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

Degenerate neuronal and circuit mechanisms important for generating rhythmic motor patterns

In 1996, we published a review article (Marder E, Calabrese RL. Physiol Rev 76: 687-717, 1996) describing the state of knowledge about the structure and function of the central pattern-generating circuits important for producing rhythmic behaviors. Although many of the core questions persist, much has changed since 1996. Here, we focus on newer studies that reveal ambiguities that complicate understanding circuit dynamics, despite the enormous technical advances of the recent past. In particular, we highlight recent studies of animal-to-animal variability and our understanding that circuit rhythmicity may be supported by multiple state-dependent mechanisms within the same animal and that robustness and resilience in the face of perturbation may depend critically on the presence of modulators and degenerate circuit mechanisms. Additionally, we highlight the use of computational models to ask whether there are generalizable principles about circuit motifs that can be found across rhythmic motor systems in different animal species.

Ih block reveals separation of timescales in pyloric rhythm response to temperature changes in Cancer borealis

Motor systems operate over a range of frequencies and relative timing (phase). We studied the role of the hyperpolarization-activated inward current (Ih) in regulating these features in the pyloric rhythm of the stomatogastric ganglion (STG) of the crab, Cancer borealis, as temperature was altered from 11°C to 21°C. Under control conditions, rhythm frequency increased monotonically with temperature, while the phases of the pyloric dilator (PD), lateral pyloric (LP), and pyloric (PY) neurons remained constant. Blocking Ih with cesium (Cs+) phase advanced PD offset, LP onset, and LP offset at 11°C, and the latter two further advanced as temperature increased. In Cs+ the frequency increase with temperature diminished and the Q10 of the frequency dropped from ~1.75 to ~1.35. Unexpectedly in Cs+, the frequency dynamics became non-monotonic during temperature transitions; frequency initially dropped as temperature increased, then rose once temperature stabilized, creating a characteristic 'jag'. Interestingly, these jags persisted during temperature transitions in Cs+ when the pacemaker was isolated by picrotoxin, although the temperature-induced change in frequency recovered to control levels. Overall, these data suggest that Ih plays an important role in maintaining smooth transitory responses and persistent frequency increases by different mechanisms in the pyloric circuitry during temperature fluctuations.

The Brain's Best Kept Secret Is Its Degenerate Structure

Degeneracy is defined as multiple sets of solutions that can produce very similar system performance. Degeneracy is seen across phylogenetic scales, in all kinds of organisms. In neuroscience, degeneracy can be seen in the constellation of biophysical properties that produce a neuron's characteristic intrinsic properties and/or the constellation of mechanisms that determine circuit outputs or behavior. Here, we present examples of degeneracy at multiple levels of organization, from single-cell behavior, small circuits, large circuits, and, in cognition, drawing conclusions from work ranging from bacteria to human cognition. Degeneracy allows the individual-to-individual variability within a population that creates potential for evolution.

Converging and Diverging Cerebellar Pathways for Motor and Social Behaviors in Mice

Evidence from clinical and preclinical studies has shown that the cerebellum contributes to cognitive functions, including social behaviors. Now that the cerebellum's role in a wider range of behaviors has been confirmed, the question arises whether the cerebellum contributes to social behaviors via the same mechanisms with which it modulates movements. This review seeks to answer whether the cerebellum guides motor and social behaviors through identical pathways. It focuses on studies in which cerebellar cells, synapses, or genes are manipulated in a cell-type specific manner followed by testing of the effects on social and motor behaviors. These studies show that both anatomically restricted and cerebellar cortex-wide manipulations can lead to social impairments without abnormal motor control, and vice versa. These studies suggest that the cerebellum employs different cellular, synaptic, and molecular pathways for social and motor behaviors. Future studies warrant a focus on the diverging mechanisms by which the cerebellum contributes to a wide range of neural functions.

Dimensionality reduction of neuronal degeneracy reveals two interfering physiological mechanisms

Neuronal systems maintain stable functions despite large variability in their physiological components. Ion channel expression, in particular, is highly variable in neurons exhibiting similar electrophysiological phenotypes, which raises questions regarding how specific ion channel subsets reliably shape intrinsic properties of neurons. Here, we use detailed conductance-based modeling to explore how stable neuronal function is achieved despite variability in channel composition among neurons. Using dimensionality reduction, we uncover two principal dimensions in the channel conductance space that capture most of the variance of the observed variability. These two dimensions correspond to two sources of variability that originate from distinct physiologically relevant mechanisms underlying the regulation of neuronal activity, providing quantitative insights into how channel composition is linked to the electrophysiological activity of neurons. These insights allow us to understand and design a model-independent, reliable neuromodulation rule for variable neuronal populations.

Homeostatic Regulation of Spike Rate within Bursts in Two Distinct Preparations

Homeostatic plasticity represents a set of mechanisms thought to stabilize some function of neural activity. Here, we identified the specific features of cellular or network activity that were maintained after the perturbation of GABAergic blockade in two different systems: mouse cortical neuronal cultures where GABA is inhibitory and motoneurons in the isolated embryonic chick spinal cord where GABA is excitatory (males and females combined in both systems). We conducted a comprehensive analysis of various spiking activity characteristics following GABAergic blockade. We observed significant variability in many features after blocking GABAA receptors (e.g., burst frequency, burst duration, overall spike frequency in culture). These results are consistent with the idea that neuronal networks achieve activity goals using different strategies (degeneracy). On the other hand, some features were consistently altered after receptor blockade in the spinal cord preparation (e.g., overall spike frequency). Regardless, these features did not express strong homeostatic recoveries when tracking individual preparations over time. One feature showed a consistent change and homeostatic recovery following GABAA receptor block. We found that spike rate within a burst (SRWB) increased after receptor block in both the spinal cord preparation and cortical cultures and then returned to baseline within hours. These changes in SRWB occurred at both single cell and population levels. Our findings indicate that the network prioritizes the burst spike rate, which appears to be a variable under tight homeostatic regulation. The result is consistent with the idea that networks can maintain an appropriate behavioral response in the face of challenges.

Ih Block Reveals Separation of Timescales in Pyloric Rhythm Response to Temperature Changes in Cancer borealis

Motor systems operate over a range of frequencies and relative timing (phase). We studied the contribution of the hyperpolarization-activated inward current (Ih) to frequency and phase in the pyloric rhythm of the stomatogastric ganglion (STG) of the crab, Cancer borealis as temperature was altered from 11°C to 21°C. Under control conditions, the frequency of the rhythm increased monotonically with temperature, while the phases of the pyloric dilator (PD), lateral pyloric (LP), and pyloric (PY) neurons remained constant. When we blocked Ih with cesium (Cs+) PD offset, LP onset, and LP offset were all phase advanced in Cs+ at 11°C, and the latter two further advanced as temperature increased. In Cs+ the steady state increase in pyloric frequency with temperature diminished and the Q10 of the pyloric frequency dropped from ~1.75 to ~1.35. Unexpectedly in Cs+, the frequency displayed non-monotonic dynamics during temperature transitions; the frequency initially dropped as temperature increased, then rose once temperature stabilized, creating a characteristic "jag". Interestingly, these jags were still present during temperature transitions in Cs+ when the pacemaker was isolated by picrotoxin, although the temperature-induced change in frequency recovered to control levels. Overall, these data suggest that Ih plays an important role in the ability of this circuit to produce smooth transitory responses and persistent frequency increases by different mechanisms during temperature fluctuations.

