Many parameter sets in a multicompartment model oscillator are robust to temperature perturbations

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.

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.

Interdependence of cellular and network properties in respiratory rhythmogenesis

How breathing is generated by the preBötzinger Complex (preBötC) remains divided between two ideological frameworks, and the persistent sodium current (INaP) lies at the heart of this debate. Although INaP is widely expressed, the pacemaker hypothesis considers it essential because it endows a small subset of neurons with intrinsic bursting or "pacemaker" activity. In contrast, burstlet theory considers INaP dispensable because rhythm emerges from "pre-inspiratory" spiking activity driven by feed-forward network interactions. Using computational modeling, we discover that changes in spike shape can dissociate INaP from intrinsic bursting. Consistent with many experimental benchmarks, conditional effects on spike shape during simulated changes in oxygenation, development, extracellular potassium, and temperature alter the prevalence of intrinsic bursting and pre-inspiratory spiking without altering the role of INaP. Our results support a unifying hypothesis where INaP and excitatory network interactions, but not intrinsic bursting or pre-inspiratory spiking, are critical interdependent features of preBötC rhythmogenesis.

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.

Neuronal morphology enhances robustness to perturbations of channel densities

Biological neurons show significant cell-to-cell variability but have the striking ability to maintain their key firing properties in the face of unpredictable perturbations and stochastic noise. Using a population of multi-compartment models consisting of soma, neurites, and axon for the lateral pyloric neuron in the crab stomatogastric ganglion, we explore how rebound bursting is preserved when the 14 channel conductances in each model are all randomly varied. The coupling between the axon and other compartments is critical for the ability of the axon to spike during bursts and consequently determines the set of successful solutions. When the coupling deviates from a biologically realistic range, the neuronal tolerance of conductance variations is lessened. Thus, the gross morphological features of these neurons enhance their robustness to perturbations of channel densities and expand the space of individual variability that can maintain a desired output pattern.

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.

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.

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.

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.

Ion Channel Degeneracy, Variability, and Covariation in Neuron and Circuit Resilience

The large number of ion channels found in all nervous systems poses fundamental questions concerning how the characteristic intrinsic properties of single neurons are determined by the specific subsets of channels they express. All neurons display many different ion channels with overlapping voltage- and time-dependent properties. We speculate that these overlapping properties promote resilience in neuronal function. Individual neurons of the same cell type show variability in ion channel conductance densities even though they can generate reliable and similar behavior. This complicates a simple assignment of function to any conductance and is associated with variable responses of neurons of the same cell type to perturbations, deletions, and pharmacological manipulation. Ion channel genes often show strong positively correlated expression, which may result from the molecular and developmental rules that determine which ion channels are expressed in a given cell type.

Neuronal oscillator robustness to multiple global perturbations

Neuronal activity depends on ion channels and biophysical processes that are strongly and differentially sensitive to physical variables such as temperature and pH. Nonetheless, neuronal oscillators can be surprisingly resilient to perturbations in these variables. We study a three-neuron pacemaker ensemble that drives the pyloric rhythm of the crab, Cancer borealis. These crabs routinely experience a number of global perturbations, including changes in temperature and pH. Although pyloric oscillations are robust to such changes, for sufficiently large deviations the rhythm reversibly breaks down. As temperature increases beyond a tipping point, oscillators transition to silence. Acidic pH deviations also show tipping points, with a reliable transition first to tonic spiking, then to silence. Surprisingly, robustness to perturbations in pH only moderately affects temperature robustness. Consistent with high animal-to-animal variability in biophysical circuit parameters, tipping points in temperature and pH vary across animals. However, the ordering and discrete classes of transitions at critical points are conserved. This implies that qualitative oscillator dynamics are preserved across animals despite high quantitative parameter variability. A universal model of bursting dynamics predicts the existence of these transition types and the order in which they occur.

