Modulation by Neuropeptides with Overlapping Targets Results in Functional Overlap in Oscillatory Circuit Activation.

Neuromodulation lends flexibility to neural circuit operation but the general notion that different neuromodulators sculpt neural circuit activity into distinct and characteristic patterns is complicated by interindividual variability. In addition, some neuromodulators converge onto the same signaling pathways, with similar effects on neurons and synapses. We compared the effects of three neuropeptides on the rhythmic pyloric circuit in the stomatogastric ganglion of male crabs, Cancer borealis Proctolin (PROC), crustacean cardioactive peptide (CCAP), and red pigment concentrating hormone (RPCH) activate the same modulatory inward current, I MI, and have convergent actions on synapses. However, while PROC targets all four neuron types in the core pyloric circuit, CCAP and RPCH target the same subset of only two neurons. After removal of spontaneous neuromodulator release, none of the neuropeptides restored the control cycle frequency, but all restored the relative timing between neuron types. Consequently, differences between neuropeptide effects were mainly found in the spiking activity of different neuron types. We performed statistical comparisons using the Euclidean distance in the multidimensional space of normalized output attributes to obtain a single measure of difference between modulatory states. Across preparations, the circuit output in PROC was distinguishable from CCAP and RPCH, but CCAP and RPCH were not distinguishable from each other. However, we argue that even between PROC and the other two neuropeptides, population data overlapped enough to prevent reliable identification of individual output patterns as characteristic for a specific neuropeptide. We confirmed this notion by showing that blind classifications by machine learning algorithms were only moderately successful.Significance Statement It is commonly assumed that distinct behaviors or circuit activities can be elicited by different neuromodulators. Yet it is unknown to what extent these characteristic actions remain distinct across individuals. We use a well-studied circuit model of neuromodulation to examine the effects of three neuropeptides, each known to produce a distinct activity pattern in controlled studies. We find that, when compared across individuals, the three peptides elicit activity patterns that are either statistically indistinguishable or show too much overlap to be labeled characteristic. We ascribe this to interindividual variability and overlapping subcellular actions of the modulators. Because both factors are common in all neural circuits, these findings have broad significance for understanding chemical neuromodulatory actions while considering interindividual variability.

On the Role of Theory and Modeling in Neuroscience.

In recent years, the field of neuroscience has gone through rapid experimental advances and a significant increase in the use of quantitative and computational methods. This growth has created a need for clearer analyses of the theory and modeling approaches used in the field. This issue is particularly complex in neuroscience because the field studies phenomena that cross a wide range of scales and often require consideration at varying degrees of abstraction, from precise biophysical interactions to the computations they implement. We argue that a pragmatic perspective of science, in which descriptive, mechanistic, and normative models and theories each play a distinct role in defining and bridging levels of abstraction, will facilitate neuroscientific practice. This analysis leads to methodological suggestions, including selecting a level of abstraction that is appropriate for a given problem, identifying transfer functions to connect models and data, and the use of models themselves as a form of experiment.

Cerebellar Contributions to the Basal Ganglia Influence Motor Coordination, Reward Processing, and Movement Vigor.

Both the cerebellum and the basal ganglia are known for their roles in motor control and motivated behavior. These two systems have been classically considered as independent structures that coordinate their contributions to behavior via separate cortico-thalamic loops. However, recent evidence demonstrates the presence of a rich set of direct connections between these two regions. Although there is strong evidence for connections in both directions, for brevity we limit our discussion to the better-characterized connections from the cerebellum to the basal ganglia. We review two sets of such connections: disynaptic projections through the thalamus and direct monosynaptic projections to the midbrain dopaminergic nuclei, the VTA and the SNc. In each case, we review the evidence for these pathways from anatomic tracing and physiological recordings, and discuss their potential functional roles. We present evidence that the disynaptic pathway through the thalamus is involved in motor coordination, and that its dysfunction contributes to motor deficits, such as dystonia. We then discuss how cerebellar projections to the VTA and SNc influence dopamine release in the respective targets of these nuclei: the NAc and the dorsal striatum. We argue that the cerebellar projections to the VTA may play a role in reward-based learning and therefore contribute to addictive behavior, whereas the projection to the SNc may contribute to movement vigor. Finally, we speculate how these projections may explain many of the observations that indicate a role for the cerebellum in mental disorders, such as schizophrenia.

