Maintaining phase of the crustacean tri-phasic pyloric rhythm

I h Block Reveals Separation of Timescales in Pyloric Rhythm Response to Temperature Changes in Cancer borealis

Motor systems operate over a range of frequencies and relative timing (phase). We studied the contribution of the hyperpolarization-activated inward current (I h ) to frequency and phase in the pyloric rhythm of the stomatogastric ganglion (STG) of the crab, Cancer borealis as temperature was altered from 11°C to 21°C. Under control conditions, the frequency of the rhythm increased monotonically with temperature, while the phases of the pyloric dilator (PD), lateral pyloric (LP), and pyloric (PY) neurons remained constant. When we blocked I h with cesium (Cs + ) PD offset, LP onset, and LP offset were all phase advanced in Cs + at 11°C, and the latter two further advanced as temperature increased. In Cs + the steady state increase in pyloric frequency with temperature diminished and the Q 10 of the pyloric frequency dropped from ∼1.75 to ∼1.35. Unexpectedly in Cs + , the frequency displayed non-monotonic dynamics during temperature transitions; the frequency initially dropped as temperature increased, then rose once temperature stabilized, creating a characteristic "jag". Interestingly, these jags were still present during temperature transitions in Cs + when the pacemaker was isolated by picrotoxin, although the temperature-induced change in frequency recovered to control levels. Overall, these data suggest that I h plays an important role in the ability of this circuit to produce smooth transitory responses and persistent frequency increases by different mechanisms during temperature fluctuations.

Thermal acclimation and habitat-dependent differences in temperature robustness of a crustacean motor circuit

Introduction

At the cellular level, acute temperature changes alter ionic conductances, ion channel kinetics, and the activity of entire neuronal circuits. This can result in severe consequences for neural function, animal behavior and survival. In poikilothermic animals, and particularly in aquatic species whose core temperature equals the surrounding water temperature, neurons experience rather rapid and wide-ranging temperature fluctuations. Recent work on pattern generating neural circuits in the crustacean stomatogastric nervous system have demonstrated that neuronal circuits can exhibit an intrinsic robustness to temperature fluctuations. However, considering the increased warming of the oceans and recurring heatwaves due to climate change, the question arises whether this intrinsic robustness can acclimate to changing environmental conditions, and whether it differs between species and ocean habitats.

Methods

We address these questions using the pyloric pattern generating circuits in the stomatogastric nervous system of two crab species, Hemigrapsus sanguineus and Carcinus maenas that have seen a worldwide expansion in recent decades.

Results and discussion

Consistent with their history as invasive species, we find that pyloric activity showed a broad temperature robustness (>30°C). Moreover, the temperature-robust range was dependent on habitat temperature in both species. Warm-acclimating animals shifted the critical temperature at which circuit activity breaks down to higher temperatures. This came at the cost of robustness against cold stimuli in H. sanguineus, but not in C. maenas. Comparing the temperature responses of C. maenas from a cold latitude (the North Sea) to those from a warm latitude (Spain) demonstrated that similar shifts in robustness occurred in natural environments. Our results thus demonstrate that neuronal temperature robustness correlates with, and responds to, environmental temperature conditions, potentially preparing animals for changing ecological conditions and shifting habitats.

Short-term synaptic dynamics control the activity phase of neurons in an oscillatory network

In oscillatory systems, neuronal activity phase is often independent of network frequency. Such phase maintenance requires adjustment of synaptic input with network frequency, a relationship that we explored using the crab, Cancer borealis, pyloric network. The burst phase of pyloric neurons is relatively constant despite a > two fold variation in network frequency. We used noise input to characterize how input shape influences burst delay of a pyloric neuron, and then used dynamic clamp to examine how burst phase depends on the period, amplitude, duration, and shape of rhythmic synaptic input. Phase constancy across a range of periods required a proportional increase of synaptic duration with period. However, phase maintenance was also promoted by an increase of amplitude and peak phase of synaptic input with period. Mathematical analysis shows how short-term synaptic plasticity can coordinately change amplitude and peak phase to maximize the range of periods over which phase constancy is achieved.

