Stimulus onset quenches neural variability: a widespread cortical phenomenon

Journal name:
Nature Neuroscience
Year published:
Published online


Neural responses are typically characterized by computing the mean firing rate, but response variability can exist across trials. Many studies have examined the effect of a stimulus on the mean response, but few have examined the effect on response variability. We measured neural variability in 13 extracellularly recorded datasets and one intracellularly recorded dataset from seven areas spanning the four cortical lobes in monkeys and cats. 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 observed 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.

At a glance


  1. Schematic illustration of possible types of across-trial firing rate variability.
    Figure 1: Schematic illustration of possible types of across-trial firing rate variability.

    (ac) We suppose that the same stimulus is delivered four times (four trials) yielding four different responses. a and b were constructed to have the same mean response across the four trials. Stimulus-driven decline in variability is shown in a. Stimulus-driven rise in variability is shown in b. Stimulus-driven decline in variability with little change in mean rate is shown in c.

  2. Analysis of intracellularly recorded membrane potential from cat V1.
    Figure 2: Analysis of intracellularly recorded membrane potential from cat V1.

    Stimuli were drifting sine-wave gratings presented at different orientations and frequencies. Spikes were removed before further analysis. Analysis employed a 50-ms sliding window (box filter) to match the 50-ms window used for the Fano factor analysis. Similar results were obtained with a shorter (5-ms) or longer (100-ms) window. (a) Data from one example neuron. Vm for individual trials (black) is plotted on top of the mean (gray). Data are shown when no stimulus was delivered, for a nonpreferred stimulus and for a preferred stimulus. The arrow marks stimulus onset. (b) Similar plot for a second example neuron. (c) The mean and variance of Vm across all 52 neurons and all stimuli. Flanking traces give s.e.m.

  3. Changes in firing-rate variability for ten datasets (one per panel).
    Figure 3: Changes in firing-rate variability for ten datasets (one per panel).

    Insets indicate stimulus type. Data are aligned on stimulus onset (arrow). For the two bottom panels (MT area/direction and MT speed), the dot pattern appeared at time zero (first arrow) and began moving at the second arrow. The mean rate (gray) and the Fano factor (black with flanking s.e.) were computed using a 50-ms sliding window. For OFC, where response amplitudes were small, a 100-ms window was used to gain statistical power. Analysis included all conditions, including nonpreferred. The Fano factor was computed after mean matching (Fig.4). The resulting stabilized means are shown in black. The mean number of trials per condition was 100 (V1), 24 (V4), 15 (MT plaids), 88 (MT dots), 35 (LIP), 10 (PRR), 31 (PMd), 106 (OFC), 125 (MTdirection and area) and 14 (MT speed).

  4. Illustration of how the mean-matched Fano factor was computed.
    Figure 4: Illustration of how the mean-matched Fano factor was computed.

    Data are from the MT plaids dataset. (a) Spike rasters for the 46 trials (one per line) recorded from one MT neuron (127) for one stimulus condition (upwards-moving plaid). Shaded areas show four locations of the sliding window, which moved in 10-ms increments. For each window location, the spike count was computed for each trial. The mean and variance (across trials) of that count then contributed one data point to the subsequent analysis. (b) The Fano factor was computed from scatter plots of the spike-count variance versus mean. Each scatter plot corresponds to a window in a. Each point plots data for one neuron and condition (red indicates the neuron and condition from a). The orange line has unity slope, the expected variance-to-mean relationship for Poisson spiking. Data above the orange line is consistent with the presence of underlying-rate variability. Gray dots show all data. Gray lines are regression fits to all data (constrained to pass through zero, weighted according to the estimated s.e.m. of each variance measurement). Gray distributions are of mean counts. These appear to have different areas because of the vertical log scale. Black points are those preserved by mean matching (Online Methods). Black distributions are thus identical to within bin resolution. Black lines are regression slopes for the mean-matched data. (c) The Fano factor versus time. Arrows indicate time points from the panels above. The gray trace (with flanking s.e.) plots the raw Fano factor, the slope of the gray lines from b. The black trace plots the mean-matched Fano factor, the slope of the black lines.

  5. Changes in the Fano factor after restricting the analysis to combinations of neuron and condition with little change in mean rate (for example, nonpreferred conditions).
    Figure 5: Changes in the Fano factor after restricting the analysis to combinations of neuron and condition with little change in mean rate (for example, nonpreferred conditions).

    (ad) The raw Fano factor for four datasets, computed based on nonresponsive conditions. Of the original neuron conditions (the response of one neuron to one condition), this analysis preserved 28% (MT, a), 49% (PRR, b), 27% (PMd, c) and 41% (MT-speed, d). A 100-ms window (rather than 50 ms) was employed to regain lost statistical power. The trace at the top of each panel shows the mean rate, averaged across all included neurons and conditions. The trace with flanking s.e. shows the Fano factor, computed with no further mean matching. Arrows indicate stimulus onset. For the MT speed dataset (d) the stimulus appeared at the very start of the record (first arrow) and began moving 256 ms later (second arrow).

