Multiple mechanisms switch an electrically coupled, synaptically inhibited neuron between competing rhythmic oscillators

Degenerate neuronal and circuit mechanisms important for generating rhythmic motor patterns

In 1996, we published a review article (Marder E, Calabrese RL. Physiol Rev 76: 687-717, 1996) describing the state of knowledge about the structure and function of the central pattern-generating circuits important for producing rhythmic behaviors. Although many of the core questions persist, much has changed since 1996. Here, we focus on newer studies that reveal ambiguities that complicate understanding circuit dynamics, despite the enormous technical advances of the recent past. In particular, we highlight recent studies of animal-to-animal variability and our understanding that circuit rhythmicity may be supported by multiple state-dependent mechanisms within the same animal and that robustness and resilience in the face of perturbation may depend critically on the presence of modulators and degenerate circuit mechanisms. Additionally, we highlight the use of computational models to ask whether there are generalizable principles about circuit motifs that can be found across rhythmic motor systems in different animal species.

Neural Processing without O2 and Glucose Delivery: Lessons from the Pond to the Clinic

Neuronal activity requires a large amount of ATP, leading to a rapid collapse of brain function when aerobic respiration fails. Here, we summarize how rhythmic motor circuits in the brain stem of adult frogs, which normally have high metabolic demands, transform to produce proper output during severe hypoxia associated with emergence from hibernation. We suggest that general principles underlying plasticity in brain bioenergetics may be uncovered by studying nonmammalian models that face extreme environments, yielding new insights to combat neurological disorders involving dysfunctional energy metabolism.

Neuropeptide modulation of bidirectional internetwork synapses

Oscillatory networks underlying rhythmic motor behaviors, and sensory and complex neural processing, are flexible, even in their neuronal composition. Neuromodulatory inputs enable neurons to switch participation between networks or participate in multiple networks simultaneously. Neuromodulation of internetwork synapses can both recruit and coordinate a switching neuron in a second network. We previously identified an example in which a neuron is recruited into dual-network activity via peptidergic modulation of intrinsic properties. We now ask whether the same neuropeptide also modulates internetwork synapses for internetwork coordination. The crab (Cancer borealis) stomatogastric nervous system contains two well-defined feeding-related networks (pyloric, food filtering, ∼1 Hz; gastric mill, food chewing, ∼0.1 Hz). The projection neuron MCN5 uses the neuropeptide Gly1-SIFamide to recruit the pyloric-only lateral posterior gastric (LPG) neuron into dual pyloric- plus gastric mill-timed bursting via modulation of LPG's intrinsic properties. Descending input is not required for a coordinated rhythm, thus intranetwork synapses between LPG and its second network must underlie coordination among these neurons. However, synapses between LPG and gastric mill neurons have not been documented. Using two-electrode voltage-clamp recordings, we found that graded synaptic currents between LPG and gastric mill neurons (lateral gastric, inferior cardiac, and dorsal gastric) were primarily negligible in saline, but were enhanced by Gly1-SIFamide. Furthermore, LPG and gastric mill neurons entrain each other during Gly1-SIFamide application, indicating bidirectional, functional connectivity. Thus, a neuropeptide mediates neuronal switching through parallel actions, modulating intrinsic properties for recruitment into a second network and as shown here, also modulating bidirectional internetwork synapses for coordination.NEW & NOTEWORTHY Neuromodulation can enable neurons to simultaneously coordinate with separate networks. Both recruitment into, and coordination with, a second network can occur via modulation of internetwork synapses. Alternatively, recruitment can occur via modulation of intrinsic ionic currents. We find that the same neuropeptide previously determined to modulate intrinsic currents also modulates bidirectional internetwork synapses that are typically ineffective. Thus, complementary modulatory peptide actions enable recruitment and coordination of a neuron into a second network.

Prediction of neural activity in connectome-constrained recurrent networks

We develop a theory of connectome-constrained neural networks in which a "student" network is trained to reproduce the activity of a ground-truth "teacher," representing a neural system for which a connectome is available. Unlike standard paradigms with unconstrained connectivity, here the two networks have the same connectivity but different biophysical parameters, reflecting uncertainty in neuronal and synaptic properties. We find that a connectome is often insufficient to constrain the dynamics of networks that perform a specific task, illustrating the difficulty of inferring function from connectivity alone. However, recordings from a small subset of neurons can remove this degeneracy, producing dynamics in the student that agree with the teacher. Our theory can also prioritize which neurons to record from to most efficiently predict unmeasured network activity. Our analysis shows that the solution spaces of connectome-constrained and unconstrained models are qualitatively different and provides a framework to determine when such models yield consistent dynamics.

Understanding molecular signaling cascades in neural disease using multi-resolution models

If the genome defines the program for the operations of a cell, signaling networks execute it. These cascades of chemical, cell-biological, structural, and trafficking events span milliseconds (e.g., synaptic release) to potentially a lifetime (e.g., stabilization of dendritic spines). In principle almost every aspect of neuronal function, particularly at the synapse, depends on signaling. Thus dysfunction of these cascades, whether through mutations, local dysregulation, or infection, leads to disease. The sheer complexity of these pathways is matched by the range of diseases and the diversity of their phenotypes. In this review, we discuss how to build computational models, how these models are essential to tackle this complexity, and the benefits of using families of models at different levels of detail to understand signaling in health and disease.

Gap junctions: The missing piece of the connectome

The central pattern generator that controls flying power in Drosophila requires desynchronized firing to drive a steady wingbeat frequency. A new study reveals how gap junctions are the key to desynchronizing the motor neurons.

Gap junctions desynchronize a neural circuit to stabilize insect flight

Insect asynchronous flight is one of the most prevalent forms of animal locomotion used by more than 600,000 species. Despite profound insights into the motor patterns¹, biomechanics^2,3 and aerodynamics underlying asynchronous flight^4,5, the architecture and function of the central-pattern-generating (CPG) neural network remain unclear. Here, on the basis of an experiment-theory approach including electrophysiology, optophysiology, Drosophila genetics and mathematical modelling, we identify a miniaturized circuit solution with unexpected properties. The CPG network consists of motoneurons interconnected by electrical synapses that, in contrast to doctrine, produce network activity splayed out in time instead of synchronized across neurons. Experimental and mathematical evidence support a generic mechanism for network desynchronization that relies on weak electrical synapses and specific excitability dynamics of the coupled neurons. In small networks, electrical synapses can synchronize or desynchronize network activity, depending on the neuron-intrinsic dynamics and ion channel composition. In the asynchronous flight CPG, this mechanism translates unpatterned premotor input into stereotyped neuronal firing with fixed sequences of cell activation that ensure stable wingbeat power and, as we show, is conserved across multiple species. Our findings prove a wider functional versatility of electrical synapses in the dynamic control of neural circuits and highlight the relevance of detecting electrical synapses in connectomics.

