The functional consequences of changes in the strength and duration of synaptic inputs to oscillatory neurons

Error Function Optimization to Compare Neural Activity and Train Blended Rhythmic Networks

We present a novel set of quantitative measures for "likeness" (error function) designed to alleviate the time-consuming and subjective nature of manually comparing biological recordings from electrophysiological experiments with the outcomes of their mathematical models. Our innovative "blended" system approach offers an objective, high-throughput, and computationally efficient method for comparing biological and mathematical models. This approach involves using voltage recordings of biological neurons to drive and train mathematical models, facilitating the derivation of the error function for further parameter optimization. Our calibration process incorporates measurements such as action potential (AP) frequency, voltage moving average, voltage envelopes, and the probability of post-synaptic channels. To assess the effectiveness of our method, we utilized the sea slug Melibe leonina swim central pattern generator (CPG) as our model circuit and conducted electrophysiological experiments with TTX to isolate CPG interneurons. During the comparison of biological recordings and mathematically simulated neurons, we performed a grid search of inhibitory and excitatory synapse conductance. Our findings indicate that a weighted sum of simple functions is essential for comprehensively capturing a neuron's rhythmic activity. Overall, our study suggests that our blended system approach holds promise for enabling objective and high-throughput comparisons between biological and mathematical models, offering significant potential for advancing research in neural circuitry and related fields.

Temporal dynamics of Na/K pump mediated memory traces: insights from conductance-based models of Drosophila neurons

Sodium potassium ATPases (Na/K pumps) mediate long-lasting, dynamic cellular memories that can last tens of seconds. The mechanisms controlling the dynamics of this type of cellular memory are not well understood and can be counterintuitive. Here, we use computational modeling to examine how Na/K pumps and the ion concentration dynamics they influence shape cellular excitability. In a Drosophila larval motor neuron model, we incorporate a Na/K pump, a dynamic intracellular Na⁺ concentration, and a dynamic Na⁺ reversal potential. We probe neuronal excitability with a variety of stimuli, including step currents, ramp currents, and zap currents, then monitor the sub- and suprathreshold voltage responses on a range of time scales. We find that the interactions of a Na⁺-dependent pump current with a dynamic Na⁺ concentration and reversal potential endow the neuron with rich response properties that are absent when the role of the pump is reduced to the maintenance of constant ion concentration gradients. In particular, these dynamic pump-Na⁺ interactions contribute to spike rate adaptation and result in long-lasting excitability changes after spiking and even after sub-threshold voltage fluctuations on multiple time scales. We further show that modulation of pump properties can profoundly alter a neuron's spontaneous activity and response to stimuli by providing a mechanism for bursting oscillations. Our work has implications for experimental studies and computational modeling of the role of Na/K pumps in neuronal activity, information processing in neural circuits, and the neural control of animal behavior.

A Feeding-Related Mechanoreceptor Identified in the Crab Cancer borealis Shares Similarities and Differences with Homologs in Other Crustaceans

AbstractSensory feedback plays an essential role in shaping rhythmic animal movements. In the crustacean stomatogastric nervous system, which is responsible for grinding and filtering food particles in the animal's foregut, a number of mechanoreceptors whose activity affects motor output have been characterized. The hepatopancreas duct receptor neurons, which are located in the pyloric region of the foregut that is responsible for filtering, are among the less well understood groups of stomatogastric mechanoreceptors. Although they were first described decades ago in a number of decapod species, many questions remain about their role in shaping the movements produced by the stomatogastric nervous system. Here we provide the first anatomical and physiological evidence that there are also hepatopancreas duct receptors in the crab Cancer borealis, and we demonstrate that hepatopancreas duct receptor spiking produced by mechanical stimulation modifies the properties of an ongoing pyloric motor program.

The voltage and spiking responses of subthreshold resonant neurons to structured and fluctuating inputs: persistence and loss of resonance and variability

We systematically investigate the response of neurons to oscillatory currents and synaptic-like inputs and we extend our investigation to non-structured synaptic-like spiking inputs with more realistic distributions of presynaptic spike times. We use two types of chirp-like inputs consisting of (i) a sequence of cycles with discretely increasing frequencies over time, and (ii) a sequence having the same cycles arranged in an arbitrary order. We develop and use a number of frequency-dependent voltage response metrics to capture the different aspects of the voltage response, including the standard impedance (Z) and the peak-to-trough amplitude envelope ([Formula: see text]) profiles. We show that Z-resonant cells (cells that exhibit subthreshold resonance in response to sinusoidal inputs) also show [Formula: see text]-resonance in response to sinusoidal inputs, but generally do not (or do it very mildly) in response to square-wave and synaptic-like inputs. In the latter cases the resonant response using Z is not predictive of the preferred frequencies at which the neurons spike when the input amplitude is increased above subthreshold levels. We also show that responses to conductance-based synaptic-like inputs are attenuated as compared to the response to current-based synaptic-like inputs, thus providing an explanation to previous experimental results. These response patterns were strongly dependent on the intrinsic properties of the participating neurons, in particular whether the unperturbed Z-resonant cells had a stable node or a focus. In addition, we show that variability emerges in response to chirp-like inputs with arbitrarily ordered patterns where all signals (trials) in a given protocol have the same frequency content and the only source of uncertainty is the subset of all possible permutations of cycles chosen for a given protocol. This variability is the result of the multiple different ways in which the autonomous transient dynamics is activated across cycles in each signal (different cycle orderings) and across trials. We extend our results to include high-rate Poisson distributed current- and conductance-based synaptic inputs and compare them with similar results using additive Gaussian white noise. We show that the responses to both Poisson-distributed synaptic inputs are attenuated with respect to the responses to Gaussian white noise. For cells that exhibit oscillatory responses to Gaussian white noise (band-pass filters), the response to conductance-based synaptic inputs are low-pass filters, while the response to current-based synaptic inputs may remain band-pass filters, consistent with experimental findings. Our results shed light on the mechanisms of communication of oscillatory activity among neurons in a network via subthreshold oscillations and resonance and the generation of network resonance.

Heterogeneous Responses to Changes in Inhibitory Synaptic Strength in Networks of Spiking Neurons

How does the dynamics of neurons in a network respond to changes in synaptic weights? Answer to this question would be important for a full understanding of synaptic plasticity. In this article, we report our numerical study of the effects of changes in inhibitory synaptic weights on the spontaneous activity of networks of spiking neurons with conductance-based synapses. Networks with biologically realistic features, which were reconstructed from multi-electrode array recordings taken in a cortical neuronal culture, and their modifications were used in the simulations. The magnitudes of the synaptic weights of all the inhibitory connections are decreased by a uniform amount subjecting to the condition that inhibitory connections would not be turned into excitatory ones. Our simulation results reveal that the responses of the neurons are heterogeneous: while the firing rate of some neurons increases as expected, the firing rate of other neurons decreases or remains unchanged. The same results show that heterogeneous responses also occur for an enhancement of inhibition. This heterogeneity in the responses of neurons to changes in inhibitory synaptic strength suggests that activity-induced modification of synaptic strength does not necessarily generate a positive feedback loop on the dynamics of neurons connected in a network. Our results could be used to understand the effects of bicuculline on spiking and bursting activities of neuronal cultures. Using reconstructed networks with biologically realistic features enables us to identify a long-tailed distribution of average synaptic weights for outgoing links as a crucial feature in giving rise to bursting in neuronal networks and in determining the overall response of the whole network to changes in synaptic strength. For networks whose average synaptic weights for outgoing links have a long-tailed distribution, bursting is observed and the average firing rate of the whole network increases upon inhibition suppression or decreases upon inhibition enhancement. For networks whose average synaptic weights for outgoing links are approximately normally distributed, bursting is not found and the average firing rate of the whole network remains approximately constant upon changes in inhibitory synaptic strength.

