Variable channel expression in identified single and electrically coupled neurons in different animals

Xolotl: An Intuitive and Approachable Neuron and Network Simulator for Research and Teaching

Conductance-based models of neurons are used extensively in computational neuroscience. Working with these models can be challenging due to their high dimensionality and large number of parameters. Here, we present a neuron and network simulator built on a novel automatic type system that binds object-oriented code written in C++ to objects in MATLAB. Our approach builds on the tradition of uniting the speed of languages like C++ with the ease-of-use and feature-set of scientific programming languages like MATLAB. Xolotl allows for the creation and manipulation of hierarchical models with components that are named and searchable, permitting intuitive high-level programmatic control over all parts of the model. The simulator's architecture allows for the interactive manipulation of any parameter in any model, and for visualizing the effects of changing that parameter immediately. Xolotl is fully featured with hundreds of ion channel models from the electrophysiological literature, and can be extended to include arbitrary conductances, synapses, and mechanisms. Several core features like bookmarking of parameters and automatic hashing of source code facilitate reproducible and auditable research. Its ease of use and rich visualization capabilities make it an attractive option in teaching environments. Finally, xolotl is written in a modular fashion, includes detailed tutorials and worked examples, and is freely available at https://github.com/sg-s/xolotl, enabling seamless integration into the workflows of other researchers.

Assessing Transcriptome Quality in Patch-Seq Datasets

Patch-seq, combining patch-clamp electrophysiology with single-cell RNA-sequencing (scRNAseq), enables unprecedented access to a neuron's transcriptomic, electrophysiological, and morphological features. Here, we present a re-analysis of five patch-seq datasets, representing cells from ex vivo mouse brain slices and in vitro human stem-cell derived neurons. Our objective was to develop simple criteria to assess the quality of patch-seq derived single-cell transcriptomes. We evaluated patch-seq transcriptomes for the expression of marker genes of multiple cell types, benchmarking these against analogous profiles from cellular-dissociation based scRNAseq. We found an increased likelihood of off-target cell-type mRNA contamination in patch-seq cells from acute brain slices, likely due to the passage of the patch-pipette through the processes of adjacent cells. We also observed that patch-seq samples varied considerably in the amount of mRNA that could be extracted from each cell, strongly biasing the numbers of detectable genes. We developed a marker gene-based approach for scoring single-cell transcriptome quality post-hoc. Incorporating our quality metrics into downstream analyses improved the correspondence between gene expression and electrophysiological features. Our analysis suggests that technical confounds likely limit the interpretability of patch-seq based single-cell transcriptomes. However, we provide concrete recommendations for quality control steps that can be performed prior to costly RNA-sequencing to optimize the yield of high-quality samples.

The Ca2+ transient as a feedback sensor controlling cardiomyocyte ionic conductances in mouse populations

Conductances of ion channels and transporters controlling cardiac excitation may vary in a population of subjects with different cardiac gene expression patterns. However, the amount of variability and its origin are not quantitatively known. We propose a new conceptual approach to predict this variability that consists of finding combinations of conductances generating a normal intracellular Ca²⁺ transient without any constraint on the action potential. Furthermore, we validate experimentally its predictions using the Hybrid Mouse Diversity Panel, a model system of genetically diverse mouse strains that allows us to quantify inter-subject versus intra-subject variability. The method predicts that conductances of inward Ca²⁺ and outward K⁺ currents compensate each other to generate a normal Ca²⁺ transient in good quantitative agreement with current measurements in ventricular myocytes from hearts of different isogenic strains. Our results suggest that a feedback mechanism sensing the aggregate Ca²⁺ transient of the heart suffices to regulate ionic conductances.

Circuit Robustness to Temperature Perturbation Is Altered by Neuromodulators

In the ocean, the crab Cancer borealis is subject to daily and seasonal temperature changes. Previous work, done in the presence of descending modulatory inputs, had shown that the pyloric rhythm of the crab increases in frequency as temperature increases but maintains its characteristic phase relationships until it "crashes" at extremely high temperatures. To study the interaction between neuromodulators and temperature perturbations, we studied the effects of temperature on preparations from which the descending modulatory inputs were removed. Under these conditions, the pyloric rhythm was destabilized. We then studied the effects of temperature on preparations in the presence of oxotremorine, proctolin, and serotonin. Oxotremorine and proctolin enhanced the robustness of the pyloric rhythm, whereas serotonin made the rhythm less robust. These experiments reveal considerable animal-to-animal diversity in their crash stability, consistent with the interpretation that cryptic differences in many cell and network parameters are revealed by extreme perturbations.

Neurotransmitter identity and electrophysiological phenotype are genetically coupled in midbrain dopaminergic neurons

Most neuronal types have a well-identified electrical phenotype. It is now admitted that a same phenotype can be produced using multiple biophysical solutions defined by ion channel expression levels. This argues that systems-level approaches are necessary to understand electrical phenotype genesis and stability. Midbrain dopaminergic (DA) neurons, although quite heterogeneous, exhibit a characteristic electrical phenotype. However, the quantitative genetic principles underlying this conserved phenotype remain unknown. Here we investigated the quantitative relationships between ion channels’ gene expression levels in midbrain DA neurons using single-cell microfluidic qPCR. Using multivariate mutual information analysis to decipher high-dimensional statistical dependences, we unravel co-varying gene modules that link neurotransmitter identity and electrical phenotype. We also identify new segregating gene modules underlying the diversity of this neuronal population. We propose that the newly identified genetic coupling between neurotransmitter identity and ion channels may play a homeostatic role in maintaining the electrophysiological phenotype of midbrain DA neurons.

The physiological variability of channel density in hippocampal CA1 pyramidal cells and interneurons explored using a unified data-driven modeling workflow

Every neuron is part of a network, exerting its function by transforming multiple spatiotemporal synaptic input patterns into a single spiking output. This function is specified by the particular shape and passive electrical properties of the neuronal membrane, and the composition and spatial distribution of ion channels across its processes. For a variety of physiological or pathological reasons, the intrinsic input/output function may change during a neuron's lifetime. This process results in high variability in the peak specific conductance of ion channels in individual neurons. The mechanisms responsible for this variability are not well understood, although there are clear indications from experiments and modeling that degeneracy and correlation among multiple channels may be involved. Here, we studied this issue in biophysical models of hippocampal CA1 pyramidal neurons and interneurons. Using a unified data-driven simulation workflow and starting from a set of experimental recordings and morphological reconstructions obtained from rats, we built and analyzed several ensembles of morphologically and biophysically accurate single cell models with intrinsic electrophysiological properties consistent with experimental findings. The results suggest that the set of conductances expressed in any given hippocampal neuron may be considered as belonging to two groups: one subset is responsible for the major characteristics of the firing behavior in each population and the other is responsible for a robust degeneracy. Analysis of the model neurons suggests several experimentally testable predictions related to the combination and relative proportion of the different conductances that should be expressed on the membrane of different types of neurons for them to fulfill their role in the hippocampus circuitry.

