When you reach for a coffee mug, your brain does not command each muscle one instruction at a time. Instead, large groups of neurons in the motor cortex fire together in coordinated, flowing patterns that collectively produce the movement. Over the past decade, researchers have shifted from studying individual neurons during reaching to studying these group-level patterns, and what they found was unexpected: the neural activity traces out smooth, often rotating trajectories through a surprisingly low-dimensional space. This discovery has reshaped how scientists think about voluntary movement and opened practical doors for brain-computer interfaces.
From Single Neurons to Population Patterns
For decades, the dominant way to study the motor cortex was to record from one neuron at a time and ask what movement feature it “encoded.” A neuron might fire fastest when the arm moved to the right, for example, leading to the idea that each cell carried a signal about direction, speed, or force. These are called representational models, because they treat each neuron as a reporter of some movement parameter. The approach worked reasonably well for building simple predictions of where the arm would go, but it left a lot of neural activity unexplained. Neurons in motor cortex do all sorts of things that do not map neatly onto any single movement variable.
The alternative, which gained traction in the 2010s, treats motor cortex as a dynamical system. Rather than asking what each neuron represents, researchers ask how the activity of the whole population evolves over time according to internal rules. A landmark study comparing these two frameworks found that the dynamical-system view explained motor cortex activity during reaching better than representational tuning models did.1PLOS Computational Biology. Neural Population Dynamics during Reaching Are Better Explained by a Dynamical System than Representational Tuning In this view, the brain is less like a switchboard sending specific commands and more like an engine whose internal momentum generates the patterns needed for movement.
Rotational Dynamics in Motor Cortex
The most striking finding to emerge from this population-level approach was that neural activity during reaching contains a strong oscillatory, rotating component. When researchers recorded from many motor cortex neurons simultaneously and used statistical tools to visualize the collective activity, the trajectories traced out roughly circular or elliptical loops through neural space. This was surprising because reaching is not a rhythmic behavior like walking. You extend your arm, grab the mug, and stop. Yet the underlying brain activity has a brief rhythmic signature.2PubMed Central. Neural population dynamics during reaching
These rotational dynamics are not an artifact of one lab or one recording setup. When different groups recorded from monkeys making reaching movements and applied similar population-level analyses, the rotational structure showed up consistently. Individual neurons display a wide variety of complex firing patterns during a reach, but at the population level, those patterns are collectively governed by rotations.3eLife. Neural population dynamics in motor cortex are different for reach and grasp The picture that emerges is of the motor cortex acting as a kind of autonomous pattern generator, one whose internal dynamics, once set in motion, produce the time-varying signals needed to drive muscles.
The Neural Manifold
A single reaching movement involves thousands of neurons, each with its own firing rate at every moment. In principle, that means the brain’s activity lives in a space with thousands of dimensions, one per neuron. In practice, because neurons are wired together and constrain each other’s activity, the population does not wander freely through that vast space. Instead, it stays confined to a much smaller surface, a “neural manifold” with far fewer dimensions.4PubMed Central. Neural Manifolds for the Control of Movement
Think of it like a marble rolling on a tabletop. The marble could, in theory, move in three dimensions, but the table constrains it to two. Similarly, the connectivity of the motor cortex constrains the population’s activity to a low-dimensional surface. The specific dimensions of that surface, sometimes called neural modes, are the building blocks the brain uses to generate movement. The time-varying activation of those few modes is what actually drives behavior, not the independent firing of any single neuron.5Neuron. Neural Population Dynamics: From Single Neurons to Neural Manifolds
This low-dimensional structure is not just an artifact of constrained lab tasks where monkeys reach to a handful of fixed targets. Recordings during unconstrained, naturalistic movements reveal similarly low-dimensional manifolds, with dimensionality only slightly higher than in laboratory settings. Decoding arm movements from the low-dimensional manifold activity works just as well as decoding from all the recorded neurons, which means the manifold captures the information that matters for movement.6bioRxiv. Low-dimensional neural manifolds for the control of constrained and unconstrained movements
Preparing to Move Without Moving
One of the most elegant findings in this field explains a puzzle that had bothered motor neuroscientists for years: neurons in motor cortex are active before a movement starts, during the preparatory period when you know where you want to reach but have not begun. If these neurons directly drive muscles, why doesn’t that preparatory activity cause premature movement?
