Resumen

D´ALESSANDRO-MARTINEZ, Antonio; CORDOVA-RANGEL, Robert  y  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

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

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