Mathematical modelling of the simultaneous diffusion of EGTA and CaEGTA and Ca2+ in a two-compartment system representing skinned smooth muscle

Author

Roderick Jon Hausser, New Jersey Institute of Technology

Document Type

Thesis

Date of Award

1-31-1987

Degree Name

Master of Science in Biomedical Engineering - (M.S.)

Department

Biomedical Engineering Committee

First Advisor

David S. Kristol

Second Advisor

Friedrich PJ Diecke

Third Advisor

Richard Clyde Parker

Abstract

Smooth muscle strips "chemically skinned" with Triton X-100 represent a two-compartment system consisting of the extracellular space (ECS) and the cytosolic space (CS) bounded by the permeabilized plasma membrane. Free [Ca²⁺] in such systems must be controlled with sufficiently high concentrations of Ca-buffers (EGTA). The presence of Ca-buffers, however, will oppose and delay any changes in [Ca²⁺] in both compartments. We have developed a model describing the simultaneous diffusion of Ca 2+ , EGTA and CaEGTA between bath and ECS, and ECS and CS and the chemical reaction between ligand and metal species in each compartment. The resulting six simultaneous differential equations were solved utilizing a 4th-order Runge-Putta-Gill algorithm. The rate-coefficients for the diffusion of Ca²⁺, EGTA and CaEGTA and the values for the ECS and CS were obtained from experiments with ⁵¹Cr-EDTA and ⁴⁵CaEGTA in intact and skinned strips of rat caudal artery (Stout and Diecke, 1983). Changes in [Ca²⁺] from relaxing concentration (18.0x10^-9 M) to test concentrations as high as 21.0x10^-6 M were simulated at constant total EGTA and for "Ca-jumps" (Moisescu and Thieleczel , 1978). The results obtained from the model are compared to observations of rates of contraction of skinned caudal artery strips under identical conditions. A major conclusion is that even under "Ca-jump" conditions, the rate of change of [Ca²⁺] in the cytosolic space remains the rate limiting step for contraction of Triton X-100 skinned caudal artery. Also the changes of [Ca²⁺] in the extracellular and cytosolic spaces is determined predominantly by the CaEGTA/EGTA ratio and therefore relies on the diffusion of these two species.

Recommended Citation

Hausser, Roderick Jon, "Mathematical modelling of the simultaneous diffusion of EGTA and CaEGTA and Ca2+ in a two-compartment system representing skinned smooth muscle" (1987). Theses. 3100.
https://digitalcommons.njit.edu/theses/3100