A computational model of system dynamics of calcium and nitric oxide in pancreatic beta-cell

Calcium (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>C</mml:mi><mml:mrow><mml:msup><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>) and nitric oxide (<i>NO</i>) play a crucial role in chemical signaling, as regulators of various cellular functions, and as cytotoxic agents under different physiological and pathological settings. These two signaling systems have been investigated in the past as individual systems in pancreatic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>β</mml:mi></mml:mrow></mml:math>-cells without considering their spatio-temporal relationships. These studies have generated limited insights, and thus, their role in regulatory and cytotoxic functions of pancreatic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>β</mml:mi></mml:mrow></mml:math>-cells is poorly understood. Therefore, an effort has been put forth to create a mathematical model to explore spatio-temporal relationships of cytosolic calcium and <i>NO</i> in a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>β</mml:mi></mml:mrow></mml:math>-cell based on the experimental and theoretical data. The model has been framed in terms of reaction-diffusion equation involving <i>ER</i> leak, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mtext>SERCA</mml:mtext></mml:mrow></mml:math> pump, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mtext>PMCA</mml:mtext></mml:mrow></mml:math> pump, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mtext>VGCC</mml:mtext></mml:mrow><mml:mtext>,</mml:mtext></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>I</mml:mi><mml:mrow><mml:msub><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math> receptor, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mtext>EGTA</mml:mtext></mml:mrow></mml:math> buffer, etc. The finite element and Crank-Nicolson methods have been used for numerical simulation. The impacts of various parameters involved in the regulation of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>C</mml:mi><mml:mrow><mml:msup><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>- <i>NO</i> dynamics for space and time have been identified from the numerical results. The regulatory and cytotoxic conditions for the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>β</mml:mi></mml:mrow></mml:math>-cell have been assessed with the help of various parameters involved in the calcium and <i>NO</i> dynamics. The proposed model provides novel insights of the impacts of changes in various calcium signaling mechanism on <i>NO</i> dynamics in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>β</mml:mi></mml:mrow></mml:math>-cell. The insights into spatio-temporal relationships of these two signaling systems can be helpful for developing various clinical applications.