Improving the study of brain-behavior relationships by revisiting basic assumptions

Neuroimaging research has been at the forefront of concerns regarding the failure of experimental findings to replicate. In the study of brain-behavior relationships, past failures to find replicable and robust effects have been attributed to methodological shortcomings. Methodological rigor is important, but there are other overlooked possibilities: most published studies share three foundational assumptions, often implicitly, that may be faulty. In this paper, we consider the empirical evidence from human brain imaging and the study of non-human animals that calls each foundational assumption into question. We then consider the opportunities for a robust science of brain-behavior relationships that await if scientists ground their research efforts in revised assumptions supported by current empirical evidence.

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.

Multiple intrinsic membrane properties are modulated in a switch from single- to dual-network activity

Neural network flexibility includes changes in neuronal participation between networks, such as the switching of neurons between single- and dual-network activity. We previously identified a neuron that is recruited to burst in time with an additional network via modulation of its intrinsic membrane properties, instead of being recruited synaptically into the second network. However, the modulated intrinsic properties were not determined. Here, we use small networks in the Jonah crab (Cancer borealis) stomatogastric nervous system (STNS) to examine modulation of intrinsic properties underlying neuropeptide (Gly1-SIFamide)-elicited neuronal switching. The lateral posterior gastric neuron (LPG) switches from exclusive participation in the fast pyloric (∼1 Hz) network, due to electrical coupling, to dual-network activity that includes periodic escapes from the fast rhythm via intrinsically generated oscillations at the slower gastric mill network frequency (∼0.1 Hz). We isolated LPG from both networks by pharmacology and hyperpolarizing current injection. Gly1-SIFamide increased LPG intrinsic excitability and rebound from inhibition and decreased spike frequency adaptation, which can all contribute to intrinsic bursting. Using ion substitution and channel blockers, we found that a hyperpolarization-activated current, a persistent sodium current, and calcium or calcium-related current(s) appear to be primary contributors to Gly1-SIFamide-elicited LPG intrinsic bursting. However, this intrinsic bursting was more sensitive to blocking currents when LPG received rhythmic electrical coupling input from the fast network than in the isolated condition. Overall, a switch from single- to dual-network activity can involve modulation of multiple intrinsic properties, while synaptic input from a second network can shape the contributions of these properties.NEW & NOTEWORTHY Neuropeptide-elicited intrinsic bursting was recently determined to switch a neuron from single- to dual-network participation. Here we identified multiple intrinsic properties modulated in the dual-network state and candidate ion channels underlying the intrinsic bursting. Bursting at the second network frequency was more sensitive to blocking currents in the dual-network state than when neurons were synaptically isolated from their home network. Thus, synaptic input can shape the contributions of modulated intrinsic properties underlying dual-network activity.

Structural variation between neuropeptide isoforms affects function in the lobster cardiac system

Neuronal responses to peptide signaling are determined by the specific binding of a peptide to its receptor(s). For example, isoforms of the same peptide family can drive distinct responses in the same circuit by having different affinities for the same receptor, by having each isoform bind to a different receptor, or by a combination of these scenarios. Small changes in peptide composition can alter the binding kinetics and overall physiological response to a given peptide. In the American lobster (Homarus americanus), native isoforms of C-type allatostatins (AST-Cs) usually decrease heartbeat frequency and alter contraction force. However, one of the three AST-C isoforms, AST-C II, drives a cardiac response distinct from the response elicited by the other two. To investigate the aspects of the peptide that might be responsible for these differential responses, we altered various features of each peptide sequence. Although the presence of an amide group at the end of a peptide sequence (amidation) is often essential for determining physiological function, we demonstrate that C-terminal amidation does not dictate the AST-C response in the lobster cardiac system. However, single amino acid substitution within the consensus sequence did account for many of the differences in specific response characteristics (e.g. contraction frequency or force).

New insights from small rhythmic circuits

Small rhythmic circuits, such as those found in invertebrates, have provided fundamental insights into how circuit dynamics depend on individual neuronal and synaptic properties. Degenerate circuits are those with different network parameters and similar behavior. New work on degenerate circuits and their modulation illustrates some of the rules that help maintain stable and robust circuit function despite environmental perturbations. Advances in neuropeptide isolation and identification provide enhanced understanding of the neuromodulation of circuits for behavior. The advent of molecular studies of mRNA expression provides new insight into animal-to-animal variability and the homeostatic regulation of excitability in neurons and networks.

On the Diverse Functions of Electrical Synapses

Electrical synapses are the neurophysiological product of gap junctional pores between neurons that allow bidirectional flow of current between neurons. They are expressed throughout the mammalian nervous system, including cortex, hippocampus, thalamus, retina, cerebellum, and inferior olive. Classically, the function of electrical synapses has been associated with synchrony, logically following that continuous conductance provided by gap junctions facilitates the reduction of voltage differences between coupled neurons. Indeed, electrical synapses promote synchrony at many anatomical and frequency ranges across the brain. However, a growing body of literature shows there is greater complexity to the computational function of electrical synapses. The paired membranes that embed electrical synapses act as low-pass filters, and as such, electrical synapses can preferentially transfer spike after hyperpolarizations, effectively providing spike-dependent inhibition. Other functions include driving asynchronous firing, improving signal to noise ratio, aiding in discrimination of dissimilar inputs, or dampening signals by shunting current. The diverse ways by which electrical synapses contribute to neuronal integration merits furthers study. Here we review how functions of electrical synapses vary across circuits and brain regions and depend critically on the context of the neurons and brain circuits involved. Computational modeling of electrical synapses embedded in multi-cellular models and experiments utilizing optical control and measurement of cellular activity will be essential in determining the specific roles performed by electrical synapses in varying contexts.

Mapping circuit dynamics during function and dysfunction

Neural circuits can generate many spike patterns, but only some are functional. The study of how circuits generate and maintain functional dynamics is hindered by a poverty of description of circuit dynamics across functional and dysfunctional states. For example, although the regular oscillation of a central pattern generator is well characterized by its frequency and the phase relationships between its neurons, these metrics are ineffective descriptors of the irregular and aperiodic dynamics that circuits can generate under perturbation or in disease states. By recording the circuit dynamics of the well-studied pyloric circuit in Cancer borealis, we used statistical features of spike times from neurons in the circuit to visualize the spike patterns generated by this circuit under a variety of conditions. This approach captures both the variability of functional rhythms and the diversity of atypical dynamics in a single map. Clusters in the map identify qualitatively different spike patterns hinting at different dynamic states in the circuit. State probability and the statistics of the transitions between states varied with environmental perturbations, removal of descending neuromodulatory inputs, and the addition of exogenous neuromodulators. This analysis reveals strong mechanistically interpretable links between complex changes in the collective behavior of a neural circuit and specific experimental manipulations, and can constrain hypotheses of how circuits generate functional dynamics despite variability in circuit architecture and environmental perturbations.