Sulfonylurea receptor coupled conductances alter the performace of two central pattern generating circuits in Cancer borealis

Neuronal activity and energy supply must maintain a fine balance for neuronal fitness. Various channels of communication between the two could impact network output in different ways. Sulfonylurea receptors (SURs) are a modification of ATP-binding cassette proteins (ABCs) that confer ATP-dependent gating on their associated ion channels. They are widely expressed and link metabolic states directly to neuronal activity. The role they play varies in different circuits, both enabling bursting and inhibiting activity in pathological conditions. The crab, Cancer borealis, has central patterns generators (CPGs) that fire in rhythmic bursts nearly constantly and it is unknown how energy availability influences these networks. The pyloric network of the stomatogastric ganglion (STG) and cardiac ganglion (GC) control rhythmic contractions of the foregut and heart respectively. Pharmacological manipulation of SURs results in opposite effects in the two CPGs. Neuronal firing completely stops in the STG when SUR-associated channels are open, and firing increases when the channels are closed. This results from a decrease in the excitability of pyloric dilator (PD) neurons, which are a part of the pacemaker kernel. The neurons of the CG, paradoxically, increase firing within bursts when SUR-associated channels are opened, and bursting slows when SUR-associated channels are closed. The channel permeability and sensitivities analyses present novel SUR-conductance biophysics, which nevertheless change activity in ways reminiscent of the predominantly studied mammalian receptor/channels. We suggest that SUR-associated conductances allow different neurons to respond to energy states in different ways through a common mechanism.

How do we get from hyperexcitability to excitotoxicity in amyotrophic lateral sclerosis?

Amyotrophic lateral sclerosis is a devastating neurodegenerative disease that, at present, has no effective cure. Evidence of increased circulating glutamate and hyperexcitability of the motor cortex in patients with amyotrophic lateral sclerosis have provided an empirical support base for the 'dying forward' excitotoxicity hypothesis. The hypothesis postulates that increased activation of upper motor neurons spreads pathology to lower motor neurons in the spinal cord in the form of excessive glutamate release, which triggers excitotoxic processes. Many clinical trials have focused on therapies that target excitotoxicity via dampening neuronal activation, but not all are effective. As such, there is a growing tension between the rising tide of evidence for the 'dying forward' excitotoxicity hypothesis and the failure of therapies that target neuronal activation. One possible solution to these contradictory outcomes is that our interpretation of the current evidence requires revision in the context of appreciating the complexity of the nervous system and the limitations of the neurobiological assays we use to study it. In this review we provide an evaluation of evidence relevant to the 'dying forward' excitotoxicity hypothesis and by doing so, identify key gaps in our knowledge that need to be addressed. We hope to provide a road map from hyperexcitability to excitotoxicity so that we can better develop therapies for patients suffering from amyotrophic lateral sclerosis. We conclude that studies of upper motor neuron activity and their synaptic output will play a decisive role in the future of amyotrophic lateral sclerosis therapy.

Thermal acclimation and habitat-dependent differences in temperature robustness of a crustacean motor circuit

Introduction

At the cellular level, acute temperature changes alter ionic conductances, ion channel kinetics, and the activity of entire neuronal circuits. This can result in severe consequences for neural function, animal behavior and survival. In poikilothermic animals, and particularly in aquatic species whose core temperature equals the surrounding water temperature, neurons experience rather rapid and wide-ranging temperature fluctuations. Recent work on pattern generating neural circuits in the crustacean stomatogastric nervous system have demonstrated that neuronal circuits can exhibit an intrinsic robustness to temperature fluctuations. However, considering the increased warming of the oceans and recurring heatwaves due to climate change, the question arises whether this intrinsic robustness can acclimate to changing environmental conditions, and whether it differs between species and ocean habitats.

Methods

We address these questions using the pyloric pattern generating circuits in the stomatogastric nervous system of two crab species, Hemigrapsus sanguineus and Carcinus maenas that have seen a worldwide expansion in recent decades.

Results and discussion

Consistent with their history as invasive species, we find that pyloric activity showed a broad temperature robustness (>30°C). Moreover, the temperature-robust range was dependent on habitat temperature in both species. Warm-acclimating animals shifted the critical temperature at which circuit activity breaks down to higher temperatures. This came at the cost of robustness against cold stimuli in H. sanguineus, but not in C. maenas. Comparing the temperature responses of C. maenas from a cold latitude (the North Sea) to those from a warm latitude (Spain) demonstrated that similar shifts in robustness occurred in natural environments. Our results thus demonstrate that neuronal temperature robustness correlates with, and responds to, environmental temperature conditions, potentially preparing animals for changing ecological conditions and shifting habitats.

Estimating the probability of early afterdepolarizations and predicting arrhythmic risk associated with long QT syndrome type 1 mutations

Early afterdepolarizations (EADs) are action potential (AP) repolarization abnormalities that can trigger lethal arrhythmias. Simulations using biophysically detailed cardiac myocyte models can reveal how model parameters influence the probability of these cellular arrhythmias; however, such analyses can pose a huge computational burden. We have previously developed a highly simplified approach in which logistic regression models (LRMs) map parameters of complex cell models to the probability of ectopic beats. Here, we extend this approach to predict the probability of EADs (P(EAD)) as a mechanistic metric of arrhythmic risk. We use the LRM to investigate how changes in parameters of the slow-activating delayed rectifier current (IKs) affect P(EAD) for 17 different long QT syndrome type 1 (LQTS1) mutations. In this LQTS1 clinical arrhythmic risk prediction task, we compared P(EAD) for these 17 mutations with two other recently published model-based arrhythmia risk metrics (AP morphology metric across populations of myocyte models and transmural repolarization prolongation based on a one-dimensional [1D] tissue-level model). These model-based risk metrics yield similar prediction performance; however, each fails to stratify clinical risk for a significant number of the 17 studied LQTS1 mutations. Nevertheless, an interpretable ensemble model using multivariate linear regression built by combining all of these model-based risk metrics successfully predicts the clinical risk of 17 mutations. These results illustrate the potential of computational approaches in arrhythmia risk prediction.

A biophysical perspective on the resilience of neuronal excitability across timescales

Neuronal membrane excitability must be resilient to perturbations that can take place over timescales from milliseconds to months (or even years in long-lived animals). A great deal of attention has been paid to classes of homeostatic mechanisms that contribute to long-term maintenance of neuronal excitability through processes that alter a key structural parameter: the number of ion channel proteins present at the neuronal membrane. However, less attention has been paid to the self-regulating 'automatic' mechanisms that contribute to neuronal resilience by virtue of the kinetic properties of ion channels themselves. Here, we propose that these two sets of mechanisms are complementary instantiations of feedback control, together enabling resilience on a wide range of temporal scales. We further point to several methodological and conceptual challenges entailed in studying these processes - both of which involve enmeshed feedback control loops - and consider the consequences of these mechanisms of resilience.

Variable task switching in the feeding network of Aplysia is a function of differential command input

Command systems integrate sensory information and then activate the interneurons and motor neurons that mediate behavior. Much research has established that the higher-order projection neurons that constitute these systems can play a key role in specifying the nature of the motor activity induced, or determining its parametric features. To a large extent, these insights have been obtained by contrasting activity induced by stimulating one neuron (or set of neurons) to activity induced by stimulating a different neuron (or set of neurons). The focus of our work differs. We study one type of motor program, ingestive feeding in the mollusc Aplysia californica, which can either be triggered when a single projection neuron (CBI-2) is repeatedly stimulated or can be triggered by projection neuron coactivation (e.g., activation of CBI-2 and CBI-3). We ask why this might be an advantageous arrangement. The cellular/molecular mechanisms that configure motor activity are different in the two situations because the released neurotransmitters differ. We focus on an important consequence of this arrangement, the fact that a persistent state can be induced with repeated CBI-2 stimulation that is not necessarily induced by CBI-2/3 coactivation. We show that this difference can have consequences for the ability of the system to switch from one type of activity to another.NEW & NOTEWORTHY We study a type of motor program that can be induced either by stimulating a higher-order projection neuron that induces a persistent state, or by coactivating projection neurons that configure activity but do not produce a state change. We show that when an activity is configured without a state change, it is possible to immediately return to an intermediate state that subsequently can be converted to any type of motor program.

