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.

Bursting Dynamics Based on the Persistent Na+ and Na+/K+ Pump Currents: A Dynamic Clamp Approach.

Life-supporting rhythmic motor functions like heart-beating in invertebrates and breathing in vertebrates require an indefatigable generation of a robust rhythm by specialized oscillatory circuits, central pattern generators (CPGs). These CPGs should be sufficiently flexible to adjust to environmental changes and behavioral goals. Continuous self-sustained operation of bursting neurons requires intracellular Na+ concentration to remain in a functional range and to have checks and balances of the Na+ fluxes met on a cycle-to-cycle basis during bursting. We hypothesize that at a high excitability state, the interaction of the Na+/K+ pump current, Ipump, and persistent Na+ current, INaP, produces a mechanism supporting functional bursting. INaP is a low voltage-activated inward current that initiates and supports the bursting phase. This current does not inactivate and is a significant source of Na+ influx. Ipump is an outward current activated by [Na+]i and is the major source of Na+ efflux. Both currents are active and counteract each other between and during bursts. We apply a combination of electrophysiology, computational modeling, and dynamic clamp to investigate the role of Ipump and INaP in the leech heartbeat CPG interneurons (HN neurons). Applying dynamic clamp to introduce additional Ipump and INaP into the dynamics of living synaptically isolated HN neurons in real time, we show that their joint increase produces transition into a new bursting regime characterized by higher spike frequency and larger amplitude of the membrane potential oscillations. Further increase of Ipump speeds up this rhythm by shortening burst duration (BD) and interburst interval (IBI).

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.

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

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

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.

Control of transitions between locomotor-like and paw shake-like rhythms in a model of a multistable central pattern generator.

The ability of the same neuronal circuit to control different motor functions is an actively debated concept. Previously, we showed in a model that a single multistable central pattern generator (CPG) could produce two different rhythmic motor patterns, slow and fast, corresponding to cat locomotion and paw shaking. A locomotor-like rhythm (~1 Hz) and a paw shake-like rhythm (~10 Hz) did coexist in our model, and, by applying a single pulse of current, we could switch the CPG from one regime to another (Bondy B, Klishko AN, Edwards DH, Prilutsky BI, Cymbalyuk G. In: Neuromechanical Modeling of Posture and Locomotion, 2016). Here we investigated the roles of slow intrinsic ionic currents in this multistability. The CPG is modeled as a half-center oscillator circuit comprising two reciprocally inhibitory neurons. Each neuron is equipped with two slow inward currents, a Na+ current ( INaS) and a Ca2+ current ( ICaS). ICaS inactivates much more slowly and at more hyperpolarized voltages than INaS. We demonstrate that INaS is the primary current driving the paw shake-like bursting. ICaS is crucial for the locomotor-like bursting, and it is inactivated during the paw shake-like activity. We investigate the sensitivity of the bursting regimes to perturbations, using a pulse of current to induce a switch from one regime to the other, and we demonstrate that the transition duration is dependent on pulse amplitude and application phase. We also investigate the modulatory roles of the strength of various currents on characteristics of these rhythms and show that their effects are regime specific. We conclude that a multistable CPG is physiologically plausible and derive testable predictions of the model. NEW & NOTEWORTHY Little is known about how a single central pattern generator could produce multiple rhythms. We describe a novel mechanism for multistability of bursting regimes with strongly distinct periods. The proposed mechanism emphasizes the role of intrinsic cellular dynamics over synaptic dynamics in the production of multistability. We describe how the temporal characteristics of multiple rhythms could be controlled by neuromodulation and how single pulses of current could produce a switch between regimes in a functional fashion.

Propensity for Bistability of Bursting and Silence in the Leech Heart Interneuron.

The coexistence of neuronal activity regimes has been reported under normal and pathological conditions. Such multistability could enhance the flexibility of the nervous system and has many implications for motor control, memory, and decision making. Multistability is commonly promoted by neuromodulation targeting specific membrane ionic currents. Here, we investigated how modulation of different ionic currents could affect the neuronal propensity for bistability. We considered a leech heart interneuron model. It exhibits bistability of bursting and silence in a narrow range of the leak current parameters, conductance (gleak ) and reversal potential (Eleak ). We assessed the propensity for bistability of the model by using bifurcation diagrams. On the diagram (gleak , Eleak ), we mapped bursting and silent regimes. For the canonical value of Eleak we determined the range of gleak which supported the bistability. We use this range as an index of propensity for bistability. We investigated how this index was affected by alterations of ionic currents. We systematically changed their conductances, one at a time, and built corresponding bifurcation diagrams in parameter planes of the maximal conductance of a given current and the leak conductance. We found that conductance of only one current substantially affected the index of propensity; the increase of the maximal conductance of the hyperpolarization-activated cationic current increased the propensity index. The second conductance with the strongest effect was the conductance of the low-threshold fast Ca2+ current; its reduction increased the propensity index although the effect was about two times smaller in magnitude. Analyzing the model with both changes applied simultaneously, we found that the diagram (gleak , Eleak ) showed a progressively expanded area of bistability of bursting and silence.