Selective neural stimulation by leveraging electrophysiological differentiation and using pre-pulsing and non-rectangular waveforms.

Efforts on selective neural stimulation have concentrated on segregating axons based on their size and geometry. Nonetheless, axons of the white matter or peripheral nerves may also differ in their electrophysiological properties. The primary objective of this study was to investigate the possibility of selective activation of axons by leveraging an assumed level of diversity in passive (Cm & Gleak) and active membrane properties (Ktemp & Gnamax). First, the stimulus waveforms with hyperpolarizing (HPP) and depolarizing pre-pulsing (DPP) were tested on selectivity in a local membrane model. The default value of membrane capacitance (Cm) was found to play a critical role in sensitivity of the chronaxie time (Chr) and rheobase (Rhe) to variations of all the four membrane parameters. Decreasing the default value of Cm, and thus the passive time constant of the membrane, amplified the sensitivity to the active parameters, Ktemp and GNamax, on Chr. The HPP waveform could selectively activate neurons even if they were diversified by membrane leakage (Gleak) only, and produced higher selectivity than DPP when parameters are varied in pairs. Selectivity measures were larger when the passive parameters (Cm & Gleak) were varied together, compared to the active parameters. Second, this novel mechanism of selectivity was investigated with non-rectangular waveforms for the stimulating phase (and HPP) in the same local membrane model. Simulation results suggest that Kt2 is the most selective waveform followed by Linear and Gaussian waveforms. Traditional rectangular pulse was among the least selective of all. Finally, a compartmental axon model confirmed the main findings of the local model that Kt2 is the most selective, but rank ordered the other waveforms differently. These results suggest a potentially novel mechanism of stimulation selectivity, leveraging electrophysiological variations in membrane properties, that can lead to various neural prosthetic applications.

Distinct Co-Modulation Rules of Synapses and Voltage-Gated Currents Coordinate Interactions of Multiple Neuromodulators.

Multiple neuromodulators act in concert to shape the properties of neural circuits. Different neuromodulators usually activate distinct receptors but can have overlapping targets. Therefore, circuit output depends on neuromodulator interactions at shared targets, a poorly understood process. We explored quantitative rules of co-modulation of two principal targets of neuromodulation: synapses and voltage-gated ionic currents. In the stomatogastric ganglion of the male crab Cancer borealis, the neuropeptides proctolin (Proc) and the crustacean cardioactive peptide (CCAP) modulate synapses of the pyloric circuit and activate a voltage-gated current (IMI) in multiple neurons. We examined the validity of a simple dose-dependent quantitative rule, that co-modulation by Proc and CCAP is predicted by the linear sum of the individual effects of each modulator up to saturation. We found that this rule is valid for co-modulation of synapses, but not for the activation of IMI, in which co-modulation was sublinear. The predictions for the co-modulation of IMI activation were greatly improved if we assumed that the intracellular pathways activated by two peptide receptors inhibit one another. These findings suggest that the pathways activated by two neuromodulators could have distinct interactions, leading to distinct co-modulation rules for different targets even in the same neuron. Given the evolutionary conservation of neuromodulator receptors and signaling pathways, such distinct rules for co-modulation of different targets are likely to be common across neuronal circuits.SIGNIFICANCE STATEMENT We examine the quantitative rules of co-modulation at multiple shared targets, the first such characterization to our knowledge. Our results show that dose-dependent co-modulation of distinct targets in the same cells by the same two neuromodulators follows different rules: co-modulation of synaptic currents is linearly additive up to saturation, whereas co-modulation of the voltage-gated ionic current targeted in a single neuron is nonlinear, a mechanism that is likely generalizable. Given that all neural systems are multiply modulated and neuromodulators often act on shared targets, these findings and the methodology could guide studies to examine dynamic actions of neuromodulators at the biophysical and systems level in sensory and motor functions, sleep/wake regulation, and cognition.

