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Neurons that sustain elevated firing in the absence of stimuli have been found in many neural systems. In graded persistent activity, neurons can sustain firing at many levels, suggesting a widely found type of network dynamics in which networks can relax to any one of a continuum of stationary states. The reproduction of these findings in model networks of nonlinear neurons has turned out to be nontrivial. A particularly insightful model has been the "bump attractor," in which a continuous attractor emerges through an underlying symmetry in the network connectivity matrix. This model, however, cannot account for data in which the persistent firing of neurons is a monotonic-rather than a bell-shaped-function of a stored variable. Here, we show that the symmetry used in the bump attractor network can be employed to create a whole family of continuous attractor networks, including those with monotonic tuning. Our design is based on tuning the external inputs to networks that have a connectivity matrix with Toeplitz symmetry. In particular, we provide a complete analytical solution of a line attractor network with monotonic tuning and show that for many other networks, the numerical tuning of synaptic weights reduces to the computation of a single parameter. [ABSTRACT FROM AUTHOR]

Summary: According to Barlow’s seminal “efficient coding hypothesis,” the coding strategy of sensory neurons should be matched to the statistics of stimuli that occur in an animal’s natural habitat. Using an automatic search technique, we here test this hypothesis and identify stimulus ensembles that sensory neurons are optimized for. Focusing on grasshopper auditory receptor neurons, we find that their optimal stimulus ensembles differ from the natural environment, but largely overlap with a behaviorally important sub-ensemble of the natural sounds. This indicates that the receptors are optimized for peak rather than average performance. More generally, our results suggest that the coding strategies of sensory neurons are heavily influenced by differences in behavioral relevance among natural stimuli. [Copyright &y& Elsevier]

Networks adapt to environmental demands by switching betweendistinct dynamical behaviors. The activity of frontal-lobe neuronsduring two-interval discrimination tasks is an example of theseadaptable dynamics. Subjects first perceive a stimulus, then hold it inworking memory, and finally make a decision by comparing it with asecond stimulus. We present a simple mutualinhibition network model thatcaptures all three task phases within a single framework. The modelintegrates both working memory and decision making because its dynamicalproperties are easily controlled without changing its connectivity.Mutual inhibition between nonlinear units is a useful design motif fornetworks that must display multiple behaviors. [ABSTRACT FROM AUTHOR]

The fundamental building block of every nervous system is the single neuron. Understanding how these exquisitely structured elements operate is an integral part of the quest to solve the mysteries of the brain. Quantitative mathematical models have proved to be an indispensable tool in pursuing this goal. We review recent advances and examine how single-cell models on five levels of complexity, from black-box approaches to detailed compartmental simulations, address key questions about neural dynamics and signal processing. [ABSTRACT FROM AUTHOR]