RECIPROCALLY INHIBITORY CIRCUITS OPERATING WITH DISTINCT MECHANISMS ARE DIFFERENTLY ROBUST TO PERTURBATION AND MODULATION

What features are important for circuit robustness? Reciprocal inhibition is a building block in many circuits. We used dynamic clamp to create reciprocally inhibitory circuits from GM neurons of the crab stomatogastric ganglion by injecting artificial synaptic and hyperpolarization-activated inward (H) currents. In "release", the active neuron controls the off/on transitions. In "escape", the inhibited neuron controls the transitions. We characterized the robustness of escape and release circuits to alterations in circuit parameters, temperature, and neuromodulation. Escape circuits rely on tight correlations between synaptic and H conductances to generate bursting but are resilient to temperature increase. Release circuits are robust to variations in synaptic and H conductances but fragile to temperature increase. The modulatory current (IMI) restores oscillations in release circuits but has little effect in escape. Thus, the same perturbation can have dramatically different effects depending on the circuits' mechanism of operation that may not be observable from circuit output.

Neural Flip-Flops III: Stomatogastric Ganglion

The stomatogastric ganglion (STG) is a group of about 30 neurons that resides on the stomach in decapod crustaceans. Its two central pattern generators (CPGs) control the chewing action of the gastric mill and the peristaltic movement of food through the pylorus to the gut. The STG has been studied extensively because it has properties that are common to all nervous systems and because of the small number of neurons and other features that make it convenient to study. So many details are known that the STG is considered a classic test case in neuroscience for the reductionist strategy of explaining the emergence of macro-level phenomena from micro-level data. In spite of the intense scrutiny the STG has received, how it generates its rhythmic patterns of bursts remains unknown.The novel neural networks presented here model the pyloric CPG of the American lobster (Homarus americanus). Each model’s connectivity is explicit, and its operation depends only on minimal neuron capabilities of excitation and inhibition. One type of model CPGs, flip-flop ring oscillators, is apparently new to engineering, making it an example of neuroscience and logic circuit design informing each other. Several testable predictions are given here, and STG phenomena are shown to support several predictions of neural flip-flops that were given in a previous paper on short-term memory.The model CPGs are not the same as the more complex pyloric CPG. But they show how neurons can be connected to produce oscillations, and there are enough similarities in significant features that they may be considered first approximations, or perhaps simplified versions, of STG architecture. The similarities include 1) mostly inhibitory synapses; 2) pairs of cells with reciprocal, inhibitory inputs, complementary outputs that are approximately 180 degrees out of phase, and state changes occurring with the high output changing first; 3) cells that have reciprocal, inhibitory inputs with more than one other cell; and 4) six cells that produce coordinated oscillations with the same period, four phases distributed approximately uniformly over the period, and half of the burst durations approximately 1/4 of the period and the other half 3/8. These variables cannot be controlled independently in the design, suggesting a similar architecture in the models and the STG.Some of the neural network designs can be derived from electronic logic circuit designs simply by moving each negation symbol from one end of a connection to the other. This does not change the logic of the network, but it changes each logic gate to one that can be implemented with a single neuron.

Estimating Transfer Entropy in Continuous Time Between Neural Spike Trains or Other Event-Based Data

Transfer entropy (TE) is a widely used measure of directed information flows in a number of domains including neuroscience. Many real-world time series in which we are interested in information flows come in the form of (near) instantaneous events occurring over time, including the spiking of biological neurons, trades on stock markets and posts to social media. However, there exist severe limitations to the current approach to TE estimation on such event-based data via discretising the time series into time bins: it is not consistent, has high bias, converges slowly and cannot simultaneously capture relationships that occur with very fine time precision as well as those that occur over long time intervals. Building on recent work which derived a theoretical framework for TE in continuous time, we present an estimation framework for TE on event-based data and develop a k-nearest-neighbours estimator within this framework. This estimator is provably consistent, has favourable bias properties and converges orders of magnitude more quickly than the discrete-time estimator on synthetic examples. We also develop a local permutation scheme for generating null surrogate time series to test for the statistical significance of the TE and, as such, test for the conditional independence between the history of one point process and the updates of another — signifying the lack of a causal connection under certain weak assumptions. Our approach is capable of detecting conditional independence or otherwise even in the presence of strong pairwise time-directed correlations. The power of this approach is further demonstrated on the inference of the connectivity of biophysical models of a spiking neural circuit inspired by the pyloric circuit of the crustacean stomatogastric ganglion, succeeding where previous related estimators have failed.AUTHOR SUMMARYTransfer Entropy (TE) is an information-theoretic measure commonly used in neuroscience to measure the directed statistical dependence between a source and a target time series, possibly also conditioned on other processes. Along with measuring information flows, it is used for the inference of directed functional and effective networks from time series data. The currently-used technique for estimating TE on neural spike trains first time-discretises the data and then applies a straightforward or “plug-in” information-theoretic estimation procedure. This approach has numerous drawbacks: it is very biased, it cannot capture relationships occurring on both fine and large timescales simultaneously, converges very slowly as more data is obtained, and indeed does not even converge to the correct value. We present a new estimator for TE which operates in continuous time, demonstrating via application to synthetic examples that it addresses these problems, and can reliably differentiate statistically significant flows from (conditionally) independent spike trains. Further, we also apply it to more biologically-realistic spike trains obtained from a biophysical model of the pyloric circuit of the crustacean stomatogastric ganglion; our correct inference of the underlying connection structure here provides an important validation for our approach where similar methods have previously failed

Rapid adaptation to elevated extracellular potassium in the pyloric circuit of the crab, Cancer borealis

Solutions with elevated extracellular potassium are commonly used as a depolarizing stimulus. We studied the effects of high potassium concentration ([K+]) on the pyloric circuit of the crab stomatogastric ganglion. A 2.5-fold increase in extracellular [K+] caused a transient loss of activity that was not due to depolarization block, followed by a rapid increase in excitability and recovery of spiking within minutes. This suggests that changing extracellular potassium can have complex and nonstationary effects on neuronal circuits.