The differential contribution of pacemaker neurons to synaptic transmission in the pyloric network of the Jonah crab, Cancer borealis.

Many neurons receive synchronous input from heterogeneous presynaptic neurons with distinct properties. An instructive example is the crustacean stomatogastric pyloric circuit pacemaker group, consisting of the anterior burster (AB) and pyloric dilator (PD) neurons, which are active synchronously and exert a combined synaptic action on most pyloric follower neurons. Previous studies in lobster have indicated that AB is glutamatergic, whereas PD is cholinergic. However, although the stomatogastric system of the crab Cancer borealis has become a preferred system for exploration of cellular and synaptic basis of circuit dynamics, the pacemaker synaptic output has not been carefully analyzed in this species. We examined the synaptic properties of these neurons using a combination of single-cell mRNA analysis, electrophysiology, and pharmacology. The crab PD neuron expresses high levels of choline acetyltransferase and the vesicular acetylcholine transporter mRNAs, hallmarks of cholinergic neurons. In contrast, the AB neuron expresses neither cholinergic marker but expresses high levels of vesicular glutamate transporter mRNA, consistent with a glutamatergic phenotype. Notably, in the combined synapses to follower neurons, 70-75% of the total current was blocked by putative glutamatergic blockers, but short-term synaptic plasticity remained unchanged, and although the total pacemaker current in two follower neuron types was different, this difference did not contribute to the phasing of the follower neurons. These findings provide a guide for similar explorations of heterogeneous synaptic connections in other systems and a baseline in this system for the exploration of the differential influence of neuromodulators.NEW & NOTEWORTHY The pacemaker-driven pyloric circuit of the Jonah crab stomatogastric nervous system is a well-studied model system for exploring circuit dynamics and neuromodulation, yet the understanding of the synaptic properties of the two pacemaker neuron types is based on older analyses in other species. We use single-cell PCR and electrophysiology to explore the neurotransmitters used by the pacemaker neurons and their distinct contribution to the combined synaptic potentials.

Frequency-dependent responses of neuronal models to oscillatory inputs in current versus voltage clamp.

Action potential generation in neurons depends on a membrane potential threshold and therefore on how subthreshold inputs influence this voltage. In oscillatory networks, for example, many neuron types have been shown to produce membrane potential ([Formula: see text]) resonance: a maximum subthreshold response to oscillatory inputs at a nonzero frequency. Resonance is usually measured by recording [Formula: see text] in response to a sinusoidal current ([Formula: see text]), applied at different frequencies (f), an experimental setting known as current clamp (I-clamp). Several recent studies, however, use the voltage clamp (V-clamp) method to control [Formula: see text] with a sinusoidal input at different frequencies [[Formula: see text]] and measure the total membrane current ([Formula: see text]). The two methods obey systems of differential equations of different dimensionality, and while I-clamp provides a measure of electrical impedance [[Formula: see text]], V-clamp measures admittance [[Formula: see text]]. We analyze the relationship between these two measurement techniques. We show that, despite different dimensionality, in linear systems the two measures are equivalent: [Formula: see text]. However, nonlinear model neurons produce different values for Z and [Formula: see text]. In particular, nonlinearities in the voltage equation produce a much larger difference between these two quantities than those in equations of recovery variables that describe activation and inactivation kinetics. Neurons are inherently nonlinear, and notably, with ionic currents that amplify resonance, the voltage clamp technique severely underestimates the current clamp response. We demonstrate this difference experimentally using the PD neurons in the crab stomatogastric ganglion. These findings are instructive for researchers who explore cellular mechanisms of neuronal oscillations.

Mechanisms of generation of membrane potential resonance in a neuron with multiple resonant ionic currents.

