Electrodiffusion in neural tissue at long timescales
Filed under:
Computational neuroscience
Geir Halnes (Department of Mathematical Sciences and Technology, Norwegian University of Life Sciences, Ås, Norway), Ivar Østby (Department of Mathematical Sciences and Technology, Norwegian University of Life Sciences, Ås, Norway), Klas Pettersen (Department of Mathematical Sciences and Technology, Norwegian University of Life Sciences, Ås, Norway), Stig W. Omholt (Centre for Integrative Genetics (CIGENE), Department of Animal Science, Norwegian University of Life Sciences, Ås, Norw), Gaute T. Einevoll (Department of Mathematical Sciences and Technology, Norwegian University of Life Sciences, Ås, Norway)
Electrical signaling in neurons is typically modeled at the timescales of integration of synaptic inputs, i.e., < 100 ms. In standard models based on the cable-equation, the key dynamical variable is the membrane potential. With the possible exception of the signal molecule Ca2+, intra- and extracellular ion concentrations are typically assumed to be constant. As synaptic activity and action-potential firing induce relatively small concentration changes of main charge carriers, this simplification is often warranted.
Commonly used measurement techniques such as fMRI based on hemodynamics and vascular dynamics probe the system at timescales of seconds or more. At these longer timescales, other neural processes become relevant: Ion pumps and membrane co-transporters actively regulate ion concentrations in the neural tissue, and also diffusion becomes an important transport mechanism (e.g. for funneling out excess potassium from regions with high neural activity).
In order to model key long-timescale neural processes, we need models that couple electrical dynamics and ionic diffusion, and that explicitly incorporate the ion concentrations in all parts of the neural tissue (neurons, astrocytes, extracellular space, vasculature). As a step in this direction, we here present an electrodiffusive scheme for modeling ion dynamics in a one-dimensional geometry for an astrocyte exchanging ions with the extracellular space through transmembrane currents.
Our scheme essentially models the extra- and intracellular concentrations (C_k(x)) of all ion species (k), and the membrane potential that follows from the resulting charge densities (ρ(x)). Compared to previous, related approaches [e.g. 1,2], our framework ensures (i) global particle/charge conservation, (ii) consistency between charge density and concentration of ion concentrations (charge carriers), and (iii) that any constraint on charges/currents (such as, e.g., ρ(x)_outside = - ρ(x)_inside) is properly translated to corresponding constraints on concentrations/particle fluxes (and vice versa). We identify the conditions under which our framework can be reduced to standard cable theory without severely violating points (i-iii).
References:
[1] Qian, N. & Sejnowski, TJ. (1989). Biological Cybernetics 62, 1-15.
[2] Chen, KC & Nicholson, C. (2000). Biophysical journal 78(6), 2776-97. DOI:10.1016/S0006-3495(00)76822-6
Commonly used measurement techniques such as fMRI based on hemodynamics and vascular dynamics probe the system at timescales of seconds or more. At these longer timescales, other neural processes become relevant: Ion pumps and membrane co-transporters actively regulate ion concentrations in the neural tissue, and also diffusion becomes an important transport mechanism (e.g. for funneling out excess potassium from regions with high neural activity).
In order to model key long-timescale neural processes, we need models that couple electrical dynamics and ionic diffusion, and that explicitly incorporate the ion concentrations in all parts of the neural tissue (neurons, astrocytes, extracellular space, vasculature). As a step in this direction, we here present an electrodiffusive scheme for modeling ion dynamics in a one-dimensional geometry for an astrocyte exchanging ions with the extracellular space through transmembrane currents.
Our scheme essentially models the extra- and intracellular concentrations (C_k(x)) of all ion species (k), and the membrane potential that follows from the resulting charge densities (ρ(x)). Compared to previous, related approaches [e.g. 1,2], our framework ensures (i) global particle/charge conservation, (ii) consistency between charge density and concentration of ion concentrations (charge carriers), and (iii) that any constraint on charges/currents (such as, e.g., ρ(x)_outside = - ρ(x)_inside) is properly translated to corresponding constraints on concentrations/particle fluxes (and vice versa). We identify the conditions under which our framework can be reduced to standard cable theory without severely violating points (i-iii).
References:
[1] Qian, N. & Sejnowski, TJ. (1989). Biological Cybernetics 62, 1-15.
[2] Chen, KC & Nicholson, C. (2000). Biophysical journal 78(6), 2776-97. DOI:10.1016/S0006-3495(00)76822-6
Preferred presentation format:
Poster
Topic:
Computational neuroscience
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