Neuronal oscillator robustness to multiple global perturbations

An unusual potassium conductance protects Caenorhabditis elegans pharyngeal muscle rhythms against environmental noise

The nematode Caenorhabditis elegans feeds by rhythmic contraction and relaxation of a neuromuscular organ called the pharynx, which draws in and filters water and bacterial food. This behavior is driven by myogenic plateau potentials, long-lasting depolarizations of the pharyngeal muscle, which are timed by neuronal input from a dedicated pharyngeal nervous system. While the timing of these plateaus' initiation has received significant attention, their mechanisms of termination remain incompletely understood. In particular, it is unclear how plateaus resist early termination by hyperpolarizing current noise. Here, we present a computational model of pharyngeal plateaus against a noisy background. We propose that an unusual, rapidly inactivating potassium conductance confers exceptional noise robustness on the system. We further investigate the possibility that a similar mechanism in other systems permits switching between plateau and spiking behavior under noisy conditions.

Increased robustness and adaptation to simultaneous temperature and elevated extracellular potassium in the pyloric rhythm of the crab, Cancer borealis

Animals must deal with numerous perturbations, oftentimes concurrently. In this study, we examine the effects of two perturbations, high extracellular potassium and elevated temperature, on the resilience of the pyloric rhythm of the crab, Cancer borealis. At control temperatures (11°C), high potassium saline (2.5× K+) depolarizes the neurons of the stomatogastric ganglion (STG), and the pyloric rhythm becomes quiescent. Over minutes, while remaining depolarized in high potassium, the pyloric network neurons adapt, and resume their spiking and bursting activity. We compared adaptation to high potassium applications at 20°C to those seen at 11°C. At 20°C, the intracellular waveforms of the neuronal activity seen in high potassium more closely resemble activity in control saline, and adaptation and recovery occur more rapidly. Spike and burst thresholds were measured using slow ramps of injected current from hyperpolarized to depolarized values of membrane potential in the presence of high potassium and at both temperatures. The maximal burst frequencies in control saline were higher at 20°C and subthreshold bursts occurred at a more hyperpolarized membrane potential at 20°C. In high potassium, subthreshold bursts were seen at 20°C, but not at 11°C, whereas spike thresholds were similar at the two temperatures. At both temperatures, a second application of high potassium showed substantially more rapid adaptation than did the first application. Together, these data show that the adaptation to high potassium saline is enhanced by high temperature.NEW & NOTEWORTHY Multiple applications of high potassium saline to the pyloric rhythm of the crab, Cancer borealis show a history-dependent adaptation process that is enhanced at high temperatures.

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.

Ion-channel degeneracy and heterogeneities in the emergence of signature physiological characteristics of dentate gyrus granule cells

Complex systems are neither fully determined nor completely random. Biological complex systems, including single neurons, manifest intermediate regimes of randomness that recruit integration of specific combinations of functionally specialized subsystems. Such emergence of biological function provides the substrate for the expression of degeneracy, the ability of disparate combinations of subsystems to yield similar function. Here, we present evidence for the expression of degeneracy in morphologically realistic models of dentate gyrus granule cells (GCs) through functional integration of disparate ion-channel combinations. We performed a 45-parameter randomized search spanning 16 active and passive ion channels, each biophysically constrained by their gating kinetics and localization profiles, to search for valid GC models. Valid models were those that satisfied 17 sub- and suprathreshold cellular-scale electrophysiological measurements from rat GCs. A vast majority (>99%) of the 15,000 random models were not electrophysiologically valid, demonstrating that arbitrarily random ion-channel combinations would not yield GC functions. The 141 valid models (0.94% of 15,000) manifested heterogeneities in and cross-dependencies across local and propagating electrophysiological measurements, which matched with their respective biological counterparts. Importantly, these valid models were widespread throughout the parametric space and manifested weak cross-dependencies across different parameters. These observations together showed that GC physiology could neither be obtained by entirely random ion-channel combinations nor is there an entirely determined single parametric combination that satisfied all constraints. The complexity, the heterogeneities in measurement and parametric spaces, and degeneracy associated with GC physiology should be rigorously accounted for while assessing GCs and their robustness under physiological and pathological conditions.NEW & NOTEWORTHY A recent study from our laboratory had demonstrated pronounced heterogeneities in a set of 17 electrophysiological measurements obtained from a large population of rat hippocampal granule cells. Here, we demonstrate the manifestation of ion-channel degeneracy in a heterogeneous population of morphologically realistic conductance-based granule cell models that were validated against these measurements and their cross-dependencies. Our analyses show that single neurons are complex entities whose functions emerge through intricate interactions among several functionally specialized subsystems.

