Abstract

Neurons in macaque cortical area MSTd are driven by visual motion and eye movement related signals. This multimodal characteristic makes MSTd an ideal system for studying the dependence of neuronal activity on different variables. Here, we analyzed the temporal structure of spiking patterns during visual motion stimulation using 2 distinct behavioral paradigms: fixation (FIX) and optokinetic response. For the FIX condition, inter- and intra-trial variability of spiking activity decreased with increasing stimulus strength, complying with a recent neurophysiological study reporting stimulus-related decline of neuronal variability. In contrast, for the optokinetic condition variability increased together with increasing eye velocity while retinal image velocity remained low. Analysis of stimulus signal variability revealed a correlation between the normalized variance of image velocity and neuronal variability, but no correlation with normalized eye velocity variance. We further show that the observed difference in neuronal variability allows classifying spike trains according to the paradigm used, even when mean firing rates (FRs) were similar. The stimulus-dependence of neuronal variability may result from the local network structure and/or the variability characteristics of the input signals, but may also reflect additional timing-based mechanisms independent of the neuron's mean FR and related to the modality driving the neuron.

Introduction

A great amount of knowledge about neuronal information processing has been gained by relating the mean neuronal firing rate (FR) to any variables supposed to be coded in the analyzed area. Besides the mean rate, however, there are more features of neural responses that may depend systematically on certain stimuli. One of these is the regularity of neuronal activity.

Neuronal variability can be measured in various ways. The Fano factor (FF), for instance, measures the variability of the spike count across trials that were recorded during identical conditions (Fano 1947). Other measures such as the coefficient of variation (CV) analyzes the variability of the inter-spike interval (ISI) within a single trial, which may be independent of the across trial variability (Cox and Lewis 1966).

The functional meaning of changing neuronal variability has been related to a broad range of factors, as, for instance, attention (Mitchell et al. 2007) or motor-preparation (Steinmetz and Moore 2010). In a recent meta-study, Churchland et al. (2010) examined the trial-to-trial variability in various cortical areas. Since each area needs appropriate stimulation to increase spiking activity, a variety of paradigms was used. As a common principle, the authors found that trial-to-trial variability in general declined during stimulation in comparison to pre-stimulus conditions.

Previous studies have analyzed neuronal variability dependence on a single stimulus variable only. However, many areas of the brain do not just code for a single stimulus variable and neuronal variability may thus depend on the stimulus dimension. The medial superior temporal (MST) cortex  is such a multimodal area: it is involved in processing visual motion stimuli, but also receives extra-retinal input about eye movements (Komatsu and Wurtz 1988; Newsome et al. 1988). Neurons in the dorsal subpart (MSTd) have large receptive fields and respond to rotating, expanding and planar large-field (LF) motion (Duffy and Wurtz 1991). Many neurons show extra-retinal, eye movement related activity during smooth pursuit eye movements (Newsome et al. 1988; Ono and Mustari 2006; Ono et al. 2010). Also during LF stimulation, neuronal response in MSTd neurons has been shown to be modulated by oculomotor signals (Bradley et al. 1996; Page and Duffy 1999; Ben Hamed et al. 2003; Bremmer et al. 2010; Brostek et al. 2011).

This combination of both visual motion and eye movement related activity makes MSTd an ideal system for analyzing neuronal activity in dependence on different stimulus dimensions. In the following, we measured the inter- and intra-trial variability of the spiking activity in MSTd neurons using 2 different paradigms and related it to the visual and oculomotor signals. We found that both variables, image and eye velocity, differentially affected neuronal variability. Spiking irregularity decreased when image velocity increased and eye velocity was kept low, but increased with increasing eye velocity and low image velocity.

Methods

Data were recorded in cortical area MSTd from 2 behaving monkeys (Macaca mulatta, 5–7 kg). The experiments were performed at the Yerkes National Primate Research Center (Atlanta, GA, United States of America) in compliance with National Institutes of Health Guide for the Care and Use of Laboratory Animals. The protocols were reviewed and approved by the Institutional Animal Care and Use Committee at Emory University. For verifying MSTd location we used functional, histological, and magnetic resonance imaging criteria. During the experiments, monkeys were seated in a primate chair with their head fixed in the horizontal stereotaxic plane in a completely dark room, except during visual stimulation (see below). Only those neurons that showed significant response to large moving visual stimuli were analyzed. Visual receptive fields of neurons were mapped by moving a probe stimulus at regularly spaced eccentricities across the visual field while the monkey fixated a stationary target spot. Most receptive fields were large (>30°) and had their center in the contralateral hemifield in accordance with known MSTd properties. Some of the data reported here were also used for other studies (Ono et al. 2010; Brostek et al. 2011). All experimental procedures are explained in detail in Ono et al. (2010).

Visual Stimuli

Visual LF stimuli (35° × 35° random dot patterns) were rear projected on a tangent screen 57 cm distant. Data were acquired only for those movement directions that were previously identified to be the preferred direction of the neuron, that is the direction which elicits maximal spiking activity for a moving LF stimulus in the analyzed neuron. Two kinds of paradigms were tested: Between trials there was a 1200 ms long period during which the monkey fixated the laser spot with the LF stimulus still visible but not moving (zero velocity condition).

  1. Fixation (FIX) with visual stimulation: The monkey fixated a small target spot located at the center of the screen. After some random time the LF stimulus started to move with constant velocity (5, 10, 15, 20, or 30°/s) in the neuron's preferred direction for a period between 1000 and 1800 ms. During presentation of the visual motion the monkey still fixated the laser spot, though this LF stimulation is known to produce a slight (<2°/s) optokinetic nystagmus (Komatsu and Wurtz 1988).

  2. Optokinetic response (OKR): The stimulus for the OKR was the same as in the FIX task, with the difference that the laser spot was turned off when the LF stimulus began to move. In this case, the monkey's eye movements followed the motion.

