Separating Spike Count Correlation from Firing Rate Correlation.

Populations of cortical neurons exhibit shared fluctuations in spiking activity over time. When measured for a pair of neurons over multiple repetitions of an identical stimulus, this phenomenon emerges as correlated trial-to-trial response variability via spike count correlation (SCC). However, spike counts can be viewed as noisy versions of firing rates, which can vary from trial to trial. From this perspective, the SCC for a pair of neurons becomes a noisy version of the corresponding firing rate correlation (FRC). Furthermore, the magnitude of the SCC is generally smaller than that of the FRC and is likely to be less sensitive to experimental manipulation. We provide statistical methods for disambiguating time-averaged drive from within-trial noise, thereby separating FRC from SCC. We study these methods to document their reliability, and we apply them to neurons recorded in vivo from area V4 in an alert animal. We show how the various effects we describe are reflected in the data: within-trial effects are largely negligible, while attenuation due to trial-to-trial variation dominates and frequently produces comparisons in SCC that, because of noise, do not accurately reflect those based on the underlying FRC.</p

Stimulus-Driven Population Activity Patterns in Macaque Primary Visual Cortex

Dimensionality reduction has been applied in various brain areas to study the activity of populations of neurons. To interpret the outputs of dimensionality reduction, it is important to first understand its outputs for brain areas for which the relationship between the stimulus and neural response is well characterized. Here, we applied principal component analysis (PCA) to trial-averaged neural responses in macaque primary visual cortex (V1) to study two fundamental, population-level questions. First, we characterized how neural complexity relates to stimulus complexity, where complexity is measured using relative comparisons of dimensionality. Second, we assessed the extent to which responses to different stimuli occupy similar dimensions of the population activity space using a novel statistical method. For comparison, we performed the same dimensionality reduction analyses on the activity of a recently-proposed V1 receptive field model and a deep convolutional neural network. Our results show that the dimensionality of the population response changes systematically with alterations in the properties and complexity of the visual stimulus

Accounting for network effects in neuronal responses using L1 regularized point process models.

Activity of a neuron, even in the early sensory areas, is not simply a function of its local receptive field or tuning properties, but depends on global context of the stimulus, as well as the neural context. This suggests the activity of the surrounding neurons and global brain states can exert considerable influence on the activity of a neuron. In this paper we implemented an L1 regularized point process model to assess the contribution of multiple factors to the firing rate of many individual units recorded simultaneously from V1 with a 96-electrode "Utah" array. We found that the spikes of surrounding neurons indeed provide strong predictions of a neuron's response, in addition to the neuron's receptive field transfer function. We also found that the same spikes could be accounted for with the local field potentials, a surrogate measure of global network states. This work shows that accounting for network fluctuations can improve estimates of single trial firing rate and stimulus-response transfer functions.</p

Time-resolved dimensionality of movie stimuli and population responses.

A: Dimensionality versus time. Left panel: visual stimuli. Center panel: monkey 1 (61 neurons). Right panel: monkey 2 (81 neurons). Error bars are standard deviations of subsampled estimates. Triangles denote mean dimensionality across time for each movie. Curves were smoothed with a Gaussian kernel with a standard deviation of 1.5 s. B: Dimensionality with growing time windows starting at the beginning of each movie. Left panel: visual stimuli. Inset: zoomed portion of the bottom-left of the plot. Center panel: monkey 1. Right panel: monkey 2. Curves were smoothed as in A. Due to the smoothing, the dimensionalities for the 1 second window do not exactly match the leftmost point in A, and those for the 30 second window do not exactly match the dimensionalities in Fig 3. C: Similarity of the basis patterns employed by the population responses across time (monkey 1). Each element in the similarity matrix corresponds to the similarity index between the sets of patterns for a pair of time points. D: Mean similarity index for visual stimuli and population responses. Error bars denote standard error over similarity indices.</p

Stimulus-Driven Population Activity Patterns in Macaque Primary Visual Cortex

<div><p>Dimensionality reduction has been applied in various brain areas to study the activity of populations of neurons. To interpret the outputs of dimensionality reduction, it is important to first understand its outputs for brain areas for which the relationship between the stimulus and neural response is well characterized. Here, we applied principal component analysis (PCA) to trial-averaged neural responses in macaque primary visual cortex (V1) to study two fundamental, population-level questions. First, we characterized how neural complexity relates to stimulus complexity, where complexity is measured using relative comparisons of dimensionality. Second, we assessed the extent to which responses to different stimuli occupy similar dimensions of the population activity space using a novel statistical method. For comparison, we performed the same dimensionality reduction analyses on the activity of a recently-proposed V1 receptive field model and a deep convolutional neural network. Our results show that the dimensionality of the population response changes systematically with alterations in the properties and complexity of the visual stimulus.</p></div

Conceptual illustration of dimensionality and basis patterns.

