dendrites and the neuronal reactivity to an electrical stimulation using external microelectrodes.

Extrasynaptic glutamate receptor activation as cellular bases for dynamic range compression in pyramidal neurons

Repetitive synaptic stimulation overcomes the ability of astrocytic processes to clear glutamate from the extracellular space, allowing some dendritic segments to become submerged in a pool of glutamate, for a brief period of time. This dynamic arrangement activates extrasynaptic NMDA receptors located on dendritic shafts. We used voltage-sensitive and calcium-sensitive dyes to probe dendritic function in this glutamate-rich location. An excess of glutamate in the extrasynaptic space was achieved either by repetitive synaptic stimulation or by glutamate iontophoresis onto the dendrites of pyramidal neurons. Two successive activations of synaptic inputs produced a typical NMDA spike, whereas five successive synaptic inputs produced characteristic plateau potentials, reminiscent of cortical UP states. While NMDA spikes were coupled with brief calcium transients highly restricted to the glutamate input site, the dendritic plateau potentials were accompanied by calcium influx along the entire dendritic branch. Once initiated, the glutamate-mediated dendritic plateau potentials could not be interrupted by negative voltage pulses. Activation of extrasynaptic NMDA receptors in cellular compartments void of spines is sufficient to initiate and support plateau potentials. The only requirement for sustained depolarizing events is a surplus of free glutamate near a group of extrasynaptic receptors. Highly non-linear dendritic spikes (plateau potentials) are summed in a highly sublinear fashion at the soma, revealing the cellular bases of signal compression in cortical circuits. Extrasynaptic NMDA receptors provide pyramidal neurons with a function analogous to a dynamic range compression in audio engineering. They limit or reduce the volume of “loud sounds” (i.e., strong glutamatergic inputs) and amplify “quiet sounds” (i.e., glutamatergic inputs that barely cross the dendritic threshold for local spike initiation). Our data also explain why consecutive cortical UP states have uniform amplitudes in a given neuron.

Mechanisms of magnetic stimulation of central nervous system neurons

Transcranial magnetic stimulation (TMS) is a stimulation method in which a magnetic coil generates a magnetic field in an area of interest in the brain. This magnetic field induces an electric field that modulates neuronal activity. The spatial distribution of the induced electric field is determined by the geometry and location of the coil relative to the brain. Although TMS has been used for several decades, the biophysical basis underlying the stimulation of neurons in the central nervous system (CNS) is still unknown. To address this problem we developed a numerical scheme enabling us to combine realistic magnetic stimulation (MS) with compartmental modeling of neurons with arbitrary morphology. The induced electric field for each location in space was combined with standard compartmental modeling software to calculate the membrane current generated by the electromagnetic field for each segment of the neuron. In agreement with previous studies, the simulations suggested that peripheral axons were excited by the spatial gradients of the induced electric field. In both peripheral and central neurons, MS amplitude required for action potential generation was inversely proportional to the square of the diameter of the stimulated compartment. Due to the importance of the fiber's diameter, magnetic stimulation of CNS neurons depolarized the soma followed by initiation of an action potential in the initial segment of the axon. Passive dendrites affect this process primarily as current sinks, not sources. The simulations predict that neurons with low current threshold are more susceptible to magnetic stimulation. Moreover, they suggest that MS does not directly trigger dendritic regenerative mechanisms. These insights into the mechanism of MS may be relevant for the design of multi-intensity TMS protocols, may facilitate the construction of magnetic stimulators, and may aid the interpretation of results of TMS of the CNS.

Transcranial magnetic stimulation (TMS) is a widely applied tool for probing cognitive function in humans and is one of the best tools for clinical treatments and interfering with cognitive tasks. Surprisingly, while TMS has been commercially available for decades, the cellular mechanisms underlying magnetic stimulation remain unclear. Here we investigate these mechanisms using compartmental modeling. We generated a numerical scheme allowing simulation of the physiological response to magnetic stimulation of neurons with arbitrary morphologies and active properties. Computational experiments using this scheme suggested that TMS affects neurons in the central nervous system (CNS) primarily by somatic stimulation. Since magnetic stimulation appears to cause somatic depolarization, its effects are highly correlated with the neuron's current threshold. Our simulations therefore predict that subpopulations of CNS neurons with different firing thresholds will respond differently to magnetic stimulation. For example, low-intensity TMS may be used to stimulate low-threshold cortical inhibitory interneurons. At higher intensities we predict that both inhibitory and excitatory neurons are activated. These predictions may be tested at the cellular level and may impact cognitive experiments in humans. Furthermore, our simulations may be used to design TMS coils, devices and protocols.