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.

Bistability of silence and seizure-like bursting.

Neuronal circuits exhibiting seizure episodes have been shown to be prone to multistability. The coexistence of normal and pathological regimes could explain why seizures suddenly start and stop. Methods developed in dynamical systems theory are powerful tools for determining the cellular mechanisms that underlie multistable seizure dynamics. Here, we present two different approaches to assess multistability in a model neuron. In this model, we identified a bursting regime and a silent regime. First, we investigated properties of a square pulse of injected current which produced a switch from seizure-like bursting into silence. By systematically varying the phase and amplitude of the pulse, we found contiguous pulse parameter sets, so-called windows, that satisfied this criterion, and we determined the dependence of these windows on the parameter gleak. As gleak increased, the size of each window scaled according to the same law as the amplitude of the saddle orbit. Second, we examined the role of each current in supporting bistability of bursting and silence. We defined the index of propensity for multistability as the range of gleak for which bursting and silence coexisted. We computed this quantity while iteratively varying the maximal conductance of each voltage-gated current one at a time. Increasing the maximal conductance of the slow potassium current or the hyperpolarization-activated current increased the range of bistability. In contrast, decreasing the maximal conductance of the persistent sodium current increased the range of bistability.

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.

Bistability of bursting and silence regimes in a model of a leech heart interneuron.

Bursting is one of the primary activity regimes of neurons. Our study is focused on determining a generic biophysical mechanism underlying the coexistence of the bursting and silent regimes observed in a neuron model. We show that the main ingredient for this mechanism is a saddle periodic orbit. The stable manifold of the orbit sets a threshold between the regimes of activity. Thus, the range of the controlling parameters, where the coexistence is observed, is limited by the bifurcations' values at which the saddle orbit appears and disappears. We show that it appears through the subcritical Andronov-Hopf bifurcation, where the equilibrium representing the silent regime loses stability, and disappears at the homoclinic bifurcation. Correspondingly, the bursting regime disappears in close proximity to the homoclinic bifurcation.

Six types of multistability in a neuronal model based on slow calcium current.

BACKGROUND: Multistability of oscillatory and silent regimes is a ubiquitous phenomenon exhibited by excitable systems such as neurons and cardiac cells. Multistability can play functional roles in short-term memory and maintaining posture. It seems to pose an evolutionary advantage for neurons which are part of multifunctional Central Pattern Generators to possess multistability. The mechanisms supporting multistability of bursting regimes are not well understood or classified. METHODOLOGY/PRINCIPAL FINDINGS: Our study is focused on determining the bio-physical mechanisms underlying different types of co-existence of the oscillatory and silent regimes observed in a neuronal model. We develop a low-dimensional model typifying the dynamics of a single leech heart interneuron. We carry out a bifurcation analysis of the model and show that it possesses six different types of multistability of dynamical regimes. These types are the co-existence of 1) bursting and silence, 2) tonic spiking and silence, 3) tonic spiking and subthreshold oscillations, 4) bursting and subthreshold oscillations, 5) bursting, subthreshold oscillations and silence, and 6) bursting and tonic spiking. These first five types of multistability occur due to the presence of a separating regime that is either a saddle periodic orbit or a saddle equilibrium. We found that the parameter range wherein multistability is observed is limited by the parameter values at which the separating regimes emerge and terminate. CONCLUSIONS: We developed a neuronal model which exhibits a rich variety of different types of multistability. We described a novel mechanism supporting the bistability of bursting and silence. This neuronal model provides a unique opportunity to study the dynamics of networks with neurons possessing different types of multistability.

Control of tumbling during the locust jump.

Locust can jump precisely to a target, yet they can also tumble during the trajectory. We propose two mechanisms that would allow the locust to control tumbling during the jump. The first is that prior to the jump, locusts adjust the pitch of their body to move the center of mass closer to the intended thrust vector. The second is that contraction of the dorsolongitudinal muscles during the jump will produce torques that counter the torque produced by thrust. We found that locusts increased their take-off angle as the initial body pitch increased, and that little tumbling occurred for jumps that observed this relationship. Simulations of locust jumping demonstrated that a pitch versus take-off angle relationship that minimized tumbling in simulated jumps was similar to the relationship observed in live locusts. Locusts were strongly biased to pitch head-upward, and performed dorsiflexions far more often than ventral flexions. The direction and magnitude of tumbling could be controlled in simulations by adjusting the tension in the dorsolongitudinal muscles. These mechanisms allowed the simulations to match the data from the live animals. Control of tumbling was also found to influence the control of jump elevation. The bias to pitch head-upwards may have an evolutionary advantage when evading a predator and so make control of tumbling important for the locust.