Resilience of circuits to environmental challenge

Animals of all kinds evolved to deal with anticipated and unanticipated changes in a variety of features in their environments. Consequently, all environmental perturbations, adaptations, and acclimation involve a myriad of factors that, together, contribute to environmental resilience. New work highlights the importance of neuromodulation in the control of environmental resilience, and illustrates that different components of the nervous system may be differentially resilient to environmental perturbations. Climate change is today pushing animals to deal with previously unanticipated environmental challenges, and therefore understanding the complex biology of adaptation and acclimation to various environmental conditions takes on new urgency.

Alterations in network robustness upon simultaneous temperature and pH perturbations

Nervous systems have evolved to function consistently in the face of the normal environmental fluctuations experienced by animals. The stomatogastric nervous system (STNS) of the crab, Cancer borealis, produces a motor output that has been studied for its remarkable robustness in response to single global perturbations. Changes in environments, however, are often complex and multifactorial. Therefore, we studied the robustness of the pyloric network in the stomatogastric ganglion (STG) in response to simultaneous perturbations of temperature and pH. We compared the effects of elevated temperatures on the pyloric rhythm at control, acid, or base pHs. In each pH recordings were made at 11°C, and then the temperature was increased until the rhythms became disorganized ("crashed"). Pyloric burst frequencies and phase relationships showed minor differences between pH groups until reaching close to the crash temperatures. However, the temperatures at which the rhythms were disrupted were lower in the two extreme pH conditions. This indicates that one environmental stress can make an animal less resilient to a second stressor.NEW & NOTEWORTHY Resilience to environmental fluctuations is important for all animals. It is common that animals encounter multiple stressful events at the same time, the cumulative impacts of which are largely unknown. This study examines the effects of temperature and pH on the nervous system of crabs that live in the fluctuating environments of the Northern Atlantic Ocean. The ranges of tolerance to one perturbation, temperature, are reduced under the influence of a second, pH.

Contribution of membrane-associated oscillators to biological timing at different timescales

Environmental rhythms such as the daily light-dark cycle selected for endogenous clocks. These clocks predict regular environmental changes and provide the basis for well-timed adaptive homeostasis in physiology and behavior of organisms. Endogenous clocks are oscillators that are based on positive feedforward and negative feedback loops. They generate stable rhythms even under constant conditions. Since even weak interactions between oscillators allow for autonomous synchronization, coupling/synchronization of oscillators provides the basis of self-organized physiological timing. Amongst the most thoroughly researched clocks are the endogenous circadian clock neurons in mammals and insects. They comprise nuclear clockworks of transcriptional/translational feedback loops (TTFL) that generate ∼24 h rhythms in clock gene expression entrained to the environmental day-night cycle. It is generally assumed that this TTFL clockwork drives all circadian oscillations within and between clock cells, being the basis of any circadian rhythm in physiology and behavior of organisms. Instead of the current gene-based hierarchical clock model we provide here a systems view of timing. We suggest that a coupled system of autonomous TTFL and posttranslational feedback loop (PTFL) oscillators/clocks that run at multiple timescales governs adaptive, dynamic homeostasis of physiology and behavior. We focus on mammalian and insect neurons as endogenous oscillators at multiple timescales. We suggest that neuronal plasma membrane-associated signalosomes constitute specific autonomous PTFL clocks that generate localized but interlinked oscillations of membrane potential and intracellular messengers with specific endogenous frequencies. In each clock neuron multiscale interactions of TTFL and PTFL oscillators/clocks form a temporally structured oscillatory network with a common complex frequency-band comprising superimposed multiscale oscillations. Coupling between oscillator/clock neurons provides the next level of complexity of an oscillatory network. This systemic dynamic network of molecular and cellular oscillators/clocks is suggested to form the basis of any physiological homeostasis that cycles through dynamic homeostatic setpoints with a characteristic frequency-band as hallmark. We propose that mechanisms of homeostatic plasticity maintain the stability of these dynamic setpoints, whereas Hebbian plasticity enables switching between setpoints via coupling factors, like biogenic amines and/or neuropeptides. They reprogram the network to a new common frequency, a new dynamic setpoint. Our novel hypothesis is up for experimental challenge.

