Analysis of neuronal ensemble activity reveals the pitfalls and shortcomings of rotation dynamics

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.

Phantom oscillations in principal component analysis

Principal component analysis (PCA) is a dimensionality reduction method that is known for being simple and easy to interpret. Principal components are often interpreted as low-dimensional patterns in high-dimensional space. However, this simple interpretation fails for timeseries, spatial maps, and other continuous data. In these cases, nonoscillatory data may have oscillatory principal components. Here, we show that two common properties of data cause oscillatory principal components: smoothness and shifts in time or space. These two properties implicate almost all neuroscience data. We show how the oscillations produced by PCA, which we call "phantom oscillations," impact data analysis. We also show that traditional cross-validation does not detect phantom oscillations, so we suggest procedures that do. Our findings are supported by a collection of mathematical proofs. Collectively, our work demonstrates that patterns which emerge from high-dimensional data analysis may not faithfully represent the underlying data.

Linking cortex and contraction-Integrating models along the corticomuscular pathway

Computational models of the neuromusculoskeletal system provide a deterministic approach to investigate input-output relationships in the human motor system. Neuromusculoskeletal models are typically used to estimate muscle activations and forces that are consistent with observed motion under healthy and pathological conditions. However, many movement pathologies originate in the brain, including stroke, cerebral palsy, and Parkinson's disease, while most neuromusculoskeletal models deal exclusively with the peripheral nervous system and do not incorporate models of the motor cortex, cerebellum, or spinal cord. An integrated understanding of motor control is necessary to reveal underlying neural-input and motor-output relationships. To facilitate the development of integrated corticomuscular motor pathway models, we provide an overview of the neuromusculoskeletal modelling landscape with a focus on integrating computational models of the motor cortex, spinal cord circuitry, α-motoneurons  and skeletal muscle in regard to their role in generating voluntary muscle contraction. Further, we highlight the challenges and opportunities associated with an integrated corticomuscular pathway model, such as challenges in defining neuron connectivities, modelling standardisation, and opportunities in applying models to study emergent behaviour. Integrated corticomuscular pathway models have applications in brain-machine-interaction, education, and our understanding of neurological disease.

Validation of a non-invasive, real-time, human-in-the-loop model of intracortical brain-computer interfaces

Objective. Despite the tremendous promise of invasive brain-computer interfaces (iBCIs), the associated study costs, risks, and ethical considerations limit the opportunity to develop and test the algorithms that decode neural activity into a user's intentions. Our goal was to address this challenge by designing an iBCI model capable of testing many human subjects in closed-loop.Approach. We developed an iBCI model that uses artificial neural networks (ANNs) to translate human finger movements into realistic motor cortex firing patterns, which can then be decoded in real time. We call the model the joint angle BCI, or jaBCI. jaBCI allows readily recruited, healthy subjects to perform closed-loop iBCI tasks using any neural decoder, preserving subjects' control-relevant short-latency error correction and learning dynamics.Main results. We validated jaBCI offline through emulated neuron firing statistics, confirming that emulated neural signals have firing rates, low-dimensional PCA geometry, and rotational jPCA dynamics that are quite similar to the actual neurons (recorded in monkey M1) on which we trained the ANN. We also tested jaBCI in closed-loop experiments, our single study examining roughly as many subjects as have been tested world-wide with iBCIs (n= 25). Performance was consistent with that of the paralyzed, human iBCI users with implanted intracortical electrodes. jaBCI allowed us to imitate the experimental protocols (e.g. the same velocity Kalman filter decoder and center-out task) and compute the same seven behavioral measures used in three critical studies.Significance. These encouraging results suggest the jaBCI's real-time firing rate emulation is a useful means to provide statistically robust sample sizes for rapid prototyping and optimization of decoding algorithms, the study of bi-directional learning in iBCIs, and improving iBCI control.

Delta-band neural tracking primarily reflects rule-based chunking instead of semantic relatedness between words

It is debated whether cortical responses matching the time scales of phrases and sentences mediate the mental construction of the syntactic chunks or are simply caused by the semantic properties of words. Here, we investigate to what extent delta-band neural responses to speech can be explained by semantic relatedness between words. To dissociate the contribution of semantic relatedness from sentential structures, participants listened to sentence sequences and paired-word sequences in which semantically related words repeated at 1 Hz. Semantic relatedness in the 2 types of sequences was quantified using a word2vec model that captured the semantic relation between words without considering sentential structure. The word2vec model predicted comparable 1-Hz responses with paired-word sequences and sentence sequences. However, empirical neural activity, recorded using magnetoencephalography, showed a weaker 1-Hz response to paired-word sequences than sentence sequences in a word-level task that did not require sentential processing. Furthermore, when listeners applied a task-related rule to parse paired-word sequences into multi-word chunks, 1-Hz response was stronger than that in word-level task on the same sequences. Our results suggest that cortical activity tracks multi-word chunks constructed by either syntactic rules or task-related rules, whereas the semantic relatedness between words contributes only in a minor way.

