Cold-Temperature Coding with Bursting and Spiking Based on TRP Channel Dynamics in Drosophila Larva Sensory Neurons.

Temperature sensation involves thermosensitive TRP (thermoTRP) and non-TRP channels. Drosophila larval Class III (CIII) neurons serve as the primary cold nociceptors and express a suite of thermoTRP channels implicated in noxious cold sensation. How CIII neurons code temperature remains unclear. We combined computational and electrophysiological methods to address this question. In electrophysiological experiments, we identified two basic cold-evoked patterns of CIII neurons: bursting and spiking. In response to a fast temperature drop to noxious cold, CIII neurons distinctly mark different phases of the stimulus. Bursts frequently occurred along with the fast temperature drop, forming a peak in the spiking rate and likely coding the high rate of the temperature change. Single spikes dominated at a steady temperature and exhibited frequency adaptation following the peak. When temperature decreased slowly to the same value, mainly spiking activity was observed, with bursts occurring sporadically throughout the stimulation. The spike and the burst frequencies positively correlated with the rate of the temperature drop. Using a computational model, we explain the distinction in the occurrence of the two CIII cold-evoked patterns bursting and spiking using the dynamics of a thermoTRP current. A two-parameter activity map (Temperature, constant TRP current conductance) marks parameters that support silent, spiking, and bursting regimes. Projecting on the map the instantaneous TRP conductance, governed by activation and inactivation processes, reflects temperature coding responses as a path across silent, spiking, or bursting domains on the map. The map sheds light on how various parameter sets for TRP kinetics represent various types of cold-evoked responses. Together, our results indicate that bursting detects the high rate of temperature change, whereas tonic spiking could reflect both the rate of change and magnitude of steady cold temperature.

Microgeometrical dendritic factors predict electrical decoupling between somatic and dendritic compartments in magnocellular neurosecretory neurons.

It is generally assumed that dendritic release of neuropeptides from magnocellular neurosecretory neurons (MNNs), a critical process involved in homeostatic functions, is an activity-dependent process that requires backpropagating action potentials (APs). Still, growing evidence indicates that dendritic release can occur in the absence of APs, and axonal APs have been shown to fail to evoke dendritic release. These inconsistencies strongly suggest that APs in MNNs may fail to backpropagating into dendrites. Here we tested whether simple factors of electrical signal attenuation could lead to effective decoupling between cell's body and dendritic release site within typical geometrical characteristics of MNN. We developed a family of linear mathematical models of MNNs and evaluated whether the somato-dendritic transfer of electrical signals is influenced by the geometrical characteristics. We determined the prerequisites for critically strong dendritic attenuation of the somatic input which are sufficient to explain the failure of APs initiated in the soma to backpropagating into dendritic compartments. Being measured in 100 µm from soma voltage attenuations down to 0.1 and 0.01 of the input value were chosen as the markers of electrical decoupling of dendritic sites from the soma, considering 0.1 insufficient for triggering dendritic spikes and 0.01 indistinguishable from background noise. The tested micro-geometrical factors were the dendritic stem diameter, varicosities, and size of peri-dendritic space limited by glial sheath wrapping. Varicosities increased the attenuation along homogeneous proximal dendrites by providing an increased current leak at the junction with the proximal dendritic section. The glial sheath wrapping a dendrite section promoted greater attenuation by increasing longitudinal resistance of the interstitial peri-dendritic space thus playing the insulating role. These decoupling effects were strengthened in the case of the dendritic stems with thinner diameters of and/or increased conductivity of the membrane. These micro-geometrical factors are biophysically realistic and predict electrical decoupling between somatic and dendritic compartments in MNNs.

Chloride-dependent mechanisms of multimodal sensory discrimination and nociceptive sensitization in Drosophila.

Individual sensory neurons can be tuned to many stimuli, each driving unique, stimulus-relevant behaviors, and the ability of multimodal nociceptor neurons to discriminate between potentially harmful and innocuous stimuli is broadly important for organismal survival. Moreover, disruptions in the capacity to differentiate between noxious and innocuous stimuli can result in neuropathic pain. Drosophila larval class III (CIII) neurons are peripheral noxious cold nociceptors and innocuous touch mechanosensors; high levels of activation drive cold-evoked contraction (CT) behavior, while low levels of activation result in a suite of touch-associated behaviors. However, it is unknown what molecular factors underlie CIII multimodality. Here, we show that the TMEM16/anoctamins subdued and white walker (wwk; CG15270) are required for cold-evoked CT, but not for touch-associated behavior, indicating a conserved role for anoctamins in nociception. We also evidence that CIII neurons make use of atypical depolarizing chloride currents to encode cold, and that overexpression of ncc69-a fly homologue of NKCC1-results in phenotypes consistent with neuropathic sensitization, including behavioral sensitization and neuronal hyperexcitability, making Drosophila CIII neurons a candidate system for future studies of the basic mechanisms underlying neuropathic pain.