Properties of layer 6 pyramidal neuron apical dendrites

Layer 6 (L6) pyramidal neurons are the only neocortical pyramidal cell type whose apical dendrite terminates in layer 4 rather than layer 1. Like layer 5 pyramidal neurons, they participate in a feedback loop with the thalamus and project to other cortical areas. Despite their unique location in the cortical microcircuit, synaptic integration in dendrites of L6 neurons has never been investigated. Given that all other neocortical pyramidal neurons perform active integration of synaptic inputs via local dendritic spike generation, we were interested to establish the apical dendritic properties of L6 pyramidal neurons. We measured active and passive properties of the apical dendrites of L6 pyramidal neurons in the somatosensory region of rat cortical slices using dual patch-clamp recordings from somata and dendrites and calcium imaging. We found that L6 pyramidal neurons share many fundamental dendritic properties with other neocortical pyramidal neurons, including the generation of local dendritic spikes under the control of dendritic inhibition, voltage-dependent support of backpropagating action potentials, timing-dependent dendritic integration, distally located I(h) channels, frequency-dependent Ca(2+) spike activation, and NMDA spike electrogenesis in the distal apical dendrite. The results suggest that L6 pyramidal neurons integrate synaptic inputs in layer 4 similar to the way other neocortical pyramidal neurons integrate input to layer 1. Thus, L6 pyramidal neurons can perform a similar associational task operating on inputs arriving at the granular and subgranular layers.

Which elements of the mammalian central nervous system are excited by low current stimulation with microelectrodes?

Low current cortex stimulation produces a sparse and distributed set of activated cells often with distances of several hundred micrometers between cell bodies and the microelectrode. A modeling study based on recently measured densities of high threshold sodium channels Nav1.2 in dendrites and soma and low threshold sodium channels Nav1.6 in the axon shall identify spike initiation sites including a discussion on dendritic spikes. Varying excitability along the neural axis has been observed while studying different electrode positions and configurations. Although the axon initial segment (AIS) and nodes of Ranvier are most excitable, many thin axons and dendrites which are likely to be close to the electrode in the densely packed cortical regions are also proper candidates for spike initiation sites. Cathodic threshold ratio for thin axons and dendrites is about 1:3, whereas 0.2 mum diameter axons passing the electrode tip in 10 mum distance can be activated by 100 mus pulses with 2.6 muA. Direct cathodic excitation of dendrites requires a minimum electrode-fiber distance, which increases with dendrite diameter. Therefore thin dendrites can profit from the stronger electrical field close to the electrode but low current stimulation cannot activate large diameter dendrites, contrary to the inverse recruitment order known from peripheral nerve stimulation. When local depolarization fails to generate a dendritic spike, stimulation is possible via intracellular current flow that initiates an action potential, for example 200 mum distant in the low threshold AIS or in certain cases at the distal dendrite ending. Beside these exceptions, spike initiation site for cathodic low current stimulation appears rather close to the electrode.

Cell type-specific thalamic innervation in a column of rat vibrissal cortex

This is the concluding article in a series of 3 studies that investigate the anatomical determinants of thalamocortical (TC) input to excitatory neurons in a cortical column of rat primary somatosensory cortex (S1). We used viral synaptophysin-enhanced green fluorescent protein expression in thalamic neurons and reconstructions of biocytin-labeled cortical neurons in TC slices to quantify the number and distribution of boutons from the ventral posterior medial (VPM) and posteromedial (POm) nuclei potentially innervating dendritic arbors of excitatory neurons located in layers (L)2–6 of a cortical column in rat somatosensory cortex. We found that 1) all types of excitatory neurons potentially receive substantial TC input (90–580 boutons per neuron); 2) pyramidal neurons in L3–L6 receive dual TC input from both VPM and POm that is potentially of equal magnitude for thick-tufted L5 pyramidal neurons (ca. 300 boutons each from VPM and POm); 3) L3, L4, and L5 pyramidal neurons have multiple (2–4) subcellular TC innervation domains that match the dendritic compartments of pyramidal cells; and 4) a subtype of thick-tufted L5 pyramidal neurons has an additional VPM innervation domain in L4. The multiple subcellular TC innervation domains of L5 pyramidal neurons may partly explain their specific action potential patterns observed in vivo. We conclude that the substantial potential TC innervation of all excitatory neuron types in a cortical column constitutes an anatomical basis for the initial near-simultaneous representation of a sensory stimulus in different neuron types.

