Cellular switches orchestrate rhythmic circuits

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.

Switching neuron contributions to second network activity

Network flexibility is important for adaptable behaviors. This includes neuronal switching, where neurons alter their network participation, including changing from single- to dual-network activity. Understanding the implications of neuronal switching requires determining how a switching neuron interacts with each of its networks. Here, we tested 1) whether "home" and second networks, operating via divergent rhythm generation mechanisms, regulate a switching neuron and 2) if a switching neuron, recruited via modulation of intrinsic properties, contributes to rhythm or pattern generation in a new network. Small, well-characterized feeding-related networks (pyloric, ∼1 Hz; gastric mill, ∼0.1 Hz) and identified modulatory inputs make the isolated crab (Cancer borealis) stomatogastric nervous system (STNS) a useful model to study neuronal switching. In particular, the neuropeptide Gly1-SIFamide switches the lateral posterior gastric (LPG) neuron (2 copies) from pyloric-only to dual-frequency pyloric/gastric mill (fast/slow) activity via modulation of LPG-intrinsic properties. Using current injections to manipulate neuronal activity, we found that gastric mill, but not pyloric, network neurons regulated the intrinsically generated LPG slow bursting. Conversely, selective elimination of LPG from both networks using photoinactivation revealed that LPG regulated gastric mill neuron-firing frequencies but was not necessary for gastric mill rhythm generation or coordination. However, LPG alone was sufficient to produce a distinct pattern of network coordination. Thus, modulated intrinsic properties underlying dual-network participation may constrain which networks can regulate switching neuron activity. Furthermore, recruitment via intrinsic properties may occur in modulatory states where it is important for the switching neuron to actively contribute to network output.NEW & NOTEWORTHY We used small, well-characterized networks to investigate interactions between rhythmic networks and neurons that switch their network participation. For a neuron switching into dual-network activity, only the second network regulated its activity in that network. In addition, the switching neuron was sufficient but not necessary to coordinate second network neurons and regulated their activity levels. Thus, regulation of switching neurons may be selective, and a switching neuron is not necessarily simply a follower in additional networks.

Node-Wise Monotone Barrier Coupling Law for Formation Control

We study a node-wise monotone barrier coupling law, motivated by the synaptic coupling of neural central pattern generators. It is illustrated that this coupling imitates the desirable properties of neural central pattern generators. In particular, the coupling law (1) allows us to assign multiple central patterns on the circle and (2) allows for rapid switching between different patterns via simple 'kicks'. In the end, we achieve full control by partitioning the state space by utilizing a barrier effect and assigning a unique steady-state behavior to each element of the resulting partition. We analyze the global behavior and study the viability of the design.

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.

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.

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.

Robust switches in thalamic network activity require a timescale separation between sodium and T-type calcium channel activations

Switches in brain states, synaptic plasticity and neuromodulation are fundamental processes in our brain that take place concomitantly across several spatial and timescales. All these processes target neuron intrinsic properties and connectivity to achieve specific physiological goals, raising the question of how they can operate without interfering with each other. Here, we highlight the central importance of a timescale separation in the activation of sodium and T-type calcium channels to sustain robust switches in brain states in thalamic neurons that are compatible with synaptic plasticity and neuromodulation. We quantify the role of this timescale separation by comparing the robustness of rhythms of six published conductance-based models at the cellular, circuit and network levels. We show that robust rhythm generation requires a T-type calcium channel activation whose kinetics are situated between sodium channel activation and T-type calcium channel inactivation in all models despite their quantitative differences.

Our brain is constantly processing information either from the environment to quickly react to incoming events or learning from experience to shape our memory. These brain states translate a collective activity of neurons interconnected via synaptic connections. Here, we focus on the thalamic network showing a transition from an active to an oscillatory mode at the population level, reverberating a switch from tonic to bursting mode at the cellular level. We are questioning how these activity fluctuations can be robustly modeled despite synaptic plasticity affecting the network configuration and the presence of neuromodulators affecting neuron intrinsic properties. To do so, we investigate six conductance-based models and their ability to reproduce activity switches at the cellular, circuit and population levels. We highlight that the robustness requires the timescale separation between the fast activation of sodium channels compared to the slow activation of T-type calcium channels. Our results show that this kinetics difference is not a computational detail but rather makes a model suitable and robust to study the interaction between switches in brain states, synaptic plasticity and neuromodulation.

Simulating Small Neural Circuits with a Discrete Computational Model

Simulations of neural activity are commonly based on differential equations. We address the question what can be achieved with a simplified discrete model. The proposed model resembles artificial neural networks enriched with additional biologically inspired features. A neuron has several states, and the state transitions follow endogenous patterns which roughly correspond to firing behavior observed in biological neurons: oscillatory, tonic, plateauing, etc. Neural interactions consist of two components: synaptic connections and extrasynaptic emission of neurotransmitters. The dynamics is asynchronous and event-based; the events correspond to the changes in neurons activity. This model is innovative in introducing discrete framework for modeling neurotransmitter interactions which play the important role in neuromodulation. We simulate rhythmic activity of small neural ensembles like central pattern generators (CPG). The modeled examples include: the biphasic rhythm generated by the half-center mechanism with the post-inhibitory rebound (like the leech heartbeat CPG), the triphasic rhythm (like in pond snail feeding CPG) and the pattern switch in the system of several neurons (like the switch between ingestion and egestion in Aplysia feeding CPG). The asynchronous dynamics allows to obtain multi-phasic rhythms with phase durations close to their biological prototypes. The perspectives of discrete modeling in biological research are discussed in the conclusion.

Control theory in biology and medicine : Introduction to the special issue

From September-December 2017, the Mathematical Biosciences Institute at Ohio State University hosted a series of workshops on control theory in biology and medicine, including workshops on control and modulation of neuronal and motor systems, control of cellular and molecular systems, control of disease / personalized medicine across heterogeneous populations, and sensorimotor control of animals and robots. This special issue presents tutorials and research articles by several of the participants in the MBI workshops.