Emergence of Extreme Paw Accelerations During Cat Paw Shaking: Interactions of Spinal Central Pattern Generator, Hindlimb Mechanics and Muscle Length-Depended Feedback.

Cat paw shaking is a spinal reflex for removing an irritating stimulus from paw by developing extremely high paw accelerations. Previous studies of paw shaking revealed a proximal-to-distal gradient of hindlimb segmental velocities/accelerations, as well as complex inter-joint coordination: passive motion-dependent interaction moments acting on distal segments are opposed by distal muscle moments. However, mechanisms of developing extreme paw accelerations during paw shaking remain unknown. We hypothesized that paw-shaking mechanics and muscle activity might correspond to a whip-like mechanism of energy generation and transfer along the hindlimb. We first demonstrated in experiments with five intact, adult, female cats that during paw shaking, energy generated by proximal muscle moments was transmitted to distal segments by joint forces. This energy transfer was mostly responsible for the segmental velocity/acceleration proximal-to-distal gradient. Distal muscle moments mostly absorbed energy of the distal segments. We then developed a neuromechanical model of hindlimb paw shaking comprised a half-center CPG, activating hip flexors and extensors, and passive viscoelastic distal muscles that produced length/velocity-depended force. Simulations reproduced whip-like mechanisms found experimentally: the proximal-to-distal velocity/acceleration gradient, energy transfer by joint forces and energy absorption by distal muscle moments, as well as atypical co-activation of ankle and hip flexors with knee extensors. Manipulating model parameters, including reversal of segmental inertia distal-to-proximal gradient, demonstrated important inertia contribution to developing the segmental velocity/acceleration proximal-to-distal gradient. We concluded that extreme paw accelerations during paw shaking result from interactions between a spinal CPG, hindlimb segmental inertia, and muscle length/velocity-depended feedback that tunes limb viscoelastic properties.

Asymmetric and transient properties of reciprocal activity of antagonists during the paw-shake response in the cat.

Mutually inhibitory populations of neurons, half-center oscillators (HCOs), are commonly involved in the dynamics of the central pattern generators (CPGs) driving various rhythmic movements. Previously, we developed a multifunctional, multistable symmetric HCO model which produced slow locomotor-like and fast paw-shake-like activity patterns. Here, we describe asymmetric features of paw-shake responses in a symmetric HCO model and test these predictions experimentally. We considered bursting properties of the two model half-centers during transient paw-shake-like responses to short perturbations during locomotor-like activity. We found that when a current pulse was applied during the spiking phase of one half-center, let's call it #1, the consecutive burst durations (BDs) of that half-center increased throughout the paw-shake response, while BDs of the other half-center, let's call it #2, only changed slightly. In contrast, the consecutive interburst intervals (IBIs) of half-center #1 changed little, while IBIs of half-center #2 increased. We demonstrated that this asymmetry between the half-centers depends on the phase of the locomotor-like rhythm at which the perturbation was applied. We suggest that the fast transient response reflects functional asymmetries of slow processes that underly the locomotor-like pattern; e.g., asymmetric levels of inactivation across the two half-centers for a slowly inactivating inward current. We compared model results with those of in-vivo paw-shake responses evoked in locomoting cats and found similar asymmetries. Electromyographic (EMG) BDs of anterior hindlimb muscles with flexor-related activity increased in consecutive paw-shake cycles, while BD of posterior muscles with extensor-related activity did not change, and vice versa for IBIs of anterior flexors and posterior extensors. We conclude that EMG activity patterns during paw-shaking are consistent with the proposed mechanism producing transient paw-shake-like bursting patterns found in our multistable HCO model. We suggest that the described asymmetry of paw-shaking responses could implicate a multifunctional CPG controlling both locomotion and paw-shaking.

Comodulation of h- and Na+/K+ Pump Currents Expands the Range of Functional Bursting in a Central Pattern Generator by Navigating between Dysfunctional Regimes.