Intrinsic Sources and Functional Impacts of Asymmetry at Electrical Synapses

Electrical synapses couple inhibitory neurons across the brain, underlying a variety of functions that are modifiable by activity. Despite recent advances, many functions and contributions of electrical synapses within neural circuitry remain underappreciated. Among these are the sources and impacts of electrical synapse asymmetry. Using multi-compartmental models of neurons coupled through dendritic electrical synapses, we investigated intrinsic factors that contribute to effective synaptic asymmetry and that result in modulation of spike timing and synchrony between coupled cells. We show that electrical synapse location along a dendrite, input resistance, internal dendritic resistance, or directional conduction of the electrical synapse itself each alter asymmetry as measured by coupling between cell somas. Conversely, we note that asymmetrical gap junction (GJ) conductance can be masked by each of these properties. Furthermore, we show that asymmetry modulates spike timing and latency of coupled cells by up to tens of milliseconds, depending on direction of conduction or dendritic location of the electrical synapse. Coordination of rhythmic activity between two cells also depends on asymmetry. These simulations illustrate that causes of asymmetry are diverse, may not be apparent in somatic measurements of electrical coupling, influence dendritic processing, and produce a variety of outcomes on spiking and synchrony of coupled cells. Our findings highlight aspects of electrical synapses that should always be included in experimental demonstrations of coupling, and when assembling simulated networks containing electrical synapses.

A dynamical systems view of neuroethology: Uncovering stateful computation in natural behaviors

State-dependent computation is key to cognition in both biological and artificial systems. Alan Turing recognized the power of stateful computation when he created the Turing machine with theoretically infinite computational capacity in 1936. Independently, by 1950, ethologists such as Tinbergen and Lorenz also began to implicitly embed rudimentary forms of state-dependent computation to create qualitative models of internal drives and naturally occurring animal behaviors. Here, we reformulate core ethological concepts in explicitly dynamical systems terms for stateful computation. We examine, based on a wealth of recent neural data collected during complex innate behaviors across species, the neural dynamics that determine the temporal structure of internal states. We will also discuss the degree to which the brain can be hierarchically partitioned into nested dynamical systems and the need for a multi-dimensional state-space model of the neuromodulatory system that underlies motivational and affective states.

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.

A Computational Neural Model for Mapping Degenerate Neural Architectures

Degeneracy in biological systems refers to a many-to-one mapping between physical structures and their functional (including psychological) outcomes. Despite the ubiquity of the phenomenon, traditional analytical tools for modeling degeneracy in neuroscience are extremely limited. In this study, we generated synthetic datasets to describe three situations of degeneracy in fMRI data to demonstrate the limitations of the current univariate approach. We describe a novel computational approach for the analysis referred to as neural topographic factor analysis (NTFA). NTFA is designed to capture variations in neural activity across task conditions and participants. The advantage of this discovery-oriented approach is to reveal whether and how experimental trials and participants cluster into task conditions and participant groups. We applied NTFA on simulated data, revealing the appropriate degeneracy assumption in all three situations and demonstrating NTFA's utility in uncovering degeneracy. Lastly, we discussed the importance of testing degeneracy in fMRI data and the implications of applying NTFA to do so.

Spontaneous generation of persistent activity in diffusively coupled cellular assemblies

The spontaneous generation of electrical activity underpins a number of essential physiological processes, and is observed even in tissues where specialized pacemaker cells have not been identified. The emergence of periodic oscillations in diffusively coupled assemblies of excitable and electrically passive cells (which are individually incapable of sustaining autonomous activity) has been suggested as a possible mechanism underlying such phenomena. In this paper we investigate the dynamics of such assemblies in more detail by considering simple motifs of coupled electrically active and passive cells. The resulting behavior encompasses a wide range of dynamical phenomena, including chaos. However, embedding such assemblies in a lattice yields spatiotemporal patterns that either correspond to a quiescent state or to partial or globally synchronized oscillations. The resulting reduction in dynamical complexity suggests an emergent simplicity in the collective dynamics of such large, spatially extended systems. Furthermore, we show that such patterns can be reproduced by a reduced model comprising only excitatory and oscillatory elements. Our results suggest a generalization of the mechanism by which periodic activity can emerge in a heterogeneous system comprising nonoscillatory elements by coupling them diffusively, provided their steady states in isolation are sufficiently dissimilar.

Neuromodulation and Individuality

Within populations, individuals show a variety of behavioral preferences, even in the absence of genetic or environmental variability. Neuromodulators affect these idiosyncratic preferences in a wide range of systems, however, the mechanism(s) by which they do so is unclear. I review the evidence supporting three broad mechanisms by which neuromodulators might affect variability in idiosyncratic behavioral preference: by being a source of variability directly upstream of behavior, by affecting the behavioral output of a circuit in a way that masks or accentuates underlying variability in that circuit, and by driving plasticity in circuits leading to either homeostatic convergence toward a given behavior or divergence from a developmental setpoint. I find evidence for each of these mechanisms and propose future directions to further understand the complex interplay between individual variability and neuromodulators.

A small, computationally flexible network produces the phenotypic diversity of song recognition in crickets

How neural networks evolved to generate the diversity of species-specific communication signals is unknown. For receivers of the signals, one hypothesis is that novel recognition phenotypes arise from parameter variation in computationally flexible feature detection networks. We test this hypothesis in crickets, where males generate and females recognize the mating songs with a species-specific pulse pattern, by investigating whether the song recognition network in the cricket brain has the computational flexibility to recognize different temporal features. Using electrophysiological recordings from the network that recognizes crucial properties of the pulse pattern on the short timescale in the cricket Gryllus bimaculatus, we built a computational model that reproduces the neuronal and behavioral tuning of that species. An analysis of the model's parameter space reveals that the network can provide all recognition phenotypes for pulse duration and pause known in crickets and even other insects. Phenotypic diversity in the model is consistent with known preference types in crickets and other insects, and arises from computations that likely evolved to increase energy efficiency and robustness of pattern recognition. The model's parameter to phenotype mapping is degenerate - different network parameters can create similar changes in the phenotype - which likely supports evolutionary plasticity. Our study suggests that computationally flexible networks underlie the diverse pattern recognition phenotypes, and we reveal network properties that constrain and support behavioral diversity.