A hierarchical model for external electrical control of an insect, accounting for inter-individual variation of muscle force properties

Cyborg control of insect movement is promising for developing miniature, high-mobility, and efficient biohybrid robots. However, considering the inter-individual variation of the insect neuromuscular apparatus and its neural control is challenging. We propose a hierarchical model including inter-individual variation of muscle properties of three leg muscles involved in propulsion (retractor coxae), joint stiffness (pro- and retractor coxae), and stance-swing transition (protractor coxae and levator trochanteris) in the stick insect Carausius morosus. To estimate mechanical effects induced by external muscle stimulation, the model is based on the systematic evaluation of joint torques as functions of electrical stimulation parameters. A nearly linear relationship between the stimulus burst duration and generated torque was observed. This stimulus-torque characteristic holds for burst durations of up to 500ms, corresponding to the stance and swing phase durations of medium to fast walking stick insects. Hierarchical Bayesian modeling revealed that linearity of the stimulus-torque characteristic was invariant, with individually varying slopes. Individual prediction of joint torques provides significant benefits for precise cyborg control.

Molecular profiling of CO2/pH-sensitive neurons in the locus coeruleus of bullfrogs reveals overlapping noradrenergic and glutamatergic cell identity

Locus coeruleus (LC) neurons regulate breathing by sensing CO2/pH. Neurons within the vertebrate LC are the main source of norepinephrine within the brain. However, they also use glutamate and GABA for fast neurotransmission. Although the amphibian LC is recognized as a site involved in central chemoreception for the control of breathing, the neurotransmitter phenotype of these neurons is unknown. To address this question, we combined electrophysiology and single-cell quantitative PCR to detect mRNA transcripts that define norepinephrinergic, glutamatergic, and GABAergic phenotypes in LC neurons activated by hypercapnic acidosis (HA) in American bullfrogs. Most LC neurons activated by HA had overlapping expression of noradrenergic and glutamatergic markers but did not show strong support for GABAergic transmission. Genes that encode the pH-sensitive K+ channel, TASK2, and acid-sensing cation channel, ASIC2, were most abundant, while Kir5.1 was present in 1/3 of LC neurons. The abundance of transcripts related to norepinephrine biosynthesis linearly correlated with those involved in pH sensing. These results suggest that noradrenergic neurons in the amphibian LC also use glutamate as a neurotransmitter and that CO2/pH sensitivity may be linkedto the noradrenergic cell identity.

Motor neurons within a network use cell-type specific feedback mechanisms to constrain relationships among ion channel mRNAs

Recently, activity has been proposed as a primary feedback mechanism used by continuously bursting neurons to coordinate ion channel mRNA relationships that underlie stable output. However, some neuron types only have intermittent periods of activity and so may require alternative mechanisms that induce and constrain the appropriate ion channel profile in different states of activity. To address this, we used the pyloric dilator (PD; constitutively active) and the lateral gastric (LG; periodically active) neurons of the stomatogastric ganglion (STG) of the crustacean Cancer borealis. We experimentally stimulated descending inputs to the STG to cause release of neuromodulators known to elicit the active state of LG neurons and quantified the mRNA abundances and pairwise relationships of 11 voltage-gated ion channels in active and silent LG neurons. The same stimulus does not significantly alter PD activity. Activation of LG upregulated ion channel mRNAs and lead to a greater number of positively correlated pairwise channel mRNA relationships. Conversely, this stimulus did not induce major changes in ion channel mRNA abundances and relationships of PD cells, suggesting their ongoing activity is sufficient to maintain channel mRNA relationships even under changing modulatory conditions. In addition, we found that ion channel mRNA correlations induced by the active state of LG are influenced by a combination of activity- and neuromodulator-dependent feedback mechanisms. Interestingly, some of these same correlations are maintained by distinct mechanisms in PD, suggesting that these motor networks use distinct feedback mechanisms to coordinate the same mRNA relationships across neuron types.NEW & NOTEWORTHY Neurons use various feedback mechanisms to adjust and maintain their output. Here, we demonstrate that different neurons within the same network can use distinct signaling mechanisms to regulate the same ion channel mRNA relationships.

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.

Heterogeneity of voltage gated sodium current density between neurons decorrelates spiking and suppresses network synchronization in Scn1b null mouse models

Voltage gated sodium channels (VGSCs) are required for action potential initiation and propagation in mammalian neurons. As with other ion channel families, VGSC density varies between neurons. Importantly, sodium current (INa) density variability is reduced in pyramidal neurons of Scn1b null mice. Scn1b encodes the VGSC β1/ β1B subunits, which regulate channel expression, trafficking, and voltage dependent properties. Here, we investigate how variable INa density in cortical layer 6 and subicular pyramidal neurons affects spike patterning and network synchronization. Constitutive or inducible Scn1b deletion enhances spike timing correlations between pyramidal neurons in response to fluctuating stimuli and impairs spike-triggered average current pattern diversity while preserving spike reliability. Inhibiting INa with a low concentration of tetrodotoxin similarly alters patterning without impairing reliability, with modest effects on firing rate. Computational modeling shows that broad INa density ranges confer a similarly broad spectrum of spike patterning in response to fluctuating synaptic conductances. Network coupling of neurons with high INa density variability displaces the coupling requirements for synchronization and broadens the dynamic range of activity when varying synaptic strength and network topology. Our results show that INa heterogeneity between neurons potently regulates spike pattern diversity and network synchronization, expanding VGSC roles in the nervous system.

A general pattern of non-spiking neuron dynamics under the effect of potassium and calcium channel modifications

Electrical activity of excitable cells results from ion exchanges through cell membranes, so that genetic or epigenetic changes in genes encoding ion channels are likely to affect neuronal electrical signaling throughout the brain. There is a large literature on the effect of variations in ion channels on the dynamics of spiking neurons that represent the main type of neurons found in the vertebrate nervous systems. Nevertheless, non-spiking neurons are also ubiquitous in many nervous tissues and play a critical role in the processing of some sensory systems. To our knowledge, however, how conductance variations affect the dynamics of non-spiking neurons has never been assessed. Based on experimental observations reported in the biological literature and on mathematical considerations, we first propose a phenotypic classification of non-spiking neurons. Then, we determine a general pattern of the phenotypic evolution of non-spiking neurons as a function of changes in calcium and potassium conductances. Furthermore, we study the homeostatic compensatory mechanisms of ion channels in a well-posed non-spiking retinal cone model. We show that there is a restricted range of ion conductance values for which the behavior and phenotype of the neuron are maintained. Finally, we discuss the implications of the phenotypic changes of individual cells at the level of neuronal network functioning of the C. elegans worm and the retina, which are two non-spiking nervous tissues composed of neurons with various phenotypes.

Neuron populations use variable combinations of short-term feedback mechanisms to stabilize firing rate

Neurons tightly regulate firing rate and a failure to do so leads to multiple neurological disorders. Therefore, a fundamental question in neuroscience is how neurons produce reliable activity patterns for decades to generate behavior. Neurons have built-in feedback mechanisms that allow them to monitor their output and rapidly stabilize firing rate. Most work emphasizes the role of a dominant feedback system within a neuronal population for the control of moment-to-moment firing. In contrast, we find that respiratory motoneurons use 2 activity-dependent controllers in unique combinations across cells, dynamic activation of an Na+ pump subtype, and rapid potentiation of Kv7 channels. Both systems constrain firing rate by reducing excitability for up to a minute after a burst of action potentials but are recruited by different cellular signals associated with activity, increased intracellular Na+ (the Na+ pump), and membrane depolarization (Kv7 channels). Individual neurons do not simply contain equal amounts of each system. Rather, neurons under strong control of the Na+ pump are weakly regulated by Kv7 enhancement and vice versa along a continuum. Thus, each motoneuron maintains its characteristic firing rate through a unique combination of the Na+ pump and Kv7 channels, which are dynamically regulated by distinct feedback signals. These results reveal a new organizing strategy for stable circuit output involving multiple fast activity sensors scaled inversely across a neuronal population.

