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Actomyosin based contraction: one mechanokinetic model from single molecules to muscle?

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ABSTRACT

Bridging the gaps between experimental systems on different hierarchical scales is needed to overcome remaining challenges in the understanding of muscle contraction. Here, a mathematical model with well-characterized structural and biochemical actomyosin states is developed to that end. We hypothesize that this model accounts for generation of force and motion from single motor molecules to the large ensembles of muscle. In partial support of this idea, a wide range of contractile phenomena are reproduced without the need to invoke cooperative interactions or ad hoc states/transitions. However, remaining limitations exist, associated with ambiguities in available data for model definition e.g.: (1) the affinity of weakly bound cross-bridges, (2) the characteristics of the cross-bridge elasticity and (3) the exact mechanistic relationship between the force-generating transition and phosphate release in the actomyosin ATPase. Further, the simulated number of attached myosin heads in the in vitro motility assay differs several-fold from duty ratios, (fraction of strongly attached ATPase cycle times) derived in standard analysis. After addressing the mentioned issues the model should be useful in fundamental studies, for engineering of myosin motors as well as for studies of muscle disease and drug development.

Electronic supplementary material: The online version of this article (doi:10.1007/s10974-016-9458-0) contains supplementary material, which is available to authorized users.

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Key elements of model. a Kinetic scheme showing myosin (M) and actomyosin (AM) biochemical states with MgATP (T), MgADP (D) and/or inorganic phosphate (P/Pi) at the active site. The MDP and AMDP states, on the one hand, and the AM*DL and AM*DH states, on the other, are assumed to be in rapid equilibrium with equilibrium constants Kw(x) and KLH(x), respectively. The AM*DL state is a strongly bound, start-of-power-stroke state. Several rate constants ki as well as equilibrium constants Ki vary with the elastic strain in the cross-bridge. b The free energy of all states as function of x (see text). Insets schematically illustrate different structural states of myosin head and lever arm at free-energy minima. c Schematic illustration of an in vitro motility assay where myosin motor fragments (heavy meromyosin; HMM) are adsorbed to a surface. The one-head, single-site assumption is illustrated: only one of the two myosin heads can bind to actin and binding is possible only to one site (dark) per 36 nm helical half-repeat of the actin filament. Key parameter values are given in Supplementary Tables S1 and S2
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Fig1: Key elements of model. a Kinetic scheme showing myosin (M) and actomyosin (AM) biochemical states with MgATP (T), MgADP (D) and/or inorganic phosphate (P/Pi) at the active site. The MDP and AMDP states, on the one hand, and the AM*DL and AM*DH states, on the other, are assumed to be in rapid equilibrium with equilibrium constants Kw(x) and KLH(x), respectively. The AM*DL state is a strongly bound, start-of-power-stroke state. Several rate constants ki as well as equilibrium constants Ki vary with the elastic strain in the cross-bridge. b The free energy of all states as function of x (see text). Insets schematically illustrate different structural states of myosin head and lever arm at free-energy minima. c Schematic illustration of an in vitro motility assay where myosin motor fragments (heavy meromyosin; HMM) are adsorbed to a surface. The one-head, single-site assumption is illustrated: only one of the two myosin heads can bind to actin and binding is possible only to one site (dark) per 36 nm helical half-repeat of the actin filament. Key parameter values are given in Supplementary Tables S1 and S2

Mentions: The model is based on the kinetic scheme in Fig. 1a with abbreviations of different states explained in the legend. The total amplitude of the force-generating power-stroke (“step-length”; from state AM*DL to states AMD and AM) was taken as 7.7 nm, slightly modified from the value of 7.35 nm in a recent model for large ensembles (Persson et al. 2013).The value of 7.7 nm is consistent with an 8 nm myosin step suggested in (Kaya and Higuchi 2010) based on optical tweezers studies that did not distinguish sub-steps. By assuming a final sub-step of 1 nm (Capitanio et al. 2006) the total value of 7.7 nm suggests a first sub-step of 6.7 nm. These step-lengths are directly reflected in the diagrams in Fig. 1b that illustrate the free energy of different states as function of the variable x. This variable represents the distance between a reference point on the myosin molecule and the nearest actin filament site, with x = 0 nm when force in the AMD/AM state is zero. The free energies of two different generic states, i and j, are related to the equilibrium constant (Kij(x)) and forward and backward rate constants (kij(x) and kji(x)) as follows:Fig. 1