Coupling between fast and slow oscillator circuits in Cancer borealis is temperature-compensated

Coupled oscillatory circuits are ubiquitous in nervous systems. Given that most biological processes are temperature-sensitive, it is remarkable that the neuronal circuits of poikilothermic animals can maintain coupling across a wide range of temperatures. Within the stomatogastric ganglion (STG) of the crab, Cancer borealis, the fast pyloric rhythm (~1 Hz) and the slow gastric mill rhythm (~0.1 Hz) are precisely coordinated at ~11°C such that there is an integer number of pyloric cycles per gastric mill cycle (integer coupling). Upon increasing temperature from 7°C to 23°C, both oscillators showed similar temperature-dependent increases in cycle frequency, and integer coupling between the circuits was conserved. Thus, although both rhythms show temperature-dependent changes in rhythm frequency, the processes that couple these circuits maintain their coordination over a wide range of temperatures. Such robustness to temperature changes could be part of a toolbox of processes that enables neural circuits to maintain function despite global perturbations.

Activity-dependent compensation of cell size is vulnerable to targeted deletion of ion channels

In many species, excitable cells preserve their physiological properties despite significant variation in physical size across time and in a population. For example, neurons in crustacean central pattern generators generate similar firing patterns despite several-fold increases in size between juveniles and adults. This presents a biophysical problem because the electrical properties of cells are highly sensitive to membrane area and channel density. It is not known whether specific mechanisms exist to sense membrane area and adjust channel expression to keep a consistent channel density, or whether regulation mechanisms that sense activity alone are capable of compensating cell size. We show that destabilising effects of growth can be specifically compensated by feedback mechanism that senses average calcium influx and jointly regulate multiple conductances. However, we further show that this class of growth-compensating regulation schemes is necessarily sensitive to perturbations that alter the expression of subsets of ion channel types. Targeted perturbations of specific ion channels can trigger a pathological response of the regulation mechanism and a failure of homeostasis. Our findings suggest that physiological regulation mechanisms that confer robustness to growth may be specifically vulnerable to deletions or mutations that affect subsets of ion channels.

Training deep neural density estimators to identify mechanistic models of neural dynamics

Mechanistic modeling in neuroscience aims to explain observed phenomena in terms of underlying causes. However, determining which model parameters agree with complex and stochastic neural data presents a significant challenge. We address this challenge with a machine learning tool which uses deep neural density estimators-trained using model simulations-to carry out Bayesian inference and retrieve the full space of parameters compatible with raw data or selected data features. Our method is scalable in parameters and data features and can rapidly analyze new data after initial training. We demonstrate the power and flexibility of our approach on receptive fields, ion channels, and Hodgkin-Huxley models. We also characterize the space of circuit configurations giving rise to rhythmic activity in the crustacean stomatogastric ganglion, and use these results to derive hypotheses for underlying compensation mechanisms. Our approach will help close the gap between data-driven and theory-driven models of neural dynamics.

Temperature compensation in a small rhythmic circuit

Temperature affects the conductances and kinetics of the ionic channels that underlie neuronal activity. Each membrane conductance has a different characteristic temperature sensitivity, which raises the question of how neurons and neuronal circuits can operate robustly over wide temperature ranges. To address this, we employed computational models of the pyloric network of crabs and lobsters. We produced multiple different models that exhibit a triphasic pyloric rhythm over a range of temperatures and explored the dynamics of their currents and how they change with temperature. Temperature can produce smooth changes in the relative contributions of the currents to neural activity so that neurons and networks undergo graceful transitions in the mechanisms that give rise to their activity patterns. Moreover, responses of the models to deletions of a current can be different at high and low temperatures, indicating that even a well-defined genetic or pharmacological manipulation may produce qualitatively distinct effects depending on the temperature.