Distinct Mechanisms Underlie Electrical Coupling Resonance and Its Interaction with Membrane Potential Resonance

Neurons in oscillatory networks often exhibit membrane potential resonance, a peak impedance at a non-zero input frequency. In electrically coupled oscillatory networks, the coupling coefficient (the ratio of post- and prejunctional voltage responses) could also show resonance. Such coupling resonance may emerge from the interaction between the coupling current and resonance properties of the coupled neurons, but this relationship has not been clearly described. Additionally, it is unknown if the gap-junction mediated electrical coupling conductance may have frequency dependence. We examined these questions by recording a pair of electrically coupled neurons in the oscillatory pyloric network of the crab Cancer borealis. We performed dual current- and voltage-clamp recordings and quantified the frequency preference of the coupled neurons, the coupling coefficient, the electrical conductance, and the postjunctional neuronal response. We found that all components exhibit frequency selectivity, but with distinct preferred frequencies. Mathematical and computational analysis showed that membrane potential resonance of the postjunctional neuron was sufficient to give rise to resonance properties of the coupling coefficient, but not the coupling conductance. A distinct coupling conductance resonance frequency therefore emerges either from other circuit components or from the gating properties of the gap junctions. Finally, to explore the functional effect of the resonance of the coupling conductance, we examined its role in synchronizing neuronal the activities of electrically coupled bursting model neurons. Together, our findings elucidate factors that produce electrical coupling resonance and the function of this resonance in oscillatory networks.

Models of the cardiac L-type calcium current: A quantitative review

The L-type calcium current (I CaL ) plays a critical role in cardiac electrophysiology, and models ofI CaL are vital tools to predict arrhythmogenicity of drugs and mutations. Five decades of measuring and modelingI CaL have resulted in several competing theories (encoded in mathematical equations). However, the introduction of new models has not typically been accompanied by a data-driven critical comparison with previous work, so that it is unclear which model is best suited for any particular application. In this review, we describe and compare 73 published mammalianI CaL models and use simulated experiments to show that there is a large variability in their predictions, which is not substantially diminished when grouping by species or other categories. We provide model code for 60 models, list major data sources, and discuss experimental and modeling work that will be required to reduce this huge list of competing theories and ultimately develop a community consensus model ofI CaL . This article is categorized under: Cardiovascular Diseases > Computational Models Cardiovascular Diseases > Molecular and Cellular Physiology.

Electrophysiological heterogeneity in large populations of rabbit ventricular cardiomyocytes

AIMS

Cardiac electrophysiological heterogeneity includes: (i) regional differences in action potential (AP) waveform, (ii) AP waveform differences in cells isolated from a single region, (iii) variability of the contribution of individual ion currents in cells with similar AP durations (APDs). The aim of this study is to assess intra-regional AP waveform differences, to quantify the contribution of specific ion channels to the APD via drug responses and to generate a population of mathematical models to investigate the mechanisms underlying heterogeneity in rabbit ventricular cells.

METHODS AND RESULTS

APD in ∼50 isolated cells from subregions of the LV free wall of rabbit hearts were measured using a voltage-sensitive dye. When stimulated at 2 Hz, average APD90 value in cells from the basal epicardial region was 254 ± 25 ms (mean ± standard deviation) in 17 hearts with a mean interquartile range (IQR) of 53 ± 17 ms. Endo-epicardial and apical-basal APD90 differences accounted for ∼10% of the IQR value. Highly variable changes in APD occurred after IK(r) or ICa(L) block that included a sub-population of cells (HR) with an exaggerated (hyper) response to IK(r) inhibition. A set of 4471 AP models matching the experimental APD90 distribution was generated from a larger population of models created by random variation of the maximum conductances (Gmax) of 8 key ion channels/exchangers/pumps. This set reproduced the pattern of cell-specific responses to ICa(L) and IK(r) block, including the HR sub-population. The models exhibited a wide range of Gmax values with constrained relationships linking ICa(L) with IK(r), ICl, INCX, and INaK.

CONCLUSION

Modelling the measured range of inter-cell APDs required a larger range of key Gmax values indicating that ventricular tissue has considerable inter-cell variation in channel/pump/exchanger activity. AP morphology is retained by relationships linking specific ionic conductances. These interrelationships are necessary for stable repolarization despite large inter-cell variation of individual conductances and this explains the variable sensitivity to ion channel block.

Energy-efficient network activity from disparate circuit parameters

Neural circuits can produce similar activity patterns from vastly different combinations of channel and synaptic conductances. These conductances are tuned for specific activity patterns but might also reflect additional constraints, such as metabolic cost or robustness to perturbations. How do such constraints influence the range of permissible conductances? Here we investigate how metabolic cost affects the parameters of neural circuits with similar activity in a model of the pyloric network of the crab Cancer borealis . We present a machine learning method that can identify a range of network models that generate activity patterns matching experimental data and find that neural circuits can consume largely different amounts of energy despite similar circuit activity. Furthermore, a reduced but still significant range of circuit parameters gives rise to energy-efficient circuits. We then examine the space of parameters of energy-efficient circuits and identify potential tuning strategies for low metabolic cost. Finally, we investigate the interaction between metabolic cost and temperature robustness. We show that metabolic cost can vary across temperatures but that robustness to temperature changes does not necessarily incur an increased metabolic cost. Our analyses show that despite metabolic efficiency and temperature robustness constraining circuit parameters, neural systems can generate functional, efficient, and robust network activity with widely disparate sets of conductances.

Multiple intrinsic membrane properties are modulated in a switch from single- to dual-network activity

Neural network flexibility includes changes in neuronal participation between networks, such as the switching of neurons between single- and dual-network activity. We previously identified a neuron that is recruited to burst in time with an additional network via modulation of its intrinsic membrane properties, instead of being recruited synaptically into the second network. However, the modulated intrinsic properties were not determined. Here, we use small networks in the Jonah crab (Cancer borealis) stomatogastric nervous system (STNS) to examine modulation of intrinsic properties underlying neuropeptide (Gly1-SIFamide)-elicited neuronal switching. The lateral posterior gastric neuron (LPG) switches from exclusive participation in the fast pyloric (∼1 Hz) network, due to electrical coupling, to dual-network activity that includes periodic escapes from the fast rhythm via intrinsically generated oscillations at the slower gastric mill network frequency (∼0.1 Hz). We isolated LPG from both networks by pharmacology and hyperpolarizing current injection. Gly1-SIFamide increased LPG intrinsic excitability and rebound from inhibition and decreased spike frequency adaptation, which can all contribute to intrinsic bursting. Using ion substitution and channel blockers, we found that a hyperpolarization-activated current, a persistent sodium current, and calcium or calcium-related current(s) appear to be primary contributors to Gly1-SIFamide-elicited LPG intrinsic bursting. However, this intrinsic bursting was more sensitive to blocking currents when LPG received rhythmic electrical coupling input from the fast network than in the isolated condition. Overall, a switch from single- to dual-network activity can involve modulation of multiple intrinsic properties, while synaptic input from a second network can shape the contributions of these properties.NEW & NOTEWORTHY Neuropeptide-elicited intrinsic bursting was recently determined to switch a neuron from single- to dual-network participation. Here we identified multiple intrinsic properties modulated in the dual-network state and candidate ion channels underlying the intrinsic bursting. Bursting at the second network frequency was more sensitive to blocking currents in the dual-network state than when neurons were synaptically isolated from their home network. Thus, synaptic input can shape the contributions of modulated intrinsic properties underlying dual-network activity.

From synapses to circuits and back: Bridging levels of understanding in animal models of Alzheimer's disease

Alzheimer's disease (AD) is a neurodegenerative disorder characterized by behavioural changes that include memory loss and cognitive decline and is associated with the appearance of amyloid-β plaques and neurofibrillary tangles throughout the brain. Although aspects of the disease percolate across multiple levels of neuronal organization, from the cellular to the behavioural, it is increasingly clear that circuits are a critical junction between the cellular pathology and the behavioural phenotypes that bookend these levels of analyses. In this review, we discuss critical aspects of neural circuit research, beginning with synapses and progressing to network activity and how they influence our understanding of disease processed in AD.