Each neuron was tested with both paradigms at different velocities. One dataset comprised all trials tested for 1 specific neuron, paradigm, and velocity. In total, 325 datasets were recorded (on average 5.8 per neuron). The mean number of trials per dataset was 31 ± 10 (mean ± std. dev.).

FIX datasets with mean eye velocity greater than 5°/s (2.5% of all FIX datasets) and OKR datasets with retinal image velocity greater than 5°/s (5.8% of all OKR datasets) were discarded for analysis. In this way, we could ensure that in FIX datasets eye velocity was close to zero, and in OKR datasets retinal image velocity was close to zero. Both variables, which are otherwise coupled by stimulus velocity, could therefore be compared quasi independently of each other.

In some trials, the constant velocity phase of LF motion was interrupted by a short high-frequency perturbation of stimulus velocity (Ono et al. 2010) consisting of 1 sinusoidal cycle (5 Hz, 10°/s amplitude). We included these trials to our analysis, as it did not affect the observed dependence of neuronal variability on image and eye velocity (Supplementary Fig. S1).

Data Collection and Preparation

Action potentials were detected using both a hardware window discriminator (Bak Electronics, MD, United States of America) and template matching algorithm (Alpha-Omega, Israel). Eye movements were recorded with standard electro-magnetic methods using scleral search coils (CNC Engineering, Seattle, WA, United States of America). Eye and target position feedback signals were processed with anti-aliasing filters at 200 Hz using 6-pole Bessel filters (latency 5 ms) before digitization at 1 kHz with 16-bit precision using a CED 1401 hardware interface. The recorded eye position traces were filtered with a Gaussian low-pass (cut-off frequency 30 Hz) and 3-point differentiated to obtain the velocity traces. Saccades were detected and removed from the eye movement traces with an algorithm as described in Ladda et al. (2007). Neuronal response was represented as a FR by convolving spike times with a Gaussian function (σ = 15 ms) and averaging over corresponding trials.

Measures of Neuronal Variability

We used 3 different measures for determining neuronal discharge irregularity:

First: The FF was calculated for time windows of 100 ms length according to 

formula

with E and Var symbolizing mean and variance, respectively, and forumla denoting the spike counts of the forumla trials.

Discharge irregularity tends to decrease with higher FRs due to the refractory period after each spike. To control for a possible effect of variable FRs on the FF, we applied in some analysis the mean-matching algorithm by  Churchland et al. (2010) using the Matlab toolbox provided by the authors (http://www.stanford.edu/~shenoy/GroupCodePacks.htm) with a window size of 50 ms. The algorithm computes the mean spike counts for all datasets. For each analyzed time point the algorithm determines a common distribution of mean spike counts across all datasets. The analyzed distribution of datasets for each time is then matched to this common distribution by randomly discarding datasets. The FF is computed for the remaining distribution of datasets by calculating the slope of the regression relating the variance to the mean of the spike counts of the analyzed datasets. This process is repeated 50 times, and the results are averaged to control for variation due to the randomness of the procedure. As the size of the analyzed distribution of datasets decreases with greater number of analyzed time points, we constrained this analysis to 100 ms steps. Due to the great difference in the FR before and during stimulation, our data had a relatively heterogeneous structure. As a result, only 13 and 18% of datasets were preserved in the mean-matched distribution for the FIX and OKR paradigms, respectively. Nevertheless, the difference between mean matched and raw FF, averaged over all datasets, was marginal (see Results).

Second: The “variance of the conditional expectation” (VarCE) is another measure of trial-to-trial variability that also intends the suppression of possible effects due to differing mean FRs. This method has been proposed by Churchland et al. (2011). According to this method, the total measured variance is divided into 2 components: the “point process variance”, which is produced by a renewal process with a given rate, and the residual VarCE. Assuming renewal process characteristics (see Results), VarCE can be estimated as 

formula

with forumla being a quantity characterizing the underlying point process. For each neuron, forumla was obtained by the minimum value of the measured FF, which was typically shortly after stimulus motion onset (see Fig. 2).

Third: The CV2 was determined as 

formula

with forumla denoting the ISIs of each analyzed spike train.

Metric-Space Analysis

For an information-theoretic analysis of our data, we used the metric-space approach developed by Victor and Purpura (1996, 1997). This method determines the extent to which experimentally measured neural responses cluster in a systematic fashion using an information-theoretic measure. The measure of clustering indicates the extent to which this candidate distance is sensitive to features of spike trains that convey stimulus-specific information. The formal structure of this approach is an embedding of spike trains into a ‘‘metric space’’. These spaces have well-defined distances but do not require the assumption of a linear structure. To measure the difference between 2 spike trains in terms of the arrangement of spikes in time, we used the so-called Dspike metric here. The analysis is performed for different a priori defined temporal precision values. These determine the maximal distance of how far the spikes in 1 trial can be displaced to match the temporal arrangement of spikes in another trial. Each displacement of a spike is accounted by a ‘‘cost’’ proportional to the distance. Also the adding or deleting of a spike has a certain ‘‘cost’’.

We applied the algorithm by using a Matlab toolbox (http://neuroanalysis.org) provided by the Weill Medical College of the Cornell University (Ithaca, NY, United States of America). All parameters were set to standard values; the clustering exponent was −2. For the original data, the standard error of transmitted information was estimated using the Jackknife method. Classifying the spike trains into different categories was considered to be feasible, when the transmitted information of the original data exceeded the range of the mean plus 2 standard deviations information of the shuffled data.

Simulated Data

To illustrate the dependence of intra-trial and inter-trial variability on the distribution of ISIs of the underlying spiking process, synthetic spike trains were generated. This was done by sampling ISIs independently and identically distributed from a gamma distribution 

formula

with shape parameter k and scale parameter s. Γ denotes the gamma function. The scale parameter was adjusted to a constant FR of 20 Hz (Maimon and Assad 2009).