The answer lies in how the neural manifold is organized. The dimensions of the manifold that actually influence muscles, the “output-potent” dimensions, are largely separate from the dimensions in which preparatory activity occurs, the “output-null” dimensions. Preparatory tuning sits almost entirely in the output-null space, with roughly four to five times more variance there than in the output-potent dimensions.7PubMed Central. Cortical activity in the null space: permitting preparation without movement In plain terms, the brain can plan a reach vigorously without any of that planning activity leaking through to the muscles, because the planning happens in neural dimensions that the downstream system effectively ignores.
This output-null trick is not limited to movement preparation. When visual perturbations jolt the system, say an unexpected shift in a cursor’s position mid-reach, the initial neural response is also restricted to output-null dimensions before eventually entering the output-potent space. The nervous system can temporarily contain a burst of activity within the circuit, keeping it hidden from muscles and spinal cord until the response has been refined.8PubMed Central. Motor Cortical Visuomotor Feedback Activity Is Initially Isolated from Downstream Targets in Output-Null Neural State Space Dimensions
The dynamics of preparation also depend on timing. When a monkey is given a delay period to plan a reach before a go signal, the population activity settles into a stable preparatory state. Without such a delay, that clean preparatory state never fully forms.9Neuron. Neural Population Dynamics during Reaching This might help explain why rushed movements tend to be less accurate: the neural initial conditions from which the dynamical system launches are not as well set. When the brain needs to plan two potential reaches simultaneously, it compromises, positioning preparatory activity at an intermediate state within the optimal subspace that reflects a trade-off between the two possible movements.10Cell Reports. Neural population dynamics during parallel planning of a pair of reach-to-grasp movements
The Timing Signal That Dwarfs Everything Else
When researchers look at what accounts for the largest share of the motor cortex population response during reaching, the answer is not reach direction or speed. It is timing. The biggest component of neural activity is condition-invariant, meaning it looks roughly the same regardless of which direction you are reaching. This component undergoes a rapid shift just before movement onset, and the timing of that shift predicts most of the trial-to-trial variation in reaction time.11eNeuro. The Largest Response Component in the Motor Cortex Reflects Movement Timing but Not Movement Type Individual neurons still carry information about which movement is made, but the dominant population-level signal is about when to move.
This condition-invariant signal appears to be shared across brain areas. Both the supplementary motor area and the primary motor cortex display a similarly organized, condition-invariant shift in population state just before movement starts, suggesting a coordinated initiation signal that spans multiple regions.12Nature Communications. Different population dynamics in the supplementary motor area and motor cortex during reaching The cyclic structure of this signal also has practical value: the phase of the condition-invariant oscillation predicts the time of peak hand speed more accurately than simply looking at instantaneous firing rates, even when the subject makes multiple corrective sub-movements within a single reach.13eNeuro. Cyclic, Condition-Independent Activity in Primary Motor Cortex Predicts Corrective Movement Behavior
Motor Cortex Versus Other Areas Along the Motor Pathway
Rotational dynamics are not equally prominent everywhere in the brain. The supplementary motor area, which sits upstream of primary motor cortex and is thought to play a role in movement planning and sequencing, shows weaker and slower rotational structure. When researchers compared how well a simple dynamical model fit each region’s population activity, motor cortex came out well ahead, while the supplementary motor area was a significantly poorer fit.14PubMed Central. Different population dynamics in the supplementary motor area and motor cortex during reaching The motor cortex also produced population patterns that more closely resembled actual muscle activity, consistent with its role as the last major cortical relay before signals descend to the spinal cord.