Multimodal parameter spaces of a complex multi-channel neuron model

One of the most common types of models that helps us to understand neuron behavior is based on the Hodgkin-Huxley ion channel formulation (HH model). A major challenge with inferring parameters in HH models is non-uniqueness: many different sets of ion channel parameter values produce similar outputs for the same input stimulus. Such phenomena result in an objective function that exhibits multiple modes (i.e., multiple local minima). This non-uniqueness of local optimality poses challenges for parameter estimation with many algorithmic optimization techniques. HH models additionally have severe non-linearities resulting in further challenges for inferring parameters in an algorithmic fashion. To address these challenges with a tractable method in high-dimensional parameter spaces, we propose using a particular Markov chain Monte Carlo (MCMC) algorithm, which has the advantage of inferring parameters in a Bayesian framework. The Bayesian approach is designed to be suitable for multimodal solutions to inverse problems. We introduce and demonstrate the method using a three-channel HH model. We then focus on the inference of nine parameters in an eight-channel HH model, which we analyze in detail. We explore how the MCMC algorithm can uncover complex relationships between inferred parameters using five injected current levels. The MCMC method provides as a result a nine-dimensional posterior distribution, which we analyze visually with solution maps or landscapes of the possible parameter sets. The visualized solution maps show new complex structures of the multimodal posteriors, and they allow for selection of locally and globally optimal value sets, and they visually expose parameter sensitivities and regions of higher model robustness. We envision these solution maps as enabling experimentalists to improve the design of future experiments, increase scientific productivity and improve on model structure and ideation when the MCMC algorithm is applied to experimental data.

Structural variation between neuropeptide isoforms affects function in the lobster cardiac system

Neuronal responses to peptide signaling are determined by the specific binding of a peptide to its receptor(s). For example, isoforms of the same peptide family can drive distinct responses in the same circuit by having different affinities for the same receptor, by having each isoform bind to a different receptor, or by a combination of these scenarios. Small changes in peptide composition can alter the binding kinetics and overall physiological response to a given peptide. In the American lobster (Homarus americanus), native isoforms of C-type allatostatins (AST-Cs) usually decrease heartbeat frequency and alter contraction force. However, one of the three AST-C isoforms, AST-C II, drives a cardiac response distinct from the response elicited by the other two. To investigate the aspects of the peptide that might be responsible for these differential responses, we altered various features of each peptide sequence. Although the presence of an amide group at the end of a peptide sequence (amidation) is often essential for determining physiological function, we demonstrate that C-terminal amidation does not dictate the AST-C response in the lobster cardiac system. However, single amino acid substitution within the consensus sequence did account for many of the differences in specific response characteristics (e.g. contraction frequency or force).

Excitatory and inhibitory neural dynamics jointly tune motion detection

Neurons integrate excitatory and inhibitory signals to produce their outputs, but the role of input timing in this integration remains poorly understood. Motion detection is a paradigmatic example of this integration, since theories of motion detection rely on different delays in visual signals. These delays allow circuits to compare scenes at different times to calculate the direction and speed of motion. Different motion detection circuits have different velocity sensitivity, but it remains untested how the response dynamics of individual cell types drive this tuning. Here, we sped up or slowed down specific neuron types in Drosophila's motion detection circuit by manipulating ion channel expression. Altering the dynamics of individual neuron types upstream of motion detectors increased their sensitivity to fast or slow visual motion, exposing distinct roles for excitatory and inhibitory dynamics in tuning directional signals, including a role for the amacrine cell CT1. A circuit model constrained by functional data and anatomy qualitatively reproduced the observed tuning changes. Overall, these results reveal how excitatory and inhibitory dynamics together tune a canonical circuit computation.

Repeated applications of high potassium elicit long-term changes in a motor circuit from the crab, Cancer borealis

We examined the effects of altered extracellular potassium concentration on the output of the well-studied pyloric circuit in the crab, Cancer borealis. Pyloric neurons initially become quiescent, then recover spiking and bursting activity in high potassium saline (2.5x[K⁺]). These changes in circuit robustness are maintained after the perturbation is removed; pyloric neurons are more robust to subsequent potassium perturbations even after several hours of wash in control saline. Despite this long-term "memory" of the stimulus history, we found no differences in neuronal activity in control saline. The circuit's adaptation is erased by both low potassium saline (0.4x[K⁺]) and direct hyperpolarizing current. Initial sensitivity of PD neurons to high potassium saline also varies seasonally, indicating that changes in robustness may reflect natural changes in circuit states. Thus, perturbation, followed by recovery of normal activity, can hide cryptic changes in neuronal properties that are only revealed by subsequent challenges.

Neuromodulation reduces interindividual variability of neuronal output

In similar states, neural circuits produce similar outputs across individuals despite substantial interindividual variability in neuronal ionic conductances and synapses. Circuit states are largely shaped by neuromodulators that tune ionic conductances. It is therefore possible that, in addition to producing flexible circuit output, neuromodulators also contribute to output similarity despite varying ion channel expression. We studied whether neuromodulation at saturating concentrations can increase the output similarity of a single identified neuron across individual animals. Using the LP neuron of the crab stomatogastric ganglion (STG), we compared the variability of f-I curves and rebound properties in the presence of neuropeptides. The two neuropeptides we used converge to activate the same target current, which increases neuronal excitability. Output variability was lower in the presence of the neuropeptides, regardless of whether the neuropeptides significantly changed the mean of the corresponding parameter or not. However, the addition of the second neuropeptide did not add further to the reduction of variability. With a family of computational LP-like models, we explored how increased excitability and target variability contribute to output similarity and found two mechanisms: Saturation of the responses and a differential increase in baseline activity. Saturation alone can reduce the interindividual variability only if the population shares a similar ceiling for the responses. In contrast, reduction of variability due to the increase in baseline activity is independent of ceiling effects.Significance StatementThe activity of single neurons and neural circuits can be very similar across individuals even though the ionic currents underlying activity are variable. The mechanisms that compensate for the underlying variability and promote output similarity are poorly understood but may involve neuromodulation. Using an identified neuron, we show that neuropeptide modulation of excitability can reduce interindividual variability of response properties at a single-neuron level in two ways. First, the neuropeptide increases baseline excitability in a differential manner, resulting in similar response thresholds. Second, the neuropeptide increases excitability towards a shared saturation level, promoting similar maximal firing rates across individuals. Such tuning of neuronal excitability could be an important mechanism compensating for interindividual variability of ion channel expression.

Combining hypothesis- and data-driven neuroscience modeling in FAIR workflows

Modeling in neuroscience occurs at the intersection of different points of view and approaches. Typically, hypothesis-driven modeling brings a question into focus so that a model is constructed to investigate a specific hypothesis about how the system works or why certain phenomena are observed. Data-driven modeling, on the other hand, follows a more unbiased approach, with model construction informed by the computationally intensive use of data. At the same time, researchers employ models at different biological scales and at different levels of abstraction. Combining these models while validating them against experimental data increases understanding of the multiscale brain. However, a lack of interoperability, transparency, and reusability of both models and the workflows used to construct them creates barriers for the integration of models representing different biological scales and built using different modeling philosophies. We argue that the same imperatives that drive resources and policy for data - such as the FAIR (Findable, Accessible, Interoperable, Reusable) principles - also support the integration of different modeling approaches. The FAIR principles require that data be shared in formats that are Findable, Accessible, Interoperable, and Reusable. Applying these principles to models and modeling workflows, as well as the data used to constrain and validate them, would allow researchers to find, reuse, question, validate, and extend published models, regardless of whether they are implemented phenomenologically or mechanistically, as a few equations or as a multiscale, hierarchical system. To illustrate these ideas, we use a classical synaptic plasticity model, the Bienenstock-Cooper-Munro rule, as an example due to its long history, different levels of abstraction, and implementation at many scales.