A Heart for Diversity: Simulating Variability in Cardiac Arrhythmia Research

In cardiac electrophysiology, there exist many sources of inter- and intra-personal variability. These include variability in conditions and environment, and genotypic and molecular diversity, including differences in expression and behavior of ion channels and transporters, which lead to phenotypic diversity (e.g., variable integrated responses at the cell, tissue, and organ levels). These variabilities play an important role in progression of heart disease and arrhythmia syndromes and outcomes of therapeutic interventions. Yet, the traditional in silico framework for investigating cardiac arrhythmias is built upon a parameter/property-averaging approach that typically overlooks the physiological diversity. Inspired by work done in genetics and neuroscience, new modeling frameworks of cardiac electrophysiology have been recently developed that take advantage of modern computational capabilities and approaches, and account for the variance in the biological data they are intended to illuminate. In this review, we outline the recent advances in statistical and computational techniques that take into account physiological variability, and move beyond the traditional cardiac model-building scheme that involves averaging over samples from many individuals in the construction of a highly tuned composite model. We discuss how these advanced methods have harnessed the power of big (simulated) data to study the mechanisms of cardiac arrhythmias, with a special emphasis on atrial fibrillation, and improve the assessment of proarrhythmic risk and drug response. The challenges of using in silico approaches with variability are also addressed and future directions are proposed.

Expansion microscopy: enabling single cell analysis in intact biological systems

There is a need for single cell analysis methods that enable the identification and localization of different kinds of biomolecules throughout cells and intact tissues, thereby allowing characterization and classification of individual cells and their relationships to each other within intact systems. Expansion microscopy (ExM) is a technology that physically magnifies tissues in an isotropic way, thereby achieving super-resolution microscopy on diffraction-limited microscopes, enabling rapid image acquisition and large field of view. As a result, ExM is well-positioned to integrate molecular content and cellular morphology, with the spatial precision sufficient to resolve individual biological building blocks, and the scale and accessibility required to deploy over extended 3-D objects like tissues and organs.

Homeostatic plasticity in neural development

Throughout life, neural circuits change their connectivity, especially during development, when neurons frequently extend and retract dendrites and axons, and form and eliminate synapses. In spite of their changing connectivity, neural circuits maintain relatively constant activity levels. Neural circuits achieve functional stability by homeostatic plasticity, which equipoises intrinsic excitability and synaptic strength, balances network excitation and inhibition, and coordinates changes in circuit connectivity. Here, we review how diverse mechanisms of homeostatic plasticity stabilize activity in developing neural circuits.

Three members of a peptide family are differentially distributed and elicit differential state-dependent responses in a pattern generator-effector system

C-type allatostatins (AST-Cs) are pleiotropic neuropeptides that are broadly conserved within arthropods; the presence of three AST-C isoforms, encoded by paralog genes, is common. However, these peptides are hypothesized to act through a single receptor, thereby exerting similar bioactivities within each species. We investigated this hypothesis in the American lobster, Homarus americanus, mapping the distributions of AST-C isoforms within relevant regions of the nervous system and digestive tract, and comparing their modulatory influences on the cardiac neuromuscular system. Immunohistochemistry showed that in the pericardial organ, a neuroendocrine release site, AST-C I and/or III and AST-C II are contained within distinct populations of release terminals. Moreover, AST-C I/III-like immunoreactivity was seen in midgut epithelial endocrine cells and the cardiac ganglion (CG), whereas AST-C II-like immunoreactivity was not seen in these tissues. These data suggest that AST-C I and/or III can modulate the CG both locally and hormonally; AST-C II likely acts on the CG solely as a hormonal modulator. Physiological studies demonstrated that all three AST-C isoforms can exert differential effects, including both increases and decreases, on contraction amplitude and frequency when perfused through the heart. However, in contrast to many state-dependent modulatory changes, the changes in contraction amplitude and frequency elicited by the AST-Cs were not functions of the baseline parameters. The responses to AST-C I and III, neither of which is COOH-terminally amidated, are more similar to one another than they are to the responses elicited by AST-C II, which is COOH-terminally amidated. These results suggest that the three AST-C isoforms are differentially distributed in the lobster nervous system/midgut and can elicit distinct behaviors from the cardiac neuromuscular system, with particular structural features, e.g., COOH-terminal amidation, likely important in determining the effects of the peptides. NEW & NOTEWORTHY Multiple isoforms of many peptides exert similar effects on neural circuits. In this study we show that each of the three isoforms of C-type allatostatin (AST-C) can exert differential effects, including both increases and decreases in contraction amplitude and frequency, on the lobster cardiac neuromuscular system. The distribution of effects elicited by the nonamidated isoforms AST-C I and III are more similar to one another than to the effects of the amidated AST-C II.

Evolving Simple Models of Diverse Intrinsic Dynamics in Hippocampal Neuron Types

The diversity of intrinsic dynamics observed in neurons may enhance the computations implemented in the circuit by enriching network-level emergent properties such as synchronization and phase locking. Large-scale spiking network models of entire brain regions offer a platform to test theories of neural computation and cognitive function, providing useful insights on information processing in the nervous system. However, a systematic in-depth investigation requires network simulations to capture the biological intrinsic diversity of individual neurons at a sufficient level of accuracy. The computationally efficient Izhikevich model can reproduce a wide range of neuronal behaviors qualitatively. Previous studies using optimization techniques, however, were less successful in quantitatively matching experimentally recorded voltage traces. In this article, we present an automated pipeline based on evolutionary algorithms to quantitatively reproduce features of various classes of neuronal spike patterns using the Izhikevich model. Employing experimental data from Hippocampome.org, a comprehensive knowledgebase of neuron types in the rodent hippocampus, we demonstrate that our approach reliably fit Izhikevich models to nine distinct classes of experimentally recorded spike patterns, including delayed spiking, spiking with adaptation, stuttering, and bursting. Importantly, by leveraging the parameter-exploration capabilities of evolutionary algorithms, and by representing qualitative spike pattern class definitions in the error landscape, our approach creates several suitable models for each neuron type, exhibiting appropriate feature variabilities among neurons. Moreover, we demonstrate the flexibility of our methodology by creating multi-compartment Izhikevich models for each neuron type in addition to single-point versions. Although the results presented here focus on hippocampal neuron types, the same strategy is broadly applicable to any neural systems.

Output variability across animals and levels in a motor system

Rhythmic behaviors vary across individuals. We investigated the sources of this output variability across a motor system, from the central pattern generator (CPG) to the motor plant. In the bilaterally symmetric leech heartbeat system, the CPG orchestrates two coordinations in the bilateral hearts with different intersegmental phase relations (Δϕ) and periodic side-to-side switches. Population variability is large. We show that the system is precise within a coordination, that differences in repetitions of a coordination contribute little to population output variability, but that differences between bilaterally homologous cells may contribute to some of this variability. Nevertheless, much output variability is likely associated with genetic and life history differences among individuals. Variability of Δϕ were coordination-specific: similar at all levels in one, but significantly lower for the motor pattern than the CPG pattern in the other. Mechanisms that transform CPG output to motor neurons may limit output variability in the motor pattern.

Variability in neural networks

Experiments on neurons in the heart system of the leech reveal why rhythmic behaviors differ between individuals.

