| Calcium Dynamics and Vasomotion in Arteries Subject to Isometric, Isobaric, and Isotonic Conditions Biophysical Journal, Volume 95, Issue 6, 15 September 2008, Pages 2728-2738 Michèle Koenigsberger, Roger Sauser, Dominique Seppey, Jean-Louis Bény and Jean-Jacques Meister Abstract In vitro, different techniques are used to study the smooth muscle cells’ calcium dynamics and contraction/relaxation mechanisms on arteries. Most experimental studies use either an isometric or an isobaric setup. However, in vivo, a blood vessel is neither isobaric nor isometric nor isotonic, as it is continuously submitted to intraluminal pressure variations arising from heart beat. We use a theoretical model of the smooth muscle calcium and arterial radius dynamics to determine whether results may be considerably different depending on the experimental conditions (isometric, isobaric, isotonic, or cyclic pressure variations). We show that isobaric conditions appear to be more realistic than isometric or isotonic situations, as the calcium dynamics is similar under cyclic intraluminal pressure variations (in vivo-like situation) and under a constant pressure (isobaric situation). The arterial contraction is less pronounced in isotonic than in isobaric conditions, and the vasoconstrictor sensitivity higher in isometric than isobaric or isotonic conditions, in agreement with experimental observations. Interestingly, the model predicts that isometric conditions may generate artifacts like the coexistence of multiple stable states. We have verified this model prediction experimentally using rat mesenteric arteries mounted on a wire myograph and stimulated with phenylephrine. Abstract | Full Text | PDF (190 kb) |
| Kinetic model for isometric contraction in smooth muscle on the basis of myosin phosphorylation hypothesis Biophysical Journal, Volume 46, Issue 1, 1 July 1984, Pages 35-44 S. Kato, T. Osa and T. Ogasawara Abstract A kinetic model was proposed to simulate an isometric contraction curve in smooth muscle on the basis of the myosin phosphorylation hypothesis. The Ca2+-calmodulin-dependent activation of myosin light-chain kinase and the phosphorylation-dephosphorylation reaction of myosin were mathematically treated. Solving the kinetic equations at a steady state, we could calculate the relationship between the Ca2+ concentration and the myosin phosphorylation. Assuming that two-head-phosphorylated myosin has an actin-activated Mg2+-ATPase activity and that this state corresponds to an active state, we computed the time courses of the myosin phosphorylation and the active state for various Ca2+ transients. The time course of the active state was converted into that of isometric tension by use of Sandow's model composed of a contractile element and a series elastic component. The model could simulate not only the isometric contraction curves for any given Ca2+ transient but also the following experimental results: the calmodulin-dependent shift of the Ca2+ sensitivity of isometric tension observed in skinned muscle fibers, the disagreement between the Ca2+ sensitivity of myosin phosphorylation and that of isometric tension at a steady state, and the disagreement between the time course of myosin phosphorylation and that of isometric tension development. Abstract | PDF (1245 kb) |
| Mathematical Simulation of Muscle Cross-Bridge Cycle and Force-Velocity Relationship Biophysical Journal, Volume 91, Issue 10, 15 November 2006, Pages 3653-3663 Leslie Chin, Pengtao Yue, James J. Feng and Chun Y. Seow Abstract Muscle contraction underlies many essential functions such as breathing, heart beating, locomotion, regulation of blood pressure, and airway resistance. Active shortening of muscle is the result of cycling of myosin cross-bridges that leads to sliding of myosin filaments relative to actin filaments. In this study, we have developed a computer program that allows us to alter the rates of transitions between any cross-bridge-states in a stochastic cycle. The cross-bridge states within the cycle are divided into six attached (between myosin cross-bridges and actin filaments) states and one detached state. The population of cross-bridges in each of the states is determined by the transition rates throughout the cycle; differential equations describing the transitions are set up as a cyclic matrix. A method for rapidly obtaining steady-state exact solutions for the cyclic matrix has been developed to reduce computation time and avoid the divergence problem associated with numerical solutions. In the seven-state model, two power strokes are assumed for each cross-bridge cycle, one before the release of inorganic phosphate, and one after. The characteristic hyperbolic force-velocity relationship observed in muscle contraction can be reproduced by the model. Deviation from the single hyperbolic behavior at low velocities can be mimicked by allowing the rate of cross-bridge-attachment to vary with velocity. The effects of [ATP], [ADP], and [P] are simulated by changing transition rates between specific states. The model has revealed new insights on how the force-velocity characteristics are related to the state transitions in the cross-bridge cycle. Abstract | Full Text | PDF (323 kb) |
Copyright © 1975 The Biophysical Society. All rights reserved.
Biophysical Journal, Volume 15, Issue 12, 1167-1180, 1 December 1975
doi:10.1016/S0006-3495(75)85893-0
Research Article
C.J. De Luca and E.J. van Dyk
Mathematical expressions are derived for some parameters of the myoelectric (ME) signal recorded during a constant force isometric contraction. The expressions are developed from a stochastic model for the motor-unit action-potential trains obtained from empirical results. The following parameters: (a) the mean rectified value, (b) the mean integrated rectified value, (c) the root-mean-square value, and (d) the power density spectrum are described as functions of contraction time and constant force of an isometric muscle contraction. The calculated parameters are compared to their corresponding empirically obtained measurements which have been reported in the literature. A discussion on the behavior of the parameters during increasing contraction time is presented. Synchronization of the motor-unit action-potential trains is shown to have a pronounced effect on the parameters of the myoelectric signal. This result should be considered when analyzing long records of myoelectric signals.