Automated optimization of a reduced layer 5 pyramidal cell model based on experimental data

Short-term Hebbian learning can implement transformer-like attention

Transformers have revolutionized machine learning models of language and vision, but their connection with neuroscience remains tenuous. Built from attention layers, they require a mass comparison of queries and keys that is difficult to perform using traditional neural circuits. Here, we show that neurons can implement attention-like computations using short-term, Hebbian synaptic potentiation. We call our mechanism the match-and-control principle and it proposes that when activity in an axon is synchronous, or matched, with the somatic activity of a neuron that it synapses onto, the synapse can be briefly strongly potentiated, allowing the axon to take over, or control, the activity of the downstream neuron for a short time. In our scheme, the keys and queries are represented as spike trains and comparisons between the two are performed in individual spines allowing for hundreds of key comparisons per query and roughly as many keys and queries as there are neurons in the network.

Heterogeneous off-target impact of ion-channel deletion on intrinsic properties of hippocampal model neurons that self-regulate calcium

How do neurons that implement cell-autonomous self-regulation of calcium react to knockout of individual ion-channel conductances? To address this question, we used a heterogeneous population of 78 conductance-based models of hippocampal pyramidal neurons that maintained cell-autonomous calcium homeostasis while receiving theta-frequency inputs. At calcium steady-state, we individually deleted each of the 11 active ion-channel conductances from each model. We measured the acute impact of deleting each conductance (one at a time) by comparing intrinsic electrophysiological properties before and immediately after channel deletion. The acute impact of deleting individual conductances on physiological properties (including calcium homeostasis) was heterogeneous, depending on the property, the specific model, and the deleted channel. The underlying many-to-many mapping between ion channels and properties pointed to ion-channel degeneracy. Next, we allowed the other conductances (barring the deleted conductance) to evolve towards achieving calcium homeostasis during theta-frequency activity. When calcium homeostasis was perturbed by ion-channel deletion, post-knockout plasticity in other conductances ensured resilience of calcium homeostasis to ion-channel deletion. These results demonstrate degeneracy in calcium homeostasis, as calcium homeostasis in knockout models was implemented in the absence of a channel that was earlier involved in the homeostatic process. Importantly, in reacquiring homeostasis, ion-channel conductances and physiological properties underwent heterogenous plasticity (dependent on the model, the property, and the deleted channel), even introducing changes in properties that were not directly connected to the deleted channel. Together, post-knockout plasticity geared towards maintaining homeostasis introduced heterogenous off-target effects on several channels and properties, suggesting that extreme caution be exercised in interpreting experimental outcomes involving channel knockouts.

Biological complexity facilitates tuning of the neuronal parameter space

The electrical and computational properties of neurons in our brains are determined by a rich repertoire of membrane-spanning ion channels and elaborate dendritic trees. However, the precise reason for this inherent complexity remains unknown, given that simpler models with fewer ion channels are also able to functionally reproduce the behaviour of some neurons. Here, we stochastically varied the ion channel densities of a biophysically detailed dentate gyrus granule cell model to produce a large population of putative granule cells, comparing those with all 15 original ion channels to their reduced but functional counterparts containing only 5 ion channels. Strikingly, valid parameter combinations in the full models were dramatically more frequent at -6% vs. -1% in the simpler model. The full models were also more stable in the face of perturbations to channel expression levels. Scaling up the numbers of ion channels artificially in the reduced models recovered these advantages confirming the key contribution of the actual number of ion channel types. We conclude that the diversity of ion channels gives a neuron greater flexibility and robustness to achieve a target excitability.

Single-neuron models linking electrophysiology, morphology, and transcriptomics across cortical cell types

Which cell types constitute brain circuits is a fundamental question, but establishing the correspondence across cellular data modalities is challenging. Bio-realistic models allow probing cause-and-effect and linking seemingly disparate modalities. Here, we introduce a computational optimization workflow to generate 9,200 single-neuron models with active conductances. These models are based on 230 in vitro electrophysiological experiments followed by morphological reconstruction from the mouse visual cortex. We show that, in contrast to current belief, the generated models are robust representations of individual experiments and cortical cell types as defined via cellular electrophysiology or transcriptomics. Next, we show that differences in specific conductances predicted from the models reflect differences in gene expression supported by single-cell transcriptomics. The differences in model conductances, in turn, explain electrophysiological differences observed between the cortical subclasses. Our computational effort reconciles single-cell modalities that define cell types and enables causal relationships to be examined.

Emergence of stochastic resonance in a two-compartment hippocampal pyramidal neuron model

In vitro studies have shown that hippocampal pyramidal neurons employ a mechanism similar to stochastic resonance (SR) to enhance the detection and transmission of weak stimuli generated at distal synapses. To support the experimental findings from the perspective of multicompartment model analysis, this paper aimed to elucidate the phenomenon of SR in a noisy two-compartment hippocampal pyramidal neuron model, which was a variant of the Pinsky-Rinzel neuron model with smooth activation functions and a hyperpolarization-activated cation current. With a bifurcation analysis of the model, we demonstrated the underlying dynamical structure responsible for the occurrence of SR. Furthermore, using a stochastically generated biphasic pulse train and broadband noise generated by the Orenstein-Uhlenbeck process as noise perturbation, both SR and suprathreshold SR were observed and quantified. Spectral analysis revealed that the distribution of spectral power under noise perturbations, in addition to inherent neurodynamics, is the main factor affecting SR behavior. The research results suggested that noise enhances the transmission of weak stimuli associated with elongated dendritic structures of hippocampal pyramidal neurons, thereby providing support for related laboratory findings.

Burst control: Synaptic conditions for burst generation in cortical layer 5 pyramidal neurons

The output of neocortical layer 5 pyramidal cells (L5PCs) is expressed by a train of single spikes with intermittent bursts of multiple spikes at high frequencies. The bursts are the result of nonlinear dendritic properties, including Na+, Ca2+, and NMDA spikes, that interact with the ~10,000 synapses impinging on the neuron's dendrites. Output spike bursts are thought to implement key dendritic computations, such as coincidence detection of bottom-up inputs (arriving mostly at the basal tree) and top-down inputs (arriving mostly at the apical tree). In this study we used a detailed nonlinear model of L5PC receiving excitatory and inhibitory synaptic inputs to explore the conditions for generating bursts and for modulating their properties. We established the excitatory input conditions on the basal versus the apical tree that favor burst and show that there are two distinct types of bursts. Bursts consisting of 3 or more spikes firing at < 200 Hz, which are generated by stronger excitatory input to the basal versus the apical tree, and bursts of ~2-spikes at ~250 Hz, generated by prominent apical tuft excitation. Localized and well-timed dendritic inhibition on the apical tree differentially modulates Na+, Ca2+, and NMDA spikes and, consequently, finely controls the burst output. Finally, we explored the implications of different burst classes and respective dendritic inhibition for regulating synaptic plasticity.

Collective behavior emerges from genetically controlled simple behavioral motifs in zebrafish

It is not understood how changes in the genetic makeup of individuals alter the behavior of groups of animals. Here, we find that, even at early larval stages, zebrafish regulate their proximity and alignment with each other. Two simple visual responses, one that measures relative visual field occupancy and one that accounts for global visual motion, suffice to account for the group behavior that emerges. Mutations in genes known to affect social behavior in humans perturb these simple reflexes in individual larval zebrafish and change their emergent collective behaviors in the predicted fashion. Model simulations show that changes in these two responses in individual mutant animals predict well the distinctive collective patterns that emerge in a group. Hence, group behaviors reflect in part genetically defined primitive sensorimotor “motifs,” which are evident even in young larvae.