Optimal closed-loop deep brain stimulation using multiple independently controlled contacts

Deep brain stimulation (DBS) is a well-established treatment option for a variety of neurological disorders, including Parkinson’s disease and essential tremor. The symptoms of these disorders are known to be associated with pathological synchronous neural activity in the basal ganglia and thalamus. It is hypothesised that DBS acts to desynchronise this activity, leading to an overall reduction in symptoms. Electrodes with multiple independently controllable contacts are a recent development in DBS technology which have the potential to target one or more pathological regions with greater precision, reducing side effects and potentially increasing both the efficacy and efficiency of the treatment. The increased complexity of these systems, however, motivates the need to understand the effects of DBS when applied to multiple regions or neural populations within the brain. On the basis of a theoretical model, our paper addresses the question of how to best apply DBS to multiple neural populations to maximally desynchronise brain activity. Central to this are analytical expressions, which we derive, that predict how the symptom severity should change when stimulation is applied. Using these expressions, we construct a closed-loop DBS strategy describing how stimulation should be delivered to individual contacts using the phases and amplitudes of feedback signals. We simulate our method and compare it against two others found in the literature: coordinated reset and phase-locked stimulation. We also investigate the conditions for which our strategy is expected to yield the most benefit.

In this paper we use computer models of brain tissue to derive an optimal control algorithm for a recently developed new generation of deep brain stimulation (DBS) devices. DBS is a treatment for a variety of neurological disorders including Parkinson’s disease, essential tremor, depression and pain. There is a growing amount of evidence to suggest that delivering stimulation according to feedback from patients, or closed-loop, has the potential to improve the efficacy, efficiency and side effects of the treatment. An important recent development in DBS technology are electrodes with multiple independently controllable contacts and this paper is a theoretical study into the effects of using this new technology. On the basis of a theoretical model, we devise a closed-loop strategy and address the question of how to best apply DBS across multiple contacts to maximally desynchronise neural populations. We demonstrate using numerical simulation that, for the systems we consider, our methods are more effective than two well-known alternatives, namely phase-locked stimulation and coordinated reset. We also predict that the benefits of using multiple contacts should depend strongly on the intrinsic neuronal response. The insights from this work should lead to a better understanding of how to implement and optimise closed-loop multi-contact DBS systems which in turn should lead to more effective and efficient DBS treatments.

First-order synchronization transition in a large population of strongly coupled relaxation oscillators

Onset and loss of synchronization in coupled oscillators are of fundamental importance in understanding emergent behavior in natural and man-made systems, which range from neural networks to power grids. We report on experiments with hundreds of strongly coupled photochemical relaxation oscillators that exhibit a discontinuous synchronization transition with hysteresis, as opposed to the paradigmatic continuous transition expected from the widely used weak coupling theory. The resulting first-order transition is robust with respect to changes in network connectivity and natural frequency distribution. This allows us to identify the relaxation character of the oscillators as the essential parameter that determines the nature of the synchronization transition. We further support this hypothesis by revealing the mechanism of the transition, which cannot be accounted for by standard phase reduction techniques.

Curated Model Development Using NEUROiD: A Web-Based NEUROmotor Integration and Design Platform

Decades of research on neuromotor circuits and systems has provided valuable information on neuronal control of movement. Computational models of several elements of the neuromotor system have been developed at various scales, from sub-cellular to system. While several small models abound, their structured integration is the key to building larger and more biologically realistic models which can predict the behavior of the system in different scenarios. This effort calls for integration of elements across neuroscience and musculoskeletal biomechanics. There is also a need for development of methods and tools for structured integration that yield larger in silico models demonstrating a set of desired system responses. We take a small step in this direction with the NEUROmotor integration and Design (NEUROiD) platform. NEUROiD helps integrate results from motor systems anatomy, physiology, and biomechanics into an integrated neuromotor system model. Simulation and visualization of the model across multiple scales is supported. Standard electrophysiological operations such as slicing, current injection, recording of membrane potential, and local field potential are part of NEUROiD. The platform allows traceability of model parameters to primary literature. We illustrate the power and utility of NEUROiD by building a simple ankle model and its controlling neural circuitry by curating a set of published components. NEUROiD allows researchers to utilize remote high-performance computers for simulation, while controlling the model using a web browser.

Predicting the effects of deep brain stimulation using a reduced coupled oscillator model

Deep brain stimulation (DBS) is known to be an effective treatment for a variety of neurological disorders, including Parkinson's disease and essential tremor (ET). At present, it involves administering a train of pulses with constant frequency via electrodes implanted into the brain. New 'closed-loop' approaches involve delivering stimulation according to the ongoing symptoms or brain activity and have the potential to provide improvements in terms of efficiency, efficacy and reduction of side effects. The success of closed-loop DBS depends on being able to devise a stimulation strategy that minimizes oscillations in neural activity associated with symptoms of motor disorders. A useful stepping stone towards this is to construct a mathematical model, which can describe how the brain oscillations should change when stimulation is applied at a particular state of the system. Our work focuses on the use of coupled oscillators to represent neurons in areas generating pathological oscillations. Using a reduced form of the Kuramoto model, we analyse how a patient should respond to stimulation when neural oscillations have a given phase and amplitude, provided a number of conditions are satisfied. For such patients, we predict that the best stimulation strategy should be phase specific but also that stimulation should have a greater effect if applied when the amplitude of brain oscillations is lower. We compare this surprising prediction with data obtained from ET patients. In light of our predictions, we also propose a new hybrid strategy which effectively combines two of the closed-loop strategies found in the literature, namely phase-locked and adaptive DBS.

Causally Investigating Cortical Dynamics and Signal Processing by Targeting Natural System Attractors With Precisely Timed (Electrical) Stimulation

Electrical stimulation is a promising tool for interacting with neuronal dynamics to identify neural mechanisms that underlie cognitive function. Since effects of a single short stimulation pulse typically vary greatly and depend on the current network state, many experimental paradigms have rather resorted to continuous or periodic stimulation in order to establish and maintain a desired effect. However, such an approach explicitly leads to forced and “unnatural” brain activity. Further, continuous stimulation can make it hard to parse the recorded activity and separate neural signal from stimulation artifacts. In this study we propose an alternate strategy: by monitoring a system in realtime, we use the existing preferred states or attractors of the network and apply short and precise pulses in order to switch between those states. When pushed into one of its attractors, one can use the natural tendency of the system to remain in such a state to prolong the effect of a stimulation pulse, opening a larger window of opportunity to observe the consequences on cognitive processing. To elaborate on this idea, we consider flexible information routing in the visual cortex as a prototypical example. When processing a stimulus, neural populations in the visual cortex have been found to engage in synchronized gamma activity. In this context, selective signal routing is achieved by changing the relative phase between oscillatory activity in sending and receiving populations (communication through coherence, CTC). In order to explore how perturbations interact with CTC, we investigate a network of interneuronal gamma (ING) oscillators composed of integrate-and-fire neurons exhibiting similar synchronization and signal routing phenomena. We develop a closed-loop stimulation paradigm based on the phase-response characteristics of the network and demonstrate its ability to establish desired synchronization states. By measuring information content throughout the model, we evaluate the effect of signal contamination caused by the stimulation in relation to the magnitude of the injected pulses and intrinsic noise in the system. Finally, we demonstrate that, up to a critical noise level, precisely timed perturbations can be used to artificially induce the effect of attention by selectively routing visual signals to higher cortical areas.

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

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

Partial synchronization of relaxation oscillators with repulsive coupling in autocatalytic integrate-and-fire model and electrochemical experiments

Experiments and supporting theoretical analysis are presented to describe the synchronization patterns that can be observed with a population of globally coupled electrochemical oscillators close to a homoclinic, saddle-loop bifurcation, where the coupling is repulsive in the electrode potential. While attractive coupling generates phase clusters and desynchronized states, repulsive coupling results in synchronized oscillations. The experiments are interpreted with a phenomenological model that captures the waveform of the oscillations (exponential increase) followed by a refractory period. The globally coupled autocatalytic integrate-and-fire model predicts the development of partially synchronized states that occur through attracting heteroclinic cycles between out-of-phase two-cluster states. Similar behavior can be expected in many other systems where the oscillations occur close to a saddle-loop bifurcation, e.g., with Morris-Lecar neurons.