Neuronal Switching between Single- and Dual-Network Activity via Modulation of Intrinsic Membrane Properties

Oscillatory networks underlie rhythmic behaviors (e.g., walking, chewing) and complex behaviors (e.g., memory formation, decision-making). Flexibility of oscillatory networks includes neurons switching between single- and dual-network participation, even generating oscillations at two distinct frequencies. Modulation of synaptic strength can underlie this neuronal switching. Here we ask whether switching into dual-frequency oscillations can also result from modulation of intrinsic neuronal properties. The isolated stomatogastric nervous system of male Cancer borealis crabs contains two well-characterized rhythmic feeding-related networks (pyloric, ∼1 Hz; gastric mill, ∼0.1 Hz). The identified modulatory projection neuron MCN5 causes the pyloric-only lateral posterior gastric (LPG) neuron to switch to dual pyloric/gastric mill bursting. Bath applying the MCN5 neuropeptide transmitter Gly¹-SIFamide only partly mimics the LPG switch to dual activity because of continued LP neuron inhibition of LPG. Here, we find that MCN5 uses a cotransmitter, glutamate, to inhibit LP, unlike Gly¹-SIFamide excitation of LP. Thus, we modeled the MCN5-elicited LPG switching with Gly¹-SIFamide application and LP photoinactivation. Using hyperpolarization of pyloric pacemaker neurons and gastric mill network neurons, we found that LPG pyloric-timed oscillations require rhythmic electrical synaptic input. However, LPG gastric mill-timed oscillations do not require any pyloric/gastric mill synaptic input and are voltage-dependent. Thus, we identify modulation of intrinsic properties as an additional mechanism for switching a neuron into dual-frequency activity. Instead of synaptic modulation switching a neuron into a second network as a passive follower, modulation of intrinsic properties could enable a switching neuron to become an active contributor to rhythm generation in the second network.SIGNIFICANCE STATEMENT Neuromodulation of oscillatory networks can enable network neurons to switch from single- to dual-network participation, even when two networks oscillate at distinct frequencies. We used small, well-characterized networks to determine whether modulation of synaptic strength, an identified mechanism for switching, is necessary for dual-network recruitment. We demonstrate that rhythmic electrical synaptic input is required for continued linkage with a "home" network, whereas modulation of intrinsic properties enables a neuron to generate oscillations at a second frequency. Neuromodulator-induced switches in neuronal participation between networks occur in motor, cognitive, and sensory networks. Our study highlights the importance of considering intrinsic properties as a pivotal target for enabling parallel participation of a neuron in two oscillatory networks.

Interrogating theoretical models of neural computation with emergent property inference

A cornerstone of theoretical neuroscience is the circuit model: a system of equations that captures a hypothesized neural mechanism. Such models are valuable when they give rise to an experimentally observed phenomenon -- whether behavioral or a pattern of neural activity -- and thus can offer insights into neural computation. The operation of these circuits, like all models, critically depends on the choice of model parameters. A key step is then to identify the model parameters consistent with observed phenomena: to solve the inverse problem. In this work, we present a novel technique, emergent property inference (EPI), that brings the modern probabilistic modeling toolkit to theoretical neuroscience. When theorizing circuit models, theoreticians predominantly focus on reproducing computational properties rather than a particular dataset. Our method uses deep neural networks to learn parameter distributions with these computational properties. This methodology is introduced through a motivational example of parameter inference in the stomatogastric ganglion. EPI is then shown to allow precise control over the behavior of inferred parameters and to scale in parameter dimension better than alternative techniques. In the remainder of this work, we present novel theoretical findings in models of primary visual cortex and superior colliculus, which were gained through the examination of complex parametric structure captured by EPI. Beyond its scientific contribution, this work illustrates the variety of analyses possible once deep learning is harnessed towards solving theoretical inverse problems.

The Drosophila Larval Locomotor Circuit Provides a Model to Understand Neural Circuit Development and Function

It is difficult to answer important questions in neuroscience, such as: "how do neural circuits generate behaviour?," because research is limited by the complexity and inaccessibility of the mammalian nervous system. Invertebrate model organisms offer simpler networks that are easier to manipulate. As a result, much of what we know about the development of neural circuits is derived from work in crustaceans, nematode worms and arguably most of all, the fruit fly, Drosophila melanogaster. This review aims to demonstrate the utility of the Drosophila larval locomotor network as a model circuit, to those who do not usually use the fly in their work. This utility is explored first by discussion of the relatively complete connectome associated with one identified interneuron of the locomotor circuit, A27h, and relating it to similar circuits in mammals. Next, it is developed by examining its application to study two important areas of neuroscience research: critical periods of development and interindividual variability in neural circuits. In summary, this article highlights the potential to use the larval locomotor network as a "generic" model circuit, to provide insight into mammalian circuit development and function.

Ion Channel Degeneracy, Variability, and Covariation in Neuron and Circuit Resilience

The large number of ion channels found in all nervous systems poses fundamental questions concerning how the characteristic intrinsic properties of single neurons are determined by the specific subsets of channels they express. All neurons display many different ion channels with overlapping voltage- and time-dependent properties. We speculate that these overlapping properties promote resilience in neuronal function. Individual neurons of the same cell type show variability in ion channel conductance densities even though they can generate reliable and similar behavior. This complicates a simple assignment of function to any conductance and is associated with variable responses of neurons of the same cell type to perturbations, deletions, and pharmacological manipulation. Ion channel genes often show strong positively correlated expression, which may result from the molecular and developmental rules that determine which ion channels are expressed in a given cell type.

The Continuity of Context: A Role for the Hippocampus

Tracking moment-to-moment change in input and detecting change sufficient to require altering behavior is crucial to survival. Here, we discuss how the brain evaluates change over time, focusing on the hippocampus and its role in tracking context. We leverage the anatomy and physiology of the hippocampal longitudinal axis, re-entrant loops, and amorphous networks to account for stimulus equivalence and the updating of an organism's sense of its context. Place cells have a central role in tracking contextual continuities and discontinuities across multiple scales, a capacity beyond current models of pattern separation and completion. This perspective highlights the critical role of the hippocampus in both spatial cognition and episodic memory: tracking change and detecting boundaries separating one context, or episode, from another.

Coupling between fast and slow oscillator circuits in Cancer borealis is temperature-compensated

Coupled oscillatory circuits are ubiquitous in nervous systems. Given that most biological processes are temperature-sensitive, it is remarkable that the neuronal circuits of poikilothermic animals can maintain coupling across a wide range of temperatures. Within the stomatogastric ganglion (STG) of the crab, Cancer borealis, the fast pyloric rhythm (~1 Hz) and the slow gastric mill rhythm (~0.1 Hz) are precisely coordinated at ~11°C such that there is an integer number of pyloric cycles per gastric mill cycle (integer coupling). Upon increasing temperature from 7°C to 23°C, both oscillators showed similar temperature-dependent increases in cycle frequency, and integer coupling between the circuits was conserved. Thus, although both rhythms show temperature-dependent changes in rhythm frequency, the processes that couple these circuits maintain their coordination over a wide range of temperatures. Such robustness to temperature changes could be part of a toolbox of processes that enables neural circuits to maintain function despite global perturbations.