A biophysical modelling platform of the cochlear nucleus and other auditory circuits: From channels to networks

Models of the auditory brainstem have been an invaluable tool for testing hypotheses about auditory information processing and for highlighting the most important gaps in the experimental literature. Due to the complexity of the auditory brainstem, and indeed most brain circuits, the dynamic behavior of the system may be difficult to predict without a detailed, biologically realistic computational model. Despite the sensitivity of models to their exact construction and parameters, most prior models of the cochlear nucleus have incorporated only a small subset of the known biological properties. This confounds the interpretation of modelling results and also limits the potential future uses of these models, which require a large effort to develop. To address these issues, we have developed a general purpose, biophysically detailed model of the cochlear nucleus for use both in testing hypotheses about cochlear nucleus function and also as an input to models of downstream auditory nuclei. The model implements conductance-based Hodgkin-Huxley representations of cells using a Python-based interface to the NEURON simulator. Our model incorporates most of the quantitatively characterized intrinsic cell properties, synaptic properties, and connectivity available in the literature, and also aims to reproduce the known response properties of the canonical cochlear nucleus cell types. Although we currently lack the empirical data to completely constrain this model, our intent is for the model to continue to incorporate new experimental results as they become available.

Tailoring Mathematical Models to Stem-Cell Derived Cardiomyocyte Lines Can Improve Predictions of Drug-Induced Changes to Their Electrophysiology

Human induced pluripotent stem cell derived cardiomyocytes (iPSC-CMs) have applications in disease modeling, cell therapy, drug screening and personalized medicine. Computational models can be used to interpret experimental findings in iPSC-CMs, provide mechanistic insights, and translate these findings to adult cardiomyocyte (CM) electrophysiology. However, different cell lines display different expression of ion channels, pumps and receptors, and show differences in electrophysiology. In this exploratory study, we use a mathematical model based on iPSC-CMs from Cellular Dynamic International (CDI, iCell), and compare its predictions to novel experimental recordings made with the Axiogenesis Cor.4U line. We show that tailoring this model to the specific cell line, even using limited data and a relatively simple approach, leads to improved predictions of baseline behavior and response to drugs. This demonstrates the need and the feasibility to tailor models to individual cell lines, although a more refined approach will be needed to characterize individual currents, address differences in ion current kinetics, and further improve these results.

Quantitative Comparison of Effects of Dofetilide, Sotalol, Quinidine, and Verapamil between Human Ex vivo Trabeculae and In silico Ventricular Models Incorporating Inter-Individual Action Potential Variability

Background:In silico modeling could soon become a mainstream method of pro-arrhythmic risk assessment in drug development. However, a lack of human-specific data and appropriate modeling techniques has previously prevented quantitative comparison of drug effects between in silico models and recordings from human cardiac preparations. Here, we directly compare changes in repolarization biomarkers caused by dofetilide, dl-sotalol, quinidine, and verapamil, between in silico populations of human ventricular cell models and ex vivo human ventricular trabeculae. Methods and Results:Ex vivo recordings from human ventricular trabeculae in control conditions were used to develop populations of in silico human ventricular cell models that integrated intra- and inter-individual variability in action potential (AP) biomarker values. Models were based on the O'Hara-Rudy ventricular cardiomyocyte model, but integrated experimental AP variability through variation in underlying ionic conductances. Changes to AP duration, triangulation and early after-depolarization occurrence from application of the four drugs at multiple concentrations and pacing frequencies were compared between simulations and experiments. To assess the impact of variability in IC50 measurements, and the effects of including state-dependent drug binding dynamics, each drug simulation was repeated with two different IC50 datasets, and with both the original O'Hara-Rudy hERG model and a recently published state-dependent model of hERG and hERG block. For the selective hERG blockers dofetilide and sotalol, simulation predictions of AP prolongation and repolarization abnormality occurrence showed overall good agreement with experiments. However, for multichannel blockers quinidine and verapamil, simulations were not in agreement with experiments across all IC50 datasets and IKr block models tested. Quinidine simulations resulted in overprolonged APs and high incidence of repolarization abnormalities, which were not observed in experiments. Verapamil simulations showed substantial AP prolongation while experiments showed mild AP shortening. Conclusions: Results for dofetilide and sotalol show good agreement between experiments and simulations for selective compounds, however lack of agreement from simulations of quinidine and verapamil suggest further work is needed to understand the more complex electrophysiological effects of these multichannel blocking drugs.

Optimized Parallel Coding of Second-Order Stimulus Features by Heterogeneous Neural Populations

Efficient processing of sensory input is essential to ensure an organism's survival in its natural environment. Growing evidence suggests that sensory neurons can optimally encode natural stimuli by ensuring that their tuning opposes stimulus statistics, such that the resulting neuronal response contains equal power at all frequencies (i.e., is "white"). Such temporal decorrelation or whitening has been observed across modalities, but the effects of neural heterogeneities on determining tuning and thus responses to natural stimuli have not been investigated. Here, we investigate how heterogeneities in sensory pyramidal neurons organized in three parallel maps representing the body surface determine responses to second-order electrosensory stimulus features in the weakly electric fish Apteronotus leptorhynchus While some sources of heterogeneities such as ON- and OFF-type responses to first-order did not affect responses to second-order electrosensory stimulus features, other sources of heterogeneity within and across the maps strongly determined responses. We found that these cells effectively performed a fractional differentiation operation on their input with exponents ranging from zero (no differentiation) to 0.4 (strong differentiation). Varying adaptation in a simple model explained these heterogeneities and predicted a strong correlation between fractional differentiation and adaptation. Using natural stimuli, we found that only a small fraction of neurons implemented temporal whitening. Rather, a large fraction of neurons did not perform any significant whitening and thus preserved natural input statistics in their responses. We propose that this information is needed to properly decode optimized information sent in parallel through temporally whitened responses based on context.

SIGNIFICANCE STATEMENT

We demonstrate that heterogeneities in the same sensory neuron type can either have no or significant influence on their responses to second-order stimulus features. While an ON- or OFF-type response to first-order stimulus attributes has no significant influence on responses to second-order stimulus features, we found that only a small fraction of sensory neurons optimally encoded natural stimuli through high-pass filtering, thereby implementing temporal whitening. Surprisingly, a large fraction of sensory neurons performed little if no filtering of stimuli, thereby preserving natural stimulus statistics. We hypothesize that this pathway is necessary to properly decode optimized information contained in temporally whitened responses based on context.

Theta-frequency selectivity in the somatic spike-triggered average of rat hippocampal pyramidal neurons is dependent on HCN channels

The ability to distill specific frequencies from complex spatiotemporal patterns of afferent inputs is a pivotal functional requirement for neurons residing in networks receiving frequency-multiplexed inputs. Although the expression of theta-frequency subthreshold resonance is established in hippocampal pyramidal neurons, it is not known if their spike initiation dynamics manifest spectral selectivity, or if their intrinsic properties are tuned to process gamma-frequency inputs. Here, we measured the spike-triggered average (STA) of rat hippocampal pyramidal neurons through electrophysiological recordings and quantified spectral selectivity in their spike initiation dynamics and their coincidence detection window (CDW). Our results revealed strong theta-frequency selectivity in the STA, which was also endowed with gamma-range CDW, with prominent neuron-to-neuron variability that manifested distinct pairwise dissociations and correlations with different intrinsic measurements. Furthermore, we demonstrate that the STA and its measurements substantially adapted to the state of the neuron defined by its membrane potential and to the statistics of its afferent inputs. Finally, we tested the effect of pharmacologically blocking the hyperpolarization-activated cyclic-nucleotide-gated (HCN) channels on the STA and found that the STA characteristic frequency reduced significantly to the delta-frequency band after HCN channel blockade. This delta-frequency selectivity in the STA emerged in the absence of subthreshold resonance, which was abolished by HCN channel blockade, thereby confirming computational predictions on the dissociation between these two forms of spectral selectivity. Our results expand the roles of HCN channels to theta-frequency selectivity in the spike initiation dynamics, apart from underscoring the critical role of interactions among different ion channels in regulating neuronal physiology.NEW & NOTEWORTHY We had previously predicted, using computational analyses, that the spike-triggered average (STA) of hippocampal neurons would exhibit theta-frequency (4-10 Hz) spectral selectivity and would manifest coincidence detection capabilities for inputs in the gamma-frequency band (25-150 Hz). Here, we confirmed these predictions through direct electrophysiological recordings of STA from rat CA1 pyramidal neurons and demonstrate that blocking HCN channels reduces the frequency of STA spectral selectivity to the delta-frequency range (0.5-4 Hz).