Combining Old and New Tricks: The Study of Genes, Neurons, and Behavior in Crayfish

For over a century the nervous system of decapod crustaceans has been a workhorse for the neurobiology community. Many fundamental discoveries including the identification of electrical and inhibitory synapses, lateral and pre-synaptic inhibition, and the Na⁺/K⁺-pump were made using lobsters, crabs, or crayfish. Key among many advantages of crustaceans for neurobiological research is the unique access to large, accessible, and identifiable neurons, and the many distinct and complex behaviors that can be observed in lab settings. Despite these advantages, recent decades have seen work on crustaceans hindered by the lack of molecular and genetic tools required for unveiling the cellular processes contributing to neurophysiology and behavior. In this perspective paper, we argue that the recently sequenced marbled crayfish, Procambarus virginalis, is suited to become a genetic model system for crustacean neuroscience. P. virginalis are parthenogenetic and produce genetically identical offspring, suggesting that germline transformation creates transgenic animal strains that are easy to maintain across generations. Like other decapod crustaceans, marbled crayfish possess large neurons in well-studied circuits such as the giant tail flip neurons and central pattern generating neurons in the stomatogastric ganglion. We provide initial data demonstrating that marbled crayfish neurons are accessible through standard physiological and molecular techniques, including single-cell electrophysiology, gene expression measurements, and RNA-interference. We discuss progress in CRISPR-mediated manipulations of the germline to knock-out target genes using the ‘Receptor-mediated ovary transduction of cargo’ (ReMOT) method. Finally, we consider the impact these approaches will have for neurophysiology research in decapod crustaceans and more broadly across invertebrates.

Initial Variability and Time-Dependent Changes of Neuronal Response Features Are Cell-Type-Specific

Different cell types are commonly defined by their distinct response features. But several studies proved substantial variability between cells of the same type, suggesting rather the appraisal of response feature distributions than a limitation to "typical" responses. Moreover, there is growing evidence that time-dependent changes of response features contribute to robust and functional network output in many neuronal systems. The individually characterized Touch (T), Pressure (P), and Retzius (Rz) cells in the medicinal leech allow for a rigid analysis of response features, elucidating differences between and variability within cell types, as well as their changes over time. The initial responses of T and P cells to somatic current injection cover a wide range of spike counts, and their first spike is generated with a high temporal precision after a short latency. In contrast, all Rz cells elicit very similar low spike counts with variable, long latencies. During prolonged electrical stimulation the resting membrane potential of all three cell types hyperpolarizes. At the same time, Rz cells reduce their spiking activity as expected for a departure from the spike threshold. In contrast, both mechanoreceptor types increase their spike counts during repeated stimulation, consistent with previous findings in T cells. A control experiment reveals that neither a massive current stimulation nor the hyperpolarization of the membrane potential is necessary for the mechanoreceptors' increase in excitability over time. These findings challenge the previously proposed involvement of slow K+-channels in the time-dependent activity changes. We also find no indication for a run-down of HCN channels over time, and a rigid statistical analysis contradicts several potential experimental confounders as the basis of the observed variability. We conclude that the time-dependent change in excitability of T and P cells could indicate a cell-type-specific shift between different spiking regimes, which also could explain the high variability in the initial responses. The underlying mechanism needs to be further investigated in more naturalistic experimental situations to disentangle the effects of varying membrane properties versus network interactions. They will show if variability in individual response features serves as flexible adaptation to behavioral contexts rather than just "randomness".

Neuromodulation Enables Temperature Robustness and Coupling Between Fast and Slow Oscillator Circuits

Acute temperature changes can disrupt neuronal activity and coordination with severe consequences for animal behavior and survival. Nonetheless, two rhythmic neuronal circuits in the crustacean stomatogastric ganglion (STG) and their coordination are maintained across a broad temperature range. However, it remains unclear how this temperature robustness is achieved. Here, we dissociate temperature effects on the rhythm generating circuits from those on upstream ganglia. We demonstrate that heat-activated factors extrinsic to the rhythm generators are essential to the slow gastric mill rhythm’s temperature robustness and contribute to the temperature response of the fast pyloric rhythm. The gastric mill rhythm crashed when its rhythm generator in the STG was heated. It was restored when upstream ganglia were heated and temperature-matched to the STG. This also increased the activity of the peptidergic modulatory projection neuron (MCN1), which innervates the gastric mill circuit. Correspondingly, MCN1’s neuropeptide transmitter stabilized the rhythm and maintained it over a broad temperature range. Extrinsic neuromodulation is thus essential for the oscillatory circuits in the STG and enables neural circuits to maintain function in temperature-compromised conditions. In contrast, integer coupling between pyloric and gastric mill rhythms was independent of whether extrinsic inputs and STG pattern generators were temperature-matched or not, demonstrating that the temperature robustness of the coupling is enabled by properties intrinsic to the rhythm generators. However, at near-crash temperature, integer coupling was maintained only in some animals while it was absent in others. This was true despite regular rhythmic activity in all animals, supporting that degenerate circuit properties result in idiosyncratic responses to environmental challenges.

Mapping circuit dynamics during function and dysfunction

Neural circuits can generate many spike patterns, but only some are functional. The study of how circuits generate and maintain functional dynamics is hindered by a poverty of description of circuit dynamics across functional and dysfunctional states. For example, although the regular oscillation of a central pattern generator is well characterized by its frequency and the phase relationships between its neurons, these metrics are ineffective descriptors of the irregular and aperiodic dynamics that circuits can generate under perturbation or in disease states. By recording the circuit dynamics of the well-studied pyloric circuit in Cancer borealis, we used statistical features of spike times from neurons in the circuit to visualize the spike patterns generated by this circuit under a variety of conditions. This approach captures both the variability of functional rhythms and the diversity of atypical dynamics in a single map. Clusters in the map identify qualitatively different spike patterns hinting at different dynamic states in the circuit. State probability and the statistics of the transitions between states varied with environmental perturbations, removal of descending neuromodulatory inputs, and the addition of exogenous neuromodulators. This analysis reveals strong mechanistically interpretable links between complex changes in the collective behavior of a neural circuit and specific experimental manipulations, and can constrain hypotheses of how circuits generate functional dynamics despite variability in circuit architecture and environmental perturbations.

Minimal requirements for a neuron to co-regulate many properties and the implications for ion channel correlations and robustness

Neurons regulate their excitability by adjusting their ion channel levels. Degeneracy – achieving equivalent outcomes (excitability) using different solutions (channel combinations) – facilitates this regulation by enabling a disruptive change in one channel to be offset by compensatory changes in other channels. But neurons must coregulate many properties. Pleiotropy – the impact of one channel on more than one property – complicates regulation because a compensatory ion channel change that restores one property to its target value often disrupts other properties. How then does a neuron simultaneously regulate multiple properties? Here, we demonstrate that of the many channel combinations producing the target value for one property (the single-output solution set), few combinations produce the target value for other properties. Combinations producing the target value for two or more properties (the multioutput solution set) correspond to the intersection between single-output solution sets. Properties can be effectively coregulated only if the number of adjustable channels (n_in) exceeds the number of regulated properties (n_out). Ion channel correlations emerge during homeostatic regulation when the dimensionality of solution space (n_in − n_out) is low. Even if each property can be regulated to its target value when considered in isolation, regulation as a whole fails if single-output solution sets do not intersect. Our results also highlight that ion channels must be coadjusted with different ratios to regulate different properties, which suggests that each error signal drives modulatory changes independently, despite those changes ultimately affecting the same ion channels.