Circuit Robustness to Temperature Perturbation Is Altered by Neuromodulators

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

Asymmetric Firing Rate from Crayfish Left and Right Caudal Photoreceptors Due to Blue and Green Monochromatic Light Pulses

Recent studies have postulated that the left and right caudal photoreceptors (CPR-L and CPR-R, respectively) of the crayfish show asymmetry of spontaneous activity in darkness and responses induced by white light. Two photopigments have been identified; the first one sensitive to blue light and the second one sensitive to green light. This study explores blue and green monochromatic light responsiveness with respect to both CPR-L and -R, as well as the effects of temperature on these photoreceptors. We performed simultaneous extracellular recordings of the firing rate of action potentials from CPRs of the crayfish Cherax quadricarinatus (n = 12). At room temperature (24 ± 1 °C), CPR-L and -R showed a significant difference in the spikes from most of the comparations. CPRs in the dark exhibited spontaneous asymmetric activity and displayed sensitivity to both monochromatic light sources. CPR responses were light intensity dependent within a range of 1.4 logarithmic intensity units, showing approximately 0.5 logarithmic intensity units more sensitivity to blue than to green light. The CPRs displayed an asymmetrical response to both colors by using a constant light intensity. At 14 (±1) °C, activity in darkness diminished while asymmetry persisted, and the CPRs improved responses for both monochromatic light sources, displaying a significant asymmetry. Here, we provide additional evidence of the asymmetric activity in darkness and light response from the CPRs. The new data allow further investigations regarding the physiological role of caudal photoreceptors in the crayfish.

Model of a bilateral Brown-type central pattern generator for symmetric and asymmetric locomotion

The coordinated activity of muscles is produced in part by spinal rhythmogenic neural circuits, termed central pattern generators (CPGs). A classical CPG model is a system of coupled oscillators that transform locomotor drive into coordinated and gait-specific patterns of muscle recruitment. The network properties of this conceptual model can be simulated by a system of ordinary differential equations with a physiologically inspired coupling locus of interactions capturing the timing relationship for bilateral coordination of limbs in locomotion. Whereas most similar models are solved numerically, it is intriguing to have a full analytical description of this plausible CPG architecture to illuminate the functionality within this structure and to expand it to include steering control. Here, we provided a closed-form analytical solution contrasted against the previous numerical method. The evaluation time of the analytical solution was decreased by an order of magnitude when compared with the numerical approach (relative errors, <0.01%). The analytical solution tested and supported the previous finding that the input to the model can be expressed in units of the desired limb locomotor speed. Furthermore, we performed parametric sensitivity analysis in the context of controlling steering and documented two possible mechanisms associated with either an external drive or intrinsic CPG parameters. The results identify specific propriospinal pathways that may be associated with adaptations within the CPG structure. The model offered several network configurations that may generate the same behavioral outcomes. NEW & NOTEWORTHY Using a simple process of leaky integration, we developed an analytical solution to a robust model of spinal pattern generation. We analyzed the ability of this neural element to exert locomotor control of the signal associated with limb speeds and tested the ability of this simple structure to embed steering control using the velocity signal in the model's inputs or within the internal connectivity of its elements.

Temperature manipulation of neuronal dynamics in a forebrain motor control nucleus

Different neuronal types within brain motor areas contribute to the generation of complex motor behaviors. A widely studied songbird forebrain nucleus (HVC) has been recognized as fundamental in shaping the precise timing characteristics of birdsong. This is based, among other evidence, on the stretching and the “breaking” of song structure when HVC is cooled. However, little is known about the temperature effects that take place in its neurons. To address this, we investigated the dynamics of HVC both experimentally and computationally. We developed a technique where simultaneous electrophysiological recordings were performed during temperature manipulation of HVC. We recorded spontaneous activity and found three effects: widening of the spike shape, decrease of the firing rate and change in the interspike interval distribution. All these effects could be explained with a detailed conductance based model of all the neurons present in HVC. Temperature dependence of the ionic channel time constants explained the first effect, while the second was based in the changes of the maximal conductance using single synaptic excitatory inputs. The last phenomenon, only emerged after introducing a more realistic synaptic input to the inhibitory interneurons. Two timescales were present in the interspike distributions. The behavior of one timescale was reproduced with different input balances received form the excitatory neurons, whereas the other, which disappears with cooling, could not be found assuming poissonian synaptic inputs. Furthermore, the computational model shows that the bursting of the excitatory neurons arises naturally at normal brain temperature and that they have an intrinsic delay at low temperatures. The same effect occurs at single synapses, which may explain song stretching. These findings shed light on the temperature dependence of neuronal dynamics and present a comprehensive framework to study neuronal connectivity. This study, which is based on intrinsic neuronal characteristics, may help to understand emergent behavioral changes.