Active Dendrites and Local Field Potentials: Biophysical Mechanisms and Computational Explorations

Neurons and glial cells are endowed with membranes that express a rich repertoire of ion channels, transporters, and receptors. The constant flux of ions across the neuronal and glial membranes results in voltage fluctuations that can be recorded from the extracellular matrix. The high frequency components of this voltage signal contain information about the spiking activity, reflecting the output from the neurons surrounding the recording location. The low frequency components of the signal, referred to as the local field potential (LFP), have been traditionally thought to provide information about the synaptic inputs that impinge on the large dendritic trees of various neurons. In this review, we discuss recent computational and experimental studies pointing to a critical role of several active dendritic mechanisms that can influence the genesis and the location-dependent spectro-temporal dynamics of LFPs, spanning different brain regions. We strongly emphasize the need to account for the several fast and slow dendritic events and associated active mechanisms - including gradients in their expression profiles, inter- and intra-cellular spatio-temporal interactions spanning neurons and glia, heterogeneities and degeneracy across scales, neuromodulatory influences, and activitydependent plasticity - towards gaining important insights about the origins of LFP under different behavioral states in health and disease. We provide simple but essential guidelines on how to model LFPs taking into account these dendritic mechanisms, with detailed methodology on how to account for various heterogeneities and electrophysiological properties of neurons and synapses while studying LFPs.

Data-driven reduction of dendritic morphologies with preserved dendro-somatic responses

Dendrites shape information flow in neurons. Yet, there is little consensus on the level of spatial complexity at which they operate. Through carefully chosen parameter fits, solvable in the least-squares sense, we obtain accurate reduced compartmental models at any level of complexity. We show that (back-propagating) action potentials, Ca²⁺ spikes, and N-methyl-D-aspartate spikes can all be reproduced with few compartments. We also investigate whether afferent spatial connectivity motifs admit simplification by ablating targeted branches and grouping affected synapses onto the next proximal dendrite. We find that voltage in the remaining branches is reproduced if temporal conductance fluctuations stay below a limit that depends on the average difference in input resistance between the ablated branches and the next proximal dendrite. Furthermore, our methodology fits reduced models directly from experimental data, without requiring morphological reconstructions. We provide software that automatizes the simplification, eliminating a common hurdle toward including dendritic computations in network models.

Simulations of Myenteric Neuron Dynamics in Response to Mechanical Stretch

Background

Intestinal sensitivity to mechanical stimuli has been studied intensively in visceral pain studies. The ability to sense different stimuli in the gut and translate these to physiological outcomes relies on the mechanosensory and transductive capacity of intrinsic intestinal nerves. However, the nature of the mechanosensitive channels and principal mechanical stimulus for mechanosensitive receptors are unknown. To be able to characterize intestinal mechanoelectrical transduction, that is, the molecular basis of mechanosensation, comprehensive mathematical models to predict responses of the sensory neurons to controlled mechanical stimuli are needed. This study aims to develop a biophysically based mathematical model of the myenteric neuron with the parameters constrained by learning from existing experimental data. Findings. The conductance-based single-compartment model was selected. The parameters in the model were optimized by using a combination of hand tuning and automated estimation. Using the optimized parameters, the model successfully predicted the electrophysiological features of the myenteric neurons with and without mechanical stimulation.

Conclusions

The model provides a method to predict features and levels of detail of the underlying physiological system in generating myenteric neuron responses. The model could be used as building blocks in future large-scale network simulations of intrinsic primary afferent neurons and their network.

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.

Modeling of lamprey reticulospinal neurons: multiple distinct parameter sets yield realistic simulations

For the lamprey and other vertebrates, reticulospinal (RS) neurons project descending axons to the spinal cord and activate motor networks to initiate locomotion and other behaviors. In the present study, a biophysically detailed computer model of lamprey RS neurons was constructed consisting of three compartments: dendritic, somatic, and axon initial segment (AIS). All compartments included passive channels. In addition, the soma and AIS had fast potassium and sodium channels. The soma included three additional voltage-gated ion channels (slow sodium and high- and low-voltage-activated calcium) and calcium-activated potassium channels. An initial manually adjusted default parameter set, which was based, in part, on modified parameters from models of lamprey spinal neurons, generated simulations of single action potentials and repetitive firing that scored favorably (0.658; maximum = 0.964) compared with experimentally derived properties of lamprey RS neurons. Subsequently, a dual-annealing search paradigm identified 4,302 viable parameter sets at local maxima within parameter space that yielded higher scores than the default parameter set, including many with much higher scores of approximately 0.85-0.87 (i.e., ~30% improvement). In addition, 5- and 2-conductance grid searches identified a relatively large number of viable parameters sets for which significant correlations were present between maximum conductances for pairs of ion channels. The present results indicated that multiple model parameter sets ("solutions") generated action potentials and repetitive firing that mimicked many of the properties of lamprey RS neurons. To our knowledge, this is the first study to systematically explore parameter space for a biophysically detailed model of lamprey RS neurons.NEW & NOTEWORTHY A computer model of lamprey reticulospinal neurons with a default parameter set produced simulations of action potentials and repetitive firing that scored favorably compared with the properties of these neurons. A dual-annealing search algorithm explored ~50 million parameter sets and identified 4,302 distinct viable parameter sets within parameter space that yielded higher/much higher scores than the default parameter set. In addition, 5- and 2-conductance grid searches identified significant correlations between maximum conductances for pairs of ion channels.

A unified computational model for cortical post-synaptic plasticity

Signalling pathways leading to post-synaptic plasticity have been examined in many types of experimental studies, but a unified picture on how multiple biochemical pathways collectively shape neocortical plasticity is missing. We built a biochemically detailed model of post-synaptic plasticity describing CaMKII, PKA, and PKC pathways and their contribution to synaptic potentiation or depression. We developed a statistical AMPA-receptor-tetramer model, which permits the estimation of the AMPA-receptor-mediated maximal synaptic conductance based on numbers of GluR1s and GluR2s predicted by the biochemical signalling model. We show that our model reproduces neuromodulator-gated spike-timing-dependent plasticity as observed in the visual cortex and can be fit to data from many cortical areas, uncovering the biochemical contributions of the pathways pinpointed by the underlying experimental studies. Our model explains the dependence of different forms of plasticity on the availability of different proteins and can be used for the study of mental disorder-associated impairments of cortical plasticity.

Apical length governs computational diversity of layer 5 pyramidal neurons

Anatomical similarity across the neocortex has led to the common assumption that the circuitry is modular and performs stereotyped computations. Layer 5 pyramidal neurons (L5PNs) in particular are thought to be central to cortical computation because of their extensive arborisation and nonlinear dendritic operations. Here, we demonstrate that computations associated with dendritic Ca2+ plateaus in mouse L5PNs vary substantially between the primary and secondary visual cortices. L5PNs in the secondary visual cortex show reduced dendritic excitability and smaller propensity for burst firing. This reduced excitability is correlated with shorter apical dendrites. Using numerical modelling, we uncover a universal principle underlying the influence of apical length on dendritic backpropagation and excitability, based on a Na+ channel-dependent broadening of backpropagating action potentials. In summary, we provide new insights into the modulation of dendritic excitability by apical dendrite length and show that the operational repertoire of L5PNs is not universal throughout the brain.

