Analyzing Short-Term Noise Dependencies of Spike-Counts in Macaque Prefrontal Cortex Using Copulas and the Flashlight Transformation

Simultaneous spike-counts of neural populations are typically modeled by a Gaussian distribution. On short time scales, however, this distribution is too restrictive to describe and analyze multivariate distributions of discrete spike-counts. We present an alternative that is based on copulas and can account for arbitrary marginal distributions, including Poisson and negative binomial distributions as well as second and higher-order interactions. We describe maximum likelihood-based procedures for fitting copula-based models to spike-count data, and we derive a so-called flashlight transformation which makes it possible to move the tail dependence of an arbitrary copula into an arbitrary orthant of the multivariate probability distribution. Mixtures of copulas that combine different dependence structures and thereby model different driving processes simultaneously are also introduced. First, we apply copula-based models to populations of integrate-and-fire neurons receiving partially correlated input and show that the best fitting copulas provide information about the functional connectivity of coupled neurons which can be extracted using the flashlight transformation. We then apply the new method to data which were recorded from macaque prefrontal cortex using a multi-tetrode array. We find that copula-based distributions with negative binomial marginals provide an appropriate stochastic model for the multivariate spike-count distributions rather than the multivariate Poisson latent variables distribution and the often used multivariate normal distribution. The dependence structure of these distributions provides evidence for common inhibitory input to all recorded stimulus encoding neurons. Finally, we show that copula-based models can be successfully used to evaluate neural codes, e. g., to characterize stimulus-dependent spike-count distributions with information measures. This demonstrates that copula-based models are not only a versatile class of models for multivariate distributions of spike-counts, but that those models can be exploited to understand functional dependencies

Correlated Activity and Corticothalamic Cell Function in the Early Mouse Visual System

Vision has long been the model for understanding cortical function. Great progress has been made in understanding the transformations that occur within some primary visual cortex (V1) layers, like the emergence of orientation selectivity in layer 4. Less is known about other V1 circuit elements, like the shaping of V1 input via corticothalamic projections, or the population structure of the cortico-cortical output in layer 2/3. Here, we use the mouse early visual system to investigate the structure and function of circuit elements in V1. We use two approaches: comparative physiology and optogenetics. We measured the structure of pairwise correlations in the output layer 2/3 using extracellular recordings. We find that despite a lack of organization in mouse V1 seen in other species, the specificity of connections preserves a correlation structure on multiple timescales. To investigate the role of corticogeniculate projections, we utilize a transgenic mouse line to specifically and reversibly manipulate these projections with millisecond precision. We find that activity of these cells results a mix of inhibition and excitation in the thalamus, is not spatiotemporally specific, and can affect correlated activity. Finally, we classify mouse thalamic cells according to stimuli used for cell classification in primates and cats, finding some, but not complete, homology to the processing streams of primate thalamus and further highlighting fundamentals of mammalian visual system organization