Results

We analyzed single-unit recordings of 56 MSTd neurons from 2 monkeys. They were stimulated with a LF random dot pattern moving with different velocities in the preferred direction of each neuron. During this stimulation, the monkeys had to either fixate a small non-moving target spot (FIX) or follow the visual movement by OKR.

FF During FIX and OKR

Figure 1 shows visual and oculomotor variables, FR and FF traces, averaged across all neurons and tested stimulus velocities for both paradigms. To equalize mean FRs of both conditions during the subsequently used testing interval between 300 and 1000 ms after stimulus onset, some datasets were discarded from this analysis. Retinal image velocity is the difference between the velocity of the moving stimulus and eye velocity. In the FIX paradigm, retinal image velocity increased with the onset of stimulus movement and remained constant during the whole trial, whereas eye velocity stayed at a minimal level (A1). For OKR, eye velocity increased gradually until about 300 ms after stimulus onset, whereas image velocity showed an initial peak and remained low after eye velocity reached its constant level (B1). In both paradigms, the averaged FR traces had transient components right after stimulus onset and sustained responses of about 40 Hz (A2, B2). The FF, however, differed remarkably between both paradigms: Both traces had values between 2.2–3 (FIX) and 1.8–2.4 (OKR) before stimulus motion onset, and a significant decrease to a value of 0.7 for FIX and 0.9 for OKR right after stimulus onset. For the FIX paradigm the FF retained this low level until the end of the trial (A3). For OKR, the FF did not sustain the low level but increased again to a level around 2 after 300 ms (B3). Thus, despite the ongoing stimulation, the trial-by-trial variability was comparable to the pre-stimulus variability.

Figure 1.

Mean traces of image and eye velocity, firing rate (FR), and Fano factor (FF) of the analyzed MSTd population for fixation (FIX) and optokinetic response (OKR) during large-field visual stimulation. A fraction of datasets (FIX: 20%; OKR: 15%) was discarded to match the averaged firing rates of both conditions during the testing interval. Data were aligned to the onset of stimulus movement (0 ms) in the preferred direction of each neuron. (A1) Desaccaded eye and retinal image velocity, averaged across all tested velocities (5, 10, 15, 20, and 30°/s) and 56 neurons, during FIX. (A2) Averaged firing rate. Dotted gray line marks the average firing rate (40 Hz) during the testing interval. (A3) Raw and mean-matched FF. Latter is constrained to 100 ms steps (see Methods). (B1–B3) show the corresponding traces for OKR. Flanking traces mark standard errors. The light gray area marks the testing interval between 300 and 1000 ms after stimulus onset, which was used for subsequent analysis.

Figure 1.

Mean traces of image and eye velocity, firing rate (FR), and Fano factor (FF) of the analyzed MSTd population for fixation (FIX) and optokinetic response (OKR) during large-field visual stimulation. A fraction of datasets (FIX: 20%; OKR: 15%) was discarded to match the averaged firing rates of both conditions during the testing interval. Data were aligned to the onset of stimulus movement (0 ms) in the preferred direction of each neuron. (A1) Desaccaded eye and retinal image velocity, averaged across all tested velocities (5, 10, 15, 20, and 30°/s) and 56 neurons, during FIX. (A2) Averaged firing rate. Dotted gray line marks the average firing rate (40 Hz) during the testing interval. (A3) Raw and mean-matched FF. Latter is constrained to 100 ms steps (see Methods). (B1–B3) show the corresponding traces for OKR. Flanking traces mark standard errors. The light gray area marks the testing interval between 300 and 1000 ms after stimulus onset, which was used for subsequent analysis.

To compensate for possible effects of temporally changing FRs, the FF was also determined using the mean-matching algorithm by Churchland et al. (2010). This procedure computes the mean spike counts for all datasets and determines a common distribution of mean spike counts across all time points. The analyzed distribution of datasets is then matched to this common distribution by randomly discarding datasets (see Methods). The raw FF, which was not mean matched but determined from all data, differed only marginally.

FF Dependence on Visual and Oculomotor Variables

Figure 2 shows spike raster plots of an example neuron for 2 different conditions during the testing interval (Fig. 1 light gray area). In this interval, all analyzed variables were almost constant for both paradigms. Whereas for FIX spiking was quite regular, the same neuron showed bursty activity in the OKR paradigm. For further analysis, we determined Pearson's correlation coefficient ρ between retinal image velocity and FF, and eye velocity and FF, respectively. The FIX paradigm with visual stimulation at different stimulus velocities yielded datasets with high image and low eye velocities, whereas the OKR paradigm yielded datasets with different low image and high eye velocity. We determined FF and both variables for each dataset, which comprised all trials, tested for 1 specific neuron, paradigm and velocity, and averaged all measures over the testing interval. The comparison of all datasets from this example neuron indicated negative correlation between FF and image velocity (ρimage vel, FF = − 0.88, P < 0.01) and positive correlation between FF and eye velocity (ρeye vel, FF = 0.85, P < 0.01), as shown in Figure 2C.

Figure 2.

Fano factor (FF) of an example neuron for different image and eye velocities. (A) Eye (black) and image (gray) velocity during the testing interval for FIX with visual stimulation at 20°/s. The corresponding spike raster plot of this dataset shows quite regular activity (FF = 0.9, CV2 = 1.0) (B) Same neuron for OKR with stimulus velocity of 20°/s. In this case, spiking activity was much more irregular (FF = 2.0, CV2 = 1.6) (C) Each dot marks FF and image or eye velocity of one dataset. The 2 example conditions are indicated by letters. All measures were averaged across the testing interval (300–1000 ms after stimulus onset). In this example neuron, FF correlates negatively with image velocity and positively with eye velocity. Linear regression lines were least squares fitted.

