Modelling Actin-Myosin Binding in Airway Smooth Muscle
Catherine
Lloyd
Auckland Bioengineering Institute, The University of Auckland
Model Status
This CellML model runs in both OpenCell and COR but to replicate the published results (the first part of figure 3b). The units have been checked and they are consistent.
Model Structure
ABSTRACT: We carried out a detailed mathematical analysis of the effects of length fluctuations on the dynamically evolving cross-bridge distributions, simulating those that occur in airway smooth muscle during breathing. We used the latch regulation scheme of Hai and Murphy (Am. J. Physiol. Cell Physiol. 255:C86-C94, 1988) integrated with Huxley's sliding filament theory of muscle contraction. This analysis showed that imposed length fluctuations decrease the mean number of attached bridges, depress muscle force and stiffness, and increase force-length hysteresis. At frequencies >0.1 Hz, the bond-length distribution of slowly cycling latch bridges changed little over the stretch cycle and contributed almost elastically to muscle force, but the rapidly cycling cross-bridge distribution changed substantially and dominated the hysteresis. By contrast, at frequencies greater than 0.033 Hz this behavior was reversed: the rapid cycling cross-bridge distribution changed little, effectively functioning as a constant force generator, while the latch bridge bond distribution changed substantially and dominated the stiffness and hysteresis. The analysis showed the dissociation of force/length hysteresis and cross-bridge cycling rates when strain amplitude exceeds 3%; that is, there is only a weak coupling between net external mechanical work and the ATP consumption required for cycling cross-bridges during the oscillatory steady state. Although these results are specific to airway smooth muscle, the approach generalizes to other smooth muscles subjected to cyclic length fluctuations.
The original paper reference is cited below:
Perturbed Equilibria of Myosin Binding in Airway Smooth Muscle: Bond-Length Distributions, Mechanics, and ATP Metabolism, Srboljub M. Mijailovich, James P. Butler, and Jeffrey J. Fredberg, 2000, Biophysical Journal, 79, 2667-2681. PubMed ID: 11053139
reaction diagram
Hai and Murphy's four-state model: the latch regulatory scheme for Ca2+-dependent smooth muscle activation and Huxley's slidin filament model. A represents the actin filament, M represents detached myosin, Mp is detached, phosphorylated myosin, AM is the actin-myosin complex, and AMp is the phosphorylated actin-myosin complex.
$\frac{d M}{d \mathrm{time}}=-(\mathrm{k1}M)+\mathrm{k2}\mathrm{Mp}+\mathrm{gx}\mathrm{AM}$
$\frac{d \mathrm{Mp}}{d \mathrm{time}}=\mathrm{gp}\mathrm{AMp}+\mathrm{k1}M-(\mathrm{k2}+\mathrm{fp})\mathrm{Mp}$
$\frac{d \mathrm{AMp}}{d \mathrm{time}}=\mathrm{fp}\mathrm{Mp}+\mathrm{k6}\mathrm{AM}-(\mathrm{k5}+\mathrm{gp})\mathrm{AMp}$
$\frac{d \mathrm{AM}}{d \mathrm{time}}=\mathrm{k5}\mathrm{AMp}-(\mathrm{k6}+\mathrm{gx})\mathrm{AM}$
$\mathrm{k1}=\begin{cases}0.35 & \text{if $(\mathrm{time}> 0.0)\land (\mathrm{time}< 5.0)$}\\ 0.060 & \text{otherwise}\end{cases}\mathrm{k6}=\mathrm{k1}\mathrm{gp2}=4.0(\mathrm{fp1}+\mathrm{gp1})\mathrm{g2}=20.0\mathrm{g1}\mathrm{g3}=3.0\mathrm{g1}\mathrm{gp3}=3.0\mathrm{gp1}$
myosin
calcium
myofilament mechanics
atp
metabolism
smooth muscle
contraction
Catherine Lloyd
keyword
2004-08-03
myosin
M
Catherine
Lloyd
May
Perturbed Equilibria of Myosin Binding in Airway Smooth Muscle: Bond-Length Distributions, Mechanics and ATP Metabolism
79
2667
2681
This is a CellML description of Mijailovich et al.'s 2000 model of calcium, cross-bridge phosphorylation and contraction.
actin-myosin complex
AM
phosphorylated myosin
Mp
The University of Auckland, Auckand Bioengineering Institute
Biophysical Journal
James
Butler
P
phosphorylated actin-myosin complex
AMp
Jeffrey
Fredburg
J
Mijailovich et al.'s 2000 model of calcium, cross-bridge phosphorylation and contraction.
The University of Auckland
Auckland Bioengineering Institute
Srboljub
Mijailovich
M
c.lloyd@auckland.ac.nz
11053139
2000-11