Fig 1.
Response properties of MT neurons to constant motion stimuli.
Blue indicates experiments on alert subjects and orange indicates experiments on anesthetized subjects throughout. (A) A cartoon of the experimental setup for measuring the response of MT neurons to steps of coherent random dot pattern motion. Monkeys maintained fixation while stimuli translated at constant speed in one of 13 or 24 directions behind a stationary aperture scaled to the excitatory receptive field. See Materials and methods for detail. (B) Sample peri-stimulus time histogram (PSTH) from a representative unit showing the time course of firing rate for different motion directions, averaged over a 10 ms sliding window. Motion onset is at 0 ms and motion offset is at 250 ms. (C) Average spike count across neurons in the alert experiments (blue) and anesthetized (orange) by direction. Circles indicate mean, error bars indicate standard deviation, and the solid traces indicates a Gaussian best fit. Responses are aligned such that the preferred stimulus direction for each neuron is taken to be 0°. (D) Average spike count variance across populations of neurons in the same manner as (C). (E) Histogram of direction selectivity indexes, DI, across both populations. (F) Histogram of variance spike count tuning indexes. (G) Histogram of response latency distributions. (H) Distribution of single-unit mutual information (Shannon) values for alert (blue bars) and anesthetized (orange bars) states, based on spike count 250 ms after stimulus motion onset, Value are corrected for finite sample size (see Materials and methods). Arrows below indicate average information for alert (1.11 bits) and anesthetized (0.40 bits). Inset: time course of the mutual information between the cumulative spike count and motion direction over time with respect to stimulus motion onset. Blue traces indicate alert-state units, orange traces anesthetized state.
Fig 2.
Fano factors differ significantly between MT responses recorded in alert versus anesthetized primates.
(A) The relationship between spike count and spike count variance in alert (blue circles) and anesthetized (orange circles) experiments. Each circle indicates a single neuron under a single stimulus condition. Histogram above shows distribution of spike counts observed in both experiments. The histogram to the right shows the distribution spike count variance values in both experiments. Stimulus directions shown are within 45° of the preferred motion direction, in 15° increments. (B) Distribution of spike count Fano factors for alert (blue) and anesthetized (orange) experiments. Solid trace indicates the best-fit lognormal distribution for each case. (C) Distribution of Fano factors as a function of spike count for alert experiments (blue) and anesthetized experiments (orange). Black circles and triangles indicate the median Fano factor binned by spike count in alert and anesthetized experiments, respectively. Error bars show the standard deviation of Fano factors in each bin. The solid and dashed traces are the linear best fit for alert and anesthetized states, respectively (r2 = 0.05 alert, r2 = 0.02 anesthetized).
Fig 3.
Fano factors show significant tuning to motion direction in the alert state.
Fano factor across stimulus directions in example neurons from (A) alert and (B) anesthetized recordings in MT. Black dots indicate Fano factor by direction. Blue and orange traces show Fano factor values smoothed by a 30° moving window for the alert and anesthetized states, respectively. Red dashed lines indicate FF = 1, as expected for Poisson firing. (C) and (D) Population FF tuning curves in each behavioral state. (C) Gray traces show the Fano factors versus stimulus direction for all neurons in the alert experiments. Stimulus directions are aligned such that the preferred stimulus direction of each neuron is 0°. The median Fano factor across the population (green) is significantly tuned for the preferred direction. The gray dashed line indicates the median Fano factor in response to a stationary, or ‘null’, stimulus. Red dashed line is at FF = 1 as predicted for a Poisson process. (D) Same as (C) but for the anesthetized data. The median Fano factor is not tuned for stimulus direction. (E) Histogram distributions of Fano factor tuning indices (FFTI) from the alert (blue) and anesthetized (orange) experiments. Orange and blue traces are Gaussian best fit. The cartoon at top right shows how FFTI is calculated using the median trace from (C).
Fig 4.
Mean-matched Fano factors preserve variability tuning.
(A) Histograms of spike counts by neuron for a given stimulus direction (left: −90°; center: preferred direction; right: + 90°) for alert (blue, throughout) and anesthetized (orange, throughout) recordings. The overlapping area is shown in gray. (B) Sample mean-matched Fano factors, with spike count distributions corresponding to the gray histograms in (A). Each circle is a sample mean. Dashed traces indicate the mean Fano factor across directions. Solid traces indicate the mean Fano factor across bootstrapped samples. (C) Fano factor tuning index (FFTI) of bootstrapped resamples for alert (FFTI = 0.143, s.d. = 0.106) and anesthetized states (FFTI = −0.020, s.d. = 0.057). (D) Distributions of FFTI for mean-matched data samples. Solid traces indicate a best-fit Gaussian curve.
Fig 5.
Behavioral state affects the spike-count autocorrelation function.
Traces indicate the average temporal autocorrelation for spike count fluctuations in alert (blue) and anesthetized (orange) conditions. To calculate autocorrelation, spikes are binned in 2 ms windows and smoothed over a running average of 5 bins. Autocorrelation is normalized by variance and averaged over the population. The time course of autocorrelation is longer under anesthesia, decaying with an exponential time constant of 88 ms compared to 29 ms in the alert state.
Fig 6.
A single parameter, gain variance, can account for the observed changes in Fano factor tuning with behavioral state.
(A-D) Model fitting captures differences in Fano factor tuning through changes in gain variance. The model is fit with the optimal α and var(g) for each population. (A) The distribution of FFTI for alert (blue, throughout) and anesthetized (orange, throughout) in the observed population (dashed trace) and the model values (solid trace). Inset: Sample tuning curves for the alert and anesthetized experiments. (B,C) The variance model predicts Fano factor direction tuning for the alert (B) and anesthetized (C) experiments. Compare model results to observed Fano factors in Fig 3C and 3D. Parameters are fit to match distribution of FFTI, but reasonably reproduce Fano factor tuning as well. (D) Sample Fano factor tunings generated by the best-fit models shown in (A-C). (E) Distribution of FFTI for alternate model fitting in which the spike count used for each neuron was replaced by the average tuning curve over all neurons recorded in each experimental condition. The α parameter is identical for all neurons and was chosen to minimize mean-squared error in the Kolmogorov-Smirnov distance between the observed and model FFTI distributions. The gain variance was fit separately for each neuron to match its observed FFTI (fit to minimize the mean-squared error). Inset: Mean tuning curves for the alert and anesthetized experiments. (F) The cumulative distribution of gain variance parameters from the model fit in (E), showing larger gain variance values in the anesthetized model.
Fig 7.
Fano factor tuning and heterogeneity both contribute to lower discriminability thresholds in MT populations.
(A) Model population with 20 homogeneous tuning curves. (B) Cramer-Rao bound in homogeneous population models of 200 neurons over time with short-range correlations (cmax = 0.1, 〈c〉 = 0.0438) and information-limiting correlations (ϵ = 4). Tuning curves are fit to the average cumulative response from motion onset up to time T. Black traces show performance of models with varying stimulus-dependent variance. The solid trace is FFTI > 0, the dashed trace is FFTI = 0, and the dotted trace is FFTI < 0. The dashed gray line indicates the stimulus discriminability threshold for smooth pursuit behavior in macaques 125 ms after pursuit initiation. The red trace indicates the bound on discriminability at 2° set by the information-limiting correlations. (C) Same as in (B) but for neuronal populations of different sizes with first-order statistics matched to the average response at time 250 ms after motion onset. (D) Sample population of 20 heterogeneous tuning curves drawn from measured tuning curves in recorded neurons. (E,F) Same as in (B,C) but for heterogeneous populations. The shaded areas show the standard deviation of the Cramer-Rao bound.