Spiking resonances in models with the same slow resonant and fast amplifying currents but different subthreshold dynamic properties

The generation of spiking resonances in neurons (preferred spiking responses to oscillatory inputs) requires the interplay of the intrinsic ionic currents that operate at the subthreshold voltage level and the spiking mechanisms. Combinations of the same types of ionic currents in different parameter regimes may give rise to different types of nonlinearities in the voltage equation (e.g., parabolic- and cubic-like), generating subthreshold (membrane potential) oscillations patterns with different properties. These nonlinearities are not apparent in the model equations, but can be uncovered by plotting the voltage nullclines in the phase-plane diagram. We investigate the spiking resonant properties of conductance-based models that are biophysically equivalent at the subthreshold level (same ionic currents), but dynamically different (parabolic- and cubic-like voltage nullclines). As a case study we consider a model having a persistent sodium and a hyperpolarization-activated (h-) currents, which exhibits subthreshold resonance in the theta frequency band. We unfold the concept of spiking resonance into evoked and output spiking resonance. The former focuses on the input frequencies that are able to generate spikes, while the latter focuses on the output spiking frequencies regardless of the input frequency that generated these spikes. A cell can exhibit one or both types of resonances. We also measure spiking phasonance, which is an extension of subthreshold phasonance (zero-phase-shift response to oscillatory inputs) to the spiking regime. The subthreshold resonant properties of both types of models are communicated to the spiking regime for low enough input amplitudes as the voltage response for the subthreshold resonant frequency band raises above threshold. For higher input amplitudes evoked spiking resonance is no longer present in these models, but output spiking resonance is present primarily in the parabolic-like model due to a cycle skipping mechanism (involving mixed-mode oscillations), while the cubic-like model shows a better 1:1 entrainment. We use dynamical systems tools to explain the underlying mechanisms and the mechanistic differences between the resonance types. Our results demonstrate that the effective time scales that operate at the subthreshold regime to generate intrinsic subthreshold oscillations, mixed-mode oscillations and subthreshold resonance do not necessarily determine the existence of a preferred spiking response to oscillatory inputs in the same frequency band. The results discussed in this paper highlight both the complexity of the suprathreshold responses to oscillatory inputs in neurons having resonant and amplifying currents with different time scales and the fact that the identity of the participating ionic currents is not enough to predict the resulting patterns, but additional dynamic information, captured by the geometric properties of the phase-space diagram, is needed.

A stable brain from unstable components: Emerging concepts and implications for neural computation

Neuroscientists have often described the adult brain in similar terms to an electronic circuit board- dependent on fixed, precise connectivity. However, with the advent of technologies allowing chronic measurements of neural structure and function, the emerging picture is that neural networks undergo significant remodeling over multiple timescales, even in the absence of experimenter-induced learning or sensory perturbation. Here, we attempt to reconcile the parallel observations that critical brain functions are stably maintained, while synapse- and single-cell properties appear to be reformatted regularly throughout adult life. In this review, we discuss experimental evidence at multiple levels ranging from synapses to neuronal ensembles, suggesting that many parameters are maintained in a dynamic equilibrium. We highlight emerging hypotheses that could explain how stable brain functions may be generated from dynamic elements. Furthermore, we discuss the impact of dynamic circuit elements on neural computations, and how they could provide living neural circuits with computational abilities a fixed structure cannot offer. Taken together, recent evidence indicates that continuous dynamics are a fundamental property of neural circuits compatible with macroscopically stable behaviors. In addition, they may be a unique advantage imparting robustness and flexibility throughout life.

Resonance modulation, annihilation and generation of anti-resonance and anti-phasonance in 3D neuronal systems: interplay of resonant and amplifying currents with slow dynamics

Subthreshold (membrane potential) resonance and phasonance (preferred amplitude and zero-phase responses to oscillatory inputs) in single neurons arise from the interaction between positive and negative feedback effects provided by relatively fast amplifying currents and slower resonant currents. In 2D neuronal systems, amplifying currents are required to be slave to voltage (instantaneously fast) for these phenomena to occur. In higher dimensional systems, additional currents operating at various effective time scales may modulate and annihilate existing resonances and generate antiresonance (minimum amplitude response) and antiphasonance (zero-phase response with phase monotonic properties opposite to phasonance). We use mathematical modeling, numerical simulations and dynamical systems tools to investigate the mechanisms underlying these phenomena in 3D linear models, which are obtained as the linearization of biophysical (conductance-based) models. We characterize the parameter regimes for which the system exhibits the various types of behavior mentioned above in the rather general case in which the underlying 2D system exhibits resonance. We consider two cases: (i) the interplay of two resonant gating variables, and (ii) the interplay of one resonant and one amplifying gating variables. Increasing levels of an amplifying current cause (i) a response amplification if the amplifying current is faster than the resonant current, (ii) resonance and phasonance attenuation and annihilation if the amplifying and resonant currents have identical dynamics, and (iii) antiresonance and antiphasonance if the amplifying current is slower than the resonant current. We investigate the underlying mechanisms by extending the envelope-plane diagram approach developed in previous work (for 2D systems) to three dimensions to include the additional gating variable, and constructing the corresponding envelope curves in these envelope-space diagrams. We find that antiresonance and antiphasonance emerge as the result of an asymptotic boundary layer problem in the frequency domain created by the different balances between the intrinsic time constants of the cell and the input frequency f as it changes. For large enough values of f the envelope curves are quasi-2D and the impedance profile decreases with the input frequency. In contrast, for f ≪ 1 the dynamics are quasi-1D and the impedance profile increases above the limiting value in the other regime. Antiresonance is created because the continuity of the solution requires the impedance profile to connect the portions belonging to the two regimes. If in doing so the phase profile crosses the zero value, then antiphasonance is also generated.

The shaping of intrinsic membrane potential oscillations: positive/negative feedback, ionic resonance/amplification, nonlinearities and time scales

The generation of intrinsic subthreshold (membrane potential) oscillations (STOs) in neuronal models requires the interaction between two processes: a relatively fast positive feedback that favors changes in voltage and a slower negative feedback that opposes these changes. These are provided by the so-called resonant and amplifying gating variables associated to the participating ionic currents. We investigate both the biophysical and dynamic mechanisms of generation of STOs and how their attributes (frequency and amplitude) depend on the model parameters for biophysical (conductance-based) models having qualitatively different types of resonant currents (activating and inactivating) and an amplifying current. Combinations of the same types of ionic currents (same models) in different parameter regimes give rise to different types of nonlinearities in the voltage equation: quasi-linear, parabolic-like and cubic-like. On the other hand, combinations of different types of ionic currents (different models) may give rise to the same type of nonlinearities. We examine how the attributes of the resulting STOs depend on the combined effect of these resonant and amplifying ionic processes, operating at different effective time scales, and the various types of nonlinearities. We find that, while some STO properties and attribute dependencies on the model parameters are determined by the specific combinations of ionic currents (biophysical properties), and are different for models with different such combinations, others are determined by the type of nonlinearities and are common for models with different types of ionic currents. Our results highlight the richness of STO behavior in single cells as the result of the various ways in which resonant and amplifying currents interact and affect the generation and termination of STOs as control parameters change. We make predictions that can be tested experimentally and are expected to contribute to the understanding of how rhythmic activity in neuronal networks emerge from the interplay of the intrinsic properties of the participating neurons and the network connectivity.

