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Application of the H-infinite control for multi-states conformational transition of calcium ion selective gating channels on excitable cellular membranes

Hirayama H.

Systems Science

2002

Vol. 28, nr 1

107-34

We introduced H infinite control theory for evaluating the noise filtering functions of biological membranes. Calcium ion selective gating channel on excitable cellular membranes was described by four subunits allosteric modeling. The modeling was characterized by cooperative positional changes of an intrinsic voltage sensitive molecule in each of the subunits and concerted conformational changes of all the subunits. We applied the H-infinite control strategy for minimizing the influence of noises as the worst disturbances on the filtering function of the calcium channel. The allosteric cooperative positioning of the S4 and concerted actions of the subunits were approximated by powers of non-dimensional parameter F/sup n/. The temporal changes in amounts of calcium channel states were described by ten differential equations. We induced the corresponding differential equations for observers and accompanied Riccati equations. The transient changes in amounts per unit membrane area of calcium ion channel species were almost parallel. Those of the observers were a variety of patterns. The change in amount of control input for the concerted opening was the smallest while those for inter open states transitions were the largest. The computed temporal changes in the worst disturbances and the worst noises showed characteristic time courses for individual channel species and observers.