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Characterizing neural spiking covariability is essential for understanding the collective activity of neural populations. Recent experiments have provided evidence of statistical dependencies among groups of neurons beyond that expected by the firing rates and pairwise correlations alone [1-3]. These "higher-order correlations" (HOCs) can be generated by common input [4] or motifs within the network architecture [5], yet a complete mechanistic understanding is lacking. We explore a novel mechanism through which higher-order correlations can be modulated: dendritic nonlinearities. We simulated the spiking activity of a simple exponential integrate-and-fire model neuron in response to two correlated presynaptic spike trains and background noise. The synaptic conductances were either summed linearly at the soma or were filtered through a nonlinear dendritic transfer function (see Figure ​Figure1),1), which was chosen to have a similar magnitude of effect on nonlinear EPSP summation as observed by active dendritic properties in pyramidal cells [6]. Using maximum entropy techniques, "triplet correlations" in the circuit were quantified as the probability of synchronous triplet spiking between the postsynaptic cell and its two presynaptic inputs beyond what could be captured by the firing rates and pairwise correlations alone, normalized by the product of the standard deviations. We found that superlinear dendrites significantly increased the level of triplet. On the other hand, saturating dendrites decorrelated triplets. These results reveal that HOCs in spiking activity are modulated by the curvature of the dendritic transfer function. Finally, this study demonstrates how intrinsic single-cell properties can tune spiking covariability in neural populations. Figure 1 A. Transfer functions depicting the summation of synaptic inputs for linear dendrites. B. Transfer function for saturating dendritic nonlinearities (solid line), as well as the identity (dotted line). C. Same as B for superlinear dendrites. D-F. "Triplet ...

Neural systems contain many cells, and an important problem is to understand if and how those neurons work together to form a functioning system. In sensory neuroscience -- which is our focus -- this function is to encode information about a stimulus so that it can be transmitted to other brain areas. An experimentally accessible, and hence popular, way to assess collective behavior is to measure the trial-to-trial covariability in the responses of multiple neurons over repeats of the same stimulus, called noise correlations. Repeat presentations of the same stimulus yield different responses on each trial, and that variability is typically correlated across different neurons [1,2] (although, see [3] for one counterexample). In the past two decades, the impact of these noise correlations on population coding has generated great interest. While nothing can add more information about the stimulus than was contained in the inputs (the data processing inequality), noise correlations determine the extent to which noise in the neural system degrades the amount of information that a neural population conveys about a stimulus (for example, see [4-6]). There are two main ways in which these noise correlations can be generated: the cells may receive common (noisy) input from (some of) the same upstream source(s), or the cells may be (recurrently) coupled to one another. At the same time, most work on noise correlations and population coding (with a few notable exceptions, including [7,8]) ignores their mechanistic origins. Interestingly, the few studies that have considered the mechanistic origins of noise correlations [7,8] have concluded that recurrent connectivity tends to hinder population coding, or has little overall effect: even though recurrent coupling can “sharpen” neural tuning curves, this advantage is more than offset by the fact that it generates harmful noise correlations. This begs the question of when -- if ever -- recurrent coupling can improve population coding, and of whether noise correlations with different mechanistic origins have different impacts on coding performance? To address these issues, we are investigating models in which groups of cells with, and without, recurrent coupling are driven by noisy inputs. The cells themselves are then noisy spike generators, and we are varying the fraction of shared inputs to the cells (which modifies the noise correlations due to common input), and the inter-neuronal connectivity, and computing the coding capacity of the resultant networks. Preliminary results indicate that, in some cases – similar to those discussed in [9] – recurrent coupling can combat the cell-intrinsic variabililty enough that the population’s coding performance is improved even though the noise correlations the are generated by that coupling do themselves hinder that coding performance. We are in the process of expanding and generalizing on this work. Support for this work came from NSF grants DMS-1122106, and CRCNS DMS-1208027 and a Burroughs- Wellcome Fund Career Award at the Scientific Interface to ESB.

Stereopsis, the ability to perceive depth, is crucial for detecting camouflaged objects and for performing tasks that require estimating distance. Understanding how our brain can so quickly estimate depth from the slightly different images from our left and right eyes, the difference of which is called binocular disparity, is still a major unsolved problem in vision research. Several previous computational studies of binocular disparity have found evidence suggesting that various properties of the primary visual cortex (V1) allow V1 to optimally process natural binocular disparity statistics. In particular, the efficient coding hypothesis suggests that the disparity tuning of V1 binocular neurons should reflect the natural range of disparities [1,2]; the cortical wiring hypothesis suggests that the orientation of ocular dominance stripes should follow the binocular disparity map [3]; and visuomotor optimization theory and the efficient coding hypothesis suggests that eye rotation strategy should be chosen to minimize binocular disparity and motor inefficiency [4,5]. In order to understand how natural binocular disparity statistics might be efficiently coded by the primary visual cortex, we constructed a simulation that links natural scene statistics to eye movements to connections between monocular neurons in V1. We generate a three-dimensional visual environment with two-point statistics and observer-object distance distribution similar to that of a natural environment; a virtual observer rotates her eyes according to the binocular version of Listing's Law to fixate on either edges of objects, centers of objects, or randomly chosen points on objects; and the resulting binocular disparities are mapped to V1 by a Schwartz conformal map fit to physiological data. The effects of two-point statistics, primary Listing's plane exorotation angle, Listing's Law coefficient, and fixation strategy can be revealed using this simulation in ways that would be very difficult (if not impossible) with experiments. For instance, to measure the effect of two-point statistics on binocular disparity statistics using this simulation, we compare the binocular disparity statistics in our more complicated three-dimensional visual environment to a visual environment with the same observer-object distance distribution but no pixel-pixel correlations. Our simulations show that the predicted ocular dominance stripe orientations and stereoscopic search zones are largely insensitive to two-point statistics of the visual environment, but very sensitive to interocular distance and eye rotation strategy. Finally, our more careful treatment of oculomotor strategy and visual environment shows that physiological oculomotor strategy cannot be explained by current visuomotor optimization theory[5]. A modified visuomotor optimization theory will likely require a better understanding of stereopsis-related processing in the visual cortex.

Sparse coding accounts for several physiological properties of primary visual cortex (V1), including the shapes of simple cell receptive fields and the highly kurtotic firing rates of V1 neurons [1]. Current spiking network models of pattern learning [2] and sparse coding [3] require direct inhibitory connections between the excitatory simple cells, in violation of Dale's Law which states that neurons can either excite or inhibit but not both. At the same time, the computational role of inhibitory neurons in cortical microcircuit function has yet to be fully explained. Here we show that adding a separate population of inhibitory neurons to a recently proposed model of V1 [3] not only brings spiking network models of sparse coding in line with Dale’s Law, but it also predicts excitatory-to-inhibitory neuron ratios and explains how inhibitory neurons may function computationally. When trained on natural images, this excitatory-inhibitory spiking circuit learns Gabor-like receptive fields as found in V1 using spiking neurons and synaptically local plasticity rules. The inhibitory cells enable sparse code formation using a novel learning rule by collaboratively discovering and suppressing correlations within the excitatory population (Figure ​(Figure1).1). The model predicts that only a small number of inhibitory cells is required relative to excitatory cells, matching physiological ratios observed in primary visual cortex. Figure 1 A. Circuit diagram of our spiking network with separate excitatory (E) and inhibitory (I) neural populations (top) compared to current single population models (bottom). This network was simulated with different numbers of excitatory and inhibitory cells. ...