Electrophysiological Evidence for Intrinsic Pacemaker Currents in Crayfish Parasol Cells

I used sharp intracellular electrodes to record from parasol cells in the semi-isolated crayfish brain to investigate pacemaker currents. Evidence for the presence of the hyperpolarization-activated inward rectifier potassium current was obtained in about half of the parasol cells examined, where strong, prolonged hyperpolarizing currents generated a slowly-rising voltage sag, and a post-hyperpolarization rebound. The amplitudes of both the sag voltage and the depolarizing rebound were dependent upon the strength of the hyperpolarizing current. The voltage sag showed a definite threshold and was non-inactivating. The voltage sag and rebound depolarization evoked by hyperpolarization were blocked by the presence of 5-10 mM Cs2+ ions, 10 mM tetraethyl ammonium chloride, and 10 mM cobalt chloride in the bathing medium, but not by the drug ZD 7288. Cs+ ions in normal saline in some cells caused a slight increase in mean resting potential and a reduction in spontaneous burst frequency. Many of the neurons expressing the hyperpolarization-activated inward potassium current also provided evidence for the presence of the transient potassium current IA, which was inferred from experimental observations of an increased latency of post-hyperpolarization response to a depolarizing step, compared to the response latency to the depolarization alone. The latency increase was reduced in the presence of 4-aminopyridine (4-AP), a specific blocker of IA. The presence of 4-AP in normal saline also induced spontaneous bursting in parasol cells. It is conjectured that, under normal physiological conditions, these two potassium currents help to regulate burst generation in parasol cells, respectively, by helping to maintain the resting membrane potential near a threshold level for burst generation, and by regulating the rate of rise of membrane depolarizing events leading to burst generation. The presence of post-burst hyperpolarization may depend upon IA channels in parasol cells.

Sensory-Motor Integration: More Variability Reduces Individuality

Motor neural networks and muscles produce identifiably common outputs, such as a trot or gallop, despite varations in intrinsic properties across individuals. New work shows that sensory input can induce the requisite decrease in across-individual variability even as it increases within-individual variability.

Electrosensory Midbrain Neurons Display Feature Invariant Responses to Natural Communication Stimuli

Neurons that respond selectively but in an invariant manner to a given feature of natural stimuli have been observed across species and systems. Such responses emerge in higher brain areas, thereby suggesting that they occur by integrating afferent input. However, the mechanisms by which such integration occurs are poorly understood. Here we show that midbrain electrosensory neurons can respond selectively and in an invariant manner to heterogeneity in behaviorally relevant stimulus waveforms. Such invariant responses were not seen in hindbrain electrosensory neurons providing afferent input to these midbrain neurons, suggesting that response invariance results from nonlinear integration of such input. To test this hypothesis, we built a model based on the Hodgkin-Huxley formalism that received realistic afferent input. We found that multiple combinations of parameter values could give rise to invariant responses matching those seen experimentally. Our model thus shows that there are multiple solutions towards achieving invariant responses and reveals how subthreshold membrane conductances help promote robust and invariant firing in response to heterogeneous stimulus waveforms associated with behaviorally relevant stimuli. We discuss the implications of our findings for the electrosensory and other systems.

Feedback control of variability in the cycle period of a central pattern generator

We address how feedback to a bursting biological pacemaker with intrinsic variability in cycle length can affect that variability. Specifically, we examine a hybrid circuit constructed of an isolated crab anterior burster (AB)/pyloric dilator (PD) pyloric pacemaker receiving virtual feedback via dynamic clamp. This virtual feedback generates artificial synaptic input to PD with timing determined by adjustable phase response dynamics that mimic average burst intervals generated by the lateral pyloric neuron (LP) in the intact pyloric network. Using this system, we measure network period variability dependence on the feedback element's phase response dynamics and find that a constant response interval confers minimum variability. We further find that these optimal dynamics are characteristic of the biological pyloric network. Building upon our previous theoretical work mapping the firing intervals in one cycle onto the firing intervals in the next cycle, we create a theoretical map of the distribution of all firing intervals in one cycle to the distribution of firing intervals in the next cycle. We then obtain an integral equation for a stationary self-consistent distribution of the network periods of the hybrid circuit, which can be solved numerically given the uncoupled pacemaker's distribution of intrinsic periods, the nature of the network's feedback, and the phase resetting characteristics of the pacemaker. The stationary distributions obtained in this manner are strongly predictive of the experimentally observed distributions of hybrid network period. This theoretical framework can provide insight into optimal feedback schemes for minimizing variability to increase reliability or maximizing variability to increase flexibility in central pattern generators driven by pacemakers with feedback.

Differential effects of conductances on the phase resetting curve of a bursting neuronal oscillator

The intrinsically oscillating neurons in the crustacean pyloric circuit have membrane conductances that influence their spontaneous activity patterns and responses to synaptic activity. The relationship between the magnitudes of these membrane conductances and the response of the oscillating neurons to synaptic input has not yet been fully or systematically explored. We examined this relationship using the phase resetting curve (PRC), which summarizes the change in the cycle period of a neuronal oscillator as a function of the input's timing within the oscillation. We first utilized a large database of single-compartment model neurons to determine the effect of individual membrane conductances on PRC shape; we found that the effects vary across conductance space, but on average, the hyperpolarization-activated and leak conductances advance the PRC. We next investigated how membrane conductances affect PRCs of the isolated pacemaker kernel in the pyloric circuit of Cancer borealis by: (1) tabulating PRCs while using dynamic clamp to artificially add varying levels of specific conductances, and (2) tabulating PRCs before and after blocking the endogenous hyperpolarization-activated current. We additionally used a previously described four-compartment model to determine how the location of the hyperpolarization-activated conductance influences that current's effect on the PRC. We report that while dynamic-clamp-injected leak current has much smaller effects on the PRC than suggested by the single-compartment model, an increase in the hyperpolarization-activated conductance both advances and reduces the noisiness of the PRC in the pacemaker kernel of the pyloric circuit in both modeling and experimental studies.

Mechanisms of gain control by voltage-gated channels in intrinsically-firing neurons

Gain modulation is a key feature of neural information processing, but underlying mechanisms remain unclear. In single neurons, gain can be measured as the slope of the current-frequency (input-output) relationship over any given range of inputs. While much work has focused on the control of basal firing rates and spike rate adaptation, gain control has been relatively unstudied. Of the limited studies on gain control, some have examined the roles of synaptic noise and passive somatic currents, but the roles of voltage-gated channels present ubiquitously in neurons have been less explored. Here, we systematically examined the relationship between gain and voltage-gated ion channels in a conductance-based, tonically-active, model neuron. Changes in expression (conductance density) of voltage-gated channels increased (Ca²⁺ channel), reduced (K⁺ channels), or produced little effect (h-type channel) on gain. We found that the gain-controlling ability of channels increased exponentially with the steepness of their activation within the dynamic voltage window (voltage range associated with firing). For depolarization-activated channels, this produced a greater channel current per action potential at higher firing rates. This allowed these channels to modulate gain by contributing to firing preferentially at states of higher excitation. A finer analysis of the current-voltage relationship during tonic firing identified narrow voltage windows at which the gain-modulating channels exerted their effects. As a proof of concept, we show that h-type channels can be tuned to modulate gain by changing the steepness of their activation within the dynamic voltage window. These results show how the impact of an ion channel on gain can be predicted from the relationship between channel kinetics and the membrane potential during firing. This is potentially relevant to understanding input-output scaling in a wide class of neurons found throughout the brain and other nervous systems.

