Movement is governed by rotational neural dynamics in spinal motor networks

A Stochastic Dynamic Operator Framework That Improves the Precision of Analysis and Prediction Relative to the Classical Spike-Triggered Average Method, Extending the Toolkit

Here we test the stochastic dynamic operator (SDO) as a new framework for describing physiological signal dynamics relative to spiking or stimulus events. The SDO is a natural extension of existing spike-triggered average (STA) or stimulus-triggered average techniques currently used in neural analysis. It extends the classic STA to cover state-dependent and probabilistic responses where STA may fail. In simulated data, SDO methods were more sensitive and specific than the STA for identifying state-dependent relationships. We have tested SDO analysis for interactions between electrophysiological recordings of spinal interneurons, single motor units, and aggregate muscle electromyograms (EMG) of major muscles in the spinal frog hindlimb. When predicting target signal behavior relative to spiking events, the SDO framework outperformed or matched classical spike-triggered averaging methods. SDO analysis permits more complicated spike-signal relationships to be captured, analyzed, and interpreted visually and intuitively. SDO methods can be applied at different scales of interest where spike-triggered averaging methods are currently employed, and beyond, from single neurons to gross motor behaviors. SDOs may be readily generated and analyzed using the provided SDO Analysis Toolkit We anticipate this method will be broadly useful for describing dynamical signal behavior and uncovering state-dependent relationships of stochastic signals relative to discrete event times.

EFFECTS OF SPINAL TRANSECTION AND LOCOMOTOR SPEED ON MUSCLE SYNERGIES OF THE CAT HINDLIMB

It was suggested that during locomotion, the nervous system controls movement by activating groups of muscles, or muscle synergies. Analysis of muscle synergies can reveal the organization of spinal locomotor networks and how it depends on the state of the nervous system, such as before and after spinal cord injury, and on different locomotor conditions, including a change in speed. The goal of this study was to investigate the effects of spinal transection and locomotor speed on hindlimb muscle synergies and their time-dependent activity patterns in adult cats. EMG activities of 15 hindlimb muscles were recorded in 9 adult cats of either sex during tied-belt treadmill locomotion at speeds of 0.4, 0.7, and 1.0 m/s before and after recovery from a low thoracic spinal transection. We determined EMG burst groups using cluster analysis of EMG burst onset and offset times and muscle synergies using non-negative matrix factorization. We found five major EMG burst groups and five muscle synergies in each of six experimental conditions (2 states × 3 speeds). In each case, the synergies accounted for at least 90% of muscle EMG variance. Both spinal transection and locomotion speed modified subgroups of EMG burst groups and the composition and activation patterns of selected synergies. However, these changes did not modify the general organization of muscle synergies. Based on the obtained results, we propose an organization for a pattern formation network of a two-level central pattern generator that can be tested in neuromechanical simulations of spinal circuits controlling cat locomotion.

An output-null signature of inertial load in motor cortex

Coordinated movement requires the nervous system to continuously compensate for changes in mechanical load across different conditions. For voluntary movements like reaching, the motor cortex is a critical hub that generates commands to move the limbs and counteract loads. How does cortex contribute to load compensation when rhythmic movements are sequenced by a spinal pattern generator? Here, we address this question by manipulating the mass of the forelimb in unrestrained mice during locomotion. While load produces changes in motor output that are robust to inactivation of motor cortex, it also induces a profound shift in cortical dynamics. This shift is minimally affected by cerebellar perturbation and significantly larger than the load response in the spinal motoneuron population. This latent representation may enable motor cortex to generate appropriate commands when a voluntary movement must be integrated with an ongoing, spinally-generated rhythm.

A model-free method to learn multiple skills in parallel on modular robots

Legged robots are well-suited for deployment in unstructured environments but require a unique control scheme specific for their design. As controllers optimised in simulation do not transfer well to the real world (the infamous sim-to-real gap), methods enabling quick learning in the real world, without any assumptions on the specific robot model and its dynamics, are necessary. In this paper, we present a generic method based on Central Pattern Generators, that enables the acquisition of basic locomotion skills in parallel, through very few trials. The novelty of our approach, underpinned by a mathematical analysis of the controller model, is to search for good initial states, instead of optimising connection weights. Empirical validation in six different robot morphologies demonstrates that our method enables robots to learn primary locomotion skills in less than 15 minutes in the real world. In the end, we showcase our skills in a targeted locomotion experiment.

