Cooperative Mechanisms in Cardiac Muscle (model 5)
Catherine
Lloyd
Bioengineering Institute, University of Auckland
Model Structure
In cardiac muscle, steady-state force-Ca2+ (F-Ca) relations exhibit more cooperativity than that predicted by the single Ca2+ binding site on troponin. The exact mechanisms underlying this high cooperativity are unknown. In their 1999 paper, J. Jeremy Rice, Raimond L. Winslow and William C. Hunter present five potential models for force generation in cardiac muscle (see the figure below). These models were constructed by assuming different subsets of three possible cooperative mechanisms:
Cooperative mechanism 1
is based on the theory that cross bridge formation between actin and myosin increases the affinity of troponin for Ca2+.
Cooperative mechanism 2
assumes that the binding of a cross bridge increases the rate of formation of neighbouring cross bridges and that multiple cross bridges can actin activation even in the absence of Ca2+.
Cooperative mechanism 2
simulates end-to-end interactions between adjacent troponin and tropomyosin.
Comparison of putative cooperative mechanisms in cardiac muscle: length dependence and dynamic responses J. Jeremy Rice, Raimond L. Winslow and William C. Hunter, 1999,
American Journal of Physiology
, 276, H1734-H1754. (Full text and PDF versions of the article are available for Journal Members on the American Journal of Physiology website.) PubMed ID: 10330260
reaction_diagrams
State diagrams for the five models of isometric force generation in cardiac muscle. T represents tropomyosin, TCa is Ca2+ bound tropomyosin, N0, N1, P0 and P1 are the non-permissive and permissive tropomyosin states.
All the models are similar in that they are structured around a functional unit of troponin, tropomyosin and actin. Tropomyosin can exist in four states, two permissive or two non-permissive (referring to whether or not the actin sites are available for binding to myosin and hence cross bridge formation). Depending on the model, one or more cross bridges exist, and these are either weakly-bound (non-force generating) or strongly bound (force generating).
The paper (cited below) tests the behaviours of the five models of force generation in cardiac myocytes. The first two models provide a baseline of performance for comparison. Models 3 to 5 are developed to incorporate more cooperative mechanisms. From the results of these simulations, which were compared to and consistent with experimental data, it is hypothesised that multiple mechanisms of cooperativity may coexist and contribute to the responses of cardiac muscle.
$T=1.0-\mathrm{TCa}$
$\frac{d \mathrm{TCa}}{d \mathrm{time}}=\mathrm{kon}\mathrm{Ca}T-\mathrm{koff\_}\mathrm{TCa}$
$\mathrm{N0}=1.0-\mathrm{P0}+\mathrm{N1}+\mathrm{P1}$
$\frac{d \mathrm{N1}}{d \mathrm{time}}=\mathrm{k1\_}\mathrm{P1}-\mathrm{g10}\mathrm{N1}+\mathrm{k1}\mathrm{N1}$
$\frac{d \mathrm{P0}}{d \mathrm{time}}=\mathrm{k1}\mathrm{N0}+\mathrm{g10}\mathrm{P1}-\mathrm{k1\_}\mathrm{P0}+\mathrm{f01}\mathrm{P0}$
