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Special Semester on Quantitative Biology analyzed by Mathematical Methods
Linz, October 1, 2007 - January 27, 2008
Inverse Problems in Neuronal Calcium Signaling

Workshop on Ion Channels, Mon, 08 Oct, 2007

Speaker: Steve Cox

Abstract

Calcium, the most important of the second messengers, sculpts and records synaptic input and modulates the excitability of both nerve and muscle. Calcium enters the cytoplasm through voltage-gated channels in the plasma membrane as well as through calcium and/or IP3 sensitive receptors on the ER membrane. We exploit the recent ability to dynamically monitor cytosolic calcium, throughout rat hippocampal pyramidal cells in slice, with sub-millisecond temporal resolution and sub-micron spatial resolution in the construction of a map of receptor and channel density. In the process we pose and solve a number of inverse problems associated with dye recordings under two stimulus protocols:
1. Focal uncaging of intracellular calcium
i. Infer from the change in cytosolic dye-buffered calcium fluorescence the
affinities and diffusivities of all relevant exogenous and endogenous
calcium buffering proteins.
ii. Infer from (1.i) the concentration of free calcium and so determine the
distribution of ER-bound ryanodine and IP3 receptors as well as plasma
membrane and ER-bound calcium extrusion pumps.
2. Suprathreshold somatic current injection
i. Infer from the change in cytosolic dye-buffered calcium fluorescence the
local concentration of free cytosolic calcium.
ii. Infer from this estimate of buffered and free calcium the associated membrane
calcium current in space and time.
iii. Infer from this calcium current the conductance density of calcium channels.
iv. Infer the full membrane potential from this knowledge of current and conductance.
v. Infer from the membrane potential the remaining gating variables and their
associated conductances.
The requisite imaging tools are drawn from
V. Iyer, T. Hoogland and P. Saggau (2006) Fast Functional Imaging of single neurons using random-access multiphoton (RAMP) microscopy, J. Neurophys. 95:535-545.
The modeling framework is drawn from
AC. Ventura, L Bruno, A Demuro, I Parker, and SP Dawson (2005) A Model-Independent Algorithm to Derive Ca2+ Fluxes Underlying Local Cytosolic Ca2+ Transients, Biophysical J. 88:2403–2421.
The mathematical and computational tools are drawn from
S. Cox (2006) An adjoint method for channel localization, Mathematical Medicine and Biology 23:139-152.

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