Showing papers by "Steven J. Cox published in 2013"

Structure-preserving model reduction of passive and quasi-active neurons

Abstract: The spatial component of input signals often carries information crucial to a neuron's function, but models mapping synaptic inputs to the transmembrane potential can be computationally expensive. Existing reduced models of the neuron either merge compartments, thereby sacrificing the spatial specificity of inputs, or apply model reduction techniques that sacrifice the underlying electrophysiology of the model. We use Krylov subspace projection methods to construct reduced models of passive and quasi-active neurons that preserve both the spatial specificity of inputs and the electrophysiological interpretation as an RC and RLC circuit, respectively. Each reduced model accurately computes the potential at the spike initiation zone (SIZ) given a much smaller dimension and simulation time, as we show numerically and theoretically. The structure is preserved through the similarity in the circuit representations, for which we provide circuit diagrams and mathematical expressions for the circuit elements. Furthermore, the transformation from the full to the reduced system is straightforward and depends on intrinsic properties of the dendrite. As each reduced model is accurate and has a clear electrophysiological interpretation, the reduced models can be used not only to simulate morphologically accurate neurons but also to examine computations performed in dendrites.

Inverse problems in neuronal calcium signaling

Abstract: Calcium is the most important of the brain’s second messengers. Thanks to engineered fluorescent indicators and caged compounds we have an excellent qualitative picture of its regulation and impact. With the advent of new scanning technology that permits one to observe the calcium signal throughout a highly branched neuron the potential exists for functional, single cell, quantitative calcium imaging. To help realize that potential we analyze a sequence of four inverse problems that infer the parameters of the cytosolic calcium buffers and plasma membrane calcium pumps and channels from the light shed by fluorescent indicators following specific stimulus protocols. Our analyses lead in each case to practical algorithms that we illustrate and test on synthetic data.