Modelling the Effects of Electrical Coupling between Unmyelinated Axons of Brainstem Neurons Controlling Rhythmic Activity

Mechanisms Underlying the Recruitment of Inhibitory Interneurons in Fictive Swimming in Developing Xenopus laevis Tadpoles

Developing spinal circuits generate patterned motor outputs while many neurons with high membrane resistances are still maturing. In the spinal cord of hatchling frog tadpoles of unknown sex, we found that the firing reliability in swimming of inhibitory interneurons with commissural and ipsilateral ascending axons was negatively correlated with their cellular membrane resistance. Further analyses showed that neurons with higher resistances had outward rectifying properties, low firing thresholds, and little delay in firing evoked by current injections. Input synaptic currents these neurons received during swimming, either compound, unitary current amplitudes, or unitary synaptic current numbers, were scaled with their membrane resistances, but their own synaptic outputs were correlated with membrane resistances of their postsynaptic partners. Analyses of neuronal dendritic and axonal lengths and their activities in swimming and cellular input resistances did not reveal a clear correlation pattern. Incorporating these electrical and synaptic properties into a computer swimming model produced robust swimming rhythms, whereas randomizing input synaptic strengths led to the breakdown of swimming rhythms, coupled with less synchronized spiking in the inhibitory interneurons. We conclude that the recruitment of these developing interneurons in swimming can be predicted by cellular input resistances, but the order is opposite to the motor-strength-based recruitment scheme depicted by Henneman's size principle. This form of recruitment/integration order in development before the emergence of refined motor control is progressive potentially with neuronal acquisition of mature electrical and synaptic properties, among which the scaling of input synaptic strengths with cellular input resistance plays a critical role.SIGNIFICANCE STATEMENT The mechanisms on how interneurons are recruited to participate in circuit function in developing neuronal systems are rarely investigated. In 2-d-old frog tadpole spinal cord, we found the recruitment of inhibitory interneurons in swimming is inversely correlated with cellular input resistances, opposite to the motor-strength-based recruitment order depicted by Henneman's size principle. Further analyses showed the amplitude of synaptic inputs that neurons received during swimming was inversely correlated with cellular input resistances. Randomizing/reversing the relation between input synaptic strengths and membrane resistances in modeling broke down swimming rhythms. Therefore, the recruitment or integration of these interneurons is conditional on the acquisition of several electrical and synaptic properties including the scaling of input synaptic strengths with cellular input resistances.

Functional brain activity is highly associated with cortical myelination in neonates

Functional organization of the human cerebral cortex is highly constrained by underlying brain structures, but how functional activity is associated with different brain structures during development is not clear, especially at the neonatal stage. Since long-range functional connectivity is far from mature in the dynamically developing neonatal brain, it is of great scientific significance to investigate the relationship between different structural and functional features at the local level. To this end, for the first time, correlation and regression analyses were performed to examine the relationship between cortical morphology, cortical myelination, age, and local brain functional activity, as well as functional connectivity strength using high-resolution structural and resting-state functional MRI data of 177 neonates (29-44 postmenopausal weeks, 98 male and 79 female) from both static and dynamic perspectives. We found that cortical myelination was most strongly associated with local brain functional activity across the cerebral cortex than other cortical structural features while controlling the age effect. These findings suggest the crucial role of cortical myelination in local brain functional development at birth, providing valuable insights into the fundamental biological basis of functional activity at this early developmental stage.

From decision to action: Detailed modelling of frog tadpoles reveals neuronal mechanisms of decision-making and reproduces unpredictable swimming movements in response to sensory signals

How does the brain process sensory stimuli, and decide whether to initiate locomotor behaviour? To investigate this question we develop two whole body computer models of a tadpole. The "Central Nervous System" (CNS) model uses evidence from whole-cell recording to define 2300 neurons in 12 classes to study how sensory signals from the skin initiate and stop swimming. In response to skin stimulation, it generates realistic sensory pathway spiking and shows how hindbrain sensory memory populations on each side can compete to initiate reticulospinal neuron firing and start swimming. The 3-D "Virtual Tadpole" (VT) biomechanical model with realistic muscle innervation, body flexion, body-water interaction, and movement is then used to evaluate if motor nerve outputs from the CNS model can produce swimming-like movements in a volume of "water". We find that the whole tadpole VT model generates reliable and realistic swimming. Combining these two models opens new perspectives for experiments.