Modulator-Gated, SUMOylation-Mediated, Activity-Dependent Regulation of Ionic Current Densities Contributes to Short-Term Activity Homeostasis

Neurons operate within defined activity limits, and feedback control mechanisms dynamically tune ionic currents to maintain this optimal range. This study describes a novel, rapid feedback mechanism that uses SUMOylation to continuously adjust ionic current densities according to changes in activity. Small ubiquitin-like modifier (SUMO) is a peptide that can be post-translationally conjugated to ion channels to influence their surface expression and biophysical properties. Neuronal activity can regulate the extent of protein SUMOylation. This study on the single, unambiguously identifiable lateral pyloric neuron (LP), a component of the pyloric network in the stomatogastric nervous system of male and female spiny lobsters (Panulirus interruptus), focused on dynamic SUMOylation in the context of activity homeostasis. There were four major findings: First, neuronal activity adjusted the balance between SUMO conjugation and deconjugation to continuously and bidirectionally fine-tune the densities of two opposing conductances: the hyperpolarization activated current (I_h) and the transient potassium current (I_A). Second, tonic 5 nm dopamine (DA) gated activity-dependent SUMOylation to permit and prevent activity-dependent regulation of I_h and I_A, respectively. Third, DA-gated, activity-dependent SUMOylation contributed to a feedback mechanism that restored the timing and duration of LP activity during prolonged modulation by 5 μm DA, which initially altered these and other activity features. Fourth, DA modulatory and metamoduatory (gating) effects were tailored to simultaneously alter and stabilize neuronal output. Our findings suggest that modulatory tone may select a subset of rapid activity-dependent mechanisms from a larger menu to achieve homeostasis under varying conditions.SIGNIFICANCE STATEMENT Post-translational SUMOylation of ion channel subunits controls their interactions. When subunit SUMOylation is dysregulated, conductance densities mediated by the channels are distorted, leading to nervous system disorders, such as seizures and chronic pain. Regulation of ion channel SUMOylation is poorly understood. This study demonstrated that neuronal activity can regulate SUMOylation to reconfigure ionic current densities over minutes, and this regulation was gated by tonic nanomolar dopamine. Dynamic SUMOylation was necessary to maintain specific aspects of neuronal output while the neuron was being modulated by high (5 μm) concentrations of dopamine, suggesting that the gating function may ensure neuronal homeostasis during extrinsic modulation of a circuit.

Phase-locking and bistability in neuronal networks with synaptic depression

We consider a recurrent network of two oscillatory neurons that are coupled with inhibitory synapses. We use the phase response curves of the neurons and the properties of short-term synaptic depression to define Poincaré maps for the activity of the network. The fixed points of these maps correspond to phase-locked modes of the network. Using these maps, we analyze the conditions that allow short-term synaptic depression to lead to the existence of bistable phase-locked, periodic solutions. We show that bistability arises when either the phase response curve of the neuron or the short-term depression profile changes steeply enough. The results apply to any Type I oscillator and we illustrate our findings using the Quadratic Integrate-and-Fire and Morris-Lecar neuron models.

The complexity of small circuits: the stomatogastric nervous system

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

QUANTITATIVE REEVALUATION OF THE EFFECTS OF SHORT- AND LONG-TERM REMOVAL OF DESCENDING MODULATORY INPUTS ON THE PYLORIC RHYTHM OF THE CRAB, CANCER BOREALIS

Neuromodulatory inputs are known to strongly influence the intrinsic excitability of individual neurons and the networks in which the targets of modulation are found. It is therefore important to understand how nervous systems respond to altered neuromodulatory environments.

The crustacean stomatogastric ganglion (STG) receives descending neuromodulatory inputs from three anterior ganglia: the paired commissural ganglia (CoGs), and the single esophageal ganglion (OG). In this paper, we provide the first detailed and quantitative analyses of the short- and long-term effects of removal of these descending inputs (decentralization) on the pyloric rhythm of the STG. Thirty minutes after decentralization, the mean frequency of the pyloric rhythm dropped from 1.20 Hz in control to 0.52 Hz. Whereas the relative phase of pyloric neuron activity was approximately constant across frequency in the controls, after decentralization this changed markedly. Nine control preparations kept for 5–6 d in vitro maintained pyloric rhythm frequencies close to their initial values. Nineteen decentralized preparations kept for 5–6 d dropped slightly in frequency from those seen at 30 min following decentralization, but then displayed stable activity over 6 d. Bouts of higher frequency activity were intermittently seen in both control and decentralized preparations, but the bouts began earlier and were more frequent in the decentralized preparations. Although the bouts may indicate that the removal of the modulatory inputs triggered changes in neuronal excitability, these changes did not produce obvious long-lasting changes in the frequency of the decentralized preparations.