An efficient analytical reduction of detailed nonlinear neuron models

Detailed conductance-based nonlinear neuron models consisting of thousands of synapses are key for understanding of the computational properties of single neurons and large neuronal networks, and for interpreting experimental results. Simulations of these models are computationally expensive, considerably curtailing their utility. Neuron_Reduce is a new analytical approach to reduce the morphological complexity and computational time of nonlinear neuron models. Synapses and active membrane channels are mapped to the reduced model preserving their transfer impedance to the soma; synapses with identical transfer impedance are merged into one NEURON process still retaining their individual activation times. Neuron_Reduce accelerates the simulations by 40-250 folds for a variety of cell types and realistic number (10,000-100,000) of synapses while closely replicating voltage dynamics and specific dendritic computations. The reduced neuron-models will enable realistic simulations of neural networks at unprecedented scale, including networks emerging from micro-connectomics efforts and biologically-inspired "deep networks". Neuron_Reduce is publicly available and is straightforward to implement.

Neuromodulation of Axon Terminals

Understanding which cellular compartments are influenced during neuromodulation underpins any rational effort to explain and optimize outcomes. Axon terminals have long been speculated to be sensitive to polarization, but experimentally informed models for CNS stimulation are lacking. We conducted simultaneous intracellular recording from the neuron soma and axon terminal (blebs) during extracellular stimulation with weak sustained (DC) uniform electric fields in mouse cortical slices. Use of weak direct current stimulation (DCS) allowed isolation and quantification of changes in axon terminal biophysics, relevant to both suprathreshold (e.g., deep brain stimulation, spinal cord stimulation, and transcranial magnetic stimulation) and subthreshold (e.g., transcranial DCS and transcranial alternating current stimulation) neuromodulation approaches. Axon terminals polarized with sensitivity (mV of membrane polarization per V/m electric field) 4 times than somas. Even weak polarization (<2 mV) of axon terminals significantly changes action potential dynamics (including amplitude, duration, conduction velocity) in response to an intracellular pulse. Regarding a cellular theory of neuromodulation, we explain how suprathreshold CNS stimulation activates the action potential at terminals while subthreshold approaches modulate synaptic efficacy through axon terminal polarization. We demonstrate that by virtue of axon polarization and resulting changes in action potential dynamics, neuromodulation can influence analog-digital information processing.

Dimensions of control for subthreshold oscillations and spontaneous firing in dopamine neurons

Dopaminergic neurons (DAs) of the rodent substantia nigra pars compacta (SNc) display varied electrophysiological properties in vitro. Despite this, projection patterns and functional inputs from DAs to other structures are conserved, so in vivo delivery of consistent, well-timed dopamine modulation to downstream circuits must be coordinated. Here we show robust coordination by linear parameter controllers, discovered through powerful mathematical analyses of data and models, and from which consistent control of DA subthreshold oscillations (STOs) and spontaneous firing emerges. These units of control represent coordinated intracellular variables, sufficient to regulate complex cellular properties with radical simplicity. Using an evolutionary algorithm and dimensionality reduction, we discovered metaparameters, which when regressed against STO features, revealed a 2-dimensional control plane for the neuron’s 22-dimensional parameter space that fully maps the natural range of DA subthreshold electrophysiology. This plane provided a basis for spiking currents to reproduce a large range of the naturally occurring spontaneous firing characteristics of SNc DAs. From it we easily produced a unique population of models, derived using unbiased parameter search, that show good generalization to channel blockade and compensatory intracellular mechanisms. From this population of models, we then discovered low-dimensional controllers for regulating spontaneous firing properties, and gain insight into how currents active in different voltage regimes interact to produce the emergent activity of SNc DAs. Our methods therefore reveal simple regulators of neuronal function lurking in the complexity of combined ion channel dynamics.

Electrophysiological activity of the neuronal membrane and concomitant ion channel properties are highly variable within groups of neurons of the same type from the same brain region. Reconciliation of the mechanisms generating neuronal activity is challenging due to the complexity of the interactions between the channel currents involved. Here we present a set of mathematical analyses that uncover the low-dimensional intracellular parameter combinations capable of regulating features of subthreshold oscillations and spontaneous firing in empirically constrained models of nigral dopaminergic neurons. This method generates, from a naive starting point, linear combinations of ion channel properties that are surprisingly capable of reliably controlling a wide variety of emergent electrophysiological activity, thereby predicting drug effects and shedding light on unsuspected compensatory mechanisms that contribute to neuronal function.

Estimating neuronal conductance model parameters using dynamic action potential clamp

BACKGROUND

Parameterization of neuronal membrane conductance models relies on data acquired from current clamp (CC) or voltage clamp (VC) recordings. Although the CC approach provides key information on a neuron's firing properties, it is often difficult to disentangle the influence of multiple conductances that contribute to the excitation properties of a real neuron. Isolation of a single conductance using pharmacological agents or heterologous expression simplifies analysis but requires extensive VC evaluation to explore the complete state behavior of the channel of interest.

NEW METHOD

We present an improved parameterization approach that uses data derived from dynamic action potential clamp (DAPC) recordings to extract conductance equation parameters. We demonstrate the utility of the approach by applying it to the standard Hodgkin-Huxley conductance model although other conductance models could be easily incorporated as well.

RESULTS

Using a fully simulated setup we show that, with as few as five action potentials previously recorded in DAPC mode, sodium conductance equation parameters can be determined with average parameter errors of less than 4% while action potential firing accuracy approaches 100%. In real DAPC experiments, we show that by "training" our model with five or fewer action potentials, subsequent firing lasting for several seconds could be predicted with ˜96% mean firing rate accuracy and 94% temporal overlap accuracy.

COMPARISON WITH EXISTING METHODS

Our DAPC-based approach surpasses the accuracy of VC-based approaches for extracting conductance equation parameters with a significantly reduced temporal overhead.

CONCLUSION

DAPC-based approach will facilitate the rapid and systematic characterization of neuronal channelopathies.

Coding Capacity of Purkinje Cells With Different Schemes of Morphological Reduction

The brain as a neuronal system has very complex structures with a large diversity of neuronal types. The most basic complexity is seen from the structure of neuronal morphology, which usually has a complex tree-like structure with dendritic spines distributed in branches. To simulate a large-scale network with spiking neurons, the simple point neuron, such as the integrate-and-fire neuron, is often used. However, recent experimental evidence suggests that the computational ability of a single neuron is largely enhanced by its morphological structure, in particular, by various types of dendritic dynamics. As the morphology reduction of detailed biophysical models is a classic question in systems neuroscience, much effort has been taken to simulate a neuron with a few compartments to include the interaction between the soma and dendritic spines. Yet, novel reduction methods are still needed to deal with the complex dendritic tree. Here, using 10 individual Purkinje cells of the cerebellum from three species of guinea-pig, mouse and rat, we consider four types of reduction methods and study their effects on the coding capacity of Purkinje cells in terms of firing rate, timing coding, spiking pattern, and modulated firing under different stimulation protocols. We found that there is a variation of reduction performance depending on individual cells and species, however, all reduction methods can preserve, to some degree, firing activity of the full model of Purkinje cell. Therefore, when stimulating large-scale network of neurons, one has to choose a proper type of reduced neuronal model depending on the questions addressed. Among these reduction schemes, Branch method, that preserves the geometrical volume of neurons, can achieve the best balance among different performance measures of accuracy, simplification, and computational efficiency, and reproduce various phenomena shown in the full morphology model of Purkinje cells. Altogether, these results suggest that the Branch reduction scheme seems to provide a general guideline for reducing complex morphology into a few compartments without the loss of basic characteristics of the firing properties of neurons.