Electrophysiological Activity of Multifunctional and Behaviorally Specialized Spinal Neurons Involved in Swimming, Scratching, and Flexion Reflex in Turtles

The adult turtle spinal cord can generate multiple kinds of limb movements, including swimming, three forms of scratching, and limb withdrawal (flexion reflex), even without brain input and sensory feedback. There are many multifunctional spinal neurons, activated during multiple motor patterns, and some behaviorally specialized neurons, activated during only one. How do multifunctional and behaviorally specialized neurons each contribute to motor output? We analyzed in vivo intracellular recordings of multifunctional and specialized neurons. Neurons tended to spike in the same phase of the hip-flexor (HF) activity cycle during swimming and scratching, though one preferred opposite phases. During both swimming and scratching, a larger fraction of multifunctional neurons than specialized neurons were highly rhythmic. One group of multifunctional neurons was active during the HF-on phase and another during the HF-off phase. Thus, HF-extensor alternation may be generated by a subset of multifunctional spinal neurons during both swimming and scratching. Scratch-specialized neurons and flexion reflex-selective neurons may instead trigger their respective motor patterns, by biasing activity of multifunctional neurons. In phase-averaged membrane potentials of multifunctional neurons, trough phases were more highly correlated between swimming and scratching than peak phases, suggesting that rhythmic inhibition plays a greater role than rhythmic excitation. We also provide the first intracellular recording of a turtle swim-specialized neuron: tonically excited during swimming but inactive during scratching and flexion reflex. It displayed an excitatory postsynaptic potential following each swim-evoking electrical stimulus and thus may be an intermediary between reticulospinal axons and the swimming CPG they activate.

Spinal interneuron population dynamics underlying flexible pattern generation

The mammalian spinal locomotor network is composed of diverse populations of interneurons that collectively orchestrate and execute a range of locomotor behaviors. Despite the identification of many classes of spinal interneurons constituting the locomotor network, it remains unclear how the network's collective activity computes and modifies locomotor output on a step-by-step basis. To investigate this, we analyzed lumbar interneuron population recordings and multi-muscle electromyography from spinalized cats performing air stepping and used artificial intelligence methods to uncover state space trajectories of spinal interneuron population activity on single step cycles and at millisecond timescales. Our analyses of interneuron population trajectories revealed that traversal of specific state space regions held millisecond-timescale correspondence to the timing adjustments of extensor-flexor alternation. Similarly, we found that small variations in the path of state space trajectories were tightly linked to single-step, microvolt-scale adjustments in the magnitude of muscle output.

One sentence summary

Features of spinal interneuron state space trajectories capture variations in the timing and magnitude of muscle activations across individual step cycles, with precision on the scales of milliseconds and microvolts respectively.

A prefrontal motor circuit initiates persistent movement

Persistence reinforces continuous action, which benefits animals in many aspects. Diverse external or internal signals may trigger animals to start a persistent movement. However, it is unclear how the brain decides to persist with current actions by selecting specific information. Using single-unit extracellular recordings and opto-tagging in awake mice, we demonstrated that a group of dorsal mPFC (dmPFC) motor cortex projecting (MP) neurons initiate a persistent movement by selectively encoding contextual information rather than natural valence. Inactivation of dmPFC MP neurons impairs the initiation and reduces neuronal activity in the insular and motor cortex. After the persistent movement is initiated, the dmPFC MP neurons are not required to maintain it. Finally, a computational model suggests that a successive sensory stimulus acts as an input signal for the dmPFC MP neurons to initiate a persistent movement. These results reveal a neural initiation mechanism on the persistent movement.