The frequency preference of neurons and synapses in a recurrent oscillatory network

A variety of neurons and synapses shows a maximal response at a preferred frequency, generally considered to be important in shaping network activity. We are interested in whether all neurons and synapses in a recurrent oscillatory network can have preferred frequencies and, if so, whether these frequencies are the same or correlated, and whether they influence the network activity. We address this question using identified neurons in the pyloric network of the crab Cancer borealis. Previous work has shown that the pyloric pacemaker neurons exhibit membrane potential resonance whose resonance frequency is correlated with the network frequency. The follower lateral pyloric (LP) neuron makes reciprocally inhibitory synapses with the pacemakers. We find that LP shows resonance at a higher frequency than the pacemakers and the network frequency falls between the two. We also find that the reciprocal synapses between the pacemakers and LP have preferred frequencies but at significantly lower values. The preferred frequency of the LP to pacemaker synapse is correlated with the presynaptic preferred frequency, which is most pronounced when the peak voltage of the LP waveform is within the dynamic range of the synaptic activation curve and a shift in the activation curve by the modulatory neuropeptide proctolin shifts the frequency preference. Proctolin also changes the power of the LP neuron resonance without significantly changing the resonance frequency. These results indicate that different neuron types and synapses in a network may have distinct preferred frequencies, which are subject to neuromodulation and may interact to shape network oscillations.

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.

Neuromodulator-evoked synaptic metaplasticity within a central pattern generator network

Synapses show short-term activity-dependent dynamics that alter the strength of neuronal interactions. This synaptic plasticity can be tuned by neuromodulation as a form of metaplasticity. We examined neuromodulator-induced metaplasticity at a graded chemical synapse in a model central pattern generator (CPG), the pyloric network of the spiny lobster stomatogastric ganglion. Dopamine, serotonin, and octopamine each produce a unique motor pattern from the pyloric network, partially through their modulation of synaptic strength in the network. We characterized synaptic depression and its amine modulation at the graded synapse from the pyloric dilator neuron to the lateral pyloric neuron (PD→LP synapse), driving the PD neuron with both long square pulses and trains of realistic waveforms over a range of presynaptic voltages. We found that the three amines can differentially affect the amplitude of graded synaptic transmission independently of the synaptic dynamics. Low concentrations of dopamine had weak and variable effects on the strength of the graded inhibitory postsynaptic potentials (gIPSPs) but reliably accelerated the onset of synaptic depression and recovery from depression independently of gIPSP amplitude. Octopamine enhanced gIPSP amplitude but decreased the amount of synaptic depression; it slowed the onset of depression and accelerated its recovery during square pulse stimulation. Serotonin reduced gIPSP amplitude but increased the amount of synaptic depression and accelerated the onset of depression. These results suggest that amine-induced metaplasticity at graded chemical synapses can alter the parameters of synaptic dynamics in multiple and independent ways.

Co-existent activity patterns in inhibitory neuronal networks with short-term synaptic depression

A network of two neurons mutually coupled through inhibitory synapses that display short-term synaptic depression is considered. We show that synaptic depression expands the number of possible activity patterns that the network can display and allows for co-existence of different patterns. Specifically, the network supports different types of n-m anti-phase firing patterns, where one neuron fires n spikes followed by the other neuron firing m spikes. When maximal synaptic conductances are identical, n-n anti-phase firing patterns are obtained and there are conductance intervals over which different pairs of these solutions co-exist. The multitude of n-m anti-phase patterns and their co-existence are not found when the synapses are non-depressing. Geometric singular perturbation methods for dynamical systems are applied to the original eight-dimensional model system to derive a set of one-dimensional conditions for the existence and co-existence of different anti-phase solutions. The generality and validity of these conditions are demonstrated through numerical simulations utilizing the Hodgkin-Huxley and Morris-Lecar neuronal models.

Precise temperature compensation of phase in a rhythmic motor pattern

Most animal species are cold-blooded, and their neuronal circuits must maintain function despite environmental temperature fluctuations. The central pattern generating circuits that produce rhythmic motor patterns depend on the orderly activation of circuit neurons. We describe the effects of temperature on the pyloric rhythm of the stomatogastric ganglion of the crab, Cancer borealis. The pyloric rhythm is a triphasic motor pattern in which the Pyloric Dilator (PD), Lateral Pyloric (LP), and Pyloric (PY) neurons fire in a repeating sequence. While the frequency of the pyloric rhythm increased about 4-fold (Q(10) approximately 2.3) as the temperature was shifted from 7 degrees C to 23 degrees C, the phase relationships of the PD, LP, and PY neurons showed almost perfect temperature compensation. The Q(10)'s of the input conductance, synaptic currents, transient outward current (I(A)), and the hyperpolarization-activated inward current (I(h)), all of which help determine the phase of LP neuron activity, ranged from 1.8 to 4. We studied the effects of temperature in >1,000 computational models (with different sets of maximal conductances) of a bursting neuron and the LP neuron. Many bursting models failed to monotonically increase in frequency as temperature increased. Temperature compensation of LP neuron phase was facilitated when model neurons' currents had Q(10)'s close to 2. Together, these data indicate that although diverse sets of maximal conductances may be found in identified neurons across animals, there may be strong evolutionary pressure to restrict the Q(10)'s of the processes that contribute to temperature compensation of neuronal circuits.