Neuronal membrane potential resonance (MPR) is associated with subthreshold and network oscillations. A number of voltage-gated ionic currents can contribute to the generation or amplification of MPR, but how the interaction of these currents with linear currents contributes to MPR is not well understood. We explored this in the pacemaker PD neurons of the crab pyloric network. The PD neuron MPR is sensitive to blockers of H- (IH) and calcium-currents (ICa). We used the impedance profile of the biological PD neuron, measured in voltage clamp, to constrain parameter values of a conductance-based model using a genetic algorithm and obtained many optimal parameter combinations. Unlike most cases of MPR, in these optimal models, the values of resonant- (fres) and phasonant- (fϕ = 0) frequencies were almost identical. Taking advantage of this fact, we linked the peak phase of ionic currents to their amplitude, in order to provide a mechanistic explanation the dependence of MPR on the ICa gating variable time constants. Additionally, we found that distinct pairwise correlations between ICa parameters contributed to the maintenance of fres and resonance power (QZ). Measurements of the PD neuron MPR at more hyperpolarized voltages resulted in a reduction of fres but no change in QZ. Constraining the optimal models using these data unmasked a positive correlation between the maximal conductances of IH and ICa. Thus, although IH is not necessary for MPR in this neuron type, it contributes indirectly by constraining the parameters of ICa.

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.

A balance of outward and linear inward ionic currents is required for generation of slow-wave oscillations.

Regenerative inward currents help produce slow oscillations through a negative-slope conductance region of their current-voltage relationship that is well approximated by a linear negative conductance. We used dynamic-clamp injections of a linear current with such conductance, INL, to explore why some neurons can generate intrinsic slow oscillations whereas others cannot. We addressed this question in synaptically isolated neurons of the crab Cancer borealis after blocking action potentials. The pyloric network consists of a distinct pacemaker and follower neurons, all of which express the same complement of ionic currents. When the pyloric dilator (PD) neuron, a member of the pacemaker group, was injected with INL with dynamic clamp, it consistently produced slow oscillations. In contrast, all follower neurons failed to oscillate with INL To understand these distinct behaviors, we compared outward current levels of PD with those of follower lateral pyloric (LP) and ventral pyloric (VD) neurons. We found that LP and VD neurons had significantly larger high-threshold potassium currents (IHTK) than PD and LP had lower-transient potassium current (IA). Reducing IHTK pharmacologically enabled both LP and VD neurons to produce INL-induced oscillations, whereas modifying IA levels did not affect INL-induced oscillations. Using phase-plane and bifurcation analysis of a simplified model cell, we demonstrate that large levels of IHTK can block INL-induced oscillatory activity whereas generation of oscillations is almost independent of IA levels. These results demonstrate the general importance of a balance between inward pacemaking currents and high-threshold K+ current levels in determining slow oscillatory activity.NEW & NOTEWORTHY Pacemaker neuron-generated rhythmic activity requires the activation of at least one inward and one outward current. We have previously shown that the inward current can be a linear current (with negative conductance). Using this simple mechanism, here we demonstrate that the inward current conductance must be in relative balance with the outward current conductances to generate oscillatory activity. Surprisingly, an excess of outward conductances completely precludes the possibility of achieving such a balance.

Membrane potential resonance frequency directly influences network frequency through electrical coupling.

Oscillatory networks often include neurons with membrane potential resonance, exhibiting a peak in the voltage amplitude as a function of current input at a nonzero (resonance) frequency (fres). Although fres has been correlated to the network frequency (fnet) in a variety of systems, a causal relationship between the two has not been established. We examine the hypothesis that combinations of biophysical parameters that shift fres, without changing other attributes of the impedance profile, also shift fnet in the same direction. We test this hypothesis, computationally and experimentally, in an electrically coupled network consisting of intrinsic oscillator (O) and resonator (R) neurons. We use a two-cell model of such a network to show that increasing fres of R directly increases fnet and that this effect becomes more prominent if the amplitude of resonance is increased. Notably, the effect of fres on fnet is independent of the parameters that define the oscillator or the combination of parameters in R that produce the shift in fres, as long as this combination produces the same impedance vs. frequency relationship. We use the dynamic clamp technique to experimentally verify the model predictions by connecting a model resonator to the pacemaker pyloric dilator neurons of the crab Cancer borealis pyloric network using electrical synapses and show that the pyloric network frequency can be shifted by changing fres in the resonator. Our results provide compelling evidence that fres and resonance amplitude strongly influence fnet, and therefore, modulators may target these attributes to modify rhythmic activity.