Oscillatory network spontaneously recovers both activity and robustness after prolonged removal of neuromodulators

Robustness of neuronal activity is a property necessary for a neuronal network to withstand perturbations, which may otherwise disrupt or destroy the system. The robustness of complex systems has been shown to depend on a number of features of the system, including morphology and heterogeneity of the activity of the component neurons, size of the networks, synaptic connectivity, and neuromodulation. The activity of small networks, such as the pyloric network of the crustacean stomatogastric nervous system, appears to be robust despite some of the factors not being consistent with the expected properties of complex systems, e.g., small size and homogeneity of the synaptic connections. The activity of the pyloric network has been shown to be stable and robust in a neuromodulatory state-dependent manner. When neuromodulatory inputs are severed, activity is initially disrupted, losing both stability and robustness. Over the long term, however, stable activity homeostatically recovers without the restoration of neuromodulatory input. The question we address in this study is whether robustness can also be restored as the network reorganizes itself to compensate for the loss of neuromodulatory input and recovers the lost activity. Here, we use temperature changes as a perturbation to probe the robustness of the network's activity. We develop a simple metric of robustness, i.e., the variances of the network phase relationships, and show that robustness is indeed restored simultaneously along with its stable network activity, indicating that, whatever the reorganization of the network entails, it is deep enough also to restore this important property.

Neurobiology and Changing Ecosystems: Mechanisms Underlying Responses to Human-Generated Environmental Impacts

Human generated environmental change profoundly affects organisms that reside across diverse ecosystems. Although nervous systems evolved to flexibly sense, respond, and adapt to environmental change, it is unclear whether the rapid rate of environmental change outpaces the adaptive capacity of complex nervous systems. Here, we explore neural systems mediating responses to, or impacted by, changing environments, such as those induced by global heating, sensory pollution, and changing habitation zones. We focus on rising temperature and accelerated changes in environments that impact sensory experience as examples of perturbations that directly or indirectly impact neural function, respectively. We also explore a mechanism involved in cross-species interactions that arises from changing habitation zones. We demonstrate that anthropogenic influences on neurons, circuits, and behaviors are widespread across taxa and require further scientific investigation to understand principles underlying neural resilience to accelerating environmental change.SIGNIFICANCE STATEMENT Neural systems evolved over hundreds of millions of years to allow organisms to sense and respond to their environments - to be receptive and responsive, yet flexible. Recent rapid, human-generated environmental changes are testing the limits of the adaptive capacity of neural systems. This presents an opportunity and an urgency to understand how neurobiological processes, including molecular, cellular, and circuit-level mechanisms, are vulnerable or resilient to changing environmental conditions. We showcase examples that range from molecular to circuit to behavioral levels of analysis across several model species, framing a broad neuroscientific approach to explore topics of neural adaptation, plasticity, and resilience. We believe this emerging scientific area is of great societal and scientific importance and will provide a unique opportunity to reexamine our understanding of neural adaptation and the mechanisms underlying neural resilience.

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.

The role of feedback and modulation in determining temperature resiliency in the lobster cardiac nervous system

Changes in ambient temperature affect all biological processes. However, these effects are process specific and often vary non-linearly. It is thus a non-trivial problem for neuronal circuits to maintain coordinated, functional output across a range of temperatures. The cardiac nervous systems in two species of decapod crustaceans, Homarus americanus and Cancer borealis, can maintain function across a wide but physiologically relevant temperature range. However, the processes that underlie temperature resilience in neuronal circuits and muscle systems are not fully understood. Here, we demonstrate that the non-isolated cardiac nervous system (i.e., the whole heart: neurons, effector organs, intrinsic feedback systems) in the American lobster, H. americanus, is more sensitive to warm temperatures than the isolated cardiac ganglion (CG) that controls the heartbeat. This was surprising as modulatory processes known to stabilize the output from the CG are absent when the ganglion is isolated. One source of inhibitory feedback in the intact cardiac neuromuscular system is nitric oxide (NO), which is released in response to heart contractions. We hypothesized that the greater temperature tolerance observed in the isolated CG is due to the absence of NO feedback. Here, we demonstrate that applying an NO donor to the isolated CG reduces its temperature tolerance. Similarly, we show that the NO synthase inhibitor L-nitroarginine (LNA) increases the temperature tolerance of the non-isolated nervous system. This is sufficient to explain differences in temperature tolerance between the isolated CG and the whole heart. However, in an intact lobster, the heart and CG are modulated by an array of endogenous peptides and hormones, many of which are positive regulators of the heartbeat. Many studies have demonstrated that excitatory modulators increase temperature resilience. However, this neuromuscular system is regulated by both excitatory and inhibitory peptide modulators. Perfusing SGRNFLRFamide, a FLRFamide-like peptide, through the heart increases the non-isolated nervous system’s tolerance to high temperatures. In contrast, perfusing myosuppressin, a peptide that negatively regulates the heartbeat frequency, decreases the temperature tolerance. Our data suggest that, in this nervous system, positive regulators of neural output increase temperature tolerance of the neuromuscular system, while modulators that decrease neural output decrease temperature tolerance.

