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Revista de la Facultad de Ingeniería Universidad Central de Venezuela

Print version ISSN 0798-4065

Abstract

D´ALESSANDRO-MARTINEZ, Antonio; CORDOVA-RANGEL, Robert  and  D´ALESSANDRO-CACERES, Engels. ONE DIMENSIONAL PHYSICAL-MATHEMATICAL MODELING OF Ca2+ ION DIFFUSION-REACTION IN BIOCONTRACTIL STRUCTURES (CASE: SMOOTH MUSCLE CELL). Rev. Fac. Ing. UCV [online]. 2012, vol.27, n.1, pp.7-17. ISSN 0798-4065.

The contraction and relaxation of smooth muscle cells is regulated by a temporal and spatial variation in the cytosolic Ca2+ ion concentration. In this work was elaborated one-dimensional physical-mathematical model based in a reaction-diffusion equation that represents Ca2+ ion transport. This equation was numerically resolved using COMSOL Multiphysics 3.4 ® (finite element based). It was designed “in silico” experiments using the firing of 1, 2 and 3 Ryanodine Receptors-Channels and the action Ca2+ATP Pump located on sarcoplasmic reticulum membrane. It was studied transient (Ca2+ sparks) and stationary space-temporal behavior of Ca2+ cytosolic concentration in locations very near and enough far of liberation sites. It was determined that the sole action of Ca2+ATP Pump does not guarantee the return to baseline concentration at end of relaxation, and thus the action of additional reaction term called leak flux was considered. It was also shown that the Ca2+ diffusion reaches its steady state about 50 times faster than when was considered the Calmodulin buffer. The impulsive release of Ca2+ ion permits to obtain a Ca2+ concentration peak in the cytosol that is seventeen (17) times the baseline concentration. Transient changes in concentration near of release site occur ten (10) times faster than the transient changes near the ends of the domain. Oscillations were observed in the Ca2+ ion concentration in the domain points when were triggered per more than 1 Ryanodine Receptors-Channel. The time elapsed to achieve steady state (relaxation) are consistent with those described in the literature for ileum cell

Keywords : Smooth muscle; Calcium ion; Diffusion-Reaction; COMSOL 3.4; Finite element; Partial differential Equation.

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