Moving further downstream, the spinal cord tells an entirely different story. Recordings from the primate cervical spinal cord during an isometric wrist task revealed no rotational dynamics at all. Instead, spinal cord populations showed low-dimensional alternating patterns. Motor cortex activity from the same task, recorded simultaneously, did display the expected rotational structure. Even cortical neurons that had direct measured effects on spinal motoneurons showed cortex-like dynamics rather than spinal-like dynamics.15bioRxiv. Spinal cord population activity lacks rotational dynamics during an alternating isometric task in macaque This tells us that the rotational dynamics are a feature of cortical computation, not something inherited from a generic property of neural circuits.
How the Brain Keeps These Patterns Stable Over Time
Neurons are unreliable narrators. The same neuron’s relationship to a given movement can drift from day to day, even week to week, a phenomenon called representational drift. If the brain relied on stable single-neuron signals, this instability would be a problem. But the manifold framework offers a way out. Research tracking motor cortex recordings over long periods has found that the mapping from the low-dimensional latent activity to behavior remains stable across years, even as the mapping from individual neurons to those latent dimensions shifts considerably. In other words, which neurons participate and how they contribute changes, but the low-dimensional “recipe” that produces behavior stays consistent.16PubMed Central. Stability of neural manifolds at minimal dimensionality despite motor representational drift
Complementary evidence from recordings using electrode grids placed on the brain surface shows that well-rehearsed movements maintain remarkably preserved manifold structure across days, even when the brain is simultaneously adapting to new contexts like controlling a brain-computer interface.17PubMed Central. Flexible regulation of representations on a drifting manifold enables long-term stable complex neuroprosthetic control The manifold appears to be the stable scaffold around which individual neurons can be swapped in and out without disrupting the overall computation.
Preserved Dynamics Across Individuals and Species
If population dynamics during reaching were highly idiosyncratic, shaped by each animal’s unique wiring and learning history, the framework would be interesting but hard to generalize. As it turns out, the dynamics are surprisingly shared. Analyses of motor cortex recordings from different monkeys performing the same reaching task found that the underlying neural dynamics were preserved across individuals. Even more remarkably, comparisons between monkey and mouse motor cortex during similar movements revealed preserved latent dynamics across species.18Nature. Preserved neural dynamics across animals performing similar behaviour This suggests that the rotational, low-dimensional population dynamics are not just a quirk of one brain but reflect something fundamental about how mammalian motor cortex generates movement.
Learning Reshapes the Manifold
When you learn a new motor skill, your neural manifold does not simply replay old patterns. Learning sculpts new population activity structures that then constrain how you can adapt further. Modeling work has shown that de novo motor learning, acquiring a completely new skill from scratch, creates geometrical properties in the neural population that shape how easily the system can adjust to subsequent perturbations.19Nature Communications. De novo motor learning creates structure in neural activity that shapes adaptation In practical terms, this means your history of skill learning leaves traces in the manifold that make some future adaptations easy and others hard.
During shorter-term adaptation, such as adjusting to a force field that pushes the arm off course, the dynamics also shift in a structured way. In premotor and motor cortex, the direct mapping between areas persists unchanged through adaptation, while the evolving output-null activity within the premotor area changes to drive the behavioral correction.20Neuron. Cortical Population Dynamics during Motor Adaptation The system adapts without overhauling its core inter-areal communication, using the null-space flexibility described earlier to accommodate new demands.