Optimizing Neural Information Capacity through Discretization

Discretization in neural circuits occurs on many levels, from the generation of action potentials and dendritic integration, to neuropeptide signaling and processing of signals from multiple neurons, to behavioral decisions. It is clear that discretization, when implemented properly, can convey many benefits. However, the optimal solutions depend on both the level of noise and how it impacts a particular computation. This Perspective discusses how current physiological data could potentially be integrated into one theoretical framework based on maximizing information. Key experiments for testing that framework are discussed.

Innexin expression in electrically coupled motor circuits

The many roles of innexins, the molecules that form gap junctions in invertebrates, have been explored in numerous species. Here, we present a summary of innexin expression and function in two small, central pattern generating circuits found in crustaceans: the stomatogastric ganglion and the cardiac ganglion. The two ganglia express multiple innexin genes, exhibit varying combinations of symmetrical and rectifying gap junctions, as well as gap junctions within and across different cell types. Past studies have revealed correlations in ion channel and innexin expression in coupled neurons, as well as intriguing functional relationships between ion channel conductances and electrical coupling. Together, these studies suggest a putative role for innexins in correlating activity between coupled neurons at the levels of gene expression and physiological activity during development and in the adult animal.

Robust transmission of rate coding in the inhibitory Purkinje cell to cerebellar nuclei pathway in awake mice

Neural coding through inhibitory projection pathways remains poorly understood. We analyze the transmission properties of the Purkinje cell (PC) to cerebellar nucleus (CN) pathway in a modeling study using a data set recorded in awake mice containing respiratory rate modulation. We find that inhibitory transmission from tonically active PCs can transmit a behavioral rate code with high fidelity. We parameterized the required population code in PC activity and determined that 20% of PC inputs to a full compartmental CN neuron model need to be rate-comodulated for transmission of a rate code. Rate covariance in PC inputs also accounts for the high coefficient of variation in CN spike trains, while the balance between excitation and inhibition determines spike rate and local spike train variability. Overall, our modeling study can fully account for observed spike train properties of cerebellar output in awake mice, and strongly supports rate coding in the cerebellum.

Detailed computer simulations of biological neurons can make an important contribution to our understanding of how the brain works. In this paper we use such a model of a neuron that represents the output from the cerebellum. We can show that the inhibition this neuron type receives from Purkinje cells in the cerebellar cortex is well suited to pass a detailed time course of movement control to the output of the cerebellum. Importantly we find that this type of coding requires a population of Purkinje cells that pass the same temporal coding of spike rate to the output neurons in the cerebellar nuclei.

Mechanisms of generation of membrane potential resonance in a neuron with multiple resonant ionic currents

Neuronal membrane potential resonance (MPR) is associated with subthreshold and network oscillations. A number of voltage-gated ionic currents can contribute to the generation or amplification of MPR, but how the interaction of these currents with linear currents contributes to MPR is not well understood. We explored this in the pacemaker PD neurons of the crab pyloric network. The PD neuron MPR is sensitive to blockers of H- (I_H) and calcium-currents (I_Ca). We used the impedance profile of the biological PD neuron, measured in voltage clamp, to constrain parameter values of a conductance-based model using a genetic algorithm and obtained many optimal parameter combinations. Unlike most cases of MPR, in these optimal models, the values of resonant- (f_res) and phasonant- (f_{ϕ = 0}) frequencies were almost identical. Taking advantage of this fact, we linked the peak phase of ionic currents to their amplitude, in order to provide a mechanistic explanation the dependence of MPR on the I_Ca gating variable time constants. Additionally, we found that distinct pairwise correlations between I_Ca parameters contributed to the maintenance of f_res and resonance power (Q_Z). Measurements of the PD neuron MPR at more hyperpolarized voltages resulted in a reduction of f_res but no change in Q_Z. Constraining the optimal models using these data unmasked a positive correlation between the maximal conductances of I_H and I_Ca. Thus, although I_H is not necessary for MPR in this neuron type, it contributes indirectly by constraining the parameters of I_Ca.

Many neuron types exhibit membrane potential resonance (MPR) in which the neuron produces the largest response to oscillatory input at some preferred (resonant) frequency and, in many systems, the network frequency is correlated with neuronal MPR. MPR is captured by a peak in the impedance vs. frequency curve (Z-profile), which is shaped by the dynamics of voltage-gated ionic currents. Although neuron types can express variable levels of ionic currents, they may have a stable resonant frequency. We used the PD neuron of the crab pyloric network to understand how MPR emerges from the interplay of the biophysical properties of multiple ionic currents, each capable of generating resonance. We show the contribution of an inactivating current at the resonant frequency in terms of interacting time constants. We measured the Z-profile of the PD neuron and explored possible combinations of model parameters that fit this experimentally measured profile. We found that the Z-profile constrains and defines correlations among parameters associated with ionic currents. Furthermore, the resonant frequency and amplitude are sensitive to different parameter sets and can be preserved by co-varying pairs of parameters along their correlation lines. Furthermore, although a resonant current may be present in a neuron, it may not directly contribute to MPR, but constrain the properties of other currents that generate MPR. Finally, constraining model parameters further to those that modify their MPR properties to changes in voltage range produces maximal conductance correlations.

A balance of outward and linear inward ionic currents is required for generation of slow-wave oscillations

Regenerative inward currents help produce slow oscillations through a negative-slope conductance region of their current-voltage relationship that is well approximated by a linear negative conductance. We used dynamic-clamp injections of a linear current with such conductance, I_NL, to explore why some neurons can generate intrinsic slow oscillations whereas others cannot. We addressed this question in synaptically isolated neurons of the crab Cancer borealis after blocking action potentials. The pyloric network consists of a distinct pacemaker and follower neurons, all of which express the same complement of ionic currents. When the pyloric dilator (PD) neuron, a member of the pacemaker group, was injected with I_NL with dynamic clamp, it consistently produced slow oscillations. In contrast, all follower neurons failed to oscillate with I_NL To understand these distinct behaviors, we compared outward current levels of PD with those of follower lateral pyloric (LP) and ventral pyloric (VD) neurons. We found that LP and VD neurons had significantly larger high-threshold potassium currents (I_HTK) than PD and LP had lower-transient potassium current (I_A). Reducing I_HTK pharmacologically enabled both LP and VD neurons to produce I_NL-induced oscillations, whereas modifying I_A levels did not affect I_NL-induced oscillations. Using phase-plane and bifurcation analysis of a simplified model cell, we demonstrate that large levels of I_HTK can block I_NL-induced oscillatory activity whereas generation of oscillations is almost independent of I_A levels. These results demonstrate the general importance of a balance between inward pacemaking currents and high-threshold K⁺ current levels in determining slow oscillatory activity.NEW & NOTEWORTHY Pacemaker neuron-generated rhythmic activity requires the activation of at least one inward and one outward current. We have previously shown that the inward current can be a linear current (with negative conductance). Using this simple mechanism, here we demonstrate that the inward current conductance must be in relative balance with the outward current conductances to generate oscillatory activity. Surprisingly, an excess of outward conductances completely precludes the possibility of achieving such a balance.