Figure 2.

Fano factor (FF) of an example neuron for different image and eye velocities. (A) Eye (black) and image (gray) velocity during the testing interval for FIX with visual stimulation at 20°/s. The corresponding spike raster plot of this dataset shows quite regular activity (FF = 0.9, CV2 = 1.0) (B) Same neuron for OKR with stimulus velocity of 20°/s. In this case, spiking activity was much more irregular (FF = 2.0, CV2 = 1.6) (C) Each dot marks FF and image or eye velocity of one dataset. The 2 example conditions are indicated by letters. All measures were averaged across the testing interval (300–1000 ms after stimulus onset). In this example neuron, FF correlates negatively with image velocity and positively with eye velocity. Linear regression lines were least squares fitted.

The results for all 56 MSTd neurons are shown in Figure 3A. In 48 neurons (86%), the FF correlated negatively with image velocity and positively with eye velocity. Figure 3B shows the mean FF dependence on both variables. In the FIX paradigm, the average FF decreased from 1.5 for small image velocity to a level of about 0.8 during high velocity. For OKR, the FF increased from 1.5 for small eye velocity to 2.1 during high eye velocity. Both changes were statistically significant (linear regression analysis: β = − 0.03, P < 0.01 and β = 0.02, P < 0.01). Note that the change in FF was not task-dependent, as the FF had identical levels at small stimulus velocities for both paradigms. Both findings, decrease of neuronal variability with the visual variable, and increase of neuronal variability with the oculomotor variable, however, only apply for cases in which one of the 2 variables is close to zero. The average FF for all FIX datasets was 1.05 ± 0.43 (mean ± std. dev.), for OKR it was 1.78 ± 0.67. The mean FF, averaged across all datasets, was 1.47 ± 0.69.

Figure 3.

Spiking irregularity decreases with image velocity and increases with eye velocity. (A) Fano factor (FF) correlates negatively with image velocity and positively with eye velocity. For each neuron ρimage vel, FF and ρeye vel, FF were determined as in the example shown in Figure 2C. Gray dots mark neurons in which neither of the correlation coefficients was significant (P > 0.05). (B) FF dependence on retinal image and eye velocity. The datasets were grouped according to their corresponding eye or image velocity. X-axis values denote upper limits, meaning that the value of 10°/s, for instance, comprises all datasets with velocities between 5 and 10°/s. The bin for 25°/s comprises all datasets with velocities greater than 20°/s. During FIX, mean eye velocity was <5°/s in each dataset. For OKR datasets image velocity was <5°/s. (C) The variance of the conditional expectation (VarCE) correlates negatively with image velocity and positively with eye velocity. (D) VarCE for both paradigms grouped into ranges of corresponding eye or retinal image velocities. (E–F) Results for the CV2. FF and VarCE were averaged over the testing interval. CV2, image and eye velocity were averaged across the testing interval and all trials. Vertical lines mark standard errors across corresponding datasets.

Figure 3.

Spiking irregularity decreases with image velocity and increases with eye velocity. (A) Fano factor (FF) correlates negatively with image velocity and positively with eye velocity. For each neuron ρimage vel, FF and ρeye vel, FF were determined as in the example shown in Figure 2C. Gray dots mark neurons in which neither of the correlation coefficients was significant (P > 0.05). (B) FF dependence on retinal image and eye velocity. The datasets were grouped according to their corresponding eye or image velocity. X-axis values denote upper limits, meaning that the value of 10°/s, for instance, comprises all datasets with velocities between 5 and 10°/s. The bin for 25°/s comprises all datasets with velocities greater than 20°/s. During FIX, mean eye velocity was <5°/s in each dataset. For OKR datasets image velocity was <5°/s. (C) The variance of the conditional expectation (VarCE) correlates negatively with image velocity and positively with eye velocity. (D) VarCE for both paradigms grouped into ranges of corresponding eye or retinal image velocities. (E–F) Results for the CV2. FF and VarCE were averaged over the testing interval. CV2, image and eye velocity were averaged across the testing interval and all trials. Vertical lines mark standard errors across corresponding datasets.

The dependency of the mean FR on image and eye velocity is shown in Figure 4. In contrast to neuronal variability, mean FR increased with increasing stimulus velocities for both paradigms (see also Brostek et al. 2011). Linear correlation analysis between FR and FF revealed slight negative correlation (ρ = − 0.17, P = 0.04) for FIX, and slight positive correlation (ρ = 0.16, P = 0.03) for OKR. We will address the apparent unexpected relationship between FF and FR in the Discussion.

Figure 4.

The firing rate (FR) increases with image and eye velocity. For each condition, FR was averaged over all trials and the testing interval. The datasets were grouped as in Figure 3. FR, image and eye velocity were averaged across the testing interval and all trials. Vertical lines mark standard errors.

Figure 4.

The firing rate (FR) increases with image and eye velocity. For each condition, FR was averaged over all trials and the testing interval. The datasets were grouped as in Figure 3. FR, image and eye velocity were averaged across the testing interval and all trials. Vertical lines mark standard errors.

Variance of the Conditional Expectation

Similar to the FF, the VarCE (Churchland et al. 2011) measures the trial-to-trial variability of spike counts. It reflects the residual variability after subtracting the component that would be produced by some point process with given mean FR. As with the mean-matching algorithm (see Fig. 1), possible effects due to differing mean FRs are compensated. This technique, however, does not discard datasets from analysis. Figure 3C and D shows the dependence between VarCE and the visual and eye movement variables. In 43 neurons (77%), VarCE correlated negatively with image velocity and positively with eye velocity. For FIX, the mean VarCE showed significant decrease from a level of about 3.9 for small image velocities, to 1.7 for high image velocities (linear regression analysis: β = − 0.11, P < 0.05). For OKR, the mean VarCE increased from 3.9 to a value of 7.0 for high eye velocities (β = 0.10, P = 0.08). The average VarCE for FIX datasets was 2.32 ± 2.91, for OKR it was 4.75 ± 4.81. The mean VarCE, averaged across all datasets, was 3.71 ± 4.27.