A modeling approach on why simple central pattern generators are built of irregular neurons

The crustacean pyloric Central Pattern Generator (CPG) is a nervous circuit that endogenously provides periodic motor patterns. Even after about 40 years of intensive studies, the rhythm genesis is still not rigorously understood in this CPG, mainly because it is made of neurons with irregular intrinsic activity. Using mathematical models we addressed the question of using a network of irregularly behaving elements to generate periodic oscillations, and we show some advantages of using non-periodic neurons with intrinsic behavior in the transition from bursting to tonic spiking (as found in biological pyloric CPGs) as building components. We studied two- and three-neuron model CPGs built either with Hindmarsh-Rose or with conductance-based Hodgkin-Huxley-like model neurons. By changing a model’s parameter we could span the neuron’s intrinsic dynamical behavior from slow periodic bursting to fast tonic spiking, passing through a transition where irregular bursting was observed. Two-neuron CPG, half center oscillator (HCO), was obtained for each intrinsic behavior of the neurons by coupling them with mutual symmetric synaptic inhibition. Most of these HCOs presented regular antiphasic bursting activity and the changes of the bursting frequencies was studied as a function of the inhibitory synaptic strength. Among all HCOs, those made of intrinsic irregular neurons presented a wider burst frequency range while keeping a reliable regular oscillatory (bursting) behavior. HCOs of periodic neurons tended to be either hard to change their behavior with synaptic strength variations (slow periodic burster neurons) or unable to perform a physiologically meaningful rhythm (fast tonic spiking neurons). Moreover, 3-neuron CPGs with connectivity and output similar to those of the pyloric CPG presented the same results.

Maladaptive neural synchrony in tinnitus: origin and restoration

Tinnitus is the conscious perception of sound heard in the absence of physical sound sources external or internal to the body, reflected in aberrant neural synchrony of spontaneous or resting-state brain activity. Neural synchrony is generated by the nearly simultaneous firing of individual neurons, of the synchronization of membrane-potential changes in local neural groups as reflected in the local field potentials, resulting in the presence of oscillatory brain waves in the EEG. Noise-induced hearing loss, often resulting in tinnitus, causes a reorganization of the tonotopic map in auditory cortex and increased spontaneous firing rates and neural synchrony. Spontaneous brain rhythms rely on neural synchrony. Abnormal neural synchrony in tinnitus appears to be confined to specific frequency bands of brain rhythms. Increases in delta-band activity are generated by deafferented/deprived neuronal networks resulting from hearing loss. Coordinated reset (CR) stimulation was developed in order to specifically counteract such abnormal neuronal synchrony by desynchronization. The goal of acoustic CR neuromodulation is to desynchronize tinnitus-related abnormal delta-band oscillations. CR neuromodulation does not require permanent stimulus delivery in order to achieve long-lasting desynchronization or even a full-blown anti-kindling but may have cumulative effects, i.e., the effect of different CR epochs separated by pauses may accumulate. Unlike other approaches, acoustic CR neuromodulation does not intend to reduce tinnitus-related neuronal activity by employing lateral inhibition. The potential efficacy of acoustic CR modulation was shown in a clinical proof of concept trial, where effects achieved in 12 weeks of treatment delivered 4–6 h/day persisted through a preplanned 4-week therapy pause and showed sustained long-term effects after 10 months of therapy, leading to 75% responders.

Intersegmental coupling and recovery from perturbations in freely running cockroaches

Cockroaches are remarkably stable runners, exhibiting rapid recovery from external perturbations. To uncover the mechanisms behind this important behavioral trait, we recorded leg kinematics of freely running animals in both undisturbed and perturbed trials. Functional coupling underlying inter-leg coordination was monitored before and during localized perturbations, which were applied to single legs via magnetic impulses. The resulting transient effects on all legs and the recovery times to normal pre-perturbation kinematics were studied. We estimated coupling architecture and strength by fitting experimental data to a six-leg-unit phase oscillator model. Using maximum-likelihood techniques, we found that a network with nearest-neighbor inter-leg coupling best fitted the data and that, although coupling strengths vary among preparations, the overall inputs entering each leg are approximately balanced and consistent. Simulations of models with different coupling strengths encountering perturbations suggest that the coupling schemes estimated from our experiments allow animals relatively fast and uniform recoveries from perturbations.

Control of abnormal synchronization in neurological disorders

In the nervous system, synchronization processes play an important role, e.g., in the context of information processing and motor control. However, pathological, excessive synchronization may strongly impair brain function and is a hallmark of several neurological disorders. This focused review addresses the question of how an abnormal neuronal synchronization can specifically be counteracted by invasive and non-invasive brain stimulation as, for instance, by deep brain stimulation for the treatment of Parkinson’s disease, or by acoustic stimulation for the treatment of tinnitus. On the example of coordinated reset (CR) neuromodulation, we illustrate how insights into the dynamics of complex systems contribute to successful model-based approaches, which use methods from synergetics, non-linear dynamics, and statistical physics, for the development of novel therapies for normalization of brain function and synaptic connectivity. Based on the intrinsic multistability of the neuronal populations induced by spike timing-dependent plasticity (STDP), CR neuromodulation utilizes the mutual interdependence between synaptic connectivity and dynamics of the neuronal networks in order to restore more physiological patterns of connectivity via desynchronization of neuronal activity. The very goal is to shift the neuronal population by stimulation from an abnormally coupled and synchronized state to a desynchronized regime with normalized synaptic connectivity, which significantly outlasts the stimulation cessation, so that long-lasting therapeutic effects can be achieved.

The integrative role of the sigh in psychology, physiology, pathology, and neurobiology

"Sighs, tears, grief, distress" expresses Johann Sebastian Bach in a musical example for the relationship between sighs and deep emotions. This review explores the neurobiological basis of the sigh and its relationship with psychology, physiology, and pathology. Sighs monitor changes in brain states, induce arousal, and reset breathing variability. These behavioral roles homeostatically regulate breathing stability under physiological and pathological conditions. Sighs evoked in hypoxia evoke arousal and thereby become critical for survival. Hypoarousal and failure to sigh have been associated with sudden infant death syndrome. Increased breathing irregularity may provoke excessive sighing and hyperarousal, a behavioral sequence that may play a role in panic disorders. Essential for generating sighs and breathing is the pre-Bötzinger complex. Modulatory and synaptic interactions within this local network and between networks located in the brainstem, cerebellum, cortex, hypothalamus, amygdala, and the periaqueductal gray may govern the relationships between physiology, psychology, and pathology. Unraveling these circuits will lead to a better understanding of how we balance emotions and how emotions become pathological.

Mechanisms of seizure propagation in 2-dimensional centre-surround recurrent networks

Understanding how seizures spread throughout the brain is an important problem in the treatment of epilepsy, especially for implantable devices that aim to avert focal seizures before they spread to, and overwhelm, the rest of the brain. This paper presents an analysis of the speed of propagation in a computational model of seizure-like activity in a 2-dimensional recurrent network of integrate-and-fire neurons containing both excitatory and inhibitory populations and having a difference of Gaussians connectivity structure, an approximation to that observed in cerebral cortex. In the same computational model network, alternative mechanisms are explored in order to simulate the range of seizure-like activity propagation speeds (0.1-100 mm/s) observed in two animal-slice-based models of epilepsy: (1) low extracellular [Formula: see text], which creates excess excitation and (2) introduction of gamma-aminobutyric acid (GABA) antagonists, which reduce inhibition. Moreover, two alternative connection topologies are considered: excitation broader than inhibition, and inhibition broader than excitation. It was found that the empirically observed range of propagation velocities can be obtained for both connection topologies. For the case of the GABA antagonist model simulation, consistent with other studies, it was found that there is an effective threshold in the degree of inhibition below which waves begin to propagate. For the case of the low extracellular [Formula: see text] model simulation, it was found that activity-dependent reductions in inhibition provide a potential explanation for the emergence of slowly propagating waves. This was simulated as a depression of inhibitory synapses, but it may also be achieved by other mechanisms. This work provides a localised network understanding of the propagation of seizures in 2-dimensional centre-surround networks that can be tested empirically.