Electrosensory neural responses to natural electro-communication stimuli are distributed along a continuum

Neural heterogeneities are seen ubiquitously within the brain and greatly complicate classification efforts. Here we tested whether the responses of an anatomically well-characterized sensory neuron population to natural stimuli could be used for functional classification. To do so, we recorded from pyramidal cells within the electrosensory lateral line lobe (ELL) of the weakly electric fish Apteronotus leptorhynchus in response to natural electro-communication stimuli as these cells can be anatomically classified into six different types. We then used two independent methodologies to functionally classify responses: one relies of reducing the dimensionality of a feature space while the other directly compares the responses themselves. Both methodologies gave rise to qualitatively similar results: while ON and OFF-type cells could easily be distinguished from one another, ELL pyramidal neuron responses are actually distributed along a continuum rather than forming distinct clusters due to heterogeneities. We discuss the implications of our results for neural coding and highlight some potential advantages.

Homeostatic plasticity of excitability in crustacean central pattern generator networks

Plasticity of excitability can come in two general forms: changes in excitability that alter neuronal output (e.g. long-term potentiation of intrinsic excitability) or excitability changes that stabilize neuronal output (homeostatic plasticity). Here we discuss the latter form of plasticity in the context of the crustacean stomatogastric nervous system, and a second central pattern generator circuit, the cardiac ganglion. We discuss this plasticity at three levels: rapid homeostatic changes in membrane conductance, longer-term effects of neuromodulation on excitability, and the impacts of activity-dependent feedback on steady-state channel mRNA levels. We then conclude with thoughts on the implications of plasticity of excitability for variability of conductance levels across populations of motor neurons.

Nonreciprocal homeostatic compensation in Drosophila potassium channel mutants

Homeostatic control of intrinsic excitability is important for long-term regulation of neuronal activity. In conjunction with many other forms of plasticity, intrinsic homeostasis helps neurons maintain stable activity regimes in the face of external input variability and destabilizing genetic mutations. In this study, we report a mechanism by which Drosophila melanogaster larval motor neurons stabilize hyperactivity induced by the loss of the delayed rectifying K⁺ channel Shaker cognate B (Shab), by upregulating the Ca²⁺-dependent K⁺ channel encoded by the slowpoke (slo) gene. We also show that loss of SLO does not trigger a reciprocal compensatory upregulation of SHAB, implying that homeostatic signaling pathways utilize compensatory pathways unique to the channel that was mutated. SLO upregulation due to loss of SHAB involves nuclear Ca²⁺ signaling and dCREB, suggesting that the slo homeostatic response is transcriptionally mediated. Examination of the changes in gene expression induced by these mutations suggests that there is not a generic transcriptional response to increased excitability in motor neurons, but that homeostatic compensations are influenced by the identity of the lost conductance.NEW & NOTEWORTHY The idea that activity-dependent homeostatic plasticity is driven solely by firing has wide credence. In this report we show that homeostatic compensation after loss of an ion channel conductance is tailored to identity of the channel lost, not its properties.

Theory of optimal balance predicts and explains the amplitude and decay time of synaptic inhibition

Synaptic inhibition counterbalances excitation, but it is not known what constitutes optimal inhibition. We previously proposed that perfect balance is achieved when the peak of an excitatory postsynaptic potential (EPSP) is exactly at spike threshold, so that the slightest variation in excitation determines whether a spike is generated. Using simulations, we show that the optimal inhibitory postsynaptic conductance (IPSG) increases in amplitude and decay rate as synaptic excitation increases from 1 to 800 Hz. As further proposed by theory, we show that optimal IPSG parameters can be learned through anti-Hebbian rules. Finally, we compare our theoretical optima to published experimental data from 21 types of neurons, in which rates of synaptic excitation and IPSG decay times vary by factors of about 100 (5–600 Hz) and 50 (1–50 ms), respectively. From an infinite range of possible decay times, theory predicted experimental decay times within less than a factor of 2. Across a distinct set of 15 types of neuron recorded in vivo, theory predicted the amplitude of synaptic inhibition within a factor of 1.7. Thus, the theory can explain biophysical quantities from first principles.

Inhibition and excitation are counterbalanced at synapses, but the conditions that constitute optimal balance are not known. Here the authors show through modelling that the properties of synaptic inhibition are fine-tuned to maintain an optimal balance in which peak excitation reaches precisely to spike threshold.

Sloppy morphological tuning in identified neurons of the crustacean stomatogastric ganglion

Neuronal physiology depends on a neuron’s ion channel composition and unique morphology. Variable ion channel compositions can produce similar neuronal physiologies across animals. Less is known regarding the morphological precision required to produce reliable neuronal physiology. Theoretical studies suggest that moraphology is tightly tuned to minimize wiring and conduction delay of synaptic events. We utilize high-resolution confocal microscopy and custom computational tools to characterize the morphologies of four neuron types in the stomatogastric ganglion (STG) of the crab Cancer borealis. Macroscopic branching patterns and fine cable properties are variable within and across neuron types. We compare these neuronal structures to synthetic minimal spanning neurite trees constrained by a wiring cost equation and find that STG neurons do not adhere to prevailing hypotheses regarding wiring optimization principles. In this highly modulated and oscillating circuit, neuronal structures appear to be governed by a space-filling mechanism that outweighs the cost of inefficient wiring.

DOI:http://dx.doi.org/10.7554/eLife.22352.001

When complex neuronal structures may not matter

Much work has explored animal-to-animal variability and compensation in ion channel expression. Yet, little is known regarding the physiological consequences of morphological variability. We quantify animal-to-animal variability in cable lengths (CV = 0.4) and branching patterns in the Gastric Mill (GM) neuron, an identified neuron type with highly-conserved physiological properties in the crustacean stomatogastric ganglion (STG) of Cancer borealis. We examined passive GM electrotonic structure by measuring the amplitudes and apparent reversal potentials (E_revs) of inhibitory responses evoked with focal glutamate photo-uncaging in the presence of TTX. Apparent E_revs were relatively invariant across sites (mean CV ± SD = 0.04 ± 0.01; 7–20 sites in each of 10 neurons), which ranged between 100–800 µm from the somatic recording site. Thus, GM neurons are remarkably electrotonically compact (estimated λ > 1.5 mm). Electrotonically compact structures, in consort with graded transmission, provide an elegant solution to observed morphological variability in the STG.

DOI:http://dx.doi.org/10.7554/eLife.23508.001

Deep sequencing of transcriptomes from the nervous systems of two decapod crustaceans to characterize genes important for neural circuit function and modulation

BACKGROUND

Crustaceans have been studied extensively as model systems for nervous system function from single neuron properties to behavior. However, lack of molecular sequence information and tools have slowed the adoption of these physiological systems as molecular model systems. In this study, we sequenced and performed de novo assembly for the nervous system transcriptomes of two decapod crustaceans: the Jonah crab (Cancer borealis) and the American lobster (Homarus americanus).

