Pairwise maximum entropy models for studying large biological systems: when they can and when they can't work

One of the most critical problems we face in the study of biological systems is building accurate statistical descriptions of them. This problem has been particularly challenging because biological systems typically contain large numbers of interacting elements, which precludes the use of standard brute force approaches. Recently, though, several groups have reported that there may be an alternate strategy. The reports show that reliable statistical models can be built without knowledge of all the interactions in a system; instead, pairwise interactions can suffice. These findings, however, are based on the analysis of small subsystems. Here we ask whether the observations will generalize to systems of realistic size, that is, whether pairwise models will provide reliable descriptions of true biological systems. Our results show that, in most cases, they will not. The reason is that there is a crossover in the predictive power of pairwise models: If the size of the subsystem is below the crossover point, then the results have no predictive power for large systems. If the size is above the crossover point, the results do have predictive power. This work thus provides a general framework for determining the extent to which pairwise models can be used to predict the behavior of whole biological systems. Applied to neural data, the size of most systems studied so far is below the crossover point

Dendritic Slow Dynamics Enables Localized Cortical Activity to Switch between Mobile and Immobile Modes with Noisy Background Input

Mounting lines of evidence suggest the significant computational ability of a single neuron empowered by active dendritic dynamics. This motivates us to study what functionality can be acquired by a network of such neurons. The present paper studies how such rich single-neuron dendritic dynamics affects the network dynamics, a question which has scarcely been specifically studied to date. We simulate neurons with active dendrites networked locally like cortical pyramidal neurons, and find that naturally arising localized activity – called a bump – can be in two distinct modes, mobile or immobile. The mode can be switched back and forth by transient input to the cortical network. Interestingly, this functionality arises only if each neuron is equipped with the observed slow dendritic dynamics and with in vivo-like noisy background input. If the bump activity is considered to indicate a point of attention in the sensory areas or to indicate a representation of memory in the storage areas of the cortex, this would imply that the flexible mode switching would be of great potential use for the brain as an information processing device. We derive these conclusions using a natural extension of the conventional field model, which is defined by combining two distinct fields, one representing the somatic population and the other representing the dendritic population. With this tool, we analyze the spatial distribution of the degree of after-spike adaptation and explain how we can understand the presence of the two distinct modes and switching between the modes. We also discuss the possible functional impact of this mode-switching ability

Reducing Crowding by Weakening Inhibitory Lateral Interactions in the Periphery with Perceptual Learning

We investigated whether lateral masking in the near-periphery, due to inhibitory lateral interactions at an early level of central visual processing, could be weakened by perceptual learning and whether learning transferred to an untrained, higher-level lateral masking known as crowding. The trained task was contrast detection of a Gabor target presented in the near periphery (4°) in the presence of co-oriented and co-aligned high contrast Gabor flankers, which featured different target-to-flankers separations along the vertical axis that varied from 2λ to 8λ. We found both suppressive and facilitatory lateral interactions at target-to-flankers distances (2λ - 4λ and 8λ, respectively) that were larger than those found in the fovea. Training reduces suppression but does not increase facilitation. Most importantly, we found that learning reduces crowding and improves contrast sensitivity, but has no effect on visual acuity (VA). These results suggest a different pattern of connectivity in the periphery with respect to the fovea as well as a different modulation of this connectivity via perceptual learning that not only reduces low-level lateral masking but also reduces crowding. These results have important implications for the rehabilitation of low-vision patients who must use peripheral vision to perform tasks, such as reading and refined figure-ground segmentation, which normal sighted subjects perform in the fovea

Cortical Surround Interactions and Perceptual Salience via Natural Scene Statistics

Spatial context in images induces perceptual phenomena associated with salience and modulates the responses of neurons in primary visual cortex (V1). However, the computational and ecological principles underlying contextual effects are incompletely understood. We introduce a model of natural images that includes grouping and segmentation of neighboring features based on their joint statistics, and we interpret the firing rates of V1 neurons as performing optimal recognition in this model. We show that this leads to a substantial generalization of divisive normalization, a computation that is ubiquitous in many neural areas and systems. A main novelty in our model is that the influence of the context on a target stimulus is determined by their degree of statistical dependence. We optimized the parameters of the model on natural image patches, and then simulated neural and perceptual responses on stimuli used in classical experiments. The model reproduces some rich and complex response patterns observed in V1, such as the contrast dependence, orientation tuning and spatial asymmetry of surround suppression, while also allowing for surround facilitation under conditions of weak stimulation. It also mimics the perceptual salience produced by simple displays, and leads to readily testable predictions. Our results provide a principled account of orientation-based contextual modulation in early vision and its sensitivity to the homogeneity and spatial arrangement of inputs, and lends statistical support to the theory that V1 computes visual salience