Central pattern generators (CPGs), specialized oscillatory neuronal networks controlling rhythmic motor behaviors such as breathing and locomotion, must adjust their patterns of activity to a variable environment and changing behavioral goals. Neuromodulation adjusts these patterns by orchestrating changes in multiple ionic currents. In the medicinal leech, the endogenous neuromodulator myomodulin speeds up the heartbeat CPG by reducing the electrogenic Na+/K+ pump current and increasing h-current in pairs of mutually inhibitory leech heart interneurons (HNs), which form half-center oscillators (HN HCOs). Here we investigate whether the comodulation of two currents could have advantages over a single current in the control of functional bursting patterns of a CPG. We use a conductance-based biophysical model of an HN HCO to explain the experimental effects of myomodulin. We demonstrate that, in the model, comodulation of the Na+/K+ pump current and h-current expands the range of functional bursting activity by avoiding transitions into nonfunctional regimes, such as asymmetric bursting and plateau-containing seizure-like activity. We validate the model by finding parameters that reproduce temporal bursting characteristics matching experimental recordings from HN HCOs under control, three different myomodulin concentrations, and Cs+ treated conditions. The matching cases are located along the border of an asymmetric regime away from the border with more dangerous seizure-like activity. We found a simple comodulation mechanism with an inverse relation between the pump and h-currents makes a good fit of the matching cases and comprises a general mechanism for the robust and flexible control of oscillatory neuronal networks.SIGNIFICANCE STATEMENT Rhythm-generating neuronal circuits adjust their oscillatory patterns to accommodate a changing environment through neuromodulation. In different species, chemical messengers participating in such processes may target two or more membrane currents. In medicinal leeches, the neuromodulator myomodulin speeds up the heartbeat central pattern generator by reducing Na+/K+ pump current and increasing h-current. In a computational model, we show that this comodulation expands the range of central pattern generator's functional activity by navigating the circuit between dysfunctional regimes resulting in a much wider range of cycle period. This control would not be attainable by modulating only one current, emphasizing the synergy of combined effects. Given the prevalence of h-current and Na+/K+ pump current in neurons, similar comodulation mechanisms may exist across species.

Contribution of the Na+/K+ Pump to Rhythmic Bursting, Explored with Modeling and Dynamic Clamp Analyses.

The Na+/K+ pump, often thought of as a background function in neuronal activity, contributes an outward current (Ipump) that responds to the internal concentration of Na+ ([Na+]i). In bursting neurons, such as those found in central pattern generator (CPG) neuronal networks that produce rhythmic movements, the [Na+]i and therefore the Ipump, can be expected to vary throughout the burst cycle. This responsiveness to electrical activity, combined with independence from membrane potential, endow Ipump with dynamical properties not common to channel-based currents (e.g., voltage- or transmitter-gated or leak channels). Moreover, in many neurons, the pump's activity is modulated by a variety of modulators, further expanding the potential role of Ipump in rhythmic bursting activity. This paper shows how to use a combination of modeling and dynamic clamp methods to determine how Ipump and its interaction with persistent Na+ current influence rhythmic activity in a CPG. Specifically, this paper will focus on a dynamic clamp protocol and computational modeling methods in heart interneurons of medicinal leeches.

Contributions of h- and Na+/K+ Pump Currents to the Generation of Episodic and Continuous Rhythmic Activities.

Developing spinal motor networks produce a diverse array of outputs, including episodic and continuous patterns of rhythmic activity. Variation in excitability state and neuromodulatory tone can facilitate transitions between episodic and continuous rhythms; however, the intrinsic mechanisms that govern these rhythms and their transitions are poorly understood. Here, we tested the capacity of a single central pattern generator (CPG) circuit with tunable properties to generate multiple outputs. To address this, we deployed a computational model composed of an inhibitory half-center oscillator (HCO). Following predictions of our computational model, we tested the contributions of key properties to the generation of an episodic rhythm produced by isolated spinal cords of the newborn mouse. The model recapitulates the diverse state-dependent rhythms evoked by dopamine. In the model, episodic bursting depended predominantly on the endogenous oscillatory properties of neurons, with Na+/K+ ATPase pump (I Pump) and hyperpolarization-activated currents (I h ) playing key roles. Modulation of either I Pump or I h produced transitions between episodic and continuous rhythms and silence. As maximal activity of I Pump decreased, the interepisode interval and period increased along with a reduction in episode duration. Decreasing maximal conductance of I h decreased episode duration and increased interepisode interval. Pharmacological manipulations of I h with ivabradine, and I Pump with ouabain or monensin in isolated spinal cords produced findings consistent with the model. Our modeling and experimental results highlight key roles of I h and I Pump in producing episodic rhythms and provide insight into mechanisms that permit a single CPG to produce multiple patterns of rhythmicity.

Na(+)/K(+) pump interacts with the h-current to control bursting activity in central pattern generator neurons of leeches.