RESULTS

Forty-two thousand, seven hundred sixty-six and sixty thousand, two hundred seventy-three contigs were assembled from C. borealis and H. americanus respectively, representing 9,489 and 11,061 unique coding sequences. From these transcripts, genes associated with neural function were identified and manually curated to produce a characterization of multiple gene families important for nervous system function. This included genes for 34 distinct ion channel types, 17 biogenic amine and 5 GABA receptors, 28 major transmitter receptor subtypes including glutamate and acetylcholine receptors, and 6 gap junction proteins - the Innexins.

CONCLUSION

With this resource, crustacean model systems are better poised for incorporation of modern genomic and molecular biology technologies to further enhance the interrogation of fundamentals of nervous system function.

Ih Equalizes Membrane Input Resistance in a Heterogeneous Population of Fusiform Neurons in the Dorsal Cochlear Nucleus

In a neuronal population, several combinations of its ionic conductances are used to attain a specific firing phenotype. Some neurons present heterogeneity in their firing, generally produced by expression of a specific conductance, but how additional conductances vary along in order to homeostatically regulate membrane excitability is less known. Dorsal cochlear nucleus principal neurons, fusiform neurons, display heterogeneous spontaneous action potential activity and thus represent an appropriate model to study the role of different conductances in establishing firing heterogeneity. Particularly, fusiform neurons are divided into quiet, with no spontaneous firing, or active neurons, presenting spontaneous, regular firing. These modes are determined by the expression levels of an intrinsic membrane conductance, an inwardly rectifying potassium current (I_Kir). In this work, we tested whether other subthreshold conductances vary homeostatically to maintain membrane excitability constant across the two subtypes. We found that I_h expression covaries specifically with I_Kir in order to maintain membrane resistance constant. The impact of I_h on membrane resistance is dependent on the level of I_Kir expression, being much smaller in quiet neurons with bigger I_Kir, but I_h variations are not relevant for creating the quiet and active phenotypes. Finally, we demonstrate that the individual proportion of each conductance, and not their absolute conductance, is relevant for determining the neuronal firing mode. We conclude that in fusiform neurons the variations of their different subthreshold conductances are limited to specific conductances in order to create firing heterogeneity and maintain membrane homeostasis.

Temperature-Robust Neural Function from Activity-Dependent Ion Channel Regulation

Many species of cold-blooded animals experience substantial and rapid fluctuations in body temperature. Because biological processes are differentially temperature dependent, it is difficult to understand how physiological processes in such animals can be temperature robust [1-8]. Experiments have shown that core neural circuits, such as the pyloric circuit of the crab stomatogastric ganglion (STG), exhibit robust neural activity in spite of large (20°C) temperature fluctuations [3, 5, 7, 8]. This robustness is surprising because (1) each neuron has many different kinds of ion channels with different temperature dependencies (Q₁₀s) that interact in a highly nonlinear way to produce firing patterns and (2) across animals there is substantial variability in conductance densities that nonetheless produce almost identical firing properties. The high variability in conductance densities in these neurons [9, 10] appears to contradict the possibility that robustness is achieved through precise tuning of key temperature-dependent processes. In this paper, we develop a theoretical explanation for how temperature robustness can emerge from a simple regulatory control mechanism that is compatible with highly variable conductance densities [11-13]. The resulting model suggests a general mechanism for how nervous systems and excitable tissues can exploit degenerate relationships among temperature-sensitive processes to achieve robust function.

Consequences of degeneracy in network function

Often distinct elements serve similar functions within a network. However, it is unclear whether this network degeneracy is beneficial, or merely a reflection of tighter regulation of overall network performance relative to individual neuronal properties. We review circumstances where data strongly suggest that degeneracy is beneficial in that it makes network function more robust. Importantly, network degeneracy is likely to have functional consequences that are not widely appreciated. This is likely to be true when network activity is configured by modulators with persistent actions, and the history of network activity potentially impacts subsequent functioning. Data suggest that degeneracy in this context may be important for the creation of latent memories, and for state-dependent task switching.

Dynamic compensation mechanism gives rise to period and duty-cycle level sets in oscillatory neuronal models

Rhythmic oscillation in neurons can be characterized by various attributes, such as the oscillation period and duty cycle. The values of these features depend on the amplitudes of the participating ionic currents, which can be characterized by their maximum conductance values. Recent experimental and theoretical work has shown that the values of these attributes can be maintained constant for different combinations of two or more ionic currents of varying conductances, defining what is known as level sets in conductance space. In two-dimensional conductance spaces, a level set is a curve, often a line, along which a particular oscillation attribute value is conserved. In this work, we use modeling, dynamical systems tools (phase-space analysis), and numerical simulations to investigate the possible dynamic mechanisms responsible for the generation of period and duty-cycle levels sets in simplified (linearized and FitzHugh-Nagumo) and conductance-based (Morris-Lecar) models of neuronal oscillations. A simplistic hypothesis would be that the tonic balance between ionic currents with the same or opposite effective signs is sufficient to create level sets. According to this hypothesis, the dynamics of each ionic current during a given cycle are well captured by some constant quantity (e.g., maximal conductances), and the phase-plane diagrams are identical or are almost identical (e.g., cubic-like nullclines with the same maxima and minima) for different combinations of these maximal conductances. In contrast, we show that these mechanisms are dynamic and involve the complex interaction between the nonlinear voltage dependencies and the effective time scales at which the ionic current's dynamical variables operate.

Synergistic plasticity of intrinsic conductance and electrical coupling restores synchrony in an intact motor network

Motor neurons of the crustacean cardiac ganglion generate virtually identical, synchronized output despite the fact that each neuron uses distinct conductance magnitudes. As a result of this variability, manipulations that target ionic conductances have distinct effects on neurons within the same ganglion, disrupting synchronized motor neuron output that is necessary for proper cardiac function. We hypothesized that robustness in network output is accomplished via plasticity that counters such destabilizing influences. By blocking high-threshold K⁺ conductances in motor neurons within the ongoing cardiac network, we discovered that compensation both resynchronized the network and helped restore excitability. Using model findings to guide experimentation, we determined that compensatory increases of both G_A and electrical coupling restored function in the network. This is one of the first direct demonstrations of the physiological regulation of coupling conductance in a compensatory context, and of synergistic plasticity across cell- and network-level mechanisms in the restoration of output.

DOI:http://dx.doi.org/10.7554/eLife.16879.001

Neurons can communicate with each other by releasing chemicals called neurotransmitters, or by forming direct connections with each other known as gap junctions. These direct connections allow electrical impulses to flow from one neuron to another via pores in the membranes between the cells. Unlike communication via neurotransmitters, gap junctions are usually thought to be hard-wired and unchanging over the life of the animal.

Lane et al. recorded electrical activity in a network of neurons that generates rhythmic heart contractions in the Jonah crab. Neurons in this network usually all fire an electrical impulse at the same time, which is crucial to make sure that the whole heart contracts at the same time. The experiments show that drugs that block potassium channel pores in the membrane cause the neurons to fire too much and at different times to each other.

However, the network of neurons soon adapted to the changes caused by the drugs and returned to working as normal. Mimicking these changes in a computer model of the neuron network, together with experimental data, showed that changes to the gap junctions play a major role in restoring normal activity to the network.