Response to coincident inputs in electrically coupled primary afferents is heterogeneous and is enhanced by H-current (IH) modulation

Electrical synapses represent a widespread modality of interneuronal communication in the mammalian brain. These contacts, by lowering the effectiveness of random or temporally uncorrelated inputs, endow circuits of coupled neurons with the ability to selectively respond to simultaneous depolarizations. This mechanism may support coincidence detection, a property involved in sensory perception, organization of motor outputs, and improvement signal-to-noise ratio. While the role of electrical coupling is well established, little is known about the contribution of the cellular excitability and its modulations to the susceptibility of groups of neurons to coincident inputs. Here, we obtained dual whole cell patch-clamp recordings of pairs of mesencephalic trigeminal (MesV) neurons in brainstem slices from rats to evaluate coincidence detection and its determinants. MesV neurons are primary afferents involved in the organization of orofacial behaviors whose cell bodies are electrically coupled mainly in pairs through soma-somatic gap junctions. We found that coincidence detection is highly heterogeneous across the population of coupled neurons. Furthermore, combined electrophysiological and modeling approaches reveal that this heterogeneity arises from the diversity of MesV neuron intrinsic excitability. Consistently, increasing these cells' excitability by upregulating the hyperpolarization-activated cationic current (I_H) triggered by cGMP results in a dramatic enhancement of the susceptibility of coupled neurons to coincident inputs. In conclusion, the ability of coupled neurons to detect coincident inputs is critically shaped by their intrinsic electrophysiological properties, emphasizing the relevance of neuronal excitability for the many functional operations supported by electrical transmission in mammals. NEW & NOTEWORTHY We show that the susceptibility of pairs of coupled mesencephalic trigeminal (MesV) neurons to coincident inputs is highly heterogenous and depends on the interaction between electrical coupling and neuronal excitability. Additionally, upregulating the hyperpolarization-activated cationic current (I_H) by cGMP results in a dramatic increase of this susceptibility. The I_H and electrical synapses have been shown to coexist in many neuronal populations, suggesting that modulation of this conductance could represent a common strategy to regulate circuit operation supported by electrical coupling.

Analysis of upper threshold mechanisms of spherical neurons during extracellular stimulation

Exceeding a certain stimulation strength can prevent the generation of somatic action potentials, as has been demonstrated in vitro with extracellularly stimulated dorsal root ganglion cells as well as retinal ganglion cells. This phenomenon, termed upper threshold, is currently thought to be a consequence of sodium current reversal in strongly depolarized regions. Here we analyze the contribution of membrane kinetics, using spherical model neurons that are stimulated externally with a microelectrode, in more detail. During extracellular pulse application, the electric field depolarizes one part and hyperpolarizes the other part of the cell. Strong transmembrane currents are generated only in the active depolarized region, changing the overall polarization level. The asymmetric membrane voltage distribution caused by the stimulus strongly influences the cell's behavior during and even after the stimulus. Effects on membrane voltage and transmembrane currents during and after the stimulus are shown and discussed in detail. Aside from the sodium current reversal, two more key mechanisms were identified in causing the upper threshold: strong potassium currents and inactivation of sodium channels. The contributions of the mechanisms involved strongly depend on cell properties, stimulus parameters, and other factors such as temperature. The conclusions presented here are based on several retinal ganglion cell models of the Fohlmeister group, a model with original Hodgkin-Huxley membrane, and a pyramidal cell model. NEW & NOTEWORTHY The upper threshold phenomenon in extracellular stimulation is analyzed in detail for spherical cells. Three main mechanisms were identified that prevent the generation of action potentials at high stimulation strengths: 1) strong potassium currents, 2) inactivating sodium ion channels, and 3) sodium current reversal. Ion channel kinetics in retinal ganglion cells, pyramidal cells, and the original Hodgkin-Huxley model were investigated under the influence of an extracellular stimulus.

Uncertainpy: A Python Toolbox for Uncertainty Quantification and Sensitivity Analysis in Computational Neuroscience

Computational models in neuroscience typically contain many parameters that are poorly constrained by experimental data. Uncertainty quantification and sensitivity analysis provide rigorous procedures to quantify how the model output depends on this parameter uncertainty. Unfortunately, the application of such methods is not yet standard within the field of neuroscience. Here we present Uncertainpy, an open-source Python toolbox, tailored to perform uncertainty quantification and sensitivity analysis of neuroscience models. Uncertainpy aims to make it quick and easy to get started with uncertainty analysis, without any need for detailed prior knowledge. The toolbox allows uncertainty quantification and sensitivity analysis to be performed on already existing models without needing to modify the model equations or model implementation. Uncertainpy bases its analysis on polynomial chaos expansions, which are more efficient than the more standard Monte-Carlo based approaches. Uncertainpy is tailored for neuroscience applications by its built-in capability for calculating characteristic features in the model output. The toolbox does not merely perform a point-to-point comparison of the "raw" model output (e.g., membrane voltage traces), but can also calculate the uncertainty and sensitivity of salient model response features such as spike timing, action potential width, average interspike interval, and other features relevant for various neural and neural network models. Uncertainpy comes with several common models and features built in, and including custom models and new features is easy. The aim of the current paper is to present Uncertainpy to the neuroscience community in a user-oriented manner. To demonstrate its broad applicability, we perform an uncertainty quantification and sensitivity analysis of three case studies relevant for neuroscience: the original Hodgkin-Huxley point-neuron model for action potential generation, a multi-compartmental model of a thalamic interneuron implemented in the NEURON simulator, and a sparsely connected recurrent network model implemented in the NEST simulator.

Parameter Optimization Using Covariance Matrix Adaptation-Evolutionary Strategy (CMA-ES), an Approach to Investigate Differences in Channel Properties Between Neuron Subtypes

Computational models in neuroscience can be used to predict causal relationships between biological mechanisms in neurons and networks, such as the effect of blocking an ion channel or synaptic connection on neuron activity. Since developing a biophysically realistic, single neuron model is exceedingly difficult, software has been developed for automatically adjusting parameters of computational neuronal models. The ideal optimization software should work with commonly used neural simulation software; thus, we present software which works with models specified in declarative format for the MOOSE simulator. Experimental data can be specified using one of two different file formats. The fitness function is customizable as a weighted combination of feature differences. The optimization itself uses the covariance matrix adaptation-evolutionary strategy, because it is robust in the face of local fluctuations of the fitness function, and deals well with a high-dimensional and discontinuous fitness landscape. We demonstrate the versatility of the software by creating several model examples of each of four types of neurons (two subtypes of spiny projection neurons and two subtypes of globus pallidus neurons) by tuning to current clamp data. Optimizations reached convergence within 1,600-4,000 model evaluations (200-500 generations × population size of 8). Analysis of the parameters of the best fitting models revealed differences between neuron subtypes, which are consistent with prior experimental results. Overall our results suggest that this easy-to-use, automatic approach for finding neuron channel parameters may be applied to current clamp recordings from neurons exhibiting different biochemical markers to help characterize ionic differences between other neuron subtypes.

Adaptive optimal input design and parametric estimation of nonlinear dynamical systems: application to neuronal modeling

OBJECTIVE

Many physical models of biological processes including neural systems are characterized by parametric nonlinear dynamical relations between driving inputs, internal states, and measured outputs of the process. Fitting such models using experimental data (data assimilation) is a challenging task since the physical process often operates in a noisy, possibly non-stationary environment; moreover, conducting multiple experiments under controlled and repeatable conditions can be impractical, time consuming or costly. The accuracy of model identification, therefore, is dictated principally by the quality and dynamic richness of collected data over single or few experimental sessions. Accordingly, it is highly desirable to design efficient experiments that, by exciting the physical process with smart inputs, yields fast convergence and increased accuracy of the model.

