Neural responses are typically characterized by computing the mean firing rate. Yet response variability can exist across trials. Many studies have examined the impact of a stimulus on the mean response, yet few have examined the impact on response variability. We measured neural variability in 13 extracellularly-recorded datasets and one intracellularly-recorded dataset from 7 areas spanning the four cortical lobes. In every case, stimulus onset caused a decline in neural variability. This occurred even when the stimulus produced little change in mean firing rate. The variability decline was observable in membrane potential recordings, in the spiking of individual neurons, and in correlated spiking variability measured with implanted 96-electrode arrays. The variability decline was observed for all stimuli tested, regardless of whether the animal was awake, behaving, or anaesthetized. This widespread variability decline suggests a rather general property of cortex: that its state is stabilized by an input.

We consider the problem of extracting smooth, low-dimensional neural trajectories that summarize the activity recorded simultaneously from many neurons on individual experimental trials. Beyond the benefit of visualizing the high-dimensional, noisy spiking activity in a compact form, such trajectories can offer insight into the dynamics of the neural circuitry underlying the recorded activity. Current methods for extracting neural trajectories involve a two-stage process: the spike trains are first smoothed over time, then a static dimensionality-reduction technique is applied. We first describe extensions of the two-stage methods that allow the degree of smoothing to be chosen in a principled way and that account for spiking variability, which may vary both across neurons and across time. We then present a novel method for extracting neural trajectories-Gaussian-process factor analysis (GPFA)-which unifies the smoothing and dimensionality-reduction operations in a common probabilistic framework. We applied these methods to the activity of 61 neurons recorded simultaneously in macaque premotor and motor cortices during reach planning and execution. By adopting a goodness-of-fit metric that measures how well the activity of each neuron can be predicted by all other recorded neurons, we found that the proposed extensions improved the predictive ability of the two-stage methods. The predictive ability was further improved by going to GPFA. From the extracted trajectories, we directly observed a convergence in neural state during motor planning, an effect that was shown indirectly by previous studies. We then show how such methods can be a powerful tool for relating the spiking activity across a neural population to the subject's behavior on a single-trial basis. Finally, to assess how well the proposed methods characterize neural population activity when the underlying time course is known, we performed simulations that revealed that GPFA performed tens of percent better than the best two-stage method.

We present experiments and analyses designed to test the idea that firing rates in premotor cortex become optimized during motor preparation, approaching their ideal values over time. We measured the across-trial variability of neural responses in dorsal premotor cortex of three monkeys performing a delayed-reach task. Such variability was initially high, but declined after target onset, and was maintained at a rough plateau during the delay. An additional decline was observed after the go cue. Between target onset and movement onset, variability declined by an average of 34%. This decline in variability was observed even when mean firing rate changed little. We hypothesize that this effect is related to the progress of motor preparation. In this interpretation, firing rates are initially variable across trials but are brought, over time, to their "appropriate" values, becoming consistent in the process. Consistent with this hypothesis, reaction times were longer if the go cue was presented shortly after target onset, when variability was still high, and were shorter if the go cue was presented well after target onset, when variability had fallen to its plateau. A similar effect was observed for the natural variability in reaction time: longer (shorter) reaction times tended to occur on trials in which firing rates were more (less) variable. These results reveal a remarkable degree of temporal structure in the variability of cortical neurons. The relationship with reaction time argues that the changes in variability approximately track the progress of motor preparation.

Video LegendsThese videos show the behavioral conditions from our different experiments. The experiment room itself was visibly dark, but the video camera could image the scene with infrared light. Bright text and numbers were added as annotations and were not seen by the monkey. Each successful trial was followed by a juice reward, indicated by a short tone followed by a click corresponding to the action of a juice dispenser. These auditory signals were heard by the monkey during the experiment. For the duration of the experiment, a piece of reflective tape was lightly wrapped around one phalanx of the monkey's left hand to track the monkey's arm movements. This tape is especially bright in the infrared videos but was not visible to the monkey during the experiments. Video 3 SuppVideo3BCIFast.mpg Movie showing fast-paced prosthetic cursor trials during BCI experiments. We showed three separate sequences, each of five cursor trials followed by a real reach. These three sequences were not performed in succession. Rather, the three sequences of five cursor trials were spliced from different times during the same experiment to better demonstrate the speed of our system. The prosthetic cursor is not visible in this video because it was flashed briefly so as to not slow the overall presentation of trials.