Modulation of neural co-firing to enhance network transmission and improve motor function after stroke

Stroke is a leading cause of disability. While neurotechnology has shown promise for improving upper limb recovery after stroke, efficacy in clinical trials has been variable. Our central thesis is that to improve clinical translation, we need to develop a common neurophysiological framework for understanding how neurotechnology alters network activity. Our perspective discusses principles for how motor networks, both healthy and those recovering from stroke, subserve reach-to-grasp movements. We focus on neural processing at the resolution of single movements, the timescale at which neurotechnologies are applied, and discuss how this activity might drive long-term plasticity. We propose that future studies should focus on cross-area communication and bridging our understanding of timescales ranging from single trials within a session to across multiple sessions. We hope that this perspective establishes a combined path forward for preclinical and clinical research with the goal of more robust clinical translation of neurotechnology.

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.

From Parametric Representation to Dynamical System: Shifting Views of the Motor Cortex in Motor Control

In contrast to traditional representational perspectives in which the motor cortex is involved in motor control via neuronal preference for kinetics and kinematics, a dynamical system perspective emerging in the last decade views the motor cortex as a dynamical machine that generates motor commands by autonomous temporal evolution. In this review, we first look back at the history of the representational and dynamical perspectives and discuss their explanatory power and controversy from both empirical and computational points of view. Here, we aim to reconcile the above perspectives, and evaluate their theoretical impact, future direction, and potential applications in brain-machine interfaces.

Cyclic, Condition-Independent Activity in Primary Motor Cortex Predicts Corrective Movement Behavior

Reaching movements are known to have large condition-independent (CI) neural activity and cyclic neural dynamics. A new precision center-out task was performed by rhesus macaques to test the hypothesis that cyclic, CI neural activity in the primary motor cortex (M1) occurs not only during initial reaching movements but also during subsequent corrective movements. Corrective movements were observed to be discrete with time courses and bell-shaped speed profiles similar to the initial movements. CI cyclic neural trajectories were similar and repeated for initial and each additional corrective submovement. The phase of the cyclic CI neural activity predicted the time of peak movement speed more accurately than regression of instantaneous firing rate, even when the subject made multiple corrective movements. Rather than being controlled as continuations of the initial reach, a discrete cycle of motor cortex activity encodes each corrective submovement.

Sequential and efficient neural-population coding of complex task information

Recent work has highlighted that many types of variables are represented in each neocortical area. How can these many neural representations be organized together without interference and coherently maintained/updated through time? We recorded from excitatory neural populations in posterior cortices as mice performed a complex, dynamic task involving multiple interrelated variables. The neural encoding implied that highly correlated task variables were represented by less-correlated neural population modes, while pairs of neurons exhibited a spectrum of signal correlations. This finding relates to principles of efficient coding, but notably utilizes neural population modes as the encoding unit and suggests partial whitening of task-specific information where different variables are represented with different signal-to-noise levels. Remarkably, this encoding function was multiplexed with sequential neural dynamics yet reliably followed changes in task-variable correlations throughout the trial. We suggest that neural circuits can implement time-dependent encodings in a simple way using random sequential dynamics as a temporal scaffold.

Neural tuning and representational geometry

A central goal of neuroscience is to understand the representations formed by brain activity patterns and their connection to behaviour. The classic approach is to investigate how individual neurons encode stimuli and how their tuning determines the fidelity of the neural representation. Tuning analyses often use the Fisher information to characterize the sensitivity of neural responses to small changes of the stimulus. In recent decades, measurements of large populations of neurons have motivated a complementary approach, which focuses on the information available to linear decoders. The decodable information is captured by the geometry of the representational patterns in the multivariate response space. Here we review neural tuning and representational geometry with the goal of clarifying the relationship between them. The tuning induces the geometry, but different sets of tuned neurons can induce the same geometry. The geometry determines the Fisher information, the mutual information and the behavioural performance of an ideal observer in a range of psychophysical tasks. We argue that future studies can benefit from considering both tuning and geometry to understand neural codes and reveal the connections between stimuli, brain activity and behaviour.

