Scientific Understanding of Consciousness
Neural Network Connectivity
Nature 466, 617–621 (29 July 2010)
Sparse coding and high-order correlations in fine-scale cortical networks
Ifije E. Ohiorhenuan, Ferenc Mechler, Keith P. Purpura, Anita M. Schmid, Qin Hu & Jonathan D. Victor
Department of Neurology and Neuroscience, Weill Cornell Medical College, New York, New York 10065, USA
Connectivity in the cortex is organized at multiple scales, suggesting that scale-dependent correlated activity is particularly important for understanding the behaviour of sensory cortices and their function in stimulus encoding. We analysed the scale-dependent structure of cortical interactions by using maximum entropy models to characterize multiple-tetrode recordings from primary visual cortex of anaesthetized macaque monkeys (Macaca mulatta). We compared the properties of firing patterns among local clusters of neurons (<300 μm apart) with those of neurons separated by larger distances (600–2,500 μm). Here we report that local firing patterns are distinctive: whereas multi-neuronal firing patterns at larger distances can be predicted by pairwise interactions, patterns within local clusters often show evidence of high-order correlations. Surprisingly, these local correlations are flexible and rapidly reorganized by visual input. Although they modestly reduce the amount of information that a cluster conveys, they also modify the format of this information, creating sparser codes by increasing the periods of total quiescence, and concentrating information into briefer periods of common activity. These results imply a hierarchical organization of neuronal correlations: simple pairwise correlations link neurons over scales of tens to hundreds of minicolumns, but on the scale of a few minicolumns, ensembles of neurons form complex subnetworks whose moment-to-moment effective connectivity is dynamically reorganized by the stimulus.
Early cortical sensory areas create internal representations of the sensory world. At the level of individual neurons, this process is reasonably well understood. For instance, in the primary visual cortex (V1) neurons respond selectively to components or features of the sensory stimulus, such as orientation or spatial frequency. But, because the activity of pairs of cortical neurons is correlated, the behaviour of a network of cortical neurons cannot be fully understood from measurements of its individual responses. Understanding the functional role of correlations among groups of neurons is challenging because of the ‘combinatorial explosion’ of possible interactions. However, the organization of cortical connectivity suggests that certain types of interactions are particularly relevant to cortical processing.
A striking anatomical feature of the neocortex is that connectivity between neurons is highly structured. Across the cortical sheet, neurons are organized over a range of spatial scales: fine-scale networks (50–100 μm) display specific, non-random connectivity. Neurons with similar responses are grouped into functional columns that span several hundred micrometres, and long-range horizontal connections link neurons together over several millimetres. The prominence of this multi-scale organization argues that scale-dependent interactions between neurons shape the behaviour of cortical networks, and the manner in which they encode sensory information. This view predicts that cortical neurons participate in multiple subnetworks whose characteristics vary with spatial scale.
Directly addressing this question requires in vivo sampling (with high temporal resolution) of neuronal populations at different spatial scales and a principled way to characterize multi-neuron activity. To do this, we combine multiple-tetrode recording with maximum entropy models. Multiple-tetrode recording in macaque primary visual cortex enables sampling of cortical activity at different scales: each tetrode isolates several neurons within a radius of ~150 μm, and we separate the tetrodes by distances ranging from 600 μm to several millimetres. A complete characterization of the activity of a network of neurons is challenging, because the number of potential interactions grows exponentially as the network size increases. Even for small networks, it is infeasible to make enough measurements to accurately estimate multi-neuron joint histograms. Here, we record from small groups of neurons (3–6) and use maximum entropy models to provide an insightful summary of the many possible interactions between them.
To determine the impact of high-order interactions on the amount of information carried, we compared the mutual information between the informative pixels and the neural responses generated under Mobs and Mpair. Higher-than-second order correlations have little effect on the overall information content. However, comparing Mpair and Mind shows that there is a mild reduction in information content due to the second-order correlations (that is, redundancy), as has been seen in previous studies in retina, primary visual cortex, and inferior temporal cortex. Thus, although it has been suggested that fine-scale pairwise correlations might result in an increase in information content (that is, synergy), we find that redundancy dominates for larger neuronal populations. This finding supports the notion that it is a strategy the cortex uses to maintain the fidelity of information in the face of variable individual neural responses, and that correlations do not increase the information conveyed by neurons.
We have analysed correlations at three spatial scales, sampled from the continuum of scales that are present in cortex. The analysis shows that correlations in cortical networks have a specific scale-dependence. Fine-scale subnetworks are characterized by a prevalence of stimulus-dependent high-order correlations and pairwise correlations which increase coding redundancy and response sparseness. In turn, these fine-scale networks are weakly synchronized by pairwise noise correlations at longer ranges. In contrast, responses of retinal networks to naturalistic stimuli and flickering chequerboards did not display high-order correlations, and pairwise interactions nearly perfectly accounted for the behaviour, even among adjacent neurons. Thus, complex scale-dependent patterns of correlations between neurons are an emergent property of cortical processing.
Cortical minicolumns have been proposed to form the smallest organizational unit in the cortex; in the macaque, they are approximately 40–60 μm in diameter. As tetrodes typically have a recording radius of 70–150 μm, our measurements of local correlations reflect cortical processing that occurs on the scale of one to a few minicolumns. Our observation that stimulus-dependent correlations affect coding strengthens the concept that locally, minicolumns interact to form functional groups. Because, as we have shown, these interactions increase coding redundancy and concentrate the output of the network into short time epochs, they are potentially useful for transmitting information to higher-order neurons in the face of noisy neuronal activity and frequent synaptic failures. Although we found that correlations at a scale of tens to hundreds of minicolumns produce significant interactions between pairs of neurons, the role of these correlations in cortical activity is still unclear. Correlations at these scales could reflect a global cortical state, such as that captured by electroencephalographic recordings. Alternatively, they may contribute to encoding of naturalistic visual input when the stimulus itself contains long-range correlations, such as extended contours, or high-order correlations.
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