Ultraflexible electrodes for recording neural activity in the mouse spinal cord during motor behavior

Implantable electrode arrays are powerful tools for directly interrogating neural circuitry in the brain, but implementing this technology in the spinal cord in behaving animals has been challenging due to the spinal cord's significant motion with respect to the vertebral column during behavior. Consequently, the individual and ensemble activity of spinal neurons processing motor commands remains poorly understood. Here, we demonstrate that custom ultraflexible 1-μm-thick polyimide nanoelectronic threads can conduct laminar recordings of many neuronal units within the lumbar spinal cord of unrestrained, freely moving mice. The extracellular action potentials have high signal-to-noise ratio, exhibit well-isolated feature clusters, and reveal diverse patterns of activity during locomotion. Furthermore, chronic recordings demonstrate the stable tracking of single units and their functional tuning over multiple days. This technology provides a path for elucidating how spinal circuits compute motor actions.

Motor cortex latent dynamics encode spatial and temporal arm movement parameters independently

The fluid movement of an arm requires multiple spatiotemporal parameters to be set independently. Recent studies have argued that arm movements are generated by the collective dynamics of neurons in motor cortex. An untested prediction of this hypothesis is that independent parameters of movement must map to independent components of the neural dynamics. Using a task where monkeys made a sequence of reaching movements to randomly placed targets, we show that the spatial and temporal parameters of arm movements are independently encoded in the low-dimensional trajectories of population activity in motor cortex: Each movement's direction corresponds to a fixed neural trajectory through neural state space and its speed to how quickly that trajectory is traversed. Recurrent neural network models show this coding allows independent control over the spatial and temporal parameters of movement by separate network parameters. Our results support a key prediction of the dynamical systems view of motor cortex, but also argue that not all parameters of movement are defined by different trajectories of population activity.

Unified control of temporal and spatial scales of sensorimotor behavior through neuromodulation of short-term synaptic plasticity

Neuromodulators have been shown to alter the temporal profile of short-term synaptic plasticity (STP); however, the computational function of this neuromodulation remains unexplored. Here, we propose that the neuromodulation of STP provides a general mechanism to scale neural dynamics and motor outputs in time and space. We trained recurrent neural networks that incorporated STP to produce complex motor trajectories-handwritten digits-with different temporal (speed) and spatial (size) scales. Neuromodulation of STP produced temporal and spatial scaling of the learned dynamics and enhanced temporal or spatial generalization compared to standard training of the synaptic weights in the absence of STP. The model also accounted for the results of two experimental studies involving flexible sensorimotor timing. Neuromodulation of STP provides a unified and biologically plausible mechanism to control the temporal and spatial scales of neural dynamics and sensorimotor behaviors.

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.

Topological structure of population activity in mouse visual cortex encodes densely sampled stimulus rotations

The primary visual cortex is one of the most well understood regions supporting the processing involved in sensory computation. Following the popularization of high-density neural recordings, it has been observed that the activity of large neural populations is often constrained to low dimensional manifolds. In this work, we quantify the structure of such neural manifolds in the visual cortex. We do this by analyzing publicly available two-photon optical recordings of mouse primary visual cortex in response to visual stimuli with a densely sampled rotation angle. Using a geodesic metric along with persistent homology, we discover that population activity in response to such stimuli generates a circular manifold, encoding the angle of rotation. Furthermore, we observe that this circular manifold is expressed differently in subpopulations of neurons with differing orientation and direction selectivity. Finally, we discuss some of the obstacles to reliably retrieving the truthful topology generated by a neural population.

A tonically active master neuron modulates mutually exclusive motor states at two timescales

Continuity of behaviors requires animals to make smooth transitions between mutually exclusive behavioral states. Neural principles that govern these transitions are not well understood. Caenorhabditis elegans spontaneously switch between two opposite motor states, forward and backward movement, a phenomenon thought to reflect the reciprocal inhibition between interneurons AVB and AVA. Here, we report that spontaneous locomotion and their corresponding motor circuits are not separately controlled. AVA and AVB are neither functionally equivalent nor strictly reciprocally inhibitory. AVA, but not AVB, maintains a depolarized membrane potential. While AVA phasically inhibits the forward promoting interneuron AVB at a fast timescale, it maintains a tonic, extrasynaptic excitation on AVB over the longer timescale. We propose that AVA, with tonic and phasic activity of opposite polarities on different timescales, acts as a master neuron to break the symmetry between the underlying forward and backward motor circuits. This master neuron model offers a parsimonious solution for sustained locomotion consisted of mutually exclusive motor states.