APPROACH

We herein introduce an adaptive framework in which optimal input design is integrated with square root cubature Kalman filters (OID-SCKF) to develop an online estimation procedure that first, converges significantly quicker, thereby permitting model fitting over shorter time windows, and second, enhances model accuracy when only few process outputs are accessible. The methodology is demonstrated on common nonlinear models and on a four-area neural mass model with noisy and limited measurements. Estimation quality (speed and accuracy) is benchmarked against high-performance SCKF-based methods that commonly employ dynamically rich informed inputs for accurate model identification.

MAIN RESULTS

For all the tested models, simulated single-trial and ensemble averages showed that OID-SCKF exhibited (i) faster convergence of parameter estimates and (ii) lower dependence on inter-trial noise variability with gains up to around 1000 ms in speed and 81% increase in variability for the neural mass models. In terms of accuracy, OID-SCKF estimation was superior, and exhibited considerably less variability across experiments, in identifying model parameters of (a) systems with challenging model inversion dynamics and (b) systems with fewer measurable outputs that directly relate to the underlying processes.

SIGNIFICANCE

Fast and accurate identification therefore carries particular promise for modeling of transient (short-lived) neuronal network dynamics using a spatially under-sampled set of noisy measurements, as is commonly encountered in neural engineering applications.

High-Resolution Multi-Scale Computational Model for Non-Invasive Cervical Vagus Nerve Stimulation

OBJECTIVES

To develop the first high-resolution, multi-scale model of cervical non-invasive vagus nerve stimulation (nVNS) and to predict vagus fiber type activation, given clinically relevant rheobase thresholds.

METHODS

An MRI-derived Finite Element Method (FEM) model was developed to accurately simulate key macroscopic (e.g., skin, soft tissue, muscle) and mesoscopic (cervical enlargement, vertebral arch and foramen, cerebral spinal fluid [CSF], nerve sheath) tissue components to predict extracellular potential, electric field (E-Field), and activating function along the vagus nerve. Microscopic scale biophysical models of axons were developed to compare axons of varying size (Aα-, Aβ- and Aδ-, B-, and C-fibers). Rheobase threshold estimates were based on a step function waveform.

RESULTS

Macro-scale accuracy was found to determine E-Field magnitudes around the vagus nerve, while meso-scale precision determined E-field changes (activating function). Mesoscopic anatomical details that capture vagus nerve passage through a changing tissue environment (e.g., bone to soft tissue) profoundly enhanced predicted axon sensitivity while encapsulation in homogenous tissue (e.g., nerve sheath) dulled axon sensitivity to nVNS.

CONCLUSIONS

These findings indicate that realistic and precise modeling at both macroscopic and mesoscopic scales are needed for quantitative predictions of vagus nerve activation. Based on this approach, we predict conventional cervical nVNS protocols can activate A- and B- but not C-fibers. Our state-of-the-art implementation across scales is equally valuable for models of spinal cord stimulation, cortex/deep brain stimulation, and other peripheral/cranial nerve models.

Systematic generation of biophysically detailed models for diverse cortical neuron types

The cellular components of mammalian neocortical circuits are diverse, and capturing this diversity in computational models is challenging. Here we report an approach for generating biophysically detailed models of 170 individual neurons in the Allen Cell Types Database to link the systematic experimental characterization of cell types to the construction of cortical models. We build models from 3D morphologies and somatic electrophysiological responses measured in the same cells. Densities of active somatic conductances and additional parameters are optimized with a genetic algorithm to match electrophysiological features. We evaluate the models by applying additional stimuli and comparing model responses to experimental data. Applying this technique across a diverse set of neurons from adult mouse primary visual cortex, we verify that models preserve the distinctiveness of intrinsic properties between subsets of cells observed in experiments. The optimized models are accessible online alongside the experimental data. Code for optimization and simulation is also openly distributed.

Dendritic small conductance calcium-activated potassium channels activated by action potentials suppress EPSPs and gate spike-timing dependent synaptic plasticity

Small conductance calcium-activated potassium channels (SK channels) are present in spines and can be activated by backpropagating action potentials (APs). This suggests they may play a critical role in spike-timing dependent synaptic plasticity (STDP). Consistent with this idea, EPSPs in both cortical and hippocampal pyramidal neurons were suppressed by preceding APs in an SK-dependent manner. In cortical pyramidal neurons EPSP suppression by preceding APs depended on their precise timing as well as the distance of activated synapses from the soma, was dendritic in origin, and involved SK-dependent suppression of NMDA receptor activation. As a result SK channel activation by backpropagating APs gated STDP induction during low-frequency AP-EPSP pairing, with both LTP and LTD absent under control conditions but present after SK channel block. These findings indicate that activation of SK channels in spines by backpropagating APs plays a key role in regulating both EPSP amplitude and STDP induction.

Development of a Computational Approach/Model to Explore NMDA Receptors Functions

Modern laboratory techniques allow studying NMDA receptors (NMDAR) either anatomically with specific antibodies coupled to sophisticated confocal microscopy, or physiologically by live imaging or electrophysiological techniques. However, NMDARs are not fixed in time and space and changes in their composition and/or distribution on the post-synaptic membrane may significantly impact the synaptic strength and overall function. The computational modeling approach therefore constitutes a complementary tool for investigating the properties of biological systems based on the knowledge provided by the lab experiments.Here, we describe a general computational method aiming at developing kinetic Markov-chain based models of NMDARs subtypes capable of reproducing various experimental results. These models are then used to make predictions on additional (non-obvious) properties and on their role in synaptic function under various physiological and pharmacological conditions. For the purpose of this book chapter, we will focus on the method used to develop a NMDAR model that includes pharmacological site of action of different compounds. Notably, this elementary model can subsequently be included in a neuron model (not described in detail here) to explore the impact of their differential distribution on synaptic functions.

A stepwise neuron model fitting procedure designed for recordings with high spatial resolution: Application to layer 5 pyramidal cells

BACKGROUND

Recent progress in electrophysiological and optical methods for neuronal recordings provides vast amounts of high-resolution data. In parallel, the development of computer technology has allowed simulation of ever-larger neuronal circuits. A challenge in taking advantage of these developments is the construction of single-cell and network models in a way that faithfully reproduces neuronal biophysics with subcellular level of details while keeping the simulation costs at an acceptable level.

NEW METHOD

In this work, we develop and apply an automated, stepwise method for fitting a neuron model to data with fine spatial resolution, such as that achievable with voltage sensitive dyes (VSDs) and Ca²⁺ imaging.

RESULT

We apply our method to simulated data from layer 5 pyramidal cells (L5PCs) and construct a model with reduced neuronal morphology. We connect the reduced-morphology neurons into a network and validate against simulated data from a high-resolution L5PC network model.

COMPARISON WITH EXISTING METHODS

Our approach combines features from several previously applied model-fitting strategies. The reduced-morphology neuron model obtained using our approach reliably reproduces the membrane-potential dynamics across the dendrites as predicted by the full-morphology model.

CONCLUSIONS

The network models produced using our method are cost-efficient and predict that interconnected L5PCs are able to amplify delta-range oscillatory inputs across a large range of network sizes and topologies, largely due to the medium after hyperpolarization mediated by the Ca²⁺-activated SK current.