Coefficient of Variation

The CV measures the variability of ISIs within a single trial. For a stationary renewal process, in which ISIs are assumed to be independent and identically distributed, it holds that FF = CV2 for the limit of long observations (Cox 1962; Cox and Lewis 1966). In the following, we used the CV2 to allow the evaluation of the renewal process hypothesis. In each dataset, CV2 was determined for the testing interval and then averaged over all trials. The dependence between CV2 and both variables is shown in Figure 3E and F. In 47 neurons (84%) CV2 correlated negatively with image velocity and positively with eye velocity. As with FF, the mean CV2 decreased significantly (linear regression analysis: β = − 0.04, P < 0.01) with retinal image velocity. In the OKR paradigm, CV2 showed increasing tendency (β = 0.02, P = 0.09) with eye velocity. This means that spiking irregularity did not only change in dependence on visual and oculomotor variables across the trials, as indicated by FF. Also within a single trial, ISIs tended to be more regular with increasing image velocity, and more irregular with an increase in eye velocity, as indicated by CV2. The average CV2 for FIX datasets was 1.12 ± 0.49, for OKR it was 1.93 ± 1.05. The mean CV2 across all datasets was 1.58 ± 0.93.

Dependencies between the analyzed measures are shown in Figure 5. There was positive correlation between all 3 measures. In particular, the correlation between FF and CV2 was quite strong. Regression analysis using a linear, zero offset model, yielded CV2 = 1.06 FF, which is in good agreement with the assumption of renewal process characteristic.

Figure 5.

Correlations between FF, VarCE, and CV2, plotted in log–log coordinates. Each dot marks one dataset. All measures were averaged as before. (A) There is a strong positive correlation between FF and CV2 (ρFF, CV2 = 0.79, P < 0.01). (B and C) Also VarCE and FF, and CV2 and VarCE, are positively correlated (ρVarCE, FF = 0.70, P < 0.01; ρCV2, VarCE = 0.53, P < 0.01).

Figure 5.

Correlations between FF, VarCE, and CV2, plotted in log–log coordinates. Each dot marks one dataset. All measures were averaged as before. (A) There is a strong positive correlation between FF and CV2 (ρFF, CV2 = 0.79, P < 0.01). (B and C) Also VarCE and FF, and CV2 and VarCE, are positively correlated (ρVarCE, FF = 0.70, P < 0.01; ρCV2, VarCE = 0.53, P < 0.01).

Influence of Eye Movements

Could the observed dependency of spiking irregularity on image and eye velocity be explained by differences in the variability of image and eye velocity? To allow a comparison with the measures used to evaluate neuronal variability, we analyzed the ‘‘normalized variance’’ of image and eye velocity, which is the variance across or within trials divided by the mean signal. As shown in Figure 6A, the normalized variance decreased with image velocity during FIX (across/within: β = − 0.02, P < 0.001), but did not change with eye velocity during OKR (across: β = − 0.003, P = 0.56; within: β = 0.005, P = 0.17). Accordingly, the normalized variance was positively correlated with FF during FIX (Fig. 6B; across: ρ = 0.32, P < 0.001; within: ρ = 0.39, P < 0.01). For OKR both measures were unrelated (across: ρ = 0.16, P = 0.12; within: ρ = 0.09, P = 0.24). Also with CV2 there was positive correlation for FIX (across: ρ = 0.24, P < 0.001; within: ρ = 0.30, P < 0.01), and no correlation for OKR (across: ρ = − 0.06, P = 0.25; within: ρ = 0.02, P = 0.45).

Figure 6.

Relation between neuronal variability and variance in eye movements. (A) The normalized variance of image velocity decreases with image velocity, the normalized variance of eye velocity is independent of eye velocity. For each dataset, the variance was determined across all trials (black curve) or within each trial (gray curve), then divided by the mean, and finally averaged over the testing interval. Both curves were slightly moved for better visual separation. The datasets were grouped according to the paradigm and the corresponding image or eye velocity. (B) Correlation between the normalized variance across trials (black dots) or within trials (gray dots) and FF. Each dot marks one dataset. Some outliers fall outside the shown range. For FIX, there is a weak correlation, which is not present during OKR. (C) Distribution of datasets, in which normalized variance of image and eye velocity correlated with CV2within the datasets. Normalized variance and CV2 were determined in every trial; then the correlation coefficient ρvar/mean, CV2 was calculated for each dataset. Black bars show datasets with significant (P < 0.05) correlation. (D) Number of saccades per trial. For each dataset the number of saccades during the testing interval was determined and averaged over all trials. Vertical lines mark standard errors.

Figure 6.

Relation between neuronal variability and variance in eye movements. (A) The normalized variance of image velocity decreases with image velocity, the normalized variance of eye velocity is independent of eye velocity. For each dataset, the variance was determined across all trials (black curve) or within each trial (gray curve), then divided by the mean, and finally averaged over the testing interval. Both curves were slightly moved for better visual separation. The datasets were grouped according to the paradigm and the corresponding image or eye velocity. (B) Correlation between the normalized variance across trials (black dots) or within trials (gray dots) and FF. Each dot marks one dataset. Some outliers fall outside the shown range. For FIX, there is a weak correlation, which is not present during OKR. (C) Distribution of datasets, in which normalized variance of image and eye velocity correlated with CV2within the datasets. Normalized variance and CV2 were determined in every trial; then the correlation coefficient ρvar/mean, CV2 was calculated for each dataset. Black bars show datasets with significant (P < 0.05) correlation. (D) Number of saccades per trial. For each dataset the number of saccades during the testing interval was determined and averaged over all trials. Vertical lines mark standard errors.

