Temperature compensation in a small rhythmic circuit

Temperature affects the conductances and kinetics of the ionic channels that underlie neuronal activity. Each membrane conductance has a different characteristic temperature sensitivity, which raises the question of how neurons and neuronal circuits can operate robustly over wide temperature ranges. To address this, we employed computational models of the pyloric network of crabs and lobsters. We produced multiple different models that exhibit a triphasic pyloric rhythm over a range of temperatures and explored the dynamics of their currents and how they change with temperature. Temperature can produce smooth changes in the relative contributions of the currents to neural activity so that neurons and networks undergo graceful transitions in the mechanisms that give rise to their activity patterns. Moreover, responses of the models to deletions of a current can be different at high and low temperatures, indicating that even a well-defined genetic or pharmacological manipulation may produce qualitatively distinct effects depending on the temperature.

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.

Brian 2, an intuitive and efficient neural simulator

Brian 2 allows scientists to simply and efficiently simulate spiking neural network models. These models can feature novel dynamical equations, their interactions with the environment, and experimental protocols. To preserve high performance when defining new models, most simulators offer two options: low-level programming or description languages. The first option requires expertise, is prone to errors, and is problematic for reproducibility. The second option cannot describe all aspects of a computational experiment, such as the potentially complex logic of a stimulation protocol. Brian addresses these issues using runtime code generation. Scientists write code with simple and concise high-level descriptions, and Brian transforms them into efficient low-level code that can run interleaved with their code. We illustrate this with several challenging examples: a plastic model of the pyloric network, a closed-loop sensorimotor model, a programmatic exploration of a neuron model, and an auditory model with real-time input.

Temperature compensation in a small rhythmic circuit

Temperature affects the conductances and kinetics of the ionic channels that underlie neuronal activity. Each membrane conductance has a different characteristic temperature sensitivity, which raises the question of how neurons and neuronal circuits can operate robustly over wide temperature ranges. To address this, we employed computational models of the pyloric network of crabs and lobsters. We employed a landscape optimization scheme introduced previously (Alonso and Marder, 2019) to produce multiple different models that exhibit triphasic pyloric rhythms over a range of temperatures. We use the currentscapes introduced in (Alonso and Marder, 2019) to explore the dynamics of model currents and how they change with temperature. We found that temperature changes the relative contributions of the currents to neuronal activity so that rhythmic activity smoothly slides through changes in mechanisms. Moreover, the responses of the models to extreme perturbations—such as gradually decreasing a current type—are often qualitatively different at different temperatures.

Brian 2: an intuitive and efficient neural simulator

To be maximally useful for neuroscience research, neural simulators must make it possible to define original models. This is especially important because a computational experiment might not only need descriptions of neurons and synapses, but also models of interactions with the environment (e.g. muscles), or the environment itself. To preserve high performance when defining new models, current simulators offer two options: low-level programming, or mark-up languages (and other domain specific languages). The first option requires time and expertise, is prone to errors, and contributes to problems with reproducibility and replicability. The second option has limited scope, since it can only describe the range of neural models covered by the ontology. Other aspects of a computational experiment, such as the stimulation protocol, cannot be expressed within this framework. “Brian” 2 is a complete rewrite of Brian that addresses this issue by using runtime code generation with a procedural equation-oriented approach. Brian 2 enables scientists to write code that is particularly simple and concise, closely matching the way they conceptualise their models, while the technique of runtime code generation automatically transforms high level descriptions of models into efficient low level code tailored to different hardware (e.g. CPU or GPU). We illustrate it with several challenging examples: a plastic model of the pyloric network of crustaceans, a closed-loop sensorimotor model, programmatic exploration of a neuron model, and an auditory model with real-time input from a microphone.

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. Although the stomatogastric system of the crab Cancer borealis has become a preferred model system for exploration of cellular and synaptic basis of circuit dynamics, in this species, the identity of the PD neuron neurotransmitter and its contribution to the total pacemaker group synaptic output remain unexplored. We examined the synaptic properties of the crab PD neuron 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. Conversely, the AB neuron does not express either of these cholinergic markers, and expresses high levels of vesicular glutamate transporter mRNA, consistent with a glutamatergic phenotype. Notably, in the combined synapses to the LP and PY neurons, the major contribution is from the glutamatergic AB neuron and only between 25-30% of the synaptic strength is due to the PD neuron. However, there was no difference between the short-term synaptic plasticity in the total pacemaker synapse compared to that of the PD neuron alone. 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.