The dynamics of different ionic currents shape the bursting activity of neurons and networks that control motor output. Despite being ubiquitous in all animal cells, the contribution of the Na(+)/K(+) pump current to such bursting activity has not been well studied. We used monensin, a Na(+)/H(+) antiporter, to examine the role of the pump on the bursting activity of oscillator heart interneurons in leeches. When we stimulated the pump with monensin, the period of these neurons decreased significantly, an effect that was prevented or reversed when the h-current was blocked by Cs(+). The decreased period could also occur if the pump was inhibited with strophanthidin or K(+)-free saline. Our monensin results were reproduced in model, which explains the pump's contributions to bursting activity based on Na(+) dynamics. Our results indicate that a dynamically oscillating pump current that interacts with the h-current can regulate the bursting activity of neurons and networks.

A codimension-2 bifurcation controlling endogenous bursting activity and pulse-triggered responses of a neuron model.

The dynamics of individual neurons are crucial for producing functional activity in neuronal networks. An open question is how temporal characteristics can be controlled in bursting activity and in transient neuronal responses to synaptic input. Bifurcation theory provides a framework to discover generic mechanisms addressing this question. We present a family of mechanisms organized around a global codimension-2 bifurcation. The cornerstone bifurcation is located at the intersection of the border between bursting and spiking and the border between bursting and silence. These borders correspond to the blue sky catastrophe bifurcation and the saddle-node bifurcation on an invariant circle (SNIC) curves, respectively. The cornerstone bifurcation satisfies the conditions for both the blue sky catastrophe and SNIC. The burst duration and interburst interval increase as the inverse of the square root of the difference between the corresponding bifurcation parameter and its bifurcation value. For a given set of burst duration and interburst interval, one can find the parameter values supporting these temporal characteristics. The cornerstone bifurcation also determines the responses of silent and spiking neurons. In a silent neuron with parameters close to the SNIC, a pulse of current triggers a single burst. In a spiking neuron with parameters close to the blue sky catastrophe, a pulse of current temporarily silences the neuron. These responses are stereotypical: the durations of the transient intervals-the duration of the burst and the duration of latency to spiking-are governed by the inverse-square-root laws. The mechanisms described here could be used to coordinate neuromuscular control in central pattern generators. As proof of principle, we construct small networks that control metachronal-wave motor pattern exhibited in locomotion. This pattern is determined by the phase relations of bursting neurons in a simple central pattern generator modeled by a chain of oscillators.

High prevalence of multistability of rest states and bursting in a database of a model neuron.

Flexibility in neuronal circuits has its roots in the dynamical richness of their neurons. Depending on their membrane properties single neurons can produce a plethora of activity regimes including silence, spiking and bursting. What is less appreciated is that these regimes can coexist with each other so that a transient stimulus can cause persistent change in the activity of a given neuron. Such multistability of the neuronal dynamics has been shown in a variety of neurons under different modulatory conditions. It can play either a functional role or present a substrate for dynamical diseases. We considered a database of an isolated leech heart interneuron model that can display silent, tonic spiking and bursting regimes. We analyzed only the cases of endogenous bursters producing functional half-center oscillators (HCOs). Using a one parameter (the leak conductance (g(leak)) bifurcation analysis, we extended the database to include silent regimes (stationary states) and systematically classified cases for the coexistence of silent and bursting regimes. We showed that different cases could exhibit two stable depolarized stationary states and two hyperpolarized stationary states in addition to various spiking and bursting regimes. We analyzed all cases of endogenous bursters and found that 18% of the cases were multistable, exhibiting coexistences of stationary states and bursting. Moreover, 91% of the cases exhibited multistability in some range of g(leak). We also explored HCOs built of multistable neuron cases with coexisting stationary states and a bursting regime. In 96% of cases analyzed, the HCOs resumed normal alternating bursting after one of the neurons was reset to a stationary state, proving themselves robust against this perturbation.

Bifurcation of synchronous oscillations into torus in a system of two reciprocally inhibitory silicon neurons: experimental observation and modeling.

Oscillatory activity in the central nervous system is associated with various functions, like motor control, memory formation, binding, and attention. Quasiperiodic oscillations are rarely discussed in the neurophysiological literature yet they may play a role in the nervous system both during normal function and disease. Here we use a physical system and a model to explore scenarios for how quasiperiodic oscillations might arise in neuronal networks. An oscillatory system of two mutually inhibitory neuronal units is a ubiquitous network module found in nervous systems and is called a half-center oscillator. Previously we created a half-center oscillator of two identical oscillatory silicon (analog Very Large Scale Integration) neurons and developed a mathematical model describing its dynamics. In the mathematical model, we have shown that an in-phase limit cycle becomes unstable through a subcritical torus bifurcation. However, the existence of this torus bifurcation in experimental silicon two-neuron system was not rigorously demonstrated or investigated. Here we demonstrate the torus predicted by the model for the silicon implementation of a half-center oscillator using complex time series analysis, including bifurcation diagrams, mapping techniques, correlation functions, amplitude spectra, and correlation dimensions, and we investigate how the properties of the quasiperiodic oscillations depend on the strengths of coupling between the silicon neurons. The potential advantages and disadvantages of quasiperiodic oscillations (torus) for biological neural systems and artificial neural networks are discussed.

