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A Mathematical Model of Airway and Pulmonary Arteriole Smooth Muscle

Inga Wang ^*, Antonio Z. Politi ^*, Nessy Tania , Yan Bai , Michael J. Sanderson  and James Sneyd ^*

^* Department of Mathematics, University of Auckland, Auckland, New Zealand; Department of Mathematics, University of Utah, Salt Lake City, Utah; and Department of Physiology, University of Massachusetts Medical School, Worcester, Massachusetts

Correspondence: Address reprint requests to James Sneyd, Dept. of Mathematics, University of Auckland, Auckland, New Zealand. E-mail: sneyd{at}math.auckland.ac.nz.

Airway hyperresponsiveness is a major characteristic of asthma and is believed to result from the excessive contraction of airway smooth muscle cells (SMCs). However, the identification of the mechanisms responsible for airway hyperresponsiveness is hindered by our limited understanding of how calcium (Ca²⁺), myosin light chain kinase (MLCK), and myosin light chain phosphatase (MLCP) interact to regulate airway SMC contraction. In this work, we present a modified Hai-Murphy cross-bridge model of SMC contraction that incorporates Ca²⁺ regulation of MLCK and MLCP. A comparative fit of the model simulations to experimental data predicts 1), that airway and arteriole SMC contraction is initiated by fast activation by Ca²⁺ of MLCK; 2), that airway SMC, but not arteriole SMC, is inhibited by a slower activation by Ca²⁺ of MLCP; and 3), that the presence of a contractile agonist inhibits MLCP to enhance the Ca²⁺ sensitivity of airway and arteriole SMCs. The implication of these findings is that murine airway SMCs exploit a Ca²⁺-dependent mechanism to favor a default state of relaxation. The rate of SMC relaxation is determined principally by the rate of release of the latch-bridge state, which is predicted to be faster in airway than in arteriole. In addition, the model also predicts that oscillations in calcium concentration, commonly observed during agonist-induced smooth muscle contraction, cause a significantly greater contraction than an elevated steady calcium concentration.