Activation mechanism of a neuromodulator-gated pacemaker ionic current

The neuromodulator-gated current ( IMI) found in the crab stomatogastric ganglion is activated by neuromodulators that are essential to induce the rhythmic activity of the pyloric network in this system. One of these neuromodulators is also known to control the correlated expression of voltage-gated ionic currents in pyloric neurons, as well as synaptic plasticity and strength. Thus understanding the mechanism by which neuromodulator receptors activate IMI should provide insights not only into how oscillations are initiated but also into how other processes, and currents not directly activated by them, are regulated. To determine what specific signaling molecules are implicated in this process, we used a battery of agonists and antagonists of common signal transduction pathways. We found that the G protein inhibitor GDPβS and the G protein activator GTPγS significantly affect IMI amplitude, suggesting that its activation is mediated by G proteins. Interestingly, when using the more specific G protein blocker pertussis toxin, we observed the expected inhibition of IMI amplitude but, unexpectedly, in a calcium-dependent fashion. We also found that antagonists of calcium- and calmodulin-associated signaling significantly reduce IMI amplitude. In contrast, we found little evidence for the role of cyclic nucleotide signaling, phospholipase C (PLC), or kinases and phosphatases, except two calmodulin-dependent kinases. In sum, these results suggest that proctolin-induced IMI is mediated by a G protein whose pertussis toxin sensitivity is altered by external calcium concentration and appears to depend on intracellular calcium, calmodulin, and calmodulin-activated kinases. In contrast, we found no support for IMI being mediated by PLC signaling or cyclic nucleotides. NEW & NOTEWORTHY Neuronal rhythmic activity is generated by either network-based or cell-autonomous mechanisms. In the pyloric network of decapod crustaceans, the activation of a neuromodulator-gated pacemaker current is crucial for the generation of rhythmic activity. This current is activated by several neuromodulators, including peptides and acetylcholine, presumably via metabotropic receptors. We have previously demonstrated a novel extracellular calcium-sensitive voltage-dependence mechanism of this current. We presently report that the activation mechanism depends on intracellular and extracellular calcium-sensitive components.

A balance of outward and linear inward ionic currents is required for the 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 this 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 distinct pacemaker group 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 using dynamic clamp, it consistently produced slow oscillations. In contrast, the lateral pyloric (LP) or ventral pyloric (VD) follower neurons, failed to oscillate with INL. To understand these distinct behaviors, we compared outward current levels of PD, LP and 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 oscillations with INL, 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 importance of a balance between inward pacemaking currents and high-threshold K+current levels in determining slow oscillatory activity.

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.Author SummaryMany neuron types exhibit membrane potential resonance (MPR) in which the neuron produces the largest response to oscillatory input at some preferred (resonant) frequency and, in many systems, the network frequency is correlated with neuronal MPR. MPR is captured by a peak in the impedance vs. frequency curve (Z-profile), which is shaped by the dynamics of voltage-gated ionic currents. Although neuron types can express variable levels of ionic currents, they may have a stable resonant frequency. We used the PD neuron of the crab pyloric network to understand how MPR emerges from the interplay of the biophysical properties of multiple ionic currents, each capable of generating resonance. We show the contribution of an inactivating current at the resonant frequency in terms of interacting time constants. We measured the Z-profile of the PD neuron and explored possible combinations of model parameters that fit this experimentally measured profile. We found that the Z-profile constrains and defines correlations among parameters associated with ionic currents. Furthermore, the resonant frequency and amplitude are sensitive to different parameter sets and can be preserved by co-varying pairs of parameters along their correlation lines. Furthermore, although a resonant current may be present in a neuron, it may not directly contribute to MPR, but constrain the properties of other currents that generate MPR. Finally, constraining model parameters further to those that modify their MPR properties to changes in voltage range produces maximal conductance correlations.

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 ( f res). Although f res has been correlated to the network frequency ( f net) 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 f res, without changing other attributes of the impedance profile, also shift f net 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 f res of R directly increases f net and that this effect becomes more prominent if the amplitude of resonance is increased. Notably, the effect of f res on f net is independent of the parameters that define the oscillator or the combination of parameters in R that produce the shift in f res, 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 f res in the resonator. Our results provide compelling evidence that f res and resonance amplitude strongly influence fnet, and therefore, modulators may target these attributes to modify rhythmic activity.