The decision to move: response times, neuronal circuits and sensory memory in a simple vertebrate

All animals use sensory systems to monitor external events and have to decide whether to move. Response times are long and variable compared to reflexes, and fast escape movements. The complexity of adult vertebrate brains makes it difficult to trace the neuronal circuits underlying basic decisions to move. To simplify the problem, we investigate the nervous system and responses of hatchling frog tadpoles which swim when their skin is stimulated. Studying the neuron-by-neuron pathway from sensory to hindbrain neurons, where the decision to swim is made, has revealed two simple pathways generating excitation which sums to threshold in these neurons to initiate swimming. The direct pathway leads to short, and reliable delays like an escape response. The other includes a population of sensory processing neurons which extend firing to introduce noise and delay into responses. These neurons provide a brief, sensory memory of the stimulus, that allows tadpoles to integrate stimuli occurring within a second or so of each other. We relate these findings to other studies and conclude that sensory memory makes a fundamental contribution to simple decisions and is present in the brainstem of a basic vertebrate at a surprisingly early stage in development.

Could electrical coupling contribute to the formation of cell assemblies?

Cell assemblies and central pattern generators (CPGs) are related types of neuronal networks: both consist of interacting groups of neurons whose collective activities lead to defined functional outputs. In the case of a cell assembly, the functional output may be interpreted as a representation of something in the world, external or internal; for a CPG, the output ‘drives’ an observable (i.e. motor) behavior. Electrical coupling, via gap junctions, is critical for the development of CPGs, as well as for their actual operation in the adult animal. Electrical coupling is also known to be important in the development of hippocampal and neocortical principal cell networks. We here argue that electrical coupling – in addition to chemical synapses – may therefore contribute to the formation of at least some cell assemblies in adult animals.

Axonal Computations

Axons functionally link the somato-dendritic compartment to synaptic terminals. Structurally and functionally diverse, they accomplish a central role in determining the delays and reliability with which neuronal ensembles communicate. By combining their active and passive biophysical properties, they ensure a plethora of physiological computations. In this review, we revisit the biophysics of generation and propagation of electrical signals in the axon and their dynamics. We further place the computational abilities of axons in the context of intracellular and intercellular coupling. We discuss how, by means of sophisticated biophysical mechanisms, axons expand the repertoire of axonal computation, and thereby, of neural computation.

Myelin and Modeling: Bootstrapping Cortical Microcircuits

Histological studies of myelin-stained sectioned cadaver brain and in vivo myelin-weighted magnetic resonance imaging (MRI) show that the cerebral cortex is organized into cortical areas with generally well-defined boundaries, which have consistent internal patterns of myelination. The process of myelination is largely driven by neural experience, in which the axonal passage of action potentials stimulates neighboring oligodendrocytes to perform their task. This bootstrapping process, such that the traffic of action potentials facilitates increased traffic, suggests the hypothesis that the specific pattern of myelination (myeloarchitecture) in each cortical area reveals the principal cortical microcircuits required for the function of that area. If this idea is correct, the observable sequential maturation of specific brain areas can provide evidence for models of the stages of cognitive development.

Spinal Shox2 interneuron interconnectivity related to function and development

Neuronal networks generating hindlimb locomotion are located in the spinal cord. The mechanisms underlying spinal rhythmogenesis are unknown but network activity and interconnectivity of excitatory interneurons likely play prominent roles. Here, we investigate interconnectivity within the Shox2 interneuron population, a subset of which has been suggested to be involved in locomotor rhythm generation, using paired recordings in isolated spinal cords or slices from transgenic mice. Sparse unidirectional connections consistent with chemical synaptic transmission and prominent bidirectional connections mediated by electrical synapses were present within distinct subsets of Shox2 interneurons. Moreover, bidirectional electrical connections were preferentially found between functionally-related Shox2 interneurons. Though prevalent in neonatal mice, electrical coupling began to decline in incidence and strength in mice ~ 3 weeks of age. Overall, our data suggest that gap junctional coupling promotes synchronization of Shox2 interneurons, and may be implicated in locomotor rhythmicity in developing mice.