Mating-driven variability in olfactory local interneuron wiring

Variations in neuronal connectivity occur widely in nervous systems from invertebrates to mammals. Yet, it is unclear how neuronal variability originates, to what extent and at what time scales it exists, and what functional consequences it might carry. To assess inter- and intraindividual neuronal variability, it would be ideal to analyze the same identified neuron across different brain hemispheres and individuals. Here, using genetic labeling and electron microscopy connectomics, we show that an identified inhibitory olfactory local interneuron, TC-LN, exhibits extraordinary variability in its glomerular innervation patterns. Moreover, TC-LN's innervation of the VL2a glomerulus, which processes food signals and modulates mating behavior, is sexually dimorphic, is influenced by female's courtship experience, and correlates with food intake in mated females. Mating also affects output connectivity of TC-LN to specific local interneurons. We propose that mating-associated variability of TC-LNs regulates how food odor is interpreted by an inhibitory network to modulate feeding.

Reciprocally inhibitory circuits operating with distinct mechanisms are differently robust to perturbation and modulation

Reciprocal inhibition is a building block in many sensory and motor circuits. We studied the features that underly robustness in reciprocally inhibitory two neuron circuits. We used the dynamic clamp to create reciprocally inhibitory circuits from pharmacologically isolated neurons of the crab stomatogastric ganglion by injecting artificial graded synaptic (I_Syn) and hyperpolarization-activated inward (I_H) currents. There is a continuum of mechanisms in circuits that generate antiphase oscillations, with ‘release’ and ‘escape’ mechanisms at the extremes, and mixed mode oscillations between these extremes. In release, the active neuron primarily controls the off/on transitions. In escape, the inhibited neuron controls the transitions. We characterized the robustness of escape and release circuits to alterations in circuit parameters, temperature, and neuromodulation. We found that escape circuits rely on tight correlations between synaptic and H conductances to generate bursting but are resilient to temperature increase. Release circuits are robust to variations in synaptic and H conductances but fragile to temperature increase. The modulatory current (I_MI) restores oscillations in release circuits but has little effect in escape circuits. Perturbations can alter the balance of escape and release mechanisms and can create mixed mode oscillations. We conclude that the same perturbation can have dramatically different effects depending on the circuits’ mechanism of operation that may not be observable from basal circuit activity.

Sensitivity to Envelope Interaural Time Differences: Modeling Auditory Modulation Filtering

For amplitude-modulated sound, the envelope interaural time difference (ITD_ENV) is a potential cue for sound-source location. ITD_ENV is encoded in the lateral superior olive (LSO) of the auditory brainstem, by excitatory-inhibitory (EI) neurons receiving ipsilateral excitation and contralateral inhibition. Between human listeners, sensitivity to ITD_ENV varies considerably, but ultimately decreases with increasing stimulus carrier frequency, and decreases more strongly with increasing modulation rate. Mechanisms underlying the variation in behavioral sensitivity remain unclear. Here, with increasing carrier frequency (4-10 kHz), as we phenomenologically model the associated decrease in ITD_ENV sensitivity using arbitrarily fewer neurons consistent across populations, we computationally model the variable sensitivity across human listeners and modulation rates (32-800 Hz) as the decreasing range of membrane frequency responses in LSO neurons. Transposed tones stimulate a bilateral auditory-periphery model, driving model EI neurons where electrical membrane impedance filters the frequency content of inputs driven by amplitude-modulated sound, evoking modulation filtering. Calculated from Fisher information in spike-rate functions of ITD_ENV, for model EI neuronal populations distinctly reflecting the LSO range in membrane frequency responses, just-noticeable differences in ITD_ENV collectively reproduce the largest variation in ITD_ENV sensitivity across human listeners. These slow to fast model populations each generally match the best human ITD_ENV sensitivity at a progressively higher modulation rate, by membrane-filtering and spike-generation properties producing realistically less than Poisson variance. Non-resonant model EI neurons are also sensitive to interaural intensity differences. With peripheral filters centered between carrier frequency and modulation sideband, fast resonant model EI neurons extend ITD_ENV sensitivity above 500-Hz modulation.

A population of in silico models identifies the interplay between Nav 1.8 conductance and potassium currents as key in regulating human dorsal root ganglion neuron excitability

Background: The Nav 1.8 sodium channel has a key role in generating repetitive action potentials in nociceptive human dorsal root ganglion neurons. Nav 1.8 is differentiated from other voltage-gated sodium channels by its unusually slow inactivation kinetics and depolarised voltage-dependence of activation. These features are particularly pronounced in the human Nav 1.8 channel and allow the channel to remain active during repolarisation. Gain-of-function mutations in Nav 1.8 have been linked to neuropathic pain and selective blockers of Nav 1.8 have been developed as potential new analgesics. However, it is not well understood how modulating the Nav 1.8 conductance alters neuronal excitability and how this depends on the balance of other ion channels expressed by nociceptive neurons. Methods: To investigate this, we developed a novel computational model of the human dorsal root ganglion neuron and used it to construct a population of models that mimicked inter-neuronal heterogeneity in ionic conductances and action potential morphology Results: By simulating changes to the Nav 1.8 conductance in the population of models, we found that moderately increasing the Nav 1.8 conductance led to increased firing rate, as expected, but increasing Nav 1.8 conductance beyond an inflection point caused firing rate to decrease. We found that the delayed rectifier and M-type potassium conductances were also critical for determining neuronal excitability. In particular, altering the delayed rectifier potassium conductance shifted the position of the Nav 1.8 inflection point and therefore the relationship between Nav 1.8 conductance and firing rate. Conclusions: Our results suggest that the effects of modulating Nav 1.8 in a nociceptive neuron can depend significantly on other conductances, particularly potassium conductances.

Women in Neuroscience: Four Women’s Contributions to Science and Society

There has been increased cognizance of gender inequity and the importance of an inclusive and diverse approach to scientific research in recent years. However, the innovative work of women scientists is still undervalued based on reports of fewer women in leadership positions, limited citations of research spearheaded by women, reduced federal grant awards, and lack of recognition. Women have been involved in trailblazing work that paved the way for contemporary scientific inquiry. The strides made in current neuroscience include contributions from women who deserve more recognition. In this review, we discuss the work of four women whose groundbreaking scientific work has made ineffaceable marks in the neuroscience field. These women are pioneers of research and innovators and, in addition, contribute to positive change that bolsters the academic community and society. This article celebrates these women scientists, their substantial impacts in neuroscience, and the positive influence of their work on advancing society and culture.

Transient and Steady-State Properties of Drosophila Sensory Neurons Coding Noxious Cold Temperature

Coding noxious cold signals, such as the magnitude and rate of temperature change, play essential roles in the survival of organisms. We combined electrophysiological and computational neuroscience methods to investigate the neural dynamics of Drosophila larva cold-sensing Class III (CIII) neurons. In response to a fast temperature change (-2 to -6°C/s) from room temperature to noxious cold, the CIII neurons exhibited a pronounced peak of a spiking rate with subsequent relaxation to a steady-state spiking. The magnitude of the peak was higher for a higher rate of temperature decrease, while slow temperature decrease (-0.1°C/s) evoked no distinct peak of the spiking rate. The rate of the steady-state spiking depended on the magnitude of the final temperature and was higher at lower temperatures. For each neuron, we characterized this dependence by estimating the temperature of the half activation of the spiking rate by curve fitting neuron's spiking rate responses to a Boltzmann function. We found that neurons had a temperature of the half activation distributed over a wide temperature range. We also found that CIII neurons responded to decrease rather than increase in temperature. There was a significant difference in spiking activity between fast and slow returns from noxious cold to room temperature: The CIII neurons usually stopped activity abruptly in the case of the fast return and continued spiking for some time in the case of the slow return. We developed a biophysical model of CIII neurons using a generalized description of transient receptor potential (TRP) current kinetics with temperature-dependent activation and Ca²⁺-dependent inactivation. This model recapitulated the key features of the spiking rate responses found in experiments and suggested mechanisms explaining the transient and steady-state activity of the CIII neurons at different cold temperatures and rates of their decrease and increase. We conclude that CIII neurons encode at least three types of cold sensory information: the rate of temperature decrease by a peak of the firing rate, the magnitude of cold temperature by the rate of steady spiking activity, and direction of temperature change by spiking activity augmentation or suppression corresponding to temperature decrease and increase, respectively.