Preparatory activity and the expansive null-space

The study of the cortical control of movement experienced a conceptual shift over recent decades, as the basic currency of understanding shifted from single-neuron tuning towards population-level factors and their dynamics. This transition was informed by a maturing understanding of recurrent networks, where mechanism is often characterized in terms of population-level factors. By estimating factors from data, experimenters could test network-inspired hypotheses. Central to such hypotheses are 'output-null' factors that do not directly drive motor outputs yet are essential to the overall computation. In this Review, we highlight how the hypothesis of output-null factors was motivated by the venerable observation that motor-cortex neurons are active during movement preparation, well before movement begins. We discuss how output-null factors then became similarly central to understanding neural activity during movement. We discuss how this conceptual framework provided key analysis tools, making it possible for experimenters to address long-standing questions regarding motor control. We highlight an intriguing trend: as experimental and theoretical discoveries accumulate, the range of computational roles hypothesized to be subserved by output-null factors continues to expand.

A prefrontal motor circuit initiates persistent movement

Persistence reinforces continuous action, which benefits animals in many aspects. Diverse information may trigger animals to start a persistent movement. However, it is unclear how the brain decides to persist with current actions by selecting specific information. Using single-unit extracellular recordings and opto-tagging in awake mice, we demonstrated that a group of dorsal mPFC (dmPFC) motor cortex projecting (MP) neurons initiate a persistent movement selectively encoding contextual information rather than natural valence. Inactivation of dmPFC MP neurons impairs the initiation and reduces neuronal activity in the insular and motor cortex. Finally, a computational model suggests that a successive sensory stimulus acts as an input signal for the dmPFC MP neurons to initiate a persistent movement. These results reveal a neural initiation mechanism on the persistent movement.

Dynamics of brain-muscle networks reveal effects of age and somatosensory function on gait

Walking is a complex motor activity that requires coordinated interactions between the sensory and motor systems. We used mobile EEG and EMG to investigate the brain-muscle networks involved in gait control during overground walking in young people, older people, and individuals with Parkinson's disease. Dynamic interactions between the sensorimotor cortices and eight leg muscles within a gait cycle were assessed using multivariate analysis. We identified three distinct brain-muscle networks during a gait cycle. These networks include a bilateral network, a left-lateralized network activated during the left swing phase, and a right-lateralized network active during the right swing. The trajectories of these networks are contracted in older adults, indicating a reduction in neuromuscular connectivity with age. Individuals with the impaired tactile sensitivity of the foot showed a selective enhancement of the bilateral network, possibly reflecting a compensation strategy to maintain gait stability. These findings provide a parsimonious description of interindividual differences in neuromuscular connectivity during gait.

Neural population dynamics reveals disruption of spinal circuits' responses to proprioceptive input during electrical stimulation of sensory afferents

While neurostimulation technologies are rapidly approaching clinical applications for sensorimotor disorders, the impact of electrical stimulation on network dynamics is still unknown. Given the high degree of shared processing in neural structures, it is critical to understand if neurostimulation affects functions that are related to, but not targeted by, the intervention. Here, we approach this question by studying the effects of electrical stimulation of cutaneous afferents on unrelated processing of proprioceptive inputs. We recorded intraspinal neural activity in four monkeys while generating proprioceptive inputs from the radial nerve. We then applied continuous stimulation to the radial nerve cutaneous branch and quantified the impact of the stimulation on spinal processing of proprioceptive inputs via neural population dynamics. Proprioceptive pulses consistently produce neural trajectories that are disrupted by concurrent cutaneous stimulation. This disruption propagates to the somatosensory cortex, suggesting that electrical stimulation can perturb natural information processing across the neural axis.