Neuronal morphologies built for reliable physiology in a rhythmic motor circuit

It is often assumed that highly-branched neuronal structures perform compartmentalized computations. However, previously we showed that the Gastric Mill (GM) neuron in the crustacean stomatogastric ganglion (STG) operates like a single electrotonic compartment, despite having thousands of branch points and total cable length >10 mm (Otopalik et al., 2017a; 2017b). Here we show that compact electrotonic architecture is generalizable to other STG neuron types, and that these neurons present direction-insensitive, linear voltage integration, suggesting they pool synaptic inputs across their neuronal structures. We also show, using simulations of 720 cable models spanning a broad range of geometries and passive properties, that compact electrotonus, linear integration, and directional insensitivity in STG neurons arise from their neurite geometries (diameters tapering from 10-20 µm to < 2 µm at their terminal tips). A broad parameter search reveals multiple morphological and biophysical solutions for achieving different degrees of passive electrotonic decrement and computational strategies in the absence of active properties.

Two central pattern generators from the crab, Cancer borealis, respond robustly and differentially to extreme extracellular pH

Animals and their neuronal circuits must maintain function despite significant environmental fluctuations. The crab, Cancer borealis, experiences daily changes in ocean temperature and pH. Here, we describe the effects of extreme changes in extracellular pH – from pH 5.5 to 10.4 – on two central pattern generating networks, the stomatogastric and cardiac ganglia of C. borealis. Given that the physiological properties of ion channels are known to be sensitive to pH within the range tested, it is surprising that these rhythms generally remained robust from pH 6.1 to pH 8.8. Unexpectedly, the stomatogastric ganglion was more sensitive to acid while the cardiac ganglion was more sensitive to base. Considerable animal-to-animal variability was likely a consequence of similar network performance arising from variable sets of underlying conductances. Together, these results illustrate the potential difficulty in generalizing the effects of environmental perturbation across circuits, even within the same animal.AbbreviationsSTGstomatogastric ganglionCGcardiac ganglionCPGcentral pattern generatorABAnterior BursterPDPyloric DilatorLPLateral PyloricPYPyloricSCSmall CellLCLarge Celllvnlateral ventricular nerveANOVAanalysis of variancePTXpicrotoxinIPSPinhibitory post-synaptic potentialLGLateral GastricMGMedial GastricLPGLateral Posterior GastricGMGastric MillDGDorsal GastricAMAnterior MedianInt1Interneuron 1mvnmedial ventricular nervedgndorsal gastric nervelgnlateral gastric nerveioninferior oesophageal nerveICInferior CardiacVDVentricular DilatorMCN1Modulatory Commissural Neuron 1VCNVentral Cardiac NeuronCPN2Commissural Projection Neuron 2CoGcommissural ganglionKDEkernel density estimateIQRinterquartile rangeCIconfidence interval

Distinct co-modulation rules of synaptic and voltage-gated currents coordinates interactions of multiple neuromodulators

Different neuromodulators usually activate distinct receptors but can have overlapping targets. Consequently, circuit output depends on neuromodulator interactions at shared targets, a poorly understood process. We explored quantitative rules of co-modulation of two principal targets: voltage-gated and synaptic ionic currents. In the stomatogastric ganglion of the crab Cancer borealis, the neuropeptides proctolin and 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 proctolin 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, where co-modulation was sublinear. 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.

The Crustacean Stomatogastric Nervous System

The crustacean stomatogastric nervous system has become one of the premier preparations used for the study of the mechanisms underlying the generation of rhythmic motor patterns. The stomatogastric ganglion (STG) contains about 30 neurons, most of which are motor neurons that innervate more than 40 sets of striated muscles that move the animal’s stomach. Descending projection neurons from the two commissural ganglia (CoGs) and the single oesophageal ganglion (OG) are important for the generation of the motor patterns produced by the STG. Identified sensory neurons project either into the CoGs to activate descending modulatory neurons, or directly into the STG.

Removal of endogenous neuromodulators in a small motor network enhances responsiveness to neuromodulation

We studied the changes in sensitivity to a peptide modulator, crustacean cardioactive peptide (CCAP), as a response to loss of endogenous modulation in the stomatogastric ganglion (STG) of the crab Cancer borealis. Our data demonstrate that removal of endogenous modulation for 24 h increases the response of the lateral pyloric (LP) neuron of the STG to exogenously applied CCAP. Increased responsiveness is accompanied by increases in CCAP receptor (CCAPr) mRNA levels in LP neurons, requires de novo protein synthesis, and can be prevented by coincubation for the 24-h period with exogenous CCAP. These results suggest that there is a direct feedback from loss of CCAP signaling to the production of CCAPr that increases subsequent response to the ligand. However, we also demonstrate that the modulator-evoked membrane current ( IMI) activated by CCAP is greater in magnitude after combined loss of endogenous modulation and activity compared with removal of just hormonal modulation. These results suggest that both receptor expression and an increase in the target conductance of the CCAP G protein-coupled receptor are involved in the increased response to exogenous hormone exposure following experimental loss of modulation in the STG. NEW & NOTEWORTHY The nervous system shows a tremendous amount of plasticity. More recently there has been an appreciation for compensatory actions that stabilize output in the face of perturbations to normal activity. In this study we demonstrate that neurons of the crustacean stomatogastric ganglion generate apparent compensatory responses to loss of peptide neuromodulation, adding to the repertoire of mechanisms by which the stomatogastric nervous system can regulate and stabilize its own output.