Convergent neuromodulation onto a network neuron can have divergent effects at the network level.

Different neuromodulators often target the same ion channel. When such modulators act on different neuron types, this convergent action can enable a rhythmic network to produce distinct outputs. Less clear are the functional consequences when two neuromodulators influence the same ion channel in the same neuron. We examine the consequences of this seeming redundancy using a mathematical model of the crab gastric mill (chewing) network. This network is activated in vitro by the projection neuron MCN1, which elicits a half-center bursting oscillation between the reciprocally-inhibitory neurons LG and Int1. We focus on two neuropeptides which modulate this network, including a MCN1 neurotransmitter and the hormone crustacean cardioactive peptide (CCAP). Both activate the same voltage-gated current (I MI ) in the LG neuron. However, I MI-MCN1 , resulting from MCN1 released neuropeptide, has phasic dynamics in its maximal conductance due to LG presynaptic inhibition of MCN1, while I MI-CCAP retains the same maximal conductance in both phases of the gastric mill rhythm. Separation of time scales allows us to produce a 2D model from which phase plane analysis shows that, as in the biological system, I MI-MCN1 and I MI-CCAP primarily influence the durations of opposing phases of this rhythm. Furthermore, I MI-MCN1 influences the rhythmic output in a manner similar to the Int1-to-LG synapse, whereas I MI-CCAP has an influence similar to the LG-to-Int1 synapse. These results show that distinct neuromodulators which target the same voltage-gated ion channel in the same network neuron can nevertheless produce distinct effects at the network level, providing divergent neuromodulator actions on network activity.

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.

Frequency preference in two-dimensional neural models: a linear analysis of the interaction between resonant and amplifying currents.

Many neuron types exhibit preferred frequency responses in their voltage amplitude (resonance) or phase shift to subthreshold oscillatory currents, but the effect of biophysical parameters on these properties is not well understood. We propose a general framework to analyze the role of different ionic currents and their interactions in shaping the properties of impedance amplitude and phase in linearized biophysical models and demonstrate this approach in a two-dimensional linear model with two effective conductances g L and g1. We compute the key attributes of impedance and phase (resonance frequency and amplitude, zero-phase frequency, selectivity, etc.) in the g(L) - g1 parameter space. Using these attribute diagrams we identify two basic mechanisms for the generation of resonance: an increase in the resonance amplitude as g1 increases while the overall impedance is decreased, and an increase in the maximal impedance, without any change in the input resistance, as the ionic current time constant increases. We use the attribute diagrams to analyze resonance and phase of the linearization of two biophysical models that include resonant (I h or slow potassium) and amplifying currents (persistent sodium). In the absence of amplifying currents, the two models behave similarly as the conductances of the resonant currents is increased whereas, with the amplifying current present, the two models have qualitatively opposite responses. This work provides a general method for decoding the effect of biophysical parameters on linear membrane resonance and phase by tracking trajectories, parametrized by the relevant biophysical parameter, in pre-constructed attribute diagrams.

The role of linear and voltage-dependent ionic currents in the generation of slow wave oscillations.

