Decoupling of timescales reveals sparse convergent CPG network in the adult spinal cord

Sparse Firing in a Hybrid Central Pattern Generator for Spinal Motor Circuits

Central pattern generators are circuits generating rhythmic movements, such as walking. The majority of existing computational models of these circuits produce antagonistic output where all neurons within a population spike with a broad burst at about the same neuronal phase with respect to network output. However, experimental recordings reveal that many neurons within these circuits fire sparsely, sometimes as rarely as once within a cycle. Here we address the sparse neuronal firing and develop a model to replicate the behavior of individual neurons within rhythm-generating populations to increase biological plausibility and facilitate new insights into the underlying mechanisms of rhythm generation. The developed network architecture is able to produce sparse firing of individual neurons, creating a novel implementation for exploring the contribution of network architecture on rhythmic output. Furthermore, the introduction of sparse firing of individual neurons within the rhythm-generating circuits is one of the factors that allows for a broad neuronal phase representation of firing at the population level. This moves the model toward recent experimental findings of evenly distributed neuronal firing across phases among individual spinal neurons. The network is tested by methodically iterating select parameters to gain an understanding of how connectivity and the interplay of excitation and inhibition influence the output. This knowledge can be applied in future studies to implement a biologically plausible rhythm-generating circuit for testing biological hypotheses.

Movement is governed by rotational neural dynamics in spinal motor networks

Although the generation of movements is a fundamental function of the nervous system, the underlying neural principles remain unclear. As flexor and extensor muscle activities alternate during rhythmic movements such as walking, it is often assumed that the responsible neural circuitry is similarly exhibiting alternating activity¹. Here we present ensemble recordings of neurons in the lumbar spinal cord that indicate that, rather than alternating, the population is performing a low-dimensional 'rotation' in neural space, in which the neural activity is cycling through all phases continuously during the rhythmic behaviour. The radius of rotation correlates with the intended muscle force, and a perturbation of the low-dimensional trajectory can modify the motor behaviour. As existing models of spinal motor control do not offer an adequate explanation of rotation^1,2, we propose a theory of neural generation of movements from which this and other unresolved issues, such as speed regulation, force control and multifunctionalism, are readily explained.

Emergence of In Vitro Preparations and Their Contribution to Understanding the Neural Control of Behavior in Vertebrates

One of the longstanding goals of the field of neuroscience is to understand the neural control of behavior in both invertebrate and vertebrate species. A series of early discoveries showed that certain motor patterns like locomotion could be generated by neuronal circuits without sensory feedback or descending control systems. These were called fictitious, or "fictive", motor programs because they could be expressed by neurons in the absence of movement. This finding lead investigators to isolate central nervous system tissue and maintain it in a dish in vitro to better study mechanisms of motor pattern generation. A period of rapid development of in vitro preparations from invertebrate species that could generate fictive motor programs from the activity of central pattern generating circuits (CPGs) emerged that was gradually followed by the introduction of such preparations from vertebrates. Here, I will review some of the notable in vitropreparations from both mammalian and non-mammalian vertebrate species developed to study the neural circuits underlying a variety of complex behaviors. This approach has been instrumental in delineating not only the cellular substrates underlying locomotion, respiration, scratching, and other behaviors, but also mechanisms underlying the modifiability of motor pathways through synaptic plasticity. In vitro preparations have had a significant impact on the field of motor systems neuroscience and the expansion of our understanding of how nervous systems control behavior. The field is ready for further advancement of this approach to explore neural substrates for variations in behavior generated by social and seasonal context, and the environment.

Transition from predictable to variable motor cortex and striatal ensemble patterning during behavioral exploration

Animals can capitalize on invariance in the environment by learning and automating highly consistent actions; however, they must also remain flexible and adapt to environmental changes. It remains unclear how primary motor cortex (M1) can drive precise movements, yet also support behavioral exploration when faced with consistent errors. Using a reach-to-grasp task in rats, along with simultaneous electrophysiological monitoring in M1 and dorsolateral striatum (DLS), we find that behavioral exploration to overcome consistent task errors is closely associated with tandem increases in M1 and DLS neural variability; subsequently, consistent ensemble patterning returns with convergence to a new successful strategy. We also show that compared to reliably patterned intracranial microstimulation in M1, variable stimulation patterns result in significantly greater movement variability. Our results thus indicate that motor and striatal areas can flexibly transition between two modes, reliable neural pattern generation for automatic and precise movements versus variable neural patterning for behavioral exploration.

It is not fully understood how behavioral flexibility is established in the context of automatic performance of a complex motor skill. Here the authors show that corticostriatal activity can flexibly transition between two modes during a reach to-grasp task in rats: reliable neural pattern generation for precise, automatic movements versus variable neural patterning for behavioral exploration.