Until now, all measures were averaged across trials and time. In the following, we analyzed whether there also exists correlation within the datasets. In Figure 6C, the normalized variance and CV2 were determined for each trial separately and then compared within every dataset. For the FIX condition, 25% of the datasets showed significant correlation of both measures within the datasets (mean ρvar/mean, CV2 = 0.18 ± 0.39), corroborating the previous results. For OKR, only few datasets showed correlation, with an average ρvar/mean, CV2 = 0.04 ± 0.35. The difference between both conditions was statistically significant (2-sample T-test: P < 0.01).

Another eye movement related influence could be saccades, since it has been reported that spiking activity is suppressed in many medial temporal (MT) and MST neurons during these rapid eye movements (Thiele et al. 2002). Such induced periods of silence might increase the regularity of spiking, similar to the refractory period. To analyze whether our findings might be affected by saccadic suppression of neuronal firing, we determined the number of saccades per trial for both paradigms (Fig. 6D). With an average of 1.6 saccades per trial, it seems unlikely that these rapid eye movements influenced neuronal variability. Furthermore, the difference between both paradigms was rather small. For FIX, there was an increase observable with image velocity. In the OKR paradigm there was only a slight change with eye velocity. Both changes were statistically not significant (P = 0.69 and 0.53, 1-way ANOVA). Linear correlation analysis between the number of saccades per trial and FF yielded no correlation for FIX (ρ = 0.01, P = 0.22) and OKR (ρ = − 0.18, P = 0.60). The removal of saccade period data from the neuronal recordings increased neuronal variability slightly but had no influence on the observed relation to image and eye velocity (Supplementary Fig. S2).

In summary, the observed decline of spiking irregularity during the FIX condition may be related to the decline of image velocity variance. The increase of neuronal variability during the OKR condition seemed to be unrelated to the eye movements themselves.

Metric-Space Analysis

The mean FR of MSTd neurons increases with both, retinal image and eye velocity (see Fig. 4). Hence, the information contained in the FR alone does not allow distinguishing between a neuron being driven by image or eye velocity. On the other hand, we could show that the neuronal variability decreases with image velocity and increases with eye velocity. Might this differential behavior in spike timing allow the separation of the 2 signals?

To further examine this question, we performed a classification analysis of our data using the metric-space approach by Victor and Purpura (1996, 1997). This analysis determines to what extent pairs of responses to the same stimulus tend to be closer to each other than pairs of responses to different stimuli. Spike trains are considered similar if they have approximately the same number of spikes, and these spikes occur at approximately the same times, that is within some a priori defined temporal precision. The extent to which experimentally measured neuronal responses cluster in a systematic fashion is determined using an information-theoretic measure. Perfect clustering into, for example, 2 categories corresponds to a maximal value of 1 bit. For control, transmitted information was also determined for surrogate datasets, in which the spike trains were randomly shuffled from both conditions. This shows whether there is sufficient data to carry out a valid analysis. If the amount of data is sufficient, then the “shuffled” curve is well separated from the original data curve, and the amount of information in the shuffled curve should be near zero.

Figure 7 shows the results for 2 example neurons, where the mean FR was similar in both conditions. The neuron shown in the left column exhibited highly distinctive differences in spiking irregularity during FIX and OKR. Maximal transmitted information of 1 bit reflects a perfect distinction between the responses for both conditions. Perfect classification was achieved for values of temporal precision in the order of 4 ms. In the case of the neuron shown on the right column, the distinction between FIX and OKR was not as pronounced as for the other example, reaching maximal transmitted information of 0.5 bit. Good clustering was achieved for a broad range of temporal precision values between 8 and 60 ms. In both examples, the original data curves were well separated from the shuffled curves. It is important to note that the estimation of transmitted information from limited samples introduces several difficulties. The metric-space method tends to underestimate the total information that is present, since only a few stereotyped hypotheses for neural codes are considered. On the other hand, the estimated information will be spuriously high because of chance proximities between the few examples of observed responses, if the number of presentations of each stimulus class is small. The large error bars in Figure 7B and D reflect these estimation problems.

Figure 7.

Metric-space analysis. (A) Spike raster plots showing regular activity for FIX (FR = 89 Hz, FF = 0.69, CV2 = 0.67) and irregular activity for OKR (FR = 79 Hz, FF = 2.58, CV2 = 2.87) during the testing interval for one example neuron. Stimulus velocity was 20°/s in both conditions. (B) Transmitted information of the original clustered data (black) and for shuffled data (gray) for different values of temporal precision. Vertical lines mark standard error for original data and double standard deviation for shuffled data. (C and D) Spike raster plots and transmitted information of a second example neuron showing regular activity for FIX (FR = 92 Hz, FF = 0.59, CV2 = 0.67) and irregular activity for OKR (FR = 106 Hz, FF = 1.70, CV2 = 1.14) during the testing interval. Here, stimulus velocity was 10°/s for both conditions. (E) Transmitted information increases with stimulus velocity. For each dataset pair maximal transmitted information was determined as in the examples above. Vertical lines mark standard errors.

Figure 7.