Activity-dependent long-term potentiation of electrical synapses in the mammalian thalamus

Activity-dependent changes of synapse strength have been extensively characterized at chemical synapses, but the relationship between physiological forms of activity and strength at electrical synapses remains poorly characterized and understood. For mammalian electrical synapses comprising hexamers of connexin36, physiological forms of neuronal activity in coupled pairs have thus far only been linked to long-term depression; activity that results in strengthening of electrical synapses has not yet been identified. Here, we performed dual whole-cell current-clamp recordings in acute slices of P11-P15 Sprague-Dawley rats of electrically coupled neurons of the thalamic reticular nucleus (TRN), a central brain area that regulates cortical input from and attention to the sensory surround. Using TTA-A2 to limit bursting, we show that tonic spiking in one neuron of a pair results in long-term potentiation of electrical synapses. We use experiments and computational modeling to show that the magnitude of plasticity expressed alters the functionality of the synapse. Potentiation is expressed asymmetrically, indicating that regulation of connectivity depends on the direction of use. Furthermore, calcium pharmacology and imaging indicate that potentiation depends on calcium flux. We thus propose a calcium-based activity rule for bidirectional plasticity of electrical synapse strength. Because electrical synapses dominate intra-TRN connectivity, these synapses and their activity-dependent modifications are key dynamic regulators of thalamic attention circuitry. More broadly, we speculate that bidirectional modifications of electrical synapses may be a widespread and powerful principle for ongoing, dynamic reorganization of neuronal circuitry across the brain.NEW & NOTEWORTHY This work reveals a physiologically relevant form of activity pairing in coupled neurons that results in long-term potentiation of mammalian electrical synapses. These findings, in combination with previous work, allow the authors to propose a bidirectional calcium-based rule for plasticity of electrical synapses, similar to those demonstrated for chemical synapses. These new insights inform the field on how electrical synapse plasticity may modify the neural circuits that incorporate them.

A dynamic role for dopamine receptors in the control of mammalian spinal networks

Dopamine is well known to regulate movement through the differential control of direct and indirect pathways in the striatum that express D₁ and D₂ receptors respectively. The spinal cord also expresses all dopamine receptors; however, how the specific receptors regulate spinal network output in mammals is poorly understood. We explore the receptor-specific mechanisms that underlie dopaminergic control of spinal network output of neonatal mice during changes in spinal network excitability. During spontaneous activity, which is a characteristic of developing spinal networks operating in a low excitability state, we found that dopamine is primarily inhibitory. We uncover an excitatory D₁-mediated effect of dopamine on motoneurons and network output that also involves co-activation with D₂ receptors. Critically, these excitatory actions require higher concentrations of dopamine; however, analysis of dopamine concentrations of neonates indicates that endogenous levels of spinal dopamine are low. Because endogenous levels of spinal dopamine are low, this excitatory dopaminergic pathway is likely physiologically-silent at this stage in development. In contrast, the inhibitory effect of dopamine, at low physiological concentrations is mediated by parallel activation of D₂, D₃, D₄ and α₂ receptors which is reproduced when endogenous dopamine levels are increased by blocking dopamine reuptake and metabolism. We provide evidence in support of dedicated spinal network components that are controlled by excitatory D₁ and inhibitory D₂ receptors that is reminiscent of the classic dopaminergic indirect and direct pathway within the striatum. These results indicate that network state is an important factor that dictates receptor-specific and therefore dose-dependent control of neuromodulators on spinal network output and advances our understanding of how neuromodulators regulate neural networks under dynamically changing excitability.

Feed-forward recruitment of electrical synapses enhances synchronous spiking in the mouse cerebellar cortex

In the cerebellar cortex, molecular layer interneurons use chemical and electrical synapses to form subnetworks that fine-tune the spiking output of the cerebellum. Although electrical synapses can entrain activity within neuronal assemblies, their role in feed-forward circuits is less well explored. By combining whole-cell patch-clamp and 2-photon laser scanning microscopy of basket cells (BCs), we found that classical excitatory postsynaptic currents (EPSCs) are followed by GABA_A receptor-independent outward currents, reflecting the hyperpolarization component of spikelets (a synapse-evoked action potential passively propagating from electrically coupled neighbors). FF recruitment of the spikelet-mediated inhibition curtails the integration time window of concomitant excitatory postsynaptic potentials (EPSPs) and dampens their temporal integration. In contrast with GABAergic-mediated feed-forward inhibition, the depolarizing component of spikelets transiently increases the peak amplitude of EPSPs, and thus postsynaptic spiking probability. Therefore, spikelet transmission can propagate within the BC network to generate synchronous inhibition of Purkinje cells, which can entrain cerebellar output for driving temporally precise behaviors.

Training deep neural density estimators to identify mechanistic models of neural dynamics

Mechanistic modeling in neuroscience aims to explain observed phenomena in terms of underlying causes. However, determining which model parameters agree with complex and stochastic neural data presents a significant challenge. We address this challenge with a machine learning tool which uses deep neural density estimators-trained using model simulations-to carry out Bayesian inference and retrieve the full space of parameters compatible with raw data or selected data features. Our method is scalable in parameters and data features and can rapidly analyze new data after initial training. We demonstrate the power and flexibility of our approach on receptive fields, ion channels, and Hodgkin-Huxley models. We also characterize the space of circuit configurations giving rise to rhythmic activity in the crustacean stomatogastric ganglion, and use these results to derive hypotheses for underlying compensation mechanisms. Our approach will help close the gap between data-driven and theory-driven models of neural dynamics.

Homeostatic mechanisms may shape the type and duration of oscillatory modulation

Neural oscillations are observed ubiquitously in the mammalian brain, but their stability is known to be rather variable. Some oscillations are tonic and last for seconds or even minutes. Other oscillations appear as unstable bursts. Likewise, some oscillations rely on excitatory AMPAergic synapses, but others are GABAergic and inhibitory. Why this diversity exists is not clear. We hypothesized Ca²⁺-dependent homeostasis could be important in finding an explanation. We tested this hypothesis in a highly simplified model of hippocampal neurons. In this model homeostasis profoundly alters the modulatory effect of neural oscillations. Under homeostasis, tonic AMPAergic oscillations actually decrease excitability and desynchronize firing. Tonic oscillations that are synaptically GABAergic-like those in real hippocampus-don't provoke a homeostatic response, however. If our simple model is correct, homeostasis can explain why the theta rhythm in the hippocampus is synaptically inhibitory: GABA has little to no intrinsic homeostatic response and so can preserve the pyramidal cell's natural dynamic range. Based on these results we speculate that homeostasis may explain why AMPAergic oscillations in cortex, and in hippocampus, often appear as bursts. Bursts do not interact with the slow homeostatic time constant and so retain their normal excitatory effect.NEW & NOTEWORTHY The intricate interplay of neuromodulators, like acetylcholine, with homeostasis is well known. The interplay between oscillatory modulation and homeostasis is not. We studied oscillatory modulation and homeostasis for the first time using a simplified model of hippocampus. We report a paradoxical result: Ca-mediated homeostasis causes AMPAergic oscillations to become effectively inhibitory. This result, along with other new observations, means homeostasis might be just as complex and important for oscillations as it is for other neuromodulators.