Toward Assessing the Functional Connectivity of Spinal Neurons

Spinal interneurons play a critical role in motor output. A given interneuron may receive convergent input from several different sensory modalities and descending centers and relay this information to just as many targets. Therefore, there is a critical need to quantify populations of spinal interneurons simultaneously. Here, we quantify the functional connectivity of spinal neurons through the concurrent recording of populations of lumbar interneurons and hindlimb motor units in the in vivo cat model during activation of either the ipsilateral sural nerve or contralateral tibial nerve. Two microelectrode arrays were placed into lamina VII, one at L3 and a second at L6/7, while an electrode array was placed on the surface of the exposed muscle. Stimulation of tibial and sural nerves elicited similar changes in the discharge rate of both interneurons and motor units. However, these same neurons showed highly significant differences in prevalence and magnitude of correlated activity underlying these two forms of afferent drive. Activation of the ipsilateral sural nerve resulted in highly correlated activity, particularly at the caudal array. In contrast, the contralateral tibial nerve resulted in less, but more widespread correlated activity at both arrays. These data suggest that the ipsilateral sural nerve has dense projections onto caudal lumbar spinal neurons, while contralateral tibial nerve has a sparse pattern of projections.

Neuronal Network Inference and Membrane Potential Model using Multivariate Hawkes Processes

BACKGROUND

In this work, we propose to catch the complexity of the membrane potential's dynamic of a motoneuron between its spikes, taking into account the spikes from other neurons around. Our approach relies on two types of data: extracellular recordings of multiple spikes trains and intracellular recordings of the membrane potential of a central neuron.

NEW METHOD

We provide a unified framework and a complete pipeline to analyze neuronal activity from data extraction to statistical inference. To the best of our knowledge, this is the first time that a Hawkes-diffusion model is investigated on such complex data. The first step of the proposed procedure is to select a subnetwork of neurons impacting the central neuron using a multivariate Hawkes process. Then we infer a jump-diffusion dynamic in which jumps are driven from a Hawkes process, the occurrences of which correspond to the spike trains of the aforementioned subset of neurons that interact with the central neuron.

RESULTS

From the Hawkes estimation step we recover a small connectivity graph which contains the central neuron, and we show that taking into account this information improves the inference of membrane potential through the proposed jump-diffusion model. A goodness of fit test is applied to validate the relevance of the Hawkes model in such context.

COMPARISON WITH EXISTING METHODS

We compare an empirical inference method and two sparse estimation procedures based on the Hawkes assumption for the reconstruction of the connectivity graph using the spike-trains. Then, the Hawkes-diffusion model is competed with the simple diffusion in terms of best fit to describe the behavior of the membrane potential of a central neuron surrounded by a network.

CONCLUSIONS

The present method takes advantage of both spike trains and membrane potential to understand the behavior of a fixed neuron. The entire code has been developed and is freely available on GitHub.

Why Firing Rate Distributions Are Important for Understanding Spinal Central Pattern Generators

Networks in the spinal cord, which are responsible for the generation of rhythmic movements, commonly known as central pattern generators (CPGs), have remained elusive for decades. Although it is well-known that many spinal neurons are rhythmically active, little attention has been given to the distribution of firing rates across the population. Here, we argue that firing rate distributions can provide an important clue to the organization of the CPGs. The data that can be gleaned from the sparse literature indicate a firing rate distribution, which is skewed toward zero with a long tail, akin to a normal distribution on a log-scale, i.e., a “log-normal” distribution. Importantly, such a shape is difficult to unite with the widespread assumption of modules composed of recurrently connected excitatory neurons. Spinal modules with recurrent excitation has the propensity to quickly escalate their firing rate and reach the maximum, hence equalizing the spiking activity across the population. The population distribution of firing rates hence would consist of a narrow peak near the maximum. This is incompatible with experiments, that show wide distributions and a peak close to zero. A way to resolve this puzzle is to include recurrent inhibition internally in each CPG modules. Hence, we investigate the impact of recurrent inhibition in a model and find that the firing rate distributions are closer to the experimentally observed. We therefore propose that recurrent inhibition is a crucial element in motor circuits, and suggest that future models of motor circuits should include recurrent inhibition as a mandatory element.

Modeling Post-Scratching Locomotion with Two Rhythm Generators and a Shared Pattern Formation

This study aimed to present a model of post-scratching locomotion with two intermixed central pattern generator (CPG) networks, one for scratching and another for locomotion. We hypothesized that the rhythm generator layers for each CPG are different, with the condition that both CPGs share their supraspinal circuits and their motor outputs at the level of their pattern formation networks. We show that the model reproduces the post-scratching locomotion latency of 6.2 ± 3.5 s, and the mean cycle durations for scratching and post-scratching locomotion of 0.3 ± 0.09 s and 1.7 ± 0.6 s, respectively, which were observed in a previous experimental study. Our findings show how the transition of two rhythmic movements could be mediated by information exchanged between their CPG circuits through routes converging in a common pattern formation layer. This integrated organization may provide flexible and effective connectivity despite the rigidity of the anatomical connections in the spinal cord circuitry.