Expression and significance of SDF-1 and its receptor CXCR4 in the retina of pregnant rats after optic nerve injury

Stromal cell–derived factor 1 (SDF-1) and its receptor CXCR4 have shown to play a role in embryonic development process, regulation of hematopoiesis, mediating immunology response, inflammatory reaction, and metastasis of malignant tumor. Recently, SDF-1 and CXCR4 are also closely related to retinal neovascularization. This study was to investigate the expression of SDF-1 and CXCR4 in the retina after optic nerve injury in pregnant rats so as to reveal its significance. A total of 12 pregnant rats were randomly divided into normal group and experimental group (after 5 days of optic nerve injury), six rats in each group; expressions of SDF-1 as well as CXCR4 in rat retina were detected by immunofluorescence staining and western blot assay. The result of immunofluorescence staining showed that the relative gray scale values of SDF-1 and CXCR4 in the experimental group were significantly higher than those in the normal group ( P < 0.05), and the result of Western blot assay showed that the expression levels of SDF-1 and CXCR4 in the experimental group were significantly higher than those in the normal group ( P < 0.05). In conclusion, SDF-1 and its receptor CXCR4 have abnormal expression in the retina of pregnant rats after optic nerve injury, which may be involved in the occurrence and development of optic nerve injury.

A simple decision to move in response to touch reveals basic sensory memory and mechanisms for variable response times

KEY POINTS

Short-term working memory and decision-making are usually studied in the cerebral cortex; in many models of simple decision making, sensory signals build slowly and noisily to threshold to initiate a motor response after long, variable delays. When touched, hatchling frog tadpoles decide whether to swim; we define the long and variable delays to swimming and use whole-cell recordings to uncover the neurons and processes responsible. Firing in sensory and sensory pathway neurons is short latency, and too brief and invariant to explain these delays, while recordings from hindbrain reticulospinal neurons controlling swimming reveal a prolonged and variable build-up of synaptic excitation which can reach firing threshold and initiate swimming. We propose this excitation provides a sensory memory of the stimulus and may be generated by small reverberatory hindbrain networks. Our results uncover fundamental network mechanisms that allow animals to remember brief sensory stimuli and delay simple motor decisions.

ABSTRACT

Many motor responses to sensory input, like locomotion or eye movements, are much slower than reflexes. Can simpler animals provide fundamental answers about the cellular mechanisms for motor decisions? Can we observe the 'accumulation' of excitation to threshold proposed to underlie decision making elsewhere? We explore how somatosensory touch stimulation leads to the decision to swim in hatchling Xenopus tadpoles. Delays measured to swimming in behaving and immobilised tadpoles are long and variable. Activity in their extensively studied sensory and sensory pathway neurons is too short-lived to explain these response delays. Instead, whole-cell recordings from the hindbrain reticulospinal neurons that drive swimming show that these receive prolonged, variable synaptic excitation lasting for nearly a second following a brief stimulus. They fire and initiate swimming when this excitation reaches threshold. Analysis of the summation of excitation requires us to propose extended firing in currently undefined presynaptic hindbrain neurons. Simple models show that a small excitatory recurrent-network inserted in the sensory pathway can mimic this process. We suggest that such a network may generate slow, variable summation of excitation to threshold. This excitation provides a simple memory of the sensory stimulus. It allows temporal and spatial integration of sensory inputs and explains the long, variable delays to swimming. The process resembles the 'accumulation' of excitation proposed for cortical circuits in mammals. We conclude that fundamental elements of sensory memory and decision making are present in the brainstem at a surprisingly early stage in development.