Reversing pathologically increased EEG power by acoustic coordinated reset neuromodulation

Acoustic Coordinated Reset (CR) neuromodulation is a patterned stimulation with tones adjusted to the patient's dominant tinnitus frequency, which aims at desynchronizing pathological neuronal synchronization. In a recent proof-of-concept study, CR therapy, delivered 4-6 h/day more than 12 weeks, induced a significant clinical improvement along with a significant long-lasting decrease of pathological oscillatory power in the low frequency as well as γ band and an increase of the α power in a network of tinnitus-related brain areas. As yet, it remains unclear whether CR shifts the brain activity toward physiological levels or whether it induces clinically beneficial, but nonetheless abnormal electroencephalographic (EEG) patterns, for example excessively decreased δ and/or γ. Here, we compared the patients' spontaneous EEG data at baseline as well as after 12 weeks of CR therapy with the spontaneous EEG of healthy controls by means of Brain Electrical Source Analysis source montage and standardized low-resolution brain electromagnetic tomography techniques. The relationship between changes in EEG power and clinical scores was investigated using a partial least squares approach. In this way, we show that acoustic CR neuromodulation leads to a normalization of the oscillatory power in the tinnitus-related network of brain areas, most prominently in temporal regions. A positive association was found between the changes in tinnitus severity and the normalization of δ and γ power in the temporal, parietal, and cingulate cortical regions. Our findings demonstrate a widespread CR-induced normalization of EEG power, significantly associated with a reduction of tinnitus severity.

Successful reconstruction of a physiological circuit with known connectivity from spiking activity alone

Identifying the structure and dynamics of synaptic interactions between neurons is the first step to understanding neural network dynamics. The presence of synaptic connections is traditionally inferred through the use of targeted stimulation and paired recordings or by post-hoc histology. More recently, causal network inference algorithms have been proposed to deduce connectivity directly from electrophysiological signals, such as extracellularly recorded spiking activity. Usually, these algorithms have not been validated on a neurophysiological data set for which the actual circuitry is known. Recent work has shown that traditional network inference algorithms based on linear models typically fail to identify the correct coupling of a small central pattern generating circuit in the stomatogastric ganglion of the crab Cancer borealis. In this work, we show that point process models of observed spike trains can guide inference of relative connectivity estimates that match the known physiological connectivity of the central pattern generator up to a choice of threshold. We elucidate the necessary steps to derive faithful connectivity estimates from a model that incorporates the spike train nature of the data. We then apply the model to measure changes in the effective connectivity pattern in response to two pharmacological interventions, which affect both intrinsic neural dynamics and synaptic transmission. Our results provide the first successful application of a network inference algorithm to a circuit for which the actual physiological synapses between neurons are known. The point process methodology presented here generalizes well to larger networks and can describe the statistics of neural populations. In general we show that advanced statistical models allow for the characterization of effective network structure, deciphering underlying network dynamics and estimating information-processing capabilities.

To appreciate how neural circuits control behaviors, we must understand two things. First, how the neurons comprising the circuit are connected, and second, how neurons and their connections change after learning or in response to neuromodulators. Neuronal connectivity is difficult to determine experimentally, whereas neuronal activity can often be readily measured. We describe a statistical model to estimate circuit connectivity directly from measured activity patterns. We use the timing relationships between observed spikes to predict synaptic interactions between simultaneously observed neurons. The model estimate provides each predicted connection with a curve that represents how strongly, and at which temporal delays, one circuit element effectively influences another. These curves are analogous to synaptic interactions of the level of the membrane potential of biological neurons and share some of their features such as being inhibitory or excitatory. We test our method on recordings from the pyloric circuit in the crab stomatogastric ganglion, a small circuit whose connectivity is completely known beforehand, and find that the predicted circuit matches the biological one — a result other techniques failed to achieve. In addition, we show that drug manipulations impacting the circuit are revealed by this technique. These results illustrate the utility of our analysis approach for inferring connections from neural spiking activity.

Potassium conductance dynamics confer robust spike-time precision in a neuromorphic model of the auditory brain stem

A fundamental question in neuroscience is how neurons perform precise operations despite inherent variability. This question also applies to neuromorphic engineering, where low-power microchips emulate the brain using large populations of diverse silicon neurons. Biological neurons in the auditory pathway display precise spike timing, critical for sound localization and interpretation of complex waveforms such as speech, even though they are a heterogeneous population. Silicon neurons are also heterogeneous, due to a key design constraint in neuromorphic engineering: smaller transistors offer lower power consumption and more neurons per unit area of silicon, but also more variability between transistors and thus between silicon neurons. Utilizing this variability in a neuromorphic model of the auditory brain stem with 1,080 silicon neurons, we found that a low-voltage-activated potassium conductance (g(KL)) enables precise spike timing via two mechanisms: statically reducing the resting membrane time constant and dynamically suppressing late synaptic inputs. The relative contribution of these two mechanisms is unknown because blocking g(KL) in vitro eliminates dynamic adaptation but also lengthens the membrane time constant. We replaced g(KL) with a static leak in silico to recover the short membrane time constant and found that silicon neurons could mimic the spike-time precision of their biological counterparts, but only over a narrow range of stimulus intensities and biophysical parameters. The dynamics of g(KL) were required for precise spike timing robust to stimulus variation across a heterogeneous population of silicon neurons, thus explaining how neural and neuromorphic systems may perform precise operations despite inherent variability.

Modifying spiking precision in conductance-based neuronal models

The temporal precision of a neuron's spiking can be characterized by calculating its "jitter," defined as the standard deviation of the timing of individual spikes in response to repeated presentations of a stimulus. Sub-millisecond jitters have been measured for neurons in a variety of experimental systems and appear to be functionally important in some instances. We have investigated how modifying a neuron's maximal conductances affects jitter using the leaky integrate-and-fire (LIF) model and an eight-conductance Hodgkin-Huxley type (HH8) model. We observed that jitter can be largely understood in the LIF model in terms of the neuron's filtering properties. In the HH8 model we found the role of individual conductances in determining jitter to be complicated and dependent on the model's spiking properties. Distinct behaviors were observed for populations with slow (<11.5 Hz) and fast (>11.5 Hz) spike rates and appear to be related to differences in a particular channel's activity at times just before spiking occurs.

Neuromodulation of neuronal circuits: back to the future

All nervous systems are subject to neuromodulation. Neuromodulators can be delivered as local hormones, as cotransmitters in projection neurons, and through the general circulation. Because neuromodulators can transform the intrinsic firing properties of circuit neurons and alter effective synaptic strength, neuromodulatory substances reconfigure neuronal circuits, often massively altering their output. Thus, the anatomical connectome provides a minimal structure and the neuromodulatory environment constructs and specifies the functional circuits that give rise to behavior.

Tuning low-voltage-activated A-current for silent gain modulation

Modulation of stimulus-response gain and stability of spontaneous (unstimulated) firing are both important for neural computation. However, biologically plausible mechanisms that allow these distinct functional capabilities to coexist in the same neuron are poorly defined. Low-threshold, inactivating (A-type) K(+) currents (I(A)) are found in many biological neurons and are historically known for enabling low-frequency firing. By performing simulations using a conductance-based model neuron, here we show that biologically plausible shifts in I(A) conductance and inactivation kinetics produce dissociated effects on gain and intrinsic firing. This enables I(A) to regulate gain without major changes in intrinsic firing rate. Tuning I(A) properties may thus represent a previously unsuspected single-current mechanism of silent gain control in neurons.

Robustness, variability, phase dependence, and longevity of individual synaptic input effects on spike timing during fluctuating synaptic backgrounds: a modeling study of globus pallidus neuron phase response properties

A neuron's phase response curve (PRC) shows how inputs arriving at different times during the spike cycle differentially affect the timing of subsequent spikes. Using a full morphological model of a globus pallidus (GP) neuron, we previously demonstrated that dendritic conductances shape the PRC in a spike frequency-dependent manner, suggesting different functional roles of perisomatic and distal dendritic synapses in the control of patterned network activity. In the present study we extend this analysis to examine the impact of physiologically realistic high conductance states on somatic and dendritic PRCs and the time course of spike train perturbations. First, we found that average somatic and dendritic PRCs preserved their shapes and spike frequency dependence when the model was driven by spatially-distributed, stochastic conductance inputs rather than tonic somatic current. However, responses to inputs during specific synaptic backgrounds often deviated substantially from the average PRC. Therefore, we analyzed the interactions of PRC stimuli with transient fluctuations in the synaptic background on a trial-by-trial basis. We found that the variability in responses to PRC stimuli and the incidence of stimulus-evoked added or skipped spikes were stimulus-phase-dependent and reflected the profile of the average PRC, suggesting commonality in the underlying mechanisms. Clear differences in the relation between the phase of input and variability of spike response between dendritic and somatic inputs indicate that these regions generally represent distinct dynamical subsystems of synaptic integration with respect to influencing the stability of spike time attractors generated by the overall synaptic conductance.