Neuronal oscillatory activity is generated by a combination of ionic currents, including at least one inward regenerative current that brings the cell towards depolarized voltages and one outward current that repolarizes the cell. Such currents have traditionally been assumed to require voltage-dependence. Here we test the hypothesis that the voltage dependence of the regenerative inward current is not necessary for generating oscillations. Instead, a current I NL that is linear in the biological voltage range and has negative conductance is sufficient to produce regenerative activity. The current I NL can be considered a linear approximation to the negative-conductance region of the current-voltage relationship of a regenerative inward current. Using a simple conductance-based model, we show that I NL , in conjunction with a voltage-gated, non-inactivating outward current, can generate oscillatory activity. We use phase-plane and bifurcation analyses to uncover a rich variety of behaviors as the conductance of I NL is varied, and show that oscillations emerge as a result of destabilization of the resting state of the model neuron. The model shows the need for well-defined relationships between the inward and outward current conductances, as well as their reversal potentials, in order to produce stable oscillatory activity. Our analysis predicts that a hyperpolarization-activated inward current can play a role in stabilizing oscillatory activity by preventing swings to very negative voltages, which is consistent with what is recorded in biological neurons in general. We confirm this prediction of the model experimentally in neurons from the crab stomatogastric ganglion.

A modeling exploration of how synaptic feedback to descending projection neurons shapes the activity of an oscillatory network.

Rhythmic activity which underlies motor output is often initiated and controlled by descending modulatory projection pathways onto central pattern generator (CPG) networks. In turn, these descending pathways receive synaptic feedback from their target CPG network, which can influence the CPG output. However, the mechanisms underlying such bi-directional synaptic interactions are mostly unexplored. We develop a reduced mathematical model, including both feed-forward and feedback circuitry, to examine how the synaptic interactions involving two projection neurons, MCN1 and CPN2, can produce and shape the activity of the gastric mill CPG in the crab stomatogastric nervous system. We use simplifying assumptions that are based on the behavior of the biological system to reduce this model down to 2 dimensions, which allows for phase plane analysis of the model output. The model shows a distinct activity for the gastric mill rhythm that is elicited when MCN1 and CPN2 are co-active compared to the rhythm elicited by MCN1 activity alone. Furthermore, the presence of feedback to the projection neuron CPN2 provides a distinct locus of pattern generation in the model which does not require reciprocally inhibitory interactions between the gastric mill CPG neurons, but is instead based on a half-center oscillator that occurs through a tri-synaptic pathway that includes CPN2. Our modeling results show that feedback to projection pathways may provide additional mechanisms for the generation of motor activity. These mechanisms can have distinct dependence on network parameters and may therefore provide additional flexibility for the rhythmic motor output.

The cerebellum directly modulates the substantia nigra dopaminergic activity.

Evidence of direct reciprocal connections between the cerebellum and basal ganglia has challenged the long-held notion that these structures function independently. While anatomical studies have suggested the presence of cerebellar projections to the substantia nigra pars compacta (SNc), the nature and function of these connections (Cb-SNc) is unknown. Here we show, in mice, that Cb-SNc projections form monosynaptic glutamatergic synapses with dopaminergic and non-dopaminergic neurons in the SNc. Optogenetic activation of Cb-SNc axons in the SNc is associated with increased SNc activity, elevated striatal dopamine levels and increased locomotion. During behavior, Cb-SNc projections are bilaterally activated before ambulation and unilateral lever manipulation. Cb-SNc projections show prominent activation for water reward and higher activation for sweet water, suggesting that the pathway also encodes reward value. Thus, the cerebellum directly, rapidly and effectively modulates basal ganglia dopamine levels and conveys information related to movement initiation, vigor and reward processing.

Dopamine modulation of Ih improves temporal fidelity of spike propagation in an unmyelinated axon.