Metric-space analysis. (A) Spike raster plots showing regular activity for FIX (FR = 89 Hz, FF = 0.69, CV2 = 0.67) and irregular activity for OKR (FR = 79 Hz, FF = 2.58, CV2 = 2.87) during the testing interval for one example neuron. Stimulus velocity was 20°/s in both conditions. (B) Transmitted information of the original clustered data (black) and for shuffled data (gray) for different values of temporal precision. Vertical lines mark standard error for original data and double standard deviation for shuffled data. (C and D) Spike raster plots and transmitted information of a second example neuron showing regular activity for FIX (FR = 92 Hz, FF = 0.59, CV2 = 0.67) and irregular activity for OKR (FR = 106 Hz, FF = 1.70, CV2 = 1.14) during the testing interval. Here, stimulus velocity was 10°/s for both conditions. (E) Transmitted information increases with stimulus velocity. For each dataset pair maximal transmitted information was determined as in the examples above. Vertical lines mark standard errors.

For the 56 neurons analyzed here, there were 122 pairs of FIX and OKR datasets recorded using the same stimulus velocity. In 120 (98%) dataset pairs it was possible to discriminate between FIX and OKR spike trains using the metric-space criterion. The average transmitted information for all dataset pairs was 0.61 ± 0.27 bit. Figure 7E shows that transmitted information increased with stimulus velocity. This result reflects the increasing differences in neuronal variability between both conditions with increasing stimulus velocity. For a stimulus velocity of 5°/s there was almost no difference in spiking irregularity between both conditions. Hence, classifying the spike trains into both categories was difficult. For 30°/s, on the other hand, the divergence in spiking irregularity was maximal and spike trains could be assigned almost perfectly to each category by their temporal spiking patterns.

Discussion

Our analysis of spiking irregularity in MSTd neurons revealed 5 major features. First, responses to LF visual stimulation do not only reflect external visual stimulation but are also modulated by eye movement signals. Second, also in MSTd the trial-to-trial variability of neuronal activity is quenched by stimulus onset. However, the change in variability of MSTd neuronal activity was not just related to stimulation, as proposed by Churchland et al. (2010). There was a sustained low level of variability during FIX, but for the OKR paradigm only a transient decline in FF was observable. Third, the relation between spiking irregularity and the 2 stimulation variables, image and eye velocity, was opposite. Both variables, which were uncoupled by using 2 orthogonal paradigms, affected the intra- and inter-trial variability of neuronal activity. At small stimulus velocities neuronal variability was similar for both paradigms, meaning that the change in variability was not task-dependent. All 3 measures analyzed here, FF, VarCE, and CV2 were negatively correlated with retinal image velocity and positively correlated with eye velocity. Fourth, the decline of neuronal variability during FIX is accompanied by a decline of the normalized variance of image velocity. The increase during OKR, however, seems to be independent of the normalized eye velocity variance. Finally, we could show that the differential behavior in neuronal variability allows discriminating which of the 2 variables, image or eye velocity, has driven neuronal activity.

Previous Measurements of Spiking Irregularity

Prior studies examined spiking irregularity in MST and neighboring MT cortex. It is, nevertheless, difficult to compare their results, as stimuli and paradigms were very different. Also, previous studies did not differentiate between changing stimulus conditions. A number of studies agree in mean FF values between 1.0 and 1.4 for paradigms as different as pursuit of a moving dot (MST, Maimon and Assad 2009), FIX of a target during whole body rotation (MSTd, Takahashi et al. 2007), FIX during visual stimulation (MT, Buracas et al. 1998), or a depth discrimination task (MT, Uka and DeAngelis 2003). The mean FF of 1.47 in our data is in good agreement with these previous findings.

Churchland et al. (2010) analyzed FF time traces in MT neurons during FIX with visual stimulation and found levels around 1.8 before stimulus onset and a sustained decline to about 1.4 during visual motion. This complies qualitatively with the results of our FIX paradigm, although we measured an even larger decline in FF (2–3 to 0.7) in our MSTd data. Some previous works found a general tendency for cells in motor cortex to fire more regularly than in visual areas (Maimon and Assad 2009; Shinomoto et al. 2009). Our results seem to contradict this principle, as in our data FF decreased with visual input and increased with the oculomotor variable. Further investigation of this aspect, however, will require data from far more areas.

Werner and Mountcastle (1963) observed in thalamic neurons a decline in CV2 from 0.9 during spontaneous activity to 0.3 during peripheral stimulation, confirming the stimulus dependence of spiking irregularity. In MT neurons CV2 values of about 1 were found (Softky and Koch 1993; Shadlen and Newsome 1998). In these studies, the paradigms consisted of a visual motion coherence discrimination task, during which the monkeys had to fixate a target spot. The mean CV2 of 1.12 during FIX for our MSTd data is in good agreement with these previous findings.

Relation Between Spiking Irregularity and FR

Due to refractory periods of up to 5 ms between each spike, neuronal activity tends to become more regular with higher FR (Berry and Meister 1998). Our observation of a weak, but significant, positive correlation between FF and FR in the OKR paradigm may exemplify an exception to the usually observed decrease in neuronal variability with increasing FR. A similar case was reported by Churchland et al. (2011), who observed parallel increase of variability and FR in LIP neurons. Also in pyramidal tract neurons spiking irregularity has been reported to increase during periods of high FR (Davies et al. 2006). In various other cortical areas, including MT, neurons were found where the FF changed notably during stimulation while the mean FR stayed constant (Churchland et al. 2010). Mochol et al. (2010) analyzed neurons in the cat's superior colliculus during visual stimulation. Interestingly, they found that for cells preferring low velocity, FR and FF were positively correlated, whereas for cells preferring high velocity the correlation was negative.

Possible Causes for Changing Neuronal Variability

A decline of neuronal variability after stimulus onset, which has been observed in a number of cortical regions, can be explained by certain topological structures of the underlying neuronal network. The stimulus-driven suppression of chaotic, spontaneous activity is a general feature of recurrent networks, a kind of structure presumed to be found in various cortical areas. The decline in variability depends on stimulus frequency and amplitude (Rajan et al. 2010). Our finding of decreasing spiking irregularity with increasing image velocity might be explained by the presence of recurrent circuitry in area MSTd.