The Slow Dynamics of Intracellular Sodium Concentration Increase the Time Window of Neuronal Integration: A Simulation Study

Changes in intracellular Na⁺ concentration ([Na⁺]_i) are rarely taken into account when neuronal activity is examined. As opposed to Ca²⁺, [Na⁺]_i dynamics are strongly affected by longitudinal diffusion, and therefore they are governed by the morphological structure of the neurons, in addition to the localization of influx and efflux mechanisms. Here, we examined [Na⁺]_i dynamics and their effects on neuronal computation in three multi-compartmental neuronal models, representing three distinct cell types: accessory olfactory bulb (AOB) mitral cells, cortical layer V pyramidal cells, and cerebellar Purkinje cells. We added [Na⁺]_i as a state variable to these models, and allowed it to modulate the Na⁺ Nernst potential, the Na⁺-K⁺ pump current, and the Na⁺-Ca²⁺ exchanger rate. Our results indicate that in most cases [Na⁺]_i dynamics are significantly slower than [Ca²⁺]_i dynamics, and thus may exert a prolonged influence on neuronal computation in a neuronal type specific manner. We show that [Na⁺]_i dynamics affect neuronal activity via three main processes: reduction of EPSP amplitude in repeatedly active synapses due to reduction of the Na⁺ Nernst potential; activity-dependent hyperpolarization due to increased activity of the Na⁺-K⁺ pump; specific tagging of active synapses by extended Ca²⁺ elevation, intensified by concurrent back-propagating action potentials or complex spikes. Thus, we conclude that [Na⁺]_i dynamics should be considered whenever synaptic plasticity, extensive synaptic input, or bursting activity are examined.

A consensus layer V pyramidal neuron can sustain interpulse-interval coding

In terms of a single neuron's long-distance communication, interpulse intervals (IPIs) are an attractive alternative to rate and binary codes. As a proxy for an IPI, a neuron's time-to-spike can be found in the biophysical and experimental intracellular literature. Using the current, consensus layer V pyramidal neuron, the present study examines the feasibility of IPI-coding and examines the noise sources that limit the information rate of such an encoding. In descending order of importance, the noise sources are (i) synaptic variability, (ii) sodium channel shot-noise, followed by (iii) thermal noise. The biophysical simulations allow the calculation of mutual information, which is about 3.0 bits/spike. More importantly, while, by any conventional definition, the biophysical model is highly nonlinear, the underlying function that relates input intensity to the defined output variable is linear. When one assumes the perspective of a neuron coding via first hitting-time, this result justifies a pervasive and simplifying assumption of computational modelers-that a class of cortical neurons can be treated as linearly additive, computational devices.

Active dendritic integration as a mechanism for robust and precise grid cell firing

Understanding how active dendrites are exploited for behaviorally relevant computations is a fundamental challenge in neuroscience. Grid cells in medial entorhinal cortex are an attractive model system for addressing this question, as the computation they perform is clear: they convert synaptic inputs into spatially modulated, periodic firing. Whether active dendrites contribute to the generation of the dual temporal and rate codes characteristic of grid cell output is unknown. We show that dendrites of medial entorhinal cortex neurons are highly excitable and exhibit a supralinear input-output function in vitro, while in vivo recordings reveal membrane potential signatures consistent with recruitment of active dendritic conductances. By incorporating these nonlinear dynamics into grid cell models, we show that they can sharpen the precision of the temporal code and enhance the robustness of the rate code, thereby supporting a stable, accurate representation of space under varying environmental conditions. Our results suggest that active dendrites may therefore constitute a key cellular mechanism for ensuring reliable spatial navigation.

Optimizing computer models of corticospinal neurons to replicate in vitro dynamics

Corticospinal neurons (SPI), thick-tufted pyramidal neurons in motor cortex layer 5B that project caudally via the medullary pyramids, display distinct class-specific electrophysiological properties in vitro: strong sag with hyperpolarization, lack of adaptation, and a nearly linear frequency-current (F-I) relationship. We used our electrophysiological data to produce a pair of large archives of SPI neuron computer models in two model classes: 1) detailed models with full reconstruction; and 2) simplified models with six compartments. We used a PRAXIS and an evolutionary multiobjective optimization (EMO) in sequence to determine ion channel conductances. EMO selected good models from each of the two model classes to form the two model archives. Archived models showed tradeoffs across fitness functions. For example, parameters that produced excellent F-I fit produced a less-optimal fit for interspike voltage trajectory. Because of these tradeoffs, there was no single best model but rather models that would be best for particular usages for either single neuron or network explorations. Further exploration of exemplar models with strong F-I fit demonstrated that both the detailed and simple models produced excellent matches to the experimental data. Although dendritic ion identities and densities cannot yet be fully determined experimentally, we explored the consequences of a demonstrated proximal to distal density gradient of I_h, demonstrating that this would lead to a gradient of resonance properties with increased resonant frequencies more distally. We suggest that this dynamical feature could serve to make the cell particularly responsive to major frequency bands that differ by cortical layer.

NEW & NOTEWORTHY

We developed models of motor cortex corticospinal neurons that replicate in vitro dynamics, including hyperpolarization-induced sag and realistic firing patterns. Models demonstrated resonance in response to synaptic stimulation, with resonance frequency increasing in apical dendrites with increasing distance from soma, matching the increasing oscillation frequencies spanning deep to superficial cortical layers. This gradient may enable specific corticospinal neuron dendrites to entrain to relevant oscillations in different cortical layers, contributing to appropriate motor output commands.

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.

Distinct current modules shape cellular dynamics in model neurons

Numerous intrinsic currents are known to collectively shape neuronal membrane potential dynamics, or neuronal signatures. Although how sets of currents shape specific signatures such as spiking characteristics or oscillations has been studied individually, it is less clear how a neuron's suite of currents jointly shape its entire set of signatures. Biophysical conductance-based models of neurons represent a viable tool to address this important question. We hypothesized that currents are grouped into distinct modules that shape specific neuronal characteristics or signatures, such as resting potential, sub-threshold oscillations, and spiking waveforms, for several classes of neurons. For such a grouping to occur, the currents within one module should have minimal functional interference with currents belonging to other modules. This condition is satisfied if the gating functions of currents in the same module are grouped together on the voltage axis; in contrast, such functions are segregated along the voltage axis for currents belonging to different modules. We tested this hypothesis using four published example case models and found it to be valid for these classes of neurons. This insight into the neurobiological organization of currents also suggests an intuitive, systematic, and robust methodology to develop biophysical single-cell models with multiple biological characteristics applicable for both hand- and automated-tuning approaches. We illustrate the methodology using two example case rodent pyramidal neurons, from the lateral amygdala and the hippocampus. The methodology also helped reveal that a single-core compartment model could capture multiple neuronal properties. Such biophysical single-compartment models have potential to improve the fidelity of large network models.

Automated evolutionary optimization of ion channel conductances and kinetics in models of young and aged rhesus monkey pyramidal neurons

Conductance-based compartment modeling requires tuning of many parameters to fit the neuron model to target electrophysiological data. Automated parameter optimization via evolutionary algorithms (EAs) is a common approach to accomplish this task, using error functions to quantify differences between model and target. We present a three-stage EA optimization protocol for tuning ion channel conductances and kinetics in a generic neuron model with minimal manual intervention. We use the technique of Latin hypercube sampling in a new way, to choose weights for error functions automatically so that each function influences the parameter search to a similar degree. This protocol requires no specialized physiological data collection and is applicable to commonly-collected current clamp data and either single- or multi-objective optimization. We applied the protocol to two representative pyramidal neurons from layer 3 of the prefrontal cortex of rhesus monkeys, in which action potential firing rates are significantly higher in aged compared to young animals. Using an idealized dendritic topology and models with either 4 or 8 ion channels (10 or 23 free parameters respectively), we produced populations of parameter combinations fitting the target datasets in less than 80 hours of optimization each. Passive parameter differences between young and aged models were consistent with our prior results using simpler models and hand tuning. We analyzed parameter values among fits to a single neuron to facilitate refinement of the underlying model, and across fits to multiple neurons to show how our protocol will lead to predictions of parameter differences with aging in these neurons.