Stimulus-Driven and Spontaneous Dynamics in Excitatory-Inhibitory Recurrent Neural Networks for Sequence Representation

Recurrent neural networks (RNNs) have been widely used to model sequential neural dynamics ("neural sequences") of cortical circuits in cognitive and motor tasks. Efforts to incorporate biological constraints and Dale's principle will help elucidate the neural representations and mechanisms of underlying circuits. We trained an excitatory-inhibitory RNN to learn neural sequences in a supervised manner and studied the representations and dynamic attractors of the trained network. The trained RNN was robust to trigger the sequence in response to various input signals and interpolated a time-warped input for sequence representation. Interestingly, a learned sequence can repeat periodically when the RNN evolved beyond the duration of a single sequence. The eigenspectrum of the learned recurrent connectivity matrix with growing or damping modes, together with the RNN's nonlinearity, were adequate to generate a limit cycle attractor. We further examined the stability of dynamic attractors while training the RNN to learn two sequences. Together, our results provide a general framework for understanding neural sequence representation in the excitatory-inhibitory RNN.

Traveling of extreme events in network of counter-rotating nonlinear oscillators

We study the propagation of rare or extreme events in a network of coupled nonlinear oscillators, where counter-rotating oscillators play the role of the malfunctioning agents. The extreme events originate from the coupled counter-oscillating pair of oscillators through a mechanism of saddle-node bifurcation. A detailed study of the propagation and the destruction of the extreme events and how these events depend on the strength of the coupling is presented. Extreme events travel only when nearby oscillators are in synchronization. The emergence of extreme events and their propagation are observed in a number of excitable systems for different network sizes and for different topologies.

A geometric framework for understanding dynamic information integration in context-dependent computation

The prefrontal cortex (PFC) plays a prominent role in performing flexible cognitive functions and working memory, yet the underlying computational principle remains poorly understood. Here, we trained a rate-based recurrent neural network (RNN) to explore how the context rules are encoded, maintained across seconds-long mnemonic delay, and subsequently used in a context-dependent decision-making task. The trained networks replicated key experimentally observed features in the PFC of rodent and monkey experiments, such as mixed selectivity, neuronal sequential activity, and rotation dynamics. To uncover the high-dimensional neural dynamical system, we further proposed a geometric framework to quantify and visualize population coding and sensory integration in a temporally defined manner. We employed dynamic epoch-wise principal component analysis (PCA) to define multiple task-specific subspaces and task-related axes, and computed the angles between task-related axes and these subspaces. In low-dimensional neural representations, the trained RNN first encoded the context cues in a cue-specific subspace, and then maintained the cue information with a stable low-activity state persisting during the delay epoch, and further formed line attractors for sensor integration through low-dimensional neural trajectories to guide decision-making. We demonstrated via intensive computer simulations that the geometric manifolds encoding the context information were robust to varying degrees of weight perturbation in both space and time. Overall, our analysis framework provides clear geometric interpretations and quantification of information coding, maintenance, and integration, yielding new insight into the computational mechanisms of context-dependent computation.

Computation Through Neural Population Dynamics

Significant experimental, computational, and theoretical work has identified rich structure within the coordinated activity of interconnected neural populations. An emerging challenge now is to uncover the nature of the associated computations, how they are implemented, and what role they play in driving behavior. We term this computation through neural population dynamics. If successful, this framework will reveal general motifs of neural population activity and quantitatively describe how neural population dynamics implement computations necessary for driving goal-directed behavior. Here, we start with a mathematical primer on dynamical systems theory and analytical tools necessary to apply this perspective to experimental data. Next, we highlight some recent discoveries resulting from successful application of dynamical systems. We focus on studies spanning motor control, timing, decision-making, and working memory. Finally, we briefly discuss promising recent lines of investigation and future directions for the computation through neural population dynamics framework.

Low-frequency stimulation enhances ensemble co-firing and dexterity after stroke

Electrical stimulation is a promising tool for modulating brain networks. However, it is unclear how stimulation interacts with neural patterns underlying behavior. Specifically, how might external stimulation that is not sensitive to the state of ongoing neural dynamics reliably augment neural processing and improve function? Here, we tested how low-frequency epidural alternating current stimulation (ACS) in non-human primates recovering from stroke interacted with task-related activity in perilesional cortex and affected grasping. We found that ACS increased co-firing within task-related ensembles and improved dexterity. Using a neural network model, we found that simulated ACS drove ensemble co-firing and enhanced propagation of neural activity through parts of the network with impaired connectivity, suggesting a mechanism to link increased co-firing to enhanced dexterity. Together, our results demonstrate that ACS restores neural processing in impaired networks and improves dexterity following stroke. More broadly, these results demonstrate approaches to optimize stimulation to target neural dynamics.