19In many experiments, neuroscientists tightly control behavior, record many trials, and obtain trial-averaged 20 firing rates from hundreds of neurons in circuits containing billions of behaviorally relevant neurons. Di-21 mensionality reduction methods reveal a striking simplicity underlying such multi-neuronal data: they can 22 be reduced to a low-dimensional space, and the resulting neural trajectories in this space yield a remarkably questions, and test it using physiological recordings from reaching monkeys. This theory reveals conceptual 28 insights into how task complexity governs both neural dimensionality and accurate recovery of dynamic 29 portraits, thereby providing quantitative guidelines for future large-scale experimental design.

Summary The process by which neural circuitry in the brain plans and executes arm movements is not well understood. Prevailing data (single-neuron and field potential recordings) do not reveal how individual neurons’ activities are coordinated within the population, and thus inferences about how the neural circuit forms a motor plan have been indirect. Here we frame and test a new ‘initial condition hypothesis’ in which the reaction time (RT) of upcoming movements may be predicted on each trial using neurons’ moment-by-moment firing rates and rates of change of those rates. Using microelectrode array recordings from premotor cortex of monkeys performing delayed-reach movements, we compare such single-trial RT predictions to those of other theories. The initial condition hypothesis model can explain approximately four-fold more RT variance than the best alternative method. Thus, the initial condition hypothesis elucidates a new view of the relationship between single-trial preparatory neural population dynamics and single-trial behavior.

Neurons in premotor and motor cortex show preparatory activity during an instructed-delay task. It has been suggested that such activity primarily reflects visuospatial aspects of the movement, such as target location or reach direction and extent. We asked whether a more dynamic feature, movement speed, is also reflected. Two monkeys were trained to reach at different speeds ("slow" or "fast," peak speed being approximately 50-100% higher for the latter) depending on target color. Targets were presented in seven directions and at two distances. Of 95 neurons with tuned delay-period activity, 95, 78, and 94% showed a significant influence of direction, distance, and instructed speed, respectively. Average peak modulations with respect to direction, distance and speed were 18, 10, and 11 spikes/s. Although robust, modulations of firing rate with target direction were not necessarily invariant: for 45% of neurons, the preferred direction depended significantly on target distance and/or instructed speed. We collected an additional dataset, examining in more detail the effect of target distance (5 distances from 3 to 12 cm in 2 directions). Of 41 neurons with tuned delay-period activity, 85, 83, and 98% showed a significant impact of direction, distance, and instructed speed. Statistical interactions between the effects of distance and instructed speed were common, but it was nevertheless clear that distance "tuning" was not in general a simple consequence of speed tuning. We conclude that delay-period preparatory activity robustly reflects a nonspatial aspect of the upcoming reach. However, it is unclear whether the recorded neural responses conform to any simple reference frame, intrinsic or extrinsic.

Some movements that animals and humans make are highly stereotyped, repeated with little variation. The patterns of neural activity associated with repeats of a movement may be highly similar, or the same movement may arise from different patterns of neural activity, if the brain exploits redundancies in the neural projections to muscles. We examined the stability of the relationship between neural activity and behavior. We asked whether the variability in neural activity that we observed during repeated reaching was consistent with a noisy but stable relationship, or with a changing relationship, between neural activity and behavior. Monkeys performed highly similar reaches under tight behavioral control, while many neurons in the dorsal aspect of premotor cortex and the primary motor cortex were simultaneously monitored for several hours. Neural activity was predominantly stable over time in all measured properties: firing rate, directional tuning, and contribution to a decoding model that predicted kinematics from neural activity. The small changes in neural activity that we did observe could be accounted for primarily by subtle changes in behavior. We conclude that the relationship between neural activity and practiced behavior is reasonably stable, at least on timescales of minutes up to 48 h. This finding has significant implications for the design of neural prosthetic systems because it suggests that device recalibration need not be overly frequent, It also has implications for studies of neural plasticity because a stable baseline permits identification of nonstationary shifts.