From the Neuroscience of Individual Variability to Climate Change

Years of basic neuroscience on the modulation of the small circuits found in the crustacean stomatogastric ganglion have led us to study the effects of temperature on the motor patterns produced by the stomatogastric ganglion. While the impetus for this work was the study of individual variability in the parameters determining intrinsic and synaptic conductances, we are confronting substantial fluctuations in the stability of the networks to extreme temperature; these may correlate with changes in ocean temperature. Interestingly, when studied under control conditions, these wild-caught animals appear to be unchanged, but it is only when challenged by extreme temperatures that we reveal the consequences of warming oceans.

Compensatory variability in network parameters enhances memory performance in the Drosophila mushroom body

Neural circuits use homeostatic compensation to achieve consistent behavior despite variability in underlying intrinsic and network parameters. However, it remains unclear how compensation regulates variability across a population of the same type of neurons within an individual and what computational benefits might result from such compensation. We address these questions in the Drosophila mushroom body, the fly's olfactory memory center. In a computational model, we show that under sparse coding conditions, memory performance is degraded when the mushroom body's principal neurons, Kenyon cells (KCs), vary realistically in key parameters governing their excitability. However, memory performance is rescued while maintaining realistic variability if parameters compensate for each other to equalize KC average activity. Such compensation can be achieved through both activity-dependent and activity-independent mechanisms. Finally, we show that correlations predicted by our model's compensatory mechanisms appear in the Drosophila hemibrain connectome. These findings reveal compensatory variability in the mushroom body and describe its computational benefits for associative memory.

WNK3 Maintains the GABAergic Inhibitory Tone, Synaptic Excitation and Neuronal Excitability via Regulation of KCC2 Cotransporter in Mature Neurons

The activation of chloride (Cl⁻)permeable gamma (γ)-aminobutyric acid type A(GABA_A) receptors induces synaptic inhibition in mature and excitation in immature neurons. This developmental “switch” in GABA function controlled by its polarity depends on the postnatal decrease in intraneuronal Cl⁻ concentration mediated by KCC2, a member of cation-chloride cotransporters (CCCs). The serine-threonine kinase WNK3 (With No Lysine [K]), is a potent regulator of all CCCs and is expressed in neurons. Here, we characterized the functions of WNK3 and its role in GABAergic signaling in cultured embryonic day 18 (E18) hippocampal neurons. We observed a decrease in WNK3 expression as neurons mature. Knocking down of WNK3 significantly hyperpolarized E_GABA in mature neurons (DIV13–15) but had no effect on immature neurons (DIV6–8). This hyperpolarized E_GABA in WNK3-deficient neurons was not due to the total expression of NKCC1 and KCC2, that remained unchanged. However, there was a reduction in phosphorylated KCC2 at the membrane, suggesting an increase in KCC2 chloride export activity. Furthermore, hyperpolarized E_GABA observed in WNK3-deficient neurons can be reversed by the KCC2 inhibitor, VU024055, thus indicating that WNK3 acts through KCC2 to influence E_GABA. Notably, WNK3 knockdown resulted in morphological changes in mature but not immature neurons. Electrophysiological characterization of WNK3-deficient mature neurons revealed reduced capacitances but increased intrinsic excitability and synaptic excitation. Hence, our study demonstrates that WNK3 maintains the “adult” GABAergic inhibitory tone in neurons and plays a role in the morphological development of neurons and excitability.

Degeneracy in the nervous system: from neuronal excitability to neural coding

Degeneracy is ubiquitous across biological systems where structurally different elements can yield a similar outcome. Degeneracy is of particular interest in neuroscience too. On the one hand, degeneracy confers robustness to the nervous system and facilitates evolvability: Different elements provide a backup plan for the system in response to any perturbation or disturbance. On the other, a difficulty in the treatment of some neurological disorders such as chronic pain is explained in light of different elements all of which contribute to the pathological behavior of the system. Under these circumstances, targeting a specific element is ineffective because other elements can compensate for this modulation. Understanding degeneracy in the physiological context explains its beneficial role in the robustness of neural circuits. Likewise, understanding degeneracy in the pathological context opens new avenues of discovery to find more effective therapies.

Integrative Models of Brain Structure and Dynamics: Concepts, Challenges, and Methods

The anatomical architecture of the brain constrains the dynamics of interactions between various regions. On a microscopic scale, neural plasticity regulates the connections between individual neurons. This microstructural adaptation facilitates coordinated dynamics of populations of neurons (mesoscopic scale) and brain regions (macroscopic scale). However, the mechanisms acting on multiple timescales that govern the reciprocal relationship between neural network structure and its intrinsic dynamics are not well understood. Studies empirically investigating such relationships on the whole-brain level rely on macroscopic measurements of structural and functional connectivity estimated from various neuroimaging modalities such as Diffusion-weighted Magnetic Resonance Imaging (dMRI), Electroencephalography (EEG), Magnetoencephalography (MEG), and functional Magnetic Resonance Imaging (fMRI). dMRI measures the anisotropy of water diffusion along axonal fibers, from which structural connections are estimated. EEG and MEG signals measure electrical activity and magnetic fields induced by the electrical activity, respectively, from various brain regions with a high temporal resolution (but limited spatial coverage), whereas fMRI measures regional activations indirectly via blood oxygen level-dependent (BOLD) signals with a high spatial resolution (but limited temporal resolution). There are several studies in the neuroimaging literature reporting statistical associations between macroscopic structural and functional connectivity. On the other hand, models of large-scale oscillatory dynamics conditioned on network structure (such as the one estimated from dMRI connectivity) provide a platform to probe into the structure-dynamics relationship at the mesoscopic level. Such investigations promise to uncover the theoretical underpinnings of the interplay between network structure and dynamics and could be complementary to the macroscopic level inquiries. In this article, we review theoretical and empirical studies that attempt to elucidate the coupling between brain structure and dynamics. Special attention is given to various clinically relevant dimensions of brain connectivity such as the topological features and neural synchronization, and their applicability for a given modality, spatial or temporal scale of analysis is discussed. Our review provides a summary of the progress made along this line of research and identifies challenges and promising future directions for multi-modal neuroimaging analyses.

Perturbation-specific responses by two neural circuits generating similar activity patterns

A fundamental question in neuroscience is whether neuronal circuits with variable circuit parameters that produce similar outputs respond comparably to equivalent perturbations.^1-4 Work on the pyloric rhythm of the crustacean stomatogastric ganglion (STG) showed that highly variable sets of intrinsic and synaptic conductances can generate similar circuit activity patterns.^5-9 Importantly, in response to physiologically relevant perturbations, these disparate circuit solutions can respond robustly and reliably,^10-12 but when exposed to extreme perturbations the underlying circuit parameter differences produce diverse patterns of disrupted activity.^7,12,13 In this example, the pyloric circuit is unchanged; only the conductance values vary. In contrast, the gastric mill rhythm in the STG can be generated by distinct circuits when activated by different modulatory neurons and/or neuropeptides.^14-21 Generally, these distinct circuits produce different gastric mill rhythms. However, the rhythms driven by stimulating modulatory commissural neuron 1 (MCN1) and bath-applying CabPK (Cancer borealis pyrokinin) peptide generate comparable output patterns, despite having distinct circuits that use separate cellular and synaptic mechanisms.^22-25 Here, we use these two gastric mill circuits to determine whether such circuits respond comparably when challenged with persisting (hormonal: CCAP) or acute (sensory: GPR neuron) metabotropic influences. Surprisingly, the hormone-mediated action separates these two rhythms despite activating the same ionic current in the same circuit neuron during both rhythms, whereas the sensory neuron evokes comparable responses despite acting via different synapses during each rhythm. These results highlight the need for caution when inferring the circuit response to a perturbation when that circuit is not well defined physiologically.