BluePyOpt: Leveraging Open Source Software and Cloud Infrastructure to Optimise Model Parameters in Neuroscience

At many scales in neuroscience, appropriate mathematical models take the form of complex dynamical systems. Parameterizing such models to conform to the multitude of available experimental constraints is a global non-linear optimisation problem with a complex fitness landscape, requiring numerical techniques to find suitable approximate solutions. Stochastic optimisation approaches, such as evolutionary algorithms, have been shown to be effective, but often the setting up of such optimisations and the choice of a specific search algorithm and its parameters is non-trivial, requiring domain-specific expertise. Here we describe BluePyOpt, a Python package targeted at the broad neuroscience community to simplify this task. BluePyOpt is an extensible framework for data-driven model parameter optimisation that wraps and standardizes several existing open-source tools. It simplifies the task of creating and sharing these optimisations, and the associated techniques and knowledge. This is achieved by abstracting the optimisation and evaluation tasks into various reusable and flexible discrete elements according to established best-practices. Further, BluePyOpt provides methods for setting up both small- and large-scale optimisations on a variety of platforms, ranging from laptops to Linux clusters and cloud-based compute infrastructures. The versatility of the BluePyOpt framework is demonstrated by working through three representative neuroscience specific use cases.

Targeted pruning of a neuron's dendritic tree via femtosecond laser dendrotomy

Neurons are classified according to action potential firing in response to current injection. While such firing patterns are shaped by the composition and distribution of ion channels, modelling studies suggest that the geometry of dendritic branches also influences temporal firing patterns. Verifying this link is crucial to understanding how neurons transform their inputs to output but has so far been technically challenging. Here, we investigate branching-dependent firing by pruning the dendritic tree of pyramidal neurons. We use a focused ultrafast laser to achieve highly localized and minimally invasive cutting of dendrites, thus keeping the rest of the dendritic tree intact and the neuron functional. We verify successful dendrotomy via two-photon uncaging of neurotransmitters before and after dendrotomy at sites around the cut region and via biocytin staining. Our results show that significantly altering the dendritic arborisation, such as by severing the apical trunk, enhances excitability in layer V cortical pyramidal neurons as predicted by simulations. This method may be applied to the analysis of specific relationships between dendritic structure and neuronal function. The capacity to dynamically manipulate dendritic topology or isolate inputs from various dendritic domains can provide a fresh perspective on the roles they play in shaping neuronal output.

Functional Effects of Schizophrenia-Linked Genetic Variants on Intrinsic Single-Neuron Excitability: A Modeling Study

BACKGROUND

Recent genome-wide association studies have identified a large number of genetic risk factors for schizophrenia (SCZ) featuring ion channels and calcium transporters. For some of these risk factors, independent prior investigations have examined the effects of genetic alterations on the cellular electrical excitability and calcium homeostasis. In the present proof-of-concept study, we harnessed these experimental results for modeling of computational properties on layer V cortical pyramidal cells and identified possible common alterations in behavior across SCZ-related genes.

METHODS

We applied a biophysically detailed multicompartmental model to study the excitability of a layer V pyramidal cell. We reviewed the literature on functional genomics for variants of genes associated with SCZ and used changes in neuron model parameters to represent the effects of these variants.

RESULTS

We present and apply a framework for examining the effects of subtle single nucleotide polymorphisms in ion channel and calcium transporter-encoding genes on neuron excitability. Our analysis indicates that most of the considered SCZ-related genetic variants affect the spiking behavior and intracellular calcium dynamics resulting from summation of inputs across the dendritic tree.

CONCLUSIONS

Our results suggest that alteration in the ability of a single neuron to integrate the inputs and scale its excitability may constitute a fundamental mechanistic contributor to mental disease, alongside the previously proposed deficits in synaptic communication and network behavior.

Prolonged Intracellular Na+ Dynamics Govern Electrical Activity in Accessory Olfactory Bulb Mitral Cells

Persistent activity has been reported in many brain areas and is hypothesized to mediate working memory and emotional brain states and to rely upon network or biophysical feedback. Here, we demonstrate a novel mechanism by which persistent neuronal activity can be generated without feedback, relying instead on the slow removal of Na⁺ from neurons following bursts of activity. We show that mitral cells in the accessory olfactory bulb (AOB), which plays a major role in mammalian social behavior, may respond to a brief sensory stimulation with persistent firing. By combining electrical recordings, Ca²⁺ and Na⁺ imaging, and realistic computational modeling, we explored the mechanisms underlying the persistent activity in AOB mitral cells. We found that the exceptionally slow inward current that underlies this activity is governed by prolonged dynamics of intracellular Na⁺ ([Na⁺]_i), which affects neuronal electrical activity via several pathways. Specifically, elevated dendritic [Na⁺]_i reverses the Na⁺-Ca²⁺ exchanger activity, thus modifying the [Ca²⁺]_i set-point. This process, which relies on ubiquitous membrane mechanisms, is likely to play a role in other neuronal types in various brain regions.

An experimental and computational study reveals a novel mechanism for persistent activity of neurons in response to transient stimulation. Instead of involving feedback mechanisms, it relies on slow changes in intracellular sodium ion concentration, leading to prolonged calcium-dependent inward current.

The accessory olfactory system is essential for chemical communication in animals during social interactions. During this process, the principle cells of the accessory olfactory bulb (AOB) may respond to transient stimulation with prolonged activity, sometimes lasting for minutes—a property known as persistent activity. This property, which has been observed in other brain areas, is usually attributed to positive feedback mechanisms either at the cellular or the network level. Here, we show how persistent activity can emerge without feedback, relying on slow changes in internal ionic concentrations, which keep a record of past neuronal activity for long periods of time. We used a combined computational and experimental approach to show that the complex interaction between various ions, their extrusion mechanisms, and the membrane potential leads to stimulus-dependent persistent activity in the AOB. The same mechanism may apply to other neuronal types in various brain regions.

TRPM8-Dependent Dynamic Response in a Mathematical Model of Cold Thermoreceptor

Cold-sensitive nerve terminals (CSNTs) encode steady temperatures with regular, rhythmic temperature-dependent firing patterns that range from irregular tonic firing to regular bursting (static response). During abrupt temperature changes, CSNTs show a dynamic response, transiently increasing their firing frequency as temperature decreases and silencing when the temperature increases (dynamic response). To date, mathematical models that simulate the static response are based on two depolarizing/repolarizing pairs of membrane ionic conductance (slow and fast kinetics). However, these models fail to reproduce the dynamic response of CSNTs to rapid changes in temperature and notoriously they lack a specific cold-activated conductance such as the TRPM8 channel. We developed a model that includes TRPM8 as a temperature-dependent conductance with a calcium-dependent desensitization. We show by computer simulations that it appropriately reproduces the dynamic response of CSNTs from mouse cornea, while preserving their static response behavior. In this model, the TRPM8 conductance is essential to display a dynamic response. In agreement with experimental results, TRPM8 is also needed for the ongoing activity in the absence of stimulus (i.e. neutral skin temperature). Free parameters of the model were adjusted by an evolutionary optimization algorithm, allowing us to find different solutions. We present a family of possible parameters that reproduce the behavior of CSNTs under different temperature protocols. The detection of temperature gradients is associated to a homeostatic mechanism supported by the calcium-dependent desensitization.