Bifurcations of Limit Cycles in a Reduced Model of the Xenopus Tadpole Central Pattern Generator

We present the study of a minimal microcircuit controlling locomotion in two-day-old Xenopus tadpoles. During swimming, neurons in the spinal central pattern generator (CPG) generate anti-phase oscillations between left and right half-centres. Experimental recordings show that the same CPG neurons can also generate transient bouts of long-lasting in-phase oscillations between left-right centres. These synchronous episodes are rarely recorded and have no identified behavioural purpose. However, metamorphosing tadpoles require both anti-phase and in-phase oscillations for swimming locomotion. Previous models have shown the ability to generate biologically realistic patterns of synchrony and swimming oscillations in tadpoles, but a mathematical description of how these oscillations appear is still missing. We define a simplified model that incorporates the key operating principles of tadpole locomotion. The model generates the various outputs seen in experimental recordings, including swimming and synchrony. To study the model, we perform detailed one- and two-parameter bifurcation analysis. This reveals the critical boundaries that separate different dynamical regimes and demonstrates the existence of parameter regions of bi-stable swimming and synchrony. We show that swimming is stable in a significantly larger range of parameters, and can be initiated more robustly, than synchrony. Our results can explain the appearance of long-lasting synchrony bouts seen in experiments at the start of a swimming episode.

Structural and functional properties of a probabilistic model of neuronal connectivity in a simple locomotor network

Although, in most animals, brain connectivity varies between individuals, behaviour is often similar across a species. What fundamental structural properties are shared across individual networks that define this behaviour? We describe a probabilistic model of connectivity in the hatchling Xenopus tadpole spinal cord which, when combined with a spiking model, reliably produces rhythmic activity corresponding to swimming. The probabilistic model allows calculation of structural characteristics that reflect common network properties, independent of individual network realisations. We use the structural characteristics to study examples of neuronal dynamics, in the complete network and various sub-networks, and this allows us to explain the basis for key experimental findings, and make predictions for experiments. We also study how structural and functional features differ between detailed anatomical connectomes and those generated by our new, simpler, model (meta-model).

Coordinated Expression of Two Types of Low-Threshold K+ Channels Establishes Unique Single Spiking of Mauthner Cells among Segmentally Homologous Neurons in the Zebrafish Hindbrain

Expression of different ion channels permits homologously-generated neurons to acquire different types of excitability and thus code various kinds of input information. Mauthner (M) series neurons in the teleost hindbrain consist of M cells and their morphological homologs, which are repeated in adjacent segments and share auditory inputs. When excited, M cells generate a single spike at the onset of abrupt stimuli, while their homologs encode input intensity with firing frequency. Our previous study in zebrafish showed that immature M cells burst phasically at 2 d postfertilization (dpf) and acquire single spiking at 4 dpf by specific expression of auxiliary Kvβ2 subunits in M cells in association with common expression of Kv1.1 channels in the M series. Here, we further reveal the ionic mechanisms underlying this functional differentiation. Pharmacological blocking of Kv7/KCNQ in addition to Kv1 altered mature M cells to fire tonically, similar to the homologs. In contrast, blocking either channel alone caused M cells to burst phasically. M cells at 2 dpf fired tonically after blocking Kv7. In situ hybridization revealed specific Kv7.4/KCNQ4 expression in M cells at 2 dpf. Kv7.4 and Kv1.1 channels expressed in Xenopus oocytes exhibited low-threshold outward currents with slow and fast rise times, while coexpression of Kvβ2 accelerated and increased Kv1.1 currents, respectively. Computational models, modified from a mouse cochlear neuron model, demonstrated that Kv7.4 channels suppress repetitive firing to produce spike-frequency adaptation, while Kvβ2-associated Kv1.1 channels increase firing threshold and decrease the onset latency of spiking. Altogether, coordinated expression of these low-threshold K⁺ channels with Kvβ2 functionally differentiates M cells among homologous neurons.