Updating perspectives on spinal cord function: motor coordination, timing, relational processing, and memory below the brain

Those studying neural systems within the brain have historically assumed that lower-level processes in the spinal cord act in a mechanical manner, to relay afferent signals and execute motor commands. From this view, abstracting temporal and environmental relations is the province of the brain. Here we review work conducted over the last 50 years that challenges this perspective, demonstrating that mechanisms within the spinal cord can organize coordinated behavior (stepping), induce a lasting change in how pain (nociceptive) signals are processed, abstract stimulus-stimulus (Pavlovian) and response-outcome (instrumental) relations, and infer whether stimuli occur in a random or regular manner. The mechanisms that underlie these processes depend upon signal pathways (e.g., NMDA receptor mediated plasticity) analogous to those implicated in brain-dependent learning and memory. New data show that spinal cord injury (SCI) can enable plasticity within the spinal cord by reducing the inhibitory effect of GABA. It is suggested that the signals relayed to the brain may contain information about environmental relations and that spinal cord systems can coordinate action in response to descending signals from the brain. We further suggest that the study of stimulus processing, learning, memory, and cognitive-like processing in the spinal cord can inform our views of brain function, providing an attractive model system. Most importantly, the work has revealed new avenues of treatment for those that have suffered a SCI.

Neuronal travelling waves explain rotational dynamics in experimental datasets and modelling

Spatiotemporal properties of neuronal population activity in cortical motor areas have been subjects of experimental and theoretical investigations, generating numerous interpretations regarding mechanisms for preparing and executing limb movements. Two competing models, representational and dynamical, strive to explain the relationship between movement parameters and neuronal activity. A dynamical model uses the jPCA method that holistically characterizes oscillatory activity in neuron populations by maximizing the data rotational dynamics. Different rotational dynamics interpretations revealed by the jPCA approach have been proposed. Yet, the nature of such dynamics remains poorly understood. We comprehensively analyzed several neuronal-population datasets and found rotational dynamics consistently accounted for by a traveling wave pattern. For quantifying rotation strength, we developed a complex-valued measure, the gyration number. Additionally, we identified parameters influencing rotation extent in the data. Our findings suggest that rotational dynamics and traveling waves are typically the same phenomena, so reevaluation of the previous interpretations where they were considered separate entities is needed.

Latent neural population dynamics underlying breathing, opioid-induced respiratory depression and gasping

Breathing is vital and must be concurrently robust and flexible. This rhythmic behavior is generated and maintained within a rostrocaudally aligned set of medullary nuclei called the ventral respiratory column (VRC). The rhythmic properties of individual VRC nuclei are well known, yet technical challenges have limited the interrogation of the entire VRC population simultaneously. Here we characterize over 15,000 medullary units using high-density electrophysiology, opto-tagging and histological reconstruction. Population dynamics analysis reveals consistent rotational trajectories through a low-dimensional neural manifold. These rotations are robust and maintained even during opioid-induced respiratory depression. During severe hypoxia-induced gasping, the low-dimensional dynamics of the VRC reconfigure from rotational to all-or-none, ballistic efforts. Thus, latent dynamics provide a unifying lens onto the activities of large, heterogeneous populations of neurons involved in the simple, yet vital, behavior of breathing, and well describe how these populations respond to a variety of perturbations.

The processing of proprioceptive signals in distributed networks: insights from insect motor control

The integration of sensory information is required to maintain body posture and to generate robust yet flexible locomotion through unpredictable environments. To anticipate required adaptations in limb posture and enable compensation of sudden perturbations, an animal's nervous system assembles external (exteroception) and internal (proprioception) cues. Coherent neuronal representations of the proprioceptive context of the body and the appendages arise from the concerted action of multiple sense organs monitoring body kinetics and kinematics. This multimodal proprioceptive information, together with exteroceptive signals and brain-derived descending motor commands, converges onto premotor networks - i.e. the local neuronal circuitry controlling motor output and movements - within the ventral nerve cord (VNC), the insect equivalent of the vertebrate spinal cord. This Review summarizes existing knowledge and recent advances in understanding how local premotor networks in the VNC use convergent information to generate contextually appropriate activity, focusing on the example of posture control. We compare the role and advantages of distributed sensory processing over dedicated neuronal pathways, and the challenges of multimodal integration in distributed networks. We discuss how the gain of distributed networks may be tuned to enable the behavioral repertoire of these systems, and argue that insect premotor networks might compensate for their limited neuronal population size by, in comparison to vertebrate networks, relying more heavily on the specificity of their connections. At a time in which connectomics and physiological recording techniques enable anatomical and functional circuit dissection at an unprecedented resolution, insect motor systems offer unique opportunities to identify the mechanisms underlying multimodal integration for flexible motor control.