Co-variation of ionic conductances supports phase maintenance in stomatogastric neurons

Neuronal networks produce reliable functional output throughout the lifespan of an animal despite ceaseless molecular turnover and a constantly changing environment. Central pattern generators, such as those of the crustacean stomatogastric ganglion (STG), are able to robustly maintain their functionality over a wide range of burst periods. Previous experimental work involving extracellular recordings of the pyloric pattern of the STG has demonstrated that as the burst period varies, the inter-neuronal delays are altered proportionally, resulting in burst phases that are roughly invariant. The question whether spike delays within bursts are also proportional to pyloric period has not been explored in detail. The mechanism by which the pyloric neurons accomplish phase maintenance is currently not obvious. Previous studies suggest that the co-regulation of certain ion channel properties may play a role in governing neuronal activity. Here, we observed in long-term recordings of the pyloric rhythm that spike delays can vary proportionally with burst period, so that spike phase is maintained. We then used a conductance-based model neuron to determine whether co-varying ionic membrane conductances results in neural output that emulates the experimentally observed phenomenon of spike phase maintenance. Next, we utilized a model neuron database to determine whether conductance correlations exist in model neuron populations with highly maintained spike phases. We found that co-varying certain conductances, including the sodium and transient calcium conductance pair, causes the model neuron to maintain a specific spike phase pattern. Results indicate a possible relationship between conductance co-regulation and phase maintenance in STG neurons.

Inhibitory feedback promotes stability in an oscillatory network

Reliability and variability of neuronal activity are both thought to be important for the proper function of neuronal networks. The crustacean pyloric rhythm (∼1 Hz) is driven by a group of pacemaker neurons (AB/PD) that inhibit and burst out of phase with all follower pyloric neurons. The only known chemical synaptic feedback to the pacemakers is an inhibitory synapse from the follower lateral pyloric (LP) neuron. Although this synapse has been studied extensively, its role in the generation and coordination of the pyloric rhythm is unknown. We examine the hypothesis that this synapse acts to stabilize the oscillation by reducing the variability in cycle period on a cycle-by-cycle basis. Our experimental data show that functionally removing the LP-pyloric dilator (PD) synapse by hyperpolarizing the LP neuron increases the pyloric period variability. The increase in pyloric rhythm stability in the presence of the LP-PD synapse is demonstrated by a decrease in the amplitude of the phase response curve of the PD neuron. These experimental results are explained by a reduced mathematical model. Phase plane analysis of this model demonstrates that the effect of the periodic inhibition is to produce asymptotic stability in the oscillation phase, which leads to a reduction in variability of the oscillation cycle period.

Responses of a bursting pacemaker to excitation reveal spatial segregation between bursting and spiking mechanisms

Central pattern generators (CPGs) frequently include bursting neurons that serve as pacemakers for rhythm generation. Phase resetting curves (PRCs) can provide insight into mechanisms underlying phase locking in such circuits. PRCs were constructed for a pacemaker bursting complex in the pyloric circuit in the stomatogastric ganglion of the lobster and crab. This complex is comprised of the Anterior Burster (AB) neuron and two Pyloric Dilator (PD) neurons that are all electrically coupled. Artificial excitatory synaptic conductance pulses of different strengths and durations were injected into one of the AB or PD somata using the Dynamic Clamp. Previously, we characterized the inhibitory PRCs by assuming a single slow process that enabled synaptic inputs to trigger switches between an up state in which spiking occurs and a down state in which it does not. Excitation produced five different PRC shapes, which could not be explained with such a simple model. A separate dendritic compartment was required to separate the mechanism that generates the up and down phases of the bursting envelope (1) from synaptic inputs applied at the soma, (2) from axonal spike generation and (3) from a slow process with a slower time scale than burst generation. This study reveals that due to the nonlinear properties and compartmentalization of ionic channels, the response to excitation is more complex than inhibition.

Variability, compensation, and modulation in neurons and circuits

I summarize recent computational and experimental work that addresses the inherent variability in the synaptic and intrinsic conductances in normal healthy brains and shows that multiple solutions (sets of parameters) can produce similar circuit performance. I then discuss a number of issues raised by this observation, such as which parameter variations arise from compensatory mechanisms and which reflect insensitivity to those particular parameters. I ask whether networks with different sets of underlying parameters can nonetheless respond reliably to neuromodulation and other global perturbations. At the computational level, I describe a paradigm shift in which it is becoming increasingly common to develop families of models that reflect the variance in the biological data that the models are intended to illuminate rather than single, highly tuned models. On the experimental side, I discuss the inherent limitations of overreliance on mean data and suggest that it is important to look for compensations and correlations among as many system parameters as possible, and between each system parameter and circuit performance. This second paradigm shift will require moving away from measurements of each system component in isolation but should reveal important previously undescribed principles in the organization of complex systems such as brains.

Differential modulation of synaptic strength and timing regulate synaptic efficacy in a motor network

Neuromodulators modify network output by altering neuronal firing properties and synaptic strength at multiple sites; however, the functional importance of each site is often unclear. We determined the importance of monoamine modulation of a single synapse for regulation of network cycle frequency in the oscillatory pyloric network of the lobster. The pacemaker kernel of the pyloric network receives only one chemical synaptic feedback, an inhibitory synapse from the lateral pyloric (LP) neuron to the pyloric dilator (PD) neurons, which can limit cycle frequency. We measured the effects of dopamine (DA), octopamine (Oct), and serotonin (5HT) on the strength of the LP→PD synapse and the ability of the modified synapse to regulate pyloric cycle frequency. DA and Oct strengthened, whereas 5HT weakened, LP→PD inhibition. Surprisingly, the DA-strengthened LP→PD synapse lost its ability to slow the pyloric oscillations, whereas the 5HT-weakened LP→PD synapse gained a greater influence on the oscillations. These results are explained by monoamine modulation of factors that determine the firing phase of the LP neuron in each cycle. DA acts via multiple mechanisms to phase-advance the LP neuron into the pacemaker's refractory period, where the strengthened synapse has little effect. In contrast, 5HT phase-delays LP activity into a region of greater pacemaker sensitivity to LP synaptic input. Only Oct enhanced LP regulation of cycle period simply by enhancing LP→PD synaptic strength. These results show that modulation of the strength and timing of a synaptic input can differentially affect the synapse's efficacy in the network.

Synaptic patterning of left-right alternation in a computational model of the rodent hindlimb central pattern generator

Establishing, maintaining, and modifying the phase relationships between extensor and flexor muscle groups is essential for central pattern generators in the spinal cord to coordinate the hindlimbs well enough to produce the basic walking rhythm. This paper investigates a simplified computational model for the spinal hindlimb central pattern generator (CPG) that is abstracted from experimental data from the rodent spinal cord. This model produces locomotor-like activity with appropriate phase relationships in which right and left muscle groups alternate while extensor and flexor muscle groups alternate. Convergence to this locomotor pattern is slow, however, and the range of parameter values for which the model produces appropriate output is relatively narrow. We examine these aspects of the model's coordination of left-right activity through investigation of successively more complicated subnetworks, focusing on the role of the synaptic architecture in shaping motoneuron phasing. We find unexpected sensitivity in the phase response properties of individual neurons in response to stimulation and a need for high levels of both inhibition and excitation to achieve the walking rhythm. In the absence of cross-cord excitation, equal levels of ipsilateral and contralateral inhibition result in a strong preference for hopping over walking. Inhibition alone can produce the walking rhythm, but contralateral inhibition must be much stronger than ipsilateral inhibition. Cross-cord excitatory connections significantly enhance convergence to the walking rhythm, which is achieved most rapidly with strong crossed excitation and greater contralateral than ipsilateral inhibition. We discuss the implications of these results for CPG architectures based on unit burst generators.