The next step following on from this research is to understand how a network of neurons ‘senses’ that it is not working normally and changes its electrical activity.

DOI:http://dx.doi.org/10.7554/eLife.16879.002

Dynamic DNA methylation regulates neuronal intrinsic membrane excitability

Epigenetic modifications, such as DNA cytosine methylation, contribute to the mechanisms underlying learning and memory by coordinating adaptive gene expression and neuronal plasticity. Transcription-dependent plasticity regulated by DNA methylation includes synaptic plasticity and homeostatic synaptic scaling. Memory-related plasticity also includes alterations in intrinsic membrane excitability mediated by changes in the abundance or activity of ion channels in the plasma membrane, which sets the threshold for action potential generation. We found that prolonged inhibition of DNA methyltransferase (DNMT) activity increased intrinsic membrane excitability of cultured cortical pyramidal neurons. Knockdown of the cytosine demethylase TET1 or inhibition of RNA polymerase blocked the increased membrane excitability caused by DNMT inhibition, suggesting that this effect was mediated by subsequent cytosine demethylation and de novo transcription. Prolonged DNMT inhibition blunted the medium component of the after-hyperpolarization potential, an effect that would increase neuronal excitability, and was associated with reduced expression of the genes encoding small-conductance Ca(2+)-activated K(+) (SK) channels. Furthermore, the specific SK channel blocker apamin increased neuronal excitability but was ineffective after DNMT inhibition. Our results suggested that DNMT inhibition enables transcriptional changes that culminate in decreased expression of SK channel-encoding genes and decreased activity of SK channels, thus providing a mechanism for the regulation of neuronal intrinsic membrane excitability by dynamic DNA cytosine methylation. This study has implications for human neurological and psychiatric diseases associated with dysregulated intrinsic excitability.

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.

Spike Pattern Structure Influences Synaptic Efficacy Variability under STDP and Synaptic Homeostasis. II: Spike Shuffling Methods on LIF Networks

Synapses may undergo variable changes during plasticity because of the variability of spike patterns such as temporal stochasticity and spatial randomness. Here, we call the variability of synaptic weight changes during plasticity to be efficacy variability. In this paper, we investigate how four aspects of spike pattern statistics (i.e., synchronous firing, burstiness/regularity, heterogeneity of rates and heterogeneity of cross-correlations) influence the efficacy variability under pair-wise additive spike-timing dependent plasticity (STDP) and synaptic homeostasis (the mean strength of plastic synapses into a neuron is bounded), by implementing spike shuffling methods onto spike patterns self-organized by a network of excitatory and inhibitory leaky integrate-and-fire (LIF) neurons. With the increase of the decay time scale of the inhibitory synaptic currents, the LIF network undergoes a transition from asynchronous state to weak synchronous state and then to synchronous bursting state. We first shuffle these spike patterns using a variety of methods, each designed to evidently change a specific pattern statistics; and then investigate the change of efficacy variability of the synapses under STDP and synaptic homeostasis, when the neurons in the network fire according to the spike patterns before and after being treated by a shuffling method. In this way, we can understand how the change of pattern statistics may cause the change of efficacy variability. Our results are consistent with those of our previous study which implements spike-generating models on converging motifs. We also find that burstiness/regularity is important to determine the efficacy variability under asynchronous states, while heterogeneity of cross-correlations is the main factor to cause efficacy variability when the network moves into synchronous bursting states (the states observed in epilepsy).

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.

Frequency Responses of Rat Retinal Ganglion Cells

There are 15–20 different types of retinal ganglion cells (RGC) in the mammalian retina, each encoding different aspects of the visual scene. The mechanism by which post-synaptic signals from the retinal network generate spikes is determined by each cell’s intrinsic electrical properties. Here we investigate the frequency responses of morphologically identified rat RGCs using intracellular injection of sinusoidal current waveforms, to assess their intrinsic capabilities with minimal contributions from the retinal network. Recorded cells were classified according to their morphological characteristics (A, B, C or D-type) and their stratification (inner (i), outer (o) or bistratified) in the inner plexiform layer (IPL). Most cell types had low- or band-pass frequency responses. A2, C1 and C4o cells were band-pass with peaks of 15–30 Hz and low-pass cutoffs above 56 Hz (A2 cells) and ~42 Hz (C1 and C4o cells). A1 and C2i/o cells were low-pass with peaks of 10–15 Hz (cutoffs 19–25 Hz). Bistratified D1 and D2 cells were also low-pass with peaks of 5–10 Hz (cutoffs ~16 Hz). The least responsive cells were the B2 and C3 types (peaks: 2–5 Hz, cutoffs: 8–11 Hz). We found no difference between cells stratifying in the inner and outer IPL (i.e., ON and OFF cells) or between cells with large and small somas or dendritic fields. Intrinsic physiological properties (input resistance, spike width and sag) had little impact on frequency response at low frequencies, but account for 30–40% of response variability at frequencies >30 Hz.

Computational implications of biophysical diversity and multiple timescales in neurons and synapses for circuit performance

Despite advances in experimental and theoretical neuroscience, we are still trying to identify key biophysical details that are important for characterizing the operation of brain circuits. Biological mechanisms at the level of single neurons and synapses can be combined as 'building blocks' to generate circuit function. We focus on the importance of capturing multiple timescales when describing these intrinsic and synaptic components. Whether inherent in the ionic currents, the neuron's complex morphology, or the neurotransmitter composition of synapses, these multiple timescales prove crucial for capturing the variability and richness of circuit output and enhancing the information-carrying capacity observed across nervous systems.

Improving cardiomyocyte model fidelity and utility via dynamic electrophysiology protocols and optimization algorithms

Mathematical models of cardiac electrophysiology are instrumental in determining mechanisms of cardiac arrhythmias. However, the foundation of a realistic multiscale heart model is only as strong as the underlying cell model. While there have been myriad advances in the improvement of cellular-level models, the identification of model parameters, such as ion channel conductances and rate constants, remains a challenging problem. The primary limitations to this process include: (1) such parameters are usually estimated from data recorded using standard electrophysiology voltage-clamp protocols that have not been developed with model building in mind, and (2) model parameters are typically tuned manually to subjectively match a desired output. Over the last decade, methods aimed at overcoming these disadvantages have emerged. These approaches include the use of optimization or fitting tools for parameter estimation and incorporating more extensive data for output matching. Here, we review recent advances in parameter estimation for cardiomyocyte models, focusing on the use of more complex electrophysiology protocols and global search heuristics. We also discuss future applications of such parameter identification, including development of cell-specific and patient-specific mathematical models to investigate arrhythmia mechanisms and predict therapy strategies.

Molecular variability elicits a tunable switch with discrete neuromodulatory response phenotypes

Recent single cell studies show extensive molecular variability underlying cellular responses. We evaluated the impact of molecular variability in the expression of cell signaling components and ion channels on electrophysiological excitability and neuromodulation. We employed a computational approach that integrated neuropeptide receptor-mediated signaling with electrophysiology. We simulated a population of neurons in which expression levels of a neuropeptide receptor and multiple ion channels were simultaneously varied within a physiological range. We analyzed the effects of variation on the electrophysiological response to a neuropeptide stimulus. Our results revealed distinct response patterns associated with low versus high receptor levels. Neurons with low receptor levels showed increased excitability and neurons with high receptor levels showed reduced excitability. These response patterns were separated by a narrow receptor level range forming a separatrix. The position of this separatrix was dependent on the expression levels of multiple ion channels. To assess the relative contributions of receptor and ion channel levels to the response profiles, we categorized the responses into six phenotypes based on response kinetics and magnitude. We applied several multivariate statistical approaches and found that receptor and channel expression levels influence the neuromodulation response phenotype through a complex though systematic mapping. Our analyses extended our understanding of how cellular responses to neuromodulation vary as a function of molecular expression. Our study showed that receptor expression and biophysical state interact with distinct relative contributions to neuronal excitability.

