On control of the function of the sodium-potassium pump in malignant cells

This paper introduces a double-layer enzyme-membrane model representing the Na⁺−K⁺ pump in living cells. We present a mathematical solution to the problem of controlling the sodium flux in malignant cells, where an inhibitor exists in the outer layer of the membrane. We give an algorithm for the numerical resolution of this problem of optimal control with illustrations. Finally, we point out the biological importance of this study.