$\frac{d \mathrm{P1}}{d \mathrm{time}}=\mathrm{k1}\mathrm{N1}+\mathrm{f01}\mathrm{P0}+\mathrm{g21}\mathrm{P2}-\mathrm{k1\_}\mathrm{P1}+\mathrm{g10}\mathrm{P1}+\mathrm{f12}\mathrm{P1}$
$\frac{d \mathrm{P2}}{d \mathrm{time}}=\mathrm{f12}\mathrm{P1}+\mathrm{g32}\mathrm{P3}-\mathrm{f23}\mathrm{P2}+\mathrm{g21}\mathrm{P2}$
$\frac{d \mathrm{P3}}{d \mathrm{time}}=\mathrm{f23}\mathrm{P2}-\mathrm{g32}\mathrm{P3}$
$\mathrm{f01}=3.0f$
$\mathrm{f12}=10.0f$
$\mathrm{f23}=7.0f$
$\mathrm{gSL}=g(2.0-\mathrm{SL\_norm}^{1.6})$
$\mathrm{g10}=1.0\mathrm{gSL}$
$\mathrm{g21}=2.0\mathrm{gSL}$
$\mathrm{g32}=3.0\mathrm{gSL}$
$\mathrm{k1}=\mathrm{k1\_}\left(\frac{\mathrm{TCa}}{\mathrm{K\_1\_2}}\right)^{N}$
$\mathrm{K\_1\_2}=\frac{1.0}{1.0+\frac{\mathrm{K\_Ca}}{1.8-\mathrm{SL\_norm}\times 1.0}}$
$N=2.6+1.0\mathrm{SL\_norm}$
$\mathrm{SL\_norm}=\frac{\mathrm{SL}-1.7}{2.3-1.7}$
$\mathrm{koff\_}=\mathrm{koff}(1.0-0.75F)$
$F=\frac{\mathrm{alpha}(\mathrm{P1}+\mathrm{N1}+2.0\mathrm{P2}+3.0\mathrm{P3})}{\mathrm{Fmax}}\mathrm{Fmax}=\mathrm{P1\_max}+2.0\mathrm{P2\_max}+3.0\mathrm{P3\_max}\mathrm{P1\_max}=\frac{\mathrm{f01}\mathrm{g21}\mathrm{g32}}{\mathrm{g10}\mathrm{g21}\mathrm{g32}+\mathrm{f01}\mathrm{g21}\mathrm{g32}+\mathrm{f01}\mathrm{f12}\mathrm{g32}+\mathrm{f01}\mathrm{f12}\mathrm{f23}}\mathrm{P2\_max}=\frac{\mathrm{f01}\mathrm{f12}\mathrm{g32}}{\mathrm{g10}\mathrm{g21}\mathrm{g32}+\mathrm{f01}\mathrm{g21}\mathrm{g32}+\mathrm{f01}\mathrm{f12}\mathrm{g32}+\mathrm{f01}\mathrm{f12}\mathrm{f23}}\mathrm{P3\_max}=\frac{\mathrm{f01}\mathrm{f12}\mathrm{f23}}{\mathrm{g10}\mathrm{g21}\mathrm{g32}+\mathrm{f01}\mathrm{g21}\mathrm{g32}+\mathrm{f01}\mathrm{f12}\mathrm{g32}+\mathrm{f01}\mathrm{f12}\mathrm{f23}}$
cardiac myocyte
myofilament mechanics
Cardiac Myocyte
electrophysiology
cooperative mechanisms
cardiac
The University of Auckland, Bioengineering Institute
2007-05-24T00:00:00+00:00
This is the CellML description of Rice et al's 5th model of isometric
force generation in cardiac myofilaments taken from their 1999 paper.
All five mathematical models published in this paper were constructed
by assuming different subsets of three putative cooperative
mechanisms.
Raimond
Winslow
L
American Journal of Physiology
The Rice et al. 1999 5th model of isometric force generation in cardiac
myofilaments
Cardiac Myocyte
c.lloyd@auckland.ac.nz
Catherine
Lloyd
May
10330260
The new version of this model has been re-coded to remove the reaction element and replace it with a simple MathML description of the model reaction kinetics. This is thought to be truer to the original publication, and information regarding the enzyme kinetics etc will later be added to the metadata through use of an ontology.
The model runs in the PCEnv simulator and gives a nice curved output.
Catherine Lloyd
keyword
John
Rice
Jeremy
William
Hunter
C
The University of Auckland
The Bioengineering Institute
Comparison of putative cooperative mechanisms in cardiac muscle: length dependence and dynamic responses (model 5)
276
H1734
H1754
1999-05
Catherine
Lloyd
May
2007-06-05T09:58:57+12:00