Modelling Feedback Excitation, Pacemaker Properties and Sensory Switching of Electrically Coupled Brainstem Neurons Controlling Rhythmic Activity

What cellular and network properties allow reliable neuronal rhythm generation or firing that can be started and stopped by brief synaptic inputs? We investigate rhythmic activity in an electrically-coupled population of brainstem neurons driving swimming locomotion in young frog tadpoles, and how activity is switched on and off by brief sensory stimulation. We build a computational model of 30 electrically-coupled conditional pacemaker neurons on one side of the tadpole hindbrain and spinal cord. Based on experimental estimates for neuron properties, population sizes, synapse strengths and connections, we show that: long-lasting, mutual, glutamatergic excitation between the neurons allows the network to sustain rhythmic pacemaker firing at swimming frequencies following brief synaptic excitation; activity persists but rhythm breaks down without electrical coupling; NMDA voltage-dependency doubles the range of synaptic feedback strengths generating sustained rhythm. The network can be switched on and off at short latency by brief synaptic excitation and inhibition. We demonstrate that a population of generic Hodgkin-Huxley type neurons coupled by glutamatergic excitatory feedback can generate sustained asynchronous firing switched on and off synaptically. We conclude that networks of neurons with NMDAR mediated feedback excitation can generate self-sustained activity following brief synaptic excitation. The frequency of activity is limited by the kinetics of the neuron membrane channels and can be stopped by brief inhibitory input. Network activity can be rhythmic at lower frequencies if the neurons are electrically coupled. Our key finding is that excitatory synaptic feedback within a population of neurons can produce switchable, stable, sustained firing without synaptic inhibition.

Sensory initiation of a co-ordinated motor response: synaptic excitation underlying simple decision-making

Key points

Deciding whether or how to initiate a motor response to a stimulus can be surprisingly slow and the underlying processes are not well understood.

The neuronal circuitry that allows frog tadpoles to swim in response to touch is well characterized and includes excitatory reticulospinal neurons that drive swim circuit neurons.

Build‐up of excitation to reticulospinal neurons is the key decision‐making step for swimming. Asymmetry in this build‐up between the two sides allows bilateral initiation at the same time as avoiding inappropriate co‐activation of motor antagonists.

Following stronger stimuli, reticulospinal neurons are excited through a trigeminal nucleus pathway and swimming starts first on the stimulated side. If this pathway fails or is lesioned, swimming starts later on the unstimulated side.

The mechanisms underlying initiation of a simple tadpole motor response may share similarities with more complex decisions in other animals, including humans.

Abstract

Animals take time to make co‐ordinated motor responses to a stimulus. How can sensory input initiate organized movements, activating all necessary elements at the same time as avoiding inappropriate co‐excitation of antagonistic muscles? In vertebrates, this process usually results in the activation of reticulospinal pathways. Young Xenopus tadpoles can respond to head‐skin touch by swimming, which may start on either side. We investigate how motor networks in the brain are organized, and whether asymmetries in touch sensory pathways avoid co‐activation of antagonists at the same time as producing co‐ordinated movements. We record from key reticulospinal neurons in the network controlling swimming. When the head skin is stimulated unilaterally, excitation builds up slowly and asymmetrically in these neurons such that those on both sides do not fire synchronously. This build‐up of excitation to threshold is the key decision‐making step and determines whether swimming will start, as well as on which side. In response to stronger stimuli, the stimulated side tends to ‘win’ because excitation from a shorter, trigeminal nucleus pathway becomes reliable and can initiate swimming earlier on the stimulated side. When this pathway fails or is lesioned, swimming starts later and on the unstimulated side. Stochasticity in the trigeminal nucleus pathway allows unpredictable turning behaviour to weaker stimuli, conferring potential survival benefits. We locate the longer, commissural sensory pathway carrying excitation to the unstimulated side and record from its neurons. These neurons fire to head‐skin stimuli but excite reticulospinal neurons indirectly. We propose that asymmetries in the sensory pathways exciting brainstem reticulospinal neurons ensure alternating and co‐ordinated swimming activity from the start.