Neural Interactions in Developing Rhythmogenic Spinal Networks: Insights From Computational Modeling

The mechanisms involved in generation of rhythmic locomotor activity in the mammalian spinal cord remain poorly understood. These mechanisms supposedly rely on both intrinsic properties of constituting neurons and interactions between them. A subset of Shox2 neurons was suggested to contribute to generation of spinal locomotor activity, but the possible cellular basis for rhythmic bursting in these neurons remains unknown. Ha and Dougherty (2018) recently revealed the presence of bidirectional electrical coupling between Shox2 neurons in neonatal spinal cords, which can be critically involved in neuronal synchronization and generation of populational bursting. Gap junctional connections found between functionally-related Shox2 interneurons decrease with age, possibly being replaced by increasing interactions through chemical synapses. Here, we developed a computational model of a heterogeneous population of neurons sparsely connected by electrical or/and chemical synapses and investigated the dependence of frequency of populational bursting on the type and strength of neuronal interconnections. The model proposes a mechanistic explanation that can account for the emergence of a synchronized rhythmic activity in the neuronal population and provides insights into the possible role of gap junctional coupling between Shox2 neurons in the spinal mechanisms for locomotor rhythm generation.

Motoneurone synchronization for intercostal and abdominal muscles: interneurone influences in two different species

The contribution of branched-axon monosynaptic inputs in the generation of short-term synchronization of motoneurones remains uncertain. Here, synchronization was measured for intercostal and abdominal motoneurones supplying the lower thorax and upper abdomen, mostly showing expiratory discharges. Synchronization in the anaesthetized cat, where the motoneurones receive a strong direct descending drive, is compared with that in anaesthetized or decerebrate rats, where the direct descending drive is much weaker. In the cat, some examples could be explained by branched-axon monosynaptic inputs, but many others could not, by virtue of peaks in cross-correlation histograms whose widths (relatively wide) and timing indicated common inputs with more complex linkages, e.g., disynaptic excitatory. In contrast, in the rat, correlations for pairs of internal intercostal nerves were dominated by very narrow peaks, indicative of branched-axon monosynaptic inputs. However, the presence of activity in both inspiration and expiration in many of the nerves allowed additional synchronization measurements between internal and external intercostal nerves. Time courses of synchronization for these often consisted of combinations of peaks and troughs, which have never been previously described for motoneurone synchronization and which we interpret as indicating combinations of inputs, excitation of one group of motoneurones being common with either excitation or inhibition of the other. Significant species differences in the circuits controlling the motoneurones are indicated, but in both cases, the roles of spinal interneurones are emphasised. The results demonstrate the potential of motoneurone synchronization for investigating inhibition and have important general implications for the interpretation of neural connectivity measurements by cross-correlation.

Neurotransmitters and Motoneuron Contacts of Multifunctional and Behaviorally Specialized Turtle Spinal Cord Interneurons

The spinal cord can appropriately generate diverse movements, even without brain input and movement-related sensory feedback, using a combination of multifunctional and behaviorally specialized interneurons. The adult turtle spinal cord can generate motor patterns underlying forward swimming, three forms of scratching, and limb withdrawal (flexion reflex). We previously described turtle spinal interneurons activated during both scratching and swimming (multifunctional interneurons), interneurons activated during scratching but not swimming (scratch-specialized interneurons), and interneurons activated during flexion reflex but not scratching or swimming (flexion reflex-selective interneurons). How multifunctional and behaviorally specialized turtle spinal interneurons affect downstream neurons was unknown. Here, we recorded intracellularly from spinal interneurons activated during these motor patterns in turtles of both sexes in vivo and filled each with dyes. We labeled motoneurons using choline acetyltransferase antibodies or earlier intraperitoneal FluoroGold injection and used immunocytochemistry of interneuron axon terminals to identify their neurotransmitter(s) and putative synaptic contacts with motoneurons. We found that multifunctional interneurons are heterogeneous with respect to neurotransmitter, with some glutamatergic and others GABAergic or glycinergic, and can directly contact motoneurons. Also, scratch-specialized interneurons are heterogeneous with respect to neurotransmitter and some directly contact motoneurons. Thus, scratch-specialized interneurons might directly excite motoneurons that are more strongly activated during scratching than forward swimming, such as hip-flexor motoneurons. Finally, and surprisingly, we found that some motoneurons are behaviorally specialized, for scratching or flexion reflex. Thus, either some limb muscles are only used for a subset of limb behaviors or some limb motoneurons are only recruited during certain limb behaviors.SIGNIFICANCE STATEMENT Both multifunctional and behaviorally specialized spinal cord interneurons have been described in turtles, but their outputs are unknown. We studied responses of multifunctional interneurons (activated during swimming and scratching) and scratch-specialized interneurons, filled each with dyes, and used immunocytochemistry to determine their neurotransmitters and contacts with motoneurons. We found that both multifunctional and scratch-specialized interneurons are heterogeneous with respect to neurotransmitter, with some excitatory and others inhibitory. We found that some multifunctional and some scratch-specialized interneurons directly contact motoneurons. Scratch-specialized interneurons may excite motoneurons that are more strongly activated during scratching than swimming, such as hip-flexor motoneurons, or inhibit their antagonists, hip-extensor motoneurons. Surprisingly, we also found that some motoneurons are behaviorally specialized, for scratching or for flexion reflex.