Kv7-specific activators hyperpolarize resting membrane potential and modulate human iPSC-derived sensory neuron excitability

Chronic pain is highly prevalent and remains a significant unmet global medical need. As part of a search for modulatory genes that confer pain resilience, we have studied two family cohorts where one individual reported much less pain than other family members that share the same pathogenic gain-of-function Nav1.7 mutation that confers hyperexcitability on pain-signaling dorsal root ganglion (DRG) neurons. In each of these kindreds, the pain-resilient individual carried a gain-of-function variant in Kv7.2 or Kv7.3, two potassium channels that stabilize membrane potential and reduce excitability. Our observation in this molecular genetic study that these gain-of-function Kv7.2 and 7.3 variants reduce DRG neuron excitability suggests that agents that activate or open Kv7 channels should attenuate sensory neuron firing. In the present study, we assess the effects on sensory neuron excitability of three Kv7 modulators-retigabine (Kv7.2 thru Kv7.5 activator), ICA-110381 (Kv7.2/Kv7.3 specific activator), and as a comparator ML277 (Kv7.1 specific activator)-in a "human-pain-in-a-dish" model (human iPSC-derived sensory neurons, iPSC-SN). Multi-electrode-array (MEA) recordings demonstrated inhibition of firing with retigabine and ICA-110381 (but not with ML277), with the concentration-response curve indicating that retigabine can achieve a 50% reduction of firing with sub-micromolar concentrations. Current-clamp recording demonstrated that retigabine hyperpolarized iPSC-SN resting potential and increased threshold. This study implicates Kv7.2/Kv7.3 channels as effective modulators of sensory neuron excitability, and suggest that compounds that specifically target Kv7.2/Kv7.3 currents in sensory neurons, including human sensory neurons, might provide an effective approach toward pain relief.

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.

New insights from small rhythmic circuits

Small rhythmic circuits, such as those found in invertebrates, have provided fundamental insights into how circuit dynamics depend on individual neuronal and synaptic properties. Degenerate circuits are those with different network parameters and similar behavior. New work on degenerate circuits and their modulation illustrates some of the rules that help maintain stable and robust circuit function despite environmental perturbations. Advances in neuropeptide isolation and identification provide enhanced understanding of the neuromodulation of circuits for behavior. The advent of molecular studies of mRNA expression provides new insight into animal-to-animal variability and the homeostatic regulation of excitability in neurons and networks.

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.

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.

In vitro cell cycle oscillations exhibit a robust and hysteretic response to changes in cytoplasmic density

Cells control the properties of the cytoplasm to ensure proper functioning of biochemical processes. Recent studies showed that cytoplasmic density varies in both physiological and pathological states of cells undergoing growth, division, differentiation, apoptosis, senescence, and metabolic starvation. Little is known about how cellular processes cope with these cytoplasmic variations. Here, we study how a cell cycle oscillator comprising cyclin-dependent kinase (Cdk1) responds to changes in cytoplasmic density by systematically diluting or concentrating cycling Xenopus egg extracts in cell-like microfluidic droplets. We found that the cell cycle maintains robust oscillations over a wide range of deviations from the endogenous density: as low as 0.2× to more than 1.22× relative cytoplasmic density (RCD). A further dilution or concentration from these values arrested the system in a low or high steady state of Cdk1 activity, respectively. Interestingly, diluting an arrested cytoplasm of 1.22× RCD recovers oscillations at lower than 1× RCD. Thus, the cell cycle switches reversibly between oscillatory and stable steady states at distinct thresholds depending on the direction of tuning, forming a hysteresis loop. We propose a mathematical model which recapitulates these observations and predicts that the Cdk1/Wee1/Cdc25 positive feedback loops do not contribute to the observed robustness, supported by experiments. Our system can be applied to study how cytoplasmic density affects other cellular processes.

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.