The study of the neuronal mechanisms that give rise to the complex behavior of singing in birds has been hotly debated lately. Many models have been tested and novel tools have been developed to try to understand the role of a key brain nucleus in the song pathway: HVC. It is believed that it is highly responsible for generating the precise timing of songs, and this has been tested by manipulating it with temperature. Results showed that cooling can stretch, but that it can also restructure or “break” the song syllables. However, single neuronal mechanisms are not yet described. To better understand this, we cooled HVC in canaries and measured spontaneous activity electrophysiologically. We found three effects: spike shape widening, spike rate reduction and changes in inter-spike-interval (ISI) distributions. To explain them, we built a computational model with a detailed description of ion channel conductances and temperature dependency. We could explain the first effect with a single neuron model. The second, could be explained adding single synapses. Finally, we showed similar ISI modifications of one of the timescales present by means of multiple stochastic inputs. In addition, we found that excitatory neurons show natural bursting behavior at normal brain temperatures and that synaptic delays are the main candidates to explain song stretching at low temperatures.

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

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

Analysis of Family Structures Reveals Robustness or Sensitivity of Bursting Activity to Parameter Variations in a Half-Center Oscillator (HCO) Model

The underlying mechanisms that support robustness in neuronal networks are as yet unknown. However, recent studies provide evidence that neuronal networks are robust to natural variations, modulation, and environmental perturbations of parameters, such as maximal conductances of intrinsic membrane and synaptic currents. Here we sought a method for assessing robustness, which might easily be applied to large brute-force databases of model instances. Starting with groups of instances with appropriate activity (e.g., tonic spiking), our method classifies instances into much smaller subgroups, called families, in which all members vary only by the one parameter that defines the family. By analyzing the structures of families, we developed measures of robustness for activity type. Then, we applied these measures to our previously developed model database, HCO-db, of a two-neuron half-center oscillator (HCO), a neuronal microcircuit from the leech heartbeat central pattern generator where the appropriate activity type is alternating bursting. In HCO-db, the maximal conductances of five intrinsic and two synaptic currents were varied over eight values (leak reversal potential also varied, five values). We focused on how variations of particular conductance parameters maintain normal alternating bursting activity while still allowing for functional modulation of period and spike frequency. We explored the trade-off between robustness of activity type and desirable change in activity characteristics when intrinsic conductances are altered and identified the hyperpolarization-activated (h) current as an ideal target for modulation. We also identified ensembles of model instances that closely approximate physiological activity and can be used in future modeling studies.

Is realistic neuronal modeling realistic?

Scientific models are abstractions that aim to explain natural phenomena. A successful model shows how a complex phenomenon arises from relatively simple principles while preserving major physical or biological rules and predicting novel experiments. A model should not be a facsimile of reality; it is an aid for understanding it. Contrary to this basic premise, with the 21st century has come a surge in computational efforts to model biological processes in great detail. Here we discuss the oxymoronic, realistic modeling of single neurons. This rapidly advancing field is driven by the discovery that some neurons don't merely sum their inputs and fire if the sum exceeds some threshold. Thus researchers have asked what are the computational abilities of single neurons and attempted to give answers using realistic models. We briefly review the state of the art of compartmental modeling highlighting recent progress and intrinsic flaws. We then attempt to address two fundamental questions. Practically, can we realistically model single neurons? Philosophically, should we realistically model single neurons? We use layer 5 neocortical pyramidal neurons as a test case to examine these issues. We subject three publically available models of layer 5 pyramidal neurons to three simple computational challenges. Based on their performance and a partial survey of published models, we conclude that current compartmental models are ad hoc, unrealistic models functioning poorly once they are stretched beyond the specific problems for which they were designed. We then attempt to plot possible paths for generating realistic single neuron models.