Modeling the calcium spike as a threshold triggered fixed waveform for synchronous inputs in the fluctuation regime

Modeling the layer 5 pyramidal neuron as a system of three connected isopotential compartments, the soma, proximal, and distal compartment, with calcium spike dynamics in the distal compartment following first order kinetics, we are able to reproduce in-vitro experimental results which demonstrate the involvement of calcium spikes in action potentials generation. To explore how calcium spikes affect the neuronal output in-vivo, we emulate in-vivo like conditions by embedding the neuron model in a regime of low background fluctuations with occasional large synchronous inputs. In such a regime, a full calcium spike is only triggered by the synchronous events in a threshold like manner and has a stereotypical waveform. Hence, in such a regime, we are able to replace the calcium dynamics with a simpler threshold triggered current of fixed waveform, which is amenable to analytical treatment. We obtain analytically the mean somatic membrane potential excursion due to a calcium spike being triggered while in the fluctuating regime. Our analytical form that accounts for the covariance between conductances and the membrane potential shows a better agreement with simulation results than a naive first order approximation.

libRoadRunner: a high performance SBML simulation and analysis library

MOTIVATION

This article presents libRoadRunner, an extensible, high-performance, cross-platform, open-source software library for the simulation and analysis of models expressed using Systems Biology Markup Language (SBML). SBML is the most widely used standard for representing dynamic networks, especially biochemical networks. libRoadRunner is fast enough to support large-scale problems such as tissue models, studies that require large numbers of repeated runs and interactive simulations.

RESULTS

libRoadRunner is a self-contained library, able to run both as a component inside other tools via its C++ and C bindings, and interactively through its Python interface. Its Python Application Programming Interface (API) is similar to the APIs of MATLAB ( WWWMATHWORKSCOM: ) and SciPy ( HTTP//WWWSCIPYORG/: ), making it fast and easy to learn. libRoadRunner uses a custom Just-In-Time (JIT) compiler built on the widely used LLVM JIT compiler framework. It compiles SBML-specified models directly into native machine code for a variety of processors, making it appropriate for solving extremely large models or repeated runs. libRoadRunner is flexible, supporting the bulk of the SBML specification (except for delay and non-linear algebraic equations) including several SBML extensions (composition and distributions). It offers multiple deterministic and stochastic integrators, as well as tools for steady-state analysis, stability analysis and structural analysis of the stoichiometric matrix.

AVAILABILITY AND IMPLEMENTATION

libRoadRunner binary distributions are available for Mac OS X, Linux and Windows. The library is licensed under Apache License Version 2.0. libRoadRunner is also available for ARM-based computers such as the Raspberry Pi. http://www.libroadrunner.org provides online documentation, full build instructions, binaries and a git source repository.

CONTACTS

hsauro@u.washington.edu or somogyie@indiana.edu

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

ViSAPy: a Python tool for biophysics-based generation of virtual spiking activity for evaluation of spike-sorting algorithms

BACKGROUND

New, silicon-based multielectrodes comprising hundreds or more electrode contacts offer the possibility to record spike trains from thousands of neurons simultaneously. This potential cannot be realized unless accurate, reliable automated methods for spike sorting are developed, in turn requiring benchmarking data sets with known ground-truth spike times.

NEW METHOD

We here present a general simulation tool for computing benchmarking data for evaluation of spike-sorting algorithms entitled ViSAPy (Virtual Spiking Activity in Python). The tool is based on a well-established biophysical forward-modeling scheme and is implemented as a Python package built on top of the neuronal simulator NEURON and the Python tool LFPy.

RESULTS

ViSAPy allows for arbitrary combinations of multicompartmental neuron models and geometries of recording multielectrodes. Three example benchmarking data sets are generated, i.e., tetrode and polytrode data mimicking in vivo cortical recordings and microelectrode array (MEA) recordings of in vitro activity in salamander retinas. The synthesized example benchmarking data mimics salient features of typical experimental recordings, for example, spike waveforms depending on interspike interval.

COMPARISON WITH EXISTING METHODS

ViSAPy goes beyond existing methods as it includes biologically realistic model noise, synaptic activation by recurrent spiking networks, finite-sized electrode contacts, and allows for inhomogeneous electrical conductivities. ViSAPy is optimized to allow for generation of long time series of benchmarking data, spanning minutes of biological time, by parallel execution on multi-core computers.

CONCLUSION

ViSAPy is an open-ended tool as it can be generalized to produce benchmarking data or arbitrary recording-electrode geometries and with various levels of complexity.

A flexible, interactive software tool for fitting the parameters of neuronal models

The construction of biologically relevant neuronal models as well as model-based analysis of experimental data often requires the simultaneous fitting of multiple model parameters, so that the behavior of the model in a certain paradigm matches (as closely as possible) the corresponding output of a real neuron according to some predefined criterion. Although the task of model optimization is often computationally hard, and the quality of the results depends heavily on technical issues such as the appropriate choice (and implementation) of cost functions and optimization algorithms, no existing program provides access to the best available methods while also guiding the user through the process effectively. Our software, called Optimizer, implements a modular and extensible framework for the optimization of neuronal models, and also features a graphical interface which makes it easy for even non-expert users to handle many commonly occurring scenarios. Meanwhile, educated users can extend the capabilities of the program and customize it according to their needs with relatively little effort. Optimizer has been developed in Python, takes advantage of open-source Python modules for nonlinear optimization, and interfaces directly with the NEURON simulator to run the models. Other simulators are supported through an external interface. We have tested the program on several different types of problems of varying complexity, using different model classes. As targets, we used simulated traces from the same or a more complex model class, as well as experimental data. We successfully used Optimizer to determine passive parameters and conductance densities in compartmental models, and to fit simple (adaptive exponential integrate-and-fire) neuronal models to complex biological data. Our detailed comparisons show that Optimizer can handle a wider range of problems, and delivers equally good or better performance than any other existing neuronal model fitting tool.

Using Strahler's analysis to reduce up to 200-fold the run time of realistic neuron models

The cellular mechanisms underlying higher brain functions/dysfunctions are extremely difficult to investigate experimentally, and detailed neuron models have proven to be a very useful tool to help these kind of investigations. However, realistic neuronal networks of sizes appropriate to study brain functions present the major problem of requiring a prohibitively high computational resources. Here, building on our previous work, we present a general reduction method based on Strahler's analysis of neuron morphologies. We show that, without any fitting or tuning procedures, it is possible to map any morphologically and biophysically accurate neuron model into an equivalent reduced version. Using this method for Purkinje cells, we demonstrate how run times can be reduced up to 200–fold, while accurately taking into account the effects of arbitrarily located and activated synaptic inputs.

Preserving axosomatic spiking features despite diverse dendritic morphology

Throughout the nervous system, cells belonging to a certain electrical class (e-class)-sharing high similarity in firing response properties-may nevertheless have widely variable dendritic morphologies. To quantify the effect of this morphological variability on the firing of layer 5 thick-tufted pyramidal cells (TTCs), a detailed conductance-based model was constructed for a three-dimensional reconstructed exemplar TTC. The model exhibited spike initiation in the axon and reproduced the characteristic features of individual spikes, as well as of the firing properties at the soma, as recorded in a population of TTCs in young Wistar rats. When using these model parameters over the population of 28 three-dimensional reconstructed TTCs, both axonal and somatic ion channel densities had to be scaled linearly with the conductance load imposed on each of these compartments. Otherwise, the firing of model cells deviated, sometimes very significantly, from the experimental variability of the TTC e-class. The study provides experimentally testable predictions regarding the coregulation of axosomatic membrane ion channels density for cells with different dendritic conductance load, together with a simple and systematic method for generating reliable conductance-based models for the whole population of modeled neurons belonging to a particular e-class, with variable morphology as found experimentally.