When Disease Disrupts the Dynamics
If healthy reaching depends on well-organized, low-dimensional rotational dynamics with cleanly separated preparation and movement subspaces, then diseases that impair movement might leave fingerprints in those dynamics. That is exactly what recent work on parkinsonism has found. In an animal model of the disease, motor cortex activity during reaching became higher-dimensional than normal, and the separation between preparatory and movement-related subspaces broke down.21PubMed Central. Parkinsonism disrupts the population-level organization of cortical dynamics In short, the tidy low-dimensional structure that healthy brains use to prepare and execute reaches was scrambled. This suggests that some movement symptoms of Parkinson’s disease may stem not from losing individual neurons’ tuning to movement parameters but from a disorganization of the population-level machinery itself.
Applications to Brain-Computer Interfaces
The population dynamics framework has had an immediate practical payoff for brain-computer interfaces. These devices read neural signals from the motor cortex and translate them into cursor movements or robotic arm commands for people with paralysis. A persistent engineering challenge is instability: the signals picked up by implanted electrodes shift over time as neurons drift, tissue heals around the electrodes, or recording quality changes. Traditional decoders, which map individual neuron activity directly to output commands, need frequent recalibration.
Manifold-based decoders sidestep this by working at the level of latent dynamics rather than raw neural firing. Because the manifold stays stable even as individual neurons change, aligning new neural data to the low-dimensional structure of previously recorded activity can restore decoder performance without any supervised recalibration. One approach demonstrated proficient cursor control in monkeys even after severe, abrupt recording instabilities were introduced.22PubMed Central. Stabilization of a brain-computer interface via the alignment of low-dimensional spaces of neural activity A more recent platform that explicitly accounts for the temporal dynamics of the manifold, not just its spatial structure, achieves stable decoding over weeks to months without any manual recalibration at all.23Nature Communications. Stabilizing brain-computer interfaces through alignment of latent dynamics
Computational Tools for Extracting Dynamics
None of these findings would be possible without advances in the algorithms used to extract low-dimensional dynamics from messy, noisy neural recordings. One widely used method, called latent factor analysis via dynamical systems, uses deep learning to infer smooth latent trajectories from single-trial spiking data. Applied to motor cortex datasets from monkeys and humans, it produces precise firing rate estimates on individual trials, predicts behavioral variables, and can even combine data from non-overlapping recording sessions months apart to improve the estimate of underlying dynamics.24PubMed Central. Inferring single-trial neural population dynamics using sequential auto-encoders
A practical limitation of these deep learning models is that they require careful tuning of many settings for each new dataset. An automated framework addresses this by searching for optimal model configurations without needing any behavioral or task information as input, making it feasible to apply the same dynamical modeling approach across different brain areas and tasks without hand-tuning every time.25PubMed Central. A large-scale neural network training framework for generalized estimation of single-trial population dynamics These tools have become a shared infrastructure for the field, letting labs around the world apply population dynamics analyses to their own data with a reasonable level of effort.
Why Trajectories Might Improve Motor Precision
The rotational, trajectory-based structure of motor cortex activity is not just descriptive. Modeling work suggests it may be functionally important for producing accurate movements. When a recurrent neural network simulating downstream motor circuits receives inputs that unfold as distinct neural trajectories, encoding both the phase and amplitude of movement over time, the resulting simulated movements are more accurate than when the network receives simple instantaneous, static-tuning signals.26PubMed Central. Neural trajectories improve motor precision The idea is that the temporal unfolding of the population pattern gives the downstream system richer, more informative instructions than a snapshot ever could. This fits with the broader theme that the brain generates movement not by issuing a single command but by launching a dynamic process whose smooth evolution over time carries the detailed information muscles need to act precisely.
Separate computational work exploring optimal feedback control offers a complementary angle. When a neural network is trained to control a realistic model of the arm and shoulder for reaching, optimizing for feedback control of the musculoskeletal system through space, the resulting network dynamics recapitulate key features of real motor cortex population activity.27bioRxiv. Optimal feedback solutions recapitulate key features of motor cortical population dynamics The rotational trajectories researchers observe in actual brains may thus emerge naturally from the computational demands of controlling a limb through space toward a goal, rather than being an arbitrary design choice of evolution.