The complexity of small circuits: the stomatogastric nervous system

The crustacean stomatogastric nervous system is a long-standing test bed for studies of circuit dynamics and neuromodulation. We give a brief update on the most recent work on this system, with an emphasis on the broader implications for understanding neural circuits. In particular, we focus on new findings underlining that different levels of dynamics taking place at different time scales all interact in multiple ways. Dynamics due to synaptic and intrinsic neuronal properties, neuromodulation, and long-term gene expression-dependent regulation are not independent, but influence each other. Extensive research on the stomatogastric system shows that these dynamic interactions convey robustness to circuit operation, while facilitating the flexibility of producing multiple circuit outputs.

From global to local: exploring the relationship between parameters and behaviors in models of electrical excitability

Models of electrical activity in excitable cells involve nonlinear interactions between many ionic currents. Changing parameters in these models can produce a variety of activity patterns with sometimes unexpected effects. Further more, introducing new currents will have different effects depending on the initial parameter set. In this study we combined global sampling of parameter space and local analysis of representative parameter sets in a pituitary cell model to understand the effects of adding K (+) conductances, which mediate some effects of hormone action on these cells. Global sampling ensured that the effects of introducing K (+) conductances were captured across a wide variety of contexts of model parameters. For each type of K (+) conductance we determined the types of behavioral transition that it evoked. Some transitions were counterintuitive, and may have been missed without the use of global sampling. In general, the wide range of transitions that occurred when the same current was applied to the model cell at different locations in parameter space highlight the challenge of making accurate model predictions in light of cell-to-cell heterogeneity. Finally, we used bifurcation analysis and fast/slow analysis to investigate why specific transitions occur in representative individual models. This approach relies on the use of a graphics processing unit (GPU) to quickly map parameter space to model behavior and identify parameter sets for further analysis. Acceleration with modern low-cost GPUs is particularly well suited to exploring the moderate-sized (5-20) parameter spaces of excitable cell and signaling models.

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

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

A temperature rise reduces trial-to-trial variability of locust auditory neuron responses

The neurophysiology of ectothermic animals, such as insects, is affected by environmental temperature, as their body temperature fluctuates with ambient conditions. Changes in temperature alter properties of neurons and, consequently, have an impact on the processing of information. Nevertheless, nervous system function is often maintained over a broad temperature range, exhibiting a surprising robustness to variations in temperature. A special problem arises for acoustically communicating insects, as in these animals mate recognition and mate localization typically rely on the decoding of fast amplitude modulations in calling and courtship songs. In the auditory periphery, however, temporal resolution is constrained by intrinsic neuronal noise. Such noise predominantly arises from the stochasticity of ion channel gating and potentially impairs the processing of sensory signals. On the basis of intracellular recordings of locust auditory neurons, we show that intrinsic neuronal variability on the level of spikes is reduced with increasing temperature. We use a detailed mathematical model including stochastic ion channel gating to shed light on the underlying biophysical mechanisms in auditory receptor neurons: because of a redistribution of channel-induced current noise toward higher frequencies and specifics of the temperature dependence of the membrane impedance, membrane potential noise is indeed reduced at higher temperatures. This finding holds under generic conditions and physiologically plausible assumptions on the temperature dependence of the channels' kinetics and peak conductances. We demonstrate that the identified mechanism also can explain the experimentally observed reduction of spike timing variability at higher temperatures.

Computational models in the age of large datasets

Technological advances in experimental neuroscience are generating vast quantities of data, from the dynamics of single molecules to the structure and activity patterns of large networks of neurons. How do we make sense of these voluminous, complex, disparate and often incomplete data? How do we find general principles in the morass of detail? Computational models are invaluable and necessary in this task and yield insights that cannot otherwise be obtained. However, building and interpreting good computational models is a substantial challenge, especially so in the era of large datasets. Fitting detailed models to experimental data is difficult and often requires onerous assumptions, while more loosely constrained conceptual models that explore broad hypotheses and principles can yield more useful insights.