Computational model of the distributed representation of operant reward memory: combinatoric engagement of intrinsic and synaptic plasticity mechanisms

Operant reward learning of feeding behavior in Aplysia increases the frequency and regularity of biting, as well as biases buccal motor patterns (BMPs) toward ingestion-like BMPs (iBMPs). The engram underlying this memory comprises cells that are part of a central pattern generating (CPG) circuit and includes increases in the intrinsic excitability of identified cells B30, B51, B63, and B65, and increases in B63-B30 and B63-B65 electrical synaptic coupling. To examine the ways in which sites of plasticity (individually and in combination) contribute to memory expression, a model of the CPG was developed. The model included conductance-based descriptions of cells CBI-2, B4, B8, B20, B30, B31, B34, B40, B51, B52, B63, B64, and B65, and their synaptic connections. The model generated patterned activity that resembled physiological BMPs, and implementation of the engram reproduced increases in frequency, regularity, and bias. Combined enhancement of B30, B63, and B65 excitabilities increased BMP frequency and regularity, but not bias toward iBMPs. Individually, B30 increased regularity and bias, B51 increased bias, B63 increased frequency, and B65 decreased all three BMP features. Combined synaptic plasticity contributed primarily to regularity, but also to frequency and bias. B63-B30 coupling contributed to regularity and bias, and B63-B65 coupling contributed to all BMP features. Each site of plasticity altered multiple BMP features simultaneously. Moreover, plasticity loci exhibited mutual dependence and synergism. These results indicate that the memory for operant reward learning emerged from the combinatoric engagement of multiple sites of plasticity.

An investigation into the nonlinear coupling between CA1 layers and the dentate gyrus

Although the activity from the dentate gyrus is known to have strong connections with other hippocampal layers, the functionality of these connections, that is, the degree to which it drives activity in the downstream regions of the hippocampus, is not well understood. This question is particularly relevant for mesoscale localfield potential (LFP) rhythms such as gamma oscillations. Following the hypothesis that fundamental features of the LFP are consistent with turbulent dynamics, we investigate the crosslayer relationship between the CA1 layers and the dentate gyrus as a function of running speed. In agreement with previous studies, same-layer spectral and bispectral analyses show that increasing input (rat speed) results in an increase of power and nonlinearity (phase coupling) between theta and gamma. The effectiveness of the connection between the 2 regions is investigated using cross-bicoherence analysis. Based on the turbulence interpretation of the evolution of spectra and bispectra as a function of the power input rate, we propose a measure for estimating the strength of the cross-frequency, cross-layer nonlinear forcing, that compares the magnitude of bicoherence (same-layer) and cross-bicoherence (cross-layer). Our results suggest that at moderate speeds gamma in CA1 is mainly driven by local theta, while the coupling of the CA1 gamma to the dentate-gyrus gamma becomes significant. Overall, these data are consistent with the hypothesis of theta-to-gamma energy cascade model for the organization of hippocampal LFP, with theta playing the role of a global pacemaker across the entire hippocampus while gamma is a local oscillation generated by through local anatomical connections. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

Molecular profiling of single neurons of known identity in two ganglia from the crab Cancer borealis

Single-cell transcriptional profiling has become a widespread tool in cell identification, particularly in the nervous system, based on the notion that genomic information determines cell identity. However, many cell-type classification studies are unconstrained by other cellular attributes (e.g., morphology, physiology). Here, we systematically test how accurately transcriptional profiling can assign cell identity to well-studied anatomically and functionally identified neurons in 2 small neuronal networks. While these neurons clearly possess distinct patterns of gene expression across cell types, their expression profiles are not sufficient to unambiguously confirm their identity. We suggest that true cell identity can only be determined by combining gene expression data with other cellular attributes such as innervation pattern, morphology, or physiology.

Understanding circuit organization depends on identification of cell types. Recent advances in transcriptional profiling methods have enabled classification of cell types by their gene expression. While exceptionally powerful and high throughput, the ground-truth validation of these methods is difficult: If cell type is unknown, how does one assess whether a given analysis accurately captures neuronal identity? To shed light on the capabilities and limitations of solely using transcriptional profiling for cell-type classification, we performed 2 forms of transcriptional profiling—RNA-seq and quantitative RT-PCR, in single, unambiguously identified neurons from 2 small crustacean neuronal networks: The stomatogastric and cardiac ganglia. We then combined our knowledge of cell type with unbiased clustering analyses and supervised machine learning to determine how accurately functionally defined neuron types can be classified by expression profile alone. The results demonstrate that expression profile is able to capture neuronal identity most accurately when combined with multimodal information that allows for post hoc grouping, so analysis can proceed from a supervised perspective. Solely unsupervised clustering can lead to misidentification and an inability to distinguish between 2 or more cell types. Therefore, this study supports the general utility of cell identification by transcriptional profiling, but adds a caution: It is difficult or impossible to know under what conditions transcriptional profiling alone is capable of assigning cell identity. Only by combining multiple modalities of information such as physiology, morphology, or innervation target can neuronal identity be unambiguously determined.

Cellular switches orchestrate rhythmic circuits

Small inhibitory neuronal circuits have long been identified as key neuronal motifs to generate and modulate the coexisting rhythms of various motor functions. Our paper highlights the role of a cellular switching mechanism to orchestrate such circuits. The cellular switch makes the circuits reconfigurable, robust, adaptable, and externally controllable. Without this cellular mechanism, the circuit rhythms entirely rely on specific tunings of the synaptic connectivity, which makes them rigid, fragile, and difficult to control externally. We illustrate those properties on the much studied architecture of a small network controlling both the pyloric and gastric rhythms of crabs. The cellular switch is provided by a slow negative conductance often neglected in mathematical modeling of central pattern generators. We propose that this conductance is simple to model and key to computational studies of rhythmic circuit neuromodulation.

Electrical synapses regulate both subthreshold integration and population activity of principal cells in response to transient inputs within canonical feedforward circuits

As information about the world traverses the brain, the signals exchanged between neurons are passed and modulated by synapses, or specialized contacts between neurons. While neurotransmitter-based synapses tend to exert either excitatory or inhibitory pulses of influence on the postsynaptic neuron, electrical synapses, composed of plaques of gap junction channels, continuously transmit signals that can either excite or inhibit a coupled neighbor. A growing body of evidence indicates that electrical synapses, similar to their chemical counterparts, are modified in strength during physiological neuronal activity. The synchronizing role of electrical synapses in neuronal oscillations has been well established, but their impact on transient signal processing in the brain is much less understood. Here we constructed computational models based on the canonical feedforward neuronal circuit and included electrical synapses between inhibitory interneurons. We provided discrete closely-timed inputs to the circuits, and characterize the influence of electrical synapse strength on both subthreshold summation and spike trains in the output neuron. Our simulations highlight the diverse and powerful roles that electrical synapses play even in simple circuits. Because these canonical circuits are represented widely throughout the brain, we expect that these are general principles for the influence of electrical synapses on transient signal processing across the brain.