Emergence of task-related spatiotemporal population dynamics in transplanted neurons

Loss of nervous system tissue after severe brain injury is a main determinant of poor functional recovery. Cell transplantation is a promising method to restore lost tissue and function, yet it remains unclear if transplanted neurons can demonstrate the population level dynamics important for movement control. Here we present a comprehensive approach for long-term single neuron monitoring and manipulation of transplanted embryonic cortical neurons after cortical injury in adult male mice performing a prehension task. The observed patterns of population activity in the transplanted network strongly resembled that of healthy networks. Specifically, the task-related spatiotemporal activity patterns of transplanted neurons could be represented by latent factors that evolve within a low dimensional manifold. We also demonstrate reliable modulation of the transplanted networks using minimally invasive epidural stimulation. Our approach may allow greater insight into how restoration of cell-type specific network dynamics in vivo can restore motor function.

Reconstructing computational system dynamics from neural data with recurrent neural networks

Computational models in neuroscience usually take the form of systems of differential equations. The behaviour of such systems is the subject of dynamical systems theory. Dynamical systems theory provides a powerful mathematical toolbox for analysing neurobiological processes and has been a mainstay of computational neuroscience for decades. Recently, recurrent neural networks (RNNs) have become a popular machine learning tool for studying the non-linear dynamics of neural and behavioural processes by emulating an underlying system of differential equations. RNNs have been routinely trained on similar behavioural tasks to those used for animal subjects to generate hypotheses about the underlying computational mechanisms. By contrast, RNNs can also be trained on the measured physiological and behavioural data, thereby directly inheriting their temporal and geometrical properties. In this way they become a formal surrogate for the experimentally probed system that can be further analysed, perturbed and simulated. This powerful approach is called dynamical system reconstruction. In this Perspective, we focus on recent trends in artificial intelligence and machine learning in this exciting and rapidly expanding field, which may be less well known in neuroscience. We discuss formal prerequisites, different model architectures and training approaches for RNN-based dynamical system reconstructions, ways to evaluate and validate model performance, how to interpret trained models in a neuroscience context, and current challenges.

A Hyperflexible Electrode Array for Long-Term Recording and Decoding of Intraspinal Neuronal Activity

Neural interfaces for stable access to the spinal cord (SC) electrical activity can benefit patients with motor dysfunctions. Invasive high-density electrodes can directly extract signals from SC neuronal populations that can be used for the facilitation, adjustment, and reconstruction of motor actions. However, developing neural interfaces that can achieve high channel counts and long-term intraspinal recording remains technically challenging. Here, a biocompatible SC hyperflexible electrode array (SHEA) with an ultrathin structure that minimizes mechanical mismatch between the interface and SC tissue and enables stable single-unit recording for more than 2 months in mice is demonstrated. These results show that SHEA maintains stable impedance, signal-to-noise ratio, single-unit yield, and spike amplitude after implantation into mouse SC. Gait analysis and histology show that SHEA implantation induces negligible behavioral effects and Inflammation. Additionally, multi-unit signals recorded from the SC ventral horn can predict the mouse's movement trajectory with a high decoding coefficient of up to 0.95. Moreover, during step cycles, it is found that the neural trajectory of spikes and low-frequency local field potential (LFP) signal exhibits periodic geometry patterns. Thus, SHEA can offer an efficient and reliable SC neural interface for monitoring and potentially modulating SC neuronal activity associated with motor dysfunctions.