  6. Application of factor analysis to data from V1 and PMd.
    Figure 6: Application of factor analysis to data from V1 and PMd.

    (a) Factor analysis was applied to covariance matrices (number of neurons × number of neurons) of spike counts, taken in an analysis window that either ended at stimulus onset (prestimulus) or began just after stimulus onset (stimulus). The measured covariance matrix was approximated as the sum of a network covariance matrix and a diagonal matrix of private noise. To produce the plots in bg, we averaged network variances across the subset of neuron and condition combinations (48% and 30% for V1, 74% and 79% for PMd) whose distribution of mean rates was matched before and after stimulus onset (similar to Fig.4). (b) Estimated variances for one V1 dataset. Network variability declined more than private variability in both absolute (P < 10−7) and relative (percent of initial value, P < 10−7) terms (paired t tests across conditions). (c) Similar plot for a V1 dataset from a second monkey (P < 0.002, absolute; P < 0.002, relative). (d) Summary comparison for V1. Changes in variability (stimulus–prestimulus) were expressed in percentage terms. Data to the left of zero indicate that network variability underwent the larger decline. The distribution includes all conditions and both datasets. The mean and s.e. are given by the black symbol at top (P < 10−7 compared with zero, paired t test). Gray symbols give individual means for each dataset. (e) Data are presented as in b and c but for one PMd dataset (G20040123). Network variability declined more in absolute (P < 0.005) and relative (P < 0.001) terms. (f) Similar plot for a second PMd dataset (G20040122; P < 0.05, absolute; P < 0.02, relative). (g) Summary comparison for PMd (distribution mean <0, P < 10−4). (h) Relationship between mean firing rate and network level (shared firing rate) variance. Data (same dataset as b) were binned by mean rate and the average network variance (± s.e.) was computed for each bin. This was done both before stimulus (gray) and after stimulus onset (black). The average was taken across neurons and conditions (each datum being averaged was, for one condition, one element of the blue diagonal in a). Distributions of mean rates are shown at bottom. The analysis in b was based on the overlapping (mean matched) portion of these distributions. (i) Similar plot for PMd (same dataset as e). See Online Methods and Supplementary Figure 6 for a description of datasets.

  7. Individual-trial neural trajectories computed using GPFA.
    Figure 7: Individual-trial neural trajectories computed using GPFA.

    (a) Projections of PMd activity into a two-dimensional state space. Each black point represents the location of neural activity on one trial. Gray traces show trajectories from 200 ms before target onset until the indicated time. The stimulus was a reach target (135°, 60 mm distant), with no reach allowed until a subsequent go cue. 15 (of 47) randomly selected trials are shown. The dataset is the same as in Figure 6e. (b) Trajectories were plotted until movement onset. Blue dots indicate 100 ms before stimulus (reach target) onset. No reach was allowed until after the go cue (green dots), 400–900 ms later. Activity between the blue and green dots thus relates to movement planning. Movement onset (black dots) was ~300 ms after the go cue. For display, 18 randomly selected trials are plotted, plus one hand-selected trial (red, trialID 211). Covariance ellipses were computed across all 47 trials. This is a two-dimensional projection of a ten-dimensional latent space. In the full space, the black ellipse is far from the edge of the blue ellipse. This projection was chosen to accurately preserve the relative sizes (on a per-dimension basis) of the true ten-dimensional volumes of the ellipsoids. Data are from the G20040123 dataset. (c) Data are presented as in b, with the same target location, but for data from another day's dataset (G20040122; red trial, trialID 793).

  8. Projections of V1 activity into a two-dimensional space using GPFA.
    Figure 8: Projections of V1 activity into a two-dimensional space using GPFA.

    Blue, black and red traces show activity before, during and after stimulus presentation (a drifting 45° grating). Data are from the dataset used in Figure 6c. (a) The mean trajectory and three trials picked by hand. The gray spot shows the average location of prestimulus activity. In a few cases (for example, upper left portion of the rightmost panel), traces were moved very slightly apart to make it clear that they traveled in parallel rather than crossed. (b) Trajectories after data were shuffled to remove correlated variability. 25 randomly selected trials are plotted (lighter traces) along with the mean (saturated traces). (c) Data are presented as in b but for the original unshuffled data.


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Author information

  1. These authors contributed equally to this work.

    • Mark M Churchland &
    • Byron M Yu


  1. Department of Electrical Engineering, Stanford University School of Medicine, Stanford University, Stanford, California, USA.

    • Mark M Churchland,
    • Byron M Yu,
    • John P Cunningham,
    • Stephen I Ryu,
    • Gopal Santhanam &
    • Krishna V Shenoy
  2. Neurosciences Program, Stanford University School of Medicine, Stanford University, Stanford, California, USA.

    • Mark M Churchland,
    • Byron M Yu,
    • Leo P Sugrue,
    • Marlene R Cohen,
    • Greg S Corrado,
    • William T Newsome,
    • Katherine M Armstrong,
    • Tirin Moore &
    • Krishna V Shenoy
  3. Gatsby Computational Neuroscience Unit, University College London, London, UK.