Amygdalocortical circuitry in schizophrenia: from circuits to molecules

Schizophrenia is a disorder in which disturbances in the integration of emotion with cognition plays a central role and probably involves several different regions, including the dorsolateral prefrontal cortex, the rostral anterior cingulate cortex, the hippocampal formation, and basolateral amygdala (BLA). Recent brain imaging studies have reported changes in volume, whereas postmortem studies point to dysfunction of the GABA and glutamate systems in these regions. Microarray-based profiles indicate that complex changes in the expression of genes associated with synaptic transmission and ion channels are involved in GABA cell dysfunction in schizophrenics. Molecular abnormalities vary considerably on the basis of sector and layer, suggesting that the unique connectivity of intrinsic and extrinsic afferents may critical in regulating the activity of genes in specific subpopulations of GABA cells. Projections of the BLA may be of particular importance to the induction of abnormal circuitry in schizophrenia, as their ingrowth during late adolescence and early adulthood may help to 'trigger' the onset of illness in susceptible individuals. A preponderance of cellular and molecular abnormalities has been found in the stratum oriens (SO) of sectors CA3/2 in which BLA afferents provide a robust innervation. These observations have lead to the development of a rodent model for the study of abnormal circuitry in this disorder. For example, single-cell recordings in hippocampal slices exposed to increased activation from the BLA have shown decreases in GABA currents in pyramidal neurons in SO of CA3/2, but not CA1, and support the validity of this model. Overall, the postmortem studies of neural circuitry abnormalities in schizophrenia are beginning to implicate specific cellular, molecular, and electrophysiological mechanism in specific subtypes of cortical neurons defined by their afferent and efferent connectivity within key corticolimbic regions.

Activity patterns govern synapse-specific AMPA receptor trafficking between deliverable and synaptic pools

In single neurons, glutamatergic synapses receiving distinct afferent inputs may contain AMPA receptors (-Rs) with unique subunit compositions. However, the cellular mechanisms by which differential receptor transport achieves this synaptic diversity remain poorly understood. In lateral geniculate neurons, we show that retinogeniculate and corticogeniculate synapses have distinct AMPA-R subunit compositions. Under basal conditions at both synapses, GluR1-containing AMPA-Rs are transported from an anatomically defined reserve pool to a deliverable pool near the postsynaptic density (PSD), but further incorporate into the PSD or functional synaptic pool only at retinogeniculate synapses. Vision-dependent activity, stimulation mimicking retinal input, or activation of CaMKII or Ras signaling regulated forward GluR1 trafficking from the deliverable pool to the synaptic pool at both synapses, whereas Rap2 signals reverse GluR1 transport at retinogeniculate synapses. These findings suggest that synapse-specific AMPA-R delivery involves constitutive and activity-regulated transport steps between morphological pools, a mechanism that may extend to the site-specific delivery of other membrane protein complexes.

Experimentally guided modelling of dendritic excitability in rat neocortical pyramidal neurones

Constructing physiologically relevant compartmental models of neurones is critical for understanding neuronal activity and function. We recently suggested that measurements from multiple locations along the soma, dendrites and axon are necessary as a data set when using a genetic optimization algorithm to constrain the parameters of a compartmental model of an entire neurone. However, recordings from L5 pyramidal neurones can routinely be performed simultaneously from only two locations. Now we show that a data set recorded from the soma and apical dendrite combined with a parameter peeling procedure is sufficient to constrain a compartmental model for the apical dendrite of L5 pyramidal neurones. The peeling procedure was tested on several compartmental models showing that it avoids local minima in parameter space. Based on the requirements of this analysis procedure, we designed and performed simultaneous whole-cell recordings from the soma and apical dendrite of rat L5 pyramidal neurones. The data set obtained from these recordings allowed constraining a simplified compartmental model for the apical dendrite of L5 pyramidal neurones containing four voltage-gated conductances. In agreement with experimental findings, the optimized model predicts that the conductance density gradients of voltage-gated K(+) conductances taper rapidly proximal to the soma, while the density gradient of the voltage-gated Na(+) conductance tapers slowly along the apical dendrite. The model reproduced the back-propagation of the action potential and the modulation of the resting membrane potential along the apical dendrite. Furthermore, the optimized model provided a mechanistic explanation for the back-propagation of the action potential into the apical dendrite and the generation of dendritic Na(+) spikes.