The roles that electrical synapses play in neural oscillations, network synchronization and rhythmicity are well established, but their roles in neuronal processing of transient inputs are much less understood. Here, we used computational models of canonical feedforward circuits and networks to investigate how electrical synapses regulate the flow of transient signals passing through those circuits. We show that because the influence of electrical synapses on coupled neighbors can be either inhibitory or excitatory, their role in network information processing is heterogeneous, and powerful. Because electrical synapses between interneurons are widespread across the brain, and in addition to a growing body of evidence for their activity-dependent plasticity, we expect the effects we describe here to play a substantial role in how the brain processes incoming sensory inputs.

Theta-gamma cascades and running speed

Oscillations in the hippocampal local field potential at theta and gamma frequencies are prominent during awake behavior and have demonstrated several behavioral correlates. Both oscillations have been observed to increase in amplitude and frequency as a function of running speed. Previous investigations, however, have examined the relationship between speed and each of these oscillation bands separately. Based on energy cascade models where "…perturbations of slow frequencies cause a cascade of energy dissipation at all frequency scales" (Buzsaki G. Rhythms of the Brain, 2006), we hypothesized that cross-frequency interactions between theta and gamma should increase as a function of speed. We examined these relationships across multiple layers of the CA1 subregion, which correspond to synaptic zones receiving different afferents. Across layers, we found a reliable correlation between the power of theta and the power of gamma, indicative of an amplitude-amplitude relationship. Moreover, there was an increase in the coherence between the power of gamma and the phase of theta, demonstrating increased phase-amplitude coupling with speed. Finally, at higher velocities, phase entrainment between theta and gamma increases. These results have important implications and provide new insights regarding how theta and gamma are integrated for neuronal circuit dynamics, with coupling strength determined by the excitatory drive within the hippocampus. Specifically, rather than arguing that different frequencies can be attributed to different psychological processes, we contend that cognitive processes occur across multiple frequency bands simultaneously with organization occurring as a function of the amount of energy iteratively propagated through the brain. NEW & NOTEWORTHY Often, the theta and gamma oscillations in the hippocampus have been believed to be a consequence of two marginally overlapping phenomena. This perspective, however, runs counter to an alternative hypothesis in which a slow-frequency, high-amplitude oscillation provides energy that cascades into higher frequency, lower amplitude oscillations. We found that as running speed increases, all measures of cross-frequency theta-gamma coupling intensify, providing evidence in favor of the energy cascade hypothesis.

Visualization of currents in neural models with similar behavior and different conductance densities

Conductance-based models of neural activity produce large amounts of data that can be hard to visualize and interpret. We introduce visualization methods to display the dynamics of the ionic currents and to display the models’ response to perturbations. To visualize the currents’ dynamics, we compute the percent contribution of each current and display them over time using stacked-area plots. The waveform of the membrane potential and the contribution of each current change as the models are perturbed. To represent these changes over a range of the perturbation control parameter, we compute and display the distributions of these waveforms. We illustrate these procedures in six examples of bursting model neurons with similar activity but that differ as much as threefold in their conductance densities. These visualization methods provide heuristic insight into why individual neurons or networks with similar behavior can respond widely differently to perturbations.

The nervous system contains networks of neurons that generate electrical signals to communicate with each other and the rest of the body. Such electrical signals are due to the flow of ions into or out of the neurons via proteins known as ion channels. Neurons have many different kinds of ion channels that only allow specific ions to pass. Therefore, for a neuron to produce an electrical signal, the activities of several different ion channels need to be coordinated so that they all open and close at certain times.

Researchers have previously used data collected from various experiments to develop detailed models of electrical signals in neurons. These models incorporate information about how and when the ion channels may open and close, and can produce numerical simulations of the different ionic currents. However, it can be difficult to display the currents and observe how they change when several different ion channels are involved.

Alonso and Marder used simple mathematical concepts to develop new methods to display ionic currents in computational models of neurons. These tools use color to capture changes in ionic currents and provide insights into how the opening and closing of ion channels shape electrical signals.

The methods developed by Alonso and Marder could be adapted to display the behavior of biochemical reactions or other topics in biology and may, therefore, be useful to analyze data generated by computational models of many different types of cells. Additionally, these methods may potentially be used as educational tools to illustrate the coordinated opening and closing of ion channels in neurons and other fundamental principles of neuroscience that are otherwise hard to demonstrate.

Wave Turbulence and Energy Cascade in the Hippocampus

Mesoscale cortical activity can be defined as the organization of activity of large neuron populations into collective action, forming time-dependent patterns such as traveling waves. Although collective action may play an important role in the cross-scale integration of brain activity and in the emergence of cognitive behavior, a comprehensive formulation of the laws governing its dynamics is still lacking. Because collective action processes are macroscopic with respect to neuronal activity, these processes cannot be described directly with methods and models developed for the microscale (individual neurons).To identify the characteristic features of mesoscopic dynamics, and to lay the foundations for a theoretical description of mesoscopic activity in the hippocampus, we conduct a comprehensive examination of observational data of hippocampal local field potential (LFP) recordings. We use the strong correlation between rat running-speed and the LFP power to parameterize the energy input into the hippocampus, and show that both the power and non-linearity of collective action (e.g., theta and gamma rhythms) increase with increased speed. Our results show that collective-action dynamics are stochastic (the precise state of a single neuron is irrelevant), weakly non-linear, and weakly dissipative. These are the principles of the theory of weak turbulence. Therefore, we propose weak turbulence a theoretical framework for the description of mesoscopic activity in the hippocampus. The weak turbulence framework provides a complete description of the cross-scale energy exchange (the energy cascade). It uncovers the mechanism governing major features of LFP spectra and bispectra, such as the physical meaning of the exponent α of power-law LFP spectra (e.g., f ^-α, where f is the frequency), the strengthening of theta-gamma coupling with energy input into the hippocampus, as well as specific phase lags associated with their interaction. Remarkably, the weak turbulence framework is consistent with the theory of self organized criticality, which provides a simple explanation for the existence of the power-law background spectrum. Together with self-organized criticality, weak turbulence could provide a unifying approach to modeling the dynamics of mesoscopic activity.

Xolotl: An Intuitive and Approachable Neuron and Network Simulator for Research and Teaching

Conductance-based models of neurons are used extensively in computational neuroscience. Working with these models can be challenging due to their high dimensionality and large number of parameters. Here, we present a neuron and network simulator built on a novel automatic type system that binds object-oriented code written in C++ to objects in MATLAB. Our approach builds on the tradition of uniting the speed of languages like C++ with the ease-of-use and feature-set of scientific programming languages like MATLAB. Xolotl allows for the creation and manipulation of hierarchical models with components that are named and searchable, permitting intuitive high-level programmatic control over all parts of the model. The simulator's architecture allows for the interactive manipulation of any parameter in any model, and for visualizing the effects of changing that parameter immediately. Xolotl is fully featured with hundreds of ion channel models from the electrophysiological literature, and can be extended to include arbitrary conductances, synapses, and mechanisms. Several core features like bookmarking of parameters and automatic hashing of source code facilitate reproducible and auditable research. Its ease of use and rich visualization capabilities make it an attractive option in teaching environments. Finally, xolotl is written in a modular fashion, includes detailed tutorials and worked examples, and is freely available at https://github.com/sg-s/xolotl, enabling seamless integration into the workflows of other researchers.