A multiconductance silicon neuron with biologically matched dynamics.

We have designed, fabricated, and tested an analog integrated-circuit architecture to implement the conductance-based dynamics that model the electrical activity of neurons. The dynamics of this architecture are in accordance with the Hodgkin-Huxley formalism, a widely exploited, biophysically plausible model of the dynamics of living neurons. Furthermore the architecture is modular and compact in size so that we can implement networks of silicon neurons, each of desired complexity, on a single integrated circuit. We present in this paper a six-conductance silicon-neuron implementation, and characterize it in relation to the Hodgkin-Huxley formalism. This silicon neuron incorporates both fast and slow ionic conductances, which are required to model complex oscillatory behaviors (spiking, bursting, subthreshold oscillations).

Heartbeat control in leeches. I. Constriction pattern and neural modulation of blood pressure in intact animals.

Two tubular hearts propel blood through the closed circulatory system of the medicinal leech. The hearts are myogenic but are driven by a centrally generated motor pattern that controls heart rate and intersegmental coordination. In two consecutive papers, we address the question of how the motor pattern is translated into the pattern of diastole and systole of leech hearts. We imaged the constriction patterns of the hearts in quiescent intact animals. In one heart, systole progresses rear-to-front (peristaltic coordination mode), whereas systole occurs nearly simultaneously in the other heart (synchronous coordination mode) with regular switches between these two coordination modes. Intersegmental phase relations between heart segments do not vary with changes in the heartbeat period. The peristaltic heart drives blood forward through itself and then rearward through the other longitudinal vessels. The synchronous heart does not seem to contribute to rearward flow along the body axis and may support segmental circulation instead. Simultaneous monitoring of heart motor neuron discharge and the constriction of the corresponding heart segment in innervated, reduced preparations enabled us later to meld the constriction pattern with the fictive motor pattern described in the following paper. Current injections into one heart modulatory neuron while monitoring intravascular pressure from the corresponding heart showed that these neurons can acutely change diastolic and systolic pressure. However, they do not determine the different systolic pressure profiles associated with the two coordination modes, which appear to result from the constriction pattern.

Bursting in leech heart interneurons: cell-autonomous and network-based mechanisms.

Rhythmic activity within the heartbeat pattern generator of the medicinal leech is based on the alternating bursting of mutually inhibitory pairs of oscillator heart interneurons (half-center oscillators). Bicuculline methiodide has been shown to block mutual inhibition between these interneurons and to cause them to spike tonically while recorded intracellularly (Schmidt and Calabrese, 1992). Using extracellular recording techniques, we show here that oscillator and premotor heart interneurons continue to burst when pharmacologically isolated with bicuculline, although the bursting is not robust in some preparations. We propose that a nonspecific leak current introduced by the intracellular microelectrode suppresses endogenous bursting activity to account for the discrepancy with results using intracellular recording. A two-parameter bifurcation diagram (E(leak) vs g(leak)) of a mathematical model of a single heart interneuron shows a narrow stripe of parameter values where bursting occurs, separating large zones of tonic spiking and silence. A similar analysis performed for a half-center oscillator model outlined a much larger area of bursting. Bursting in the half-center oscillator model is also less sensitive to variation in the maximal conductances of voltage-gated currents than in the single-neuron model. Thus, in addition to ensuring appropriate bursting characteristics such as period, phase, and duty cycles, the half-center configuration enhances oscillation robustness, making them less susceptible to random or imposed changes in membrane parameters. Endogenous bursting, in turn, ensures appropriate bursting if the strength of mutual inhibition is weakened and limits the minimum period of the half-center oscillator to a period near that of the single neuron.

Oscillatory network controlling six-legged locomotion. Optimization of model parameters.

The model of a legged locomotory system is optimized to ensure stable motion, reliable with respect to different initial conditions. The cost function suggested is based on the frequency of the model's loss of stability evaluated for randomly chosen initial leg positions. The optimized model can start from the majority of allowed leg configurations, demonstrating stable walking at low and moderate speeds. Furthermore, an acceleration procedure is designed to permit the model to pick up practically every speed and then walk successfully.