Actomyosin based contraction: one mechanokinetic model from single molecules to muscle?
Key elements of model. a Kinetic scheme showing myosin (M) and actomyosin (AM) biochemical states with MgATP (T), MgADP (D) and/or inorganic phosphate (P/Pi) at the active site. The MDP and AMDP states, on the one hand, and the AM*DL and AM*DH states, on the other, are assumed to be in rapid equilibrium with equilibrium constants Kw(x) and KLH(x), respectively. The AM*DL state is a strongly bound, start-of-power-stroke state. Several rate constants ki as well as equilibrium constants Ki vary with the elastic strain in the cross-bridge. b The free energy of all states as function of x (see text). Insets schematically illustrate different structural states of myosin head and lever arm at free-energy minima. c Schematic illustration of an in vitro motility assay where myosin motor fragments (heavy meromyosin; HMM) are adsorbed to a surface. The one-head, single-site assumption is illustrated: only one of the two myosin heads can bind to actin and binding is possible only to one site (dark) per 36 nm helical half-repeat of the actin filament. Key parameter values are given in Supplementary Tables S1 and S2
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5383694&req=5

Fig1: Key elements of model. a Kinetic scheme showing myosin (M) and actomyosin (AM) biochemical states with MgATP (T), MgADP (D) and/or inorganic phosphate (P/Pi) at the active site. The MDP and AMDP states, on the one hand, and the AM*DL and AM*DH states, on the other, are assumed to be in rapid equilibrium with equilibrium constants Kw(x) and KLH(x), respectively. The AM*DL state is a strongly bound, start-of-power-stroke state. Several rate constants ki as well as equilibrium constants Ki vary with the elastic strain in the cross-bridge. b The free energy of all states as function of x (see text). Insets schematically illustrate different structural states of myosin head and lever arm at free-energy minima. c Schematic illustration of an in vitro motility assay where myosin motor fragments (heavy meromyosin; HMM) are adsorbed to a surface. The one-head, single-site assumption is illustrated: only one of the two myosin heads can bind to actin and binding is possible only to one site (dark) per 36 nm helical half-repeat of the actin filament. Key parameter values are given in Supplementary Tables S1 and S2
Mentions: The model is based on the kinetic scheme in Fig. 1a with abbreviations of different states explained in the legend. The total amplitude of the force-generating power-stroke (“step-length”; from state AM*DL to states AMD and AM) was taken as 7.7 nm, slightly modified from the value of 7.35 nm in a recent model for large ensembles (Persson et al. 2013).The value of 7.7 nm is consistent with an 8 nm myosin step suggested in (Kaya and Higuchi 2010) based on optical tweezers studies that did not distinguish sub-steps. By assuming a final sub-step of 1 nm (Capitanio et al. 2006) the total value of 7.7 nm suggests a first sub-step of 6.7 nm. These step-lengths are directly reflected in the diagrams in Fig. 1b that illustrate the free energy of different states as function of the variable x. This variable represents the distance between a reference point on the myosin molecule and the nearest actin filament site, with x = 0 nm when force in the AMD/AM state is zero. The free energies of two different generic states, i and j, are related to the equilibrium constant (Kij(x)) and forward and backward rate constants (kij(x) and kji(x)) as follows:Fig. 1

View Article: PubMed Central - PubMed

ABSTRACT

Bridging the gaps between experimental systems on different hierarchical scales is needed to overcome remaining challenges in the understanding of muscle contraction. Here, a mathematical model with well-characterized structural and biochemical actomyosin states is developed to that end. We hypothesize that this model accounts for generation of force and motion from single motor molecules to the large ensembles of muscle. In partial support of this idea, a wide range of contractile phenomena are reproduced without the need to invoke cooperative interactions or ad hoc states/transitions. However, remaining limitations exist, associated with ambiguities in available data for model definition e.g.: (1) the affinity of weakly bound cross-bridges, (2) the characteristics of the cross-bridge elasticity and (3) the exact mechanistic relationship between the force-generating transition and phosphate release in the actomyosin ATPase. Further, the simulated number of attached myosin heads in the in vitro motility assay differs several-fold from duty ratios, (fraction of strongly attached ATPase cycle times) derived in standard analysis. After addressing the mentioned issues the model should be useful in fundamental studies, for engineering of myosin motors as well as for studies of muscle disease and drug development.

Electronic supplementary material: The online version of this article (doi:10.1007/s10974-016-9458-0) contains supplementary material, which is available to authorized users.

No MeSH data available.


Related in: MedlinePlus