A central control circuit for encoding perceived food value

Hunger state can substantially alter the perceived value of a stimulus, even to the extent that the same sensory cue can trigger antagonistic behaviors. How the nervous system uses these graded perceptual shifts to select between opposed motor patterns remains enigmatic. Here, we challenged food-deprived and satiated Lymnaea to choose between two mutually exclusive behaviors, ingestion or egestion, produced by the same feeding central pattern generator. Decoding the underlying neural circuit reveals that the activity of central dopaminergic interneurons defines hunger state and drives network reconfiguration, biasing satiated animals toward the rejection of stimuli deemed palatable by food-deprived ones. By blocking the action of these neurons, satiated animals can be reconfigured to exhibit a hungry animal phenotype. This centralized mechanism occurs in the complete absence of sensory retuning and generalizes across different sensory modalities, allowing food-deprived animals to increase their perception of food value in a stimulus-independent manner to maximize potential calorific intake.

Predicting how and when hidden neurons skew measured synaptic interactions

A major obstacle to understanding neural coding and computation is the fact that experimental recordings typically sample only a small fraction of the neurons in a circuit. Measured neural properties are skewed by interactions between recorded neurons and the “hidden” portion of the network. To properly interpret neural data and determine how biological structure gives rise to neural circuit function, we thus need a better understanding of the relationships between measured effective neural properties and the true underlying physiological properties. Here, we focus on how the effective spatiotemporal dynamics of the synaptic interactions between neurons are reshaped by coupling to unobserved neurons. We find that the effective interactions from a pre-synaptic neuron r′ to a post-synaptic neuron r can be decomposed into a sum of the true interaction from r′ to r plus corrections from every directed path from r′ to r through unobserved neurons. Importantly, the resulting formula reveals when the hidden units have—or do not have—major effects on reshaping the interactions among observed neurons. As a particular example of interest, we derive a formula for the impact of hidden units in random networks with “strong” coupling—connection weights that scale with 1/N, where N is the network size, precisely the scaling observed in recent experiments. With this quantitative relationship between measured and true interactions, we can study how network properties shape effective interactions, which properties are relevant for neural computations, and how to manipulate effective interactions.

No experiment in neuroscience can record from more than a tiny fraction of the total number of neurons present in a circuit. This severely complicates measurement of a network’s true properties, as unobserved neurons skew measurements away from what would be measured if all neurons were observed. For example, the measured post-synaptic response of a neuron to a spike from a particular pre-synaptic neuron incorporates direct connections between the two neurons as well as the effect of any number of indirect connections, including through unobserved neurons. To understand how measured quantities are distorted by unobserved neurons, we calculate a general relationship between measured “effective” synaptic interactions and the ground-truth interactions in the network. This allows us to identify conditions under which hidden neurons substantially alter measured interactions. Moreover, it provides a foundation for future work on manipulating effective interactions between neurons to better understand and potentially alter circuit function—or dysfunction.

Dopamine maintains network synchrony via direct modulation of gap junctions in the crustacean cardiac ganglion

The Large Cell (LC) motor neurons of the crab cardiac ganglion have variable membrane conductance magnitudes even within the same individual, yet produce identical synchronized activity in the intact network. In a previous study we blocked a subset of K+ conductances across LCs, resulting in loss of synchronous activity (Lane et al., 2016). In this study, we hypothesized that this same variability of conductances makes LCs vulnerable to desynchronization during neuromodulation. We exposed the LCs to serotonin (5HT) and dopamine (DA) while recording simultaneously from multiple LCs. Both amines had distinct excitatory effects on LC output, but only 5HT caused desynchronized output. We further determined that DA rapidly increased gap junctional conductance. Co-application of both amines induced 5HT-like output, but waveforms remained synchronized. Furthermore, DA prevented desynchronization induced by the K+ channel blocker tetraethylammonium (TEA), suggesting that dopaminergic modulation of electrical coupling plays a protective role in maintaining network synchrony.

Synchronous tonic-to-bursting transitions in a neuronal hub motif

We study a heterogeneous neuronal network motif where a central node (hub neuron) is connected via electrical synapses to other nodes (peripheral neurons). Our numerical simulations show that the networked neurons synchronize in three different states: (i) robust tonic, (ii) robust bursting, and (iii) tonic initially evolving to bursting through a period-doubling cascade and chaos transition. This third case displays interesting features, including the carrying on of a characteristic firing rate found in the single neuron tonic-to-bursting transition.

Circuit Robustness to Temperature Perturbation Is Altered by Neuromodulators

In the ocean, the crab Cancer borealis is subject to daily and seasonal temperature changes. Previous work, done in the presence of descending modulatory inputs, had shown that the pyloric rhythm of the crab increases in frequency as temperature increases but maintains its characteristic phase relationships until it "crashes" at extremely high temperatures. To study the interaction between neuromodulators and temperature perturbations, we studied the effects of temperature on preparations from which the descending modulatory inputs were removed. Under these conditions, the pyloric rhythm was destabilized. We then studied the effects of temperature on preparations in the presence of oxotremorine, proctolin, and serotonin. Oxotremorine and proctolin enhanced the robustness of the pyloric rhythm, whereas serotonin made the rhythm less robust. These experiments reveal considerable animal-to-animal diversity in their crash stability, consistent with the interpretation that cryptic differences in many cell and network parameters are revealed by extreme perturbations.

Coupled Oscillators Model of Hyperexcitable Neuroglial Networks

Glial populations within neuronal networks of the brain have recently gained much interest in the context of hyperexcitability and epilepsy. In this paper, we present an oscillator-based neuroglial model capable of generating Spontaneous Electrical Discharges (SEDs) in hyperexcitable conditions. The network is composed of 16 coupled Cognitive Rhythm Generators (CRGs), which are oscillator-based mathematical constructs previously described by our research team. CRGs are well-suited for modeling assemblies of excitable cells, and in this network, each represents one of the following populations: excitatory pyramidal cells, inhibitory interneurons, astrocytes, and microglia. We investigated various pathways leading to hyperexcitability, and our results suggest an important role for astrocytes and microglia in the generation of SEDs of various durations. Analysis of the resultant SEDs revealed two underlying duration distributions with differing properties. Particularly, short and long SEDs are associated with deterministic and random underlying processes, respectively. The mesoscale of this model makes it well-suited for (a) the elucidation of glia-related hypotheses in hyperexcitable conditions, (b) use as a testing platform for neuromodulation purposes, and (c) a hardware implementation for closed-loop neuromodulation.