Characterization of voltage-gated Ca(2+) conductances in layer 5 neocortical pyramidal neurons from rats

Neuronal voltage-gated Ca(2+) channels are involved in electrical signalling and in converting these signals into cytoplasmic calcium changes. One important function of voltage-gated Ca(2+) channels is generating regenerative dendritic Ca(2+) spikes. However, the Ca(2+) dependent mechanisms used to create these spikes are only partially understood. To start investigating this mechanism, we set out to kinetically and pharmacologically identify the sub-types of somatic voltage-gated Ca(2+) channels in pyramidal neurons from layer 5 of rat somatosensory cortex, using the nucleated configuration of the patch-clamp technique. The activation kinetics of the total Ba(2+) current revealed conductance activation only at medium and high voltages suggesting that T-type calcium channels were not present in the patches. Steady-state inactivation protocols in combination with pharmacology revealed the expression of R-type channels. Furthermore, pharmacological experiments identified 5 voltage-gated Ca(2+) channel sub-types - L-, N-, R- and P/Q-type. Finally, the activation of the Ca(2+) conductances was examined using physiologically derived voltage-clamp protocols including a calcium spike protocol and a mock back-propagating action potential (mBPAP) protocol. These experiments enable us to suggest the possible contribution of the five Ca(2+) channel sub-types to Ca(2+) current flow during activation under physiological conditions.

Circuitry-based gene expression profiles in GABA cells of the trisynaptic pathway in schizophrenics versus bipolars

Significant reductions in GABAergic cell numbers and/or activity have been demonstrated in the hippocampus of subjects with schizophrenia and bipolar disorder. To understand how different subpopulations of interneurons are regulated, laser microdissection and gene expression profiling have been used to "deconstruct" the trisynaptic pathway, so that subtypes of GABA cells could be defined by their location in various layers of CA3/2 and CA1. The results suggest that the cellular endophenotypes for SZ and BD may be determined by multiple factors that include unique susceptibility genes for the respective disorders and altered integration among hippocampal GABA cells with extrinsic and intrinsic afferent fiber systems. The extensive and intricate data that has come from this study has provided insights into how a complex circuit, like the trisynaptic pathway, may be regulated in human hippocampus in both health and disease.

A paradoxical isopotentiality: a spatially uniform noise spectrum in neocortical pyramidal cells

Membrane ion channels and synapses are among the most important computational elements of nerve cells. Both have stochastic components that are reflected in random fluctuations of the membrane potential. We measured the spectral characteristics of membrane voltage noise in vitro at the soma and the apical dendrite of layer 4/5 (L4/5) neocortical neurons of rats near the resting potential. We found a remarkable similarity between the voltage noise power spectra at the soma and the dendrites, despite a marked difference in their respective input impedances. At both sites, the noise levels and the input impedance are voltage dependent; in the soma, the noise level increased from σ = 0.33 ± 0.28 mV at 10 mV hyperpolarization from the resting potential to σ = 0.59 ± 0.3 at a depolarization of 10 mV. At the dendrite, the noise increased from σ = 0.34 ± 0.28 to σ = 0.56 ± 0.30 mV, respectively. TTX reduced both the input impedance and the voltage noise, and eliminated their voltage dependence at both locations. We describe a detailed compartmental model of a L4/5 neuron with simplified electrical properties that successfully reproduces the difference in input impedance between dendrites and soma and demonstrates that spatially uniform conductance-base noise sources leads to an apparent isopotential structure which exhibits a uniform power spectra of voltage noise at all locations. We speculate that a homogeneous distribution of noise sources insures that variability in synaptic amplitude as well as timing of action potentials is location invariant.

Space-clamp problems when voltage clamping neurons expressing voltage-gated conductances

The voltage-clamp technique is applicable only to spherical cells. In nonspherical cells, such as neurons, the membrane potential is not clamped distal to the voltage-clamp electrode. This means that the current recorded by the voltage-clamp electrode is the sum of the local current and of axial currents from locations experiencing different membrane potentials. Furthermore, voltage-gated currents recorded from a nonspherical cell are, by definition, severely distorted due to the lack of space clamp. Justifications for voltage clamping in nonspherical cells are, first, that the lack of space clamp is not severe in neurons with short dendrites. Second, passive cable theory may be invoked to justify application of voltage clamp to branching neurons, suggesting that the potential decay is sufficiently shallow to allow spatial clamping of the neuron. Here, using numerical simulations, we show that the distortions of voltage-gated K(+) and Ca(2+) currents are substantial even in neurons with short dendrites. The simulations also demonstrate that passive cable theory cannot be used to justify voltage clamping of neurons due to significant shunting to the reversal potential of the voltage-gated conductance during channel activation. Some of the predictions made by the simulations were verified using somatic and dendritic voltage-clamp experiments in rat somatosensory cortex. Our results demonstrate that voltage-gated K(+) and Ca(2+) currents recorded from branching neurons are almost always severely distorted.