How can motor systems retain performance over a wide temperature range? Lessons from the crustacean stomatogastric nervous system

Marine invertebrates, such as lobsters and crabs, deal with a widely and wildly fluctuating temperature environment. Here, we describe the effects of changing temperature on the motor patterns generated by the stomatogastric nervous system of the crab, Cancer borealis. Over a broad range of "permissive" temperatures, the pyloric rhythm increases in frequency but maintains its characteristic phase relationships. Nonetheless, at more extreme high temperatures, the normal triphasic pyloric rhythm breaks down, or "crashes". We present both experimental and computational approaches to understanding the stability of both single neurons and networks to temperature perturbations, and discuss data that shows that the "crash" temperatures themselves may be environmentally regulated. These approaches provide insight into how the nervous system can be stable to a global perturbation, such as temperature, in spite of the fact that all biological processes are temperature dependent.

Motor neuronal activity varies least among individuals when it matters most for behavior

How does motor neuronal variability affect behavior? To explore this question, we quantified activity of multiple individual identified motor neurons mediating biting and swallowing in intact, behaving Aplysia californica by recording from the protractor muscle and the three nerves containing the majority of motor neurons controlling the feeding musculature. We measured multiple motor components: duration of the activity of identified motor neurons as well as their relative timing. At the same time, we measured behavioral efficacy: amplitude of grasping movement during biting and amplitude of net inward food movement during swallowing. We observed that the total duration of the behaviors varied: Within animals, biting duration shortened from the first to the second and third bites; between animals, biting and swallowing durations varied. To study other sources of variation, motor components were divided by behavior duration (i.e., normalized). Even after normalization, distributions of motor component durations could distinguish animals as unique individuals. However, the degree to which a motor component varied among individuals depended on the role of that motor component in a behavior. Motor neuronal activity that was essential for the expression of biting or swallowing was similar among animals, whereas motor neuronal activity that was not essential for that behavior varied more from individual to individual. These results suggest that motor neuronal activity that matters most for the expression of a particular behavior may vary least from individual to individual. Shaping individual variability to ensure behavioral efficacy may be a general principle for the operation of motor systems.

Robust circuit rhythms in small circuits arise from variable circuit components and mechanisms

Small central pattern generating circuits found in invertebrates have significant advantages for the study of the circuit mechanisms that generate brain rhythms. Experimental and computational studies of small oscillatory circuits reveal that similar rhythms can arise from disparate mechanisms. Animal-to-animal variation in the properties of single neurons and synapses may underly robust circuit performance, and can be revealed by perturbations. Neuromodulation can produce altered circuit performance but also ensure reliable circuit function.

Phase maintenance in a rhythmic motor pattern during temperature changes in vivo

Central-pattern-generating neural circuits function reliably throughout an animal's life, despite constant molecular turnover and environmental perturbations. Fluctuations in temperature pose a problem to the nervous systems of poikilotherms because their body temperature follows the ambient temperature, thus affecting the temperature-dependent dynamics of various subcellular components that constitute neuronal circuits. In the crustacean stomatogastric nervous system, the pyloric circuit produces a triphasic rhythm comprising the output of the pyloric dilator, lateral pyloric, and pyloric constrictor neurons. In vitro, the phase relationships of these neurons are maintained over a fourfold change in pyloric frequency as temperature increases from 7°C to 23°C. To determine whether these temperature effects are also found in intact crabs, in the presence of sensory feedback and neuromodulator-rich environments, we measured the temperature dependence of the pyloric frequency and phases in vivo by implanting extracellular electrodes into Cancer borealis and Cancer pagurus and shifting tank water temperature from 11°C to 26°C. Pyloric frequency in the intact crab increased significantly with temperature (Q10 = 2-2.5), while pyloric phases were generally conserved. For a subset of the C. borealis experiments, animals were subsequently dissected and the stomatogastric ganglion subjected to a similar temperature ramp in vitro. We found that the maximal frequency attained at high temperatures in vivo is lower than it is under in vitro conditions. Our results demonstrate that, over a wide temperature range, the phases of the pyloric rhythm in vivo are generally preserved, but that the frequency range is more restricted than it is in vitro.