We studied how conduction delays of action potentials in an unmyelinated axon depended on the history of activity and how this dependence was changed by the neuromodulator dopamine (DA). The pyloric dilator axons of the stomatogastric nervous system in the lobster, Homarus americanus, exhibited substantial activity-dependent hyperpolarization and changes in spike shape during repetitive activation. The conduction delays varied by several milliseconds per centimeter, and, during activation with realistic burst patterns or Poisson-like patterns, changes in delay occurred over multiple timescales. The mean delay increased, whereas the resting membrane potential hyperpolarized with a time constant of several minutes. Concomitantly with the mean delay, the variability of delay also increased. The variability of delay was not a linear or monotonic function of instantaneous spike frequency or spike shape parameters, and the relationship between these parameters changed with the increase in mean delay. Hyperpolarization was counteracted by a hyperpolarization-activated inward current (I(h)), and the magnitude of I(h) critically determined the temporal fidelity of spike propagation. Pharmacological block of I(h) increased the change in delay and the variability of delay, and increasing I(h) by application of DA diminished both. Consequently, the temporal fidelity of pattern propagation was substantially improved in DA. Standard measurements of changes in excitability or delay with paired stimuli or tonic stimulation failed to capture the dynamics of spike conduction. These results indicate that spike conduction can be extremely sensitive to the history of axonal activity and to the presence of neuromodulators, with potentially important consequences for temporal coding.

Distinct Mechanisms Underlie Electrical Coupling Resonance and Its Interaction with Membrane Potential Resonance.

Neurons in oscillatory networks often exhibit membrane potential resonance, a peak impedance at a non-zero input frequency. In electrically coupled oscillatory networks, the coupling coefficient (the ratio of post- and prejunctional voltage responses) could also show resonance. Such coupling resonance may emerge from the interaction between the coupling current and resonance properties of the coupled neurons, but this relationship has not been clearly described. Additionally, it is unknown if the gap-junction mediated electrical coupling conductance may have frequency dependence. We examined these questions by recording a pair of electrically coupled neurons in the oscillatory pyloric network of the crab Cancer borealis. We performed dual current- and voltage-clamp recordings and quantified the frequency preference of the coupled neurons, the coupling coefficient, the electrical conductance, and the postjunctional neuronal response. We found that all components exhibit frequency selectivity, but with distinct preferred frequencies. Mathematical and computational analysis showed that membrane potential resonance of the postjunctional neuron was sufficient to give rise to resonance properties of the coupling coefficient, but not the coupling conductance. A distinct coupling conductance resonance frequency therefore emerges either from other circuit components or from the gating properties of the gap junctions. Finally, to explore the functional effect of the resonance of the coupling conductance, we examined its role in synchronizing neuronal the activities of electrically coupled bursting model neurons. Together, our findings elucidate factors that produce electrical coupling resonance and the function of this resonance in oscillatory networks.

Modulation by neuropeptides with overlapping targets results in functional overlap in oscillatory circuit activation.

Neuromodulation lends flexibility to neural circuit operation but the general notion that different neuromodulators sculpt neural circuit activity into distinct and characteristic patterns is complicated by interindividual variability. In addition, some neuromodulators converge onto the same signaling pathways, with similar effects on neurons and synapses. We compared the effects of three neuropeptides on the rhythmic pyloric circuit in the crab Cancer borealis stomatogastric nervous system. Proctolin (PROC), crustacean cardioactive peptide (CCAP), and red pigment concentrating hormone (RPCH) all activate the same modulatory inward current, IMI, and have convergent actions on synapses. However, while PROC targets all four neuron types in the core pyloric circuit, CCAP and RPCH target the same subset of only two neurons. After removal of spontaneous neuromodulator release, none of the neuropeptides restored the control cycle frequency, but all restored the relative timing between neuron types. Consequently, differences between neuropeptide effects were mainly found in the spiking activity of different neuron types. We performed statistical comparisons using the Euclidean distance in the multidimensional space of normalized output attributes to obtain a single measure of difference between modulatory states. Across preparations, circuit output in PROC was distinguishable from CCAP and RPCH, but CCAP and RPCH were not distinguishable from each other. However, we argue that even between PROC and the other two neuropeptides, population data overlapped enough to prevent reliable identification of individual output patterns as characteristic for a specific neuropeptide. We confirmed this notion by showing that blind classifications by machine learning algorithms were only moderately successful.