Kinetics of two voltage-gated K+ conductances in substantia nigra dopaminergic neurons

The substantia nigra (SN) is part of the basal ganglia which is a section in the movement circuit in the brain. Dopaminergic neurons (DA) constitute the bulk of substantia nigra neurons and are related to diseases such as Parkinson's disease. Aiming at describing the mechanism of action potential firing in these cells, the current research examined the biophysical characteristics of voltage-gated K+ conductances in the dopaminergic neurons of the SN. The outside-out configuration of the patch-clamp technique was used to measure from dopaminergic neurons in acute brain slices. Two types of K+ voltage-gated conductances, a fast-inactivating A-type-like K+ conductance (K(fast)) and a slow-inactivating delayed rectifier-like K+ conductance (K(slow)), were isolated in these neurons using kinetic separation protocols. The data suggested that a fast-inactivating conductance was due to 69% of the total voltage-gated K+ conductances, while the remainder of the voltage-gated K+ conductance was due to the activation of a slow-inactivating K+ conductance. The two voltage-gated K+ conductances were analyzed assuming a Hodgkin-Huxley model with two activation and one inactivation gate. The kinetic models obtained from this analysis were used in a numerical simulation of the action potential. This simulation suggested that K(fast) may be involved in the modulation of the height and width of action potentials initiated at different resting membrane potentials while K(slow) may participate in action potential repolarization. This mechanism may indicate that SN dopaminergic neurons may perform analog coding by modulation of action potential shape.

Lock-and-key mechanisms of cerebellar memory recall based on rebound currents

A basic question for theories of learning and memory is whether neuronal plasticity suffices to guide proper memory recall. Alternatively, information processing that is additional to readout of stored memories might occur during recall. We formulate a "lock-and-key" hypothesis regarding cerebellum-dependent motor memory in which successful learning shapes neural activity to match a temporal filter that prevents expression of stored but inappropriate motor responses. Thus, neuronal plasticity by itself is necessary but not sufficient to modify motor behavior. We explored this idea through computational studies of two cerebellar behaviors and examined whether deep cerebellar and vestibular nuclei neurons can filter signals from Purkinje cells that would otherwise drive inappropriate motor responses. In eyeblink conditioning, reflex acquisition requires the conditioned stimulus (CS) to precede the unconditioned stimulus (US) by >100 ms. In our biophysical models of cerebellar nuclei neurons this requirement arises through the phenomenon of postinhibitory rebound depolarization and matches longstanding behavioral data on conditioned reflex timing and reliability. Although CS-US intervals<100 ms may induce Purkinje cell plasticity, cerebellar nuclei neurons drive conditioned responses only if the CS-US training interval was >100 ms. This bound reflects the minimum time for deinactivation of rebound currents such as T-type Ca2+. In vestibulo-ocular reflex adaptation, hyperpolarization-activated currents in vestibular nuclei neurons may underlie analogous dependence of adaptation magnitude on the timing of visual and vestibular stimuli. Thus, the proposed lock-and-key mechanisms link channel kinetics to recall performance and yield specific predictions of how perturbations to rebound depolarization affect motor expression.

Axon Initial Segment Kv1 Channels Control Axonal Action Potential Waveform and Synaptic Efficacy

Action potentials are binary signals that transmit information via their rate and temporal pattern. In this context, the axon is thought of as a transmission line, devoid of a role in neuronal computation. Here, we show a highly localized role of axonal Kv1 potassium channels in shaping the action potential waveform in the axon initial segment (AIS) of layer 5 pyramidal neurons independent of the soma. Cell-attached recordings revealed a 10-fold increase in Kv1 channel density over the first 50 microm of the AIS. Inactivation of AIS and proximal axonal Kv1 channels, as occurs during slow subthreshold somatodendritic depolarizations, led to a distance-dependent broadening of axonal action potentials, as well as an increase in synaptic strength at proximal axonal terminals. Thus, Kv1 channels are strategically positioned to integrate slow subthreshold signals, providing control of the presynaptic action potential waveform and synaptic coupling in local cortical circuits.