De novo transcriptome assembly for the lobster Homarus americanus and characterization of differential gene expression across nervous system tissues

BACKGROUND

The American lobster, Homarus americanus, is an important species as an economically valuable fishery, a key member in marine ecosystems, and a well-studied model for central pattern generation, the neural networks that control rhythmic motor patterns. Despite multi-faceted scientific interest in this species, currently our genetic resources for the lobster are limited. In this study, we de novo assemble a transcriptome for Homarus americanus using central nervous system (CNS), muscle, and hybrid neurosecretory tissues and compare gene expression across these tissue types. In particular, we focus our analysis on genes relevant to central pattern generation and the identity of the neurons in a neural network, which is defined by combinations of genes distinguishing the neuronal behavior and phenotype, including ion channels, neurotransmitters, neuromodulators, receptors, transcription factors, and other gene products.

RESULTS

Using samples from the central nervous system (brain, abdominal ganglia), abdominal muscle, and heart (cardiac ganglia, pericardial organs, muscle), we used RNA-Seq to characterize gene expression patterns across tissues types. We also compared control tissues with those challenged with the neuropeptide proctolin in vivo. Our transcriptome generated 34,813 transcripts with known protein annotations. Of these, 5,000-10,000 of annotated transcripts were significantly differentially expressed (DE) across tissue types. We found 421 transcripts for ion channels and identified receptors and/or proteins for over 20 different neurotransmitters and neuromodulators. Results indicated tissue-specific expression of select neuromodulator (allostatin, myomodulin, octopamine, nitric oxide) and neurotransmitter (glutamate, acetylcholine) pathways. We also identify differential expression of ion channel families, including kainite family glutamate receptors, inward-rectifying K(+) (IRK) channels, and transient receptor potential (TRP) A family channels, across central pattern generating tissues.

CONCLUSIONS

Our transcriptome-wide profiles of the rhythmic pattern generating abdominal and cardiac nervous systems in Homarus americanus reveal candidates for neuronal features that drive the production of motor output in these systems.

Variability in cardiac electrophysiology: Using experimentally-calibrated populations of models to move beyond the single virtual physiological human paradigm

Physiological variability manifests itself via differences in physiological function between individuals of the same species, and has crucial implications in disease progression and treatment. Despite its importance, physiological variability has traditionally been ignored in experimental and computational investigations due to averaging over samples from multiple individuals. Recently, modelling frameworks have been devised for studying mechanisms underlying physiological variability in cardiac electrophysiology and pro-arrhythmic risk under a variety of conditions and for several animal species as well as human. One such methodology exploits populations of cardiac cell models constrained with experimental data, or experimentally-calibrated populations of models. In this review, we outline the considerations behind constructing an experimentally-calibrated population of models and review the studies that have employed this approach to investigate variability in cardiac electrophysiology in physiological and pathological conditions, as well as under drug action. We also describe the methodology and compare it with alternative approaches for studying variability in cardiac electrophysiology, including cell-specific modelling approaches, sensitivity-analysis based methods, and populations-of-models frameworks that do not consider the experimental calibration step. We conclude with an outlook for the future, predicting the potential of new methodologies for patient-specific modelling extending beyond the single virtual physiological human paradigm.

Modeling the Influence of Ion Channels on Neuron Dynamics in Drosophila

Voltage gated ion channels play a major role in determining a neuron's firing behavior, resulting in the specific processing of synaptic input patterns. Drosophila and other invertebrates provide valuable model systems for investigating ion channel kinetics and their impact on firing properties. Despite the increasing importance of Drosophila as a model system, few computational models of its ion channel kinetics have been developed. In this study, experimentally observed biophysical properties of voltage gated ion channels from the fruitfly Drosophila melanogaster are used to develop a minimal, conductance based neuron model. We investigate the impact of the densities of these channels on the excitability of the model neuron. Changing the channel densities reproduces different in situ observed firing patterns and induces a switch from integrator to resonator properties. Further, we analyze the preference to input frequency and how it depends on the channel densities and the resulting bifurcation type the system undergoes. An extension to a three dimensional model demonstrates that the inactivation kinetics of the sodium channels play an important role, allowing for firing patterns with a delayed first spike and subsequent high frequency firing as often observed in invertebrates, without altering the kinetics of the delayed rectifier current.

Multivariate analysis of electrophysiological diversity of Xenopus visual neurons during development and plasticity

Biophysical properties of neurons become increasingly diverse over development, but mechanisms underlying and constraining this diversity are not fully understood. Here we investigate electrophysiological characteristics of Xenopus tadpole midbrain neurons across development and during homeostatic plasticity induced by patterned visual stimulation. We show that in development tectal neuron properties not only change on average, but also become increasingly diverse. After sensory stimulation, both electrophysiological diversity and functional differentiation of cells are reduced. At the same time, the amount of cross-correlations between cell properties increase after patterned stimulation as a result of homeostatic plasticity. We show that tectal neurons with similar spiking profiles often have strikingly different electrophysiological properties, and demonstrate that changes in intrinsic excitability during development and in response to sensory stimulation are mediated by different underlying mechanisms. Overall, this analysis and the accompanying dataset provide a unique framework for further studies of network maturation in Xenopus tadpoles.

Monoaminergic tone supports conductance correlations and stabilizes activity features in pattern generating neurons of the lobster, Panulirus interruptus

Experimental and computational studies demonstrate that different sets of intrinsic and synaptic conductances can give rise to equivalent activity patterns. This is because the balance of conductances, not their absolute values, defines a given activity feature. Activity-dependent feedback mechanisms maintain neuronal conductance correlations and their corresponding activity features. This study demonstrates that tonic nM concentrations of monoamines enable slow, activity-dependent processes that can maintain a correlation between the transient potassium current (I_A) and the hyperpolarization activated current (I_h) over the long-term (i.e., regulatory change persists for hours after removal of modulator). Tonic 5 nM DA acted through an RNA interference silencing complex (RISC)- and RNA polymerase II-dependent mechanism to maintain a long-term positive correlation between I_A and I_h in the lateral pyloric neuron (LP) but not in the pyloric dilator neuron (PD). In contrast, tonic 5 nM 5HT maintained a RISC-dependent positive correlation between I_A and I_h in PD but not LP over the long-term. Tonic 5 nM OCT maintained a long-term negative correlation between I_A and I_h in PD but not LP; however, it was only revealed when RISC was inhibited. This study also demonstrated that monoaminergic tone can also preserve activity features over the long-term: the timing of LP activity, LP duty cycle and LP spike number per burst were maintained by tonic 5 nM DA. The data suggest that low-level monoaminergic tone acts through multiple slow processes to permit cell-specific, activity-dependent regulation of ionic conductances to maintain conductance correlations and their corresponding activity features over the long-term.