Functional consequences of animal-to-animal variation in circuit parameters

How different are the neuronal circuits for a given behavior across individual animals? To address this question, we measured multiple cellular and synaptic parameters in individual preparations to see how they correlated with circuit function, using neurons and synapses in the pyloric circuit of the stomatogastric ganglion of the crab Cancer borealis. There was considerable preparation-to-preparation variability in the strength of two identified synapses, in the amplitude of a modulator-evoked current and in the expression of six ion channel genes. Nonetheless, we found strong correlations across preparations among these parameters and attributes of circuit performance. These data illustrate the importance of making multidimensional measurements from single preparations for understanding how variability in circuit output is related to the variability of multiple circuit parameters.

Modulation of stomatogastric rhythms

Neuromodulation by peptides and amines is a primary source of plasticity in the nervous system as it adapts the animal to an ever-changing environment. The crustacean stomatogastric nervous system is one of the premier systems to study neuromodulation and its effects on motor pattern generation at the cellular level. It contains the extensively modulated central pattern generators that drive the gastric mill (chewing) and pyloric (food filtering) rhythms. Neuromodulators affect all stages of neuronal processing in this system, from membrane currents and synaptic transmission in network neurons to the properties of the effector muscles. The ease with which distinct neurons are identified and their activity is recorded in this system has provided considerable insight into the mechanisms by which neuromodulators affect their target cells and modulatory neuron function. Recent evidence suggests that neuromodulators are involved in homeostatic processes and that the modulatory system itself is under modulatory control, a fascinating topic whose surface has been barely scratched. Future challenges include exploring the behavioral conditions under which these systems are activated and how their effects are regulated.

Robust microcircuit synchronization by inhibitory connections

Microcircuits in different brain areas share similar architectural and biophysical properties with compact motor networks known as central pattern generators (CPGs). Consequently, CPGs have been suggested as valuable biological models for understanding of microcircuit dynamics and particularly, their synchronization. We use a well known compact motor network, the lobster pyloric CPG to study principles of intercircuit synchronization. We couple separate pyloric circuits obtained from two animals via artificial synapses and observe how their synchronization depends on the topology and kinetic parameters of the computer-generated synapses. Stable in-phase synchronization appears when electrically coupling the pacemaker groups of the two networks, but reciprocal inhibitory connections produce more robust and regular cooperative activity. Contralateral inhibitory connections offer effective synchronization and flexible setting of the burst phases of the interacting networks. We also show that a conductance-based mathematical model of the coupled circuits correctly reproduces the observed dynamics illustrating the generality of the phenomena.

Probing the dynamics of identified neurons with a data-driven modeling approach

In controlling animal behavior the nervous system has to perform within the operational limits set by the requirements of each specific behavior. The implications for the corresponding range of suitable network, single neuron, and ion channel properties have remained elusive. In this article we approach the question of how well-constrained properties of neuronal systems may be on the neuronal level. We used large data sets of the activity of isolated invertebrate identified cells and built an accurate conductance-based model for this cell type using customized automated parameter estimation techniques. By direct inspection of the data we found that the variability of the neurons is larger when they are isolated from the circuit than when in the intact system. Furthermore, the responses of the neurons to perturbations appear to be more consistent than their autonomous behavior under stationary conditions. In the developed model, the constraints on different parameters that enforce appropriate model dynamics vary widely from some very tightly controlled parameters to others that are almost arbitrary. The model also allows predictions for the effect of blocking selected ionic currents and to prove that the origin of irregular dynamics in the neuron model is proper chaoticity and that this chaoticity is typical in an appropriate sense. Our results indicate that data driven models are useful tools for the in-depth analysis of neuronal dynamics. The better consistency of responses to perturbations, in the real neurons as well as in the model, suggests a paradigm shift away from measuring autonomous dynamics alone towards protocols of controlled perturbations. Our predictions for the impact of channel blockers on the neuronal dynamics and the proof of chaoticity underscore the wide scope of our approach.

Sensory-induced modification of two motor patterns in the crab, Cancer pagurus

Sensory input is pervasive among motor networks and continuously adapts motor patterns to changing circumstances. To elucidate common principles of sensorimotor integration, it is beneficial to characterize sensory influences on motor network operation and compare these influences between species. To facilitate such comparison, we have studied the influence of the anterior gastric receptor (AGR) - a proprioceptor that has been characterized in detail in two lobster species - on the pyloric (filtering of food) and gastric mill (chewing of food) motor patterns in the crab Cancer pagurus. AGR has a bipolar cell body in the stomatogastric ganglion; it was activated by tension increase in gastric mill powerstroke muscles. While two spike initiation zones accounted for its spontaneous activity, active membrane properties (sag potentials, spike frequency adaptation) contributed to the AGR response to current injections. When activated, AGR diminished spike activities in two pyloric motor neurons and prolonged the pyloric cycle period. Furthermore, AGR excited gastric mill protractor neurons, inhibited the retractor neuron and evoked phase-independent resetting of the gastric mill rhythm. Repetitive spike trains entrained the rhythm to both longer and shorter cycle periods. All AGR actions seemed to be mediated via at least two premotor projection neurons in the spatially distant commissural ganglia. The response of the gastric mill neurons was independent of AGR firing frequency. Our results suggest that homologous proprioceptors can elicit similar effects on motor patterns while utilizing different mechanisms. This work thus provides an initial framework for future studies to determine underlying common principles.

Parameter space analysis suggests multi-site plasticity contributes to motor pattern initiation in Tritonia

This research examines the mechanisms that initiate rhythmic activity in the episodic central pattern generator (CPG) underlying escape swimming in the gastropod mollusk Tritonia diomedea. Activation of the network is triggered by extrinsic excitatory input but also accompanied by intrinsic neuromodulation and the recruitment of additional excitation into the circuit. To examine how these factors influence circuit activation, a detailed simulation of the unmodulated CPG network was constructed from an extensive set of physiological measurements. In this model, extrinsic input alone is insufficient to initiate rhythmic activity, confirming that additional processes are involved in circuit activation. However, incorporating known neuromodulatory and polysynaptic effects into the model still failed to enable rhythmic activity, suggesting that additional circuit features are also required. To delineate the additional activation requirements, a large-scale parameter-space analysis was conducted (~2 x 10(6) configurations). The results suggest that initiation of the swim motor pattern requires substantial reconfiguration at multiple sites within the network, especially to recruit ventral swim interneuron-B (VSI) activity and increase coupling between the dorsal swim interneurons (DSIs) and cerebral neuron 2 (C2) coupling. Within the parameter space examined, we observed a tendency for rhythmic activity to be spontaneous and self-sustaining. This suggests that initiation of episodic rhythmic activity may involve temporarily restructuring a nonrhythmic network into a persistent oscillator. In particular, the time course of neuromodulatory effects may control both activation and termination of rhythmic bursting.

Understanding Circuit Dynamics Using the Stomatogastric Nervous System of Lobsters and Crabs

Studies of the stomatogastric nervous systems of lobsters and crabs have led to numerous insights into the cellular and circuit mechanisms that generate rhythmic motor patterns. The small number of easily identifiable neurons allowed the establishment of connectivity diagrams among the neurons of the stomatogastric ganglion. We now know that (a) neuromodulatory substances reconfigure circuit dynamics by altering synaptic strength and voltage-dependent conductances and (b) individual neurons can switch among different functional circuits. Computational and experimental studies of single-neuron and network homeostatic regulation have provided insight into compensatory mechanisms that can underlie stable network performance. Many of the observations first made using the stomatogastric nervous system can be generalized to other invertebrate and vertebrate circuits.