How far neuroscience is from understanding brains

The cellular biology of brains is relatively well-understood, but neuroscientists have not yet generated a theory explaining how brains work. Explanations of how neurons collectively operate to produce what brains can do are tentative and incomplete. Without prior assumptions about the brain mechanisms, I attempt here to identify major obstacles to progress in neuroscientific understanding of brains and central nervous systems. Most of the obstacles to our understanding are conceptual. Neuroscience lacks concepts and models rooted in experimental results explaining how neurons interact at all scales. The cerebral cortex is thought to control awake activities, which contrasts with recent experimental results. There is ambiguity distinguishing task-related brain activities from spontaneous activities and organized intrinsic activities. Brains are regarded as driven by external and internal stimuli in contrast to their considerable autonomy. Experimental results are explained by sensory inputs, behavior, and psychological concepts. Time and space are regarded as mutually independent variables for spiking, post-synaptic events, and other measured variables, in contrast to experimental results. Dynamical systems theory and models describing evolution of variables with time as the independent variable are insufficient to account for central nervous system activities. Spatial dynamics may be a practical solution. The general hypothesis that measurements of changes in fundamental brain variables, action potentials, transmitter releases, post-synaptic transmembrane currents, etc., propagating in central nervous systems reveal how they work, carries no additional assumptions. Combinations of current techniques could reveal many aspects of spatial dynamics of spiking, post-synaptic processing, and plasticity in insects and rodents to start with. But problems defining baseline and reference conditions hinder interpretations of the results. Furthermore, the facts that pooling and averaging of data destroy their underlying dynamics imply that single-trial designs and statistics are necessary.

The organization of spinal neurons: Insights from single cell sequencing

To understand how the spinal cord enacts complex sensorimotor functions, researchers have studied, classified, and functionally probed it's many neuronal populations for over a century. Recent developments in single-cell RNA-sequencing can characterize the gene expression signatures of the entire set of spinal neuron types and can simultaneously provide an unbiased view of their relationships to each other. This approach has revealed that the location of neurons predicts transcriptomic variability, as dorsal spinal neurons become highly distinct over development as ventral spinal neurons become less so. Temporal specification is also a major source of gene expression variation, subdividing many of the canonical embryonic lineage domains. Together, birthdate and cell body location are fundamental organizing features of spinal neuron diversity.

Periodic solutions in next generation neural field models

We consider a next generation neural field model which describes the dynamics of a network of theta neurons on a ring. For some parameters the network supports stable time-periodic solutions. Using the fact that the dynamics at each spatial location are described by a complex-valued Riccati equation we derive a self-consistency equation that such periodic solutions must satisfy. We determine the stability of these solutions, and present numerical results to illustrate the usefulness of this technique. The generality of this approach is demonstrated through its application to several other systems involving delays, two-population architecture and networks of Winfree oscillators.

Spinal Interneurons: Diversity and Connectivity in Motor Control

The spinal cord is home to the intrinsic networks for locomotion. An animal in which the spinal cord has been fully severed from the brain can still produce rhythmic, patterned locomotor movements as long as some excitatory drive is provided, such as physical, pharmacological, or electrical stimuli. Yet it remains a challenge to define the underlying circuitry that produces these movements because the spinal cord contains a wide variety of neuron classes whose patterns of interconnectivity are still poorly understood. Computational models of locomotion accordingly rely on untested assumptions about spinal neuron network element identity and connectivity. In this review, we consider the classes of spinal neurons, their interconnectivity, and the significance of their circuit connections along the long axis of the spinal cord. We suggest several lines of analysis to move toward a definitive understanding of the spinal network.

Spinal cords: Symphonies of interneurons across species

Vertebrate movement is orchestrated by spinal inter- and motor neurons that, together with sensory and cognitive input, produce dynamic motor behaviors. These behaviors vary from the simple undulatory swimming of fish and larval aquatic species to the highly coordinated running, reaching and grasping of mice, humans and other mammals. This variation raises the fundamental question of how spinal circuits have changed in register with motor behavior. In simple, undulatory fish, exemplified by the lamprey, two broad classes of interneurons shape motor neuron output: ipsilateral-projecting excitatory neurons, and commissural-projecting inhibitory neurons. An additional class of ipsilateral inhibitory neurons is required to generate escape swim behavior in larval zebrafish and tadpoles. In limbed vertebrates, a more complex spinal neuron composition is observed. In this review, we provide evidence that movement elaboration correlates with an increase and specialization of these three basic interneuron types into molecularly, anatomically, and functionally distinct subpopulations. We summarize recent work linking neuron types to movement-pattern generation across fish, amphibians, reptiles, birds and mammals.