Nevertheless, our observation may also be explained by another, probably more obvious, hypothesis. We could show that the normalized variance of image velocity decreases with increasing stimulus strength. The increase in regularity of spiking activity might simply reflect this reduction of the stimulus signal variability. This, however, requires that neuronal activity is able to capture high-frequency fluctuations in the stimulus signal. Most MSTd neurons fulfill this requirement during visual LF stimulation (Ono et al. 2010). The observed relation between the variability of sensory input and neuronal activity might also be important for the interpretation of earlier findings, which often were explained by an underlying recurrent network structure. Nevertheless, both hypotheses are not contradicting each other and might also coexist.

Our second finding of an increase in neuronal variability during the OKR condition remains unexplained by both hypotheses. The normalized variance of eye velocity was neither related to stimulus strength, nor neuronal variability. Also a stimulus-dependent combination of suppression and enhancement of spontaneous activity cannot be implemented by a simple recurrent network structure. A network topology that might explain this finding would need to be asymmetrical and process both stimuli differently.

Alternatively, the opposite behavior for image and eye velocity could also result from fundamental differences in the properties of the 2 signals that form visual and oculomotor input to MSTd. It is assumed that the retinal image velocity signal is projected through connections from visual area MT into MSTd (Tusa and Ungerleider 1988). In MT neurons spiking irregularity declines with visual motion stimulation (Churchland et al. 2010), similar to our observations in MSTd. However, the source of the oculomotor signal is still disputed. Analysis of neuronal latency has shown that MSTd neurons usually start firing before the onset of OKR eye movements (Kawano et al. 1994; Brostek et al. 2011). This argues for an internally generated efference copy, rather than sensory origin of the eye velocity signal. One possibility is that thalamic projections (Tanaka 2005) directly convey extra-retinal information to MSTd and that these signals already carry the irregularity. Whereas for a long time it was assumed that MT does not receive extra-retinal input (Newsome et al. 1988), a recent work found that neurons in this area use eye movement signals to code depth-sign from motion parallax (Nadler et al. 2009). Wherever the oculomotor input to MSTd originates from, the regularity properties of this signal remain to be investigated.

Evidence for Temporal Coding?

In many neuronal systems, it could be shown that aside from mean FR the temporal pattern of spiking activity may also carry important information (MacKay and McCulloch 1952; Richmond et al. 1987; Softky 1995; Buracas and Albright 1999; Rieke et al. 1999; Singer 1999). For instance, in auditory neurons the mean FR represents some combination of amplitude and frequency of a tone. At the same time, there is the tendency for ISIs to cluster around integer multiples of the stimulus period, allowing the separation of frequency and amplitude information (Evans 1982). Also in cortical areas spiking irregularity has been used as an evidence to support the temporal coding hypotheses (Softky and Koch 1993; Stein et al. 2005).

In MSTd neurons the mean FR, which is the reciprocal of the mean ISI, codes some non-linear combination of visual and eye movement related signals (Ben Hamed et al. 2003; Brostek et al. 2011). At the same time, the variance of the ISI decreases with visual and increases with oculomotor stimulation. As we could show, this independent temporal code may allow the separation of the 2 signals, similar to phase locking in auditory neurons.

In a renewal process ISIs are assumed to be independent and identically distributed (Cox 1962). The approximate one-to-one relation between FF and CV2 observed in our data argues for the renewal assumption. Both across-trial and within-trial variability are determined by the distribution of ISIs of the corresponding renewal process, as schematically illustrated in Figure 8. The gamma distribution is an appropriate approximation for the distribution of ISIs in most neuronal systems (Stein 1965). A change in spiking irregularity is associated with a modification of the ISI distribution. This again may result from changing membrane properties in single neurons, circuit properties of networks of neurons, or a combination of both. Miura et al. (2007), for instance, proposed a network architecture, where the FR could be decoupled from the ISI distribution by proper balance of excitatory and inhibitory inputs. However, the questions whether the change of the ISI distribution in dependence of visual and oculomotor input has a functional meaning, and whether the additional information, embodied in changing spiking irregularity, is actually used by MSTd and subsequent areas, or reflects just an epiphenomenon, remain to be solved by future investigations.

Figure 8.

Spiking irregularity changes with inter-spike interval (ISI) distribution. (A) Gamma distributions for 3 different shape parameters k. (B) Simulated spike trains. ISIs were sampled from the 3 different gamma distributions according to a renewal process. The firing rate is 20 Hz in all 3 cases. For k = 0.2, spiking activity is bursty and highly variable from trial to trial (FF = CV2 = 2.3). For k = 1, we get a Poisson process (FF = CV2 = 1). For k = 5 spiking activity is very regular (FF = CV2 = 0.2).

Figure 8.

Spiking irregularity changes with inter-spike interval (ISI) distribution. (A) Gamma distributions for 3 different shape parameters k. (B) Simulated spike trains. ISIs were sampled from the 3 different gamma distributions according to a renewal process. The firing rate is 20 Hz in all 3 cases. For k = 0.2, spiking activity is bursty and highly variable from trial to trial (FF = CV2 = 2.3). For k = 1, we get a Poisson process (FF = CV2 = 1). For k = 5 spiking activity is very regular (FF = CV2 = 0.2).

Supplementary Material

Supplementary material can be found at: http://www.cercor.oxfordjournals.org/.

Funding

This work was supported by the German Federal Ministry of Education and Research Grants 01GQ0440 (BCCN), 01EO0901 (IFB), and National Institutes of Health Grants EY06069, RR000166.

Notes

We are grateful to Seiji Ono for help in collecting the initial neurophysiological data. Furthermore, we thank Thomas Eggert and Paul MacNeilage for helpful discussions. Conflict of Interest: None declared.

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