    • Byron M Yu &
    • Maneesh Sahani
  4. Howard Hughes Medical Institute, Stanford University School of Medicine, Stanford University, Stanford, California, USA.

    • Leo P Sugrue,
    • Marlene R Cohen,
    • Greg S Corrado &
    • William T Newsome
  5. Department of Neurobiology, Stanford University School of Medicine, Stanford University, Stanford, California, USA.

    • William T Newsome,
    • Katherine M Armstrong &
    • Tirin Moore
  6. Department of Psychology and Committee on Computational Neuroscience, University of Chicago, Chicago, Illinois, USA.

    • Andrew M Clark,
    • Paymon Hosseini,
    • Benjamin B Scott &
    • David C Bradley
  7. Department of Neuroscience and Center for the Neural Basis of Cognition, University of Pittsburgh, Pittsburgh, Pennsylvania, USA.

    • Matthew A Smith
  8. Department of Neuroscience, Albert Einstein College of Medicine, Bronx, New York, USA.

    • Adam Kohn
  9. Center for Neural Science, New York University, New York, New York, USA.

    • Adam Kohn &
    • J Anthony Movshon
  10. Department of Anatomy and Neurobiology, Washington University School of Medicine, St. Louis, Missouri, USA.

    • Steve W Chang &
    • Lawrence H Snyder
  11. Howard Hughes Medical Institute, W.M. Keck Foundation Center for Integrative Neuroscience and Department of Physiology, University of California San Francisco, San Francisco, California, USA.

    • Stephen G Lisberger
  12. Section of Neurobiology, School of Biological Sciences, University of Texas at Austin, Austin, Texas, USA.

    • Nicholas J Priebe
  13. Department of Neurobiology and Physiology, Northwestern University, Evanston, Illinois, USA.

    • Ian M Finn &
    • David Ferster
  14. Department of Neurosurgery, Stanford University School of Medicine, Stanford University, Stanford, California, USA.

    • Stephen I Ryu
  15. Department of Bioengineering, Stanford University, Stanford, California, USA.

    • Krishna V Shenoy


M.M.C. wrote the manuscript, performed the Fano factor and factor analyses and created the figures. GPFA was developed by B.M.Y., J.P.C., M.S. and K.V.S. This application of factor analysis was devised by M.M.C. and B.M.Y. The mean-matched Fano factor was developed by M.M.C. and K.V.S. The conception for the study arose from conversations between M.M.C., K.V.S., B.M.Y., D.C.B., M.R.C., W.T.N. and J.A.M. V1 data (extracellular) were collected in the laboratory of J.A.M. by M.A.S. and A.K. and in the laboratory of A.K. V4 data were collected in the laboratory of T.M. by K.M.A. MT (plaid) data were collected in the laboratory of D.C.B. by A.M.C., P.H. and B.B.S. MT (dots) data were collected in the laboratory of W.T.N. by M.R.C. LIP and OFC data were collected in the laboratory of W.T.N. by L.P.S. using an experimental design developed by L.P.S. and G.S.C. PRR data were collected in the laboratory of L.H.S. by S.W.C. PMd data were collected in the laboratory of K.V.S. by B.M.Y., S.I.R., G.S. and M.M.C. MT (direction/area and speed) data were collected by N.J.P. and M.M.C. in the laboratory of S.G.L. Intracellularly recorded V1 data were collected by N.J.P. and I.M.F. in the laboratory of D.F. All authors contributed to manuscript revisions and editing, particularly J.A.M., W.T.N., L.P.S., D.F., J.P.C., B.M.Y. and K.V.S.

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Supplementary information

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  1. Supplementary Text and Figures (1M)

    Supplementary Figures 1–8 and Supplementary Notes 1–3


  1. Supplementary Video 1 (492K)

    A movie version of Figure 7a. Data are from PMd, and show the decline in across-trial variance after the onset of the stimulus (a reach target). The movie spans 750 ms, beginning 400 ms before stimulus onset and ending 350 ms after. The movie ends before the go cue is given. Each black dot shows the state of PMd on one trial. Fifteen randomly-chosen trials are shown. Dots turn blue for a brief moment at the time of stimulus onset. Note the subsequent drop in the variance of the dot locations (i.e., a drop in firing-rate variance). This feature of the response is at least as clear as the change in mean dot location (i.e., the change in mean firing rates). G20040123 dataset.

  2. Supplementary Video 2 (1M)

    As in Supplementary Video 1, but more time is shown and the trajectory of the RT-outlier trial is now included (red). The movie spans ~1500 ms. This time-span differs slightly across trials, as they have different go-cue and movement-onset times. At the time of the go cue, each dot turns green and further progress is halted. Progress resumes once all trials have passed the time of their respective go cues. This re-aligns the data to the go cue, much as is commonly done in PSTH's. Traces end at movement onset.

  3. Supplementary Video 3 (508K)

    As in Supplementary Video 1, but for the G20040122 PMd dataset (that shown in Figure 7c).

  4. Supplementary Video 4 (1M)

    As in Supplementary Video 2, but for the G20040122 PMd dataset (that shown in Figure 7c).

Additional data