Persistence is driven by a prefrontal motor circuit

Persistence provides a long-lasting effect on actions, including avoiding predators and storing energy, and hence is crucial for the survival (Adolphs and Anderson, 2018). However, how the brain loads persistence on movements is unknown. Here, we demonstrate that being persistent is determined at the initial phase of movement, and this persistency will be sustained until the terminal signaling. The neural coding of persistent movement phases (initial or terminal) is independent from the judgement (i.e. valence) (Li et al., 2022; Wang et al., 2018) upon the external stimuli. Next, we identify a group of dorsal medial prefrontal cortex (dmPFC) motor cortex projecting (MP) neurons (Wang and Sun, 2021), which encodes the initial phase of a persistent movement rather than the valence. Inactivation of dmPFC MP neurons impairs the initiation of persistency and reduce the neural activity in the insular and motor cortex. Finally, a MP network-based computational model suggests that an intact, successive sensory stimulus acts as a triggering signal to direct the initiation of persistent movements. These findings reveal a neural mechanism that transforms the brain state from neutral to persistent during a movement.

Comparing representations and computations in single neurons versus neural networks

Single-neuron-level explanations have been the gold standard in neuroscience for decades. Recently, however, neural-network-level explanations have become increasingly popular. This increase in popularity is driven by the fact that the analysis of neural networks can solve problems that cannot be addressed by analyzing neurons independently. In this opinion article, I argue that while both frameworks employ the same general logic to link physical and mental phenomena, in many cases the neural network framework provides better explanatory objects to understand representations and computations related to mental phenomena. I discuss what constitutes a mechanistic explanation in neural systems, provide examples, and conclude by highlighting a number of the challenges and considerations associated with the use of analyses of neural networks to study brain function.

A cellular taxonomy of the adult human spinal cord

The mammalian spinal cord functions as a community of cell types for sensory processing, autonomic control, and movement. While animal models have advanced our understanding of spinal cellular diversity, characterizing human biology directly is important to uncover specialized features of basic function and human pathology. Here, we present a cellular taxonomy of the adult human spinal cord using single-nucleus RNA sequencing with spatial transcriptomics and antibody validation. We identified 29 glial clusters and 35 neuronal clusters, organized principally by anatomical location. To demonstrate the relevance of this resource to human disease, we analyzed spinal motoneurons, which degenerate in amyotrophic lateral sclerosis (ALS) and other diseases. We found that compared with other spinal neurons, human motoneurons are defined by genes related to cell size, cytoskeletal structure, and ALS, suggesting a specialized molecular repertoire underlying their selective vulnerability. We include a web resource to facilitate further investigations into human spinal cord biology.

Precise Spiking Motifs in Neurobiological and Neuromorphic Data

Why do neurons communicate through spikes? By definition, spikes are all-or-none neural events which occur at continuous times. In other words, spikes are on one side binary, existing or not without further details, and on the other, can occur at any asynchronous time, without the need for a centralized clock. This stands in stark contrast to the analog representation of values and the discretized timing classically used in digital processing and at the base of modern-day neural networks. As neural systems almost systematically use this so-called event-based representation in the living world, a better understanding of this phenomenon remains a fundamental challenge in neurobiology in order to better interpret the profusion of recorded data. With the growing need for intelligent embedded systems, it also emerges as a new computing paradigm to enable the efficient operation of a new class of sensors and event-based computers, called neuromorphic, which could enable significant gains in computation time and energy consumption-a major societal issue in the era of the digital economy and global warming. In this review paper, we provide evidence from biology, theory and engineering that the precise timing of spikes plays a crucial role in our understanding of the efficiency of neural networks.