<p><i>A</i>: The activity of three neurons can be plotted in a 3-d population firing rate space, where each axis represents the firing rate of one neuron. The population activity evolves over time (blue trace), and occupies a 2-d plane (blue shade). The basis patterns are orthogonal axes that define this 2-d plane. <i>B</i>: The activity of three neurons can also be represented as time-varying firing rates or peri-stimulus time histograms, PSTHs. The activity can be decomposed into a weighted sum of basis patterns (red and green) and a mean offset (gray). Each basis pattern is weighted by a time-varying latent variable. Note that basis patterns are mutually orthogonal, by definition. <i>C</i>: The activity of the same three neurons as in <i>B</i>, but for a different stimulus. Same conventions as in <i>B</i>.</p

Dimensionality of model responses to individual gratings and movies.

<p><i>A</i>: Block diagram of the RF model. We considered the activity in the model at four different components (<i>R</i>₁, <i>R</i>₂, <i>R</i>₃, <i>R</i>₄). <i>B</i>: Dimensionality of model activity versus number of orientations, computed in the same manner as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005185#pcbi.1005185.g002" target="_blank">Fig 2<i>B</i></a>. <i>C</i>: Dimensionality of model activity versus angle offset between two orientations, computed in the same manner as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005185#pcbi.1005185.g002" target="_blank">Fig 2<i>D</i></a>. <i>D</i>: Dimensionality and variance of model responses to movies, computed in the same manner as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005185#pcbi.1005185.g003" target="_blank">Fig 3<i>C</i></a>. Results are based on 100 model neurons.</p

Assessing similarity of basis patterns.

<p><i>A</i>: Conceptual illustration for two neurons, where <i>v</i>_<i>A</i> denotes the basis pattern for one condition and <i>v</i>_<i>B</i> denotes the basis pattern for another condition. As <i>v</i>_<i>B</i> is rotated away from <i>v</i>_<i>A</i>, the question is at which point do we consider <i>v</i>_<i>A</i> and <i>v</i>_<i>B</i> to span two dimensions. <i>B</i>: The transition from one to two dimensions in <i>A</i> depends on the rank threshold <i>t</i>. For <i>t</i> = 0.5, the transition occurs when the angle between <i>v</i>_<i>A</i> and <i>v</i>_<i>B</i> is near 45 degrees.</p

Dimensionality of population responses to individual gratings.

<p><i>A</i>: The complexity of the stimulus was varied by combining a different number of consecutive orientations. The least complex stimulus consisted of a single orientation, and more complex stimuli included two or five orientations. <i>B</i>: Dimensionality of population activity versus number of orientations. Bottom three curves correspond to the number of dimensions needed to explain 70%, 80%, and 90% of the variance. Top gray curve corresponds to the number of dimensions expected by chance for the 90% variance threshold. Error bars represent the standard error across monkeys and all possible combinations of consecutive orientations. <i>C</i>: Varying the rank threshold for a fixed variance threshold (90%). Same data as in <i>B</i>. Each curve represents the dimensionality of the population response as the number of consecutive orientations varies, for a particular rank threshold <i>t</i>. Error bars are computed as in <i>B</i>. <i>D</i>: Dimensionality of population activity versus angle offset between two orientations (bottom black curve). Chance dimensionality (top gray curve) and error bars are computed as in <i>B</i>. <i>E</i>: Basis patterns describing the largest percentage of variance for the population responses to three example orientations (90° apart) for one monkey. Each pattern is a unit vector with a norm of 1. Percentages denote the percent variance explained by each pattern.</p

Similarity of basis patterns across stimuli.

<p><i>A</i>: Basis patterns describing the largest percentage of variance for the population responses to the gratings, natural, and noise movies for monkey 2. Each pattern is a unit vector with a norm of 1. Percentages denote percent variance explained by each pattern. <i>B</i>: Dimensionality of visual stimuli for individual movies (teal dots), and combinations of two (orange dots) or three (purple dots) movies. The teal dots correspond to where the curves intersect the dashed lines in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005185#pcbi.1005185.g003" target="_blank">Fig 3<i>B</i></a>. Black brackets denote the range of possible dimensionalities (bottom of the black bracket corresponds to overlapping patterns; top of the black bracket corresponds to orthogonal patterns). Gray dots indicate dimensionalities expected by chance, and error bars represent the standard deviation of 100 random samples. The similarity index <i>s</i> indicates if patterns overlap more than expected by chance (<i>s</i> > 0) or are closer to orthogonal than expected by chance (<i>s</i> < 0). <i>C</i>: Dimensionality of population activity, for individual and combinations of movies. Same conventions as in <i>B</i>. Error bars represent standard deviations of the subsampled estimates. <i>D</i>: Venn diagram that summarizes the similarity of basis patterns across stimuli. The size of each ellipse indicates the number of basis patterns, and the overlap indicates the extent to which basis patterns are shared by different stimuli.</p