Modeling Calcium Diffusion in Chondroitin Sulfate using a Bimolecular Reaction Scheme

Abstract

Ca2+ diffusion in brain extracellular space (ECS) regulates local Ca2+ concentration and influences synaptic transmission and neuronal excitability. Ca2+ diffusion is controlled by ECS geometry and extracellular matrix, a major component of which is chondroitin sulfate (CS). Previous experiments (Hrabetova et al., J. Physiol. 2009, 587:4029) show that Ca2+ movement is reduced when interacting with CS, however the process still obeys the diffusion equation. This implies that Ca2+-CS interaction can be modeled as a fast equilibrium bimolecular reaction (FEBR; Nicholson et al. Comput. Visual Sci., 2012, 10.1007/s00791-012-0185-9). The FEBR would provide an alternative to solving the Poisson-Boltzmann equation for electrostatic interactions between negatively charged CS and mobile cations.Our objectives were 1) to test whether the FEBR model describes previous experimental data, 2) if so, to determine the dissociation constant Kd, (ratio between backward and forward rate constants), 3) to explore the effect of background Ca2+ and/or Na+ on Ca2+ diffusion and 4) use a Monte Carlo simulator (MCell; www.mcell.org) to verify results.We developed analytical expressions for the Ca2+ effective diffusion coefficient in the presence of CS and compared results to experimental data with different background Ca2+ and CS concentrations (Magdelenat et al., Biopolymers, 1974, 13:1535; Maroudas et al., Biophys. Chem., 1988, 32:257). This validated the FEBR approach and provided estimates of Kd (0.01 to 0.1 mM) in agreement with literature data. Kd values were resolved into forward and backward rate constants using the Damkohler formula and the results further tested with MCell. Finally, we extended the work to include additional background Na+.We conclude that the FEBR model captures the main features of Ca2+ diffusion in CS matrix and can be extended to interactions involving multiple cations. Supported by NIH/NINDS grant R01-NS-28642.